Probability representation entropy for spin-state tomogram

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材料科学与工程专业英语词汇

材料科学与工程专业英语词汇1. 物理化学物理化学是研究物质结构、性质、变化规律及其机理的基础科学，是材料科学与工程的重要理论基础之一。

物理化学主要包括以下几个方面：热力学：研究物质状态和过程中能量转换和守恒的规律。

动力学：研究物质变化过程中速率和机理的规律。

电化学：研究电流和物质变化之间的相互作用和关系。

光化学：研究光和物质变化之间的相互作用和关系。

表面化学：研究物质表面或界面处发生的现象和规律。

结构化学：研究物质分子或晶体结构及其与性质之间的关系。

统计力学：用统计方法处理大量微观粒子行为，从而解释宏观物理现象。

中文英文物理化学physical chemistry热力学thermodynamics动力学kinetics电化学electrochemistry光化学photochemistry表面化学surface chemistry结构化学structural chemistry统计力学statistical mechanics状态方程equation of state熵entropy自由能free energy化学势chemical potential相平衡phase equilibrium化学平衡chemical equilibrium反应速率reaction rate反应级数reaction order反应机理reaction mechanism活化能activation energy催化剂catalyst电池battery电极electrode电解质electrolyte电位potential电流密度current density法拉第定律Faraday's law腐蚀corrosion中文英文光敏材料photosensitive material光致变色photochromism光致发光photoluminescence光催化photocatalysis表面张力surface tension润湿wetting吸附adsorption膜membrane分子轨道理论molecular orbital theory晶体结构crystal structure点阵lattice空间群space group对称元素symmetry element对称操作symmetry operationX射线衍射X-ray diffraction2. 量子与统计力学量子与统计力学是物理学的两个重要分支，是材料科学与工程的重要理论基础之一。

Example-based metonymy recognition for proper nouns

Example-Based Metonymy Recognition for Proper NounsYves PeirsmanQuantitative Lexicology and Variational LinguisticsUniversity of Leuven,Belgiumyves.peirsman@arts.kuleuven.beAbstractMetonymy recognition is generally ap-proached with complex algorithms thatrely heavily on the manual annotation oftraining and test data.This paper will re-lieve this complexity in two ways.First,it will show that the results of the cur-rent learning algorithms can be replicatedby the‘lazy’algorithm of Memory-BasedLearning.This approach simply stores alltraining instances to its memory and clas-siﬁes a test instance by comparing it to alltraining examples.Second,this paper willargue that the number of labelled trainingexamples that is currently used in the lit-erature can be reduced drastically.Thisﬁnding can help relieve the knowledge ac-quisition bottleneck in metonymy recog-nition,and allow the algorithms to be ap-plied on a wider scale.1IntroductionMetonymy is aﬁgure of speech that uses“one en-tity to refer to another that is related to it”(Lakoff and Johnson,1980,p.35).In example(1),for in-stance,China and Taiwan stand for the govern-ments of the respective countries:(1)China has always threatened to use forceif Taiwan declared independence.(BNC) Metonymy resolution is the task of automatically recognizing these words and determining their ref-erent.It is therefore generally split up into two phases:metonymy recognition and metonymy in-terpretation(Fass,1997).The earliest approaches to metonymy recogni-tion identify a word as metonymical when it vio-lates selectional restrictions(Pustejovsky,1995).Indeed,in example(1),China and Taiwan both violate the restriction that threaten and declare require an animate subject,and thus have to be interpreted metonymically.However,it is clear that many metonymies escape this characteriza-tion.Nixon in example(2)does not violate the se-lectional restrictions of the verb to bomb,and yet, it metonymically refers to the army under Nixon’s command.(2)Nixon bombed Hanoi.This example shows that metonymy recognition should not be based on rigid rules,but rather on statistical information about the semantic and grammatical context in which the target word oc-curs.This statistical dependency between the read-ing of a word and its grammatical and seman-tic context was investigated by Markert and Nis-sim(2002a)and Nissim and Markert(2003; 2005).The key to their approach was the in-sight that metonymy recognition is basically a sub-problem of Word Sense Disambiguation(WSD). Possibly metonymical words are polysemous,and they generally belong to one of a number of pre-deﬁned metonymical categories.Hence,like WSD, metonymy recognition boils down to the auto-matic assignment of a sense label to a polysemous word.This insight thus implied that all machine learning approaches to WSD can also be applied to metonymy recognition.There are,however,two differences between metonymy recognition and WSD.First,theo-retically speaking,the set of possible readings of a metonymical word is open-ended(Nunberg, 1978).In practice,however,metonymies tend to stick to a small number of patterns,and their la-bels can thus be deﬁned a priori.Second,classic 71WSD algorithms take training instances of one par-ticular word as their input and then disambiguate test instances of the same word.By contrast,since all words of the same semantic class may undergo the same metonymical shifts,metonymy recogni-tion systems can be built for an entire semantic class instead of one particular word(Markert and Nissim,2002a).To this goal,Markert and Nissim extracted from the BNC a corpus of possibly metonymical words from two categories:country names (Markert and Nissim,2002b)and organization names(Nissim and Markert,2005).All these words were annotated with a semantic label —either literal or the metonymical cate-gory they belonged to.For the country names, Markert and Nissim distinguished between place-for-people,place-for-event and place-for-product.For the organi-zation names,the most frequent metonymies are organization-for-members and organization-for-product.In addition, Markert and Nissim used a label mixed for examples that had two readings,and othermet for examples that did not belong to any of the pre-deﬁned metonymical patterns.For both categories,the results were promis-ing.The best algorithms returned an accuracy of 87%for the countries and of76%for the orga-nizations.Grammatical features,which gave the function of a possibly metonymical word and its head,proved indispensable for the accurate recog-nition of metonymies,but led to extremely low recall values,due to data sparseness.Therefore Nissim and Markert(2003)developed an algo-rithm that also relied on semantic information,and tested it on the mixed country data.This algo-rithm used Dekang Lin’s(1998)thesaurus of se-mantically similar words in order to search the training data for instances whose head was sim-ilar,and not just identical,to the test instances. Nissim and Markert(2003)showed that a combi-nation of semantic and grammatical information gave the most promising results(87%). However,Nissim and Markert’s(2003)ap-proach has two major disadvantages.Theﬁrst of these is its complexity:the best-performing al-gorithm requires smoothing,backing-off to gram-matical roles,iterative searches through clusters of semantically similar words,etc.In section2,I will therefore investigate if a metonymy recognition al-gorithm needs to be that computationally demand-ing.In particular,I will try and replicate Nissim and Markert’s results with the‘lazy’algorithm of Memory-Based Learning.The second disadvantage of Nissim and Mark-ert’s(2003)algorithms is their supervised nature. Because they rely so heavily on the manual an-notation of training and test data,an extension of the classiﬁers to more metonymical patterns is ex-tremely problematic.Yet,such an extension is es-sential for many tasks throughout theﬁeld of Nat-ural Language Processing,particularly Machine Translation.This knowledge acquisition bottle-neck is a well-known problem in NLP,and many approaches have been developed to address it.One of these is active learning,or sample selection,a strategy that makes it possible to selectively an-notate those examples that are most helpful to the classiﬁer.It has previously been applied to NLP tasks such as parsing(Hwa,2002;Osborne and Baldridge,2004)and Word Sense Disambiguation (Fujii et al.,1998).In section3,I will introduce active learning into theﬁeld of metonymy recog-nition.2Example-based metonymy recognition As I have argued,Nissim and Markert’s(2003) approach to metonymy recognition is quite com-plex.I therefore wanted to see if this complexity can be dispensed with,and if it can be replaced with the much more simple algorithm of Memory-Based Learning.The advantages of Memory-Based Learning(MBL),which is implemented in the T i MBL classiﬁer(Daelemans et al.,2004)1,are twofold.First,it is based on a plausible psycho-logical hypothesis of human learning.It holds that people interpret new examples of a phenom-enon by comparing them to“stored representa-tions of earlier experiences”(Daelemans et al., 2004,p.19).This contrasts to many other classi-ﬁcation algorithms,such as Naive Bayes,whose psychological validity is an object of heavy de-bate.Second,as a result of this learning hypothe-sis,an MBL classiﬁer such as T i MBL eschews the formulation of complex rules or the computation of probabilities during its training phase.Instead it stores all training vectors to its memory,together with their labels.In the test phase,it computes the distance between the test vector and all these train-ing vectors,and simply returns the most frequentlabel of the most similar training examples.One of the most important challenges inMemory-Based Learning is adapting the algorithmto one’s data.This includesﬁnding a represen-tative seed set as well as determining the rightdistance measures.For my purposes,however, T i MBL’s default settings proved more than satis-factory.T i MBL implements the IB1and IB2algo-rithms that were presented in Aha et al.(1991),butadds a broad choice of distance measures.Its de-fault implementation of the IB1algorithm,whichis called IB1-IG in full(Daelemans and Van denBosch,1992),proved most successful in my ex-periments.It computes the distance between twovectors X and Y by adding up the weighted dis-tancesδbetween their corresponding feature val-ues x i and y i:∆(X,Y)=ni=1w iδ(x i,y i)(3)The most important element in this equation is theweight that is given to each feature.In IB1-IG,features are weighted by their Gain Ratio(equa-tion4),the division of the feature’s InformationGain by its split rmation Gain,the nu-merator in equation(4),“measures how much in-formation it[feature i]contributes to our knowl-edge of the correct class label[...]by comput-ing the difference in uncertainty(i.e.entropy)be-tween the situations without and with knowledgeof the value of that feature”(Daelemans et al.,2004,p.20).In order not“to overestimate the rel-evance of features with large numbers of values”(Daelemans et al.,2004,p.21),this InformationGain is then divided by the split info,the entropyof the feature values(equation5).In the followingequations,C is the set of class labels,H(C)is theentropy of that set,and V i is the set of values forfeature i.w i=H(C)− v∈V i P(v)×H(C|v)2This data is publicly available and can be downloadedfrom /mnissim/mascara.73P F86.6%49.5%N&M81.4%62.7%Table1:Results for the mixed country data.T i MBL:my T i MBL resultsN&M:Nissim and Markert’s(2003)results simple learning phase,T i MBL is able to replicate the results from Nissim and Markert(2003;2005). As table1shows,accuracy for the mixed coun-try data is almost identical to Nissim and Mark-ert’sﬁgure,and precision,recall and F-score for the metonymical class lie only slightly lower.3 T i MBL’s results for the Hungary data were simi-lar,and equally comparable to Markert and Nis-sim’s(Katja Markert,personal communication). Note,moreover,that these results were reached with grammatical information only,whereas Nis-sim and Markert’s(2003)algorithm relied on se-mantics as well.Next,table2indicates that T i MBL’s accuracy for the mixed organization data lies about1.5%be-low Nissim and Markert’s(2005)ﬁgure.This re-sult should be treated with caution,however.First, Nissim and Markert’s available organization data had not yet been annotated for grammatical fea-tures,and my annotation may slightly differ from theirs.Second,Nissim and Markert used several feature vectors for instances with more than one grammatical role andﬁltered all mixed instances from the training set.A test instance was treated as mixed only when its several feature vectors were classiﬁed differently.My experiments,in contrast, were similar to those for the location data,in that each instance corresponded to one vector.Hence, the slightly lower performance of T i MBL is prob-ably due to differences between the two experi-ments.Theseﬁrst experiments thus demonstrate that Memory-Based Learning can give state-of-the-art performance in metonymy recognition.In this re-spect,it is important to stress that the results for the country data were reached without any se-mantic information,whereas Nissim and Mark-ert’s(2003)algorithm used Dekang Lin’s(1998) clusters of semantically similar words in order to deal with data sparseness.This fact,togetherAcc RT i MBL78.65%65.10%76.0%—Figure1:Accuracy learning curves for the mixed country data with and without semantic informa-tion.in more detail.4Asﬁgure1indicates,with re-spect to overall accuracy,semantic features have a negative inﬂuence:the learning curve with both features climbs much more slowly than that with only grammatical features.Hence,contrary to my expectations,grammatical features seem to allow a better generalization from a limited number of training instances.With respect to the F-score on the metonymical category inﬁgure2,the differ-ences are much less outspoken.Both features give similar learning curves,but semantic features lead to a higherﬁnal F-score.In particular,the use of semantic features results in a lower precisionﬁg-ure,but a higher recall score.Semantic features thus cause the classiﬁer to slightly overgeneralize from the metonymic training examples.There are two possible reasons for this inabil-ity of semantic information to improve the clas-siﬁer’s performance.First,WordNet’s synsets do not always map well to one of our semantic la-bels:many are rather broad and allow for several readings of the target word,while others are too speciﬁc to make generalization possible.Second, there is the predominance of prepositional phrases in our data.With their closed set of heads,the number of examples that beneﬁts from semantic information about its head is actually rather small. Nevertheless,myﬁrst round of experiments has indicated that Memory-Based Learning is a sim-ple but robust approach to metonymy recogni-tion.It is able to replace current approaches that need smoothing or iterative searches through a the-saurus,with a simple,distance-based algorithm.Figure3:Accuracy learning curves for the coun-try data with random and maximum-distance se-lection of training examples.over all possible labels.The algorithm then picks those instances with the lowest conﬁdence,since these will contain valuable information about the training set(and hopefully also the test set)that is still unknown to the system.One problem with Memory-Based Learning al-gorithms is that they do not directly output prob-abilities.Since they are example-based,they can only give the distances between the unlabelled in-stance and all labelled training instances.Never-theless,these distances can be used as a measure of certainty,too:we can assume that the system is most certain about the classiﬁcation of test in-stances that lie very close to one or more of its training instances,and less certain about those that are further away.Therefore the selection function that minimizes the probability of the most likely label can intuitively be replaced by one that max-imizes the distance from the labelled training in-stances.However,ﬁgure3shows that for the mixed country instances,this function is not an option. Both learning curves give the results of an algo-rithm that starts withﬁfty random instances,and then iteratively adds ten new training instances to this initial seed set.The algorithm behind the solid curve chooses these instances randomly,whereas the one behind the dotted line selects those that are most distant from the labelled training exam-ples.In theﬁrst half of the learning process,both functions are equally successful;in the second the distance-based function performs better,but only slightly so.There are two reasons for this bad initial per-formance of the active learning function.First,it is not able to distinguish between informativeandFigure4:Accuracy learning curves for the coun-try data with random and maximum/minimum-distance selection of training examples. unusual training instances.This is because a large distance from the seed set simply means that the particular instance’s feature values are relatively unknown.This does not necessarily imply that the instance is informative to the classiﬁer,how-ever.After all,it may be so unusual and so badly representative of the training(and test)set that the algorithm had better exclude it—something that is impossible on the basis of distances only.This bias towards outliers is a well-known disadvantage of many simple active learning algorithms.A sec-ond type of bias is due to the fact that the data has been annotated with a few features only.More par-ticularly,the present algorithm will keep adding instances whose head is not yet represented in the training set.This entails that it will put off adding instances whose function is pp,simply because other functions(subj,gen,...)have a wider variety in heads.Again,the result is a labelled set that is not very representative of the entire training set.There are,however,a few easy ways to increase the number of prototypical examples in the train-ing set.In a second run of experiments,I used an active learning function that added not only those instances that were most distant from the labelled training set,but also those that were closest to it. After a few test runs,I decided to add six distant and four close instances on each iteration.Figure4 shows that such a function is indeed fairly success-ful.Because it builds a labelled training set that is more representative of the test set,this algorithm clearly reduces the number of annotated instances that is needed to reach a given performance.Despite its success,this function is obviously not yet a sophisticated way of selecting good train-76Figure5:Accuracy learning curves for the organi-zation data with random and distance-based(AL) selection of training examples with a random seed set.ing examples.The selection of the initial seed set in particular can be improved upon:ideally,this seed set should take into account the overall dis-tribution of the training examples.Currently,the seeds are chosen randomly.Thisﬂaw in the al-gorithm becomes clear if it is applied to another data set:ﬁgure5shows that it does not outper-form random selection on the organization data, for instance.As I suggested,the selection of prototypical or representative instances as seeds can be used to make the present algorithm more robust.Again,it is possible to use distance measures to do this:be-fore the selection of seed instances,the algorithm can calculate for each unlabelled instance its dis-tance from each of the other unlabelled instances. In this way,it can build a prototypical seed set by selecting those instances with the smallest dis-tance on average.Figure6indicates that such an algorithm indeed outperforms random sample se-lection on the mixed organization data.For the calculation of the initial distances,each feature re-ceived the same weight.The algorithm then se-lected50random samples from the‘most proto-typical’half of the training set.5The other settings were the same as above.With the present small number of features,how-ever,such a prototypical seed set is not yet always as advantageous as it could be.A few experiments indicated that it did not lead to better performance on the mixed country data,for instance.However, as soon as a wider variety of features is taken into account(as with the organization data),the advan-pling can help choose those instances that are most helpful to the classiﬁer.A few distance-based al-gorithms were able to drastically reduce the num-ber of training instances that is needed for a given accuracy,both for the country and the organization names.If current metonymy recognition algorithms are to be used in a system that can recognize all pos-sible metonymical patterns across a broad variety of semantic classes,it is crucial that the required number of labelled training examples be reduced. This paper has taken theﬁrst steps along this path and has set out some interesting questions for fu-ture research.This research should include the investigation of new features that can make clas-siﬁers more robust and allow us to measure their conﬁdence more reliably.This conﬁdence mea-surement can then also be used in semi-supervised learning algorithms,for instance,where the clas-siﬁer itself labels the majority of training exam-ples.Only with techniques such as selective sam-pling and semi-supervised learning can the knowl-edge acquisition bottleneck in metonymy recogni-tion be addressed.AcknowledgementsI would like to thank Mirella Lapata,Dirk Geer-aerts and Dirk Speelman for their feedback on this project.I am also very grateful to Katja Markert and Malvina Nissim for their helpful information about their research.ReferencesD.W.Aha, D.Kibler,and M.K.Albert.1991.Instance-based learning algorithms.Machine Learning,6:37–66.W.Daelemans and A.Van den Bosch.1992.Generali-sation performance of backpropagation learning on a syllabiﬁcation task.In M.F.J.Drossaers and A.Ni-jholt,editors,Proceedings of TWLT3:Connection-ism and Natural Language Processing,pages27–37, Enschede,The Netherlands.W.Daelemans,J.Zavrel,K.Van der Sloot,andA.Van den Bosch.2004.TiMBL:Tilburg Memory-Based Learner.Technical report,Induction of Linguistic Knowledge,Computational Linguistics, Tilburg University.D.Fass.1997.Processing Metaphor and Metonymy.Stanford,CA:Ablex.A.Fujii,K.Inui,T.Tokunaga,and H.Tanaka.1998.Selective sampling for example-based wordsense putational Linguistics, 24(4):573–597.R.Hwa.2002.Sample selection for statistical parsing.Computational Linguistics,30(3):253–276.koff and M.Johnson.1980.Metaphors We LiveBy.London:The University of Chicago Press.D.Lin.1998.An information-theoretic definition ofsimilarity.In Proceedings of the International Con-ference on Machine Learning,Madison,USA.K.Markert and M.Nissim.2002a.Metonymy res-olution as a classification task.In Proceedings of the Conference on Empirical Methods in Natural Language Processing(EMNLP2002),Philadelphia, USA.K.Markert and M.Nissim.2002b.Towards a cor-pus annotated for metonymies:the case of location names.In Proceedings of the Third International Conference on Language Resources and Evaluation (LREC2002),Las Palmas,Spain.M.Nissim and K.Markert.2003.Syntactic features and word similarity for supervised metonymy res-olution.In Proceedings of the41st Annual Meet-ing of the Association for Computational Linguistics (ACL-03),Sapporo,Japan.M.Nissim and K.Markert.2005.Learning to buy a Renault and talk to BMW:A supervised approach to conventional metonymy.In H.Bunt,editor,Pro-ceedings of the6th International Workshop on Com-putational Semantics,Tilburg,The Netherlands. G.Nunberg.1978.The Pragmatics of Reference.Ph.D.thesis,City University of New York.M.Osborne and J.Baldridge.2004.Ensemble-based active learning for parse selection.In Proceedings of the Human Language Technology Conference of the North American Chapter of the Association for Computational Linguistics(HLT-NAACL).Boston, USA.J.Pustejovsky.1995.The Generative Lexicon.Cam-bridge,MA:MIT Press.78。

机器学习总结

sklearn 1.17. Neural network models (supervised)神经网络模型(监督学习)Warning :This implementation is not intended for large-scale applications. In particular, scikit-learn offers no GPU support. For much faster, GPU-based implementations, as well as frameworks offering much more flexibility to build deep learning architectures, see Related Projects.警告:此实现不适用于大规模应用。

特别是scikit-learn 不提供图形处理器支持。

有关更快、基于GPU 的实现，以及为构建深度学习架构提供更大灵活性的框架，请参见相关项目。

Deep neural networks etc.深度神经网络pylearn2: A deep learning and neural network library build on theano with scikit-learn like interface.pylearn2: 一个深度学习和神经网络库建立在具有scikit- learn 类接口的theano 之上。

sklearn_theano: scikit-learn compatible estimators, transformers, and datasets which use Theano internallysklearn_theano: sklearn 在内部使用theano 的兼容估计器、转换器和数据集.nolearn: A number of wrappers and abstractions around existing neural network librariesnolearn:围绕现有神经网络库的许多包装器和抽象keras : Deep Learning library capable of running on top of either TensorFlow or Theano.keras :能够在tensorflow 或thetano 上运行的深度学习库。

entropy zero2 指令

entropy zero2 指令From a scientific perspective, the problem of entropy zero2 指令 can be seen as a challenge to understand and manipulate the fundamental principles of information theory. Entropy is a crucial concept in this field, as it providesa measure of the amount of information or uncertainty in a system. The zero2 指令, as a specific instruction relatedto entropy, may have implications for how information is processed, stored, and transmitted. Scientists and researchers may be interested in exploring the potential applications of this command in various information technology and communication systems.From a technological perspective, the problem ofentropy zero2 指令 may be seen as an opportunity to develop new algorithms, protocols, or systems that can leverage the concept of entropy for practical applications. For example, the zero2 指令 may be used to optimize data compression algorithms, improve the security of cryptographic systems,or enhance the efficiency of communication protocols.Technologists and engineers may be motivated to explore the potential benefits and challenges of incorporating this command into their technological solutions.From a philosophical perspective, the problem of entropy zero2 指令 raises questions about the nature of information, uncertainty, and order in the universe. Entropy is often associated with the concept of disorder or chaos, and the zero2 指令 may be seen as a symbolic representation of the struggle to control or manipulatethis inherent randomness. Philosophers and thinkers may be interested in exploring the implications of this problemfor our understanding of the fundamental principles that govern the universe.In conclusion, the problem of entropy zero2 指令 is a multifaceted issue that has implications for science, technology, and philosophy. It challenges us to grapple with the fundamental principles of information theory, the potential applications of entropy in technological systems, and the philosophical implications of uncertainty and disorder in the universe. By approaching this problem frommultiple perspectives, we can gain a deeper understanding of its significance and potential impact on various aspects of human knowledge and experience.。

1.1 On The Promise of Bayesian Inference for

tatistics in Astronomical Investigation
3
admitting uncertainty in terms of a prior distribution for (bjI). Also, expecting low counts implies b will be rather small (see also the paper by John Nousek, this volume, in discussion of low count radiation from SN1987A). Using a prior p(sjbI) that is uniform over a `large' range (and does not depend on b), Loredo proceeds to summary inferences based on the posterior p(sjnbI) in his equation (5.13). Throughout the paper, such uniform priors are adopted as a routine on the basis of representing suitable forms of `ignorance' about the quantity concerned. If any area of Bayesian inference has received too much attention during the last couple of decades it is surely the search for unique and `objective' representation of ignorance { see 4] for a recent and partial review of the eld. The maximum entropy school has been in uential in physical sciences, as referenced by Loredo, and particularly predominant in expounding the view that a single prior may be found, in any given situation, to represent vagueness in the sense of maximum entropy subject to certain `plausible' assumptions that typically stand for little more than mathematical convenience in determining a unique solution in the resulting MaxEnt framework. There is nothing unique, objective or otherwise scienti cally persuasive about uniform priors for location parameters, or any of the plethora of vague, reference or indi erence priors that abound. In investigations which admit an `objective' (de ned simply as consensus of informed observers) data model as here (ie. p(njsI)), analysis should necessarily involve study of sensitivity to qualitative and quantitative aspects of the prior, including assessments of pre-data predictive validity of the fdata modelg:fpriorg combination, and post-data determination of the mapping from prior to posterior for ranges of scienti cally plausible priors. The issue of pre-data validity is addressed through the implied (prior) R predictive distribution for the data, here p(njbI) = p(njsI)p(sjbI)ds. When n is observed, the value of this density function provides the normalising constant in Bayes' theorem (C ?1 in Loredo's equation (5.6)). Prior to the data, however, this distribution describes the investigator's view of experimental outcome. A uniform prior over a very large range translates essentially into a similar (though discrete) uniform p(njbI), which most observers would be quite concerned about as a plausible and scienti cally valid representation of expectations. The issue is particularly acute in problems of low counts and source detection when s (when non-zero) will be tend to be small | reasonable priors for s, and thus predictions about n, should surely re ect this. Competing `reference' priors (and there are many { 4]), lead to posteriors that can di er markedly with low counts s, though all such priors claim some form of `vagueness' and `uniformity' (on some scale). Scienti c investigation must involve careful and thorough consideration of initial information, modes of incorporation of such information in summary inferences, and exploration of sensitivity to prior assumptions (which includes model and data assumptions and well as priors for model parameters { and sometimes the distinction is unclear and even irrelevant

Probability and Stochastic Processes

Probability and Stochastic Processes Probability and stochastic processes are fundamental concepts in the field of mathematics and have wide-ranging applications in various fields such as engineering, finance, and science. Understanding these concepts is crucial for making informed decisions in uncertain and random environments. In this response, we will delve into the significance of probability and stochastic processes, their real-world applications, and the challenges associated with studying and applying these concepts. Probability is the branch of mathematics that deals with the likelihood of a particular event or outcome occurring. It provides a framework for quantifying uncertainty and making predictions based on available information. Stochastic processes, on the other hand, are mathematical models that describe the evolution of random variables over time. These processes are used to analyze and predict the behavior of complex systems that exhibit random behavior. One of the key reasons why probability and stochastic processes are important is their role in decision-making under uncertainty. In many real-world scenarios, decisions need to be made in the presence of incomplete information and unpredictable outcomes. Probability theory provides a systematic way to evaluate the likelihood of different outcomes and make rational decisions based on this assessment. Stochastic processes, on the other hand, are used to model and analyze random phenomena such as stock prices, weather patterns, and the spread of diseases. In the field of engineering, probability and stochastic processes are used to design and analyze systems that operate in uncertain environments. For example, in the design of communication systems, engineers use probability theory to analyze the performance of error-correcting codes and stochastic processes to model the behavior of wireless channels. Similarly, in the field of finance, these concepts are used to model the behavior of financial markets, price derivatives, and manage risk. Despite their wide-ranging applications, studying probability and stochastic processes can be challenging due to their abstract nature and the need for a strong mathematical foundation. Many students find it difficult to grasp the concepts of probability, random variables, and stochastic processes, as they often require a shift in thinking from deterministic to probabilistic reasoning. Moreover, the mathematical tools and techniques used to analyze these concepts,such as measure theory and stochastic calculus, can be quite advanced and require a significant amount of time and effort to master. In addition to the academic challenges, there are also practical difficulties in applying probability and stochastic processes to real-world problems. For example, in financial modeling, accurately predicting stock prices or interest rates using stochastic processes is a complex task that requires sophisticated mathematical models and large amounts of historical data. Furthermore, the assumptions made in these models, such as the independence of random variables or the stationarity of processes, may not always hold in practice, leading to inaccuracies in predictions. In conclusion, probability and stochastic processes are essential tools for understanding and navigating the uncertainties of the world. From decision-making under uncertainty to modeling complex systems, these concepts play a crucial role in a wide range of fields. However, mastering these concepts and applying them to real-world problems can be challenging due to their abstract nature and the complexity of the mathematical techniques involved. Nonetheless, the rewards of understanding and applying probability and stochastic processes are immense, as they provide a powerful framework for making informed decisions and predicting the behavior of random phenomena.。

信息论与编码理论中的英文单词和短语

信息论与编码理论中的英文单词和短语读书破万卷下笔如有神信息论与编码理论bits (binary digits)比natural digits自然entropy function熵函数Theories ofInformationprobability vector可能向conditional entropy条件熵and Codingdiscrete memory channel离散记忆信transition probability过渡可能性output产marginal distritution边际分布介绍第一章mutual information互信heuristic启发joint entropy联合熵Introduction Chapter 1 Venn diagram维恩Markov chain马尔可夫链information theory信息definite function限定函coding theory编码理tandem串emit发data-processing configuration数据过程配bit字convex combination凸组binary二进manipulation操binary symmetric source二进制对称shorthand速记binary symmetric channel二进制对称信communication system通信系统raw bit error probability 原始字节错误率continuous source outputs 连续信息输出encode编码coder 编码员bit error probability 字节错误率map 映射noise 噪音destination目标redundant 冗余data-processing theorem 数据过程定理cross check 相互校验discrete quantization 离散量化codding algorithm 编码算法refinement /精炼改进error pattern 错误模式density密度synthesis 综合mean value theorem 中值定理Hamming code汉明码superficial resemblance 表面相似single-error-correcting code 单独错误校正码mesh网格rate速率differential entropy 微分熵binary entropy function 二进制熵函数Jensen inequality 琴生不等式capacity能量determinate channel确定信道channel coding theory信道编码理论第二章信息理论Information TheoryChapter 2读书破万卷下笔如有神第三章离散无记忆信第四章离散无记忆信源和扭曲道和容量成本率方程方程Chapter 4 Discrete DiscreteMemoryless Sources and Memory less Channels Chapter 3their Rate-Distortion Equations and their Capacity-Cost Equationssource alphabetinput sign system源字母输入符号系discrete memoryless sourcesoutput sign system输出符号系离散无记忆信source statisticsimagine想统计object signmemoryless assumption目标符无记忆假distortionaverage cost平均成扭distortion measurecapacity-cost equation扭曲容量成本方average distortiontest-source平均扭验证源test channeln-dimensional admissible test sources维容许验证测试通distortion rate扭曲admissible cost容许成source coding theorem源编码定r-symmetry对backwards test channel向后测试通道rate of system系统比率Hamming distortion measure 哈莫名扭曲度rates above channel capacity 超过信道容量率error probability distortion rate 错误扭曲率length 长data-compression theorem 数据压缩定理bits per symbol 每个符号的比特destination symbols 目的符号decoding rule 编码规则data compression scheme 数据压缩系统distinct code 区别代码penalty function 罚函数indicator function 指示函数unrestricted sum 无限制和random coding 随机编码inner sum内部和expected value期望值weak law of large numbers 弱大数定律decoding sphere 编码范围第五章高斯信道和信源Chapter 5 Gaussian Channel and Sourcevoltage 伏特transmit 传送signal信号．读书破万卷下笔如有神source statisticswatts信源统rate of transmissiondissipate传送耗conflictjoule焦冲source-channel coding theoremwhite Gaussian noise process白高斯噪声过理noise spectral density噪声错误密data-processing theorem数据传输定bandwidth带intermediate vector中间向band-limited波段限worst-case distortion最坏扭power-limited功率限per-symbol basis每个符号基n-th capacity-cost function项容量成decomposition分函transmitted codingsquared-error传送编平方错affordoinkoverallcapacity-costfunction总的容量成本负density数噪声密tradeoff交arithmetic-geometric average value几何均算realizable region可实现区Gaussiandiscrete-timememoryless离散时间无记standpoint观点source高斯信源mean-squared error criterion第一部分访问gaussion distribution 高斯分布per-symbol均值平方错误标准第七章Gaussiansource高斯信源每个符先进标题per-symbol mean-squared distortion号均值平方扭曲Chapter 7 Survey of Advanced Topics for 信道编码第六章信源-Part One理论twin pearls孪生珍珠finite Abelian commutative group有限阿贝尔交换群Source-Channel Coding Theory Chapter 6 ergodic random process各态经历随机过程information source 信息源entropy熵noisy source 噪声源additive ergodic noise channel添加各态噪音信data processing 道数据处理asymptotic average property quantization 量子化渐进线均分性质Gaussian process modulation 高斯过程调节multiterminal channel successive block多终端信道连续块feedback emit channel output symbols反馈发出信道输出符号seeder 发送人one-to-one correspondence 一对一通信receiver接受人test source 实验来源multi-access channel 多通道信道source sequence 信源序列erasure symbol 擦掉符号destination sequence 目的序列contradiction矛盾读书破万卷下笔如有神rate比率practical standpoint实际观broadcast channel广播信generator matrix生成矩capacity region容量区row space行空high degree of symmetry 高对称parity-check matrix奇偶校验矩test sources测试信canonical form规范形input signal channel输入符号信error pattern错误模global maximum全局最coset傍additive ergodic noise添加各态噪symmetric channel对称信reliability exponent of channel信道的可靠性Hamming wight汉明table lookupcritical rate关键表格查standard arraylinear code线性标准排italicizedtime-varying convolutional强时间改变卷积metric spaceencoder-channel-decoder度量空编信译Hamming distanceouter channel汉明距外部信interectinner code内部编穿minimum weightouter code最小权外部编single-error-correctingweak converse弱颠单错误校perfect codesstrong converse强颠完全repetition codesterm术重复binary Hamming codesrate of transmission二进制汉明传输detecterror exponent错误指检e-correctingstrong similarity电子校强近H-detectingrather duality选择两重检Fparity-check matrixdistortion rate theory扭曲率理类似校验矩double-error-detectingsource coding method源编码双错误检weight enumeratorsingle-letter distortion measure单字母扭曲度权重计数homomorphismimplication含同multiplicative groupconfiguration轮趋于增加组indeterminate error probability 错误可能性不确定half-plane bound 半平面界reception接待discrete-time stable离散时间稳定高第九章循环码斯信源stable Gaussian sequence 稳定高斯序列spectral density 谱密度Chapter 9 Cyclic Codes tree codes树码burst errors突发性错误definition of innocuous-appearing 表面无害定理cyclic shift 循环位移第八章线性码trivial cyclic 一般循环no-information code无信息码Linear codesChapter 8读书破万卷下笔如有神depth-3 interleavingsingle-parity-check code单等价校验度交interleaving operationno-equivalent code无等价交错操elaborate algorithmright cyclic shift右循环位复杂算Fire codegenerating function法尔母函Fire constructiongenerator polynomial法尔结生成多项burst-trapping algorithmreciprocal爆发阻塞算互惠burst-error-correcting codecyclic property爆发错误校正循环性decomposition分left-justified左对transmitted codeword传送编trap陷阱，阻shift-register encoder转换登记编burst-error pattern爆发错误模flip-flops adders突变加法Meggitt lemma米戈蒂引constant multipliers常数乘法shift-register切换显delay延circuit环impulse response脉冲响leftmost flip-flop y香最左面的突state vector状态向量state polynomial 状态多项式input stream 输入流reverse order 反顺序第十章农码和相关linear recursion 线性递归rightmost flip-flop 最右面的突变的码mod-2 adder 模2加法器cyclic 循环two-field二域Chapter 10 Shannon Codes and Related primitive polynomial 原始多项式Codes decoding cycle 译码循环circular journey 循环旅程Shannon code香农码lower shift register 低位移寄存器Vandermonde determinant theory范德蒙德行列式burst-error-correcting 突发错误校正理论pattern 模式original parity-check matrix 初始相同检验矩burst description 突发描述阵location 位置minimal polynomial 最小多项式ambiguity 含糊不清key equation关键方程zero run零操作discrete Fourier transform 离散傅里叶变换burst-error correcting code 突发错误校正码time-domain 时间领域Abramson bounds 阿布拉门逊界frequency-domain 频数领域strict Abramson bound严格阿布拉门逊subtlety 细致界time shift 时间转换weak Abramson bound 弱阿布拉门逊界phase shift 相位转换Reiger bound Reiger界support set 支撑集合loose松散evaluator polynomial 评估多项式Abramson code 阿布拉门逊码formal derivative规范派生interleaving 交错frequency-domain recursion 频数主导递归De-interleaving交错De读书破万卷下笔如有神frequency-domainsubscript下频数Golay codelocator polynomial戈莱定位多项extended Golay codeerror pattern扩展戈莱错误模byte implementationtwisted error pattern字节工扭曲错误模table loopreduced mode表复原模error location错误定位error-evaluator polynomial 错误评估多项式Euclid algorithm 欧几里得算法第十一章卷积码quotient 份额facilitate促进time-domain approach 时间主导方法Chapter 11 Convolution Codes error-locator 错误定位器trial and error 试错法matrix polynomial矩阵多项pseudocode fragment伪码片shift-register approach转移登记方recursion递scalar matrix纯量矩abnormal反state-diagram approach状态图方elaborate theory复杂理memory记忆，内multiple-error-correcting linear code多倍错误校正constraint length约束长性k-tudecode character代码字L-th section截平maximum-distance separable codes最大距离可分state-diagram状态interpolation property插值法性track轨道，足information set信息集trellis diagram格子interpolation algorithm插值算survivors幸存recursive completion递归结Viterbi decoding algorithm维特比译码算pseudocode伪path weight enumerator路权重concatenated coding 连锁elaborate labels复杂burst-error-correction爆发错误校complete path enumerator完全路径depict描error events错误时间unfactor 非因子first error probability 最早错误可能性flaw缺陷bit error probability 比特错误可能性erasure symbol 擦掉符号free distance自由距离transmitted symbol 传递符号sequential decoding algorithm 连续译码算法enlarge扩大tree diagram 树形图minimum-distance decoding 最小距离译码binary tree 二进制树erasure set擦除集合bifurcation 分枝erasure-location polynomial擦除位置多项式abandoned 抛弃errors and erasures-locator-polynomial错误擦除位置多stack algorithm 栈算法项式Fano algorithm 法诺算法errors-and-erasures-evaluator 错误擦除评估多different lengths 差异长度polynomial项式flowchart流程图modified syndrome polynomial 修正综合多项式polynomial multiplication多项式乘法．读书破万卷下笔如有神第十二章变量长度源编码Chapter 12 Variable-length Source Codingmethod of variable-length source 变量长度源编码coding法string of length k 长度串kempty string 空字符串substring子串。

非概率抽样方法

非概率抽样方法非概率抽样方法是一种用于数据收集的重要技术，它可以帮助研究人员从大概数据中提取准确和可靠的信息。

它在社会科学研究中拥有重要的作用，而且可以大大减少研究成本，提高研究水平。

非概率抽样（Non-probability Sampling）是一种基于研究过程中合理推断和可行性考量的样本选择方法。

在非概率抽样中，对象的选择是靠研究者的技术和专业知识完成的，所以研究者应该拥有充足的知识和经验，从而掌握合理的抽样方法。

与概率抽样不同，非概率抽样没有任何数学原则可以依据，而是基于研究人员在实际操作过程中的合理推断，从而得到有效的数据。

非概率抽样主要有三种形式：熵抽样、机会抽样和指定抽样。

熵抽样（Entropy Sampling）被认为是非概率抽样的一种。

它的样本数量比传统的抽样方法更少，但同时也更具泛化能力，因此在概率抽样和指定抽样之间受到青睐。

熵抽样的核心思想是根据样本的熵（即信息量）来评估对象的权重，从而挑选出合理的样本。

机会抽样（Opportunity Sampling）是非概率抽样中最普遍和最常用的抽样方法。

它是根据研究者的判断和可行性考量，从研究所在的社会中挑选出有代表性的样本进行抽样。

该抽样方法既能满足研究需求，又能为研究代表性提供有效性，因此在社会科学研究中大受欢迎。

指定抽样（Design Sampling）是一种非概率抽样，它的特点是根据指定的样本特征，从具有代表性的人群中挑选出有效的样本进行抽样。

指定抽样的重要性体现在，它能够确保研究的全面性和有效性，从而提高研究水平。

此外，非概率抽样方法也有一些不足之处，首先是无法保证样本抽取的全面性，从而无法从抽样质量上来保证研究的可靠性。

其次，研究者容易受到主观偏见的影响，因而无法保证研究结果的准确性。

况且，非概率抽样往往耗费的时间比概率抽样更长，这就意味着研究者必须花费更多的精力和资源来确保样本抽取的正确性。

此外，非概率抽样也会增加研究成本，使研究员面临更大的投入与收获的不平衡问题。

有关于熵的曲线

有关于熵的曲线英文文档：Entropy is a fundamental concept in thermodynamics and information theory, representing the degree of disorder or randomness in a system.The curve related to entropy can be understood in different contexts, such as the entropy curve in thermodynamics or the entropy curve in information theory.In thermodynamics, the entropy curve is a graphical representation of the change in entropy of a system during a process.The entropy of a system can be calculated using the equation:S = k * ln(W)where S is the entropy, k is Boltzmann"s constant, and W is the number of microstates associated with the system.The entropy curve typically shows the entropy of the system plotted against the temperature or the amount of energy transferred.In information theory, the entropy curve represents the entropy of a source, which is a measure of the uncertainty or unpredictability of the information produced by the source.The entropy of a source can be calculated using the equation:H = -Σp(x) * ln(p(x))where H is the entropy, p(x) is the probability of occurrence of eachsymbol in the source, and the sum is taken over all possible symbols x.The entropy curve in information theory typically shows the entropy of the source plotted against the number of symbols or the amount of information produced.Both types of entropy curves provide valuable insights into the behavior and characteristics of systems in their respective domains.By analyzing the entropy curves, scientists and engineers can make predictions and optimize the performance of systems in various applications, such as data compression, communication, and energy conversion.中文文档：熵是一个基本的热力学和信息论概念，代表系统中的无序或随机性程度。

专业英语词汇翻译

A spherical system of coordinates球面坐标系统Absolute scale绝对温标Absolute temperature 绝对温度Absolute zero 绝对零度Acute angle锐角Adiabatic process绝热过程Adjacent临近的Amount of heat 热量Amplitude振幅Analytical expression解Angular momentum角动量Angular velocity角速度Annihilate消灭Appreciable可感知的Approximate solution近似解Arbitrarily任意的变换莫测的Assume that 假设At constant pressure定压比热At rest静止的Axial symmetry轴对称Axis of rotation旋转轴Be independent of 独立的Be proportional to 与……成比例Bend使弯曲的Capacitor电容器Center of mass质心Centripetal force向心力Cgs 厘米-克-秒(Centimeter-Gram-Second) Change in jumps 跳跃的变化Chaotic无序的Charge by conduct 负责的行为Charge by induction 感应电荷Circulation motion圆周运动Classical mechanics经典力学Coefficient系数Coherent连贯的Combustion engine内燃机Comparison 参照物Compensate 补偿，抵消Conductor导体Consecutive 连贯的Consequently结果，因此Conservation保存保护Considerable 相当大的Constant常量Constructive interference 干涉Coordinate system坐标系Coulomb’s law库伦定律Counter-phase相位差Cross-sectional 分类排列Curl卷曲，Curvilinear motion曲线运动Cyclic process循环过程Decrement衰减率Denominator分母Density密度Derivative倒数Destructive interference破坏性干扰Developing发展中Deviation from脱离逸出Diatomic双原子的Difference差异Diffraction衍射Dimension 维Discrete value离散值Displacement位移Distance 距离疏远Distribution function分布函数Divergence 分歧Dynamics动力学Elastic collision弹性碰撞Electric dipole弹性偶极子Electric field 弹性场Electric potential 弹性势Electric potential energy弹性势能Electrically polarized电极化的Electrodynamics电动力学Electromagnetic电磁的Electron电子Electrostatic静电的Elementary mass元素的质量Embodiment体现具体化Emulsion感光乳剂Energy能量精力Energy level 能级Entropy 熵Equilibrium均衡Equipartition principle均分原理Ether乙醚Exposure暴露External force外力Factor因素First law of thermodynamics热力学第一定律Focal plane焦平面Fraunhofer diffraction夫琅和费衍射Free fall自由落体Friction摩擦力Gamma photon伽马射线General theory relativity广义相对论Geometrical几何的Gradient梯度Gravity重力，地心引力Grow proportionally to 正比增长Harmonic function调和函数Harmonic oscillator谐波发射器Heat 高温热度Heat capacity 热熔Heat engine热机Heat transfer热传递Hence因此Histogram直方图Hologram 全息图Holography 全系摄影Homogeneous(反应堆)燃烧和减速剂均匀调和的Huygens’ Principle 惠更斯原理Hypothetical medium 假设介质Ideal gass理想气体Identical 同一的，完全相同的Illuminate说明Impart 给予Impulse脉冲Inalienable不可分割的Incident light入射光Inclination倾向爱好,斜角倾角Incoherent语无伦次的Increase增加Increment增量Inertia惯性Inertial reference frame惯性参考系Infrared radiation 红外线照射Initial moment 初力矩Instantaneous瞬间的Insulator 绝缘体Integral 完整的Interference 干涉Internal energy 内能Internal force内力Intra-molecular energy 分子内能Isotropic 单折射性，各向同性Kinematics运动学Law of cosine law余弦定理Length contraction长度收缩Macroscopic宏观的Mass质量Mass-energy conversion质能转换定理Mean distance 平均距离Mechanical equivalent of heat热功当量Mechanics力学Molar heat gas capacity 摩尔热能Molecular physics分子物理学Momentum势能Monatomic单原子的Monochromatic light单色光Motion动作Multiply多样的，乘Neutron中子Newton’s first law牛顿第一定律Non-equilibrium state非平衡态Normal acceleration法向加速度Normal to 垂直于Nuclei原子核Nucleon 核子Numerator 分子Object beam 物体光束Obtuse angle钝角Operator话务员Overlap 重叠Polarization两极化Parallel axis theorem平行轴的定理Parallel beams平行光束Parallel rays平行光Parallelogram method平行四边形法则Parameter of state状态参数Perfectly rigid body 完全刚体Perpendicular垂直的Phase difference相位差Phenomena现象Piston活塞Point charge点电荷Point particle质点Power功率Preference优先权Principle of relativity相对论Probability可能性Probability distribution function概率分布函数Projection 投射Propagate传播繁殖Proton质子Pseudoscopic幻视镜Quantitative conclusion定量的结论Quasi-static 准静态的Radian弧度Radius半径Rarefaction稀薄的Real image实像Rectilinear motion 直线运动Redistribution重新分配Reference frame参考系Reference wave参考波Relative atomic mass of an element元素的相对原子质量Relative molecular mass of substance物质相对分子质量Relaxation process弛豫过程Relaxation time 弛豫时间Reversible process可逆过程Rotational inertia转动惯量Scalar标量Scalar field标量场Semiconductor半导体Semitransparent 半透明的Solid angle立体角Spatial coherence 空间相干性Special theory of relativity狭义相对论Specific heat capacity 比热容Speed 速度速率Stationary 固定的Subscript下标Superpose 重叠的Superposition叠加Symmetry对称的Temperature温度Temporal coherence 时间相干性Terminal velocity末速度Test charge监测电荷The difference on optical path 光路的区别The equation of state of an ideal gass理想盖斯方程The magnitude of a vector向量的大小The number of degree of freedom自由度数量The reciprocal of 倒数The refractive index折射率The right-hand screw rule右手螺旋定则The second derivative of 二阶导数The tangential acceleration切向加速度Thermodynamic temperature scale热力学温标Three dimensional三维的Time averaged value时间平均价值Time dilation时间扩张Timepiece计时器Torque力矩Torsion balance扭秤Trajectory轨迹Translation motion平移运动Triatomic三原子的Tuning fork音叉Twin paradox孪生子谬论Ultraviolet light紫外线Undeformable bodyUniform circular motion匀速圆周运动Unit time单位时间Vector field 矢量场Vectors矢量Velocity 速率Virtual image虚像Wave length 波长Wave number波数Weight重量1, For a stationary field, the work done on a particle by the forces of the field may dependon the initial and final position of the particle and not depend on the path along which the particle moved. Forces having such a property are called conservative.对于一个固定的场，由场力作用在粒子上的功可能依赖于粒子的初始位置和末位置，而不依赖于粒子移动的路径.。

卡梅伦液压数据手册（第 20 版）说明书

11
iv
⌂
CONTENTS OF SECTION 1
☰ Hydraulics
⌂ Cameron Hydraulic Data ☰
Introduction. . . . . . . . . . . . . ................................................................ 1-3 Liquids. . . . . . . . . . . . . . . . . . . ...................................... .......................... 1-3
4
Viscosity etc.
Steam data....................................................................................................................................................................................... 6
1 Liquid Flow.............................................................................. 1-4
Viscosity. . . . . . . . . . . . . . . . . ...................................... .......................... 1-5 Pumping. . . . . . . . . . . . . . . . . ...................................... .......................... 1-6 Volume-System Head Calculations-Suction Head. ........................... 1-6, 1-7 Suction Lift-Total Discharge Head-Velocity Head............................. 1-7, 1-8 Total Sys. Head-Pump Head-Pressure-Spec. Gravity. ...................... 1-9, 1-10 Net Positive Suction Head. .......................................................... 1-11 NPSH-Suction Head-Life; Examples:....................... ............... 1-11 to 1-16 NPSH-Hydrocarbon Corrections.................................................... 1-16 NPSH-Reciprocating Pumps. ....................................................... 1-17 Acceleration Head-Reciprocating Pumps. ........................................ 1-18 Entrance Losses-Specific Speed. .................................................. 1-19 Specific Speed-Impeller. .................................... ........................ 1-19 Specific Speed-Suction...................................... ................. 1-20, 1-21 Submergence.. . . . . . . . . ....................................... ................. 1-21, 1-22 Intake Design-Vertical Wet Pit Pumps....................................... 1-22, 1-27 Work Performed in Pumping. ............................... ........................ 1-27 Temperature Rise. . . . . . . ...................................... ........................ 1-28 Characteristic Curves. . ...................................... ........................ 1-29 Affinity Laws-Stepping Curves. ..................................................... 1-30 System Curves.. . . . . . . . ....................................... ........................ 1-31 Parallel and Series Operation. .............................. ................. 1-32, 1-33 Water Hammer. . . . . . . . . . ...................................... ........................ 1-34 Reciprocating Pumps-Performance. ............................................... 1-35 Recip. Pumps-Pulsation Analysis & System Piping...................... 1-36 to 1-45 Pump Drivers-Speed Torque Curves. ....................................... 1-45, 1-46 Engine Drivers-Impeller Profiles. ................................................... 1-47 Hydraulic Institute Charts.................................... ............... 1-48 to 1-52 Bibliography.. . . . . . . . . . . . ...................................... ........................ 1-53

电子信息科学与技术专业外语单词汇总

[image sensor摄像传感器]
[image understanding图像理解]
[interstate highway州际公路]
[in a nutshell简而言之]
[iterative method迭代法]
[information transfer信息传递]
[international standard国际标准]
[Parseval’s theorem巴塞瓦尔定理]
[quantum level 量化电平]
[RAM随机存取存储器,内存（random access memory)]
[round off舍入，用四舍五入化为整数]
[radio wave无线电波]
[radiating power发射功率]
[random pulses随机脉冲]
[ALU算术逻辑单元,运算器(arithmetic logic unit)]
[ASIC专用集成电路application specific integrated circuit]
[ADPCM自适应差分脉码调制(adaptive differential PCM)]
[ALU算术逻辑单元，运算器(arithmetic logic unit)]
[network operator网络运营商，网络操作员]
[nonlinear operation 非线性运算]
[optical receiver光接收器]
[open architecture开放型结构]
[OOP面向对象程序设计(object oriented programming)]
[log pulse PCM quantizer对数脉冲PCM量化器]

probability density function estimation

Probability Density Function Estimation using theMinMax MeasureMunirathnam Srikanth,H.K.Kesavan,and Peter H.RoeAbstract—The problem of initial probability assignment con-sistent with the available information about a probabilistic systemis called a direct problem.Jaynes’maximum entropy principle(MaxEnt)provides a method for solving direct problems when theavailable information is in the form of moment constraints.Onthe other hand,given a probability distribution,the problem offinding a set of constraints which makes the given distribution amaximum entropy distribution is called an inverse problem.A method based on the MinMax measure to solve the above in-verse problem is presented here.The MinMax measure of infor-mation,defined by Kapur,Baciu and Kesavan[1],is a quantita-tive measure of the information contained in a given set of momentconstraints.It is based on both maximum and minimum entropy.Computational issues in the determination of the MinMax mea-sure arising from the complexity in arriving at minimum entropyprobability distributions(MinEPD)are discussed.The method tosolve inverse problems using the MinMax measure is illustrated bysolving the problem of estimating a probability density function ofa random variable based on sample data.Index Terms—Entropy optimization,maximum entropy prin-ciple,minimum entropy,MinMax measure,Shannon entropy measure.I.I NTRODUCTIONT HE PRINCIPAL objective of analysis of a probabilistic system is to determine the discrete probabilities of a set of events(or the continuous probability density function over an interval)conditioned upon the available knowledge.This problem of initial probability assignment consistent with avail-able information is called the direct problem.Various methods from the disciplines of probability and statistics exist to solve this problem.In this paper,we explore the problem from the point of view of information theory.Jaynes’(1957)maximum entropy principle(MaxEnt)[2]provides a method for solving direct problems when the available information is in the form of moment constraints.Letwithpro.Suppose the information avail the form of the natural constraint ofprobabilities Manuscript received October12,1998;revised June21,1999.Thi supported in part by the Natural Sciences and Engineering Research Canada.M.Srikanth is with the Department of Computer Science and E State University of New Y ork at Buffalo,Buffalo,NY14228-2583H.K.Kesavan and P.H.Roe are with the Department of Syste Engineering,University of W aterloo,W aterloo,ON,Canada.Publisher Item Identifier S1094-6977(00)02040-X.the problem of probability density function(p.d.f.)estimation from sample data is illustrated in Section VI.II.M INIMUM E NTROPY AND THE M IN M AX M EASURE Previous attempts to solve the inverse problem and to define a measure of information contained in a constraint set were based on MaxEnt.Kapur,Baciu,and Kesavan identified the ambiguity in such measures[1]and defined the MinMax measure based on both maximum and minimum entropy.When the only information available is given by the nat-ural constraint(1),the MaxEPD is the uniformdistribution.The corre-sponding minimum entropy probability distribution is one ofthe,-distinct values or outcomes of the random variable.Theminimum entropy probability distributions represent the mostbiased and least uniform distributions consistent with theavailable information.In the presence of additional information,the choice of prob-ability distributions is reduced.A restricted set of probabilitydistributions has a smaller maximum entropyvalue,.Thus,each additional piece of information inthe form of moment constraintson.In general,every additional constraint reduces the uncer-tainty gap givenby.Let,the MinMax measure is evaluated withrespect to the naturalconstraint,(5)III.C OMPUTIONAL I SSUESThe computation of the MinMax measure for a given set ofconstraints,valuesfor.The problem of Shannon entropy maximization is a convexminimization problem.The Lagrange multiplier method[7],[5]can be used to obtain an analytical solution for the MaxEPD.Using this method,the maximization of the Shannon entropymeasure subject to(1)and(2)givesnonlinear equationsin.The least-squares method[7]can be used to determine theLagrange multipliers.This is achieved by minimizing the sumof the squares of theresiduals(11)where,SRIKANTH et al.:PROBABLITY DENSITY FUNCTION ESTIMATION USING THE MINMAX MEASURE79 at a vertex of the convexpolytope:.In practice,discrete approximations of the continuous inte-grals are used to solve the entropy optimization problems.Thenumerical approximation is based on some sample valuesofvalues,[a,b],is dividedintobe the values corresponding to thepoints is ap-proximatedbythat is different from the uniform distribution,the search is for a set of constraints subject to which thegiven distribution can be regarded as a maximum entropydistribution.This is based on the assumption that all probabilitydistributions are maximum entropy distributions with respectto some set of constraints.Solution methods for some specificinverse problems based on MaxEnt are discussed in[4]and[5],[16].A general method for solving an inverse problem isto try various constraint sets and select the one that makes thegiven distribution a maximum entropy distribution.One suchconstraint set will exist if the probability distribution is of theform of(6)or(15)[5].Kapur[16]states that a nonexponentialprobability distribution can be approximated by a maximumentropy distribution.In this case,the inverse problem can besolved by finding a set of constraints which gives rise to themaximum entropy approximation.Letwhereis assumedto be the naturalconstraint,asand,ing the values of maximum and minimum en-tropies,the MinMax measure for each of the constraintsets,,is computedusing80IEEE TRANSACTIONS ON SYSTEMS,MAN,AND CYBERNETICS—PART C:APPLICATIONS AND REVIEWS,VOL.30,NO.1,FEBRUARY 2000The MinMaxmeasure,,gives the amount of information contained in the constraintsetas.The problem of selecting a “right”constraint set is an in-verse problem.The method presented in Section V is used tosolve this problem.For various sets of constraints,the corresponding MinMax measure values are calculated.This requires the maximum and minimum entropy values to be computed.The methods identi-fied in Section III for solving the maximum and minimum en-tropy problems are used in computing the MinMax measure.In both of these problems,the continuous integrals are approx-imated to their discrete equivalents.Of all the constraints sets considered,the one with maximum MinMax measure value is selected as the solution to the inverse problem.This corresponds to the constraint set which gives the most information about the system among the constraints sets considered.The corre-sponding maximum entropy distribution is accepted as a good estimate of the probability distribution of the system.When the available information is in the form of sample data,the moment values of the probability distribution are calculated using the frequency distribution of the data.Let thesample databeand be the minimum and maximum valuesof,is partitionedinto.The corresponding probability distributionis givenby.Let therepresentativebinsbe ,the expectationvaluein (14)is obtainedas.Let-valuesare.Algebraic momentconstraints()are used to construct the constraint sets for this problem.Sinceis trans-formedto.The probability distribution for the given1Thedata taken from [17].SRIKANTH et al.:PROBABLITY DENSITY FUNCTION ESTIMATION USING THE MINMAX MEASURE 81TABLE IM OMENT V ALUES FOR THE T RANSFORMEDF RACTURE T OUGHNESS VALUESTABLE IIM AX E NT ,M IN E NT ,AND M IN M AX V ALUESFORF RACTURET OUGHNESS PROBLEMsample data based on the above partitioningis.Accordingly,the moment values forvarious algebraic moment constraints are given in Table I.Table II gives the constraint sets considered for this problem and their corresponding MaxEnt,MinEnt,and the MinMax values.In this specific example,a constraintsetis partitioned into smaller sized in-tervals.Fig.3shows the maximum entropy distribution when the number of bins is set to 32.This gives a better approxima-tion of the observed probability distribution.Generating the minimum entropy probability distribution,and hence computing the minimum entropy value,is the slowest step in calculating the MinMax measure for a given set of constraints.Also,the method for solving theminimumFig.1.Plot of S and MinMax values for the fracture toughnessproblem.Fig.2.MaxEPD for fracture toughness:Plot for 8-bins.entropy problem generatesa82IEEE TRANSACTIONS ON SYSTEMS,MAN,AND CYBERNETICS—PART C:APPLICATIONS AND REVIEWS,VOL.30,NO.1,FEBRUARY2000Fig.3.MaxEPD for fracture toughness:Plot for32-bins.inference.The MinMax measure is a quantitative measure of the information contained in a given set of constraints.In the problem of estimating probability density function,the MinMax measure is used to discriminate between different constraint sets.Of the constraint sets considered,the one with the maximum MinMax measure has the most information about the probabilistic system.This constraint set is used in the context of maximum entropy principle to estimate the probability density function.The calculation of the MinMax measure for a constraint set involves computing the maximum and minimum entropy values.This may involve generating the MaxEPD and a MinEPD.While the former is a convex minimization problem and has polynomial solutions,the minimum entropy problem is known to be NP-Hard.An approximate algorithm is used to solve the minimum entropy problem.Howeverm faster and accurate algorithms are required exploring minimum entropy and its applications.The method described in Section III for minimum entropy problem uses only the properties of a concave function.The properties of Shannon entropy measure can be used to improve the algorithm.Also,other global optimization techniques,like difference of convex functions and interval methods,need to be explored for this problem. The distinguishing feature of the MinMax measure is that it deals with the moments of the probability distribution,un-like the entropy measures,whose focus is on the uncertainty of a probability distribution[1].The knowledge of one or more moments of a probability distribution is not equivalent to the knowledge of the probability distribution.However,with addi-tional consistent moments our knowledge improves toward that of the probability distribution.For a particular set of moment constraints,the knowledge of their moment values is equivalent to that of the probability distribution.The constraints in that set are called the characterizing moments of the probability ing the characterizing moments,the Shannon entropy measure can be used to obtain the corresponding probability dis-tribution.Thus,the MinMax measure can be used in the search for a set of moment constraints such that their knowledge is equivalent to the knowledge of the distribution.R EFERENCES[1]J.N.Kapur,G.Baciu,and H.K.Kesavan,“The MinMax informationmeasure,”Int.J.Syst.Sci.,vol.26,no.1,pp.1–12,1995.[2] E.T.Jaynes,“Information theory and statistical mechanics,”Phys.Rev.,vol.106,pp.361–373,1957.[3] C.E.Shannon,“A mathematical theory of communication,”Bell Syst.Tech.J.,vol.27,pp.379–423,623–659,1948.[4]J.N.Kapur and H.K.Kesavan,Generalized Maximum Entropy Prin-ciple(with Applications).Waterloo,Canada:Sandford Educational Press,1989.[5],Entropy OptimIzation Principles with Applications.New York:Academic,1992.[6]S.D.Pietra,V.D.Pietra,and fferty,“Inducing features of randomfields,”IEEE Trans.Pattern Anal.Machine Intell.,vol.19,pp.380–390, Apr.1997.[7]R.Fletcher,Practical Methods of Optimization.New York:Wiley,1991.[8]L.E.Scales,Introduction to Nonlinear Optimization.London,U.K.:Macmillan,1985.[9]J.N.Kapur,G.Baciu,and H.K.Kesavan,“On the relationship betweenvariance and minimum entropy,”Int.Pub.Univ.of Waterloo,1994. [10]L.Yuan and H.K.Kesavan,“Minimum entropy and information mea-sure,”IEEE Trans.Syst.,Man,Cybern.,vol.28,no.3,pp.488–491, 1998.[11]S.Munirathnam,H.K.Kesavan,and P.Roe,“Computation of theminmax measure,”in Information Theory and Maximum Entropy Principle:A Festschrift for J.N.Kapur,Karmeshu,Ed.New Delhi, India:Jawaharlal Nehru Univ.,1998.[12] A.T.Phillips and J.B.Rosen,“Sufficient conditions for solving linearlyconstrained separable concave global minimization problems,”J.Global Optimization,vol.3,pp.79–94,1993.[13]H.P.Benson,“Concave minimization:Theory,applications andalgorithms,”in Handbook of Global Optimization,R.Horst and P.M.Pardalos,Eds.Norwood,MA:Kluwer Academic,1995.[14]S.Munirathnam,“The role of minmax entropy measure in probabilisticsystems design,”M.S.Thesis,Univ.of Waterloo,Waterloo,Canada, 1998.[15]S.S.Chapta and R.P.Canale,Numerical Methods for Engineers.NewYork:McGraw-Hill,1988.[16]J.N.Kapur,Measures of Information and their Applications.NewDelhi,India:Wiley Eastern,1994.[17]J.N.Siddall,Probabilistic Engineering Design:Principles and Appli-cations.New York:Marcel Dekker,1983.Munirathnam Srikanth was born in Chennai,India.He received the M.Sc.(Hons)degree in math-ematics and M.Sc.(Tech)degree in computer sciencefrom the Birla Institute of Technology and Science,Pilani,India in1991,and the M.A.Sc.degree insystems design engineering from the Universityof Waterloo,ON,Canada in1998.He is currentlypursuing the Ph.D.degree in computer science at theState University of New York at Buffalo,Buffalo,NY.His research interests include entropy optimiza-tion,speech recognition,information retrieval,and languagemodeling.H.K.Kesavan had his early education in scienceand electrical engineering from Bangalore,India.Later,he received the Master’s degree in electricalengineering from the University of Illinois and thePh.D.degree from the Michigan State University,East Lansing,MI.He has been a Full Professor since1962,and,in addition,he has served in several administrativepositions.He has served as the Chairman of theElectrical Engineering Department at the Universityof Waterloo,and later as the Founding Chairman of the Department of Systems Design Engineering.He also served as the First Chairman of the Electrical Engineering and Director of the Computer Centre at IIT Kanpur.He has published numerous papers and also four books in his chosen discipline of system theory.Currently,he holds the title of Distinguished Professor Emeritus at the University of Waterloo.SRIKANTH et al.:PROBABLITY DENSITY FUNCTION ESTIMATION USING THE MINMAX MEASURE83 Peter H.Roe received the B.A.Sc.degree inengineering physics from the University of Toronto,Toronto,ON,Canada,in1959,the M.Sc.degreein applied mathematics and the Ph.D.degreein electrical engineering from the University ofWaterloo,Waerloo,ON,Canada,in1960,and1963,respectively.He is currently a Professor and Associate Chair forGraduate Studies in the Systems Design EngineeringDepartment at the University of Waterloo.He wasAssociate Dean of Engineering for Graduate Studiesand Associate Dean of Engineering for Undergraduate Studies among other ad-ministrative appointments at the University of Waterloo.He has held visiting po-sitions at the Thayer School of Engineering,Dartmouth College,Hanover NH,the Nova Scotia Technical College,Halifax,NS,Canada,The Open University,Milton Keynes,U.K.,the Universite de Technologie de Compiegne,France,andthe Ecole Superieure des Ingenieurs de Marseille,France.His current researchinterests include graph theoretic system models,bond graph applications,com-puter networks,and analysis of systems under uncertainty.。

熵,次序和无序(英文书：entropy and art an essay on disorder and order)

ENTROPY AND ARTAN ESSAY ON DISORDER AND ORDERRUDOLF ARNHEIMA BSTRACT.Order is a necessary condition for anything the hu-man mind is to understand.Arrangements such as the layout of a city or building,a set of tools,a display of merchandise,the ver-bal exposition of facts or ideas,or a painting or piece of music are called orderly when an observer or listener can grasp their overall structure and the ramiﬁcation of the structure in some detail.Or-der makes it possible to focus on what is alike and what is differ-ent,what belongs together and what is segregated.When noth-ing superﬂuous is included and nothing indispensable left out, one can understand the interrelation of the whole and its parts, as well as the hierarchic scale of importance and power by which some structural features are dominant,others subordinate.2RUDOLF ARNHEIMC ONTENTSPart1.3EFUL ORDER32.REFLECTIONS OF PHYSICAL ORDER43.DISORDER AND DEGRADATION74.WHAT THE PHYSICIST HAS IN MIND11RMATION AND ORDER136.PROBABILITY AND STRUCTURE177.EQUILIBRIUM218.TENSION REDUCTION AND WEAR AND TEAR229.THE VIRTUE OF CONSTRAINTS2510.THE STRUCTURAL THEME27 Part2.3211.ORDER IN THE SECOND PLACE3212.THE PLEASURES OF TENSION REDUCTION3513.HOMEOSTASIS IS NOT ENOUGH3914.A NEED FOR COMPLEXITY4015.ART MADE SIMPLE4316.CALL FOR STRUCTURE46 References48ENTROPY AND ART AN ESSAY ON DISORDER AND ORDER3 Part1.EFUL ORDERIn many instances,order is apprehendedﬁrst of all by the senses. The observer perceives an organized structure in the shapes and col-ors or sounds facing him.But it is hard,perhaps impossible,toﬁnd examples in which the order of a given object or event is limited to what is directly apparent in perception.Rather,the perceivable order tends to be manifested and understood as a reﬂection of an under-lying order,whether physical,social,or cognitive.Our kinesthetic sense tells us through our muscular reactions whether a device or engine works with a smooth ordering of its parts;in fact,it informs us similarly about the perfect or imperfect functioning of our own bodies.The spatial layout of a building reﬂects and serves the distri-bution and interconnections of various functions;the groupings of the cans and packages on the shelves of a store guide the customer to the ordered varieties of household goods,and the shapes and col-ors of a painting or the sounds of a piece of music symbolize the interaction of meaningful entities.Since outer order so often represents inner or functional order,or-derly form must not be evaluated by itself,that is,apart from its relation to the organization it signiﬁes.The form may be quite or-derly and yet misleading,because its structure does not correspond to the order it stands for.Blaise Pascal observes in his Pensees[54, 1,no.27]:“Those who make antitheses by forcing the words are like those who make false windows for symmetry’s sake:their rule is not to speak right but to make rightﬁgures.”A lack of correspondence between outer and inner order produces a clash of orders,which is to say that it introduces an element of disorder.External orderliness hiding disorder may be experienced as of-fensive.Michel Butor,discussing the New York City of the1950’s, speaks of marvelous walls of glass with their delicate screens of hor-izontals and verticals,in which the sky reﬂects itself;but inside those buildings all the scraps of Europe are piled up in confusion.Those admirable large rectangles,in plan or elevation,make the teeming chaos to which they are basically unrelated particularly intolerable. The magniﬁcent grid is artiﬁcially imposed upon a continent that has not produced it;it is a law one endures[18,p.354]. Furthermore,order is a necessary condition for making a structure function.A physical mechanism,be it a team of laborers,the body of an animal,or a machine,can work only if it is in physical order.4RUDOLF ARNHEIMThe mechanism must be organized in such a way that the various forces constituting it are properly attuned to one another.Functions must be assigned in keeping with capacity;duplications and con-ﬂicts must be avoided.Any progress requires a change of order.A revolution must aim at the destruction of the given order and will succeed only by asserting an order of its own.Order is a prerequisite of survival;therefore the impulse to pro-duce orderly arrangements is inbred by evolution.The social or-ganizations of animals,the spatial formations of travelling birds or ﬁshes,the webs of spiders and bee hives are examples.A pervasive striving for order seems to be inherent also in the human mind-an inclination that applies mostly for good practical reasons.2.REFLECTIONS OF PHYSICAL ORDER However,practicality is not the only consideration.There are forms of behavior suggesting a different impulse.Why would experiments in perception show that the mind organizes visual patterns sponta-neously in such a way that the simplest available structure results? To be sure,one might surmise that all perception involves a desire to understand and that the simplest,most orderly structure facilitates understanding.If a lineﬁgure(Figure2.1a)can be seen as a combi-nation of square and circle,it is more readily apprehended than the combination of three units indicated in Figure2.1b.Even so,another explanation imposes itself when one remembers that such elemen-tary perceptual behavior is but a reﬂection of analogous physiologi-cal processes taking place in the brain.If there were independent ev-idence to make it likely that a similar tendency toward orderly struc-ture exists in these brain processes also,one might want to think of perceptual order as the conscious manifestation of a more universal physiological and indeed physical phenomenon.The corresponding activities in the brain would have to beﬁeld processes because only when the forces constituting a process are sufﬁciently free to interact can a pattern organize itself spontaneously according to the structure prevailing in the whole.No known fact prevents us from assuming that suchﬁeld processes do indeed take place in the sensory areas of the brain.They are quite common inENTROPY AND ART AN ESSAY ON DISORDER AND ORDER5(a)(b)F IGURE2.1.Lineﬁgure of a square and circle. physics.It was Wolfgang Kohler who,impressed by the gestalt law of simple structure in psychology,surveyed corresponding phenom-ena in the physical sciences in his book on the“physical gestalten,”a naturphilosophische investigation published in1920[38].In a later paper he noted:In physics we have a simple rule about the nature of equi-libria,a rule which was independently established by threephysicists:E.Mach,P.Curie,and W.Voigt.They observedthat in a state of equilibrium,processes-or materials-tendto assume the most even and regular distributions of whichthey are capable under the given conditions[40,p.500].Two examples may convey an idea of this sort of physical behav-ior.The physicist Sir Joseph J.Thomson once illustrated the equilib-rium of corpuscles in a plane by the behavior of magnetized needles pushed through cork discs thatﬂoat on water.The needles,having their poles all pointing the same way,repel each other like the atomic corpuscles.A large magnet is placed above the surface of the water, its lower pole being of the opposite sign to that of the upper poles6RUDOLF ARNHEIMF IGURE2.2.Fuel tankﬁlled with clear oil and coloredwater of equal density.of theﬂoating magnets.Under these conditions,the needles,which repel each other but are attracted by the larger magnet,will arrange themselves on the surface of the water around the center of attrac-tion in the simplest possible form:three needles in a triangle,four at the comers of a square,ﬁve at the comers of a pentagon.Thus or-derly shape results from the balancing of the antagonistic forces[65, p.110].The same kind of effect can be observed in another demon-stration(Plate2.2),intended to simulate the behavior of propellant gases and liquids under conditions of zero-gravity.A lucite model of the Centaur fuel tank isﬁlled with clear oil and colored water. Both are of equal density and do not mix,“and the natural surface of the water forms an interface of constant equal tension between them,which is almost like a membrane.”Variously agitated or ro-tated,the segregating surface assumes all sorts of accidental shapes. But when outside interference ceases,the forces inherent in the two liquids organize themselves to constitute an overall state of equilib-rium or minimum tension,which results in perfectly regular spheri-cal shape-the simplest shape available under the circumstances.ENTROPY AND ART AN ESSAY ON DISORDER AND ORDER7 Such demonstrations show that orderly form will come about as the visible result of physical forces establishing,underﬁeld condi-tions,the most balanced conﬁgurations attainable.This is true for inorganic as well as organic systems,for the symmetries of crystals as well as those ofﬂowers or animal bodies.What shall we make of this similarity of organic and inorganic striving?Is it by mere coin-cidence that order,developing everywhere in organic evolution as a condition of survival and realized by man in his mental and physi-cal activities,is also striven for by inanimate nature,which knows no purpose?The preceding examples have shown that the forces constituting a physicalﬁeld have no alternative.They cannot cease to rearrange themselves until they block each other’s movement by attaining a state of balance.The state of balance is the only one in which the system remains at rest,and balance makes for order because it rep-resents the simplest possible conﬁguration of the system’s compo-nents.A proper version of order,however,is also a prerequisite of good functioning and is aspired to for this reason also by organic nature and by man.3.DISORDER AND DEGRADATIONThe vision of such harmonious striving for order throughout na-ture is disturbingly contradicted by one of the most inﬂuential state-ments on the behavior of physical forces,namely,the Second Law of Thermodynamics.The most general account physicists are willing to give of changes in time is often formulated to mean that the mate-rial world moves from orderly states to an ever-increasing disorder and that theﬁnal situation of the universe will be one of maximal disorder.Thus Max Planck,in his lectures on theoretical physics de-livered at Columbia University in1920,said:Therefore,it is not the atomic distribution,but rather thehypothesis of elementary disorder,which forms the realkernel of the principle of increase of entropy and,there-fore,the preliminary condition for the existence of entropy.Without elementary disorder there is neither entropy norirreversible process[56,p.50].8RUDOLF ARNHEIMAnd in a recent book,Angrist and Hepler formulate the Second Lawas follows:“Microscopic disorder(entropy)of a system and its sur-roundings(all of the relevant universe)does not spontaneously de-crease”[3,p.151].In this sense,therefore,entropy is deﬁned as thequantitative measure of the degree of disorder in a system-a deﬁnitionthat,as we shall see,is in need of considerable interpretation.Modern science,then,maintains on the one hand that nature,bothorganic and inorganic,strives towards a state of order and that man’sactions are governed by the same tendency.It maintains on the otherhand that physical systems move towards a state of maximum disor-der.This contradiction in theory calls for clariﬁcation.Is one of the Apparentparadox two assertions wrong?Are the two parties talking about different things or do they attach different meanings to the same words?The First Law of Thermodynamics referred to the conservation ofenergy.It stated that energy may be changed from one form to an-other but is neither created nor destroyed.This could sound un-pleasant if one took it to mean(as one of the leading physicists of thetime,John Tyndall,actually did[66])that“the law of conservationexcludes both creation and annihilation”[34,p.1062].The popular connotations of the Second Law of Thermodynamicswere quite different.When it began to enter the public consciousnessa century or so ago,it suggested an apocalyptic vision of the courseof events on earth.The Second Law stated that the entropy of theworld strives towards a maximum,which amounted to saying thatthe energy in the universe,although constant in amount,was subjectto more and more dissipation and degradation.These terms had adistinctly negative ring.They were congenial to a pessimistic,moodof the times.Stephen G.Brush,in a paper on thermodynamics andhistory,points out that in1857there were published in France Bene-dict Auguste Morel’s“Trait´e des d´e g´e n´e rescences physiques,intel-lectuelles et morales de l’esp`e ce humaine”[50]as well as CharlesBaudelaire’s“Lesﬂeurs du mal”[17,p.505].The sober formulationsof Clausius,Kelvin,and Boltzmann were suited to become a cosmicmemento mori,pointing to the underlying cause of the gradual de-cay of all things physical and mental.According to Henry Adams’witty treatise,The Degradation of the Democratic Dogma,“to the vul-gar and ignorant historian it meant only that the ash heap was con-stantly increasing in size”[1,p.142].The sun was getting smaller,the earth colder,and no day passed without the French or Germannewspapers producing some uneasy discussion of supposed socialdecrepitude;falling off of the birthrate;decline of rural population;lowering of army standards;multiplication of suicides;increase ofENTROPY AND ART AN ESSAY ON DISORDER AND ORDER9 insanity or idiocy,of cancer,of tuberculosis;signs of nervous exhaus-tion,of enfeebled vitality,“habits”of alcoholism and drugs,failure of eyesight in the young and so on,without end...[1,p.186].This was in1910.In1892,Max Nordau had published his famous Degeneration-a book most symptomatic of theﬁn de siecle mood, although it cannot be said to imply that mankind as a whole was on its way out[51].In his diatribe of nearly a thousand pages,the Hungarian physician and writer,basing his contentions on the work of Morel and Lombroso,denounced the wealthy city dwellers and their artists,composers,and writers as hysterics and degenerates. For instance,he thought that the pictorial style of the Impressionists was due to the nystagmus found in the eyes of“degenerates”and the partial anesthesia of the retinae in hysterics.He attributed the high incidence of degeneration to nervous exhaustion produced by modern technology as well as to alcohol,tobacco,narcotics,syphilis. But he predicted that in the twentieth century mankind would prove healthy enough to either tolerate modern life without harm or reject it as intolerable[51,p.508].Today we no longer regard the universe as the cause of our own undeserved troubles but perhaps,on the contrary,as the last refuge from the mismanagement of our earthly affairs.Even so,the law of entropy continues to make for a bothersome discrepancy in the humanities and helps to maintain the artiﬁcial separation from the natural ncelot L.Whyte,acutely aware of the problem, formulated it by asking:“What is the relation of the two cosmic tendencies:towards mechanical disorder(entropy principle)and to-wards geometrical order(in crystals,molecules,organisms,etc.)?”[69,p.27].The visual arts have recently presented us with two stylistic trends which,atﬁrst look,may seem quite different from each other but which the present investigation may reveal to have common roots. On the one hand,there is a display of extreme simplicity,initiated as early as1913by the Russian painter Kasimir Malevich’s Suprematist black square on a white ground[21,p.342].This tendency has a long history in the more elementary varieties of ornamentation as well as the frugal design of many functional objects through the ages.In our own day,we have pictures limited to a few parallel stripes,canvases evenly stained with a single color,bare boxes of wood or metal,and so forth.The other tendency,relying on accidental or deliberately produced disorder,can be traced back to a predilection for composi-tions of randomly gathered subject matter in Dutch still lifes,untidy10RUDOLF ARNHEIMscenes of social criticism in the generation of Hogarth,groups of un-related individuals in French genre scenes of the nineteenth century, and so on[4].In modern painting we note the more or less controlled splashes and sprays of paint,in sculpture a reliance on chance tex-tures,tears or twists of various materials,and found objects.Related symptoms in other branches of art are the use of random sequences of words or pages in literature,or a musical performance presenting nothing but silence so that the audience may listen to the noises of the street outside.In the writings of the composer John Cage,one ﬁnds observations such as the following:I asked him what a musical score is now.He said that’s agood question.I said:Is it aﬁxed relationship of parts?Hesaid:Of course not;that would be insulting.[19,p.27] Magazine and newspaper critics often discuss these phenomena with the bland or tongue-in-cheek objectivity of the reporter.Or they at-tribute to elementary signs the power of consummate symbols,for instance,by accepting a simple arrow as the expression of cosmic soaring or descent,or the crushed remains of an automobile as an image of social turmoil.When they condemn such work,they tend to accuse the artists of impertinence and lack of talent or imagination without at the same time evaluating the work as symptomatic and analyzing its cause and purpose.Aesthetic and scientiﬁc principles do not seem to be readily at hand.Occasional explicit references to entropy can be found in critical writing.Richard Kostelanetz,in an article on“Inferential Arts,”quotes Robert Smithson’s Entropy and the New Monuments as saying of re-cent towering sculptures of basic shapes that they are“not built for the ages but rather against the ages”and“have provided a visible analogue for the Second Law of Thermodynamics”[42,p.22].Surely the popular use of the notion of entropy has changed.If during the last century it served to diagnose,explain,and deplore the degrada-tion of culture,it now provides a positive rationale for“minimal”art and the pleasures of chaos.ENTROPY AND ART AN ESSAY ON DISORDER AND ORDER114.WHAT THE PHYSICIST HAS IN MINDTuming from the bravura of the market place to the theoretical issues,one may want to askﬁrst of all:What is it that induces physi-cists to describe the end state of certain material systems as one of maximal disorder,that is,to use descriptive terms of distinctly neg-ative connotation?For the answer one must look at their view of (a)the shape situations and(b)the dynamic conﬁgurations prevail-ing in early and late states of physical systems.Here one discovers,ﬁrst of all,that the processes measured by the principle of entropy are perceived as the gradual or sudden destruction of inviolate ob-jects-a degradation involving the breaking-up of shape,the disso-lution of functional contexts,the abolition of meaningful location.P. ndsberg in a lecture,Entropy and the Unity of Knowledge,chooses the following characteristic example:Tidy away all your children’s toys in a toy cupboard,andthe probability ofﬁnding part of a toy in a cubic centimeteris highly peaked in the region of the cupboard.Release arandomizing inﬂuence in the form of an untidy child,andthe distribution for the system will soon spread[45,p.16]. The child’s playroom can indeed serve as an example of disorder-especially if we do not grant the child a hearing to defend the hid-den order of his own toy arrangements as he sees them.But the messed-up room is not a good example of aﬁnal thermodynamic state.The child may have succeeded in breaking all the functional and formal ties among his implements by destroying the initial or-der and replacing it with one of many possible,equally arbitrary arrangements.Thereby he may have increased the probability that the present kind of state may come about by chance,which amounts to a respectable increase of entropy.He may even have dispersed the pieces of a jigsaw puzzle or broken aﬁre engine,thereby extend-ing disintegration somewhat beyond the relations among complete objects to include the relations among parts.Nevertheless,the child is a very inefﬁcient randomizer.Failing to grind his belongings to a powder of independent molecules,he has preserved islands of untouched order everywhere.In fact,it is only because of this failure that the state of his room can be called disorderly.Disorder“is not the absence of all order but rather the clash of uncoordinated orders”[5,p.125].12RUDOLF ARNHEIMThe random whirling of elementary particles,however,does notmeet this deﬁnition of disorder.Although it may have come about Randomnessby dissolution,it is actually a kind of order.This will become clearer is order!if I refer to another common model for the increase of entropy,namely shufﬂing[23,Ch.4].The usual interpretation of this operation is thatby shufﬂing,say,a deck of cards one converts an initial order into areasonably perfect disorder.This,however,can be maintained onlyif any particular initial sequence of cards in the deck is considered anorder and if the purpose of the shufﬂing operation is ignored.Ac-tually,of course,the deck is shufﬂed because all players are to havethe chance of receiving a comparable assortment of cards.To thisend,shufﬂing,by aiming at a random sequence,is meant to create ahomogeneous distribution of the various kinds of cards throughoutthe deck.This homogeneity is the order demanded by the purposeof the operation.To be sure,it is a low level of order and,in fact,alimiting case of order because the only structural condition it fulﬁllsis that a sufﬁciently equal distribution shall prevail throughout thesequence.A very large number of particular sequences can meet thiscondition;but it is an order nevertheless,similar,for example,to thesort of symmetry of a somewhat higher order that would exist in theinitial set-up of a game in which every player would be dealt onecard of each kind systematically.Before shufﬂing,the initial sequence of the cards in the deck,ifconsidered by and for itself,may have been quite orderly.Perhaps allthe aces or all the deuces were lying together.But this order wouldbe like the false windows in Pascal’s example.It would be in discordwith the very different order required for the game,and the falserelation between form and function would constitute an element ofdisorder.ENTROPY AND ART AN ESSAY ON DISORDER AND ORDER13 The orderliness inherent in the homogeneity of a sufﬁciently large random distribution is easily overlooked because the probability sta-tistics of the entropy principle is no more descriptive of structure than a thermometer is of the nature of heat.Cyril S.Smith has observed:“Like molecular structure earlier,quantum mechanics began almost as a notational device,and even today physicists tend to ignore the rather obvious spatial structure underlying their energy-level notation”[62,p.642].Pure thermodynamics,in the words of Planck,“knows noth-ing of an atomic structure and regards all substances as absolutely contin-uous”([56,p.41];[39]).In fact,the term disorder,when used by physi-cists in this connection,is intended to mean no more than that“the single elements,with which the statistical approach operates,behave in complete independence from one another”[55,p.42].It follows that the entropy principle deﬁnes order simply as an improbable arrangement of elements,regardless of whether the macro-shape of this arrangement is beautifully structured or most arbitrarily deformed;and it calls disorder the dissolution of such an improbable arrangement.RMATION AND ORDERThe absurd consequences of neglecting structure but using the concept of order just the same are evident if one examines the present termi-nology of information theory.Here order is described as the carrier of information,because information is deﬁned as the opposite of entropy, and entropy is a measure of disorder.To transmit information means to induce order.This sounds reasonable enough.Next,since entropy grows with the probability of a state of affairs,information does the opposite:it increases with its improbability.The less likely an event is to happen,the more information does its occurrence represent.This again seems reasonable.Now what sort of sequence of events will be least predictable and therefore carry a maximum of information? Obviously a totally disordered one,since when we are confronted with chaos we can never predict what will happen next.The conclu-sion is that total disorder provides a maximum of information;and since information is measured by order,a maximum of order is con-veyed by a maximum of disorder.Obviously,this is a Babylonian muddle.Somebody or something has confounded our language.14RUDOLF ARNHEIMThe cause of the trouble is that when we commonly talk about or-der we mean a property of structure.In a purely statistical sense,on the other hand,the term order can be used to describe a sequence or arrangement of items unlikely to come about by mere chance.Now in a world of totally unrelated items,which has the throwing of dice as its paradigm,all particular sequences or arrangements of items are equally unlikely to occur,whether a series of straight sixes or a totally irregular but particular sequence of the six digits.In the language of information theory,which ignores structure,each of these sequences carries a maximum amount of information,i.e.,of order, unless the procedure happens to be applied to a world that exhibits regularities.Structure means to the information theorist nothing bet-ter than that certain sequences of items can be expected to occur. Suppose you watch a straight line growing a vapor trail in the sky or a black mark in an animatedﬁlm or on the pad of an artist.In a world of pure chance,the probability of the line continuing in the same direction is minimal.It is reciprocal to the inﬁnite number of directions the line may take.In a structured world,there is some probability that the straight line will continue to be straight.A per-son concerned with structure can attempt to derive this probability from his understanding of the structure.How likely is the airplane suddenly to change its course?Given the nature of theﬁlm or the artist’s drawing,how likely is the straight line to continue?The in-formation theorist,who persists in ignoring structure,can handle this situation only by deriving from earlier events a measure of how long the straightness is likely to continue.He asks:What was the length of the straight lines that occurred before in the same situation or in comparable ones?Being a gambler,he takes a blind chance on the future,on the basis of what happened in the past.If he bets on the regularity of straightness,it is only because straightness has been observed before or has been decreed by the rules of the game.A par-ticular form of crookedness would do just as well as the straight line, if it happened to meet the statistical condition,in a world in which crookedness were the rule.Naturally,most of the time such predic-tions will be laborious and untrustworthy.Few things in this world can be safely predicted from the frequency of their previous occur-rence alone;and the voluntary abstinence by which pure statistics of this kind rejects any other criterion,that is to say,any understanding of structure,will make calculations very difﬁcult.Any predictable regularity is termed redundant by the informa-tion theorist because he is committed to economy:every statement must be limited to what is needed.He shares this commitment with。

概率熵归一化pqn原理

概率熵归一化pqn原理概率熵归一化（Probability, Quantity, and Normalization，简称PQN）是一种用于自然语言处理（NLP）任务中的特征归一化方法。

PQN的原理是基于信息论的概念，通过将特征数据转化为概率分布并计算熵值，然后对熵值进行归一化处理，从而提高特征的区分能力和表达效果。

PQN的核心思想是将特征数据视为随机变量的概率分布，并通过计算特征的熵值来衡量不确定性。

熵值越大，表示特征的不确定性越高，也就意味着特征具有更多的区分能力。

因此，PQN认为在NLP任务中，熵值越大的特征对区分不同类别的文本具有更强的表达能力。

首先，PQN将特征数据转化为概率分布。

通常情况下，特征数据可以是词频、TF-IDF、词向量等表示文本的表示形式。

将特征数据转化为概率分布的方法有多种，比如对特征数据进行归一化处理，使得所有特征的和等于1，即特征数据之和为1的概率分布。

然后，PQN计算特征的熵值。

熵是信息论中一个重要的概念，表示随机变量的不确定性度量。

在NLP任务中，特征的熵值可以衡量特征对文本分类任务的表达能力，熵值越大表示特征的区分能力越强。

最后，PQN对熵值进行归一化处理。

归一化的目的是将熵值映射到一个固定的范围内，使得不同特征的熵值可以进行比较。

常用的归一化方法有线性归一化和指数归一化等。

线性归一化将熵值映射到[0,1]的范围内，指数归一化则通过对熵值进行指数操作，将熵值映射到[0,1]的范围内。

PQN的优点在于能够提高特征的表达能力和区分能力。

通过将特征数据转化为概率分布，PQN可以更好地捕捉到不同特征之间的差异，使得更重要的特征获得更大的权重，进而提高特征的表达效果。

同时，通过对熵值进行归一化处理，PQN可以消除不同特征之间的尺度差异，使得不同特征的熵值可以进行比较，提高特征的区分能力。

然而，PQN也存在一些限制。

首先，PQN需要将特征数据转化为概率分布，这可能需要对特征数据进行其中一种预处理，增加了计算的复杂性。

外森比克不等式推论

外森比克不等式推论英文回答：The Jensen's inequality is a fundamental result in mathematical analysis that relates the convexity of a function to the inequality of its expected value. The inequality states that for any convex function f(x) and any probability distribution P, the expected value of f(X) is greater than or equal to f(E(X)), where X is a random variable with distribution P.One important consequence of the Jensen's inequality is the Hölder's inequality, which provides a bound on the product of two functions. Hölder's inequality states that for any two functions f(x) and g(x), both of which are non-negative and integrable over a given interval, the integral of their product is less than or equal to the product of their integrals raised to a certain exponent.Mathema tically, it can be expressed as ∫(f(x)g(x))dx ≤ ( ∫f(x)^p dx )^(1/p) ( ∫g(x)^q dx )^(1/q), where p and qare positive real numbers such that 1/p + 1/q = 1.Another consequence of the Jensen's inequality is the Cauchy-Schwarz inequality, which provides a bound on the inner product of two vectors. The Cauchy-Schwarz inequality states that for any two vectors u and v in a given inner product space, the absolute value of their inner product is less than or equal to the product of their norms. Mathematical ly, it can be expressed as |<u, v>| ≤ ||u|| ||v||, where <u, v> denotes the inner product of u and v, and ||u|| and ||v|| denote the norms of u and v, respectively.In addition, the Jensen's inequality is also used in probability theory to prove the subadditivity of entropy. The entropy of a random variable measures the amount of uncertainty associated with its outcomes. The subadditivity of entropy states that the entropy of the sum of two random variables is less than or equal to the sum of their individual entropies. This property is important in the study of information theory and has applications in various fields, including data compression and cryptography.Overall, the Jensen's inequality is a powerful tool in mathematical analysis and has numerous applications in various branches of mathematics and other fields. It provides a framework for understanding the relationship between convexity and inequality, and its consequences have wide-ranging implications.中文回答：外森比克不等式是数学分析中的一个基本结果，它将函数的凸性与其期望值的不等式联系起来。

inverse Gamma distribution

Inverse-gamma distribution Inverse-gamma Probability density functionCumulative distribution functionparameters:shape (real)scale (real)support:pdf:cdf:mean:formode:variance:for skewness:forex.kurtosis:forentropy:mgf:cf:In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution. Perhaps the chief use of the inverse gamma distribution is in Bayesian statistics, where it serves as the conjugate prior of the variance of a normal distribution. However, it is commonamong Bayesians to consider an alternative parametrization of the normal distribution in terms of the precision, defined as the reciprocal of the variance, which allows the gamma distribution to be used directly as a conjugate prior.CharacterizationProbability density functionThe inverse gamma distribution's probability density function is defined over the supportwith shape parameter and scale parameter .Cumulative distribution functionThe cumulative distribution function is the regularized gamma functionwhere the numerator is the upper incomplete gamma function and the denominator is the gamma function. Many math packages allow you to compute Q, the regularized gamma function, directly.PropertiesIt is possible to show that for andwhere is the digamma function.Related distributions•If then•If then (inverse-chi-squared distribution)•If then (scaled-inverse-chi-squared distribution)•If (Gamma distribution) then•If (Lévy distribution) then•Inverse gamma distribution is a special case of type 5 Pearson distribution• A multivariate generalization of the inverse-gamma distribution is the inverse-Wishart distribution.Derivation from Gamma distributionThe pdf of the gamma distribution isand define the transformation then the resulting transformation isReplacing with ; with ; and with results in the inverse-gamma pdf shown aboveArticle Sources and Contributors4 Article Sources and ContributorsInverse-gamma distribution Source: /w/index.php?oldid=456392677 Contributors: Benwing, Biostatprof, Btyner, Cburnett, Cquike, Dstivers, Fnielsen, Giftlite,Iwaterpolo, Josevellezcaldas, Kastchei, M27315, MarkSweep, Melcombe, MisterSheik, PAR, Qwfp, Rfinlay@, Rlendog, Rphlypo, Sheppa28, Slavatrudu, Tomi, User A1, 28anonymous editsImage Sources, Licenses and ContributorsImage:Inverse gamma pdf.png Source: /w/index.php?title=File:Inverse_gamma_pdf.png License: GNU General Public License Contributors: Alejo2083, CburnettImage:Inverse gamma cdf.png Source: /w/index.php?title=File:Inverse_gamma_cdf.png License: GNU General Public License Contributors: Alejo2083, Cburnett LicenseCreative Commons Attribution-Share Alike 3.0 Unported///licenses/by-sa/3.0/。

熵值法英文

熵值法英文Entropy method, also known as information entropy method, is a multi-criteria decision-making method based on information theory. It was proposed by Shannon in 1948. Entropy method uses the concept of entropy to measure the degree of uncertainty and information of a system, and converts the qualitative factors into quantitative ones for decision-making. It has been widely appliedin various fields such as economics, management, and engineering.In the entropy method, the decision problem is transformed into a mathematical model. The decision matrix is established based on the evaluation criteria and alternatives. The first step is to calculate the weighted normalized decision matrix. The weights of the criteria are calculated by using information entropy and Shannon's entropy formula. The criteria with higher entropy value are considered more important. The decision matrix is then normalized to eliminate the effect of different measurement units or scales.After obtaining the weighted normalized decision matrix, the next step is to calculate the entropy values of each alternative. The entropy value of an alternative is calculated based on the probability distribution of the alternative under each criterion. A lower entropy value indicates a higher degree of certainty and information. The entropy value of an alternative is then multiplied by the weight of the corresponding criterion to obtain the weighted entropy value.The last step is to calculate the comprehensive entropy value of each alternative. The comprehensive entropy value is obtained by summing up the weighted entropy values of all criteria. Thealternative with the lowest comprehensive entropy value is considered the best choice.The entropy method has several advantages. First, it can effectively deal with complex decision-making problems with multiple criteria. Second, it avoids the subjectivity and inconsistency of subjective judgment. Third, it provides a clear and objective ranking of alternatives based on the entropy values.However, there are also limitations to the entropy method. It assumes that the criteria and alternatives are independent, which may not always hold in real-world situations. It can also be sensitive to the choice of decision matrix size and criteria weights. Therefore, it is important to carefully select the criteria and properly determine their weights in order to obtain reliable results.In conclusion, the entropy method is a useful tool for multi-criteria decision-making. It provides a systematic and objective approach to evaluate and rank alternatives. By utilizing the concept of entropy, it effectively measures the degree of uncertainty and information in a decision-making problem. Despite its limitations, the entropy method has been widely applied and has made significant contributions to various fields.。

机器学习sklearn（二十五）：模型评估（五）量化预测的质量（二）分类指标

机器学习sklearn（⼆⼗五）：模型评估（五）量化预测的质量（⼆）分类指标分类指标模块实现了⼏个 loss, score, 和 utility 函数来衡量 classification （分类）性能。

某些 metrics （指标）可能需要 positive class （正类），confidence values（置信度值）或binary decisions values （⼆进制决策值）的概率估计。

⼤多数的实现允许每个样本通过sample_weight参数为 overall score （总分）提供 weighted contribution （加权贡献）。

其中⼀些仅限于⼆分类⽰例:调⽤功能(y_true, probas_pred)Compute precision-recall pairs for different probability thresholds(y_true, y_score[, pos_label, …])Compute Receiver operating characteristic (ROC)其他也可以在多分类⽰例中运⾏:调⽤功能(y1, y2[, labels, weights, …])Cohen’s kappa: a statistic that measures inter-annotator agreement.(y_true, y_pred[, labels, …])Compute confusion matrix to evaluate the accuracy of a classification(y_true, pred_decision[, labels, …])Average hinge loss (non-regularized)(y_true, y_pred[, …])Compute the Matthews correlation coefficient (MCC)有些还可以在 multilabel case （多重⽰例）中⼯作:调⽤功能(y_true, y_pred[, normalize, …])Accuracy classification score.(y_true, y_pred[, …])Build a text report showing the main classification metrics(y_true, y_pred[, labels, …])Compute the F1 score, also known as balanced F-score or F-measure(y_true, y_pred, beta[, labels, …])Compute the F-beta score(y_true, y_pred[, labels, …])Compute the average Hamming loss.(y_true, y_pred[, …])Jaccard similarity coefficient score(y_true, y_pred[, eps, normalize, …])Log loss, aka logistic loss or cross-entropy loss.(y_true, y_pred)Compute precision, recall, F-measure and support for each class(y_true, y_pred[, labels, …])Compute the precision(y_true, y_pred[, labels, …])Compute the recall(y_true, y_pred[, normalize, …])Zero-one classification loss.⼀些通常⽤于 ranking:调⽤功能(y_true, y_score[, k])Discounted cumulative gain (DCG) at rank K.(y_true, y_score[, k])Normalized discounted cumulative gain (NDCG) at rank K.有些⼯作与 binary 和 multilabel （但不是多类）的问题:调⽤功能(y_true, y_score[, …])Compute average precision (AP) from prediction scores(y_true, y_score[, average, …])Compute Area Under the Curve (AUC) from prediction scores在以下⼩节中，我们将介绍每个这些功能，前⾯是⼀些关于通⽤ API 和 metric 定义的注释。

极大似然最大熵概率密度估计及其优化解法

极大似然最大熵概率密度估计及其优化解法吴福仙;温卫东【摘要】针对经典最大熵概率密度估计中拉格朗日乘子计算目前存在高度非线性、计算精度不高或有时难以收敛等问题,提出了一种"最大似然+逐次优化"的方法.基于最大似然估计法,推导建立了简化的拉格朗日优化函数;在此基础上,基于样本原点矩约束,提出了逐次寻优算法.根据优化过程不稳定,重新推导了拉格朗日乘子的线性变换公式,避免矩阵求逆运算引起的奇异现象.针对几种常见的概率分布类型及可靠性问题,采用极大似然最大熵概率密度估计法与经典型最大熵概率密度估计法分别计算概率密度及可靠度的对比表明:极大似然最大熵概率密度估计法的优化函数非线性程度低,形式简单,而且"极大似然最大熵概率密度估计+逐次优化法计算"精度高,收敛性好.%Aiming at high nonlinearity,low computational accuracy or hard convergence of Lagrangian multiplier calculation in the probability density function estimation by the classic maximum entropy method,a new method combining the maximum likelihood estimation (MLE)maximum entropy probability density method with the sequential updating methodis proposed in this grangian optimization function with low nonlinearity is established on the basis of MLE.Furthermore,the sequential updating method is proposed which is constrained by the sample origin moments.Because of unsteady in the process of optimization,the transformation formula of Lagrangian multiplier is deduced again to avoid singularity phenomenon caused by matrix inversion.By analyzing several common distribution and reliability issues using the MLE maximum entropy probability density method and the classic maximum entropyprobability density method,it is found that the MLE maximum entropy probability density method has advantage of low nonlinearity and simple form in the optimization function,while the new combination method does well in computational accuracy and optimization convergence.【期刊名称】《南京航空航天大学学报》【年(卷),期】2017(049)001【总页数】7页(P110-116)【关键词】概率密度估计;可靠性;极大似然估计;最大熵;逐次优化【作者】吴福仙;温卫东【作者单位】南京航空航天大学能源与动力学院,南京,210016;南京航空航天大学能源与动力学院,南京,210016【正文语种】中文【中图分类】TK05可靠性分析中，经常需要由离散的实验数据求出概率分布曲线，进而计算可靠度。