Blind equalization by direct examination of the input sequences
Inattentional blindness versus inattentional amnesia for fixated but ignored words
2.对有意义的熟悉词与字母串组成的词再认 测验的脑电反应进行对比。 当注意字母串时，左侧区域网络产生了强 激活，包括后侧颞叶，顶叶和前额皮层。 这与前人关于机能障碍和词汇加工的功能 图像的研究一致。 因为词与辅音有很多差异（比如，拼法和 发音，词的状态，语义），激活可能包含 所有词相关的加工。 我们的结果与前人脑成像的研究一致，在 非词汇任务中也发现了与词相关的激活。
假设：
当忽略字母串注意图片时，有意义的词是 否会产生不同的脑电波。 A.如果可以产生对忽略词的无意视盲，那么 就会发现对词和非词的激活类似。 B.相反，如果词的加工正如通常所认为的那 样是完全自动的，那么会发现对忽略词的 不同的激活，因为它们是自动觉察的，那 么不注意的作用就与无意遗忘类似，而不 是无意视盲。
3.词的加工是否自动发生的这个问题上依然存 在争论。 需要注意的是，当不注意字母串时，对词与对 辅音反应趋势类似。脑成像的数据说明，词的 加工依赖于注意，与以前的心理学上和功能图 像上得到的完全自动的结果相反。 如果不注意词只受到无意遗忘的影响，那么即 使因为是自动加工而不对它们进行注意，在它 们呈现的时候，也会出现对词和辅音串的不同 反应。 相反，如果忽略词真的发生了无意视盲，那么 在不注意词时，对注意词的不同反应就会完全 消除。我们的结果支持了后者。
ቤተ መጻሕፍቲ ባይዱ
因而，从这个意义上说，“无意视盲” inattentional blindness和“无意遗忘” inattentional amnesia这两种解释是不能绝对 分离的。 Rees等人利用fMRI进行了静态无意视盲实验， 其主要目的是为了验证“fixated but ignored words”究竟是由于无意视盲还是无意遗忘引 起的。脑成像结果证实了前者。
盲均衡算法的基本原理
盲均衡算法的基本原理The basic principle of blind equalization algorithm lies in its ability to estimate the channel response from the observed received signal without relying on any known training sequences. 这种盲均衡算法的基本原理在于它可以从接收到的信号中估计通道响应，而无需依赖于任何已知的训练序列。
In other words, it can adaptively adjust the equalizer coefficients to minimize the distortion caused by the channel and recover the original transmitted signal. 换句话说，它可以自适应地调整均衡器系数，以最小化由信道引起的失真，并恢复原始发送信号。
This is particularly useful in scenarios where the channel characteristics are unknown or change over time, such as wireless communication systems or underwater acoustic channels. 这在信道特性未知或随时间变化的场景中特别有用，比如无线通信系统或水下声学通道。
By using blind equalization algorithms, one can achieve reliable communication even in challenging environments without prior knowledge of the channel. 通过使用盲均衡算法，可以在没有通道先验知识的情况下，在具有挑战性的环境中实现可靠的通信。
Blind deconvolution by means of the richardsonlucy algorithm
58J.Opt.Soc.Am.A/Vol.12,No.1/January1995Fish et al.Blind deconvolution by means of theRichardson–Lucy algorithmD.A.Fish,A.M.Brinicombe,andE.R.PikeDepartment of Physics,King’s College London,Strand,London WC2R2LS,UKJ.G.WalkerDepartment of Electrical and Electronic Engineering,University Park,University of Nottingham,Nottingham NG72RD,UKReceived April7,1994;revised manuscript received August8,1994;accepted August22,1994A blind deconvolution algorithm based on the Richardson–Lucy deconvolution algorithm is presented.Itsperformance in the presence of noise is found to be superior to that of other blind deconvolution algorithms.Results are presented and compared with results obtained from implementation of a Weiner filter blinddeconvolution algorithm.The algorithm is developed further to incorporate functional forms of the point-spread function with unknown parameters.In the presence of noise the point-spread function can beevaluated with1.0%error,and the object can be reconstructed with a quality near that of the deconvolutionprocess with a known point-spread function.1.INTRODUCTIONBlind deconvolution is the term given to an image-restoration technique in which complete knowledge of both the point-spread function(PSF)and the object are not available.Ayers and Dainty1proposed a scheme that essentially generalized the Feinup phase retrieval algorithm.2The technique is iterative,and a priori knowledge is limited to the nonnegativity of images.In each iteration one obtains estimates of the object and the PSF by simple inverse filtering.Davey et al.3proposed a similar scheme,but their algorithm assumed further a priori knowledge,i.e.,that the object support was known.In their study a Weiner-type filter was used to obtain estimates of the object and the PSF.This method thus permitted better noise compensation.In this paper a Weiner filter blind deconvolution algo-rithm is implemented and is compared with a new al-gorithm based on the Richardson–Lucy4,5deconvolution. The Richardson–Lucy algorithm has proved to be robust in the presence of noise;therefore we thought that a blind deconvolution algorithm based on this technique might have advantages over the Ayers–Dainty and the Davey–Lane–Bates algorithms.The results shown here con-firm the high noise tolerance of our new algorithm.To improve further the performance of this type of algorithm,we incorporated extra a priori knowledge by assuming a functional form for the PSF.It was thought that this method would produce better results because the number of unknowns is reduced from thousands of pixel values to a small number of parameters that describe the PSF.It is likely that blind deconvolution performed in this manner would find use in many areas in which it is not possible to know exactly how an optical system is aberrated but which could be characterized by a few free parameters.One example of such an application is in telescopes in space,where unknown fluctuations of mirrors,which are due to time-varying gravitational fields,do not permit exact knowledge of the PSF.2.BLIND DECONVOLUTION BY THE RICHARDSON–LUCY ALGORITHMThe Richardson–Lucy deconvolution algorithm has be-come popular in the fields of astronomy and medical imag-ing.Initially it was derived from Bayes’s theorem in the early1970’s by Richardson and Lucy.4,5In the early 1980’s it was rederived by Shepp and Vardi6as an al-gorithm to solve positron emission tomography imaging problems,in which Poissonian statistics are dominant. Their method used a maximum-likelihood solution,which was found by use of the expectation maximization algo-rithm of Dempster et al.7The reason for the popularity of the Richardson–Lucy algorithm is its implementation of maximum likelihood and its apparent ability to pro-duce reconstructed images of good quality in the presence of high noise levels.We therefore assumed that a blind form of this algorithm would have the same characteris-tics.A blind deconvolution algorithm similar to the one shown here was also developed by Holmes8by use of the expectation maximization algorithm of Dempster et al.7 We begin with a brief review of the Richardson–Lucy deconvolution method and then present the blind form of the algorithm.The Richardson–Lucy algorithm was developed from Bayes’s theorem.Because it relates con-ditional probabilities the algorithm takes into account statistical fluctuations in the signal and therefore has the ability to reconstruct noisy images.Bayes’s theorem is given byP͑x j y͒P͑y j x͒P͑x͒ZP͑y j x͒P͑x͒d x,(1)where P͑y j x͒is the conditional probability of an event y,given event x.P͑x͒is the probability of an event x, and P͑x j y͒is the inverse conditional probability,i.e.,the probability of event x,given event y.The probability P͑x͒can be identified as the object distribution f͑x͒;the0740-3232/95/010058-08$06.00©1995Optical Society of AmericaFish et al.Vol.12,No.1/January1995/J.Opt.Soc.Am.A59Fig.1.Blind deconvolution based on the Richardson–Lucy algorithm.conditional probability P͑y j x͒can be identified as the PSF centered at x,i.e.,g͑y,x͒;and the probability P͑y͒can be identified as the degraded image or convolution c͑y͒.This inverse relation permits the derivation of the iterative algorithmf i11͑x͒Z g͑y,x͒c͑y͒d yZg͑y,z͒f i͑z͒d zf i͑x͒,(2)where i is the iteration number.If an isoplanatic condi-tion exists,then Eq.(2)can be written in terms of con-volutions:f i11͑x͒Ω∑c͑x͒f i∏≠g͑2x͒æf i͑x͒,(3)where≠is the convolution operation.The PSF g͑x͒isknown,so one finds the object f͑x͒by iterating Eq.(3)until convergence.An initial guess is required for theobject f0͑x͒to start the algorithm.Then,in subsequent iterations,because of the form of the algorithm,large de-viations in the guess from the true object are lost rapidlyin initial iterations,whereas detail is added more slowlyin subsequent iterations.Advantages of this algorithminclude a nonnegativity constraint if the initial guessf0͑x͒$0.Also,energy is conserved as the iteration pro-ceeds,which is easily seen by integration of both sides of Eq.(2)over x.In the blind form of this algorithm two of these deconvo-lution steps are required.At the k th blind iteration it isassumed that the object is known from the k21iteration.The PSF g k͑x͒is then calculated for a specified number of Richardson–Lucy iterations,as in Eq.(4)below,where the i index represents the Richardson–Lucy iteration. This equation is essentially an inverse of Eq.(3),inas-much as the object and the PSF have reverse roles,and it calculates the PSF from the object.Then f k͑x͒is calcu-lated for the same number of Richardson–Lucy iterations. This is done with the PSF evaluated from the full itera-tion of Eq.(4).In this case the iteration is performed in the normal manner of Eq.(3),as shown in Eq.(5)below. The degraded image is again given as c͑x͒in both Eqs.(4) and(5).The loop is repeated as required.One writesg i11k͑x͒Ω∑c͑x͒g i k k21∏≠f k21͑2x͒æg i k͑x͒,(4) f i11k͑x͒Ω∑c͑x͒f i k͑x͒≠g k͑x͒∏≠g k͑2x͒æf i k͑x͒.(5)The above equations are shown in one dimension; the extension for two-dimensional images is straight-forward.Initial guesses are made for the object f00͑x͒and the PSF g00͑x͒,and an algorithm loop of the form shown in Fig.1is performed.No positivity constraints are required because the above equations always ensure positivity.The algorithm is different from the Holmes8 algorithm,as only two Richardson–Lucy iterations are performed within one blind iteration,one for an object evaluation and one for the PSF evaluation.It was found that the simulated images used did not perform well with this type of iteration but that when the number of Richardson–Lucy iterations within one blind itera-tion was increased to approximately ten a much better performance was obtained.To test this algorithm against another blind deconvo-lution algorithm for comparison of performance purposes the Davey et al.3blind deconvolution algorithm with a Weiner filter was implemented.In the implementation used here the support constraint used by Davey et al.was not used because no support constraint was used for the Richardson–Lucy blind deconvolution algorithm.A convolution was created from a Gaussian to model the PSF and a cross(the object);these can be seen in Fig.2.All the images are64364pixels.Photon noise was added to the image by generation of a random num-ber lying on a Poisson distribution with the mean of the pixel value of the noiseless image,and the numbers that were generated for all the pixels then formed the noisy image.It was found that,with this type of image and ap-proximately1.5%noise(where the percentage value is the(a)(b)(c)Fig.2.(a)Simulated object,(b)Gaussian PSF,and(c)their convolution with1.5%Poissonian noise.60J.Opt.Soc.Am.A/Vol.12,No.1/January1995Fish et al.(a)(b)Fig.3.Blind deconvolution by the Weiner filter algorithm. Reconstructions of the object(left)and the PSF(right)with(a) zero noise and(b)1.5%noise.standard deviation divided by the intensity at the bright-est point in the image),good reconstructions could be ob-tained.Figure3shows reconstructions by means of the blind Weiner filter algorithm;Fig.3(a)shows the noise-less case,in which the images shown are the best-error object(left)and the PSF(right)after400iterations.The term best error refers to the least error between the origi-nal convolution and the convolution of the reconstructed object and the PSF.Figure3(a)shows the case of1.5% noise;the reconstructions have deteriorated,but the cross is still distinguishable.Noise levels much above this fig-ure resulted in unrecognizable reconstructions.The blind Richardson–Lucy algorithm performed far better on the same image.In Fig.4(a)images are shown with1.5%and10.0%noise(left and right,respectively). Figures4(b)and4(c)show reconstructions for both these cases,respectively.It can immediately be seen that the performance of this algorithm is far superior to the pre-vious algorithm.Good reconstructions are obtained at both noise levels.The algorithm was applied to many other images for which Gaussian PSF’s were used,and it was found that as long as the blurring of the PSF was not too severe then reasonable reconstructions could gener-ally be obtained,in some cases with noise levels as high as15%.3.SEMIBLIND DECONVOLUTIONAs mentioned in Section1,further a priori information could be incorporated by assuming knowledge of the form of the PSF.In a real situation it may be known that a telescope suffers from spherical aberration,but be-cause of time-varying factors such as the changing gravi-tational field that exists around a telescope in orbit the extent of this aberration may not be known.This situ-ation would reduce the number of unknown variables in the deconvolution from perhaps thousands of pixel values to one or two unknown constants.We have termed this approach semiblind deconvolution.A.Weiner Semiblind AlgorithmThis algorithm used the blind deconvolution with a Weiner filter as its basis.The only part of the algo-rithm altered was the image-plane constraints on the PSF.In the blind algorithm the constraint was just nonnegativity.This constraint was replaced by a least-squares-fitting procedure.Initially convolutions were created with Gaussians,so Gaussians of varying widths were compared with the evaluated PSF.The Gauss-ian giving the least error in fitting was then chosen as the PSF,and the next object guess was evaluated with this PSF.To illustrate how well this algorithm performed in the absence of noise,Fig.5shows the reconstructions of the object and the PSF at every iteration.In this particular case the images are all1283128pixels.This algorithm converged within three iterations and produced a perfect reconstruction of the satellite object.When we tried to(a)(b)(c)Fig.4.Blind deconvolution by the Richardson–Lucy algorithm.(a)Convolutions with1.5%(left)and10.0%(right)noise.(b) Reconstructions of the object(left)and the PSF(right)at the 1.5%noise level.(c)Reconstructions of the object(left)and the PSF(right)at the10.0%noise level.Fish et al.Vol.12,No.1/January1995/J.Opt.Soc.Am.A61(a)(b)(c)(d)Fig.5.Semiblind deconvolution by a Weiner filter-based algorithm.(a)True object(left),random starting guess of the object(center), and noiseless convolution(right).(b)Object(left)and PSF(right)from the first iteration.(c)Object(left)and PSF(right)from the second iteration.(d)Object(left)and PSF(right)from the third iteration.reconstruct with noisy images,however,the algorithm always converged on the delta-function solution,i.e.,a Gaussian of smallest possible width was evaluated as the PSF.Even with noise values less than0.1%the algorithm performed poorly.We therefore tried using the Richardson–Lucy algorithm.B.Semiblind Deconvolution by theRichardson–Lucy AlgorithmThe semiblind form of the algorithm took as its basis the blind algorithm.A number of blind iterations were performed,and then a least-squares fit on the function evaluated as the PSF was found.A PSF was then created with the fitting parameters,and then another series of blind iterations was performed,with this PSF being used as the starting point.This procedure was then repeated for a specified number of iterations.Ini-tially,simple one-variable PSF forms were chosen,i.e., Gaussians of unknown width.In some cases the results for this algorithm showed remarkable noise tolerance.In Fig.6results are shown for semiblind deconvolution on a series of point sources.62J.Opt.Soc.Am.A/Vol.12,No.1/January1995Fish et al.(a)(b)Fig.6.Semiblind deconvolution by the Richardson–Lucy-based algorithm.(a)Object(left)and convolution(right)with20.0% noise.(b)Reconstruction of the object(left)and the fitted Gauss-ian PSF(right).(a)(b)(c)parison of Richardson–Lucy semiblind deconvolu-tion with standard deconvolution algorithms.(a)Reconstruc-tion by semiblind deconvolution with a0.1-pixel step width.(b) Reconstruction by Fourier regularization.(c)Reconstruction by the Richardson–Lucy algorithm.The image contained approximately20.0%noise.The reconstruction shown is good,considering the noise level.The algorithm was also tried on the noisy image of the cross used earlier for the pure blind deconvolution re-search.Although the PSF was fitted in each iteration with a Gaussian of the correct size,the results were not good;in fact,the pure blind deconvolution results were better.Therefore it was decided that a Gaussian fitting process should be performed after the blind deconvolu-tion and then a specified number of Richardson–Lucy it-erations performed with the guessed Gaussian.The step width in Gaussian fitting was obviously important:with the step width of1pixel for the Gaussian radius at the 1͞e height,the correct PSF width of3pixels was guessed.(a)(b)Fig.8.Many-variable semiblind deconvolution.(a)Object (left)and PSF(right).(b)Convolution with1.0%noise.(a)(b)Fig.9.Reconstructions of the image shown in Fig.8.(a) Richardson–Lucy deconvolution after1000iterations.(b) Semiblind deconvolution after15iterations:object(left)and PSF(right).Fish et al .Vol.12,No.1/January 1995/J.Opt.Soc.Am.A63(a)(b)Fig.10.Error graphs for the 1.0%noise image shown in Fig.8.(a)Fitting parameters A 2,C 1,C 2with iteration number.(b)Percentage error in the PSF with iteration number.At a step width of 0.1pixel the Gaussian width obtained was 3.2pixels.The results for both cases are similar and are shown in Fig.7(a)for the 0.1-pixel case.The results show that the slight error made in finding the width of the Gaussian PSF does not make the re-constructions significantly worse.This is probably due to the high level of noise on the image,which results in the loss of a large amount of information.To show the impressiveness of these results straightforward deconvo-lutions with a Weiner filter and the Richardson–Lucy al-gorithm are shown in Figs.7(b)and 7(c).It can be seen that the semiblind deconvolution results are comparable with the usual methods of deconvolution.To extend this research to cases in which it may be used in realistic situations,more than one fitting variable may be needed to describe the PSF accurately.To test this possibility,a simple PSF was created that had the functional formy ͑r ͒X k ∑A k r 2exp ͑1.0͒C k 21B k ∏exp µ2r 2C k 2∂,(6)where r is the radius and the variables A k ,B k ,C k were given the values A 10.0,A 20.1,B 11.0,B 20.0,C 11.0,C 25.0.Then the variables A 2,C 1,C 2were allowed to change their values,so that the PSF was a Gaussian plus a Gaussian times its radius squared.Incorrect values for these variables were introduced into the program,and a PSF was created.Then,as before,a blind deconvolu-tion process evaluated a new object and a new PSF.A PSF with the functional form given above and with free variables A 2,C 1,C 2was fitted to the evaluated PSF by a Levenberg–Marquardt 9nonlinear least-squares-fitting routine.This routine returned new values for A 2,C 1,C 2,and the process was repeated for a specified number of iterations.The simulated object and the PSF used to illustrate this algorithm are shown in Fig.8(a),and a 1.0%noise convo-lution is shown in Fig.8(b)(the object used was the cross shown above).To compare the results of this semiblind deconvolution algorithm a Richardson–Lucy deconvolu-tion was performed with 1000iterations with the known PSF.The result of this process is shown in Fig.9(a)and can be compared with the results of 15iterations of the semiblind deconvolution algorithm shown in Fig.9(b).The results compare well.In Fig.10(a)the variation of the fitting parameters A 2,C 1,C 2with iteration number are shown.The start-ing values introduced into the program were A 20.5,C 13.0,C 27.0,giving a 74.0%error in the PSF.It (a)(b)(c)Fig.11.Reconstructions of an image with 4.0%noise.(a)4.0%noise image.(b)Richardson–Lucy deconvolution after 1000iterations.(c)Semiblind deconvolution after 15iterations:ob-ject (left)and PSF (right).64J.Opt.Soc.Am.A /Vol.12,No.1/January 1995Fish et al .can be seen that at this noise level the algorithm is con-verging on the correct values.This convergence is high-lighted by Fig.10(b),which shows the percentage error in the PSF with iteration number.This result is slightly false because the true PSF will not be known in a real situation,but the figure shows the convergent properties of the algorithm,which do not occur in cases such as the Ayers–Dainty,the blind Weiner,and the blind Richardson–Lucy algorithms.In the case of the blind Richardson–Lucy algorithm,the image shown in Fig.8(b)was used for comparison with the results of the semi-blind algorithm.It was found that the algorithm did not converge to the correct values for the fitting parameters,and in fact the algorithm eventually diverged.The final values for the fitting parameters from the semiblind al-gorithm were A 20.102,C 11.06,C 25.03,with an overall error in the PSF evaluation of 1.09%.At 2.0%,3.0%,and 4.0%noise levels similar results were obtained,and convergence was seen at the correct values of the fitting variables.The results of the 4.0%noise image are shown in Fig.11.This figure shows the Richardson–Lucy deconvolution after 1000iterationsand(a)(b)Fig.12.Error graphs for the 4.0%noise image.(a)Fitting parameters A 2,C 1,C 2with iteration number.(b)Percentage error in the PSF with iterationnumber.(a)(b)Fig.13.Error graphs for a 6.0%noise image.(a)Fitting pa-rameters A 2,C 1,C 2with iteration number.(b)Percentage er-ror in the PSF with iteration number.the semiblind deconvolution after 15iterations.Again the results compare quite well.Figure 12shows the variation in the fitting parameters and the percentage error in the PSF with iteration number.Again conver-gence is evident.When the same image with 6.0%noise was tried,the results were not so good.Figure 13shows the variation of fitting parameter and the percentage er-ror in the PSF,and it can be seen that convergence is reached after eight iterations and that the algorithm then starts to diverge.It therefore appears that the algorithm has a certain noise tolerance.4.CONCLUSIONS A blind deconvolution algorithm has been presented here that is based on the Richardson–Lucy algorithm.The algorithm presented is similar to that presented by Holmes,8but the implementation given here seems to have a more stable performance on the images chosen.The noise tolerance of the present algorithm is also far better than that of algorithms such as the Ayers–Dainty 1and the Weiner filter algorithms,used for comparison purposes in this paper.Fish et al.Vol.12,No.1/January1995/J.Opt.Soc.Am.A65In many real situations it may be the case that some knowledge of the PSF can be obtained.Therefore func-tional forms for the PSF’s were chosen with a number of unknown variables.It was found that accurate decon-volutions of a quality near that of a deconvolution with full knowledge of the PSF can be made.It is hoped that this research can be extended to real images with PSF’s containing unknown amounts of aberration,with the al-gorithm evaluating both the aberration coefficients and the object.ACKNOWLEDGMENTSThe authors are grateful to the U.S.Army Research Office for supporting this research under a project en-titled“Diffraction limited imaging using aberrated optics,”grant DAAL03-92-G-0142.REFERENCES1.G.R.Ayers and J.C.Dainty,“Iterative blind deconvolutionmethod and its applications,”Opt.Lett.13,547–549(1988).2.J.R.Feinup,“Phase retrieval algorithms:a comparison,”Appl.Opt.21,2758–2769(1982).3. B.L.K.Davey,ne,and R.H.T.Bates,“Blind decon-volution of noisy complex-valued image,”mun.69, 353–356(1989).4.W.H.Richardson,“Bayesian-based iterative method of imagerestoration,”J.Opt.Soc.Am.62,55–59(1972).5.L.B.Lucy,“An iterative technique for the rectification ofobserved distributions,”Astron.J.79,745–754(1974).6.L.A.Shepp and Y.Vardi,“Maximum likelihood reconstruc-tions for emission tomography,”IEEE Trans.Med.Imaging MI-1,113–122(1982).7. A.P.Dempster,ird,and D.B.Rubin,“Maximumlikelihood from incomplete data via the EM algorithm,”J.R.Stat.Soc.39,1–38(1977).8.T.J.Holmes,“Blind deconvolution of quantum-limited inco-herent imagery:maximum likelihood approach,”J.Opt.Soc.Am.A9,1052–1061(1992).9.W.H.Press, B.P.Flannery,J. A.Teukolsky,and W.T.Vetterling,Numerical Recipes:the Art of Scientific Comput-ing(Cambridge U.Press,Cambridge,1988).。
新高考一卷英语试题
2022年普通高等学校招生全国统一考试英语本试卷共10页，满分120分。
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每段对话仅读一遍。
1. What will the speakers do next?A. Check the map.B. Leave the restaurant.C. Park the car.2. Where are the speakers?A. At a bus stop.B. At home.C. At the airport.3. What did the speakers do last week?A. They had a celebration dinner.B. They went to see a newborn baby.C. They sent a mail to their neighbors.4. Why does the man make the phone call?A. To cancel a weekend trip.B. To make an appointment.C. To get some information.5. What does the man probably want to do?A. Do some exercise.B. Get an extra key.C. Order room service.第二节(共15小题；每小题1.5分，满分22.5分)听下面5段对话或独白。
法律英语学习-美国证据规则
法律英语学习| 美国证据规则美国的证据规则（或证据法）是关于证据的可采性(admissibility)、相关性(relevancy)、价值量(weight)和充分性(sufficiency)以及证明责任(Burden of Proof)等问题的法律原则和规则的总称。
证据的可采性处于核心的地位。
确定一个证据是否可以采用，主要应考察其实质性(materiality)、证明性(probativeness)和有效性(competency)。
而实质性和证明性合在一起即构成了相关性。
由于美国律师们在就对方证据提出反对时经常使用无相关性（irrelevant）、无实质性(immaterial)、无有效性（incompetent）这三个概念，所以证据的可采性规则也被概况为“三无”规则（”three I’s”）。
按照美国的传统法律，证据有两种基本类型(types of evidence)和三种基本形式(forms of evidence)。
两种基本类型包括直接证据(direct evidence)和间接证据(indirect evidence)或旁证(circumstantial evidence)。
三种基本形式包括言词证据(testimonial evidence)、实物证据(tangible evidence)和司法认知(judicial notice)。
其中，言词证据(testimonial evidence)是指为证人公开在法庭上所作的宣誓证词(sworn statements)。
广义而言，这类证据包括证人在宣誓后所作的口头和书面陈述，以及警察在审讯期间从证人、受害者或嫌疑犯取得的证词。
实物证据(tangible evidence)是指案件中的“展示物品”(physical exhibit)，它包括实在证据(real evidence)和示意证据(demonstrative evidence)。
前者指案件中“实实在在的东西”，如杀人用的枪、伪造的支票等；后者只能表明案件中某些情况的视听材料，如现场模型、图示等。
翻译资格考试技巧之消除因缺乏背景知识而误译
翻译资格考试技巧之消除因缺乏背景知识而误译
翻译资格考试技巧之消除因缺乏背景知识而误译
译者如不了解所译内容的背景，也易造成望文生义。
1. Anyone who has tugged heavy hand baggage down endless airport corridors, or waited for a deluged flight in a sterile lounge will bow how user unfriendly many airports are in design terms .
[误译]任何人只要他曾拖着沉重的随身行李，走过无止境的.机场走廊，或者曾在枯燥乏味的休息室里等候延误的班机，都会体会到许多机场在设计上对旅客多么不方便。
[分析]此处endless 误译为“无止境的”，实际上作“环状的”解（circular,with the ends joined ）,一般大型国际机场，从候机室通向各跑道的走廊呈环状，两头是相联接的。
[正译] ……，走过环形的机场走廊，……
2. I am/ we are carrying currency or monetary instruments over $ 10000 U.S. or foreign equivalent.
[误译]我（我们）携带有货币或价值超过10000美元的仪器或相当于10000美元的外币的仪器。
[分析]原译将instruments 作“仪器”解，显然是缺乏背景知识和脱离上下文所造成的失误。
此处系指“证券，票据”；monetary instruments 应译“金融证券”。
[正译]我（我们）携带超过10000美元或等值外币现金或金融证券。
2022年考研考博-考博英语-首都师范大学考试全真模拟易错、难点剖析AB卷(带答案)试题号：99
2022年考研考博-考博英语-首都师范大学考试全真模拟易错、难点剖析AB卷（带答案）一.综合题(共15题)1.单选题They bought the land with an eye （）building a school for children in the village.问题1选项A.toB.ofC.atD.with【答案】A【解析】考查固定搭配。
固定搭配with an eye to “着眼于，考虑到”。
句意：他们考虑为这个村子的小孩修建一所学校而买了这块地。
答案A2.单选题His inability to learn foreign language was an （）to his career.问题1选项A.shortageB.disturbanceC.occurrenceD.obstacle【答案】D【解析】考查名词辨析。
shortage “短缺”；disturbance“打扰”；occurrence “发生，出现”；obstacle “障碍”。
句意：他没有学习外语的能力，这成为他职业生涯的一个障碍。
根据上下文句意可知D项符合题意，答案D3.单选题These varied racial groups have learned to live together in peace and（），setting an example well worth following.问题1选项A.harmonyB.graceC.rhythmD.relief【答案】A【解析】考查固定搭配。
harmony和睦，融洽； grace 优雅；rhythm 节奏，韵律；relief救济，减轻；peace and harmony和谐和平，是固定搭配。
句意：这些不同的种族群体已学会和平共处地生活在一起，树立了值得学习的榜样。
答案A4.单选题Only a selected number of landladies in the neighborhood have been allowed by the university to take in（）.问题1选项A.lodgersB.residentsC.settlersD.inhabitants【答案】A【解析】考查名词辨析。
英语二盲选技巧
Blind Selection Techniques in English as a Second LanguageIntroduction:Learning a new language can be a challenging journey, especially when it comes to developing listening and speaking skills. One effective strategy that language learners can employ is blind selection techniques. These techniques involve utilizing various activities and resources without any prior knowledge of the content, forcing learners to rely solely on their listening and comprehension skills. In the context of English as a Second Language (ESL), blind selection techniques can help learners improve their proficiency and gain confidence in understanding and responding to everyday conversations.Benefits of Blind Selection Techniques:1.Enhancing Listening Skills:Blind selection techniques force learners to focus on auditory input and decipher meaning without relying on visual cues. This practice strengthens their listening skills and helps them develop the ability to understand spoken English in a variety of accents and contexts.2.Improving Speaking Skills:Through blind selection techniques, learners are exposed to a wide range of speech patterns, vocabulary, and expressions. This exposure helps them internalize these patterns, enabling them to reproduce them accurately when speaking. Additionally, by engaging in interactive activities and games, learners can practice formulating responses and contribute to conversations more confidently.Blind Selection Activities and Resources:1.Dialogue Listening:Provide learners with a collection of dialogues containing everyday scenarios such as ordering food at a restaurant, making a phone call, or asking for directions. Without prior knowledge of the content, learners randomly select a dialogue and listen to it. Afterward, they can practice summarizing the dialogue, answering comprehension questions, or role-playing the conversation.2.Podcast Roulette:Have learners randomly select a podcast episode without knowing the topic or guests. Bylistening to the podcast, they can practice extracting main ideas, understanding the context, and expanding their vocabulary through exposure to new words and expressions. This activity encourages independent learning and exposes learners to different voices and opinions.3.Song Interpretation:Select a range of songs from various genres and let learners blindly choose a song to listen to. After listening, they can analyze and interpret the lyrics, focusing on vocabulary, idiomatic expressions, and specific cultural references. This activity helps learners develop a deeper understanding of English culture while improving their listening comprehension skills.4.News Surprise:Provide learners with a collection of news articles. Without knowing the headlines or topics, learners select an article to read aloud. Afterward, they can engage in discussions about the article's content, express opinions, and summarize key points. This activity encourages critical thinking, improves reading comprehension, and enhances the ability to express ideas fluently.Conclusion:Blind selection techniques can be powerful tools in learning ESL, as they allow learners to develop their listening and speaking skills through authentic and unpredictable content. By engaging in a variety of blind selection activities and utilizing a range of resources, learners can improve their proficiency, gain confidence in understanding different accents, and actively participate in conversations. Incorporating blind selection techniques into English language learning fosters independence, creativity, and adaptability - all essential qualities for successful language acquisition.。
临床试验岗位招聘笔试题与参考答案(某大型集团公司)
招聘临床试验岗位笔试题与参考答案(某大型集团公司)(答案在后面)一、单项选择题（本大题有10小题，每小题2分，共20分）1、临床试验中，以下哪个阶段主要关注药物的安全性和耐受性？A、I期临床试验B、II期临床试验C、III期临床试验D、IV期临床试验2、在临床试验中，以下哪个术语表示研究对象的随机分配？A、随机化B、盲法C、安慰剂D、对照组3、某大型集团公司正在进行一项新药的临床试验，根据《药物临床试验质量管理规范》（GCP），以下关于临床试验注册的描述，哪项是错误的？A、临床试验应在开始前进行注册，并确保信息的真实、准确、完整B、临床试验注册信息应在临床试验结束后6个月内更新C、临床试验注册信息应向所有潜在受试者公开D、临床试验注册信息应在中国临床试验注册中心（ChiCTR）进行注册4、临床试验中，以下哪项措施不属于伦理审查委员会（IRB）的职责范围？A、审查临床试验方案的设计B、评估受试者的知情同意情况C、监督临床试验过程中的数据安全D、批准临床试验的启动5、临床试验中，以下哪项不是临床试验对象的入选标准？（）A. 年龄在18至70岁之间B. 具有明确的疾病诊断C. 患者签署知情同意书D. 近期接受过其他药物治疗6、在临床试验中，以下哪项不是数据管理的主要任务？（）A. 收集、整理和存储试验数据B. 质量控制和数据审核C. 进行统计分析D. 监督临床试验的伦理审查7、临床试验中，以下哪个文件不属于临床试验方案的重要组成部分？A. 患者知情同意书B. 研究药物的安全信息C. 研究者的职责描述D. 试验药物的剂量和给药方案8、在临床试验中，以下哪种行为违反了研究者的伦理责任？A. 确保患者充分了解试验目的和风险B. 患者要求退出试验时，研究者同意并协助其退出C. 在患者不知情的情况下收集个人信息D. 及时向伦理委员会报告不良事件9、临床试验过程中，以下哪项不是研究者应遵守的伦理准则？A. 研究者应确保受试者充分理解研究目的、方法和风险B. 研究者应保护受试者的隐私和个人信息C. 研究者可以在未告知受试者的情况下，修改研究方案D. 研究者应保证受试者获得适当的医疗照顾二、多项选择题（本大题有10小题，每小题4分，共40分）1、以下哪些是临床试验中必须遵循的原则？（）A、保护受试者的权益和安全B、确保试验数据的真实性和可靠性C、遵守伦理准则D、追求经济效益最大化E、尊重受试者的知情同意权2、以下哪些是临床试验设计中可能使用的随机化方法？（）A、简单随机化B、分层随机化C、区组随机化D、最小化方法E、匹配随机化3、临床试验岗位中，以下哪些是临床试验方案设计阶段需要考虑的重要因素？A. 研究目的和研究问题B. 受试者选择标准C. 药物或治疗方法的剂量D. 数据收集和分析方法E. 研究伦理问题4、以下哪些是临床试验中常见的临床试验类型？A. 随机对照试验（RCT）B. 开放标签试验C. 观察性研究D. 前瞻性队列研究E. 回顾性研究5、以下哪些是临床试验中常见的伦理审查要求？（）A. 确保受试者知情同意B. 设立数据监查委员会C. 进行受试者隐私保护D. 确保临床试验报告的透明度E. 遵守国际临床试验标准6、在临床试验设计中，以下哪些因素可能影响样本量的大小？（）A. 预期治疗效果B. 估计的疗效差异C. 病例数分布D. 统计检验的显著性水平E. 受试者的脱落率7、在设计临床试验时，以下哪些因素需要考虑以确保试验的有效性和伦理道德？A. 确定主要终点和次要终点B. 选择合适的对照组类型C. 确保有足够的样本量来检测治疗效果D. 只招募健康的受试者以减少变量E. 获得受试者的知情同意F. 在试验开始后随意修改主要终点以适应数据8、下列关于盲法试验的说法，哪些是正确的？A. 盲法试验有助于减少偏倚B. 单盲试验意味着只有研究者知道受试者分配情况C. 双盲试验中，受试者和研究者都不知道分组情况D. 开放标签试验比双盲试验更可靠E. 三盲试验指的是受试者、研究者以及数据分析人员都不知晓分组情况9、关于临床试验的伦理审查，以下哪些说法是正确的？A. 临床试验的伦理审查应确保受试者的权益和福祉B. 伦理审查委员会应由非利益相关者组成C. 伦理审查过程应在临床试验开始前完成D. 伦理审查结果对临床试验的开展有约束力E. 伦理审查不需要在临床试验过程中持续进行三、判断题（本大题有10小题，每小题2分，共20分）1、在临床试验中，安慰剂的作用是为了测试药物的有效性，它是一种具有治疗效果的药物。
【AAAI2021】缓解语言模型政治偏见
【AAAI2021】缓解语言模型政治偏见
当前的大规模语言模型可能由于其训练数据而产生政治偏见，当将它们部署在现实环境中时可能会导致严重的问题。
在本文中，我们提出了用于衡量GPT-2生成中的政治偏见的指标，并提出了一种强化学习（RL）框架，用于缓解生成的文本中的政治偏见。
通过使用来自词嵌入或分类器的奖励，我们的RL框架无需访问训练数据或要求对模型进行重新训练即可指导去偏见生成。
在对政治偏见敏感的三个属性（性别、位置和主题）的实证实验中，我们的方法根据我们的指标和人工评估很好地减少了偏见，同时保持了可读性和语义一致性。
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选择盲的国外研究综述
选择盲的国外研究综述摘要】选择盲是指个体不能觉察他们的偏好与决策结果之间的不匹配，即人们不能发现真实偏好被操纵。
这一现象在行为经济学中普遍存在。
对选择盲的解释主要有记忆表征和选择偏好理论，而选择盲的影响因素则包括选项相似性、时间、情绪和虚假反馈方式等。
选择盲是一个稳健的、可重复的、戏剧化的过程，在选择偏好中普遍存在，对人们的偏好改变有着不可忽视的重要影响。
由于选择盲的普遍性与独特性，及其在决策中的重要作用，对选择盲的心理机制和影响因素的研究具有巨大的理论意义和应用价值，未来的研究应该对选择盲的心理机制与产生根源、影响因素等方面作进一步探讨。
【关键词】选择盲；记忆表征理论；选择偏好理论【中图分类号】R3 【文献标识码】A 【文章编号】1007-8231（2017）04-0001-03理性决策理论认为个体的偏好是确定的、不变的，决策者将根据自己的偏好进行选择。
然而，越来越多的研究表明，即使是最简单的选择任务，你也可能不知道自己真正的选择是什么。
不仅如此，你还可能为自己未曾做过的选择辩护。
选择盲目性（choice blindness）是证明个体选择偏好改变的证据，是行为经济学中一种极为普遍的现象（McLaughlin & Somerville，2013）。
选择盲是指个体不能觉察他们的偏好与决策结果之间的不匹配，Johansson，Hall，Sikstr?m和Olsson （2005）首次提出了选择盲的概念，并在实验室实验和现场实验中证实了这一现象的存在。
在经典实验室研究中，被试的任务是在成对呈现的女性面孔照片中选出更有吸引力的面孔（如图1）。
随后，实验人员将被试选择的那张照片呈现给他们，并让他们解释为什么觉得这张照片更有吸引力。
然而，在部分选择中，实验人员给予被试虚假反馈，即并未将被试最初选择的真实偏好照片呈现给他们，而是被试最开始未选择的非偏好照片，即虚假偏好图片。
在虚假反馈的选择中，尽管两张照片非常不同，但只有不到30％的被试发现呈现的照片不是自己所选择的。
理解临床试验随机化
我们以区组长度4为例：
1. 2.
3. 4.
一个区组内的4个研究对象可以有6种排列方式：1. AABB, 2. ABAB, 3. ABBA, 4. BAAB, 5. BABA, 6. BBAA 确定好所有的排列形式后，接下来需要将6个区组随机排列。我们可以用 各种方式（如SPSS、Excel、SAS等）产生一串随机数字，比如： 92591264823981721367278057575098834352688429029…… 因为只有6种排列方式，因此可以只选择1-6之间的数字， 25126423121362555343526422…… 按照上述随机数字排列区组。当然，也可以采用其它方法随机排列区 组。 至此，区组随机化就完成了，两组人数完全相等。
对照
对照药的选择 对照药物的选择分为阳性对照药(即有活性的药物)和阴 性对照药(即安慰剂)。新药为注册申请进行临床试验， 阳性对照药原则上应选同一药物家族中公认较好的品种。 新药上市后为了证实对某种疾病或某种病症具有优于其 他药物的优势，可选择特定的适应症和选择对这种适应 症公认最有效的药物(可以和试验药不同结构类型、不同 家族但具有类似作用的药物)作为对照。 对照分组的英文术语为Arm。
分层随机化例子
随机化实施手段
信封法
随机方案编写好后，我们最常用的一种方法是使用信封进 行方案隐藏。以前使用的普通信封是“按顺序编码、不透 光、密封的信封”，即将每个分组方案装入一个不透光的 信封，信封外面写上编码，密封后交给研究者，待有研究 对象进入研究时，如果符合入选标准和排除标准，给病人 编号，再打开相应编号的信封，按信封内的分组方案进行 干预。每个研究对象所接受的治疗方案由生成的随机序列 决定。
随机号管理
厌恶性盲区（schlepblindness）-管理资料
厌恶性盲区（schlepblindness）-管理资料本文的作者 Paul Graham 是著名的Y Combinator投资公司的创始人之一，他写过很多关于LISP语言的书，目前正在研究开发Arc——一种LISP语言的方言，厌恶性盲区(schlep blindness)。
这世界上还有很多伟大的创业想法未被发掘出来，就在我们鼻子底下。
我们之所以不能发现它们，其中一个原因就是我把它称作schlep blindness的现象。
Schlep这个词最初来自一种犹太语，传入美国后被广泛的使用。
它的意思是单调乏味、令人生厌的工作。
没人喜欢这样的事，程序员们尤其不喜欢。
大多数创业的开发者都希望只需要写出一些好用的软件，放到某个服务器上，然后就可以看着财源滚滚而来——不要跟用户去交谈，不要跟其它公司打交道，不要处理别人有问题的代码。
也许有这种可能，但我们从未遇到过。
在Y Combinator创业投资公司，我们要做很多事情，其中一个事情就是告诉软件开发者们单调乏味的事是无可避免的。
是的，你不可只通过写代码来开创一个事业。
我还记得我是怎样明白这些的。
那是在1995年，我当时还在信誓旦旦的告诉自己只要写好代码就能开创一个公司。
但很快，从实践中我认识到，单调乏味的事情不仅不可避免，而且是公司业务的重要组成部分。
一个公司正是由它从事的那些单调乏味的业务定义出来的。
对待单调乏味的事，你应该采取跟你面对一个冰冷的游泳池时同样的方法：跳进去。
这并不是说你要主动寻找那些无聊的事去做，只是在当它出现在通往伟大事业的道路上时，你永远不要回避退缩。
对于讨厌单调乏味的事，这其中最危险的东西是，我们对此无意识。
我们的无意识甚至会让我们看不见那些牵涉到讨厌的单调乏味的事情的好创意。
这就是厌恶性盲区(schlep blindness)。
这种现象并不局限在创业问题上。
例如，大多数人都没有意识到应该应该保持一个像奥林匹克运动员那样的体型。
他们的无意识为他们做出了抉择，使他们从该做的事情上退缩。
设盲
“双盲双模拟”方法
药物临床试验时，若试验药与对照药的 剂型不一样，双盲法的实施可采取： 试验药＋与对照药剂型一样的安慰剂； 对照药＋与试验药剂型一样的安慰剂，
双盲单模拟
试验药+模拟空白/对照药 试验药/对照药+模拟空白 这是由于试验药/对照药同剂型用法用量不
一致所设盲的！
非盲试验
临床医师、研究人员和研究对象本人均知道分组 情况和接受什么治疗措施。
ห้องสมุดไป่ตู้ 单盲法
在实施一个试验方案时，对于受试者所 施加的处理因素（如选用药物），只有受 试者不知道。
双盲法
指受试者、研究者、监查员或数据分析者 均不知道治疗分配
优点：可以在很大程度上减少研究对象和研究人员主观因素 对研究结果的影响，可以获得准确的试验数据。
缺点：与单盲比较，设计复杂，需要制定严格管理制度和保 密措施；由于种种原因“双盲”可遭到破坏；不适用于危 重病例
缺点：非盲临床试验结论常不可靠 分配到对照组的患者因多种原因退出试验
设盲 （Blinding）
设盲（Blinding／Masking）
临床试验中使一方或多方不知道受试 者治疗分配的程序。
2020/2/3
2003研究生临床试验课
2
目的 意义 种类
目的：为了克服可能来自研究者或受试者的主观 因素所导致的偏倚。
意义：在于对提出的假说得到一个可靠的，无偏 倚的论证。
种类：单盲法 双盲法 双盲双摸拟 双盲单摸拟
语义差分法
语义差分法
语义差分法由概念和若干量尺构成。
这里的"概念"，既包括词、句、段和文章那样的语言符号，也包括像图形，色彩、声音等有感情意义的知觉符号。
这里的“量尺”，是用两个意义相反的形容词作为两极而构成的。
由美国心理学家奥斯古德于1957年提出的一种心理学研究方法，又称SD法。
奥斯古德等人认为，人类对概念或词汇具有颇为广泛的
共同的感情意义，而不因文化和言语的差别有多大的变化。
因此，对“智力高的和言语流利的研究对象”，直接询问一个概念的含义是有效的。
实验心理学复习题及答案
实验心理学单选题1.事后回溯设计是：前实验设计2.在加因素法反应时中，刺激与数目选择反应时的关系是：线性关系3.与古典心理物理学相比，信号检测论的优点是：能将辨别力与判断标准加以分离4.补笔测验用来研究：内隐记忆5.某小学90%以上的学生成绩在30分以下，这种现象是：地板效应6.注意研究中，所使用的双作业操作范式应遵循的原则：互补研究7.铁钦纳在1901年出版了一部著作，其中对感知觉的研究和心理物理法进行了大量论述，并致力于将实验心理学建立成一个新的学科体系，该著作是：《实验心理学》8.依据误差对阈限进行间接测量的方法是：平均差误法9.A、B、C反应时比较：B>C>A10.支持知觉直接性观点的是：“视崖”知觉实验11.动作稳定测量仪（九洞仪）可用于考察：情绪特征12.华生做的儿童恐惧实验中，采用的研究方法是：刺激---反应法13.通常用来测量个体距离判断水平的仪器是：深度知觉仪14.学习一系列单字后，把学过的与未学过的单字随机混在一起，并呈现给被试，要求被试辨认出学过的单字。
这种检查记忆效果的方法是：再认法15.在试验研究中，衡量自变量与因变量关系明确程度的是：内部效度16.在心理学实验研究中要选取多种指标来评价实验研究的成败，这些指标是：效度和信度17.信号检测论实验的方法有：评价法和有无法多选题1.有人想检验课堂教学中屏幕上呈现的四种类型的文字颜色与背景色搭配是否影响学生的学习效果，结果没有发现这四种搭配类型的学习效果之间存在差异。
可能的解释是A．文字颜色与背景色搭配本来就与学习效果无关B．所挑选的文字颜色与背景色的四种搭配类型之间差异过小C．对学习效果的测量不准确 D．授课教师的差异削弱了文字颜色与背景色搭配类型的影响效果2.记忆研究中，材料呈现方法有：全部呈现法、提示法、对偶联合法3.等响曲线反映的响度听觉特点有：频率是影响响度的一个因素、不同频率的声音有不同的响度增长率、声强提高，响度级也相应增加4.ROC曲线能反映出：信号的先定概率对报准率和虚报率的影响、信号检测标准变化时报准率与虚报率的变化、不同观察者的敏感性指标5.常用来对错误记忆进行定量研究的手段有：关联效应研究、词语掩蔽效应研究6.用于内隐记忆研究的加工分离程序，其基本假设包括：意识性提取的操作表现为全或无、意识性提取和自动提取是彼此独立的加工过程、自动提取在包含和排除测验中的性质是一样的、意识性提取在包含和排除测验中的性质是一样的7.测量记忆保持量的方法有：再认法、重构法、节省法、词干补笔法8.实验心理学早期杰出的三位心理学家：冯特、费希纳、艾宾浩斯9.下列方法属于长时记忆实验研究中的回忆法的是：对偶回忆法、自由回忆法、再认法概念解析1.实验性分离在实验中将两个对象或概念区分开来，从实验操作上说，就是如果操纵一个自变量能使两个对象发生不同的变化，那么久可以认为这两个对象在本质上是不同的，也就是出现了实验性分离。
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We have here studied the problem of blind deconvolution by direct examination of the input sequences. First, the identi ability problem of a noise-free FIR channel model was investigated. We know from the theory of system identi cation that the channel model is identi able if the input is known and persistently exciting of order n. Here, when the input is unknown but belongs to a nite alphabet we have the following: The channel model and the input sequence are simultaneously identi able if the input sequence is persistently exciting of order 2n ? 1. The complexity of the problem is determined by the time instant when the input sequence is per-
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Figure 2: Bit-error as a function of the measurement noise for the Viterbi algorithm when the channel model is known (dashed) and for the algorithm with 64 Kalman lters when the channel model is estimated without training sequence (solid). by Algorithm 1 with 64 parallel lters. The true measurement noise variance was used and the variance (Q) of the random walk was chosen to 0.01. The total bit error probability is estimated by comparing the estimated and the true input sequence and is shown by the dashed line in Figure 2. In Figure 3 a typical parameter convergence is shown. The convergence to the true parameter settings is quite fast and the tracking ability is very good.
1] S. Haykin. Digital Communication. John Wiley & Sons, Inc., 1988. 2] A.J. Viterbi. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans. Inform. Theory, 13:260{269, 1967. 3] S. Bellini. Blind equalization. Alta Frequenza, LVII:445{450, 1988. 4] A. Benveniste and M. Goursat. Blind equalizers. IEEE Transactions on Communications, 32:871{ 883, 1984. 5] Z. Ding. Application Aspects of Blind Adaptive Equalizers in QAM Data Communications. PhD thesis, Cornell University, 1990. 6] G.J. Foschini. Equalizing without altering or detecting data. AT&T Technical Journal, 64, 1985. 7] C.R. Johnson. Admissibility in blind adaptive channel equalization. IEEE Control Systems Magazine, 11:3{15, 1991. 8] L. Ljung and T Soderstrom. Theory and Practice of Recursive Identi cation. MIT Press, Cambridge MA, 1983. 9] F. Gustafsson and B. Wahlberg. Blind equalization by direct examination of the input sequences. Technical report, "Linkoping University, Dept. of EE", Linkoping, Sep 1991. 10] W.C.Y Lee. Mobile Communications Engineering. McGraw-Hill, 1982.
Theorem 2 Consider the model (4). The a posteriori probability of Uti is given by
thus eliminating the use of a separate decoder. It can also be used to incorporate a training sequence in a very natural way, by letting p(Uttrain) = 1. However, most often the inputs are considered as independent variables so the ML estimate is equivalent to the MAP estimate. The problem in implementing Theorem 2 directly, is the exponential increase in the number of input sequences, and thus Kalman lters. We will now give a recursively implementable approximation of the MAP estimator. It contains a xed number, K , of lters. In words, only sequences that have turned out to be likely are considered, the others are rejected. Algorithm 1 Suppose there are K candidate sequences Uti given at time t and that their relative a posteriori probabilities p(Uti jYt) have been computed. i 1. Compute p(Ut+1 jYt+1) by using Theorem 2 for the KM sequences obtained by considering all expansions of the sequences at time t. 2. Reject all but the K most probable sequences | i that is, those who have the largest p(Ut+1 jYt+1). In this section we will examine how Algorithm 1 performs in the case of a Rayleigh fading communication channel. Rayleigh fading is an important problem in mobile communication where the receiver is moving, which causes a time-varying channel characteristics. For and a thoroughly treatment of fading in mobile communication, see 10]. The input is assumed to belong to the nite alphabet f?1; +1; ?i; +ig, with equal probability for each symbol. An input sequence of length 100 was ltered through a simulated Rayleigh fading channel and Gaussian noise with variance was added. 100 di erent realizations of the input sequence, the noise sequence and the channel was used throughout all simulations. The magnitude of the noise was changed so the noise variance is 0.001, 0.002, 0.005, 0.01, 0.02, 0.05 and 0.1, respectively. To get a feeling for the problems involved in estimating the input sequence we begin with computing an upper bound of the performance of any algorithm. This is here done by cheating and assuming that the time-varying channel really is known to the receiver so the Viterbi algorithm applies, which is in this case optimal in the maximumlikelihood sense. The estimated bit error probability is shown in Figure 2, where the rst value, corresponding to the smallest , is zero and is not shown. The input sequence was then estimated