Eulerian subgraphs containing given edges
泊松融合原理和python代码
泊松融合原理和python代码【原创版】目录1.泊松融合原理概述2.Python 代码实现泊松融合原理3.泊松融合原理的应用正文1.泊松融合原理概述泊松融合原理是一种概率论中的经典理论,由法国数学家泊松提出。
泊松融合原理描述了一个事件在特定时间间隔内发生的概率与另一个事件在相同时间间隔内发生的次数之间的关系。
具体而言,泊松融合原理表明,一个事件在时间间隔Δt 内发生的次数服从泊松分布,即P(X=k)=e^(-λΔt) * (λΔt)^k / k!,其中λ是事件的平均发生率,X 是事件在时间间隔Δt 内发生的次数,k 是事件发生的次数。
2.Python 代码实现泊松融合原理为了验证泊松融合原理,我们可以使用 Python 编写代码模拟事件的发生过程。
以下是一个简单的 Python 代码示例:```pythonimport randomimport mathdef poisson_fusion(lambda_value, dt, num_trials):"""泊松融合原理模拟:param lambda_value: 事件的平均发生率:param dt: 时间间隔:param num_trials: 模拟次数:return: 事件在时间间隔内发生的次数"""count = 0for _ in range(num_trials):# 随机生成一个 0 到 dt 之间的时间间隔t = random.uniform(0, dt)# 计算在时间间隔内事件发生的次数k = int(lambda_value * t)# 计算泊松分布的概率poisson_prob = math.exp(-lambda_value * t) * (lambda_value * t) ** k / k# 根据泊松分布概率随机生成事件发生的次数count += random.choice([0, 1, 2, 3, 4],p=poisson_prob)return count# 示例lambda_value = 1 # 事件的平均发生率为 1dt = 1 # 时间间隔为 1um_trials = 1000 # 模拟次数为 1000# 模拟事件在时间间隔内发生的次数counts = [poisson_fusion(lambda_value, dt, num_trials) for _in range(num_trials)]# 计算平均值和方差mean = sum(counts) / num_trialsvariance = sum((count - mean) ** 2 for count in counts) / num_trialsprint("平均值:", mean)print("方差:", variance)```3.泊松融合原理的应用泊松融合原理在实际应用中有很多场景,例如统计学、保险、生物学等领域。
tpo32三篇托福阅读TOEFL原文译文题目答案译文背景知识
tpo32三篇托福阅读TOEFL原文译文题目答案译文背景知识阅读-1 (2)原文 (2)译文 (5)题目 (7)答案 (16)背景知识 (16)阅读-2 (25)原文 (25)译文 (28)题目 (31)答案 (40)背景知识 (41)阅读-3 (49)原文 (49)译文 (53)题目 (55)答案 (63)背景知识 (64)阅读-1原文Plant Colonization①Colonization is one way in which plants can change the ecology of a site.Colonization is a process with two components:invasion and survival.The rate at which a site is colonized by plants depends on both the rate at which individual organisms(seeds,spores,immature or mature individuals)arrive at the site and their success at becoming established and surviving.Success in colonization depends to a great extent on there being a site available for colonization–a safe site where disturbance by fire or by cutting down of trees has either removed competing species or reduced levels of competition and other negative interactions to a level at which the invading species can become established.For a given rate of invasion,colonization of a moist,fertile site is likely to be much more rapid than that of a dry, infertile site because of poor survival on the latter.A fertile,plowed field is rapidly invaded by a large variety of weeds,whereas a neighboring construction site from which the soil has been compacted or removed to expose a coarse,infertile parent material may remain virtually free of vegetation for many months or even years despite receiving the same input of seeds as the plowed field.②Both the rate of invasion and the rate of extinction vary greatly among different plant species.Pioneer species-those that occur only in the earliest stages of colonization-tend to have high rates of invasion because they produce very large numbers of reproductive propagules(seeds,spores,and so on)and because they have an efficient means of dispersal(normally,wind).③If colonizers produce short-lived reproductive propagules,they must produce very large numbers unless they have an efficient means of dispersal to suitable new habitats.Many plants depend on wind for dispersal and produce abundant quantities of small,relatively short-lived seeds to compensate for the fact that wind is not always a reliable means If reaching the appropriate type of habitat.Alternative strategies have evolved in some plants,such as those that produce fewer but larger seeds that are dispersed to suitable sites by birds or small mammals or those that produce long-lived seeds.Many forest plants seem to exhibit the latter adaptation,and viable seeds of pioneer species can be found in large numbers on some forest floors. For example,as many as1,125viable seeds per square meter were found in a100-year-old Douglas fir/western hemlock forest in coastal British Columbia.Nearly all the seeds that had germinated from this seed bank were from pioneer species.The rapid colonization of such sites after disturbance is undoubtedly in part a reflection of the largeseed band on the forest floor.④An adaptation that is well developed in colonizing species is a high degree of variation in germination(the beginning of a seed’s growth). Seeds of a given species exhibit a wide range of germination dates, increasing the probability that at least some of the seeds will germinate during a period of favorable environmental conditions.This is particularly important for species that colonize an environment where there is no existing vegetation to ameliorate climatic extremes and in which there may be great climatic diversity.⑤Species succession in plant communities,i.e.,the temporal sequence of appearance and disappearance of species is dependent on events occurring at different stages in the life history of a species. Variation in rates of invasion and growth plays an important role in determining patterns of succession,especially secondary succession. The species that are first to colonize a site are those that produce abundant seed that is distributed successfully to new sites.Such species generally grow rapidly and quickly dominate new sites, excluding other species with lower invasion and growth rates.The first community that occupies a disturbed area therefore may be composed of specie with the highest rate of invasion,whereas the community of the subsequent stage may consist of plants with similar survival ratesbut lower invasion rates.译文植物定居①定居是植物改变一个地点生态环境的一种方式。
The primal-dual method for approximation algorithms and its application to network design p
1
Introduction
Many problems of interest in combinatorial optimization are considered unlikely to have efficient algorithms; most of these problems are N P -hard, and unless P = N P they do not have polynomialtime algorithms to find an optimal solution. Researchers in combinatorial optimization have considered several approaches to deal with N P -hard problems. These approaches fall into one of two classes. The first class contains algorithms that find the optimal solution but do not run in polynomial time. Integer programming is an example of such an approach. Integer programmers attempt to develop branch-and-bound (or branch-and-cut, etc.) algorithms for dealing with particular problems such that the algorithm runs quickly enough in practice for instances of interest, although the algorithm is not guaranteed to be efficient for all instances. The second class contains algorithms that run in polynomial time but do not find the optimal solution for all instances. Heuristics and metaheuristics (such as simulated annealing or genetic algorithms) are one approach in this class. Typically researchers develop a heuristic for a problem and empirically demonstrate its effectiveness on instances of interest. In this survey, we will consider another approach in this second class called approximation algorithms. Approximation algorithms are polynomial-time heuristics for N P -hard problems whose solution values are provably close to optimum for all instances of the problem. More formally, an α-approximation algorithm for an optimization problem is an algorithm that runs in polynomial time and produces a solution whose value is within a factor of α of the value of an optimal solution. The parameter α is called the performance guarantee or the approximation ratio of the algorithm. We assume that the value of any feasible solution is nonnegative for the problems we consider; extensions of the notion of performance guarantee have been developed in other cases, but we will not discuss them here. This survey will follow the convention that α ≥ 1 for minimization problems and α ≤ 1 for maximization problems, so that a 2-approximation algorithm for a minimization problem produces a solution of value no more than twice the optimal value, 1 and a 2 -approximation algorithm for a maximization problem produces a solution of value at least
外文翻译---基于离散混沌映射的图像加密并行算法
3.转换
3.1.A-转换
在A转换中,A代表加,能被形式化的定义如下:
a+b=c(1)
加法被定义为按位与操作
转换A有三个基本性质:
(2.1)a+a=0
(2.2)a+b=b+a(2)
(2.3)(a+b)+c=a+(b+c)
在并行模式计算时,许多的PE可以同时读取或写入相同的内存区域(即临界区),
这往往会导致意想不到的执行程序。因此,有必要在关键区域使用一些并行技术管理。
2.2.并行图像的加密框架
为了满足上述要求,我们提出了一个并行图像加密的框架,这是一个四个步骤的过程:
步骤1:整个图像被划分成若干块。
步骤2:每个PE负责确定数量块。一个区域内的像素可以充分使用有效的混乱和扩散进行操作加密。
附件C:译文
基于离散混沌映射的图像加密并行算法
摘要:
最近,针对图像加密提出了多种基于混沌的算法。然而,它们都无法在并行计算环境中有效工作。在本文中,我们提出了一个并行图像加密的框架。基于此框架内,一个使用离散柯尔莫哥洛夫流映射的新算法被提出。它符合所有并行图像加密算法的要求。此外,它是安全、快速的。这些特性使得它是一个很好的基于并行计算平台上的图像加密选择。
这个框架可以非常有效的实现整个图像的扩散。但是,它是不适合在并行计算环境中运行。这是因为当前像素的处理无法启动直到前一个像素已加密。即使有多个处理元素(PE),这种计算仍然是在一个串行模式下工作。此限制了其应用平台,因为许多基于FPGA / CPLD或者数字电路的设备可以支持并行处理。随着并行计算技术的应用,加密速度可以大大加快。
The Algorithmic Aspects of Uncrowded Hypergraphs
Abstract
ห้องสมุดไป่ตู้
1 Introduction
A fundamental problem in Computer Science and Mathematics is to nd a large independent set in an arbitrary graph 6 , 14 , 20 . Recall, that for a graph G = V; E with vertex set V and edgeset E V 2 a subset I V of the vertex set is called independent, if the subgraph induced on I contains no edges e 2 E , i.e., E I 2 = ;. The maximum cardinality of an independent set I is called the independence number G of G . It is well-known, that nding in a graph G an independent set of size G is an NP-hard problem, even for graphs with bounded maximum degree. This suggests to look for approximation algorithms with guaranteed performance ratio which is the quotient of the sizes of the optimal and the found solution in the worst case. The results of Arora, Lund, Motwani, Sudan and Szegedy 10 on interactive proof systems show that, with respect to polynomial time algorithms, there is no constant performance ratio for the independent set problem for graphs on n vertices, indeed no ratio of n1=4 unless P = NP , cf. the work of Bellare, Goldreich and Sudan 13 . Recently, Hstad 26 showed that there is a no performance ratio of n1=2, unless NP = P , and no such ratio of n1, unless NP = coR. With respect to polynomial time algorithms, for triangle-free graphs with maximum degree , a performance ratio of O= ln was given in 23 , 27 , and moreover, if they contain no
超几何分布的英语
超几何分布的英语Here is an essay on the topic of the hypergeometric distribution, written in English with more than 1000 words. The title and any additional instructions have been omitted as requested.The hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement. In other words, it models the probability of obtaining a certain number of items with a desired characteristic from a finite population, given that the population is not replenished after each draw. This distribution is particularly useful in situations where the population size is relatively small, and the sampling is done without replacement, such as in quality control, survey sampling, and experimental design.The hypergeometric distribution is characterized by three parameters: the population size (N), the number of items with the desired characteristic in the population (K), and the number of items drawn from the population (n). The probability mass function (PMF) of the hypergeometric distribution is given by the formula:P(X = x) = (C(K, x) * C(N-K, n-x)) / C(N, n)where:- X is the random variable representing the number of items with the desired characteristic in the n draws- x is the observed value of X- C(a, b) is the binomial coefficient, which represents the number of ways to choose b items from a itemsThe hypergeometric distribution is related to the binomial distribution, but the key difference is that in the binomial distribution, the trials are independent and the probability of success remains constant, whereas in the hypergeometric distribution, the trials are not independent and the probability of success changes with each draw.One of the main applications of the hypergeometric distribution is in quality control. Suppose a manufacturer has produced a batch of N items, and K of them are defective. The manufacturer wants to inspect a sample of n items to determine the quality of the batch. The hypergeometric distribution can be used to calculate the probability of finding x defective items in the sample, which can help the manufacturer make decisions about the batch.Another application of the hypergeometric distribution is in survey sampling. Suppose a researcher wants to estimate the proportion ofa certain characteristic in a population, but the population size is relatively small. The researcher can draw a sample of n individuals from the population and use the hypergeometric distribution to calculate the probability of observing a certain number of individuals with the desired characteristic.The hypergeometric distribution also has applications in experimental design. For example, in a clinical trial, researchers may want to compare the effectiveness of a new drug to a placebo. The researchers can assign participants to the treatment or control group using a hypergeometric distribution, which ensures that the number of participants in each group is balanced.One of the key properties of the hypergeometric distribution is that it is a discrete distribution, meaning that the random variable X can only take on integer values. This property makes the distribution particularly useful in situations where the population size is finite and the sampling is done without replacement.Another important property of the hypergeometric distribution is that it is unimodal, meaning that the probability mass function has a single peak. The location of the peak depends on the values of the three parameters (N, K, and n), and the distribution can be left-skewed, right-skewed, or symmetric depending on the values of these parameters.The hypergeometric distribution also has several special cases. For example, when the population size N is large compared to the sample size n, the hypergeometric distribution approaches the binomial distribution. Similarly, when the number of items with the desired characteristic K is small compared to the population size N, the hypergeometric distribution approaches the Poisson distribution.In addition to its applications in quality control, survey sampling, and experimental design, the hypergeometric distribution has also been used in other areas, such as genetics, ecology, and finance. For example, in genetics, the hypergeometric distribution can be used to model the probability of observing a certain number of mutations in a gene sequence, while in ecology, it can be used to model the probability of observing a certain number of species in a sample of a habitat.Overall, the hypergeometric distribution is a powerful and versatile probability distribution that has numerous applications in a wide range of fields. Its ability to model the probability of success in a finite population without replacement makes it a valuable tool for researchers and practitioners in many different domains.。
哈工大博士学位论文模板
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基于柯西变异的海洋捕食算法
基于柯西变异的海洋捕食算法
基于柯西变异的海洋捕食算法是一种基于柯西变异算子的优化算法。
柯西变异是一种常用于模拟退火算法和粒子群优化算法中的变异操作,可以有效地增加算法的多样性和探索能力。
海洋捕食算法是一种模拟自然界中捕食行为的优化算法,其基本思想是将问题的解空间看作是一个海洋生态系统,包括被捕食者(候选解)和捕食者(优秀解)。
在算法的每一轮迭代中,被捕食者根据自身适应度采取某种策略来逃避捕食者的追击,而捕食者则根据被捕食者的位置进行捕食。
柯西变异的海洋捕食算法则将柯西变异操作引入海洋捕食算法中,以增加算法的多样性和探索能力。
具体而言,算法在每一轮迭代中,采用柯西变异操作来对被捕食者的位置进行变异,产生一些新的候选解,然后根据适应度函数来评估这些新的候选解的质量。
接着,通过选择一定数量的优质候选解作为新的被捕食者,同时保留部分优秀解作为捕食者,继续进行下一轮迭代。
通过引入柯西变异操作,海洋捕食算法能够在搜索过程中保持一定的多样性,并且对解空间中的局部最优解有一定的跳出能力。
这样可以在搜索过程中更好地保持解空间的探索能力,增加算法找到全局最优解的概率。
综上所述,基于柯西变异的海洋捕食算法是一种结合了柯西变异操作的海洋捕食算法,通过引入柯西变异操作来增加算法的多样性和探索能力,从而提高算法的全局搜索能力。
社科院最新题库-国际经济学
1.林德重叠需求论的假设条件和主要观点。
重叠需求理论是由瑞典经济学家林德提出,其理论核心是:两国之间贸易关系的密切程度是由两国的需求结构与收入水平决定的。
重叠需求理论有两个假设条件: 1、消费者行为假设:假设在一国之内,需求受消费者的收入水平决定。
不同收入阶层的消费者偏好不同,收入越高的消费者就越偏好奢侈品,收入越低的消费者就越偏好必需品,但如果消费者收入水平相同,则其偏好也相同。
2、两国需求重叠的假定:厂商根据消费者的收入水平与需求结构来决定其生产方向与内容,而生产的必要条件是对其产品有效需求的存在;如果两国的平均收入水平相近,则两国的需求结构也必定相似。
反之,如果两国的收入水平相差很大,则他们的需求结构也必存在显著的差异。
重叠需求理论的基本观点是,重叠需求是国际贸易产生的一个独立条件。
两国之间的需求结构若是越接近,则两国之间进行贸易的基础就越雄厚。
当两国的人均收入水平越接近时,则重叠需求的范围也就越大,两国重复需要的商品都有可能成为贸易品。
如果各国的国民收入不断提高,则由于收入水平的提高,新的重复需要的商品便不断地出现,贸易也相应地不断扩大,贸易中的新品种就会不断地出现。
所以,收入水平相似的国家,互相间的贸易关系就可能越密切;反之,如果收入水平相差悬殊,则两国之间重复需要的商品就可能很少,贸易的密切程度也就很小。
2.国际贸易比较优势理论比较优势可以表述为:在两国之间,劳动生产率的差距并不是在任何产品上都是相等的。
每个国家都应集中生产并出口具有比较优势的产品,进口具有比较劣势的产品(即“两优相权取其重,两劣相衡取其轻”),双方均可节省劳动力,获得专业化分工提高劳动生产率的好处。
假设条(1)假定贸易中只有两个国家和两种商品(X与Y商品),这一个假设的目的是为了用一个二维的平面图来说明这一理论。
(2)两国在生产中使用不同的技术。
技术的不同导致劳动生产率的不同进而导致成本的不同。
(3)模型只假定在物物交换条件下进行,没有考虑复杂的商品流通,而且假定1个单位的X产品和一个单位的Y产品等价(不过他们的生产成本不等)。
图论Subgraphs
40
2 Subgraphs
2.1 Subgraphs and Supergraphs
Edge and Vertex Deletion Given a graph G, there are two natural ways of deriving smaller graphs from G. If e is an edge of G, we may obtain a graph on m − 1 edges by deleting e from G but leaving the vertices and the remaining edges intact. The resulting graph is denoted by G \ e. Similarly, if v is a vertex of G, we may obtain a graph on n − 1 vertices by deleting from G the vertex v together with all the edges incident with v . The resulting graph is denoted by G − v . These operations of edge deletion and vertex deletion are illustrated in Figure 2.1.
e v
G
G\e
G−v
Fig. 2.1. Edge-deleted and vertex-deleted subgraphs of the Petersen graph
The graphs G \ e and G − v defined above are examples of subgraphs of G. We call G \ e an edge-deleted subgraph, and G − v a vertex-deleted subgraph. More generally, a graph F is called a subgraph of a graph G if V (F ) ⊆ V (G), E (F ) ⊆ E (G), and ψF is the restriction of ψG to E (F ). We then say that G contains F or that F is contained in G, and write G ⊇ F or F ⊆ G, respectively. Any subgraph F of G can be obtained by repeated applications of the basic operations of edge and vertex deletion; for instance, by first deleting the edges of G not in F and then deleting the vertices of G not in F . Note that the null graph is a subgraph of every graph. We remark in passing that in the special case where G is vertex-transitive, all vertex-deleted subgraphs of G are isomorphic. In this case, the notation G − v is used to denote any vertex-deleted subgraph. Likewise, we write G \ e to denote any edge-deleted subgraph of an edge-transitive graph G. A copy of a graph F in a graph G is a subgraph of G which is isomorphic to F . Such a subgraph is also referred to as an F -subgraph of G; for instance, a K3 -subgraph is a triangle in the graph. An embedding of a graph F in a graph G is an isomorphism between F and a subgraph of G. For each copy of F in G, there are aut(F ) embeddings of F in G. A supergraph of a graph G is a graph H which contains G as a subgraph, that is, H ⊇ G. Note that any graph is both a subgraph and a supergraph of itself.
专八英语阅读
英语专业八级考试TEM-8阅读理解练习册(1)(英语专业2012级)UNIT 1Text AEvery minute of every day, what ecologist生态学家James Carlton calls a global ―conveyor belt‖, redistributes ocean organisms生物.It’s planetwide biological disruption生物的破坏that scientists have barely begun to understand.Dr. Carlton —an oceanographer at Williams College in Williamstown,Mass.—explains that, at any given moment, ―There are several thousand marine species traveling… in the ballast water of ships.‖ These creatures move from coastal waters where they fit into the local web of life to places where some of them could tear that web apart. This is the larger dimension of the infamous无耻的,邪恶的invasion of fish-destroying, pipe-clogging zebra mussels有斑马纹的贻贝.Such voracious贪婪的invaders at least make their presence known. What concerns Carlton and his fellow marine ecologists is the lack of knowledge about the hundreds of alien invaders that quietly enter coastal waters around the world every day. Many of them probably just die out. Some benignly亲切地,仁慈地—or even beneficially — join the local scene. But some will make trouble.In one sense, this is an old story. Organisms have ridden ships for centuries. They have clung to hulls and come along with cargo. What’s new is the scale and speed of the migrations made possible by the massive volume of ship-ballast water压载水— taken in to provide ship stability—continuously moving around the world…Ships load up with ballast water and its inhabitants in coastal waters of one port and dump the ballast in another port that may be thousands of kilometers away. A single load can run to hundreds of gallons. Some larger ships take on as much as 40 million gallons. The creatures that come along tend to be in their larva free-floating stage. When discharged排出in alien waters they can mature into crabs, jellyfish水母, slugs鼻涕虫,蛞蝓, and many other forms.Since the problem involves coastal species, simply banning ballast dumps in coastal waters would, in theory, solve it. Coastal organisms in ballast water that is flushed into midocean would not survive. Such a ban has worked for North American Inland Waterway. But it would be hard to enforce it worldwide. Heating ballast water or straining it should also halt the species spread. But before any such worldwide regulations were imposed, scientists would need a clearer view of what is going on.The continuous shuffling洗牌of marine organisms has changed the biology of the sea on a global scale. It can have devastating effects as in the case of the American comb jellyfish that recently invaded the Black Sea. It has destroyed that sea’s anchovy鳀鱼fishery by eating anchovy eggs. It may soon spread to western and northern European waters.The maritime nations that created the biological ―conveyor belt‖ should support a coordinated international effort to find out what is going on and what should be done about it. (456 words)1.According to Dr. Carlton, ocean organism‟s are_______.A.being moved to new environmentsB.destroying the planetC.succumbing to the zebra musselD.developing alien characteristics2.Oceanographers海洋学家are concerned because_________.A.their knowledge of this phenomenon is limitedB.they believe the oceans are dyingC.they fear an invasion from outer-spaceD.they have identified thousands of alien webs3.According to marine ecologists, transplanted marinespecies____________.A.may upset the ecosystems of coastal watersB.are all compatible with one anotherC.can only survive in their home watersD.sometimes disrupt shipping lanes4.The identified cause of the problem is_______.A.the rapidity with which larvae matureB. a common practice of the shipping industryC. a centuries old speciesD.the world wide movement of ocean currents5.The article suggests that a solution to the problem__________.A.is unlikely to be identifiedB.must precede further researchC.is hypothetically假设地,假想地easyD.will limit global shippingText BNew …Endangered‟ List Targets Many US RiversIt is hard to think of a major natural resource or pollution issue in North America today that does not affect rivers.Farm chemical runoff残渣, industrial waste, urban storm sewers, sewage treatment, mining, logging, grazing放牧,military bases, residential and business development, hydropower水力发电,loss of wetlands. The list goes on.Legislation like the Clean Water Act and Wild and Scenic Rivers Act have provided some protection, but threats continue.The Environmental Protection Agency (EPA) reported yesterday that an assessment of 642,000 miles of rivers and streams showed 34 percent in less than good condition. In a major study of the Clean Water Act, the Natural Resources Defense Council last fall reported that poison runoff impairs损害more than 125,000 miles of rivers.More recently, the NRDC and Izaak Walton League warned that pollution and loss of wetlands—made worse by last year’s flooding—is degrading恶化the Mississippi River ecosystem.On Tuesday, the conservation group保护组织American Rivers issued its annual list of 10 ―endangered‖ and 20 ―threatened‖ rivers in 32 states, the District of Colombia, and Canada.At the top of the list is the Clarks Fork of the Yellowstone River, whereCanadian mining firms plan to build a 74-acre英亩reservoir水库,蓄水池as part of a gold mine less than three miles from Yellowstone National Park. The reservoir would hold the runoff from the sulfuric acid 硫酸used to extract gold from crushed rock.―In the event this tailings pond failed, the impact to th e greater Yellowstone ecosystem would be cataclysmic大变动的,灾难性的and the damage irreversible不可逆转的.‖ Sen. Max Baucus of Montana, chairman of the Environment and Public Works Committee, wrote to Noranda Minerals Inc., an owner of the ― New World Mine‖.Last fall, an EPA official expressed concern about the mine and its potential impact, especially the plastic-lined storage reservoir. ― I am unaware of any studies evaluating how a tailings pond尾矿池,残渣池could be maintained to ensure its structural integrity forev er,‖ said Stephen Hoffman, chief of the EPA’s Mining Waste Section. ―It is my opinion that underwater disposal of tailings at New World may present a potentially significant threat to human health and the environment.‖The results of an environmental-impact statement, now being drafted by the Forest Service and Montana Department of State Lands, could determine the mine’s future…In its recent proposal to reauthorize the Clean Water Act, the Clinton administration noted ―dramatically improved water quality since 1972,‖ when the act was passed. But it also reported that 30 percent of riverscontinue to be degraded, mainly by silt泥沙and nutrients from farm and urban runoff, combined sewer overflows, and municipal sewage城市污水. Bottom sediments沉积物are contaminated污染in more than 1,000 waterways, the administration reported in releasing its proposal in January. Between 60 and 80 percent of riparian corridors (riverbank lands) have been degraded.As with endangered species and their habitats in forests and deserts, the complexity of ecosystems is seen in rivers and the effects of development----beyond the obvious threats of industrial pollution, municipal waste, and in-stream diversions改道to slake消除the thirst of new communities in dry regions like the Southwes t…While there are many political hurdles障碍ahead, reauthorization of the Clean Water Act this year holds promise for US rivers. Rep. Norm Mineta of California, who chairs the House Committee overseeing the bill, calls it ―probably the most important env ironmental legislation this Congress will enact.‖ (553 words)6.According to the passage, the Clean Water Act______.A.has been ineffectiveB.will definitely be renewedC.has never been evaluatedD.was enacted some 30 years ago7.“Endangered” rivers are _________.A.catalogued annuallyB.less polluted than ―threatened rivers‖C.caused by floodingD.adjacent to large cities8.The “cataclysmic” event referred to in paragraph eight would be__________.A. fortuitous偶然的,意外的B. adventitious外加的,偶然的C. catastrophicD. precarious不稳定的,危险的9. The owners of the New World Mine appear to be______.A. ecologically aware of the impact of miningB. determined to construct a safe tailings pondC. indifferent to the concerns voiced by the EPAD. willing to relocate operations10. The passage conveys the impression that_______.A. Canadians are disinterested in natural resourcesB. private and public environmental groups aboundC. river banks are erodingD. the majority of US rivers are in poor conditionText CA classic series of experiments to determine the effects ofoverpopulation on communities of rats was reported in February of 1962 in an article in Scientific American. The experiments were conducted by a psychologist, John B. Calhoun and his associates. In each of these experiments, an equal number of male and female adult rats were placed in an enclosure and given an adequate supply of food, water, and other necessities. The rat populations were allowed to increase. Calhoun knew from experience approximately how many rats could live in the enclosures without experiencing stress due to overcrowding. He allowed the population to increase to approximately twice this number. Then he stabilized the population by removing offspring that were not dependent on their mothers. He and his associates then carefully observed and recorded behavior in these overpopulated communities. At the end of their experiments, Calhoun and his associates were able to conclude that overcrowding causes a breakdown in the normal social relationships among rats, a kind of social disease. The rats in the experiments did not follow the same patterns of behavior as rats would in a community without overcrowding.The females in the rat population were the most seriously affected by the high population density: They showed deviant异常的maternal behavior; they did not behave as mother rats normally do. In fact, many of the pups幼兽,幼崽, as rat babies are called, died as a result of poor maternal care. For example, mothers sometimes abandoned their pups,and, without their mothers' care, the pups died. Under normal conditions, a mother rat would not leave her pups alone to die. However, the experiments verified that in overpopulated communities, mother rats do not behave normally. Their behavior may be considered pathologically 病理上,病理学地diseased.The dominant males in the rat population were the least affected by overpopulation. Each of these strong males claimed an area of the enclosure as his own. Therefore, these individuals did not experience the overcrowding in the same way as the other rats did. The fact that the dominant males had adequate space in which to live may explain why they were not as seriously affected by overpopulation as the other rats. However, dominant males did behave pathologically at times. Their antisocial behavior consisted of attacks on weaker male,female, and immature rats. This deviant behavior showed that even though the dominant males had enough living space, they too were affected by the general overcrowding in the enclosure.Non-dominant males in the experimental rat communities also exhibited deviant social behavior. Some withdrew completely; they moved very little and ate and drank at times when the other rats were sleeping in order to avoid contact with them. Other non-dominant males were hyperactive; they were much more active than is normal, chasing other rats and fighting each other. This segment of the rat population, likeall the other parts, was affected by the overpopulation.The behavior of the non-dominant males and of the other components of the rat population has parallels in human behavior. People in densely populated areas exhibit deviant behavior similar to that of the rats in Calhoun's experiments. In large urban areas such as New York City, London, Mexican City, and Cairo, there are abandoned children. There are cruel, powerful individuals, both men and women. There are also people who withdraw and people who become hyperactive. The quantity of other forms of social pathology such as murder, rape, and robbery also frequently occur in densely populated human communities. Is the principal cause of these disorders overpopulation? Calhoun’s experiments suggest that it might be. In any case, social scientists and city planners have been influenced by the results of this series of experiments.11. Paragraph l is organized according to__________.A. reasonsB. descriptionC. examplesD. definition12.Calhoun stabilized the rat population_________.A. when it was double the number that could live in the enclosure without stressB. by removing young ratsC. at a constant number of adult rats in the enclosureD. all of the above are correct13.W hich of the following inferences CANNOT be made from theinformation inPara. 1?A. Calhoun's experiment is still considered important today.B. Overpopulation causes pathological behavior in rat populations.C. Stress does not occur in rat communities unless there is overcrowding.D. Calhoun had experimented with rats before.14. Which of the following behavior didn‟t happen in this experiment?A. All the male rats exhibited pathological behavior.B. Mother rats abandoned their pups.C. Female rats showed deviant maternal behavior.D. Mother rats left their rat babies alone.15. The main idea of the paragraph three is that __________.A. dominant males had adequate living spaceB. dominant males were not as seriously affected by overcrowding as the otherratsC. dominant males attacked weaker ratsD. the strongest males are always able to adapt to bad conditionsText DThe first mention of slavery in the statutes法令,法规of the English colonies of North America does not occur until after 1660—some forty years after the importation of the first Black people. Lest we think that existed in fact before it did in law, Oscar and Mary Handlin assure us, that the status of B lack people down to the 1660’s was that of servants. A critique批判of the Handlins’ interpretation of why legal slavery did not appear until the 1660’s suggests that assumptions about the relation between slavery and racial prejudice should be reexamined, and that explanation for the different treatment of Black slaves in North and South America should be expanded.The Handlins explain the appearance of legal slavery by arguing that, during the 1660’s, the position of white servants was improving relative to that of black servants. Thus, the Handlins contend, Black and White servants, heretofore treated alike, each attained a different status. There are, however, important objections to this argument. First, the Handlins cannot adequately demonstrate that t he White servant’s position was improving, during and after the 1660’s; several acts of the Maryland and Virginia legislatures indicate otherwise. Another flaw in the Handlins’ interpretation is their assumption that prior to the establishment of legal slavery there was no discrimination against Black people. It is true that before the 1660’s Black people were rarely called slaves. But this shouldnot overshadow evidence from the 1630’s on that points to racial discrimination without using the term slavery. Such discrimination sometimes stopped short of lifetime servitude or inherited status—the two attributes of true slavery—yet in other cases it included both. The Handlins’ argument excludes the real possibility that Black people in the English colonies were never treated as the equals of White people.The possibility has important ramifications后果,影响.If from the outset Black people were discriminated against, then legal slavery should be viewed as a reflection and an extension of racial prejudice rather than, as many historians including the Handlins have argued, the cause of prejudice. In addition, the existence of discrimination before the advent of legal slavery offers a further explanation for the harsher treatment of Black slaves in North than in South America. Freyre and Tannenbaum have rightly argued that the lack of certain traditions in North America—such as a Roman conception of slavery and a Roman Catholic emphasis on equality— explains why the treatment of Black slaves was more severe there than in the Spanish and Portuguese colonies of South America. But this cannot be the whole explanation since it is merely negative, based only on a lack of something. A more compelling令人信服的explanation is that the early and sometimes extreme racial discrimination in the English colonies helped determine the particular nature of the slavery that followed. (462 words)16. Which of the following is the most logical inference to be drawn from the passage about the effects of “several acts of the Maryland and Virginia legislatures” (Para.2) passed during and after the 1660‟s?A. The acts negatively affected the pre-1660’s position of Black as wellas of White servants.B. The acts had the effect of impairing rather than improving theposition of White servants relative to what it had been before the 1660’s.C. The acts had a different effect on the position of white servants thandid many of the acts passed during this time by the legislatures of other colonies.D. The acts, at the very least, caused the position of White servants toremain no better than it had been before the 1660’s.17. With which of the following statements regarding the status ofBlack people in the English colonies of North America before the 1660‟s would the author be LEAST likely to agree?A. Although black people were not legally considered to be slaves,they were often called slaves.B. Although subject to some discrimination, black people had a higherlegal status than they did after the 1660’s.C. Although sometimes subject to lifetime servitude, black peoplewere not legally considered to be slaves.D. Although often not treated the same as White people, black people,like many white people, possessed the legal status of servants.18. According to the passage, the Handlins have argued which of thefollowing about the relationship between racial prejudice and the institution of legal slavery in the English colonies of North America?A. Racial prejudice and the institution of slavery arose simultaneously.B. Racial prejudice most often the form of the imposition of inheritedstatus, one of the attributes of slavery.C. The source of racial prejudice was the institution of slavery.D. Because of the influence of the Roman Catholic Church, racialprejudice sometimes did not result in slavery.19. The passage suggests that the existence of a Roman conception ofslavery in Spanish and Portuguese colonies had the effect of _________.A. extending rather than causing racial prejudice in these coloniesB. hastening the legalization of slavery in these colonies.C. mitigating some of the conditions of slavery for black people in these coloniesD. delaying the introduction of slavery into the English colonies20. The author considers the explanation put forward by Freyre andTannenbaum for the treatment accorded B lack slaves in the English colonies of North America to be _____________.A. ambitious but misguidedB. valid有根据的but limitedC. popular but suspectD. anachronistic过时的,时代错误的and controversialUNIT 2Text AThe sea lay like an unbroken mirror all around the pine-girt, lonely shores of Orr’s Island. Tall, kingly spruce s wore their regal王室的crowns of cones high in air, sparkling with diamonds of clear exuded gum流出的树胶; vast old hemlocks铁杉of primeval原始的growth stood darkling in their forest shadows, their branches hung with long hoary moss久远的青苔;while feathery larches羽毛般的落叶松,turned to brilliant gold by autumn frosts, lighted up the darker shadows of the evergreens. It was one of those hazy朦胧的, calm, dissolving days of Indian summer, when everything is so quiet that the fainest kiss of the wave on the beach can be heard, and white clouds seem to faint into the blue of the sky, and soft swathing一长条bands of violet vapor make all earth look dreamy, and give to the sharp, clear-cut outlines of the northern landscape all those mysteries of light and shade which impart such tenderness to Italian scenery.The funeral was over,--- the tread鞋底的花纹/ 踏of many feet, bearing the heavy burden of two broken lives, had been to the lonely graveyard, and had come back again,--- each footstep lighter and more unconstrained不受拘束的as each one went his way from the great old tragedy of Death to the common cheerful of Life.The solemn black clock stood swaying with its eternal ―tick-tock, tick-tock,‖ in the kitchen of the brown house on Orr’s Island. There was there that sense of a stillness that can be felt,---such as settles down on a dwelling住处when any of its inmates have passed through its doors for the last time, to go whence they shall not return. The best room was shut up and darkened, with only so much light as could fall through a little heart-shaped hole in the window-shutter,---for except on solemn visits, or prayer-meetings or weddings, or funerals, that room formed no part of the daily family scenery.The kitchen was clean and ample, hearth灶台, and oven on one side, and rows of old-fashioned splint-bottomed chairs against the wall. A table scoured to snowy whiteness, and a little work-stand whereon lay the Bible, the Missionary Herald, and the Weekly Christian Mirror, before named, formed the principal furniture. One feature, however, must not be forgotten, ---a great sea-chest水手用的储物箱,which had been the companion of Zephaniah through all the countries of the earth. Old, and battered破旧的,磨损的, and unsightly难看的it looked, yet report said that there was good store within which men for the most part respect more than anything else; and, indeed it proved often when a deed of grace was to be done--- when a woman was suddenly made a widow in a coast gale大风,狂风, or a fishing-smack小渔船was run down in the fogs off the banks, leaving in some neighboring cottage a family of orphans,---in all such cases, the opening of this sea-chest was an event of good omen 预兆to the bereaved丧亲者;for Zephaniah had a large heart and a large hand, and was apt有…的倾向to take it out full of silver dollars when once it went in. So the ark of the covenant约柜could not have been looked on with more reverence崇敬than the neighbours usually showed to Captain Pennel’s sea-chest.1. The author describes Orr‟s Island in a(n)______way.A.emotionally appealing, imaginativeB.rational, logically preciseC.factually detailed, objectiveD.vague, uncertain2.According to the passage, the “best room”_____.A.has its many windows boarded upB.has had the furniture removedC.is used only on formal and ceremonious occasionsD.is the busiest room in the house3.From the description of the kitchen we can infer that thehouse belongs to people who_____.A.never have guestsB.like modern appliancesC.are probably religiousD.dislike housework4.The passage implies that_______.A.few people attended the funeralB.fishing is a secure vocationC.the island is densely populatedD.the house belonged to the deceased5.From the description of Zephaniah we can see thathe_________.A.was physically a very big manB.preferred the lonely life of a sailorC.always stayed at homeD.was frugal and saved a lotText BBasic to any understanding of Canada in the 20 years after the Second World War is the country' s impressive population growth. For every three Canadians in 1945, there were over five in 1966. In September 1966 Canada's population passed the 20 million mark. Most of this surging growth came from natural increase. The depression of the 1930s and the war had held back marriages, and the catching-up process began after 1945. The baby boom continued through the decade of the 1950s, producing a population increase of nearly fifteen percent in the five years from 1951 to 1956. This rate of increase had been exceeded only once before in Canada's history, in the decade before 1911 when the prairies were being settled. Undoubtedly, the good economic conditions of the 1950s supported a growth in the population, but the expansion also derived from a trend toward earlier marriages and an increase in the average size of families; In 1957 the Canadian birth rate stood at 28 per thousand, one of the highest in the world. After the peak year of 1957, thebirth rate in Canada began to decline. It continued falling until in 1966 it stood at the lowest level in 25 years. Partly this decline reflected the low level of births during the depression and the war, but it was also caused by changes in Canadian society. Young people were staying at school longer, more women were working; young married couples were buying automobiles or houses before starting families; rising living standards were cutting down the size of families. It appeared that Canada was once more falling in step with the trend toward smaller families that had occurred all through theWestern world since the time of the Industrial Revolution. Although the growth in Canada’s population had slowed down by 1966 (the cent), another increase in the first half of the 1960s was only nine percent), another large population wave was coming over the horizon. It would be composed of the children of the children who were born during the period of the high birth rate prior to 1957.6. What does the passage mainly discuss?A. Educational changes in Canadian society.B. Canada during the Second World War.C. Population trends in postwar Canada.D. Standards of living in Canada.7. According to the passage, when did Canada's baby boom begin?A. In the decade after 1911.B. After 1945.C. During the depression of the 1930s.D. In 1966.8. The author suggests that in Canada during the 1950s____________.A. the urban population decreased rapidlyB. fewer people marriedC. economic conditions were poorD. the birth rate was very high9. When was the birth rate in Canada at its lowest postwar level?A. 1966.B. 1957.C. 1956.D. 1951.10. The author mentions all of the following as causes of declines inpopulation growth after 1957 EXCEPT_________________.A. people being better educatedB. people getting married earlierC. better standards of livingD. couples buying houses11.I t can be inferred from the passage that before the IndustrialRevolution_______________.A. families were largerB. population statistics were unreliableC. the population grew steadilyD. economic conditions were badText CI was just a boy when my father brought me to Harlem for the first time, almost 50 years ago. We stayed at the hotel Theresa, a grand brick structure at 125th Street and Seventh avenue. Once, in the hotel restaurant, my father pointed out Joe Louis. He even got Mr. Brown, the hotel manager, to introduce me to him, a bit punchy强力的but still champ焦急as fast as I was concerned.Much has changed since then. Business and real estate are booming. Some say a new renaissance is under way. Others decry责难what they see as outside forces running roughshod肆意践踏over the old Harlem. New York meant Harlem to me, and as a young man I visited it whenever I could. But many of my old haunts are gone. The Theresa shut down in 1966. National chains that once ignored Harlem now anticipate yuppie money and want pieces of this prime Manhattan real estate. So here I am on a hot August afternoon, sitting in a Starbucks that two years ago opened a block away from the Theresa, snatching抓取,攫取at memories between sips of high-priced coffee. I am about to open up a piece of the old Harlem---the New York Amsterdam News---when a tourist。
euler ancestral sampling 解析 -回复
euler ancestral sampling 解析-回复Euler ancestral sampling 解析Euler ancestral sampling 是一种基于欧拉遗传算法的采样方法,可以用于从给定的目标分布中生成样本。
它基于马尔可夫链蒙特卡洛(MCMC)方法,在概率图模型中得到了广泛应用。
本文将逐步解析Euler ancestral sampling 的原理及应用,并探讨其优缺点。
1. 欧拉遗传算法欧拉遗传算法是一种基于遗传算法的优化方法,其灵感来源于生物学中的遗传进化。
该算法主要通过模拟生物个体遗传和变异过程来寻找最优解。
而Euler ancestral sampling 是将欧拉遗传算法与概率图模型相结合的一种技术。
2. 概率图模型概率图模型是一种用于描述随机变量之间依赖关系的图模型。
它将概率分布表示为一个图,其中节点代表随机变量,边表示变量之间的依赖关系。
常见的概率图模型有贝叶斯网络和马尔可夫随机场等。
利用概率图模型可以对复杂的概率分布进行建模,并进行各种推断和预测。
3. Euler ancestral sampling 的原理Euler ancestral sampling 是一种基于概率图模型的采样方法,在给定概率图模型的条件下,生成符合目标分布的样本。
它通过构建马尔可夫链蒙特卡洛采样算法,在模型中进行状态转移,最终生成样本。
具体而言,Euler ancestral sampling 的过程如下:- 初始化:随机选择一个初始状态,作为当前样本。
- 遗传变异:根据概率图模型中的条件概率,对当前样本进行变异,得到新的样本。
- 选择操作:根据变异后的样本与目标概率分布之间的距离评估,选择保留样本或丢弃样本。
- 迭代操作:通过遗传变异和选择操作,循环进行,直到满足采样需求的样本数量。
4. Euler ancestral sampling 的应用Euler ancestral sampling 在许多领域都得到了广泛的应用:- 受限玻尔兹曼机(RBM)的采样:RBM 是一种无向概率图模型,常用于降维、特征选择和生成模型。
数学家高斯(课堂PPT)
1795年高斯进入 HYPERLINK 哥廷根大学 。1796年,19岁的高斯得到了一个数 学史上极重要的结果,就是《正十七边形尺规作图之理论与方法》。1798年转入黑 尔姆施泰特大学,翌年因证明代数基本定理获博士学位。
1801年, HYPERLINK 高斯 又证明了形如"Fermat素数"边数的正多边形可以由 尺规作出。
1796年,约翰 卡尔 弗里德里希 高斯证明了可以尺规作正十七边形。1807年高斯成 为 HYPERLINK blank" 哥廷根 大学教授和哥廷根天文台台长。1818年—1826年 间, HYPERLINK
汉诺威 公国的大地测量工作由 HYPERLINK
高斯 主导。1840年高斯与韦伯一同画出世界上第一张地球磁场图。
数学家高斯(课堂PPT)
演讲人
约翰 卡尔 弗里德里希 高斯(Johann Carl Friedrich Gauß),男,1777年4月30日 出生于不伦瑞克,德国著名数学家、物理学家、天文学家、几何学家, HYPERLINK blank" 大地测量 学家,
毕业于Carolinum学院(现 HYPERLINK blank" 布伦瑞克工业大学 ),也 就是众人熟识的高斯,与欧拉并称数学史上两大巨星。
约翰 卡尔 弗里德里希 高斯(1777年4月30日—1855年2月23日),生 于不伦瑞克,卒于哥廷根,哥廷根学派的先驱之一。
约翰 卡尔 弗里德里希 高斯的成就遍布于数学的各个领域,在内蕴几何、数论、双 曲几何、微分几何、超几何级数、复分析以及椭圆分析等方面均有开创性贡献。他 十分注重数学的应用,并且在对天文学、 HYPERLINK " 大地测量学 和磁学的研究 中也偏重于用数学方法进行研究。
欧洲野生甘蓝的核质遗传多样性和群体遗传结构分析
( 业 部 油 料 作 物 生 物 学 重 点 开 放 实 验 室 , 国农 科 院 油 料 作 物 研 究 所 , 农 中 湖北 武 汉 40 6 ) 30 2
摘要: 了鳃欧洲野生甘蓝遗 传背景 , 为 以栽 培 甘 蓝 、 蓝 型 油 菜 和 白菜 型 油 菜 作 对 比 , 引 进 的 7个 生 态 地 理 甘 对
i cu i g 2 wi oea e n l d n l B. lr c a,3 B.n pu n n r p d a s a d o e B. a a. Nu la c e rDNA sa ay e sn p c f wa n l z d u i g6 s e i c SRAP p i — i rm e swh c e e ae 5 p l mo p i a d . Cl se n e ei tu t r n lsss o d t a c —g o r p ia r ih g n r td 7 oy r h c b n s u tra d g n t sr c u e a ay i h we h t e o c 7 e ga hcl g o so l oea e o p F, D a d G r l se e no 3 i d pe d n u c a s s E elit s ca s, rup fwi B. lr c a g u d r n we e c u t r d i t n e n e ts b ls e . fl n o G ub l s
群体共 8 野生甘蓝材料进行 了核质遗传 多样性 和群体遗 传结构分 析。利用 l 0份 O对特异性 S R引物分 析叶绿体 S 基因组多样性 , 获得 8个差 异性标记 , 将参试 9 4份材料划分为 3类 , 即甘蓝 ( 含栽培 和野生甘 蓝 ) 甘蓝型油菜和 白 、
阿兰图灵
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在剑桥,图灵可称得上是一个怪才,一举一动常常出人意料。他是个单身汉和长跑运动员。在他的 同事和学生中间,这位衣着随便、不打领带的著名教授,不善言辞,有些木讷、害羞,常咬指甲, 但他更多地以 自己杰出的才智赢得了人们的敬意。图灵每天骑自行车上班,因为患过敏性鼻炎,一遇到花粉,就 会鼻涕不止,大打喷嚏。于是,他就常常在上班途中戴防毒面具,招摇过市,这早已成为剑桥的一 大奇观。图灵的自行车经常半路掉链子,但他就是不肯去车铺修理。每次骑车时,他总是嘴里念念 有词,在心里细细计算,这链条也怪,总是转到一定的圈数就滑落了,而图灵竟然能够做到在链条 下滑前一刹那停车,让旁观者佩服不已,以为图灵在玩杂技。后来图灵又居然在脚踏车旁装了一个 小巧的机械记数器,到圈数时就停,歇口气换换脑子,再重新运动起来。 1936年,图灵向伦敦权威的数学杂志投了一篇论文,题为《论数字计算在决断难题中的应 用》。在这篇开创性的论文中,图灵给“可计算性”下了一个严格的数学定义,并提出著名的“图 灵机”(Turing Machine)的设想。“图灵机”不是一种具体的机器,而是一种思想模型,可制造 一种十分简单但运算能力极强的计算机装置,用来计算所有能想像得到的可计算函数。装置由一个 控制器和一根假设两端无界的工作带(起存储器的作用)组成。工作带被划分为大小相同的方格,每 一格上可书写一个给定字母表上的符号。控制器可以在带上左右移动,它带有一个读写头,可读出 控制器所访问的格子上的符号,也能改写或抹去这一符号,最后便会得出一个你期待的结果。外行 人看了会坠入云里雾里,而内行人则称它是“阐明现代电脑原理的开山之作”,并冠以“理想计算 机”的名称。这篇论文在纸上谈了一把兵,创造出一个“图灵机”来。但现代通用电脑确实是用相 应的程序来完成任何设定好的任务。这一理论奠定了整个现代计算机的理论基础。“图灵机”更在 电脑史上与“冯· 诺依曼机”齐名,被永远载入计算机的发展史中。 图灵机理论不仅解决了纯数学基础理论问题,一个巨大的“意外”收获则是,理论上证明了研 制通用数字计算机的可行性。虽然早在100年前的1834年,巴贝奇(Chark Babbage,1792~ 1871)就设计制造了“分析 机”以说明具体的数字计算,但他的失败之处是没能证明“必然可行”。图灵机理论不仅证明了研 制“通用机”的可行性,而且比世界上第一台由德国人朱斯(K· Zuze)于1941年制造的通用程序控 制计算机Z-3整整早5年。这不得不使人惊叹这一理论的深刻意义。
遗传学中英文词汇
中英文词汇--------------------------------------------------------------------------------近端着丝粒染色体(Acrocentric chromosome)——着丝粒靠近染色体端部的染色体。
加和原则(Additivity principle)——如果两个事件相互排斥,那么获得其中一个或另一个的概率为它们的各自概率之和。
等位基因(Allele)——在一既定基因座上一个基因的替换形式。
等位基因特异性寡核苷酸(Allele-specific oligonucleotide,ASO)——设计合成的寡核苷酸,可在适当条件下与特异序列杂交而不与其相关的序列杂交。
用针对每个等位基因序列设计的ASO甚至可容易地检出单个核苷酸的变异。
在几种设计相似、用来区分密切相关等位基因的方法中,ASO还可用作PCR引物。
等位基因异质性(Allelic heterogeneity)——在同一遗传基因座上,由不同的突变等位基因引起的相同或相似的表型。
α1-抗胰蛋白酶(α1-Antitrypsin)——是抑制弹性蛋白酶活性的一种丝氨酸蛋白酶抑制剂,该抑制剂的缺乏(如α1-抗胰蛋白酶不足)将导致严重的慢性肺和肝脏疾病。
Alu重复序列(Alu repetitive sequence)——位于基因间或内含子DNA中的中等重复序列,含有限制性内切酶AluⅠ的识别位点,这些序列长约300bp,并在人类基因组中重复出现约500,000次。
羊膜穿刺术(Amniocentesis)——一种产前诊断的方法,通常在妊娠4至6月抽取羊膜囊内婴儿四周的羊水进行。
扩增(Amplification)——一段DNA序列多个拷贝的产生。
非整倍体(Aneuploid)——指单倍体非整倍数的任何染色体数目。
通常非整倍体是指单条染色体的额外拷贝(三体性),或缺少单条染色体(单体性)。
由减数分裂或有丝分裂过程中染色体不分离所致。
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2. Preliminaries In [3], Catlin deÿned the collapsible graphs. Let R ⊆ V (G ). A subgraph of G is called an R-subgraph if both G − E ( ) is connected and v ∈ R if and only if v has odd degree in . A graph G is collapsible if for any even subset R of V (G ), G has an R-subgraph. Catlin showed [3] that every vertex of G is lying in a unique maximal collapsible subgraph of G . The collection of all collapsible graphs is denoted by CL. Clearly CL ⊂ SL. The contraction G=H is obtained from G by contracting each edge of H and deleting the resulting loops. The reduction of G is obtained from G by contracting all maximal
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collapsible subgraphs, and is denoted by G . A graph G is reduced if G is the reduction of some graph. Theorem 2.1 (Catlin [3]). Let G be a graph. Each of the following holds. (i) [3, Theorem 5] G reduced i G has no nontrivial collapsible subgraph. (ii) [3, Theorem 8] If G is reduced; then G is simple; and contains no K3 ; and (G )63; and G can be covered by at most two edge-disjoint forests. (iii) [3, Theorem 8] If G is reduced; then for any H ⊆ G; either H ∈ {K1 ; K2 } or |E (H )|62|V (H )| − 4. (iv) [3, Theorem 3] If H is a collapsible subgraph of G; then G ∈ CL if and only if G=H ∈ CL. (v) [3, Theorem 3] If H is a collapsible subgraph of G; then G ∈ SL if and only if G=H ∈ SL. The following result proves a conjecture of Catlin in [5], and generalizes Theorems 1.2 and 1.3. Theorem 2.2 (Catlin et al. [6]). Let G be a connected graph. If F (G )62; then either G ∈ CL; or the reduction of G is in {K2 ; K2; t ; (t ¿1)}. Let (G ) denote the maximum number of edge-disjoint spanning trees of G . Catlin recently proved a relationship between (G ) and Ä (G ), the edge-connectivity. Theorem 2.3 (Catlin [5]). Let G be a graph and let p¿1 be an integer. The following are equivalent: (i) Ä (G )¿2p. (ii) For any X ⊆ E (G ) with |X |6p; (G − X )¿p. Let G be a graph and let X ⊆ E (G ). The graph GX is obtained from G by replacing each edge e ∈ X with ends ue and ve by a (ue ; ve )-path Pe of length 2, where the internal vertex w(e) of the path Pe is newly added. Lemma 2.4. Let p¿2 be an integer; let G be a graph and let X ⊆ E (G ). Each of the following holds: (i) G has a spanning eulerian subgraph H such that X ⊆ E (H ) if and only if GX ∈ SL = SE(0). (ii) G ∈ SE(l) if and only if for any X ⊆ E (G ) with |X |6l; GX ∈ SL. (iii) (G − X )¿2 if and only if (GX )¿2. (iv) If F (G ) = 0 (that is; (G )¿2) and if X = {e1 ; e2 } ⊆ E (G ); then F (GX )62.
Abstract For an integer l¿0, deÿne SE(l) to be the family of graphs such that G ∈ SE(l) if and only if for any edge subset X ⊆ E (G ) with |X |6l, G has a spanning eulerian subgraph H with X ⊆ E (H ). The graphs in SE(0) are known as supereulerian graphs. Let f(l) be the minimum value of k such that every k -edge-connected graph is in SE(l). Jaeger and Catlin independently proved f(0) = 4. We shall determine f(l) for all values of l¿0. Another problem concerning the existence of eulerian subgraphs containing given edges is also discussed, and former results in [J. Graph Theory 1 (1977) 79 –84] and [J. Graph Theory 3 (1979) 91–93] are extended. c 2001 Elsevier Science B.V. All rights reserved. Keywords: Eulerian subgraph; Supereulerian graph; Collapsible graph
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Theorem 1.1 (Boesch et al. [1] and Jaeger [7]). Let H H . The following are equivalent:
Байду номын сангаас
be a subgraph of a graph
E-mail address: hjlai@ (H.-J. Lai) 0012-365X/01/$ - see front matter c 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 3 6 5 X ( 0 0 ) 0 0 0 7 0 - 4
1. Introduction Graphs in this note are ÿnite and loopless. Undeÿned terms and notation are from [2]. We use H ⊆ G to denote the fact that H is a subgraph of G . For a graph G , O(G ) denotes the set of all vertices of odd degree in G . A graph G with O(G ) = ∅ is an even graph, and a connected even graph is an eulerian graph. A graph is supereulerian if it has a spanning eulerian subgraph. The collection of all supereulerian graphs will be denoted by SL. For the literature on the subject of supereulerian graphs, see Catlin’s excellent survey [4]. As indicated by the authors in [1], characterizing supereulerian graphs appears very di cult. Pulleyblank in [8] pointed out that the problem of determining if a graph G is supereulerian is NP-complete. A bond is a minimal edge-cut. A bond X of G is an odd bond if |X | is odd. In [1] Boesch et al. proved Theorem 1.1 below, and in [7], Jaeger presented an elegant simple proof.