ON AUTOMORPHISM GROUPS OF SIMPLE ARGUESIAN LATTICES
自证预言一元思辨类英语作文
自证预言一元思辨类英语作文Self-Fulfilling Prophecy: A Monological Dialectic.The self-fulfilling prophecy, an intriguing phenomenon in the social sciences, posits that beliefs, expectations, and preconceptions can shape reality and bring about the anticipated outcomes. This monological dialectic explores the intricate interplay between individual perceptions, social interactions, and the ultimate manifestation of events.At the outset, it is imperative to recognize that beliefs are not mere ephemeral thoughts; they are powerful cognitive anchors that influence how humans perceive and interact with the world around them. When individuals hold certain beliefs about themselves, others, or their circumstances, these beliefs act as filters through which they interpret their experiences. For instance, if an individual believes that they are destined for success, they may approach challenges with greater confidence andoptimism, thereby increasing the likelihood of achieving their goals. Conversely, if an individual believes that they are inherently incapable, they may develop a pessimistic mindset that hinders their progress.The social environment plays a pivotal role in shaping and reinforcing beliefs. Through interactions with others, individuals absorb prevailing norms, values, and expectations. These societal influences can either validate or challenge existing beliefs, leading to their strengthening or modification. For example, if a group of peers constantly affirms an individual's abilities, the individual's self-belief may grow over time. However, if the same peers express doubt and skepticism, theindividual's confidence may dwindle.The self-fulfilling prophecy becomes a reality when beliefs translate into tangible actions. Motivated by their beliefs, individuals engage in behaviors that align with their expectations. If they believe they are capable, they may undertake ambitious endeavors and persevere in the face of obstacles. If they believe they are limited, they mayshy away from challenges and resign themselves to mediocrity. In this way, beliefs become self-reinforcing, creating a feedback loop that perpetuates the anticipated outcomes.The implications of self-fulfilling prophecies are profound. They demonstrate the power of human perception and the potential for both positive and negative outcomes. On the one hand, self-fulfilling prophecies can fuel progress, innovation, and personal growth. When individuals believe in their abilities, they may achieve remarkable feats that would have otherwise seemed impossible. On the other hand, self-fulfilling prophecies can also perpetuate inequality, discrimination, and social ills. If marginalized groups are subjected to persistent messages of inferiority, they may internalize these beliefs and limit their own opportunities.Recognizing the influence of self-fulfilling prophecies is crucial for fostering positive change. Educators, policymakers, and social activists must challenge harmful stereotypes and cultivate environments that nurture self-belief and empower individuals to fulfill their potential. By promoting a growth mindset and encouraging individuals to challenge their limiting beliefs, we can mitigate the negative effects of self-fulfilling prophecies and create a more just and equitable society.In conclusion, the self-fulfilling prophecy is a powerful force that shapes our experiences and influences the course of our lives. By understanding the interplay between beliefs, expectations, and actions, we can harness the power of positive self-fulfilling prophecies to achieve our goals and create a more fulfilling future.。
英文论文-argument的分析
SAMPLE ANSWERS FROM SPEECHES BY DONALD TRUMP AND HILLARYCLINTONAudienceTrumpTrump directs his speech to highly receptive “fellow Republicans” (27), particularly those who want to protect the Second Amendment (105). Trump, however, risks alienating Republican base voters because he minimizes God in his address. He references God on two occasions: he alludes to the “promised land” (25) from the Book of Genesis and he invokes God to elevate his status (51). Because Trump rarely makes religious references and does not end the speech with the customary “God bless America,” he risks alie nating Republican base voters who are highly religious. Generally, Trump also engages those who are tired of the status quo in Washington, who are tired of “the politicians” (35) because “politicians are all talk, no action” (26).Trump also appeals to dominant white culture by directing racial remarks against Mexican “rapists” (6), China, Japan, South and Latin America, and the Middle East. In effect, his prejudicial remarks are particularly directed to white xenophobes.Trump’s address is also directed to both upper and lower class Americans. He appeals to the upper class by promising to invest his own money in the country (67) and to renegotiate their trade bill (115), which will provide incentives to wealthy business owners and benefit the U.S. econom y. He also appeals to lower class Americans by using colloquial diction, such as “gonna”(26), “fellas” (67), and “losers” (92), and by reanimating the “dead” “American Dream” as upward economic mobility through job creation. The poor are those who “don’t need the rhetoric [and] want a job” (30), and who appreciate Trump’s efforts to “Save Medicare, Medicaid and Social Security without cuts” (113). In effect, he appeals to the poorly educated, lower class audience because his language, which is devoid of political and economic jargon, and simple sentence structure can be easily understood.Trump’s “love [of] the military” (11) also appeals to veterans and soldiers.ClintonClinton directs her speech to highly receptive democratic base voters. However, she also appeals to swing voters because her domestic policy primarily focuses on creating an “inclusive society”(17), and she declares her intention to be a “President for all Americans” (41). Clinton also appeals to religious audiences by revealing her Christian background. She shares her experiences at her Methodist Church (21) and ends her speech with “God bless America” (47).In addition, Clinton recognizes minority groups. In particular, she acknowledges “Mexicans” (21), “immigrants” (17), “gay people” (17), “LGBT” (24), “women” (17, 24), “women of color”(29), college students (22, 28), “young people . . . people with disabilities, and people of color”(34). Clinton’s address is directed to both middle- and lower-class Americans. She explicitly direct s her “Four Fights” to these two economic groups: “the middle class” and “the poor” (22). She shares her parents’ occupations, which created her “middle-class life” (4): her father was a small business owner and her mother was a housemaid. She also refers to middle-classoccupations, such as “kindergarten teachers” (9), and working-class occupations, such as “factory workers . . . food servers” (11), and “truckers” (11). Clinton also addresses “poor people” (21, 23). She appeals to this group’s needs with t he prospect of upward mobility: “children climb out of poverty” (18). She does not appeal to the upper classes, often criticizing Republicans for pandering to “the wealthiest” (7), “the wealthy” (15), “those at the top” (6), “corporations . . . CEOs . . . hedge fund managers” (9), “multi-national corporations” (13), and “billionaires” (10). Clinton also directly addresses “veterans” (11).ArgumentTrump’s speech is generally one-sided because it does not dwell on opposing views. It does have a moment of refutatio when Trump attacks those who challenge his anti-Washington persona: “Somebody said [mentioning his net worth] is ‘crass.’ It’s not crass” (77). It also incorporates elements of the classical argument, particularly the exordium, narratio, propositio, and confirmatio. Trump’s exordium is a statement of urgency based on fear: “Our country is in serious trouble” (2). His extended narratio, which provides the context for his speech, elaborates on this fear by specifying the reasons for its existence: “Mexico [is] bringing drugs . . . crime . . . rapists” (6); “Islamic terrorism is becom[ing] rich” (9); “We have nothing” (13); “our gross domestic product is below zero” (15); “our real unemployment is . . . from 18 to 20 percent” (17); “Our enemies are getting stronger . . . our nuclear arsenal doesn’t work” (20); “we have a disaster called . . . Obamacare” (22); “Doctors are quitting” (33); and “President Obama . . . wasn’t a cheerleader; he was the opposite” (44). His propositio is delayed until ¶ 49, where he declares his candidacy for the president of the United States. His confirmatio is a series of reasons why he would make a great president: he “will be the greatest jobs president that God ever created” (52); he knows “the smartest negotiators in the world” (58); he doesn’t “need anybody’s money” (67) because he is “really rich” (68), so cannot be influenced by politicians and lobbyists (67); he will “build a great wall . . . and will have Mexico pay for it” (97); he will be tough on “ISIS” (98); he will “back up the Second Amendment” (102), “rebuild the country’s infrastructure” (106), save social security (113), and reduce debt (116).Clinton’s speech is generally one-sided because it does not dwell on opposing views. However, Clinton does include a Toulminian qualifying statement, recognizing her fallibility and the existence of counterarguments: “I won’t get everything right. Lord knows I’ve made my share of mistakes. Well, there’s no shortage of people pointing them out!” (43). There is also th e implied counterargument, although never explicitly stated, that Clinton addresses at the close of her speech: Can a woman be president? Clinton’s closing assertion is a resounding “yes” in response to this implied query: “An America where a father can te ll his daughter: yes, you can be anything you want to be. Even President of the United States” (46). The speech also incorporates classical narratio, propositio, and confirmatio. The extended narratio from ¶2 to 10 outlines Clinton’s credentials as senato r and Secretary of State (3), America’s basic values of equal opportunity (4-5), and the loss of these values as a result of Republican rule and their support of the wealthy (6-10). Her propositio is delayed until ¶ 11, where she announces her candidacy fo r “President of the United States.” Her confirmatio from ¶ 11 to 22 explains whom she plans to represent as a president (minorities, the middle class, and the poor—not the wealthy). Her confirmatio then specifies how she will represent these groups through her domestic policy, what she calls the“Four Fights” (23). These include creating jobs (26), strengthening America’s families (29), “harnessing America’s power, smarts, and values to maintain . . . leadership for peace, security, and prosperity” (31), and “reforming . . . government” (34). The confirmatio closes with an explanation of why she is personally equipped to carry out this task, particularly as a woman: her mother’s influence is highlighted to inform her credibility.ClaimsTrumpTrump predominantly relies on fact claims. Fact claims serve to elicit fear: “Our country is in serious trouble” (20), “they are beating us economically” (4), “we have nothing” (13), “They can’t get jobs” (18), “They’re killing us” (28), “Our vets have been abandoned” (39), “We owe China $1.3 trillion” (54), “we’re in a bubble” (116), “the American dream is dead” (119). They are also used by Trump to undermine the authority of his opponents: “He’s not a leader” (43), “He’s actually a negative force” (44), “Our president doesn’t have a clue” (57). Fact claims further reinforce Trump’s authority: “I don’t need anybody’s money” (67), “I’m really rich” (68), “I have assets” (85), “Nobody can do that like me” (107). These fact claims are often presented as facts prope r through legitimizing assertions such as “It’s true” (6) and “That’s right”(18).Trump makes value claims to commend soldiers—“They’re great” (12); lobbyists—“They’re great” (36); Americans citizens—“We have tremendous people” (50); General Services—“wh o are terrific people” (110); and himself—“we’re really good . . . we had a really good plan . . . we had a great financial statement” (110). He also uses value claims to criticize the opposition: “he’s a bad negotiator” (57), “They’re not good” (59), and “It’s not a good thing” (64).Policy claims with “should,” “must,” or “ought” are absent from the speech; instead, Trump issues commands, thereby reinforcing his authority: “We have to repeal Obamacare” (34), “We have to stop” (37), “We got to make the country rich” (70), “We have to rebuild our infrastructure” (113), “Have to do it” (113).ClintonClinton also relies on fact claims. She uses fact claims to explain her credentials: “I represented our country many times” (2), “I served as Secretary of State” (3), “As a Senator from New York, I dedicated myself to getting our city and state the help we needed to recover” (31). Clinton relies on fact claims to convey American ideals and rally patriotism: “Prosperity and democracy are part of your basic bar gain too” (10), “We’re problem solvers, not deniers” (15), “The story of America is a story of hard-fought, hard-won progress” (45). She also uses fact claims to critique her opposition: “Republicans twice cut taxes for the wealthiest, borrowed money from other countries to pay for two wars, and family incomes dropped” (7); “Our political system is so paralyzed by gridlock” (14); “They shame and blame women” (17); “They turn their backs on gay people” (17), “They reject what it takes to build an inclusive economy” (17).Clinton also uses policy claims. In part, policy claims rally support: “if you do your part you ought to be able to get ahead” (5); “We should welcome the support of all Americans who want to go forward together with us” (24). Clinton also uses policy claims to outline her plan of action: “our next president must work with congress” (15). Her anaphoric repetition of “I believe you should . . .” in ¶ 29-30 emphasizes her vision of the future as president.Clinton uses value claims to reinforce the legitimacy of American principles—“That still sounds good to me” (3)—and to rally patriotism—“America is strong” (29); “No other country on Earth is better positioned . . . No other country is better equipped . . . No other country is better prepar ed . . .” (31); “We’re a better, stronger, more prosperous country . . .” (45).AppealsTrumpTrump primarily appeals to pathos by relying on fallacies. He uses scare tactics, usually in the form of hyperbolic statements, to elicit fear about the s tate of the economy (“we have nothing,” “we’re dying,” “The American dream is dead”), about Obamacare (“It’s a disaster”), against immigrants (“They’re rapists”) and against terrorists (“they’ve become rich”).Trump appeals to ethos when he establishes his credibility as a self-made man with a very high net worth: “I’m really rich . . . . So the total is $8,737,540,00” (89). He alludes to other figures of authority, such as “a friend who’s a doctor” (33), “The head of Ford, who I know” (61), “the negotiat ors in the world” (60), and the current “General Patton or . . . General MacArthur” (99). However, because none are explicitly named, the appeal to credibility is compromised. He also attempts to undermine the ethos of Democratic Secretary of State John Kerry, President Obama, and politicians in general by using ad hominem abusive: “Secretary Kerry . . . has absolutely no concept of negotiation . . . and then goes into a bicycle race at 72 years old, and falls and breaks his leg” (100); “[Obama] is actually a negative force” (44); “[Politicians] will never make America great again . . . They’re controlled fully by the Lobbyists” (35).Trump also appeals to logos. He appeals to logos by using and questioning statistics. He undermines Obamacare through statistical data—“Yesterday, it came out that costs are going up for people up 29, 39, 49, and even 55 percent” (23)—and questions the current low unemployment rate—“it’s a statistic that’s full of nonsense” (19). However, because these statistics do not have sources, their authority is compromised. He also appeals to logos by relying on logical fallacies, such as false analogies—“We are like a third world country” (111)—faulty generalizations—“We don’t have victories anymore” (2), “there are no jobs” (18), “The American dream is dead” (119)—and post hoc, particularly when he fails to consider unemployment as a result of anything other than increased work in China and Mexico (18). ClintonClinton uses ethos to build her own credibility. She lists her professional and personal credentials as a senator (2), Secretary of State (3, 35), a member of the Armed Services Committee (31), anattendee in “the Situation Room on the day we got bin Laden” (32), her husband’s wife (3), her mother’s daughter (19, 44), a grandmother (41), and a Christian (21). She also appeals to the credibility of past democratic presidents, such as Franklin Roosevelt (2), Bill Clinton (5), and Barack Obama (5). In addition, Clinton attempts to undermine the ethos of Republicans by recognizing their tax cuts for the wealthy (7), their denial of climate change (17), and their negative responses to women, immigrants, and the gay community (17).Clinton also appeals to pathos. She appeals to emotion by sharing her mother’s abandonment story (19-20) and hardship narrative (44). The use of sensory descriptions, such as “she had nothing to eat” (20), particularly elicits sympathy and sorrow. Clinton also provokes fear through the use of a scare tactic when she claims Republicans want to take away health insurance without providing alternatives (17).In addition, Clinton uses logos. She refers to statistics: “In fact, 80 percent of the brain is developed by the age of three” (28). She also relies on logical deductions, particularly with the use of “because” clauses (25, 29) and “If-then” constructions (4, 15, 23). Further, she appeals to logos by using logical fallacies, such as the oversimplified cause fallacy: “when our families are strong, America is strong” (29, 33).。
a simple rule for the evolution of cooperation on graphs and social netwarks
A simple rule for the evolution of cooperation on graphs and social networksHisashi Ohtsuki 1,2,Christoph Hauert 2,Erez Lieberman 2,3&Martin A.Nowak 2A fundamental aspect of all biological systems is cooperation.Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals 1–4.Human society is based to a large extent on mechanisms that promote cooperation 5–7.It is well known that in unstructured populations,natural selection favours defectors over cooperators.There is much current interest,however,in studying evolutionary games in structured populations and on graphs 8–17.These efforts recognize the fact that who-meets-whom is not random,but determined by spatial relationships or social networks 18–24.Here we describe a surprisingly simple rule that is a good approxi-mation for all graphs that we have analysed,including cycles,spatial lattices,random regular graphs,random graphs and scale-free networks 25,26:natural selection favours cooperation,if the benefit of the altruistic act,b ,divided by the cost,c ,exceeds the average number of neighbours,k ,which means b /c >k .In this case,cooperation can evolve as a consequence of ‘social viscosity’even in the absence of reputation effects or strategic complexity.A cooperator is someone who pays a cost,c ,for another individual to receive a benefit,b .A defector pays no cost and does not distribute any benefits.In evolutionary biology,cost and benefit are measured in terms of fitness.Reproduction can be genetic or cultural.In the latter case,the strategy of someone who does well is imitated by others.In an unstructured population,where all individuals are equally likely to interact with each other,defectors have a higher average payoff than unconditional cooperators.Therefore,natural selection increases the relative abundance of defectors and drives cooperators to extinction.These evolutionary dynamics hold for the deterministic setting of the replicator equation 27,28and for stochastic game dynamics of finite populations 29.In our model,the players of an evolutionary game occupy the vertices of a graph.The edges denote links between individuals in terms of game dynamical interaction and biological reproduction.We assume that the graph is fixed for the duration of the evolutionary dynamics.Consider a population of N individuals consisting of cooperators and defectors.A cooperator helps all individuals to whom it is connected.If a cooperator is connected to k other individuals and i of those are cooperators,then its payoff is bi 2ck .A defector does not provide any help,and therefore has no costs,but it can receive the benefit from neighbouring cooperators.If a defector is connected to j cooperators,then its payoff is bj .The fitness of an individual is given by a constant term,denoting the baseline fitness,plus the payoff that arises from the game.Strong selection means that the payoff is large compared to the baseline fitness;weak selection means the payoff is small compared to the baseline fitness.The idea behind weak selection is that many different factors contribute to the overall fitness of an individual,and the game under consideration is just one of those factors.At first,we will study the following update rule for evolutionary dynamics (Fig.1):in each time step,a random individual is chosen to die,and the neighbors compete for the empty site proportional to their fitness.We call this mechanism ‘death–birth’updating,because it involves a death event followed by a ter we will investigate other update mechanisms.Let us explore whether natural selection can favour cooperation on certain graphs.To do this,we need to calculate the probability that a single cooperator starting in a random position turns the whole population from defection to cooperation.If selection neither favours nor opposes cooperation,then this probability is 1/N ,which is the fixation probability of a neutral mutant.If the fixationLETTERSFigure 1|The rules of the game.Each individual occupies the vertex of a graph and derives a payoff,P ,from interactions with adjacent individuals.A cooperator (blue)pays a cost,c ,for each neighbour to receive a benefit,b .A defector (red)pays no cost and provides no benefit.The fitness of a player is given by 12w þwP ,where w measures the intensity of selection.Strong selection means w ¼1.Weak selection means w ,,1.For ‘death–birth’updating,at each time step,a random individual is chosen to die (grey);subsequently the neighbours compete for the empty site in proportion to their fitness.In this example,the central,vacated vertex will change from a defector to a cooperator with a probability F C /(F C þF D ),where the total fitness of all adjacent cooperators and defectors is F C ¼4ð12w Þþð10b 216c Þw and F D ¼4(12w )þ3bw ,respectively.1Department of Biology,Kyushu University,Fukuoka 812-8581,Japan.2Program for Evolutionary Dynamics,Department of Organismic and Evolutionary Biology,Department of Mathematics,3Department of Applied Mathematics,Harvard University,Cambridge,Massachusetts 02138,USA.probability of a single cooperator is greater than1/N,then selection favours the emergence of cooperation.We also calculate thefixation probability of a single defector in a population of cooperators,and compare the twofixation probabilities.The traditional well-mixed population of evolutionary game theory is represented by the complete graph,where all vertices are connected. In this special situation,cooperators are always opposed by selection. This is the fundamental intuition of classical evolutionary game theory.But what happens on other graphs?Let usfirst consider a cycle.Each individual is linked to two neighbours.A single cooperator could be wiped out immediately or take over one of its two neighbours.A cluster of two cooperators could expand to three cooperators or revert to a single cooperator.In any case,the lineage starting from one cooperator always forms a single cluster of cooperators,which cannot fragment into pieces.This fact allows a straightforward calculation.Wefind that selection favours cooperation if b/c.2.This result holds for weak selection and large population size.Next,we study regular graphs,where each individual has exactly k neighbours.Such graphs include cycles,spatial lattices and random regular graphs.For all such graphs,a direct calculation of thefixation probability is impossible,because a single invader can lead to very complicated patterns:the emerging cluster usually breaks into many pieces,allowing a large number of conceivable geometric configura-tions.In general,the inherent complexity of games on graphs makes analytical investigations almost always impossible.Nevertheless,we can calculate thefixation probability of a ran-domly placed mutant for any two-person,two-strategy game on a regular graph by using pair approximation and diffusion approxi-mation(see Supplementary Information).In particular,wefind that cooperators have afixation probability greater than1/N and defectors have afixation probability less than1/N,if:b=c.kThe ratio of benefit to cost of the altruistic act has to exceed the degree,k,which is given by the number of neighbours per individual. This condition is derived for weak selection and under the assump-tion that the population size,N,is much larger than the degree,k. Wefind excellent agreement with numerical simulations(Fig.2). For a given population size,b/c.k is a necessary condition for selection to favour cooperators.As the population size increases,the discrepancy between b/c.k and the numerical simulations becomes smaller.Moreover,wefind that the rule also holds for random graphs25and scale-free networks26,27,where individuals differ in the number of their neighbours.Here k denotes the average degree of the graph.Scale-free networksfit slightly less well than random graphs, presumably because they have a larger variance of the degree distribution.The intuitive justification for the b/c.k rule is illustrated in Fig.3. Consider one cooperator and one defector competing for an empty site.The payoff for the cooperator is P C¼bq C j C(k21)2ck.The payoff for the defector is P D¼bq C j D(k21).Theconditional Figure2|The simple rule,b/c>k,is in good agreement with numericalsimulations.The parameter k denotes the degree of the graph,which isgiven by the(average)number of neighbours per individual.Thefirst rowillustrates the type of graph for k¼2(a)and k¼4(b–e).The second andthird rows show simulation data for population sizes N¼100and N¼500.Thefixation probability,r,of cooperators is determined by the fraction ofruns where cooperators reachedfixation out of106runs under weakselection,w¼0.01.Each type of graph is simulated for different(average)degrees ranging from k¼2to k¼10.The arrows mark b/c¼k.The dottedhorizontal line indicates thefixation probability1/N of neutral evolution.The data suggest that b/c.k is necessary but not sufficient.The discrepancyis larger for non-regular graphs(d,e)with high average degree(k¼10).This is not surprising given that the derivation of the rule is for regulargraphs and in the limit N..k.Note that the larger population size,N¼500,gives better agreement.Interactive online tutorials can be found athttp://univie.ac.at/virtuallabs.NATURE|Vol441|25May2006LETTERSprobability to find a cooperator next to a cooperator is q C j C and to find a cooperator next to a defector is q C j D .The cooperator pays cost c for all of its k neighbours and receives benefit b from each cooperator among its k 21neighbours,excluding the contested site.The defector pays no cost,but receives benefit b from each cooperator among its k 21neighbours,also excluding the contested site.The payoff that comes from the contested site is excluded,because it contributes equally to the cooperator and the defector and therefore cancels out.If P C .P D ,then selection favours the cooperator.Pair-approximation shows that (k 21)(q C j C 2q C j D )¼1for weak selection.Thus,the cooperator has on average one more cooperator neighbour than the defector.Therefore,we obtain P C 2P D ¼b 2ck ,which leads to the b /c .k rule.We have also explored other update mechanisms.Suppose at each time step a random individual is chosen to update its strategy;it will stay with its own strategy or imitate one of the neighbours pro-portional to fitness.For this ‘imitation’updating,we find that cooperators are favoured if b /c .k þ2.This result can be obtained with an exact calculation for the cycle and with pair approximation for regular graphs.Again,there is good agreement with numerical simulations (Supplementary Fig.4).Mathematically,imitation updating can be obtained from our earlier death–birth updating by adding loops to every vertex.Therefore,each individual is also its own neighbour.Let us define the connectivity,k ,of a vertex as the total number of links connected to that vertex,noting that a loop is connected twice.Then the simple rule b /c .k holds both for the imitation and death–birth updating.There are also update rules for which selection can never favour cooperators.For example,let us consider ‘birth–death’updating:at each time step an individual is selected for reproduction pro-portional to fitness,and the offspring replaces a randomly chosen neighbour.In this case,selection always favours defectors,because only the payoff of individuals right at the boundary between cooperators and defectors matters,and there cooperators are always at a disadvantage (Fig.3b).In the two other models,the payoffs of individuals that are one place removed from the boundary also play a role,which gives cooperation a chance to survive.Using a different model,van Baalen and Rand 11have derived a condition for the initial invasion of cooperators.In their model,the vertices of a spatial lattice (or a graph)are either empty or occupied by cooperators or defectors.There are birth,death and migration events.Implicitly,they have shown that without migration a few cooperators can successfully invade a population of defectors if b /c .k 2/(k 21).The difference between this result and ours is not surprising.The invasion condition of ref.11examines whether rare cooperators are able to increase in abundance,whereas our fixation probability includes the whole evolutionary trajectory including the initial invasion and propagation of cooperators as well as the final extinction of defectors.For a comparison of invasion and fixation criteria see Wild and Taylor 30.Thus,we have shown that evolutionary dynamics on graphs can favour cooperation over defection if the benefit to cost ratio,b /c ,of the altruistic act exceeds the average connectivity,k .The fewer connections there are,the easier it is for natural selection to promote cooperation.In our present analysis,all connections are equally strong.A next step will be to explore graphs with weighted edges.In social networks,people might have a substantial number of connec-tions,but only very few of them are strong.Hence,the ‘effective’average degree,k ,of many relevant networks could be small,thereby making selection of cooperation on graphs a powerful option.Our study is theoretically motivated,but has implications for empirical research.For example,one can envisage an experiment where people are asked to play a non-repeated Prisoner’s Dilemma within a given network.Certain network structures should promote cooperative behaviour more than others.In particular,more cooperation should emerge if connectivity is low.Moreover,in certain animal species there exist complicated social networks.Observational studies could reveal how network structure affects the level of cooperation;higher connectivity should reduce cooperation.In this paper,as a logical first step,we have studied the simplest possible interaction between unconditional cooperators and defectors,but in an extended approach,both in terms of theory and experiment,it will be interesting to see which strategies of direct or indirect reciprocity evolve on particular networks.Finally,we note the beautiful similarity of our finding with Hamilton’s rule 1,which states that kin selection can favour cooperation provided b /c .1/r ,where r is the coefficient of genetic relatedness between individuals.The similarity makes sense.In our framework,the average degree of a graph is an inverse measure of social relatedness (or social viscosity).The fewer friends I have the more strongly my fate is bound to theirs.Received 7December 2005;accepted 26January 2006.1.Hamilton,W.D.The genetical evolution of social behaviour.J.Theor.Biol.7,1–-16(1964).2.Trivers,R.The evolution of reciprocal altruism.Q.Rev.Biol.46,35–-57(1971).3.Axelrod,R.&Hamilton,W.D.The evolution of cooperation.Science 211,1390–-1396(1981).4.Wilson,E.O.Sociobiology (Harvard Univ.Press,Cambridge,Massachusetts,1975).5.Wedekind,C.&Milinski,M.Cooperation through image scoring in humans.Science 288,850–-852(2000).6.Fehr,E.&Fischbacher,U.The nature of human altruism.Nature 425,785–-791(2003).7.Nowak,M.A.&Sigmund,K.Evolution of indirect reciprocity.Nature 437,1291–-1298(2005).8.Nowak,M.A.&May,R.M.Evolutionary games and spatial chaos.Nature 359,826–-829(1992).9.Killingback,T.&Doebeli,M.Spatial evolutionary game theory:Hawks andDoves revisited.Proc.R.Soc.Lond.B 263,1135–-1144(1996).10.Nakamaru,M.,Matsuda,H.&Iwasa,Y.The evolution of cooperation in alattice-structured population.J.Theor.Biol.184,65–-81(1997).Figure 3|Some intuition for games on graphs.a ,For death–birth updating,we must consider a cooperator and a defector competing for an empty site.The pair-approximation calculation shows that for weak selection thecooperator has one more cooperator among its k 21other neighbours than does the defector.Hence,the cooperator has a higher chance to win the empty site if b /c .k .b ,For birth–death updating,we must consider a cooperator–defector pair competing for the next reproduction event.Again the cooperator has one more cooperator among its k 21other neighbours than the defector,but the focal cooperator is also a neighbour of the defector.Hence,both competitors are linked to the same number of cooperators,and therefore the defector has a higher payoff.For birth–death updating,selection does not favour cooperation.c ,On a cycle (k ¼2),the situation is simple.A direct calculation,for weak selection and large population size,leads to the following results.For birth–death updating,the boundary between a cluster of cooperators and defectors tends to move in favour of defectors.For death–birth updating,the cooperator cluster expands if b /c .2.For imitation updating,the cooperator cluster expands if b /c .4.LETTERSNATURE |Vol 441|25May 200611.van Baalen,M.&Rand,D.A.The unit of selection in viscous populations andthe evolution of altruism.J.Theor.Biol.193,631–-648(1998).12.Mitteldorf,J.&Wilson,D.S.Population viscosity and the evolution of altruism.J.Theor.Biol.204,481–-496(2000).13.Hauert,C.,De Monte,S.,Hofbauer,J.&Sigmund,K.Volunteering as red queenmechanism for cooperation in public goods games.Science296,1129–-1132(2002).14.Le Galliard,J.,Ferriere,R.&Dieckman,U.The adaptive dynamics of altruism inspatially heterogeneous populations.Evolution57,1–-17(2003).15.Hauert,C.&Doebeli,M.Spatial structure often inhibits the evolution ofcooperation in the snowdrift game.Nature428,643–-646(2004).16.Ifti,M.,Killingback,T.&Doebeli,M.Effects of neighbourhood size andconnectivity on the spatial continuous prisoner’s dilemma.J.Theor.Biol.231, 97–-106(2004).17.Santos,F.C.&Pacheco,J.M.Scale-free networks provide a unifyingframework for the emergence of cooperation.Phys.Rev.Lett.95,098104(2005).18.Levin,S.A.&Paine,R.T.Disturbance,patch formation,and communitystructure.Proc.Natl A71,2744–-2747(1974).19.Durrett,R.&Levin,S.A.The importance of being discrete(and spatial).Theor.Popul.Biol.46,363–-394(1994).20.Hassell,M.P.,Comins,H.N.&May,R.M.Species coexistence andself-organizing spatial dynamics.Nature370,290–-292(1994).21.Skyrms,B.&Pemantle,R.A dynamic model of social network formation.Proc.Natl A97,9340–-9346(2000).22.Abramson,G.&Kuperman,M.Social games in a social network.Phys.Rev.E63,030901(2001).23.Szabo´,G.&Vukov,J.Cooperation for volunteering and partially randompartnership.Phys.Rev.E69,036107(2004).24.Lieberman,E.,Hauert,C.&Nowak,M.A.Evolutionary dynamics on graphs.Nature433,312–-316(2005).25.Watts,D.J.&Strogatz,S.H.Collective dynamics of‘small-world’networks.Nature393,440–-442(1998).26.Barabasi,A.&Albert,R.Emergence of scaling in random networks.Science286,509–-512(1999).27.Taylor,P.D.&Jonker,L.Evolutionary stable strategies and game dynamics.Math.Biosci.40,145–-156(1978).28.Hofbauer,J.&Sigmund,K.Evolutionary Games and Population Dynamics(Cambridge Univ.Press,Cambridge,UK,1998).29.Nowak,M.A.,Sasaki,A.,Taylor,C.&Fudenberg,D.Emergence ofcooperation and evolutionary stability infinite populations.Nature428,646–-650(2004).30.Wild,G.&Taylor,P.D.Fitness and evolutionary stability in gametheoretic models offinite populations.Proc.R.Soc.Lond.B271,2345–-2349 (2004).Supplementary Information is linked to the online version of the paper at /nature.Acknowledgements Support from the John Templeton Foundation,JSPS, NDSEG and Harvard-MIT HST is gratefully acknowledged.The Program for Evolutionary Dynamics at Harvard University is sponsored by Jeffrey Epstein. Author Information Reprints and permissions information is available at /reprintsandpermissions.The authors declare no competing financial interests.Correspondence and requests for materials should be addressed to M.A.N.(martin_nowak@).NATURE|Vol441|25May2006LETTERS。
GRE47种类比关系
GRE47种类比关系GRE词汇之类比47大关系1.个体组成团体的关系一个集合体的名词和一个表示个体的名词放在一起，由多个个体可以组成一个集合体，如choir和inger，cat和actor，orchetra和intrumentalit，flock和bird，chool和fih，herd和cattle，oldier 和army，colony和bacterium，armada和vehicle，fuillade和projectile，barrage和e某ploive，gravel和pebble，nation和citizen。
有时需考虑这个个体在组成团体时的规律性及团体自身的特点，如matri某和number只能对应crytal和atom而不能对应ga和molecule。
再如tile组成moaic，titch组成ampler，还有array和number，formation和oldier。
2.人和其特点的关系(1)人和其性格特点的正／反面关系正面，如：zealot和fervor，altruit和elf1ene，partian和allegiance，diplomat和tact，inventor和ingenuity，coward和craven，dupe和credulou，acrobat和agility，boor和inenitive，loner和olitary，urgeon和de某terity，blowhard和boatfu1，toady 和obequiou，upplicant和humility，adverary和reitance，reclue和withdrawn，bigot和biaed，wag和humorou，dolt和tupid。
反面，如：maverick和conformity，tickler和appro某imation，purit和adulteration，heretic和orthodo某y，poeur和incerity，reclue和gregarioune，coward和brave，philanthropit和elfih，neophyte和e某perience，boor和enitivity，yokel和ophitication。
分组有问题英语作文
分组有问题英语作文Grouping Issues in English CompositionIn English composition, grouping is an essential part of organizing ideas and presenting them effectively. However, some common issues may arise during the process of grouping. Let's discuss some of these issues and ways to overcome them:1. Lack of coherence: Sometimes, the ideas or arguments within a group may not flow smoothly or connect logically. This can result in a lack of coherence and make the writing difficult to follow. To overcome this, it is important to ensure that each point within a group relates clearly to the main topic and that the ideas progress in a logical order.2. Imbalanced groups: In some cases, groups may be imbalanced, with one group containinga lot of information while others lack substance. This can create an uneven presentation or leave certain aspects underexplored. To address this, it is important to divide the content evenly among the groups, ensuring that each has sufficient material to support the main topic.3. Overlapping content: In certain situations, there might be a tendency to repeat or overlap information across different groups. This can lead to redundancy and confuse the readers. To avoid this, it is crucial to carefully review each group and eliminate any unnecessary repetition of ideas.4. Failure to address counterarguments: Effective grouping should consider counterarguments and address them appropriately. Failing to do so can weaken the overall argument. It is important to anticipate potential counterarguments and allocate a separate group to address them, presenting convincing evidence or refutations.5. Lack of proper transitions: Smooth transitions between groups are crucial for maintaining the flow of the composition. Without proper transitions, the reader might find it difficult to understand the connections between different ideas or groups. To overcome this, include clear and concise transitional phrases or sentences that guide the reader from one group to another.By being aware of and addressing these common grouping issues, you can enhance the clarity and coherence of your English composition. Remember to review your work carefully, ensuring that each group serves a specific purpose and contributes effectively to the overall composition.。
acl 2023随笔 自然语言中的复杂推理
acl 2023随笔自然语言中的复杂推理自然语言中的复杂推理自然语言是人类交流和表达思想的主要方式之一。
然而，尽管人类在日常对话中能够轻松地进行复杂的推理，但要让计算机系统能够理解和进行类似的推理却是一项巨大的挑战。
在人工智能领域，自然语言处理（NLP）的发展旨在使计算机系统能够理解和处理自然语言。
其中一个重要的研究方向是如何使计算机系统能够进行复杂推理。
复杂推理是指基于已知事实和逻辑规则，通过推导和演绎得出新的结论。
这种推理过程需要对语义、逻辑和常识等多个层面进行综合考虑。
例如，当我们听到一句话“如果今天下雨，那么我就会带伞”，我们可以根据这个条件来判断如果今天确实下雨了，那么我就会带伞。
这种推理过程涉及到条件语句、逻辑关系以及我们对天气和带伞习惯等方面的常识。
在自然语言处理中，实现复杂推理需要解决多个问题。
首先是语义表示问题。
自然语言中存在歧义和多义现象，同一句话可能有不同的解释。
因此，需要将自然语言转化为计算机能够理解的形式，如逻辑形式或图形表示。
其次是推理规则的建模问题。
推理规则是指根据已知事实和逻辑规则进行推导和演绎的方法。
这些规则需要能够覆盖自然语言中各种复杂的推理情况，并且能够灵活地应对不同的语境和背景知识。
最后是常识表示和推理问题。
常识是人类在日常生活中积累的一种普遍知识，它对于理解和进行复杂推理至关重要。
因此，需要将常识以某种方式表示，并将其融入到推理过程中。
近年来，随着深度学习技术的发展，自然语言处理取得了一些重要进展。
例如，基于神经网络的模型可以通过大量数据进行训练，并学习到自然语言中的一些模式和规律。
这些模型可以用于语义表示、句法分析、情感分析等任务，并在某种程度上实现了对复杂推理的支持。
然而，目前仍然存在许多挑战和限制。
首先，复杂推理需要对大量的背景知识和常识进行建模。
目前的自然语言处理模型往往只能处理局部的语义和逻辑关系，对于全局的推理和常识表示仍然存在困难。
其次，复杂推理需要对不同层面的信息进行综合考虑，包括语义、逻辑、常识等。
Exceptional unitary representations of semisimple Lie groups, Representation Theory 1
EXCEPTIONAL UNITARY REPRESENTATIONS OF SEMISIMPLE LIE GROUPS
Received by the editors June 19, 1996 and, in revised form, August 5, 1996. 1991 Mathematics Subject Classi cation. Primary 22E46, 22E47. Presented to the Society August 7, 1995 at the AMS Summer Meeting in Burlington, Vermont. 1
q l u l u q
Let G be a simple Lie group with nite center, let K be a maximal compact subgroup, and suppose that rank G = rank K. Let g0 = k0 p0 be the corresponding Cartan decomposition of the Lie algebra, and let g = k p be the complexi cation. In this paper we investigate some representations of G rst studied in EPWW] that are closely related to a fundamental kind of discrete series representations of G. We are especially interested in the Langlands parameters associated to these representations. We begin with some background. In an e ort to nd unusual irreducible unitary representations of G in the case that G=K is Hermitian symmetric, Wallach W1] studied \analytic continuations of holomorphic discrete series." When G=K is Hermitian symmetric, p splits as the direct sum of two abelian subspaces p+ and p; , and k p+ is a parabolic subalgebra of g. An irreducible representation of K leads via this parabolic subalgebra to a generalized Verma module that is a (g K) module. If the highest weight of satis es suitable inequalities, this (g K) module arises from a holomorphic discrete series representation HC1]. Wallach W1] studied the \scalar case," in which is one-dimensional. By adjusting on the center of k, he was able to move in a one-parameter family. For values of outside the range that yields holomorphic discrete series, he determined necessary and su cient conditions for the unique irreducible quotient of the generalized Verma module to be in nitesimally unitary.
如何使用马尔可夫逻辑进行语言生成的模型评估(四)
马尔可夫逻辑是一种用于语言生成的模型评估方法，它可以帮助我们判断一个语言生成模型的好坏。
在这篇文章中，我们将探讨如何使用马尔可夫逻辑进行语言生成模型评估，并且分析其优缺点以及在实际应用中的作用。
**1. 马尔可夫逻辑模型的基本原理**马尔可夫逻辑模型是一种基于马尔可夫链的语言生成模型评估方法。
它基于马尔可夫链的理论，假设当前状态的转移概率只与前一个状态有关，与更早的状态无关。
这意味着我们可以用一个有限的状态空间和转移矩阵来描述一个语言生成模型的行为。
**2. 马尔可夫逻辑在语言生成模型中的应用**在语言生成模型中，我们可以将待评估的模型看作一个马尔可夫链的状态空间，每个状态对应一个可能的语言生成结果。
然后，我们可以利用已有的语料库数据，通过统计上一个状态到下一个状态的转移概率，来构建模型的转移矩阵。
通过这个转移矩阵，我们可以评估模型的生成结果与实际语料库的拟合程度，从而判断模型的好坏。
**3. 优缺点分析**马尔可夫逻辑模型的优点在于它简单、直观、易于理解和计算。
同时，它不需要大量的参数估计和复杂的计算过程，适用于大规模的语料库数据。
但是，马尔可夫逻辑模型也存在一些缺点，比如它假设当前状态的转移概率只与前一个状态有关，这在某些情况下可能不符合实际情况。
另外，由于马尔可夫链的状态空间是有限的，这也限制了模型对于复杂语言生成的适用性。
**4. 实际应用**在实际应用中，马尔可夫逻辑模型可以用于评估各种类型的语言生成模型，比如自然语言处理模型、机器翻译模型、对话生成模型等。
通过对模型生成结果与实际语料库的拟合程度进行评估，我们可以及时发现模型的问题并进行改进，从而提高语言生成模型的质量和效果。
**5. 总结**马尔可夫逻辑模型是一种有效的语言生成模型评估方法，它可以帮助我们判断一个语言生成模型的好坏。
虽然它存在一些局限性，但在实际应用中仍然具有重要作用。
未来，随着深度学习和自然语言处理技术的发展，我们可以预见马尔可夫逻辑模型在语言生成模型评估中的更广泛应用。
数学词汇
mapimagefixed pointcomposite functionone to one / injectiveonto / surjectivebijectiveinverse functionreciprocaldenominatorsymmetric with respect to the y axis / the origin / the line y=x abscissax/y interceptordinateanalytic geometryparabolahyperbolaconic sections 二次曲线系coefficientspoint-slope formuladirectrix 准线vertex focuslatus rectum 过焦点平行于准线的弦radius, centertangent linedegenerate 退化major axis / minor axiseccentricity e=c/adifference 差branch 支asymptotes 渐近线focal axispolynomial equationsquadratic polynomial 二次多项式quadratic formuladiscriminant判别式division algorithm / remainder theoremquotientfundamental theorem of algebra multiplicity 重根conjugate radical 共轭根the complex conjugate 共轭复数‘monic (an=1)the rational roots theoremlogarithm 对数GRE用log x表示lnx trigonometry 三角几何complementary 互余cos = complementary sinetangent / cotangent / secant / cosecant terminal side 终边quadrant 象限arbitrary angle 钝角trig function 三角函数periodicity 周期性periodequidistant 等距sequence 序列convergent / divergent(minus) infinitymonotonic 单调bounded 有界the sandwich (or squeeze) theorem approach A from above (右逼近A) continuous functionThe Intermediate Value Theorem 中值定理derivative 导数secant line 割线tangent line 切线normal line 法线differential 微分的linear appropriationimplicit differentiation 隐函数求导concave up (convex) f’’>0concave down (concave) f’’<0inflection point 拐点local minimum / absolute minimumcritical point / stationary point (f’=0) nth-derivative test fn>0 极小，反之极大adjacent sides 毗连的边relate rates dy/dt= r dx/dt indefinite integration 不定积分intersect 曲线相交rectangular (or Cartesian) coordinates polar coordinatescardioids 心形线r=2a(1+cos(sita)) solids of revolution 旋转体infinite series 无穷极数harmonic seriesp-seriesalternation seriespower seriesthe radius of convergencethe interval of convergence arccosine functionarcsine functiondomainadjoint 伴随阵determinantexpected valueprobability density function derivativeinflection pointrankeigenvalueeigenvetoreigenspacesubsetpolyhedron 多面体vertices / vertexinverse of the matrixorthogonal 正交height 多项式系数绝对值和+最高次tracepolynomialidempotent 幂等A2=Anilpotent 幂零scalar 数量阵fixed pointthe qth roots of unitycoset 陪集dot/scalar product 点积projAB B在A的投影cross producttriple scalar product （A*B）•C magnitude 模parametric equation 参数方程symmetric equation （直线）对称式generator, elements cracking p111 arbitrarylevel curve of height 等高线contour curve 轮廓线（被平面截的截面）hyperboloid 双曲面circular poraboloidcylindrical coordinatesspherical coordinatespartial derivativedirectional derivativesgradientsaddle point cracking p131Hessian matrixline integralThe Fundamental Theorem of Calculus for Line Integral 势场内线积分只与起止点有关gradient field My=Nxconservative 值与路值无关Green Theorem cracking p152ordinary/partial differential equation (ODE/PDE)homogeneous of degree n n阶齐次exact differentialintegrating function 积分因子inconsistent （线性方程组）无解commutative 交换的invertible 可逆的associative 传递性coefficient matrixaugmented matrix 增广矩阵Gaussian Eliminationechelon formparameter 参数nullspacelinear combinationspan 几个向量的所有线性组合trivial combination即linearly independentbasis a minimal spanning set for a vector space dimension 基中向量数normal vector 法向量column space / row spaceLaplace expansions 即按某行/列展开adjugate matrix 共轭矩阵Cramer’s Rule克莱莫法则scalar 数乘linear operation=linear transformationkernel / nullity / range / rankRank plus Nullity TheoremCayley-Hamilton Theorem p(A)=0 divisibility, factor, multipleprime number, compositegreatest common divisor (gcd)least common multiple (lcm)the congruence equation ax=b(mod n)the Euclidean Algorithm 欧氏算法cracking p222 congruence 余数binary operation on S S S*Sassociate ：a•(b•c)=(a•b)•c semigroup条件identity 单位元semigroup+identity=monoidmonoid+inverse=groupabelian groupgeneral/special linear groupSn symmetric group对称群（阶为n!）S3为最小的6阶非阿贝尔对称群alternating group 置换群（同上）polygon 多边形equilateral triangle 等边三角形isosceles triangle 等腰三角形Dn nth dihedral group :order(Dn)=2n additive group of integers modulo n multiplicative group of integers modulo p cyclic groupKlein four-group, or viergruppeproper subgroupnontrivial subgroupgenerators 生成元finitely generatedisomorphism 同构homomorphism 同态monomorphism 单同态epimorphism 满同态endomorphism 自同态automorphism 自同构direct product (a, b) cracking p237direct sum 同上if abelianelementary divisors/ invariant factors cracking p238normal subgruoup 正规子群inner automorphism induced by aunity 环乘法单位元unit 存在乘法逆的非零元素ring with unity 幺环commutative ringsubringcharacteristicring of integersring of integers modulo n (Zn, +, •)ring of Gaussian integers Z(i)ring of polynomials in x over R R[x]ring of real-valued functions on R RR 交换幺环evaluation (or substitution) homomorphism at a cracking p249 Frobenius endomorphism f(a)=app is a prime numberbinomial theorem 二项式定理integral domain 整环left/right zero divisor 零因子cancellation law a!=0, ac=ab, them c=bdivision ring 无零因子的环field= commutative division ring又，有限整环是域strictly-skew field= noncommutative division ring体real quatenion 四元素体Boolean ring 该环中元素idempotent subset > supersetuniversal setcomplement of B relative to A A-B union / intersectionsymmetric difference (A-B)U(B-A)Cartesian product 笛卡尔积open / closed intervalcardinality (cardinal number) 元素数countably infinitealgebraic numbers cracking p267 power set of Alevels of infinitycardinal number of continuumtranscendental numberscombination, permutationbinomial coefficientpigeonhole principle 抽屉原理probabilityBoolean algebra (or algebra) of sets on S: E指the power set of S 的子集probability measure on E cracking p274distribution functionvariance, standard deviationthe normal distribution 正态分布standard normal distributionbinomial distribution 二项分布imaginary unit iprinciple argument 幅角主值sample space (S), outcomes (S中元素), events（E中元素，S的子集）independent独立, mutually exclusive相斥Bernoulli trialspolar form, exponential formprincipal logarithmprincipal value of zwhyperbolic function 双曲函数Laplace equation / harmonic uxx+uyy=0entire function 在复平面内解析disk of convergencepunctured open disk cracking p312singularity, isolated singularitypole of order nsimple pole (n=1) double pole (n=2)essential singularityannulus 环面singular (or principal ) part / analytic partresidueHausdorff spaceindiscrete / trivial topologyinterior, exterior, boundary, limit point, closure interior+boundary=closurelower-limit topology B=[a,b)connectedcovering, open coveringcompactnessnorm of a point cracking p290 Euclidean metric 欧氏度量square metricopen map != continuous 一来一去，方向反homeomorphism = continuous + open map upper bound, bounded abovelub=suremum (sup)glb=infimum (inf)complete space = no holesLebesgue measurable setssingletonLebesgue measurable functionLebsegue integrablestep function cracking p296index of a group 子群中元素的最小公共阶tangent 相切loop 循环inradius 内径trajectory 轨迹centroid 重心clusterpartial fraction expansionsufficient / necessary condition先是issue，45分钟，完了以后紧接着argue，然后是10分钟的休息时间，你可以选择跳过。
Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transced
This definition is motivated by the following properties: 1) it is M¨ obius invariant, 2) a smooth map f : D ⊂ C → C is conformal (holomorphic or antiholomorphic) if and only if
c
1
Introduction
In this paper we discuss a very interesting and rich object: circle patterns mimicking the holomorphic maps z c and log(z ). Discrete z 2 and log(z ) were guessed by Schramm and Kenyon (see [25]) as examples from the class of s of the square grid introduced by Schramm in [24]. This class opens a new page in the classical theory of circle packings, enjoying new golden age after Thurston’s idea [26] about approximating the Riemann mapping by circle packings: it turned out that these circle patterns are governed by discrete integrable equation (the stationary Hirota equation), thus providing one with the whole machinery of the integrable system theory ([11]). The striking analogy between circle patterns and holomorphic maps resulted in the development of discrete analytic function theory (for a good survey see[13]). Classical circle packings comprised of disjoint open disks were later generalized to circle patterns where the disks may overlap. Discrete versions of uniformization theorem, maximum principle, Schwarz’s lemma and rigidity properties and Dirichlet principle were established ([19],[16],[24]). Different underlying combinatorics were considered: Schramm introduced square grid circle patterns, generalized by Bobenko and Hoffmann to hexagonal patterns with constant intersection angles in [8], hexagonal circle patterns with constant multi-ratios were studied by Bobenko, Hoffman and Suris in [7]. The difficult question of convergence was settled by Rodin and Sullivan [22] for general circle packings, He and Schramm [15] showed that the convergence is C ∞ for hexagonal packings, the uniform convergence for square grid circle patterns was established by Schramm [24]. On the other hand not very many examples are known: for circle packings with the hexagonal combinatorics the only explicitly described examples are Doyle spirals, which are discrete analogues of exponential maps [12], and conformally symmetric packings, which are analogues 1
高考英语应用文分类讨论思维
高考英语应用文分类讨论思维In the realm of human cognition, the concept of the dual nature of thought holds significant weight. Thoughts, the building blocks of our mental landscapes, exhibit a duality that manifests in both positive and negative facets.On one hand, thoughts serve as the architects of innovation and progress. They spark creativity, fuel ingenuity, and drive individuals and societies towards advancement. Positive thoughts have the power to uplift spirits, inspire action, and pave the way for transformative change. They are the seeds from which great accomplishments grow, shaping the course of history and propelling humanity forward.Conversely, the same cognitive prowess that breeds innovation can also give rise to negativity and stagnation. Negative thoughts, if left unchecked, have the potential to sow seeds of doubt, breed fear, and inhibit personal growth. They can cloud judgment, foster anxiety, and hinder individuals from realizing their full potential. The dual nature of thought is a double-edged sword, capable of both elevating andimpeding our intellectual and emotional development.In navigating the labyrinth of our minds, it is essential to recognize and harness the dual nature of thought. By cultivating mindfulness and fostering a positive mental outlook, we can steer our cognitive faculties towards constructive ends. Understanding that our thoughts possess the power to shape our reality empowers us to choose the path of growth and resilience. Embracing the duality of thought equips us with the tools to navigate life's challenges with clarity, purpose, and fortitude.中文翻译：思维的两面性在人类认知领域中具有重要意义。
Automorphisms in Gauge Theories and the Definition of CP and P
1
Contents
1 Introduction 2 Examples 3 Conditions for CP–type transformations: gauge bosons and fermions 3.1 The pure gauge sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Fermions and gauge interactions . . . . . . . . . . . . . . . . . . . . . . . 4 Automorphisms of Lc 4.1 Types of automorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Some examples of non–simple groups . . . . . . . . . . . . . . . . . . . . 4.3 Irreps and automorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The existence of CP in gauge theories and Condition B 5.1 The automorphism associated with CP . . . . . . . . . . . . . . . . . . . 5.2 Canonical and generalized CP transformations . . . . . . . . . . . . . . . 6 On the general solution of Condition B 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 On the definition of parity . . . . . . . . . . . . . . . . . . . . . . . . . . 7 CP–type transformations in the Higgs sector 7.1 Pseudoreal scalars and CP transformations . . . . . . . . . . . . . . . . . 7.2 Real scalars in complex disguise and CP transformations . . . . . . . . . 7.3 The general case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Yukawa couplings and CP–type symmetries 8.1 The condition on Yukawa couplings . . . . . . . . . . . . . . . . . . . . . 8.2 Real Clebsch–Gordan coefficients and the generalized CP condition . . . 8.3 Solutions of the generalized CP condition . . . . . . . . . . . . . . . . . . 9 C–type transformations 9.1 Charge conjugation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Compatibility of CP and C . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 An example with G = SU (2)L × SU (2)R × U (1)B−L . . . . . . . . . . . . 10 Comments and conclusions Appendices A Notation and conventions B Facts about semisimple Lie groups 3 6 12 12 14 16 16 18 19 20 20 21 23 23 26 28 28 30 33 35 35 36 37 41 41 43 45 47 51 51 52
随机分组存在的问题英语作文
随机分组存在的问题英语作文Title: Problems with Random Grouping in Educational SettingsRandom grouping, a common practice in educational settings, involves assigning students to groups without considering individual differences or specific criteria. While this method may seem efficient and fair, it often overlooks the complex dynamics of learning and social interactions, leading to several problems that can hinder educational outcomes and student satisfaction. In this essay, I will discuss the main issues associated with random grouping and suggest more nuanced alternatives.One significant issue with random grouping is the potential for heterogeneity in skill levels within groups. When students are assigned randomly, there is a risk of placing high-performing students together with low-performing ones. This can lead to situations where stronger students may do most of the work, while their peers disengage or rely on others to carry the weight of the group's tasks. Conversely, groups composed of predominantly struggling students may lack the collective knowledge and skills needed to complete tasks effectively, leading to frustration and diminished learningoutcomes.Another problem arises from the lack of consideration for social dynamics. Random grouping does not account for interpersonal relationships, personalities, or conflicts between students. Placing students who do not cooperate well into the same group can create tension and conflict, undermining the collaborative spirit intended by group work. Personal compatibility plays a crucial role in effective teamwork; ignoring these factors can derail the group process and result in a suboptimal learning environment.Moreover, random grouping often ignores students' preferences and interests. Students bring diverse backgrounds, experiences, and motivations to the classroom. Engaging students in group selection processes can help foster a sense of ownership and commitment to the group's success. When students are involved in choosing their group members or at least selecting their roles within a group, they are more likely to feel valued and motivated to contribute positively to the group's activities.In addressing these issues, educators might consider alternative grouping strategies that take into account student abilities, social dynamics, and personal interests. For instance,adopting a "mixed-ability" grouping approach could balance skill levels while still allowing for diversity within groups. Additionally, utilizing team-building activities at the beginning of a project can help establish positive social dynamics, regardless of how the groups were formed. Furthermore, giving students some autonomy in group formation can enhance engagement and respect individual preferences.In conclusion, while random grouping may seem like a straightforward solution for organizing students, it often presents more problems than benefits. By recognizing the complexity of classroom dynamics and embracing more thoughtful grouping strategies, educators can create a more supportive and effective learning environment that caters to the diverse needs of their students. It is essential to strive for methods that optimize both academic achievement and the social experience of education, ensuring that all students have the opportunity to thrive in collaborative settings.。
英文拼写纠错 预训练模型
英文拼写纠错预训练模型随着科技的发展，许多拼写纠错的工具和技术都有所改进。
今天我们要谈论的是神经机器翻译中的一个技术：英文拼写纠错预训练模型。
英文拼写纠错是自然语言处理中一个重要的任务，广泛应用于电子邮件、搜索引擎、聊天机器人等领域。
传统的基于词典的拼写纠错方法，经常会遇到词语识别的问题，因此需要借助从历史文本中收集的大规模语料来解决拼写纠错问题。
英文拼写纠错预训练模型是基于神经网络的一种解决方案，它可以有效地检测出输入文本中存在的拼写错误，并且可以提出修改建议。
该模型不仅可以有效地检测出拼写错误，还可以检测出把词汇拼写错误，以及错误重新组合成组合语句错误等。
模型的大致架构如下：首先，我们使用语料库将句子进行分词，然后使用神经网络模型对分词后的句子中的每一个分词进行编码，编码过程使用到了词向量，词向量是自然语言处理中非常重要的一部分，它可以把一个词表示成一个实数向量，从而有效地表示出该词的相关概念。
接下来，使用具有多层卷积神经网络的序列模型对编码后的词向量进行提取，当模型经过训练后，它便可以检测出输入文本中存在的各种拼写错误，并提出相应的修改建议。
此外，这种英文拼写纠错预训练模型还可以用于多任务的自然语言处理任务，比如问答系统、机器翻译等。
除了可以检测出拼写错误，该模型还可以用于语义理解任务，它可以捕捉出句子中字面理解和标点错误，使得自然语言处理过程变得更准确。
综上所述，英文拼写纠错预训练模型是一种建立在神经网络模型上的解决方案，可以有效地检测出输入文本中存在的拼写错误，并且支持多任务自然语言处理任务，它不仅可以有效地检测出拼写错误，还可以检测出词汇拼写错误，以及错误重新组合成组合语句错误等。
可见，英文拼写纠错预训练模型在自然语言处理领域具有非常重要的应用价值，可以提供准确、可靠的拼写纠错服务，为自然语言处理应用提供精确、可靠的基础。
对偏科展开讨论英语作文
对偏科展开讨论英语作文English:Having a tendency to specialize in a particular subject or skill can have both advantages and disadvantages. On one hand, being able to focus on a specific area allows individuals to become experts in that field, leading to a deeper understanding and greater success. For example, someone who excels in mathematics may go on to pursue a career in finance or engineering, where their specialized knowledge sets them apart from others. However, this kind of specialization can also have downsides. It may limit one's opportunities for growth and development in other areas, potentially leading to a lack of well-rounded knowledge or skills. In today's fast-paced and ever-changing world, versatility and adaptability are becoming increasingly important, making it essential for individuals to have a broad range of abilities.Translated content:在某一特定学科或技能上有偏向性既有优点又有缺点。
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ON AUTOMORPHISM GROUPS OFSIMPLE ARGUESIAN LATTICESE.T.SCHMIDTAbstract.Let G be a group.In this paper we prove that there exists a simplearguesian lattice M whose automorphism group is isomorphic to G.A lattice L is called interval…nite,if every interval of L is…nite.In this note we give a new proof of a theorem of Christian Herrmann[3].This theorem was proved by G.Grätzer and E.T.Schmidt[2]for…nite groups and later by Christian Herrmann[3]in the present form.Theorem.Every group G can be represented as the automorphism group of an interval…nite,simple,arguesian lattice M.Let G be a given group.By R.Frucht[1],there exists an undirected graph h V;E i with no loops whose automorphism group is isomorphic to G(that is,V is a set and the set E of edges is a subset of two-elements subsets of V).We begin our construction with this graph.We consider…rst a vector space V over the two element…eld Z2with a basis V0. We assume that V and V0have the same cardinality,i.e.j V j=j V0j.Then we can identify the vertices of the graph with the basis elements of this vector space,that means,we can consider the elements v0;v1;v2;:::of V as the basis elements of the vector space V.Let A be the lattice of all…nitely generated subspaces of the vector space V.This lattice A is obviously a simple,atomistic,arguesian lattice.The vector space V is over the two element…eld Z2,consequently every line contains three points.The subspace generated by v i will be denoted by the same letter v i. The lattice A has the following three types of atoms:1.The atoms v i,i2I(i.e.the elements of the basis),these form the set V andI an arbitrary index set;2.Consider the third point v i+v j(i;j2I)of the line v i;v j spanned by v i andv j.Some of these v i+v j-s correspond to edges of the graph(i.e.f v i;v j g isa edge),in this case v i+v j will be denoted by v ij.All these atoms form asubset W;3.All other atoms.We consider the given G as a subgroup of the automorphism group of A To the vertices of the Frucht graph correspond the atoms v i2V;i2I and to the edges f v i;v j g correspond the atoms v ij,these determine the edges in V.Obviously, every permutation of the v i-s can be extended to an automorphism of A and every Date:July10,1998.1991Mathematics Subject Classi…cation.Primary06C05;Secondary08A35.Key words and phrases.Automorphism group,lattice,simple,modular,arguesian.The research of the author was supported by the Hungarian National Foundation for Scienti…c Research,under Grant No.T023186.12 E.T.SCHMIDTautomorphism of A is determined by its restriction to the basis V.Indeed,if®and¯are two automorphisms of A such that their restrictions to V are the same,then the restriction of°=®¯¡1is the identity map"of V.By any extension of"(i.e. automorphism with the property that its restriction to V is")the atoms v i andv j are…xed elements,conseqently v i+v j must be…xed.Similarly,(v i+v j)+v k must be a…xd element.In this way we get that by an extension of"all atoms are …xed elements which means that this extension is the identity mapping of A.It follows that all automorphisms with the property that V and W are invariant form a group isomorphic to G.To ensure that we have no more automorphisms than the graph we must label the vertices and the edges,i.e the atoms v i2V and v ij2W. This will be done by lattices which are glued to A.The idea of the gluing is the following.The ideal(v i]of A has two elements.We will de…ne a special lattice F1 with a two element dual ideal D1which is therefore isomorphic to(v i].Similarly, for every v ij2W we use a lattice F2with the dual ideal D2.For every i2I we consider an isomorphic copy F1i of F1with the dual ideal D1i and similarly the lattices F2ij»=F2with the dual ideal D2ij.We can apply the gluing construction for the lattices A,F1i and F2ij simultaneously,identifying the ideal(v i]with D1i and(v ij]with D2ij.On this way we get a join-semilattice and M is the arguesian lattice generated by this con…guration.First we de…ne the lattices F1,F2.We give the description of M as a sublattice of a vectorspace lattice and prove that this is a simple arguesian lattice with the given automorphism group.N is the chain of all nonnegative integers and N¤denotes the chain of the nonpositive integers.Take the direct product C2£N¤,(where C2denotes the two element lattice).In this direct product for every i2N the elements(0;¡i¡1);(1;¡i¡1);(0;¡i);(1;¡i)form a“covering square”(isomorphc to C2£C2).Into these“covering squares”,for i=0;1;:::we insert one more elemwnt z i so that a copy of M3,the…ve element non distributive modular lattice,is obtained.The resulting lattice is F1,see Figure1a.The lattice F2is similar but we don’t insert z0,into the…rst“covering square”,see Figure1b.The dual ideal consisting of (0;0)and(1;0)etc.of F1is D1.We use isomorphic copies of F1and F2to label the v i-s and the v ij-s.AUTOMORPHISMS OF SIMPLE ARGUESIAN LATTICES3 F1is a simple arguesian lattice and it has exactly one nontrivial automorphism ®,where®(z0)=(0;0)and®(0;0)=(z0).F2is a rigid(has no nontrivial au-tomorphism)arguesian lattice,its congruence lattice is the four element Boolean lattice.We de…ne our lattice M as a sublattice of a vectorspace lattice K=L(W)of a vectorspace W over Z2.Take the set f u j k;v j;j2I;k2N g as a basis of W. Let z j k be the third point of the line spanned by u j k and v j.De…ne the following subspaces,(where[X]denotes the subspace spanned by the set X):o=[u j k;j2 I;k2N];v i=[v i;u j k;j2I;k2N]=[v i;o].The convex sublattice of K, generated by(as lattice)v i-s form a sublattice isomorphic to A,we identify A with this sublattice.Set u i0=o;u i1=[u j k;j2I;k2N;u j k=u i0];u i2=[u j k;i2I;k2N;u j k= u i0;u i1]:::.Then u i0>u i1>u i2>:::is a a chain of type!¤.The convex sublattice generated by these chains will be denoted by C.Take the sublattice A[C,then A is a dual ideal and C is an ideal of this lattice.We adjoin further elements w i0;w i1;w i2;:::and z i1;z i2;z i3:::,which are de…ned as follows:.w i1=[u i1;v i];w i2=[u k2;v i];w i3=[u k3;v i]:::andz i1=[u i1;z i1];z i2=[u i2;z i2];z i3=[u i3;z i3]:::.Then the join of the chains u i0>u i1>u i2>:::and w i0>w i1>w i2>::: form a sublattice isomorphic to C2£N¤.For every j,u i j;z i j+1and w i j+1generete M3.For every i2I all these elements form a sublattice,the‡ap F1i=f u i0;u i1;u i2:::g[f w i0;w i1;w i2:::g[f z i1;z i2;z i3:::g isomorphic to the lattice F1.Similarly,we de…ne for the elements v ij the‡apsF2ij=f u ij0;u ij1;u ij2:::g[f w ij0;w ij1;w ij2:::g[f z ij2;z ij3;z ij4:::g isomor-phic to F2.Let M be A[C[(F1i;F2ij j i;j2I).M can be vizulised as follows:Figure2It is easy to see that M is a sublattice of K.The lattice K is an arguesian lattice, consequently M is again arguesian.We prove that.M is simple.We know that A4 E.T.SCHMIDTand the F1i-s are simple lattices and the intervals[u i k;u i k+1]and[u j k;u j k+1]resp. [u ij k;u ij k+1]and[u j k;u j k+1]are projective in C.These imply that any two prime intervals are projective,which proves that M is a simple lattice.M contains the chains w i1>w i2>w i3>:::and w ij0>w ij1>w ij2:::, where w i1;w i2;:::resp.w ij1;w ij2:::,(i;j2I)are meet irreducible elements.and M has no other chains of this type.Then for any automorphism the image of w i1 must be w j1for some j and similarly the image of u ij1is some u kl1.This yields that the restriction of an automorphism to the atoms of the dual ideal A of M is a permutation,where V and W are invariant.This proves that the automorphim group of M is isomorphic to G.References[1]R.Frucht,Herstellung von graphen mit vorgegebener abstrakter pos.Math.6(1938),239–250.[2]G.Grätzer and E.T.Schmidt,On…nite automorphism groups of simple arguesian lattices,Submitted for publication in Studia Sci.Math.[3]Ch.Herrmann,On automorphism groups of Arguesian lattices,Acta Math.Acad.Sci.Hungar.,Mathematical Institute of the Technical University of Budapest,M½u egyetem rkp.3, H-1521Budapest,HungaryE-mail address:schmidt@math.bme.huURL:http://www.bme.math/˜schmidt/。