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# Population Structure Promotes the Evolution of Intuitive Cooperation and Inhibits Deliberation

Scientific Reportsvolume 8, Article number: 6293 (2018) | Download Citation

## Abstract

Spatial structure is one of the most studied mechanisms in evolutionary game theory. Here, we explore the consequences of spatial structure for a question which has received considerable empirical and theoretical attention in recent years, but has not yet been studied from a network perspective: whether cooperation relies on intuitive predispositions or deliberative self-control. We examine this question using a model which integrates the “dual-process” framework from cognitive science with evolutionary game theory, and considers the evolution of agents who are embedded within a social network and only interact with their neighbors. In line with past work in well-mixed populations, we find that selection favors either the intuitive defector strategy which never deliberates, or the dual-process cooperator strategy which intuitively cooperates but uses deliberation to switch to defection when doing so is payoff-maximizing. We find that sparser networks (i.e., smaller average degree) facilitate the success of dual-process cooperators over intuitive defectors, while also reducing the level of deliberation that dual-process cooperators engage in; and that these results generalize across different kinds of networks. These observations demonstrate the important role that spatial structure can have not just on the evolution of cooperation, but on the co-evolution of cooperation and cognition.

## Introduction

Understanding the evolution of cooperation, which is collectively beneficial but individually costly, is a major focus of research in a wide range of fields including computer science, psychology, economics, and evolutionary biology. To that end, a great deal of work has illuminated various mechanisms which can promote the evolution of cooperative behavior1. In recent years, work on the evolution of cooperation has begun to consider not just cooperative or non-cooperative choices, but also the cognitive processes underlying these choices2,3,4 (for a mini-review, see ref.5). This work has explored cognition using the “dual-process” framework6,7,8,9, in which decisions are made based on two different cognitive processes: (1) Automatic, intuitive and relatively effortless yet inflexible processes; versus (2) controlled, deliberate and relatively effortful but flexible processes.

Motivating the theoretical investigation of intuition, deliberation and the evolution of cooperation is a body of empirical work using economic game experiments10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31. In these studies, participants make incentivized choices about paying costs to benefit others, and are experimentally induced to rely relatively more on intuition or deliberation. For example, participants may be placed under time pressure, made to complete another cognitively demanding task while making their decision, or simply asked to respond using their intuition or careful reasoning. A meta-analysis of studies examining positively non-zero-sum cooperation games of the type typically studied in evolutionary game theory models (e.g., the Prisoner’s Dilemma, PD) found that intuitive gut responses tend to support cooperation, while deliberation undermines cooperation in games where defection is strictly payoff-maximizing (e.g., 1-shot PDs) but supports cooperation in games where cooperation can pay off (e.g., repeated games)32. [Note that while a subsequent multi-lab pre-registered replication project raised questions about a causal effect of time pressure on cooperation in 1-shot social dilemmas11, 66% of participants in the time pressure condition of those experiments did not respond within the allotted time12, and a more recent pre-registered study solved this non-compliance problem and confirmed prior conclusions that cooperation was higher under time pressure than time delay24]. Similar results regarding intuitive cooperation were also found in a field experiment on real-world helping behavior33, and when analyzing interviews with people who risked their lives to save strangers34. This pattern of results was explained by a verbal theory, the Social Heuristics Hypothesis (SHH)16,35. The SHH postulates that typically advantageous (i.e., long-run payoff maximizing) behaviors become automatized as intuitive default responses, whereas deliberation can override these intuitive defaults to better match the strategic details of the current situation at hand.

Evolutionary game theoretic models of the co-evolution of cognition and cooperation sought to explore this question formally, conceptualizing intuition versus deliberation as a trade-off between ease and flexibility, and asking what intuitive and deliberation behaviors would be favored by natural selection2,3,4. The results have indicated that when future consequences are sufficiently likely, natural selection favors a “dual-process cooperation” strategy that accords with the experimental results: this strategy is intuitively predisposed to cooperate, but uses deliberation to overrule that predisposition and instead defect when doing so is payoff-maximizing (e.g., in 1-shot anonymous interactions).

This prior work on the co-evolution of cooperation and cognition, however, has only considered well-mixed populations. A separate (and much older) line of work examining structured populations has shown that the topology of interaction affects the evolution of cooperation36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53. In particular, non-random interactions can facilitate the evolution of cooperation, even allowing cooperation to succeed in 1-shot Prisoner’s Dilemma games. Experimental work has also explored the role of structure, and although some studies have found little impact of structure on cooperation54,55,56,57,58,59,60, it has been shown that structure does promote cooperation when particular theoretically-derived conditions are satisfied61.

None of this work on population structure, however, has considered the role of intuition versus deliberation. Here we bridge these two approaches to investigate the effect of interaction structure on the co-evolution of cognition and cooperation. We explore conditions (network structures and frequency of one-shot versus repeated games) under which natural selection favors costly deliberation over intuition, as well as cooperative over selfish intuitive responses. In doing so, we shed light on the role of network structure in shaping not only our actions, but also the thought processes that give rise to those actions.

To do so, we adapt a model of the co-evolution of cooperation and cognition proposed for well-mixed populations2. In each generation, agents play a series of Prisoner Dilemma (PD) games in which they can either choose to always defect (ALLD) or to play the reciprocal strategy tit-for-tat (TFT) which cooperates in the first period and then copies the partner’s move from the previous period. The PD games come in one of two types: with probability 1-p it is a one-shot anonymous game (in which defecting is strictly payoff-maximizing); whereas with probability p it is an infinitely repeated game (such that it is payoff-maximizing to play the same strategy as the partner). Cognition is modeled as follows. In each game, each agent can either choose her strategy using a generalized intuitive strategy that is independent of the game type; or she can pay a cost (stochastically sampled decision-by-decision) to deliberate and tailor her strategy choice to whether the game is one-shot or repeated. Thus, each agent has a strategy vector that contains the following four elements: S i , the probability of TFT when the agent decides intuitively and is agnostic to the game type; S 1 , the probability of TFT in one-shot PDs when the agent deliberates and tailors her strategy; S r , the probability of TFT in repeated PDs when the agent deliberates and tailors her strategy; and T, the maximum cost which the agent is willing to pay to deliberate. In each interaction, the agent’s cost of deliberation (d*) is drawn from a uniform distribution [0,1]. The cognitive processing mode (intuition versus deliberation) is then determined by the cost threshold T: if d* ≤ T, the agent pays the cost and deliberates, and if d* > T, the agent plays both games with the same generalized strategy S i .

Our key contribution is to add interaction structure to this model. We do so by specifying a network where agents are represented as nodes and only interact with their immediate neighbors, and where agents update their strategies using the death-birth process with exponential fitness. In this evolutionary dynamic, each generation every agent has a fixed strategy vector and accumulates payoffs across games with all of her neighbors; and then at the end of each generation, an agent is randomly selected to update, and her strategy is replaced with a neighbor selected proportional to an exponential function of the neighbors’ game scores (or, with probability u, a mutation occurs and a randomly drawn strategy is substituted instead)62. This process can represent either genetic evolution, in which case the updating agent dies and the replacing agent reproduces, or cultural evolution/social learning, in which case the updating agent imitates the replacing agent’s strategy. Within this model setup, we examine the influence of population structure on the coevolution of cooperation and cognition by determining the impact of varying the average number of neighbors on the evolutionary outcomes.

## Results

We begin by examining the evolutionary outcomes on cycles, networks in which each agent is connected to k/2 neighbors on each side (for a total of k neighbors). In particular, we consider the average value of each strategy parameter in steady state, and ask how these values vary based on p (probability of repeated games) and k (number of neighbors). Figure 1A shows the average value of S i (intuitive response) as a function of p and k. To summarize the impact of k on S i , we fit a Sigmoid function to the S i curve for each value of k and then use that to find the critical value of p at which S i equals 0.5 (which we refer to as p*) - representing the probability of repeated games at which the predominant intuitive strategy transitions from defection to cooperation (Fig. 1B). Figure 2A shows the value of the deliberation cost threshold T as a function of p for different values of k, and Fig. 2B summarizes the results by showing the maximum value of T over all p’s (T max ) for each value of k.

We see that for high values of k (highly connected networks) the results match those found previously in well-mixed populations2: For low values of p, intuitive defectors (ID) who never deliberate (S i  = 0, T = 0) are dominant (deliberative strategies S 1 and S r rarely used and thus dominated by neutral drifted around 0.5 - Fig. 3); but once p becomes sufficiently high, the dual-process cooperator (DC) strategy (S i  = 1, S r  = 1, S 1  = 0, T = c(1-p)) dominates (and as T approaches 0, S 1 and S r are used less and less, and thus get pulled back towards 0.5 by neutral drift - Fig. 3).

As the number of neighbors in the network (as thus density of connections) decreases, however, we observe marked impacts on both S i and T: the emergence of the dual-process cooperator strategy (S i  = 1) takes place at lower values of p, and these dual-process cooperators engage in less deliberation (T max decreases). These results are visualized more fully in Fig. 4, which shows heatmaps of S i and T as a function of k and p. In sum, we see that as in the well-mixed population, there are only two dominant strategies: for high values of k and low values of p the intuitive defectors (ID) who never deliberate are dominant, while for low values of k and high values of p the dual-process cooperator (DC) strategy dominates. Rather than introducing new successful strategies, interaction structure makes it easier for the DC strategy to succeed, and reduces the amount of deliberation DC agents are willing to engage in.

So far, we looked at the evolutionary dynamics on cycles with homogeneous structure. We now demonstrate the robustness of our results to considering various network structures that are heterogeneous (i.e., not all agents have the same number of neighbors).To do so, we generated heterogeneous networks using the following network models: Watts-Strogatz Small-World63, Barabási-Albert Scale-Free64, and Erdős-Rény65 random networks. Figure 5 summarizes how changing average degree k influences the evolutionary outcomes for each network structure. We see that p* and Tmax follow an extremely similar pattern across all network structures, showing that our results are robust to heterogeneous networks. Furthermore, the extreme level of similarity suggests that the effect of structure on the coevolution of cooperation and cognition is mainly driven by the sparsity of connections within the network, rather than other properties of the network structure.

## Discussion

Our results demonstrate how network topology, and in particular sparsity of connections, can have an important impact on the co-evolution of cooperation and cognition: a small number of neighbors per agent results in higher cooperation even when repeated interactions is rare; it also increases the tendency of agents to rely more on intuitive impulses. This was true across a range of different network structures. More broadly, our results show the robustness of dual-process cooperation to relaxing the unrealistic assumption of random matching: even in structured populations, evolution only ever favors agents who (i) always intuitively defect, or (ii) are intuitively predisposed to cooperate but who, when deliberating, switch to defection if it is in their self-interest to do so. However, the specific conditions under which this transition between the two strategies occurs depends strongly on the network structure, with more spare networks allowing dual-process cooperation to dominate for lower probabilities of repeated games; and the specifics of the dual-process strategy also varying with population structure, such that more sparse networks lead to less willingness to deliberate.

Why is this so? Reducing the number of neighbors (k) in the cycle leads to greater assortment66: When agents only interact with their neighbors in a sparse network, the emergence of clusters in which agents interact with other agents who have similar strategies is facilitated. Formation of clusters helps cooperators to more likely interact with other cooperators and collect mutual benefits of cooperation. This increases cooperators’ payoffs relative to defectors and helps stabilize cooperation. Hence, decreasing k makes cooperation more beneficial in the 1-shot game and results in transition to DC for lower values of p. For very low values of k (k < b/c, where b and c are, respectively, benefit and cost of cooperation42) the favored strategy is always cooperation across all p values. This increase in assortment also reduces the value of deliberation (and thus reduces the cost that agents are willing to pay to deliberate T), because as the likelihood that your partner has the same strategy as you increases, it becomes less beneficial to switch to defection in 1-shot games: strategies that switch to defection will wind up interacting with other strategies who also defect. The results we present here using structured populations correspond nicely to prior work2 who vary assortment mathematically, without explicitly modeling population structure.

In our model, we made the simplifying assumption that the cost of deliberation was drawn from a uniform distribution, which has been shown to influence the evolutionary dynamics3: other distributions allow the success of a strategy which intuitively defects and uses deliberation to cooperate in repeated games. Considering the impact of network structure with alternative distributions of deliberation costs is therefore an important direction for future research. Similarly, we assumed that intuition was totally insensitive to context whereas deliberation was perfectly sensitive. As previous work has shown that allowing intuition to be somewhat sensitive to context can allow the success of a “dual-process attender” strategy which distinguishes between one-shot and repeated games even when using intuition4, the interaction between context-sensitive intuition and spatial structure is also an important direction for future work.

Another promising extension is to consider a case where the probability of repeated game is not the same for all agents, but it is a function of the way agents are connected through the network: In real world settings, people who are interacting within a densely connected community are more likely to be engaged in interactions that carry future consequences while people who are socially distanced from each other are less concerned about their future interactions. Hence, making the value of p heterogeneous as a function of agents’ local structure can be a natural future direction. It would also be informative to consider the coevolution of cooperation and cognition on dynamic networks, where there structure is not fixed but instead can evolve over time or can be altered by the agents67. Finally, our findings regarding the impact of interaction structure on the co-evolution of cognition and cooperation also suggest that extending models of the evolution of intuition and deliberation in anti-coordination contexts (e.g., using snowdrift games) and in non-cooperative contexts68,69,70 to include non-random interactions will be a valuable direction for future work. The topology of interaction is a key feature of our world, and has important impacts on both how we act and how we think.

## Model

Our results are produced using agent-based simulations. In our simulations, agents play with and adopt strategies of their immediate neighbors in the network with population size N = 100. In each encounter between two agents, the players can choose to either play TFT or ALLD. With probability p the game is a 1-shot PD with payoff matrix $$[\begin{array}{cc}R=(b-c) & S=-c\\ T=b & P=0\end{array}]$$ and with probability (1-p) they play an infinite repeated PD where agents play the stage-game from the 1-shot PD each period, yielding average payoff per round of $$[\begin{array}{cc}R=(b-c) & S=0\\ T=0 & P=0\end{array}]$$ where b = 4 and c = 1 in our simulations. The strategy of agent $$i\in \{1,\ldots ,N\}$$ is characterized by $${s}_{i}=({S}_{i}^{i},{S}_{r}^{i},{S}_{1}^{i},{T}^{i})$$ specifying the behavior of the agent when she decides intuitively (TFT with probability $${S}_{i}^{i}$$ independent from the game type) and when she decides deliberately (TFT with probability $${S}_{1}^{i}$$ in the 1-shot game and TFT with probability $${S}_{r}^{i}$$ in the repeated game). $${T}^{i}$$ determines the maximum cost which the agent is willing to pay to deliberate: In each interaction, a random cost d* is drawn from uniform distribution [0,1], if d* ≤ T i the agent deliberates and tailors her strategies and plays TFT in the 1-shot game with probability $${S}_{1}^{i}$$ and plays TFT in the repeated game with probability $${S}_{r}^{i}$$, otherwise she uses the intuitive strategy and plays TFT with the same probability $${S}_{i}^{i}$$ regardless of game type. Once all agents have completed interactions with all their neighbors, payoffs are calculated and evolution occurs. We use Moran death-birth process with exponential payoff function. In each generation, an agent i is randomly selected to change strategy. The agent i adopts the strategy of another agent j in the neighborhood who is selected with probability $$W({s}_{j}\,\to {s}_{i})=\exp (w{\pi }_{j})$$ where $${{\rm{\pi }}}_{j}\,\,$$is the averaged expected payoff of agent j by her degree and w is the selection intensity. With probability u mutation occurs and instead a random strategy is chosen. In our simulations, we used w = 4 for the selection intensity (strong selection) and u = 0.01 for mutation rate.

To generate homogenous networks, we used cycles where the number of neighbors for each node $${\rm{k}}\in [2,4,\ldots ,40]$$. To generate heterogeneous network structures with varying average degree, we used the following network models: Watts-Strogatz Small-World networks where the number of neighbors for each node in the ring structure $${\rm{k}}\in [2,4,\ldots ,40]$$ and rewiring probability $${{\rm{p}}}_{{\rm{rw}}}=0.2,\,\,$$Barabási-Albert Scale-Free networks where the number of edges to add in each time step $$m\in [1,2,\ldots ,23]$$, and Erdős-Rényi random networks where probability of edge creation $${{\rm{p}}}_{{\rm{ec}}}\in [0.02,0.04,\ldots ,0.4]$$. We ran the simulations for different values of p (discretized with resolution 0.1) on each network structure. At the beginning of each simulation run, each agent’s strategy is initialized from independent uniform distributions. Each simulation run continued over a number of generations until no more than one agent updates its strategy for a consecutive window of 104 generations, as in prior work71,72. To enhance convergence, we considered a noise threshold of ε = 0.05 for strategies difference below which agents do not adopt a new strategy. All results are averaged over 1000 initializations. The simulations were done in parallel using the Yale computing cluster.

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Tomlin, D. A., Rand, D. G., Ludvig, E. & Cohen, J. D. The evolution and devolution of cognitive control: The costs of deliberation in a competitive world. Sci. Rep. 5, 11002 (2015).

71. 71.

Gianetto, D. A. & Heydari, B. Network Modularity is essential for evolution of cooperation under uncertainty. Scientific reports 5 (2015).

72. 72.

Mosleh, M. & Heydari, B. Fair Topologies: Community Structures and Network Hubs Drive Emergence of Fairness Norms. Scientific Reports 7 (2017).

## Acknowledgements

We gratefully acknowledge helpful comments from Adam Bear, and funding the Templeton World Charity Foundation (grant no. TWCF0209), the Defense Advanced Research Projects Agency NGS2 program (grant no. D17AC00005), and the National Institutes of Health (grant no. P30-AG034420).

## Author information

### Affiliations

1. #### Department of Psychology, Yale University, New Haven, CT, 06511, USA

• Mohsen Mosleh
•  & David G. Rand
2. #### Department of Economics, Yale University, New Haven, CT, 06511, USA

• David G. Rand
3. #### School of Management, Yale University, New Haven, CT, 06511, USA

• David G. Rand

### Contributions

M.M. and D.G.R. designed the research, M.M. performed the research and analyzed the data, and M.M. and D.G.R. wrote the paper.

### Competing Interests

The authors declare no competing interests.

### Corresponding authors

Correspondence to Mohsen Mosleh or David G. Rand.

### DOI

https://doi.org/10.1038/s41598-018-24473-1


text:
## 12 HL: The Standard Normal Distribution

Complete the following questions before our next class.

It is know that the foot size, $$X$$of a Tyrannosaurus rex is normally distributed with $$\textrm{P}(X\geq 70)=0.43$$ and $$\textrm{P}(X\leq 30)=0.24$$. Find the mean and standard deviation of the Tyrannosaurus rex foot size.

You can have some time in class tomorrow to work on the questions below, but you should get a start on these tonight. (Also, we’ve now finished the chapter on continuous probability distributions!)

Exercise 28E.1 question 1
Exercise 28E.2 questions 3, 4abde, 5
Exercise 28F.1 questions 6 and 9
Exercise 28F.2 questions 5 and 9

## 12 HL: The Normal Distribution

Complete the following questions before our next class.

Exercise 28C.2 questions 3abd, 4
Exercise 28D.1 questions 1, 3, 6
Exercise 28D.2 questions 1, 3, 6 (why does question 6 not involve a normal distribution?), 8, 10

## 11 SL: Double Angle Identities

Complete the following questions before our next class.

(black book)
Exercise 9D questions 2–6, 9ace, 12ab, 16

## 12 HL: Continuous Probability Distributions

Complete the following questions before our next class.

Exercise 27H questions 2, 3, 5
Exercise 28A questions 1, 6, 8, 9
Exercise 28B questions 1, 2, 4, 7, 12 (long!)

## 11 SL: Trigonometric Equations

Complete the following questions before our next class.

(black book)
Exercise 9B questions 1 and 5 (word problems)
Exercise 9C.1 questions 1d, 2ad
Exercise 9C.2 questions 1 (first column), 2ade
Exercise 9C.3 questions 1 (first column), 2a, 3ad, 4ace

## 11 SL: The Ambiguous Case + Trigonometry Problems

Complete the following questions before our next class.

Exercise 8F (red book) questions 1 and 3
Exercise 8E (red book) questions 1, 5, 8, 10, 14

## 12 HL: The Binomial Distribution

Complete the following questions before our next class. (Give the calculator questions a try, but don’t worry if you get stuck, as we’ll talk about those in class.)

Exercise 27F questions 1, 3, 6
Exercise 27G questions 1, 3, 5, 8, 11

## 12 HL: Properties of the Expectation Function

Complete the following questions before our next class.

Exercise 27E questions 1–3, 5

## 12 HL: Variance and Standard Deviation for Probability Distributions

Complete the following questions before our next class.

Exercise 27D questions 1, 4, 8, 10

## 11 SL: The Cosine Rule

Complete the following questions before our next class.

(Red Book) Exercise 8C questions 1abc, 2, 6, 9

format: plain


text:
$$~$$

I am a postdoc at the University of Lausanne and pricing actuary at Vaudoise Assurances. My research interests include statistical theory and practice, actuarial modelling and probability theory.

$$~$$


text: Students should have the ability to solve linear equations, convert linear equations to the slope/intercept form, and graph linear equations in the slope/intercept form. Solving quadratic equations by factoring. This section of the site will give access to different systems of linear equations worksheets. Solving quadratic equations by completing square. Systems of Linear Equations Three Variables Including solving systems of linear equations by substitution worksheet doc, system of linear equations word problems worksheet pdf, algebra 2 systems of linear equations worksheet answers, solving systems of linear equations by graphing worksheet lesson 8 1, solving systems of linear equations by substitution worksheet answers, image source: … CBSE Class 8 Linear Equations in One Variable Worksheet (1) Worksheets have become an integral part of the education system. D. Russell. 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text:
## staceyyyy1 3 years ago Find The Value Of: 3 Times X Over The Square Root Of X Cubed.

1. campbell_st

$\frac{3x}{\sqrt{x^3}}$ it can't be solved but it can be simplified $\frac{3x}{\sqrt{x^2 \times x}} = \frac{3x}{x \sqrt{x}}$ cancel the common factor of x leaves $\frac{3}{\sqrt{x}}$

2. staceyyyy1

THANK YOU!!(:


text:
By Sammarize, 6 years ago, translation, ,

Hello!

Welcom to the todays round! Note that this is last possibility to training before VK Cup on Codeforces — don't miss your chance! I hope, everybody will find interesting problems for him, you will not have misunderstanding with statements and there will have a harmony beteen your your solutions and our tests.

I'm an author of todays round. My name is Valeriy Samoylov, a graduated student of SPb SU. I want to thank Artem Rakhov (RAD) and Gerald Agapov (Gerald) for great help in investigation of problems.

And so I want to thank Maria Belova for translation of the statements and Alexanber Kouprin (Alex_KPR) for the statement prereading and the picture =)

Please, pay attantion to unusual problems cost in the first division:

500 — 1000 — 1500 — 2500 — 2500

And without surprise in the second division:

500 — 1000 — 1500 — 2000 — 2500

Good luck for all!

Round is postponed to 30 minutes by technically reasons. Registration is ending in 21:25.

•
• +118
•

By MikeMirzayanov, 6 years ago, translation, ,

### Overview

The VK Cup Championship is an open computer programming competition that is held by VK, Codeforces and Saratov State University. VK is the largest European social network with more than a 100 million active users. The Championship Final Round will be held in July in St. Petersburg. Top 50 contestants of the Round 3 will be invited to the Finals, with trip expenses covered by the organizing committee.

### Eligibility

You are young and you like to solve programming problems? Then this championship is for you! Anyone meeting the following criteria is eligible to compete in the VK Cup:

• must be at least 14 years and at most 23 complete years of age (by the moment of registration);
• current employees of VK and/or members of organizing committee/jury are ineligible to participate in the VK Cup;
• must be eligible for participation in Codeforces contests.

Thus, the intended audience of the championship are mainly high school and university students. To participate in the championship, you have to register beforehand.

Only individuals are allowed to take part in the Championship. No teams, no joint discussions and etc.

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• +436
•

By Nickolas, 6 years ago, translation, ,

Anybody feels like sharing the thoughts about Challenge24 online round? Like who was in which team and who solved what? I miss the detailed information — participants' countries and total points earned is too little :-)

Here is the list of teams known so far:

Place Team Team members
1 Havka-papstvo Egor, Petr, pashka
4 Charles_University_Legion fhlasek, mimino, k21
5 Progopedia maksay, kit1980, Nickolas
8 Unpretired Michael, ilyakor, Vasiliy Astahov
9 DrinkLess arseny30, valich, levlam
13 _NiN_ ashmelev, mmatrosov, Anton Demidov
14 Saratov.SU2.Retired ralekseenkov, ivanromanov, Igor Kulkin
18 despise_oimaster sevenkplus, wuzhengkai, Zekun Ni
20 any_random Zhukov_Dmitry, zeliboba, ifsmirnov
22 PigsAndHedgehogs Joshik, andrewzta, dgozman
27 Accept_iterator asaveljevs, ulzha, visockas
34 KNURE_Team SkorKNURE, DryukAlex, Daiver19
36 LT_United Leonid, KrK, Lomir

•
• +40
•

By Endagorion, 6 years ago, translation, ,

Hello everyone. I'm Mikhail Tikhomirov and I'm the author of today round. I want to say big thanks to Gerald Agapov (Gerald) and Artem Rakhov (RAD) for great help in preparing this contest, and also Maria Belova for translating the statements into English (Delinur).

Today round is for contestants from both divisions. Each division has five problems, which intersect, as always. Score distributions are also standard (500-1000-1500-2000-2500). In short, it's a usual round. Or not?.. =)

Hope that problems will be interesting, tests will be secure, server will be fast, solutions — (mostly) correct, and the round will be rated. =) Wish you best of luck!

Round finished, thank you all for participating!

Results:

div1:

div2:

Editorial is finally up!

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• +321
•

By Nickolas, 6 years ago, translation, ,

Here goes a review of the problems. I tried to set them so that each of them shows a certain aspect of the language — a commonly used verb or a specific feature. Once it was recognized and found, the solution should become evident.

#### 153A - A + B

Let me note right away that the sample code provided in the blog post does work both in Custom test and in ideone (as well as locally), as long as the numbers are written one per line and (attention!) each of them, including the last one, is followed by the end-of-line character. The last '\n' is not shown in the tests, but it is there, and COBOL minds it. All test cases at Codeforces are generated with this in mind, so there should be no problems like this when the code is submitted.

The most evident COBOL feature is storing numbers in decimal notation, with width set by the programmer. In this case we focused on the fact that by default the number is printed in a fixed-width way, padded with leading zeros if needed. These zeros where what you needed to get rid of.

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• +34
•

By Nickolas, 6 years ago, translation, ,

The round is over, I hope you have enjoyed it. Here is the editorial.

The language of this round is COBOL (dialect COBOL85), one of the oldest programming languages (date of “birth”: 1959, so it’s twice older than I am). Despite being so old, it’s still in active use, though not in programming competitions, so I think it should be enough of a surprise for you :-)

The problem "A+B" (numbers A and B given in separate lines) can be solved in a following way:

       IDENTIFICATION DIVISION.
PROGRAM-ID. SOLUTION.

DATA DIVISION.
WORKING-STORAGE SECTION.
01 A        PIC 9(10)   VALUE ZEROES.
01 B        PIC 9(10)   VALUE ZEROES.
01 STR      PIC X(10).

PROCEDURE DIVISION.
ACCEPT STR
MOVE STR TO A
ACCEPT STR
MOVE STR TO B
DISPLAY B
STOP RUN.

Announcement of Surprise Language Round #5

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• +166
•

By Gerald, 6 years ago, translation, ,

#### 152A - Marks

In this problem you should do exactly what is written in the statement. Here is rough code of solution:

for (int i = 0; i < n; ++i){
bool wasBest = false;
for(int j = 0; j < m; ++j){
bool isBest = true;
for(int k = 0; k < n; ++k)
if(a[k][j] > a[i][j])
isBest = false;
if(isBest)
wasBest = true;
}
if(wasBest)
ans++;
}

#### 152B - Steps

Let's find a formula for the position (x, y) and vector (dx, dy), how many steps to stop the boy can do. You should use "almost" binary search, for example, see the code written by RAD.

for (long long cof = 1100000000; cof; cof /= 2)
while (onField(xc + cof * dx, yc + cof * dy)) {
xc = xc + cof * dx;
yc = yc + cof * dy;
ans += cof;
}

#### 152C - Pocket Book

In this task, it was necessary to understand that in position 1 Vasya can get any name of a special form. More exactly, it's the name of form s = s1 s2 s3 s4 ... sm, where s1 — the first letter of any of the names, s2 — the second letter of any of the names, ... smm-th letter of any of the names. Then the answer to the problem is the product of cnti (1 ≤ i ≤ m), where cnti is a number of different letters in the names placed in position i.

#### 152D - Frames

It was necessary to understand if there are two borders or not.

Let's distinguish those x — and y-coordinates, in which there are at least 3 consecutive symbols '#', becouse the length of each border is no less then 3. It is clear that the coordinates of the corners of borders should be chosen only from those selected x and y. In general, the various selected x no more then 4 and various selected y no more then 4.

Except that case when the height or width of the first border is 3, and length of the second side of this border is more than 3, and one side of the second border fills a part of the inside first at least.

For example:

#######
#######
#######
#.....#
#######

The first border:

#######
#.....#
#######
.......
.......

The second border:

.......
#######
#.....#
#.....#
#######

There are 7 different y-coordinates in the example.

Carefully processed these cases separately, it is quite simple. (Let's choose 4 y-coordinates: minimum, maximum, second minimum and second maximum).

Otherwise, if the amount selected x — and y-coordinates no more then 4, then let's choose opposite corners of the first and second borders and verify that the selected borders — the correct borders and there are no other characters '#'. Checking is carried out at O(n + m) or O(1) (using partial sums).

#### 152E - Garden

The solution of this problem is based on dynamic programming. dp[mask][v] — the value of the minimum correct concrete cover, if we consider as important elements only elements of the mask mask, and there are additionally covered the vertex v = (i, j) of the field.

There are two types of transfers.

First of all we can, as if to cut coverage on the vertex v. Then you need to go through subpattern of vertex submask, which will go to the left coverage and make an optimizing transfer. Update dp[mask][v] with the value dp[submask][v] + dp[mask ^ submask][v] - cost(v).

Second, perhaps in the vertex v in the optimal coverage mask mask, which covers the vertex v, you can not make the cut separating the set of vertices. In this case, this vertex forms something a kind of <>. And there a vertex u exists, on which we can make the cut, with the whole shortest path from a vertex u to v belongs to the optimal coverage. Let's precalculate the shortest paths between all pairs of cells. Now to make this transition, we should count the value of dynamics dp[mask][v] for all vertices v only on the basis of the first transition. Now you can make the second transition. For all u, dp[mask][v], update the value of dp[mask][u] + dist(v, u) - cost(u).

Let's process separately state in which exactly one bit in the mask, and the vertex which corresponding to this bit is equal to v. In this case the answer is equal to cost(v), of course.

Thus, each solution is obtained for the O(min(3k·n·m, 2k·(n·m)2)).

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• +30
•

By Polichka, 6 years ago, translation, ,

Good day!

We have got over two weeks of our new term. And we are glad to see you on our regular rating Codeforces round for Div.2 participants. And all who wants can take part in this competition.

This round has been prepared by a team of three people: Gerald, NALP and Polichka. We are grateful for their help in preparation and translation to Artem Rakhov(RAD), Mike Mirzayanov (MikeMirzayanov) and Maria Belova(Delinur).

Today Peter entangled in the tables:-( And you can help him! It's rather easy!

Score distribution: 500-1000-1500-2500-2500

Easy solutions and high rating to all!

UPD:

Thanks all for participation!

•
• +95
•

By SergeiFedorov, 6 years ago, translation, ,

### 150E - Freezing with Style

1. If there exists a path with the median  ≥ k, for some k, then there exists a path with the median  ≥ q, for each q ≤ k. That means we can use binary search to calculate the answer. So now the task is: is there any path with the median greater or equal to Mid ?

2. We will calc the edge as  + 1 if it's wight  ≥ Mid, or as  - 1 in other case. Now we only need to check if there exists a path with legal length and the sum greater than or equal to zero.

3. Let's denote some node V as a root.

4. All paths can be divided into two types: that contains v, and that do not. Now we are to process all first-type paths and run the algorithm on all subtrees. That is so-called divide-and-conquer strategy.

5. We can trivially show that it is always possible to choose such vertex v that all it's subtrees will have size less than or equal to the size of the whole tree. That means that each node will be proccessed in LogN trees max.

6. So, if we solve the task for one level of recursion in O(F(N)), we'll solve it in time O(F(N) * log2(N)) on the whole.

7. First, lets get O(N * Log(N)). For each node we shall calc it's deepness, cost of the path to the root ans the first edge (the number of the root's subtree). It will be better now to use 2 and 0 as the edges costs, instead of -1 and 1. Now we shall process root's subtrees one by one. For each node we want to know if there exists a node u in any other subtree such that the

Unable to parse markup [type=CF_TEX]

and cost[v] - deep[v] + cost[u] - deep[u] ≥ 0. To do that we need to know the maximum of the function (cost[u] - deep[u]) with the deep values between max(0, L - deep[v]) and R - deep[v] inclusive. To achieve O(N * log(N)) you need only to use segment tree.
8. To achieve an AC contestants were to write all code optimally, or to think of one more idea. It is possible to have O(N) on one level of recursion and O(N * log2(N)) in total if you sort roots subtrees in non-decreasing order and use any structure that can answer getmax query on all segments of length (R - L + 1) and all prefixes and suffixes.

Best of luck to you in upsolving this problem!

### 150D - Mission Impassable

In this problem you have to use dynamic programming. For our convenience we will calulate three type of values:

Best[l][r] — best result player can achieve on the segment [l, r].

Full[l][r] — best result player can achieve on the segment from [l, r] if he fully destroys it.

T[l][r][Len] — best result player can achieve on the segment from [l, r] and remain the palindrome of length len and only it.

Now solution:

1. Full[l][r]. Let's look which move will be the last. This will be removing the palindrome of length len and c[len] ≥ 0. What is the best result we can achieve? c[len] + T[l][r][len].

2. Best[l][r]. Either we will destroy all subtring from l to r, either there exists a letter which we did not touch. That means that all our moves lies fully to the left or fully to the rigth to that position. So Best[l][r] = Full[l][r] or Best[l][r] = Best[l][m] + Best[m + 1][r] for some m, l ≤ m < r.

3. T[l][r][len]. len = 0, len = 1 — two special cases, which is easy to solve without any dynamic. In other case, let's take a look on the left-most position. It either will lie in the result string or not. If not, then let's find the first position which does. Denote it as m (l < m ≤ r). Everything what lies to the left need to be fully deleted. So the answer is Full[l][m - 1] + T[m][r][len] (for l < m ≤ r). Similarly, for the right-most letters. If it does not lies in the result string we remove everything to the right and our result is T[l][m][len] + Full[m + 1][r] (for l ≤ m < r). The last option: both left-most and rigth-most letters lies in the result string. It is possible only if s[l] = s[r]. So our result is T[l + 1][r - 1][len - 2] (only if s[l] =  = s[r]).

### 150C - Smart Cheater

1. First lets use the linearity of expected value and solve task independently for each passanger.

2. For each path segment (route between neighboring stations) we calculate expected value of profit in case we do not sell a ticket for this segment. In case we sell it the expectation of profit is 0.

3. Now we only need to find the subsegment of segment [a, b] of maximal sum for each passanger.

4. That's easy to do by the segment tree, we only need to calc four values for each node:

best — the maximal sum of elements on some subsegment

max_left — the maximal sum on prefix

max_right — the maximal sum on suffix

sum — the sum of all elements

### 150B - Quantity of Strings

We can offer you two solitions:

1. You can build a graph with positions in sting as a nodes and equality in any substring of length k as edges. Lets denote e the number of components in the graph. The answer is me.

2. Analyze four cases:

• k = 1 or к > n, the answer is mn.
• k = n, the answer is m(n + 1) / 2.
• k mod 2 = 1, any string like abababab... is ok, so the answer is m2.
• k mod 2 = 0, all symbols coincide and the answer is m.

### 150A - Win or Freeze

• if Q is prime or Q = 1 than it's victory.

• We loose if: Q = p * q or Q = p2, where p and q are prime.

• It is quite obvious that it is always possible to move in bad position in any other case. That means all other numbers grants us the victory.

We only have to check if Q has a divisor of the loose type. We can easily do it in O(sqrt(Q)) time.

### 151B - Phone Numbers

In this task you were to implement the described selection of the maximum elements.

### 151A - Soft Drinking

Soda will be enough for gas = (K * L) / (N * l) toasts.

Limes will last for laim = (C * D) / N toasts.

Salt is enough for sol = P / (p * N) toasts.

Total result: res = min(gas, laim, sol).

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• +68
•

By GlebsHP, 6 years ago, translation, ,

Hello everybody!

Today's round will be held by SergeiFedorov and me. We have done our best to make it diverse (different task complexity and themes) and rated (we know it's important). Your questions, wishes and constructive criticism (destructive we already can do :-)) leave in comments.

The contestants will plunge into the cold February of Nvodske and will be to help one's friends to survive the cold. Just imagine all responsibility!)

On this occasion I would like to thank all Codeforces team for the great job, they are doing, Artem Rakhov (RAD) for his help in task preparations, Maria Belova (Delinur) for problems translation, my mom, my dad, our soundman and Tuscany winemakers, for us didn't fall ill while preparing this round.

Distribution will be something like:

div. 1: 500-500-1000-1500-3000 (yeah, it really costs 3000)

div. 2: 500-1000-1500-1500-3000

Good luck & have fun!


text:
# Is it proper to request a specific paper here?

I am looking for an old paper; I clearly remember that I have found it a few years ago but could not find the paper anymore. Not sure if it is proper to ask here. Anyway, the paper I am looking for is

Goldsmith, Deborah Louise
Homotopy of braids—in answer to a question of E. Artin.
Topology Conference
(Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973),
pp. 91–96. Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974.

But do let me know if it is improper to ask this type of question here.

• Did you want to ask this on meta? (I.e., you are asking: Is question like this allowed?) Or maybe you wanted to ask on the main site. (So your question is where to find the paper.) – Martin Sleziak Nov 27 '14 at 7:32
• Related post on meta: “Help me find a paper”-type questions – Martin Sleziak Nov 27 '14 at 7:32
• Basically I am more interested in finding the specific paper mentioned. Not sure where should I look for it. – Zuriel Nov 27 '14 at 7:37
• So it would be more appropriate to ask this on the main site. If your institution has access you can simply download it from the publisher; doi: 10.1007/BFb0064014. If not you can try to find someone who has access and is willing to send you the article. – Martin Sleziak Nov 27 '14 at 7:40
• Thanks @MartinSleziak! Just realize that my institution has access and I have already found the paper. Many thanks again for your kind assistance! – Zuriel Nov 27 '14 at 7:49
• @MartinSleziak I apologize for my poor memory... After finding this paper and when I save it, I found a copy in my computer. – Zuriel Nov 27 '14 at 7:57
• Lame attempt for a joke: Of course you found a copy in your computer. That's what saving a file does. More seriously: No harm done, such things happen. – Martin Sleziak Nov 27 '14 at 7:59
• If you don't know about it yet: ams.org/mathscinet is a tremendously helpful tool for finding published papers, if you have access to it. Otherwise, simply typing the title of the paper in google works 75% of the time, I'd say (whether it's on arXiv or on someone's personal page). – Najib Idrissi Nov 27 '14 at 8:39

## 1 Answer

Based on my experience, it is certainly acceptable to ask for someone to summarize a narrow portion of a paper, eg. the proof of a Lemma or the requirements of a construction, or to help you locate a library resource that has the paper (if not available on-line).

However asking someone (other than the author) to send you an actual copy of a paper opens up some copyright issues that Math.SE should not be in the middle of, and there are also the logistical details of carrying out a delivery. In addition this would fall into the category of "unlikely to benefit future readers".

I'm not trying to be the copyright police here, but I do think we can draw a useful line that should not be crossed.

• On the other hand, if the question is phrased, for example, as "How can I find an old article from LNM? Is it possible that they are available online?" I'd think that such question would be ok. And if OP mentions in some question that they are not able to find some paper (in any kind of question), I would not see as a bad thing offering the paper to the OP. (I would prefer to do it per e-mail, outside the site, but most users don't advertise their e-mail address in the profile.) I've made similar points in an answer to a related question. – Martin Sleziak Nov 30 '14 at 7:04
• Just to clarify: My comment was intended as a reaction to "unlikely to benefit future readers" and copyright issues in your post. I'll add that there have been some copyright related discussions on meta in the past. For example, this post seems relevant. (And maybe a few other posts.) – Martin Sleziak Nov 30 '14 at 7:06


text:
• ### Measurement of shower development and its Moli\ere radius with a four-plane LumiCal test set-up(1705.03885)

March 12, 2018 physics.ins-det
A prototype of a luminometer, designed for a future e+e- collider detector, and consisting at present of a four-plane module, was tested in the CERN PS accelerator T9 beam. The objective of this beam test was to demonstrate a multi-plane tungsten/silicon operation, to study the development of the electromagnetic shower and to compare it with MC simulations. The Moli\ere radius has been determined to be 24.0 +/- 0.6 (stat.) +/- 1.5 (syst.) mm using a parametrization of the shower shape. Very good agreement was found between data and a detailed Geant4 simulation.
• ### Higgs Physics at the CLIC Electron-Positron Linear Collider(1608.07538)

June 5, 2017 hep-ph, hep-ex
The Compact Linear Collider (CLIC) is an option for a future e+e- collider operating at centre-of-mass energies up to 3 TeV, providing sensitivity to a wide range of new physics phenomena and precision physics measurements at the energy frontier. This paper is the first comprehensive presentation of the Higgs physics reach of CLIC operating at three energy stages: sqrt(s) = 350 GeV, 1.4 TeV and 3 TeV. The initial stage of operation allows the study of Higgs boson production in Higgsstrahlung (e+e- -> ZH) and WW-fusion (e+e- -> Hnunu), resulting in precise measurements of the production cross sections, the Higgs total decay width Gamma_H, and model-independent determinations of the Higgs couplings. Operation at sqrt(s) > 1 TeV provides high-statistics samples of Higgs bosons produced through WW-fusion, enabling tight constraints on the Higgs boson couplings. Studies of the rarer processes e+e- -> ttH and e+e- -> HHnunu allow measurements of the top Yukawa coupling and the Higgs boson self-coupling. This paper presents detailed studies of the precision achievable with Higgs measurements at CLIC and describes the interpretation of these measurements in a global fit.
• The Compact Linear Collider (CLIC) is a multi-TeV high-luminosity linear e+e- collider under development. For an optimal exploitation of its physics potential, CLIC is foreseen to be built and operated in a staged approach with three centre-of-mass energy stages ranging from a few hundred GeV up to 3 TeV. The first stage will focus on precision Standard Model physics, in particular Higgs and top-quark measurements. Subsequent stages will focus on measurements of rare Higgs processes, as well as searches for new physics processes and precision measurements of new states, e.g. states previously discovered at LHC or at CLIC itself. In the 2012 CLIC Conceptual Design Report, a fully optimised 3 TeV collider was presented, while the proposed lower energy stages were not studied to the same level of detail. This report presents an updated baseline staging scenario for CLIC. The scenario is the result of a comprehensive study addressing the performance, cost and power of the CLIC accelerator complex as a function of centre-of-mass energy and it targets optimal physics output based on the current physics landscape. The optimised staging scenario foresees three main centre-of-mass energy stages at 380 GeV, 1.5 TeV and 3 TeV for a full CLIC programme spanning 22 years. For the first stage, an alternative to the CLIC drive beam scheme is presented in which the main linac power is produced using X-band klystrons.
• ### Measurement of the cross-section ratio sigma_{psi(2S)}/sigma_{J/psi(1S)} in deep inelastic exclusive ep scattering at HERA(1606.08652)

June 29, 2016 hep-ex
The exclusive deep inelastic electroproduction of $\psi(2S)$ and $J/\psi(1S)$ at an $ep$ centre-of-mass energy of 317 GeV has been studied with the ZEUS detector at HERA in the kinematic range $2 < Q^2 < 80$ GeV$^2$, $30 < W < 210$ GeV and $|t| < 1$ GeV$^2$, where $Q^2$ is the photon virtuality, $W$ is the photon-proton centre-of-mass energy and $t$ is the squared four-momentum transfer at the proton vertex. The data for $2 < Q^2 < 5$ GeV$^2$ were taken in the HERA I running period and correspond to an integrated luminosity of 114 pb$^{-1}$. The data for $5 < Q^2 < 80$ GeV$^2$ are from both HERA I and HERA II periods and correspond to an integrated luminosity of 468 pb$^{-1}$. The decay modes analysed were $\mu^+\mu^-$ and $J/\psi(1S) \pi^+\pi^-$ for the $\psi(2S)$ and $\mu^+\mu^-$ for the $J/\psi(1S)$. The cross-section ratio $\sigma_{\psi(2S)}/\sigma_{J/\psi(1S)}$ has been measured as a function of $Q^2, W$ and $t$. The results are compared to predictions of QCD-inspired models of exclusive vector-meson production.
• ### Search for a narrow baryonic state decaying to ${pK^0_S}$ and ${\bar{p}K^0_S}$ in deep inelastic scattering at HERA(1604.02220)

June 3, 2016 hep-ph, hep-ex
A search for a narrow baryonic state in the $pK^0_S$ and $\bar{p}K^0_S$ system has been performed in $ep$ collisions at HERA with the ZEUS detector using an integrated luminosity of 358 pb$^{-1}$ taken in 2003-2007. The search was performed with deep inelastic scattering events at an $ep$ centre-of-mass energy of 318 GeV for exchanged photon virtuality, $Q^2$, between 20 and 100 $\rm{} GeV^{2}$. Contrary to evidence presented for such a state around 1.52 GeV in a previous ZEUS analysis using a sample of 121 pb$^{-1}$ taken in 1996-2000, no resonance peak was found in the $p(\bar{p})K^0_S$ invariant-mass distribution in the range 1.45-1.7 GeV. Upper limits on the production cross section are set.
• ### Combined QCD and electroweak analysis of HERA data(1603.09628)

May 13, 2016 hep-ph, hep-ex
A simultaneous fit of parton distribution functions (PDFs) and electroweak parameters to HERA data on deep inelastic scattering is presented. The input data are the neutral current and charged current inclusive cross sections which were previously used in the QCD analysis leading to the HERAPDF2.0 PDFs. In addition, the polarisation of the electron beam was taken into account for the ZEUS data recorded between 2004 and 2007. Results on the vector and axial-vector couplings of the Z boson to u- and d-type quarks, on the value of the electroweak mixing angle and the mass of the W boson are presented. The values obtained for the electroweak parameters are in agreement with Standard Model predictions.
• ### Limits on the effective quark radius from inclusive $ep$ scattering at HERA(1604.01280)

April 5, 2016 hep-ph, hep-ex
The high-precision HERA data allows searches up to TeV scales for Beyond the Standard Model contributions to electron-quark scattering. Combined measurements of the inclusive deep inelastic cross sections in neutral and charged current $ep$ scattering corresponding to a luminosity of around 1 fb$^{-1}$ have been used in this analysis. A new approach to the beyond the Standard Model analysis of the inclusive $ep$ data is presented; simultaneous fits of parton distribution functions together with contributions of "new physics" processes were performed. Results are presented considering a finite radius of quarks within the quark form-factor model. The resulting 95% C.L. upper limit on the effective quark radius is $0.43\cdot 10^{-16}$ cm.
• ### Measurement of the cross-section ratio sigma_{psi(2S)}/sigma_{J/psi(1S)} in deep inelastic exclusive ep scattering at HERA(1601.03699)

Jan. 14, 2016 hep-ex
The exclusive deep inelastic electroproduction of $\psi(2S)$ and $J/\psi(1S)$ at an $ep$ centre-of-mass energy of 317 GeV has been studied with the ZEUS detector at HERA in the kinematic range $2 < Q^2 < 80$ GeV$^2$, $30 < W < 210$ GeV and $|t| < 1$ GeV$^2$, where $Q^2$ is the photon virtuality, $W$ is the photon-proton centre-of-mass energy and $t$ is the squared four-momentum transfer at the proton vertex. The data for $2 < Q^2 < 5$ GeV$^2$ were taken in the HERA I running period and correspond to an integrated luminosity of 114 pb$^{-1}$. The data for $5 < Q^2 < 80$ GeV$^2$ are from both HERA I and HERA II periods and correspond to an integrated luminosity of 468 pb$^{-1}$. The decay modes analysed were $\mu^+\mu^-$ and $J/\psi(1S) \,\pi^+\pi^-$ for the $\psi(2S)$ and $\mu^+\mu^-$ for the $J/\psi(1S)$. The cross-section ratio $\sigma_{\psi(2S)}/\sigma_{J/\psi(1S)}$ has been measured as a function of $Q^2, W$ and $t$. The results are compared to predictions of QCD-inspired models of exclusive vector-meson production.
• ### Production of exclusive dijets in diffractive deep inelastic scattering at HERA(1505.05783)

Dec. 17, 2015 hep-ex
Production of exclusive dijets in diffractive deep inelastic $e^\pm p$ scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 372 pb$^{-1}$. The measurement was performed for $\gamma^*-p$ centre-of-mass energies in the range $90 < W < 250$ GeV and for photon virtualities $Q^2 > 25$ GeV$^2$. Energy and transverse-energy flows around the jet axis are presented. The cross section is presented as a function of $\beta$ and $\phi$, where $\beta=x/x_{\rm I\!P}$, $x$ is the Bjorken variable and $x_{\rm I\!P}$ is the proton fractional longitudinal momentum loss. The angle $\phi$ is defined by the $\gamma^*-$dijet plane and the $\gamma^*-e^\pm$ plane in the rest frame of the diffractive final state. The $\phi$ cross section is measured in bins of $\beta$. The results are compared to predictions from models based on different assumptions about the nature of the diffractive exchange.
• ### Performance of fully instrumented detector planes of the forward calorimeter of a Linear Collider detector(1411.4431)

June 1, 2015 physics.ins-det
Detector-plane prototypes of the very forward calorimetry of a future detector at an e+e- collider have been built and their performance was measured in an electron beam. The detector plane comprises silicon or GaAs pad sensors, dedicated front-end and ADC ASICs, and an FPGA for data concentration. Measurements of the signal-to-noise ratio and the response as a function of the position of the sensor are presented. A deconvolution method is successfully applied, and a comparison of the measured shower shape as a function of the absorber depth with a Monte-Carlo simulation is given.
• ### The study of the photon structure function at the ILC energy range(1503.07373)

March 26, 2015 hep-ph, hep-ex
At the future $e^{+}e^{-}$ linear collider ILC/CLIC it will be able to measure the photon structure functions in a wider range of kinematic variables x and $Q^{2}$ in comparison to the previous results of experiments at LEP. The classical way to measure the photon structure functions is the study of $e^{+}e^{-} \rightarrow e^{+}e^{-} {\gamma}{\gamma} \rightarrow e^{+}e^{-}$ X process, where X is the leptonic or hadronic final state. For the study of the QED and hadronic photon structure functions the simulations of two-photon processes were performed at the ILC center-of-mass energy equal to 500 GeV using the PYTHIA and the ILCSoft package. The analysis used information related to the forward detectors, tracking detectors and calorimeters which are parts of the ILD detector concept.
• ### ECFA Detector R&D Panel, Review Report(1411.4924)

Nov. 19, 2014 physics.ins-det
Two special calorimeters are foreseen for the instrumentation of the very forward region of an ILC or CLIC detector; a luminometer (LumiCal) designed to measure the rate of low angle Bhabha scattering events with a precision better than 10$^{-3}$ at the ILC and 10$^{-2}$ at CLIC, and a low polar-angle calorimeter (BeamCal). The latter will be hit by a large amount of beamstrahlung remnants. The intensity and the spatial shape of these depositions will provide a fast luminosity estimate, as well as determination of beam parameters. The sensors of this calorimeter must be radiation-hard. Both devices will improve the e.m. hermeticity of the detector in the search for new particles. Finely segmented and very compact electromagnetic calorimeters will match these requirements. Due to the high occupancy, fast front-end electronics will be needed. Monte Carlo studies were performed to investigate the impact of beam-beam interactions and physics background processes on the luminosity measurement, and of beamstrahlung on the performance of BeamCal, as well as to optimise the design of both calorimeters. Dedicated sensors, front-end and ADC ASICs have been designed for the ILC and prototypes are available. Prototypes of sensor planes fully assembled with readout electronics have been studied in electron beams.


text:
Graphcx

A collection of graph analysis and drawing algorithms

Galaxy layout of tree82inc.

History

I began working on graphcx as a project on genetic algorithms at the University of Limerick in 2016. The mandatory implementation was largely extended with a flexible OpenGL based visualization module and bunch of interesting algorithms.

The propably most interesting part is an implementation of the Sampled Spectral Distance Embedding algorithm, which was presented by Çivril, Magdon-Ismail and Bocek-Rivele at the 14th International Symposium on Graph Drawing, Karlsruhe, 2006. http://dx.doi.org/10.1007/978-3-540-70904-6_5

The euclidean distances between vertices in a SSDE layout approximate the underlying graph-theoretical distances. An obvious application is to combine SSDE on a global scale with a further local optimizer (e.g. a force-directed algorithm) to speed up the drawing process and circumvent bad local energy minima.

• Written in Java, depends on la4j and jogl.
• Build system / dependency management: gradle.
• Source: GitHub

Functionality & Algorithms

• Genetic optimization by simulated annealing:
• Grid or circular layout
• $$\sum\limits_i ||e_i||_2$$ or #EdgeIntersections as fitness criteria.
• Galaxy: A straight-forward force directed implementation. The name is due to the typical shape this algorithm produces.
• Fruchterman-Reingold algorithm.
• Dijkstra shortest-path.
• General graph handling, representation and conversion.
• OpenGL based visualization which nicely depicts optimization progress.

Todo

• Add rudimentary interface to avoid recompiling b/c of parameter changes.
• Port OpenGL to Vulcan just for fun and out of interest.
• Add more algorithms.

Sample Layouts:

Simulated annealing grid layout of tree82inc, using $\sum\limits_i ||e_i||_2$ as a fitness criterion.

SSDE layout of tree82inc.

Grid layout of matrix1inc, using $\sum\limits_i ||e_i||_2$ as a fitness criterion.

Galaxy layout of originalinc.

By @Oliver Wiedemann in
Tags :


text:
# Estimating the break point in a broken stick / piecewise linear model with random effects in R [code and output included]

Can someone please tell me how to have R estimate the break point in a piecewise linear model (as a fixed or random parameter), when I also need to estimate other random effects?

I've included a toy example below that fits a hockey stick / broken stick regression with random slope variances and a random y-intercept variance for a break point of 4. I want to estimate the break point instead of specifying it. It could be a random effect (preferable) or a fixed effect.

library(lme4)
str(sleepstudy)

#Basis functions
bp = 4
b1 <- function(x, bp) ifelse(x < bp, bp - x, 0)
b2 <- function(x, bp) ifelse(x < bp, 0, x - bp)

#Mixed effects model with break point = 4
(mod <- lmer(Reaction ~ b1(Days, bp) + b2(Days, bp) + (b1(Days, bp) + b2(Days, bp) | Subject), data = sleepstudy))

#Plot with break point = 4
xyplot(
Reaction ~ Days | Subject, sleepstudy, aspect = "xy",
layout = c(6,3), type = c("g", "p", "r"),
xlab = "Days of sleep deprivation",
ylab = "Average reaction time (ms)",
panel = function(x,y) {
panel.points(x,y)
panel.lmline(x,y)
pred <- predict(lm(y ~ b1(x, bp) + b2(x, bp)), newdata = data.frame(x = 0:9))
panel.lines(0:9, pred, lwd=1, lty=2, col="red")
}
)

Output:

Linear mixed model fit by REML
Formula: Reaction ~ b1(Days, bp) + b2(Days, bp) + (b1(Days, bp) + b2(Days, bp) | Subject)
Data: sleepstudy
AIC  BIC logLik deviance REMLdev
1751 1783 -865.6     1744    1731
Random effects:
Groups   Name         Variance Std.Dev. Corr
Subject  (Intercept)  1709.489 41.3460
b1(Days, bp)   90.238  9.4994  -0.797
b2(Days, bp)   59.348  7.7038   0.118 -0.008
Residual               563.030 23.7283
Number of obs: 180, groups: Subject, 18

Fixed effects:
Estimate Std. Error t value
(Intercept)   289.725     10.350  27.994
b1(Days, bp)   -8.781      2.721  -3.227
b2(Days, bp)   11.710      2.184   5.362

Correlation of Fixed Effects:
(Intr) b1(D,b
b1(Days,bp) -0.761
b2(Days,bp) -0.054  0.181

-

Another approach would be to wrap the call to lmer in a function that is passed the breakpoint as a parameter, then minimize the deviance of the fitted model conditional upon the breakpoint using optimize. This maximizes the profile log likelihood for the breakpoint, and, in general (i.e., not just for this problem) if the function interior to the wrapper (lmer in this case) finds maximum likelihood estimates conditional upon the parameter passed to it, the whole procedure finds the joint maximum likelihood estimates for all the parameters.

library(lme4)
str(sleepstudy)

#Basis functions
bp = 4
b1 <- function(x, bp) ifelse(x < bp, bp - x, 0)
b2 <- function(x, bp) ifelse(x < bp, 0, x - bp)

#Wrapper for Mixed effects model with variable break point
foo <- function(bp)
{
mod <- lmer(Reaction ~ b1(Days, bp) + b2(Days, bp) + (b1(Days, bp) + b2(Days, bp) | Subject), data = sleepstudy)
deviance(mod)
}

search.range <- c(min(sleepstudy$Days)+0.5,max(sleepstudy$Days)-0.5)
foo.opt <- optimize(foo, interval = search.range)
bp <- foo.opt$minimum bp [1] 6.071932 mod <- lmer(Reaction ~ b1(Days, bp) + b2(Days, bp) + (b1(Days, bp) + b2(Days, bp) | Subject), data = sleepstudy)  To get a confidence interval for the breakpoint, you could use the profile likelihood. Add, e.g., qchisq(0.95,1) to the minimum deviance (for a 95% confidence interval) then search for points where foo(x) is equal to the calculated value: foo.root <- function(bp, tgt) { foo(bp) - tgt } tgt <- foo.opt$objective + qchisq(0.95,1)
lb95 <- uniroot(foo.root, lower=search.range[1], upper=bp, tgt=tgt)
ub95 <- uniroot(foo.root, lower=bp, upper=search.range[2], tgt=tgt)
lb95$root [1] 5.754051 ub95$root
[1] 6.923529

Somewhat asymmetric, but not bad precision for this toy problem. An alternative would be to bootstrap the estimation procedure, if you have enough data to make the bootstrap reliable.

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Thank you -- that was very helpful. Is this technique called a two-stage estimation procedure, or does it have a standard name that I could refer to / look up? –  lockedoff Dec 13 '11 at 18:39
It's maximum likelihood, or would be if lmer maximized the likelihood (I think the default is actually REML, you need to pass a parameter REML=FALSE to lmer to get ML estimates). just estimated in a nested manner rather than all at once. I've added some clarification at the front of the answer. –  jbowman Dec 13 '11 at 19:40
I had some optimization problems and wide CIs when inverting the profile likelihood with my real data, but got narrower bootstrap CIs in my implementation. Were you envisioning a nonparametric bootstrap with sampling with replacement on subjects' data vectors? I.e., for the sleepstudy data, this would entail sampling with replacement from the 18 (subject) vectors of 10 data points, without doing any resampling within a subject's data vector. –  lockedoff Dec 14 '11 at 21:10
Yes, I was envisioning a nonparametric bootstrap as you describe, but partially that's because I don't know much about advanced bootstrap techniques that may (or may not) be applicable. The profile likelihood-based CIs and bootstrap are both asymptotically accurate, but it could well be that the bootstrap is significantly better for your sample. –  jbowman Dec 14 '11 at 23:56
+1 for the code –  Andrew Dec 15 '11 at 12:21
You could try a MARS model. However, I'm not sure how to specify random effects. earth(Reaction~Days+Subject, sleepstudy)


text:
# zbMATH — the first resource for mathematics

Decomposition of an elementary curve into Jordan curves. (Czech) Zbl 0149.19802

##### MSC:
 54F50 Topological spaces of dimension $$\leq 1$$; curves, dendrites
topology


text:
## Twisted Superalgebras and Cohomologies of the N=2 Superconformal Quantum Mechanics    [PDF]

Laurent Baulieu, Francesco Toppan
We prove that the invariance of the N=2 superconformal quantum mechanics is controlled by subalgebras of a given twisted superalgebra made of 6 fermionic (nilpotent) generators and 6 bosonic generators (including a central charge). The superconformal quantum mechanics actions are invariant under this quite large twisted superalgebra. On the other hand, they are fully determined by a subalgebra with only 2 fermionic and 2 bosonic (the central charge and the ghost number) generators. The invariant actions are Q_i-exact (i=1,2,...,6), with a Q_{i'}-exact (i'\neq i) antecedent for all 6 fermionic generators. It follows that the superconformal quantum mechanics actions with Calogero potentials are uniquely determined even if, in its bosonic sector, the twisted superalgebra does not contain the one-dimensional conformal algebra sl(2), but only its Borel subalgebra. The general coordinate covariance of the non-linear sigma-model for the N=2 supersymmetric quantum mechanics in a curved target space is fully implied only by its worldline invariance under a pair of the 6 twisted supersymmetries. The transformation connecting the ordinary and twisted formulations of the N=2 superconformal quantum mechanics is explicitly presented.
View original: http://arxiv.org/abs/1108.4370