Density excitations of a harmonically trapped ideal gas

The dynamic structure factor of a harmonically trapped Bose gas has been calculated well above the Bose-Einstein condensation temperature by treating the gas cloud as a canonical ensemble of noninteracting classical particles. The static structure factor is found to vanish as wavenumber squared in the long-wavelength limit. We also incorporate a relaxation mechanism phenomenologically by including a stochastic friction force to study the dynamic structure factor. A significant temperature dependence of the density-fluctuation spectra is found. The Debye-Waller factor has been calculated for the trapped thermal cloud as function of wavenumber and of particle number. A substantial difference is found between clouds of small and large particle number

Social Simulation and Analysis of the Dynamics of Criminal Hot Spots

Contains fulltext : 194199.pdf (publisher's version ) (Open Access)Within the field of Criminology, the spatio-temporal dynamics of crime are an important subject of study. In this area, typical questions are how the behaviour of offenders, targets, and guardians can be explained and predicted, as well as the emergence and displacement of criminal hot spots. In this article we present a combination of software tools that can be used as an experimental environment to address such questions. In particular, these tools comprise an agent-based simulation model, a verification tool, and a visualisation tool. The agent-based simulation model specifically focuses on the interplay between hot spots and reputation. Using this environment, a large number of simulation runs have been performed, of which results have been formally analysed. Based on these results, we argue that the presented environment offers a valuable approach to analyse the dynamics of criminal hot spots.19 p

Topological Correlations in a Layer Adsorbed on a Crystal Surface

The incoherent scattering of electrons by a layer adsorbed at a single crystal surface is determined by the topological correlations of elements forming the adsorbed layer. The model for the description of atoms or molecules adsorbed on the surface is formulated in terms of occupation operators which are expressed in terms of pseudospin operators with a given spin value. The correlations can be determined by the fluctuation dissipation theorem in connection with the susceptibility or given directly by means of the Green functions properly chosen. An example of the topological or chemical disorder of two components is considered in detail. The calculations of the topological correlations allow us to find the incoherent scattering amplitude as a function of the surface coverage which can be experimentally detected.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Approximate well-supported Nash equilibria in symmetric bimatrix games

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed strategy. The smallest constant $\varepsilon$ currently known for which there is a polynomial-time algorithm that computes an $\varepsilon$-well-supported Nash equilibrium in bimatrix games is slightly below $2/3$. In this paper we study this problem for symmetric bimatrix games and we provide a polynomial-time algorithm that gives a $(1/2+\delta)$-well-supported Nash equilibrium, for an arbitrarily small positive constant $\delta$

Formalisation of Dynamic Properties of Multi-Issue Negotiation

This document contains a number of formal dynamic properties that are relevant for multi-issue negotiation

The development of children's political competence in a primary school: A quest

This research explores how children recount and account for their developing political competence at primary school. To access participants’ experience and perceptions of political participation and agency and the structures and practices within which they operate, I designed a post-structurally informed ethnographic study for a large junior school in the South West of England. The result was a range of qualitative and participative data gathering methods which emphasised the importance and value of children’s voices and testimony: interviews, observations, diaries, analytical discussions and ethnographic field notes. The resulting data comprise a collection of participant accounts and interpretations of living and learning in school. In contrast to my research approach, my findings identify a construction of the child as deficient, incompetent and untrustworthy, destabilising children’s emergent confidence as political beings and severely limiting the effectiveness of educational initiatives to engage them in active political participation. As a result, forms of political participation and self-expression are muted: children are encouraged to develop a conservative, self-preserving form of agency hidden from view and often characterised by self-doubt and self-suppression, counter to curricular expectations of political participation in school and community life. However, using Foucauldian theoretical tools, I argue that some children’s responses to the pressure of the school’s normalising structures and practices creatively build an effective, but subaltern, political competence, allowing children to exercise agency in strategic conformity and resistance. Being unrecognised, though, outside the surveillance of the curriculum and its enforcers, this learning is not readily available for teachers and the school to engage with and nurture. This presents both a missed opportunity for primary education and a threat to the stability and sustainability of children’s credible political agency. Empowering children requires seeing them as politically capable and competent, rather than lesser adults, deficient and lacking in citizenship competence

Justice Kennedy and the Environment: Property, States\u27 Rights, and a Persistent Search for Nexus

Justice Anthony Kennedy, now clearly the pivot of the Roberts Court, is the Court\u27s crucial voice in environmental law cases. Kennedy\u27s central role was never more evident than in the two most celebrated environmental cases of the last few years, Kelo v. City of New London and Rapanos v. United States, as he supplied the critical vote in both. Kennedy has in fact been the needle of the Supreme Court\u27s environmental law compass since his nomination in 1988. Although he wrote surprisingly few environmental law opinions over his first eighteen years on the Court, Kennedy was in the majority an astonishing ninety-six percent of the time (as compared to his generic record of being in the majority slightly over sixty percent of the time). This article examines Kennedy\u27s environmental law record on the Court, as well as his preceding thirteen years on the Ninth Circuit. The article evaluates all of the environmental law cases in which he wrote an opinion over those three decades and catalogues his voting record in all Supreme Court cases in which he participated. One striking measure of Kennedy\u27s influence is that he has written just one environmental dissent while on the Court, and that was on states\u27 rights grounds, one of his chief priorities. We believe that Kennedy is considerably more interested in allowing trial judges to resolve cases on the basis of context than in establishing broadly-applicable doctrine. That is, he is a doctrinal minimalist. By consistently demanding a demonstrated nexus between doctrine and facts, he has shown an intolerance for elevating abstract philosophy over concrete justice. And, despite his unassailable devotion to states\u27 rights, Kennedy has been quite willing to find federal preemption when it serves deregulation purposes. On the other hand, he is far from an anti-regulatory zealot, although he prefers only one level of governmental regulation. At what might be close to the mid-point in his Court career-and with his power perhaps at its zenith-Justice Kennedy is clearly not someone any litigant can ignore. We hope this article gives both environmental litigants and academics a fertile resource to till. Although Kennedy\u27s environmental record has been sparse until lately, he may be receptive to environmental claims if they are factually well-grounded and do not conflict with his overriding concern for states\u27 rights. The article concludes with some comparisons between Kennedy and Justice Oliver Wendell Holmes

Polylogarithmic Supports are required for Approximate Well-Supported Nash Equilibria below 2/3

In an epsilon-approximate Nash equilibrium, a player can gain at most epsilon in expectation by unilateral deviation. An epsilon well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with positive probability must have payoff within epsilon of the best response payoff. Daskalakis, Mehta and Papadimitriou conjectured that every win-lose bimatrix game has a 2/3-well-supported Nash equilibrium that uses supports of cardinality at most three. Indeed, they showed that such an equilibrium will exist subject to the correctness of a graph-theoretic conjecture. Regardless of the correctness of this conjecture, we show that the barrier of a 2/3 payoff guarantee cannot be broken with constant size supports; we construct win-lose games that require supports of cardinality at least Omega((log n)^(1/3)) in any epsilon-well supported equilibrium with epsilon < 2/3. The key tool in showing the validity of the construction is a proof of a bipartite digraph variant of the well-known Caccetta-Haggkvist conjecture. A probabilistic argument shows that there exist epsilon-well-supported equilibria with supports of cardinality O(log n/(epsilon^2)), for any epsilon> 0; thus, the polylogarithmic cardinality bound presented cannot be greatly improved. We also show that for any delta > 0, there exist win-lose games for which no pair of strategies with support sizes at most two is a (1-delta)-well-supported Nash equilibrium. In contrast, every bimatrix game with payoffs in [0,1] has a 1/2-approximate Nash equilibrium where the supports of the players have cardinality at most two.Comment: Added details on related work (footnote 7 expanded

Approximate Well-supported Nash Equilibria below Two-thirds

In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm exists. An epsilon-well-supported Nash equilibrium (epsilon-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most epsilon less than the best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee

An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares a number of approximation methods and exact methods. In particular, we explore the trade-off between the quality of approximate equilibrium and the required running time to find one. We found that the existing library GAMUT, which has been the de facto standard that has been used to test exact methods, is insufficient as a test bed for approximation methods since many of its games have pure equilibria or other easy-to-find good approximate equilibria. We extend the breadth and depth of our study by including new interesting families of bimatrix games, and studying bimatrix games upto size $2000 \times 2000$. Finally, we provide new close-to-worst-case examples for the best-performing algorithms for finding approximate Nash equilibria