Threshold games and cooperation on multiplayer graphs

Objective: The study investigates the effect on cooperation in multiplayer games, when the population from which all individuals are drawn is structured - i.e. when a given individual is only competing with a small subset of the entire population. Method: To optimize the focus on multiplayer effects, a class of games were chosen for which the payoff depends nonlinearly on the number of cooperators - this ensures that the game cannot be represented as a sum of pair-wise interactions, and increases the likelihood of observing behaviour different from that seen in two-player games. The chosen class of games are named "threshold games", and are defined by a threshold, $M > 0$, which describes the minimal number of cooperators in a given match required for all the participants to receive a benefit. The model was studied primarily through numerical simulations of large populations of individuals, each with interaction neighbourhoods described by various classes of networks. Results: When comparing the level of cooperation in a structured population to the mean-field model, we find that most types of structure lead to a decrease in cooperation. This is both interesting and novel, simply due to the generality and breadth of relevance of the model - it is likely that any model with similar payoff structure exhibits related behaviour. More importantly, we find that the details of the behaviour depends to a large extent on the size of the immediate neighbourhoods of the individuals, as dictated by the network structure. In effect, the players behave as if they are part of a much smaller, fully mixed, population, which we suggest an expression for.Comment: in PLOS ONE, 4th Feb 201

An O(M(n) log n) algorithm for the Jacobi symbol

The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n) log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and Zimmermann. Our implementation - which to our knowledge is the first to run in time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010

Unbiased flux calibration methods for spectral-line radio observations

Position and frequency switching techniques used for the removal of the bandpass dependence of radio astronomical spectra are presented and discussed in detail. Both methods are widely used, although the frequency dependence of the system temperature and/or noise diode is often neglected. This leads to systematic errors in the calibration that potentially have a significant impact on scientific results, especially when using large-bandwidth receivers or performing statistical analyses. We present methods to derive an unbiased calibration using a noise diode, which is part of many heterodyne receivers. We compare the proposed methods and describe the advantages and bottlenecks of the various approaches. Monte Carlo simulations are used to qualitatively investigate both systematics and the error distribution of the reconstructed flux estimates about the correct flux values for the new methods but also the 'classical' case. Finally, the determination of the frequency-dependent noise temperature of the calibration diode using hot-cold measurements or observations of well-known continuum sources is also briefly discussed.Comment: 25 pages, 30 figures. Accepted for publication in A&

Optical conductivity for a dimer in the Dynamic Hubbard model

The Dynamic Hubbard Model represents the physics of a multi-band Hubbard model by using a pseudo-spin degree of freedom to dynamically modify the on-site Coulomb interaction. Here we use a dimer system to obtain analytical results for this model. The spectral function and the optical conductivity are calculated analytically for any number of electrons, and the distribution of optical spectral weight is analyzed in great detail. The impact of polaron-like effects due to overlaps between pseudo-spin states on the optical spectral weight distribution is derived analytically. Our conclusions support results obtained previously with different models and techniques: holes are less mobile than electrons.Comment: 11 pages, 4 figure

Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory

Top Physics in WHIZARD

In this talk we summarize the top physics setup in the event generator WHIZARD with a main focus on lepton colliders. This includes full six-, eight- and ten-fermion processes, factorized processes and spin correlations. For lepton colliders, QCD NLO processes for top quark physics are available and will be discussed. A special focus is on the top-quark pair threshold, where a special implementation combines a non-relativistic effective field theory calculation augmented by a next-to-leading threshold logarithm resummation with a continuum relativistic fixed-order QCD NLO simulation.Comment: 6 pages, 2 figures, Talk presented at the International Workshop on Future Linear Colliders (LCWS15), Whistler, Canada, 2-6 November 201

Bromination of Graphene and Graphite

We present a density functional theory study of low density bromination of graphene and graphite, finding significantly different behaviour in these two materials. On graphene we find a new Br2 form where the molecule sits perpendicular to the graphene sheet with an extremely strong molecular dipole. The resultant Br+-Br- has an empty pz-orbital located in the graphene electronic pi-cloud. Bromination opens a small (86meV) band gap and strongly dopes the graphene. In contrast, in graphite we find Br2 is most stable parallel to the carbon layers with a slightly weaker associated charge transfer and no molecular dipole. We identify a minimum stable Br2 concentration in graphite, finding low density bromination to be endothermic. Graphene may be a useful substrate for stabilising normally unstable transient molecular states

Detecting Generalized Synchronization Between Chaotic Signals: A Kernel-based Approach

A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization. It is also shown that the dynamical change of the coupling coefficient between two chaotic systems can be captured by the proposed approach.Comment: 20 pages, 15 figures. massively revised as a full paper; issues on the choice of parameters by cross validation, tests by surrogated data, etc. are added as well as additional examples and figure

On the Stability of Formato, Acetato, Propionato, Butyrato, Glycolato and Chloroacetato Complexes of Cobalt, Nickel, Copper, Zinc, Cadmium and Lead

Stability constants of formato, acetato, propionato, butyrato, glycolato and chloroacetato complexes of cobalt, nickel, copper, zinc, cadmium and lead have been determined by the potentiometric method. The change of concentration of hydrogen ions in the monocarboxylate buffer has been measured. Stability constants have been obtained by means of a digital computer applying the Gauss Z programme devised by R. S. Tobias. On the basis of these results as well as the results obtained in the former investigations by the polarographic and spectrophotometric method, the stability of the investigated monocarboxylato complexes has been discussed and the corresponding orders of stability were established

Phase diagrams of the 2D t-t'-U Hubbard model from an extended mean field method

It is well-known from unrestricted Hartree-Fock computations that the 2D Hubbard model does not have homogeneous mean field states in significant regions of parameter space away from half filling. This is incompatible with standard mean field theory. We present a simple extension of the mean field method that avoids this problem. As in standard mean field theory, we restrict Hartree-Fock theory to simple translation invariant states describing antiferromagnetism (AF), ferromagnetism (F) and paramagnetism (P), but we use an improved method to implement the doping constraint allowing us to detect when a phase separated state is energetically preferred, e.g. AF and F coexisting at the same time. We find that such mixed phases occur in significant parts of the phase diagrams, making them much richer than the ones from standard mean field theory. Our results for the 2D t-t'-U Hubbard model demonstrate the importance of band structure effects.Comment: 6 pages, 5 figure