Spatial flocking: Control by speed, distance, noise and delay

Fish, birds, insects and robots frequently swim or fly in groups. During their 3 dimensional collective motion, these agents do not stop, they avoid collisions by strong short-range repulsion, and achieve group cohesion by weak long-range attraction. In a minimal model that is isotropic, and continuous in both space and time, we demonstrate that (i) adjusting speed to a preferred value, combined with (ii) radial repulsion and an (iii) effective long-range attraction are sufficient for the stable ordering of autonomously moving agents in space. Our results imply that beyond these three rules ordering in space requires no further rules, for example, explicit velocity alignment, anisotropy of the interactions or the frequent reversal of the direction of motion, friction, elastic interactions, sticky surfaces, a viscous medium, or vertical separation that prefers interactions within horizontal layers. Noise and delays are inherent to the communication and decisions of all moving agents. Thus, next we investigate their effects on ordering in the model. First, we find that the amount of noise necessary for preventing the ordering of agents is not sufficient for destroying order. In other words, for realistic noise amplitudes the transition between order and disorder is rapid. Second, we demonstrate that ordering is more sensitive to displacements caused by delayed interactions than to uncorrelated noise (random errors). Third, we find that with changing interaction delays the ordered state disappears at roughly the same rate, whereas it emerges with different rates. In summary, we find that the model discussed here is simple enough to allow a fair understanding of the modeled phenomena, yet sufficiently detailed for the description and management of large flocks with noisy and delayed interactions. Our code is available at http://github.com/fij/flocComment: 12 pages, 7 figure

Hyperons in neutron-star cores and two-solar-mass pulsar

Recent measurement of mass of PSR J1614-2230 rules out most of existing models of equation of state (EOS) of dense matter with high-density softening due to hyperonization or a phase transition to quark matter or a boson condensate. We look for a solution of an apparent contradiction between the consequences stemming from up-to-date hypernuclear data, indicating appearance of hyperons at 3 nuclear densities and existence of a two-solar-mass neutron star. We consider a non-linear relativistic mean field (RMF) model involving baryon octet coupled to meson fields. An effective lagrangian includes quartic terms in the meson fields. The values of the parameters of the model are obtained by fitting semi-empirical parameters of nuclear matter at the saturation point, as well as potential wells for hyperons in nuclear matter and the strength of the Lambda-Lambda attraction in double-Lambda hypernuclei. We propose a non-linear RMF model which is consistent with up-to-date semiempirical nuclear and hypernuclear data and allows for neutron stars with hyperon cores and M larger than 2 solar masses. The model involves hidden-strangenes scalar and vector mesons, coupled to hyperons only, and quartic terms involving vector meson fields. Our EOS involving hyperons is stiffer than the corresponding nucleonic EOS (with hyperons artificially suppressed) above five nuclear densities. Required stiffening is generated by the quartic terms involving hidden-strangeness vector meson.Comment: 7 pages, 5 figures. Main results of this paper were already presented at the MODE-SNR-PWN Workshop in Bordeaux, France, November 15-17, 2010, and in a poster at the CompStar 2011 Workshop in Catania, Italy, May 9-12, 2011. The paper is being submitted to Astronomy & Astrophysic

A Generalized Sznajd Model

In the last decade the Sznajd Model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a new version of the Sznajd model with a generalized bounded confidence rule - a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this new model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabasi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd Model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.Comment: 19 pages with 8 figures. Submitted to Physical Review

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Adaptive hybrid optimization strategy for calibration and parameter estimation of physical models

A new adaptive hybrid optimization strategy, entitled squads, is proposed for complex inverse analysis of computationally intensive physical models. The new strategy is designed to be computationally efficient and robust in identification of the global optimum (e.g. maximum or minimum value of an objective function). It integrates a global Adaptive Particle Swarm Optimization (APSO) strategy with a local Levenberg-Marquardt (LM) optimization strategy using adaptive rules based on runtime performance. The global strategy optimizes the location of a set of solutions (particles) in the parameter space. The LM strategy is applied only to a subset of the particles at different stages of the optimization based on the adaptive rules. After the LM adjustment of the subset of particle positions, the updated particles are returned to the APSO strategy. The advantages of coupling APSO and LM in the manner implemented in squads is demonstrated by comparisons of squads performance against Levenberg-Marquardt (LM), Particle Swarm Optimization (PSO), Adaptive Particle Swarm Optimization (APSO; the TRIBES strategy), and an existing hybrid optimization strategy (hPSO). All the strategies are tested on 2D, 5D and 10D Rosenbrock and Griewank polynomial test functions and a synthetic hydrogeologic application to identify the source of a contaminant plume in an aquifer. Tests are performed using a series of runs with random initial guesses for the estimated (function/model) parameters. Squads is observed to have the best performance when both robustness and efficiency are taken into consideration than the other strategies for all test functions and the hydrogeologic application

Quantum Probabilities as Behavioral Probabilities

We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.Comment: Latex file, 32 page

Experience-weighted Attraction Learning in Normal Form Games

In ‘experience-weighted attraction’ (EWA) learning, strategies have attractions that reflect initial predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter δ that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded, relative to reinforcement of chosen strategies according to received payoffs. The other key features are two discount rates, φ and ρ, which separately discount previous attractions, and an experience weight. EWA includes reinforcement learning and weighted fictitious play (belief learning) as special cases, and hybridizes their key elements. When δ= 0 and ρ= 0, cumulative choice reinforcement results. When δ= 1 and ρ=φ, levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs. Using three sets of experimental data, parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample. Estimates of δ are generally around .50, φ around .8 − 1, and ρ varies from 0 to φ. Reinforcement and belief-learning special cases are generally rejected in favor of EWA, though belief models do better in some constant-sum games. EWA is able to combine the best features of previous approaches, allowing attractions to begin and grow flexibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do