Transitions between nonsymmetric and symmetric steady states near a triple eigenvalue

We examine the existence of nonuniform steady-state solutions of a certain class of reaction-diffusion equations. Our analysis concentrates on the case where the first bifurcation is near a triple eigenvalue. We derive the conditions for a continuous transition between nonsymmetric and symmetric solutions when the bifurcation parameter progressively increases from zero. Finally, we give an example of a four variables model which presents the possibility of a triple eigenvalue

Imperfect Bifurcation Near a Double Eigenvalue: Transitions Between Nonsymmetric and Symmetric Patterns

We examine the existence of nonsymmetric and symmetric steady state solutions of a general class of reaction-diffusion equations. Our study consists of two parts: (i) By analyzing the bifurcation from a uniform reference state to nonuniform regimes, we demonstrate the existence of a unique symmetric solution (basic wave number two) which becomes linearly stable when it surpasses a critical amplitude. (We assume that the first bifurcation point corresponds to the emergence of the simplest nonsymmetric steady state solutions.) (ii) This result is not affected when a parameter is nonuniformly distributed in the system. However, one of the two possible branches of nonsymmetric solutions may disappear from the bifurcation diagram. Our analysis is motivated by the fact that experimental observations of pattern transitions during morphogenesis are interpreted in terms of the dynamics of stable concentration gradients. We have shown that in addition to the values of the physico-chemical parameters, these structures can be selected by two different mechanisms: (i) the linear stability of the nonuniform patterns, (ii) the effects of a small and nonuniform variation of a parameter in the spatial domain

New Relations for Excited Baryons in Large N_c QCD

We show that excited baryons in large N_c QCD form multiplets, within which masses are first split at O(1/N_c). The dominant couplings of resonances to various mesons are highly constrained: The N(1535) decays at leading 1/N_c order exclusively to eta-N rather than pi-N, and vice versa for the N(1650). This multiplet structure is reproduced by a simple large N_c quark model, well studied in the literature, that describes resonances as single-quark excitations.Comment: 4 pages, no figures, ReVTeX 4. Includes new discussion of previous work on excited baryon tower

Context dependence of the event-related brain potential associated with reward and punishment

The error-related negativity (ERN) is an event-related brain potential elicited by error commission and by presentation of feedback stimuli indicating incorrect performance. In this study, the authors report two experiments in which participants tried to learn to select between response options by trial and error, using feedback stimuli indicating monetary gains and losses. The results demonstrate that the amplitude of the ERN is determined by the value of the eliciting outcome relative to the range of outcomes possible, rather than by the objective value of the outcome. This result is discussed in terms of a recent theory that holds that the ERN reflects a reward prediction error signal associated with a neural system for reinforcement learning

Diquarks, Pentaquarks and Dibaryons

We explore the connection between pentaquarks and dibaryons composed of three diquarks in the framework of the diquark model. With the available experimental data on H dibaryon, we estimate the Pauli blocking and annihilation effects and constrain the $P=-$ pentaquark $SU(3)_F$ singlet mass. Using the $\Theta^+$ pentaquark mass, we estimate $P=-$ dibaryon mass

A subset solution to the sign problem in random matrix simulations

We present a solution to the sign problem in dynamical random matrix simulations of a two-matrix model at nonzero chemical potential. The sign problem, caused by the complex fermion determinants, is solved by gathering the matrices into subsets, whose sums of determinants are real and positive even though their cardinality only grows linearly with the matrix size. A detailed proof of this positivity theorem is given for an arbitrary number of fermion flavors. We performed importance sampling Monte Carlo simulations to compute the chiral condensate and the quark number density for varying chemical potential and volume. The statistical errors on the results only show a mild dependence on the matrix size and chemical potential, which confirms the absence of sign problem in the subset method. This strongly contrasts with the exponential growth of the statistical error in standard reweighting methods, which was also analyzed quantitatively using the subset method. Finally, we show how the method elegantly resolves the Silver Blaze puzzle in the microscopic limit of the matrix model, where it is equivalent to QCD.Comment: 18 pages, 11 figures, as published in Phys. Rev. D; added references; in Sec. VB: added discussion of model satisfying the Silver Blaze for all N (proof in Appendix E

Mini-Publics as an innovation in spatial governance

Mini-publics—deliberative fora made up of randomly selected, representative groups of citizens—have attracted considerable interest as a means of resolving perceived weaknesses in existing forms of governance. In this paper, we consider the use of a mini-public or citizens’ assembly to constitute an ad hoc governance space based on the Travel to Work Area of Cambridge in the United Kingdom rather than working within the existing local government boundaries within which transport infrastructure is usually governed. Through this case study, we explore the question of embedding mini-publics in the wider processes of policy and decision-making. More specifically this is the question of the extent to which they ought to be permitted to inform and even assume responsibility for local-level transport policy decisions. We argue that, if they are to become more widely used, then it will be necessary to understand the practices associated with such democratic experiments and their potential to transform existing governance networks in contested areas of spatial policy