Vector valued Macdonald polynomials

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type $A_{N-1}$. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and the symmetrization of the Macdonald polynomials. The main tool of the study is the Yang-Baxter graph. We show that these Macdonald polynomials can be easily computed following this graph. We give also an interpretation of the symmetrization and the bilinear forms applied to the Macdonald polynomials in terms of the Yang-Baxter graph.Comment: 85 pages, 5 figure

Phase transition in the Countdown problem

Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We then derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.Comment: Submitted for publicatio

Chaos control in random Boolean networks by reducing mean damage percolation rate

Chaos control in Random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. This paper proposes a new control method in which controlled nodes can exert an active impact on the network. Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions. Simulation results show that the number of nodes needed to achieve control is largely reduced compared to previous method. Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control.Comment: 10 pages, 2 figure

Powers of the Vandermonde determinant, Schur Functions, and recursive formulas

Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, we give recursive formulas for the coefficient of the Schur function s_{\m} in the decomposition of an even power of the Vandermonde determinant in $n + 1$ variables in terms of the coefficient of the Schur function s_{\l} in the decomposition of the same even power of the Vandermonde determinant in $n$ variables if the Young diagram of \m is obtained from the Young diagram of \l by adding a tetris type shape to the top or to the left. An extended abstract containing the statement of the results presented here appeared in the Proceedings of FPSAC11Comment: 23 pages; extended abstract appeared in the Proceedings of FPSAC1

Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

Enhancing urban autonomy : towards a new political project for cities.

As the 21st Century world assumes an increasingly urban landscape, the question of how definitive urban spaces are to be governed intensifies. At the heart of this debate lies a question about the degree and type of autonomy that towns and cities might have in shaping their economic, environmental, social and cultural geography. This paper aims to examine this question. Starting with the premise that the degree of autonomy any particular town or city has is inherently an empirical question – one which can only be conceptualised in relational terms vis-à-vis the distributed, networked and territorialised responsibilities and powers of the city and the nation-state and other zones of connection – we examine four different contexts where debates over autonomy have intensified in recent history (Brazil, UK, India and South Africa). Drawing on recent respective histories, we identify key elements and enablers in the making of urban autonomy: a characteristic that exists in a variety of guises and forms and creates a patchwork landscape of differentially powerful fragments. We reveal how, beyond its characteristic as a political ideal, autonomy surfaces as a practice that emerges from within specific sectors of particular societies and through their relationship with national and regional politics. Four alternative forms of urban autonomy are delineated: fragmented, coerced (or enclave), distributed and networked. We contend that the spatial templates for autonomy are not predetermined but can be enhanced in multiple different sites and forms of political space within the city. This enhancement appears essential for the integration and strengthening of capacities for sustainable and just forms of development throughout the urban

The Partition Function of Multicomponent Log-Gases

We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\beta} = 1 and {\beta} = 4) ensembles extended to multicomponent ensembles.Comment: 14 page

Algebraic invariants of five qubits

The Hilbert series of the algebra of polynomial invariants of pure states of five qubits is obtained, and the simplest invariants are computed.Comment: 4 pages, revtex. Short discussion of quant-ph/0506073 include

Prolactin responses to stress induced by a competitive swimming effort

Purpose:The aim of the present study was to investigate the changes in prolactin (PRL) plasma concentrations induced by competitive swimming practice. Methods:Twenty-three males, 13 trained swimmers (experimental group) and 10 sedentary and healthy students (age-matched control group) took part in this investigation. The swimmers were assessed at three points: basal conditions, pre-and post-swimming competition (100 m freestyle), whereas subjects from the control group only undertook the basal trial. The variables analysed were: several body composition measures, anxiety level (STAI questionnaire), PRL and lactic acid concentrations. Results:No statistical differences were observed in PRL basal levels between groups. An evident PRL response to pre-competition psychological stress was observed in the experimental group, since the PRL plasma concentration rosefrom 4.02±0.53 ng/ml (basal conditions) to 5.52±0.53 ng/ml (p≤0.05). The PRL response to the competitive effort produced an important increase in its plasma concentration (10.07±1.59 ng/ml), showed statistical differences from pre-competition (p≤0.01) and from basal conditions (p≤0.001). A significant rise in plasma lactate levels just at the end of the effort was found, although it did not correlate with PRL levels in the same situation. Conclusion:While we observed a remarkable response of PRL to psychological and physiological stress induced by a short term competitive effort in swimming, no changes in PRL basal levels were exhibitedwith swim training. More research is needed to clarify these findings