Weights of Markov Traces on Hecke algebras

We compute the weights, i.e. the values at the minimal idempotents, for the Markov trace on the Hecke algebra of type $B$ and type $D$. In order to prove the weight formula, we define representations of the Hecke algebra of type $B$ onto a reduced Hecke algebre of type $A$. To compute the weights for type $D$ we use the inclusion of the Hecke algebra of type $D$ into the Hecke algebra of type $B$.Comment: 23 pages. see also http://math.ucsd.edu/~rorellan

The Hopf algebra of uniform block permutations. Extended abstract

We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a factorizable inverse monoid. This Hopf algebra contains the Hopf algebra of permutations of Malvenuto and Reutenauer and the Hopf algebra of symmetric functions in non-commuting variables of Gebhard, Rosas, and Sagan.Comment: Extended abstrac

Complete Monotonicity of Fractional Kinetic Functions

The introduction of a fractional differential operator defined in terms of the Riemann-Liouville derivative makes it possible to generalize the kinetic equations used to model relaxation in dielectrics. In this context such fractional equations are called fractional kinetic relaxation equations and their solutions, called fractional kinetic relaxation functions, are given in terms of Mittag-Leffler functions. These fractional kinetic relaxation functions generalize the kinetic relaxation functions associated with the Debye, Cole-Cole, Cole-Davidson and Havriliak-Negami models, as the latter functions become particular cases of the fractional solutions, obtained for specific values of the parameter specifying the order of the derivative. The aim of this work is to analyse the behavior of these fractional functions in the time variable. As theoretical tools we use the theorem by Bernstein on the complete monotonicity of functions together with Titchmarsh's inversion formula. The last part of the paper contains the graphics of some of those functions, obtained by varying the value of the parameter in the fractional differential operator and in the corresponding Mittag-Leffler functions. The graphics were made with Mathematica 10.4.Comment: 28 pages, 38 figure

A micro-structured continuum modelling compacting fluid-saturated grounds: the effects of pore-size scale parameter

The effect of a "pore-size" length-scale parameter l on compaction of grounds with fluid inclusions is studied. They are modelled as continua endowed with micro-structure by means of the macro-modelling procedure proposed in [2]. We show the dependence of field evolution equations on the micro-structure parameter l and compare our model with the homogenized asymptotic ones. The consideration of the pore size 1 allows us to forecast the onset of micro-displacement waves as a consequence of a ground settling and to suggest a possible description of the genesis of certain microearthquakes [5] [6].Comment: 18 page

Nonparametric estimation of a regression function using the gamma kernel method in ergodic processes

In this paper we consider the nonparametric estimation of density and regression functions with non-negative support using a gamma kernel procedure introduced by Chen (2000). Strong uniform consistency and asymptotic normality of the corresponding estimators are established under a general ergodic assumption on the data generation process. Our results generalize those of Shi and Song (2016), obtained in the classic i.i.d. framework, and the works of Bouezmarni and Rombouts (2008, 2010b) and Gospodinov and Hirukawa (2007) for mixing time series.Comment: 29 page

Using Dissortative Mating Genetic Algorithms to Track the Extrema of Dynamic Deceptive Functions

Traditional Genetic Algorithms (GAs) mating schemes select individuals for crossover independently of their genotypic or phenotypic similarities. In Nature, this behaviour is known as random mating. However, non-random schemes - in which individuals mate according to their kinship or likeness - are more common in natural systems. Previous studies indicate that, when applied to GAs, negative assortative mating (a specific type of non-random mating, also known as dissortative mating) may improve their performance (on both speed and reliability) in a wide range of problems. Dissortative mating maintains the genetic diversity at a higher level during the run, and that fact is frequently observed as an explanation for dissortative GAs ability to escape local optima traps. Dynamic problems, due to their specificities, demand special care when tuning a GA, because diversity plays an even more crucial role than it does when tackling static ones. This paper investigates the behaviour of dissortative mating GAs, namely the recently proposed Adaptive Dissortative Mating GA (ADMGA), on dynamic trap functions. ADMGA selects parents according to their Hamming distance, via a self-adjustable threshold value. The method, by keeping population diversity during the run, provides an effective means to deal with dynamic problems. Tests conducted with deceptive and nearly deceptive trap functions indicate that ADMGA is able to outperform other GAs, some specifically designed for tracking moving extrema, on a wide range of tests, being particularly effective when speed of change is not very fast. When comparing the algorithm to a previously proposed dissortative GA, results show that performance is equivalent on the majority of the experiments, but ADMGA performs better when solving the hardest instances of the test set.Comment: Technical report complementing Carlos Fernandes' Ph

Self-Regulated Artificial Ant Colonies on Digital Image Habitats

Artificial life models, swarm intelligent and evolutionary computation algorithms are usually built on fixed size populations. Some studies indicate however that varying the population size can increase the adaptability of these systems and their capability to react to changing environments. In this paper we present an extended model of an artificial ant colony system designed to evolve on digital image habitats. We will show that the present swarm can adapt the size of the population according to the type of image on which it is evolving and reacting faster to changing images, thus converging more rapidly to the new desired regions, regulating the number of his image foraging agents. Finally, we will show evidences that the model can be associated with the Mathematical Morphology Watershed algorithm to improve the segmentation of digital grey-scale images. KEYWORDS: Swarm Intelligence, Perception and Image Processing, Pattern Recognition, Mathematical Morphology, Social Cognitive Maps, Social Foraging, Self-Organization, Distributed Search.Comment: 8 pages, 17 figures, full pictures in http://alfa.ist.utl.pt/~cvrm/staff/vramos/Vramos-WCLC05b.pd

Detecting topological sectors in continuum Yang-Mills theory and the fate of BRST symmetry

In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition function into partial contributions associated with different sectors, containing center vortices and correlated monopoles. We show that, on each sector, the gauge fixed path-integral displays a BRST symmetry, however, it cannot be globally extended due to sector dependent boundary conditions on the ghost fields. These are nice features as they would permit to discuss the independence of the partial contributions on gauge parameters,, while opening a window for the space of quantum states to be different from the perturbative one, which would be implied if topological configurations were removed.Comment: 7 pages, REVTe

On Self-Regulated Swarms, Societal Memory, Speed and Dynamics

We propose a Self-Regulated Swarm (SRS) algorithm which hybridizes the advantageous characteristics of Swarm Intelligence as the emergence of a societal environmental memory or cognitive map via collective pheromone laying in the landscape (properly balancing the exploration/exploitation nature of our dynamic search strategy), with a simple Evolutionary mechanism that trough a direct reproduction procedure linked to local environmental features is able to self-regulate the above exploratory swarm population, speeding it up globally. In order to test his adaptive response and robustness, we have recurred to different dynamic multimodal complex functions as well as to Dynamic Optimization Control problems, measuring reaction speeds and performance. Final comparisons were made with standard Genetic Algorithms (GAs), Bacterial Foraging strategies (BFOA), as well as with recent Co-Evolutionary approaches. SRS's were able to demonstrate quick adaptive responses, while outperforming the results obtained by the other approaches. Additionally, some successful behaviors were found. One of the most interesting illustrate that the present SRS collective swarm of bio-inspired ant-like agents is able to track about 65% of moving peaks traveling up to ten times faster than the velocity of a single individual composing that precise swarm tracking system.Comment: 11 pages, 8 figures, http://alfa.ist.utl.pt/~cvrm/staff/vramos/refs_2005.html, KEYWORDS: Dynamic Optimization, Dynamic Optimal Control problems, Swarm Intelligence, Self-Organization, Societal Implicit Memory. Submitted to ALIFE-X, Int. Conf. on the Simulation and Synthesis of Living Systems, Bloomington, Indiana, USA, June 3-7, 200

SimOutUtils - Utilities for analyzing time series simulation output

SimOutUtils is a suite of MATLAB/Octave functions for studying and analyzing time series-like output from stochastic simulation models. More specifically, SimOutUtils allows modelers to study and visualize simulation output dynamics, perform distributional analysis of output statistical summaries, as well as compare these summaries in order to assert the statistical equivalence of two or more model implementations. Additionally, the provided functions are able to produce publication quality figures and tables showcasing results from the specified simulation output studies.Comment: The peer-reviewed version of this paper is published in the Journal of Open Research Software at http://doi.org/10.5334/jors.110 . This version is typeset by the authors and differs only in pagination and typographical detai