Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure

Quantum Analogy of Poisson Geometry, Related Dendriform Algebras and Rota-Baxter Operators

We will introduce an associative (or quantum) version of Poisson structure tensors. This object is defined as an operator satisfying a "generalized" Rota-Baxter identity of weight zero. Such operators are called generalized Rota-Baxter operators. We will show that generalized Rota-Baxter operators are characterized by a cocycle condition so that Poisson structures are so. By analogy with twisted Poisson structures, we propose a new operator "twisted Rota-Baxter operators" which is a natural generalization of generalized Rota-Baxter operators. It is known that classical Rota-Baxter operators are closely related with dendriform algebras. We will show that twisted Rota-Baxter operators induce NS-algebras which is a twisted version of dendriform algebra. The twisted Poisson condition is considered as a Maurer-Cartan equation up to homotopy. We will show the twisted Rota-Baxter condition also is so. And we will study a Poisson-geometric reason, how the twisted Rota-Baxter condition arises.Comment: 18 pages. Final versio

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Ensaio preliminar de sorgo granífero.

O objetivo deste trabalho foi o de testar 45 variedades de sorgo em Afrânio-PE, oriundos de uma seleção anterior realizada pelo Programa de Sorgo e Milheto-IPA-PE, em Serra Talhada. Foram incluidas 4 variedades já testadas na região, como controle, perfazendo um total de 49 repetições

A conjugate for the Bargmann representation

In the Bargmann representation of quantum mechanics, physical states are mapped into entire functions of a complex variable z*, whereas the creation and annihilation operators $\hat{a}^\dagger$ and $\hat{a}$ play the role of multiplication and differentiation with respect to z*, respectively. In this paper we propose an alternative representation of quantum states, conjugate to the Bargmann representation, where the roles of $\hat{a}^\dagger$ and $\hat{a}$ are reversed, much like the roles of the position and momentum operators in their respective representations. We derive expressions for the inner product that maintain the usual notion of distance between states in the Hilbert space. Applications to simple systems and to the calculation of semiclassical propagators are presented.Comment: 15 page

An in-reachability based classification of invariant synchrony patterns in weighted coupled cell networks

This paper presents an in-reachability based classification of invariant synchrony patterns in Coupled Cell Networks (CCNs). These patterns are encoded through partitions on the set of cells, whose subsets of synchronized cells are called colors. We study the influence of the structure of the network in the qualitative behavior of invariant synchrony sets, in particular, with respect to the different types of (cumulative) in-neighborhoods and the in-reachability sets. This motivates the proposed approach to classify the partitions into the categories of strong, rooted and weak, according to how their colors are related with respect to the connectivity structure of the network. Furthermore, we show how this classification system acts under the partition join ($\vee$) operation, which gives us the synchrony pattern that corresponds to the intersection of synchrony sets.Comment: 48 pages, 19 figures, 3 table

Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach

We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically we show that the effects of the low dimensional chaotic environment are in many ways similar to those produced by thermal baths. The classical correlation and response functions play important roles in both classical and quantum formulations. Our results are qualitatively similar to the high temperature regime of the Caldeira-Leggett model.Comment: 31 pages, 4 figure

Métodos de cálculo de taxa lotação em pastagens com suplementação.

A taxa de lotação é a relação entre o número de unidades animais (UA) e a área por eles ocupada. O uso da unidade animal no cálculo da taxa de lotação tem a finalidade de padronizar o efeito das diferentes categorias animais sobre o pasto. O fornecimento de suplementação alimentar provoca distorções no cálculo da taxa de lotação. O objetivo desse trabalho foi determinar uma alternativa de cálculo de taxa de lotação para animais a pasto recebendo suplementação alimentar. A taxa de lotacão foi calculada assumindo que 1 UA corresponde a 1 animal de 454 e que 1 UA corresponde a um animal consumindo 12kg MS/dia. O consumo de forragem foi estimado pelo Corne" Net Carbohydrate and Protein System (CNCPS 3.0). Em todos os períodos, a taxa de lotação calculada a partir do peso vivo dos anímais foi mais elevada que aquela calculada com base na estimativa do consumo de matéria seca, com variações de 0,6 a 11,8 unidades de taxa de lotação. Para vacas em lactação sob pastejo, o concentrado pode representar mais de 50% do consumo total de matéria seca. Concluiu-se que o cálculo da taxa de lotação com base no peso vivo dos animais não é adequado quando os animais recebem suplementação alimentar. O cálculo da taxa de lotação a partir da estimativa do consumo de matéria seca de forragem é uma alternativa viável, porém os modelos de simulação que estimatimam consumo de matéria seca dos animais precisam ser aprimorados e validados para condições tropicais