•We propose a cellular automata approach to texture recognition.•Transition function based on local binary features.•Chaotic evolution controlled by a weighting parameter.•The method is evaluated on ...the classification of benchmark textures.•State-of-the-art methods are outperformed in terms of classification accuracy.
Texture recognition is one of the most important tasks in computer vision and, despite the recent success of learning-based approaches, there is still need for model-based solutions. This is especially the case when the amount of data available for training is not sufficiently large, a common situation in several applied areas, or when computational resources are limited. In this context, here we propose a method for texture descriptors that combines the representation power of complex objects by cellular automata with the known effectiveness of local descriptors in texture analysis. The method formulates a new transition function for the automaton inspired by local binary descriptors. It counterbalances the new state of each cell with the previous state, in this way introducing an idea of “controlled deterministic chaos”. The descriptors are obtained from the distribution of cell states. The proposed descriptors are applied to the classification of texture images both on benchmark data sets and a real-world problem, i.e., that of identifying plant species based on the texture of their leaf surfaces. Our proposal outperforms other classical and state-of-the-art approaches, especially in the real-world problem, thus revealing its potential to be applied in numerous practical tasks involving texture recognition at some stage.
Abstract
We obtain new characterizations for nonuniform and uniform asymptotic behaviors of variational systems in infinite dimensional spaces, following the line of studies recently developed in ...Dragičević et al. (J Differ Equ 268:4786–4829, 2020, J Dyn Differ Equ 34:1107–1137, 2022, Appl Math Comput 414:1–22, 2022, J Math Anal Appl 515:1–37, 2022). First, we give complete descriptions for both nonuniform and uniform stability by means of some nonuniform conditions of convergence for series of suitable nonlinear trajectories. We apply our criteria to present a novel method of exploring the robustness of the nonuniform exponential stability under additive and multiplicative perturbations and we also deduce some consequences for the robustness of the uniform exponential stability. After that, we obtain characterizations for nonuniform and uniform instability in terms of certain nonuniform conditions imposed to the sums of some well-chosen series of nonlinear trajectories. We apply our results to provide a new technique of exploring the robustness of the nonuniform exponential instability under additive and multiplicative perturbations and discuss the consequences for uniform exponential instability. Hence, for both stability and instability we generalize the previous Zabczyk type results and extend their applicability. Next, as another class of applications, we provide nonuniform criteria of Rolewicz type for stability and instability of skew-product semiflows. Thus, we extend the Zabczyk–Rolewicz type methods in two directions: by giving local conditions for global behaviors and by employing specific nonuniform boundedness conditions. Our criteria can be applied to broad classes of discrete and continuous variational dynamical systems.
In this paper we investigate stability of the integrability property of skew products of interval maps under small
-smooth perturbations satisfying some conditions. We obtain here (sufficient) ...conditions of the partial integrability for maps under considerations. These conditions are formulated in the terms of properties of the unperturbed skew product. We give also the example of the partially integrable map.
Boolean Networks can be converted to discrete linear dynamical systems on finite spaces by a semi-tensor-product approach. This approach has been used by many to study the dynamics and control of ...Boolean systems. However, the process of getting the linear representation using the semi-tensor-product method is complicated even for a simple three-node network and requires the help of a computer program. In this work, we show that we can skip the semi-tensor process and obtain the same linear representation with a straightforward mapping. Moreover, our approach produces a large number of isomorphic representations which provides a flexible framework. Importantly, it could simplify the analytical study of networks with unspecified number of nodes that have some structure.
Decreasing sandpiles model the dynamics of configurations where each position i∈N contains a finite number of stacked grains hi, such that hi≥hi+1 (decrease property). Grains move according to a ...decreasing local rule R=(r1,r2,…,rp) such that rj≥rj+1, meaning that rj grains move from columns i to i+j for all 1≤j≤p, if it does not contradict the decrease property. We are interested in the fixed point reached starting from a finite number of grains on a unique column.
In 21, we proved the emergence of wave patterns periodically covering fixed points, for rules of the form (1,…,1) (Kadanoff sandpile models). The present work is a significative extension: for large classes of decreasing sandpile model instances, we prove the emergence of patterns of various shapes periodically covering fixed points. We introduce new automata to analyze their asymptotic structure, and use the least action principle. The difficulty of understanding the behavior of sandpile models, despite the simplicity of the rules, is what makes the problem challenging.
Entropy on abelian groups Dikranjan, Dikran; Giordano Bruno, Anna
Advances in mathematics (New York. 1965),
08/2016, Letnik:
298
Journal Article
Recenzirano
Odprti dostop
We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy. The basic properties of the algebraic entropy are given, as well ...as various examples. The main result of this paper is the Addition Theorem showing that the algebraic entropy is additive in appropriate sense with respect to invariant subgroups. We give several applications of the Addition Theorem, among them the Uniqueness Theorem for the algebraic entropy in the category of all abelian groups and their endomorphisms. Furthermore, we point out the delicate connection of the algebraic entropy with the Mahler measure and Lehmer Problem in Number Theory.
•The Boolean algebra concept of nested canalization is generalized.•Expected average c-sensitivities of nested canalizing functions are computed.•A unique polynomial form of nested canalizing ...functions is provided.•An explicit formula for the number of nested canalizing functions is presented.•An accurate approximation for the number of nested canalizing functions is derived.
This paper provides a collection of mathematical and computational tools for the study of robustness in nonlinear gene regulatory networks, represented by time- and state-discrete dynamical systems taking on multiple states. The focus is on networks governed by nested canalizing functions (NCFs), first introduced in the Boolean context by S. Kauffman. After giving a general definition of NCFs we analyze the class of such functions. We derive a formula for the normalized average c-sensitivities of multistate NCFs, which enables the calculation of the Derrida plot, a popular measure of network stability. We also provide a unique canonical parametrized polynomial form of NCFs. This form has several consequences. We can easily generate NCFs for varying parameter choices, and derive a closed form formula for the number of such functions in a given number of variables, as well as an asymptotic formula. Finally, we compute the number of equivalence classes of NCFs under permutation of variables. Together, the results of the paper represent a useful mathematical framework for the study of NCFs and their dynamic networks.
PDF
