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Hasimoto-Beltran R.,Center for Research in Mathematics
Proceedings - 3rd International Conference on Multimedia Information Networking and Security, MINES 2011

We present a new LUT design consisting of a non-iterative plaintext transformation and a high dimensionally (K-map) populated dynamic Look-Up Table with random access that outperforms the security and speed of previous LUT based schemes. Experimental analysis of the proposed scheme reveals excellent statistical properties, sensitivity to plaintext/system-key changes, robustness to differential and chosen plaintext attack, and high performance for real-time multimedia communications. © 2011 IEEE. Source

Segura C.,Center for Research in Mathematics | Coello Coello C.A.,National Polytechnic Institute of Mexico | Hernandez-Diaz A.G.,Pablo De Olavide University
Information Sciences

Differential Evolution is an efficient metaheuristic for continuous optimization that suffers from the curse of dimensionality. A large amount of experimentation has allowed researchers to find several potential weaknesses in Differential Evolution. Some of these weaknesses do not significantly affect its performance when dealing with low-dimensional problems, so the research community has not paid much attention to them. The aim of this paper is to provide a better insight into the reasons of the curse of dimensionality and to propose techniques to alleviate this problem. Two different weaknesses are revisited and schemes for dealing with them are devised. The schemes increase the diversity of trial vectors and improve on the exploration capabilities of Differential Evolution. Some important mathematical properties induced by our proposals are studied and compared against those of related schemes. Experimentation with a set of problems with up to 1000 dimensions and with several variants of Differential Evolution shows that the weaknesses analyzed significantly affect the performance of Differential Evolution when used on high-dimensional optimization problems. The gains of the proposals appear when highly exploitative schemes are used. Our proposals allow for high-quality solutions with small populations, meaning that the most significant advantages emerge when dealing with large-scale optimization problems, where the benefits of using small populations have previously been shown. © 2015 Elsevier Inc. Source

Barrera G.,Center for Research in Mathematics | Barrera G.,Institute Matematica Pura e Aplicada | Jara M.,Institute Matematica Pura e Aplicada
Journal of Statistical Physics

We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semiflow of a deterministic differential equation which is perturbed by adding to the dynamics a white noise of small variance. Under suitable hypothesis on the potential we will prove that the family of perturbed stochastic differential equations present a profile cut-off phenomenon with respect to the total variation distance. We also prove a local cut-off phenomenon in a neighborhood of the local minima (metastable states) of multi-well potential. © 2016, Springer Science+Business Media New York. Source

Debruyne M.,University of Antwerp | Hubert M.,Catholic University of Leuven | Van Horebeek J.,Center for Research in Mathematics
Computational Statistics and Data Analysis

Kernel Principal Component Analysis extends linear PCA from a Euclidean space to any reproducing kernel Hilbert space. Robustness issues for Kernel PCA are studied. The sensitivity of Kernel PCA to individual observations is characterized by calculating the influence function. A robust Kernel PCA method is proposed by incorporating kernels in the Spherical PCA algorithm. Using the scores from Spherical Kernel PCA, a graphical diagnostic is proposed to detect points that are influential for ordinary Kernel PCA. © 2009 Elsevier B.V. All rights reserved. Source

Almasalha F.,Applied Science Private University | Hasimoto-Beltran R.,Center for Research in Mathematics | Khokhar A.A.,Illinois Institute of Technology

Due to pervasive communication infrastructures, a plethora of enabling technologies is being developed over mobile and wired networks. Among these, video streaming services over IP are the most challenging in terms of quality, real-time requirements and security. In this paper, we propose a novel scheme to efficiently secure variable length coded (VLC) multimedia bit streams, such as H.264. It is based on code word error diffusion and variable size segment shuffling. The codeword diffusion and the shuffling mechanisms are based on random operations from a secure and computationally efficient chaos-based pseudo-random number generator. The proposed scheme is ubiquitous to the end users and can be deployed at any node in the network. It provides different levels of security, with encrypted data volume fluctuating between 5.5-17%. It works on the compressed bit stream without requiring any decoding. It provides excellent encryption speeds on different platforms, including mobile devices. It is 200% faster and 150% more power efficient when compared with AES software-based full encryption schemes. Regarding security, the scheme is robust to well-known attacks in the literature, such as brute force and known/chosen plain text attacks. © 2014 by the authors. Source

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