Solving ℓp ⁣\ell^p\!-norm regularization with tensor kernels

In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast recent findings suggesting kernel methods cannot be extended beyond Hilbert setting. Numerical experiments confirm the effectiveness of the method

Modeling Time Series of Real Systems using Genetic Programming

Analytic models of two computer generated time series (Logistic map and Rossler system) and two real time series (ion saturation current in Aditya Tokamak plasma and NASDAQ composite index) are constructed using Genetic Programming (GP) framework. In each case, the optimal map that results from fitting part of the data set also provides a very good description of rest of the data. Predictions made using the map iteratively range from being very good to fair.Comment: 10 pages, 9 figures, submitted to Physical Review

Information, complexity and entropy: a new approach to theory and measurement methods

In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have the following features and motivations: -we give a new computable definition of information and complexity which allows to give a computable characterization of the K-S entropy; -these definitions make sense even for a single orbit and can be measured by suitable data compression algorithms; hence they can be used in simulations and in the analysis of experimental data; -the asymptotic behavior of these quantities allows to compute not only the Kolmogorov-Sinai entropy but also other quantities which give a measure of the chaotic behavior of a dynamical system even in the case of null entropy.Comment: 30 pages, 6 figure

Separating a mixture of chaotic signals

Chaos is popularly associated with its property of sensitivity to initial conditions. In this paper we will show that there can be a flip side to this property which is quite fascinating and highly useful in many applications. As a result, we can mix a large number of chaotic signals and one completely arbitrary signal and later a recipient of this transformed and weighted mixture can separate each of the signals, one by one. The chaotic signals, could be generated by various maps which belong to the logistic family. The arbitrary signal, could be a message, some random noise, some periodic signal or a chaotic signal generated by a source, either belonging or not belonging to the family. The key behind this procedure is a family of maps which can dovetail into each other without altering each of their predecessor's symbolic sequence.Comment: 9 pages, 7 figures. This paper was presented at International Conference on Non-linear Dynamics and Chaos: Advances and Perspectives, 17--21 September 2007, Aberdeen, U

Exploiting ergodicity of the logistic map using deep-zoom to improve security of chaos-based cryptosystems

This paper explores the deep-zoom properties of the chaotic k-logistic map, in order to propose an improved chaos-based cryptosystem. This map was shown to enhance the random features of the Logistic map, while at the same time reducing the predictability about its orbits. We incorporate its strengths to security into a previously published cryptosystem to provide an optimal pseudo-random number generator (PRNG) as its core operation. The result is a reliable method that does not have the weaknesses previously reported about the original cryptosystem.Comment: 11 pages, 6 figure

Learning and inference in knowledge-based probabilistic model for medical diagnosis

Based on a weighted knowledge graph to represent first-order knowledge and combining it with a probabilistic model, we propose a methodology for the creation of a medical knowledge network (MKN) in medical diagnosis. When a set of symptoms is activated for a specific patient, we can generate a ground medical knowledge network composed of symptom nodes and potential disease nodes. By Incorporating a Boltzmann machine into the potential function of a Markov network, we investigated the joint probability distribution of the MKN. In order to deal with numerical symptoms, a multivariate inference model is presented that uses conditional probability. In addition, the weights for the knowledge graph were efficiently learned from manually annotated Chinese Electronic Medical Records (CEMRs). In our experiments, we found numerically that the optimum choice of the quality of disease node and the expression of symptom variable can improve the effectiveness of medical diagnosis. Our experimental results comparing a Markov logic network and the logistic regression algorithm on an actual CEMR database indicate that our method holds promise and that MKN can facilitate studies of intelligent diagnosis.Comment: 32 pages, 8 figure

Image Encryption Algorithm Using Natural Interval Extensions

It is known that chaotic systems have widely been used in cryptography. Generally, floating point simulations are used to generate pseudo-random sequence of numbers. Although, it is possible to find some works on the degradation of chaotic systems due to finite precision of digital computers, little attention has been paid to exploit this limitation to formulate efficient process for image encode. This article proposes a novel image encryption method using natural interval extensions. The sequence of arithmetic operations is different in each natural interval extension. This is what we need to produce two different sequences; the difference between these sequences is used to generate the lower bound error, which has been shown to present satisfactory pseudo-random properties. The approach has been successfully tested using the Chua's circuit as the chaotic system. The secret key has presented good properties for encrypting the Lena image.Comment: BTSym'18 - Brazilian Techonology Symposium, 2018, Campinas. 5 page

Functional Dynamics I : Articulation Process

The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a self-reference term $f \circ f$, introduced by recalling that operation in a biological system is often applied to itself, as is typically seen in rules in the natural language or genes. Starting from an inarticulate network, two types of fixed points are formed as an invariant structure with iterations. The function is folded with time, until it has finite or infinite piecewise-flat segments of fixed points, regarded as articulation. For an initial logistic map, attracted functions are classified into step, folded step, fractal, and random phases, according to the degree of folding. Oscillatory dynamics are also found, where function values are mapped to several fixed points periodically. The significance of our results to prototype categorization in language is discussed.Comment: 48 pages, 15 figeres (5 gif files

Compressive sampling with chaotic dynamical systems

We investigate the possibility of using different chaotic sequences to construct measurement matrices in compressive sampling. In particular, we consider sequences generated by Chua, Lorenz and Rossler dynamical systems and investigate the accuracy of reconstruction when using each of them to construct measurement matrices. Chua and Lorenz sequences appear to be suitable to construct measurement matrices. We compare the recovery rate of the original sequence with that obtained by using Gaussian, Bernoulli and uniformly distributed random measurement matrices. We also investigate the impact of correlation on the recovery rate. It appears that correlation does not influence the probability of exact reconstruction significantly.Comment: 19th Telecommunications Forum TELFOR 2011, November 2011, Belgrade, Serbi

AX-DBN: An Approximate Computing Framework for the Design of Low-Power Discriminative Deep Belief Networks

The power budget for embedded hardware implementations of Deep Learning algorithms can be extremely tight. To address implementation challenges in such domains, new design paradigms, like Approximate Computing, have drawn significant attention. Approximate Computing exploits the innate error-resilience of Deep Learning algorithms, a property that makes them amenable for deployment on low-power computing platforms. This paper describes an Approximate Computing design methodology, AX-DBN, for an architecture belonging to the class of stochastic Deep Learning algorithms known as Deep Belief Networks (DBNs). Specifically, we consider procedures for efficiently implementing the Discriminative Deep Belief Network (DDBN), a stochastic neural network which is used for classification tasks, extending Approximation Computing from the analysis of deterministic to stochastic neural networks. For the purpose of optimizing the DDBN for hardware implementations, we explore the use of: (a)Limited precision of neurons and functional approximations of activation functions; (b) Criticality analysis to identify nodes in the network which can operate at reduced precision while allowing the network to maintain target accuracy levels; and (c) A greedy search methodology with incremental retraining to determine the optimal reduction in precision for all neurons to maximize power savings. Using the AX-DBN methodology proposed in this paper, we present experimental results across several network architectures that show significant power savings under a user-specified accuracy loss constraint with respect to ideal full precision implementations