Embedding HMMs-based models in a Euclidean space: the topological hidden Markov models

Current extensions of hidden Markov models such as structural, hierarchical, coupled, and others have the power to classify complex and highly organized patterns. However, one of their major limitations is the inability to cope with topology: When applied to a visible observation (VO) sequence, the traditional HMM-based techniques have difficulty predicting the n-dimensional shape formed by the symbols of the VO sequence. To fulfill this need, we propose a novel paradigm named “topological hidden Markov models” (THMMs) that classifies VO sequences by embedding the nodes of an HMM state transition graph in a Euclidean space. This is achieved by modeling the noise embedded in the shape generated by the VO sequence. We cover the first and second level topological HMMs. We describe five basic problems that are assigned to a second level topological hidden Markov model: (1) sequence probability evaluation, (2) statistical decoding, (3) structural decoding, (4) topological decoding, and (5) learning. To show the significance of this research, we have applied the concept of THMMs to: (i) predict the ASCII class assigned to a handwritten numeral, and (ii) map protein primary structures to their 3D folds. The results show that the second level THMMs outperform the SHMMs and the multi-class SVM classifiers significantly.     

A high quality and small shadow size visual secret sharing scheme based on hybrid strategy for grayscale images

Many secret sharing schemes for digital images have been developed in recent decades. Traditional schemes typically must deal with the problem of computational complexity, and other visual secret sharing schemes come with a higher transmission cost and storage cost; that is, each shadow size is m times as big as the original secret image. The new (2,n) secret sharing scheme for grayscale images proposed in this paper is based a combination of acceptable image quality using block truncation coding (BTC), high compression ratio discrete wavelet transform (DWT) and good subjective performance of the vector quantization (VQ) technique. Experimental results confirm that our proposed scheme not only generates a high quality reconstructed original image but also generates small, random-like grayscale shadows.     

A goodness-of-fit test for Archimedean copula models in the presence of right censoring

A goodness-of-fit testing procedure for Archimedean copula (AC) models is developed based on right-censored data. The proposed approach extends an existing method, which is suitable for the Clayton model, to general AC models. Asymptotic properties of the proposed test statistics under the true model assumption are derived. Simulation analysis shows that the proposed test has reasonable performance. Finally, two real data examples are analyzed for illustrative purposes.     

Robust model selection with flexible trimming

The forward search provides data-driven flexible trimming of a C_p statistic for the choice of regression models that reveals the effect of outliers on model selection. An informed robust model choice follows. Even in small samples, the statistic has a null distribution indistinguishable from an F distribution. Limits on acceptable values of the C_p statistic follow. Two examples of widely differing size are discussed. A powerful graphical tool is the generalized candlestick plot, which summarizes the information on all forward searches and on the choice of models. A comparison is made with the use of M-estimation in robust model choice.     

Finding an Euclidean anti--centrum location of a set of points

An obnoxious facility is to be located inside a polygonal region of the plane, maximizing the sum of the k smallest weighted Euclidean distances to n given points, each protected by some polygonal forbidden region. For the unweighted case and k fixed an O(n²logn) time algorithm is presented. For the weighted case a thorough study of the relevant structure of the multiplicatively weighted order-k-Voronoi diagram leads to the design of an O(kn³+n³logn) time algorithm for finding an optimal solution to the anti-t-centrum problem for every t=1,…,k, simultaneously.     

Global existence and nonexistence for degenerate parabolic equations with nonlinear boundary flux

In this paper, by constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions of global existence for nonnegative solutions to a degenerate parabolic system with completely coupled boundary conditions, which generalize the recent results of, for instance, Cui [Z. Cui, Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions, Nonlinear Anal. 68 (2008) 3201–3208], Zhou–Mu [J. Zhou, C. Mu, Algebraic criteria for global existence or blow-up for a boundary coupled system of nonlinear diffusion equations, Appl. Anal. 86 (2007) 1185–1197] etc.     

On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

In this paper, we investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. The results are obtained by using the α-resolvent family (S_α(t))_t≥0 on a complex Banach space X combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.     

On a new class of analytic functions associated with conic domain

The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk E onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain.