Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

Identification of a class of non-linear systems

This paper considers the on-line identification of a non-linear system in terms of a Hammerstein model, with a zero-memory non-linear gain followed by a linear system. The linear part is represented by a Laguerre expansion of its impulse response and the non-linear part by a polynomial. The identification procedure involves determination of the coefficients of the Laguerre expansion of correlation functions and an iterative adjustment of the parameters of the non-linear gain by gradient methods. The method is applicable to situations involving a wide class of input signals. Even in the presence of additive correlated noise, satisfactory performance is achieved with the variance of the error converging to a value close to the variance of the noise. Digital computer simulation establishes the practicability of the scheme in different situations.

A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

Automata and logics over finitely varying functions

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called View the MathML source’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of View the MathML source’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

A new class of separators and planarity of chordal graphs

We introduce a new class of clique separators, called base sets, for chordal graphs. Base sets of a chordal graph closely reflect its structure. We show that the notion of base sets leads to structural characterizations of planar k-trees and planar chordal graphs. Using these characterizations, we develop linear time algorithms for recognizing planar k-trees and planar chordal graphs. These algorithms are extensions of the Lexicographic_Breadth_First_Search algorithm for recognizing chordal graphs and are much simpler than the general planarity checking algorithm. Further, we use the notion of base sets to prove the equivalence of hamiltonian 2-trees and maximal outerplanar graphs.

On the Fekete-Szego problem for concave univalent functions

We consider the Fekete-Szego problem with real parameter lambda for the class Co(alpha) of concave univalent functions. (C) 2010 Elsevier Inc. All rights reserved.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

CM defect and Hilbert functions of monomial curves

In this article we consider a semigroup ring R = KGamma] of a numerical semigroup Gamma and study the Cohen- Macaulayness of the associated graded ring G(Gamma) := gr(m), (R) := circle plus(n is an element of N) m(n)/m(n+1) and the behaviour of the Hilbert function H-R of R. We define a certain (finite) subset B(Gamma) subset of F and prove that G(Gamma) is Cohen-Macaulay if and only if B(Gamma) = empty set. Therefore the subset B(Gamma) is called the Cohen-Macaulay defect of G(Gamma). Further, we prove that if the degree sequence of elements of the standard basis of is non-decreasing, then B(F) = empty set and hence G(Gamma) is Cohen-Macaulay. We consider a class of numerical semigroups Gamma = Sigma(3)(i=0) Nm(i) generated by 4 elements m(0), m(1), m(2), m(3) such that m(1) + m(2) = mo m3-so called ``balanced semigroups''. We study the structure of the Cohen-Macaulay defect B(Gamma) of Gamma and particularly we give an estimate on the cardinality |B(Gamma, r)| for every r is an element of N. We use these estimates to prove that the Hilbert function of R is non-decreasing. Further, we prove that every balanced ``unitary'' semigroup Gamma is ``2-good'' and is not ``1-good'', in particular, in this case, c(r) is not Cohen-Macaulay. We consider a certain special subclass of balanced semigroups Gamma. For this subclass we try to determine the Cohen-Macaulay defect B(Gamma) using the explicit description of the standard basis of Gamma; in particular, we prove that these balanced semigroups are 2-good and determine when exactly G(Gamma) is Cohen-Macaulay. (C) 2011 Published by Elsevier B.V.

Adaptive optimal tuning of a general class of stable LTI systems with restricted inputs

The problem addressed is one of model reference adaptive control (MRAC) of asymptotically stable plants of unknown order with zeros located anywhere in the s-plane except at the origin. The reference model is also asymptotically stable and lacking zero(s) at s = 0. The control law is to be specified only in terms of the inputs to and outputs of the plant and the reference model. For inputs from a class of functions that approach a non-zero constant, the problem is formulated in an optimal control framework. By successive refinements of the sub-optimal laws proposed here, two schemes are finally design-ed. These schemes are characterized by boundedness, convergence and optimality. Simplicity and total time-domain implementation are the additional striking features. Simulations to demonstrate the efficacy of the control schemes are presented.

Reduced Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and /spl thetas/-D Techniques

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems. First proper orthogonal decomposition based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. Next, a suboptimal controller is designed using the emerging /spl thetas/-D technique for lumped parameter systems. This time domain sub-optimal control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state feedback form. Numerical results for a real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good suboptimal control design technique for distributed parameter systems.

Lossless and lossy image compression using Boolean function minimization

A novel approach for lossless as well as lossy compression of monochrome images using Boolean minimization is proposed. The image is split into bit planes. Each bit plane is divided into windows or blocks of variable size. Each block is transformed into a Boolean switching function in cubical form, treating the pixel values as output of the function. Compression is performed by minimizing these switching functions using ESPRESSO, a cube based two level function minimizer. The minimized cubes are encoded using a code set which satisfies the prefix property. Our technique of lossless compression involves linear prediction as a preprocessing step and has compression ratio comparable to that of JPEG lossless compression technique. Our lossy compression technique involves reducing the number of bit planes as a preprocessing step which incurs minimal loss in the information of the image. The bit planes that remain after preprocessing are compressed using our lossless compression technique based on Boolean minimization. Qualitatively one cannot visually distinguish between the original image and the lossy image and the value of mean square error is kept low. For mean square error value close to that of JPEG lossy compression technique, our method gives better compression ratio. The compression scheme is relatively slower while the decompression time is comparable to that of JPEG.

A New Class of Exactly Solvable Interacting Fermion Models in One Dimension

We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be salved exactly via a simple unitary transformation. Nevertheless, correlation functions exhibit nontrivial interaction-dependent exponents. A similar model defined on a lattice is introduced and solved. Various generalizations, e.g., to the case of internal symmetries of the fermions, are discussed. The present treatment also clarifies certain aspects of Luttinger's original solution of the "Luttinger model."

Features of a unique intronless cluster of class I small heat shock protein genes in tandem with box C/D snoRNA genes on chromosome 6 in tomato (Solanum lycopersicum)

Physical clustering of genes has been shown in plants; however, little is known about gene clusters that have different functions, particularly those expressed in the tomato fruit. A class I 17.6 small heat shock protein (Sl17.6 shsp) gene was cloned and used as a probe to screen a tomato (Solanum lycopersicum) genomic library. An 8.3-kb genomic fragment was isolated and its DNA sequence determined. Analysis of the genomic fragment identified intronless open reading frames of three class I shsp genes (Sl17.6, Sl20.0, and Sl20.1), the Sl17.6 gene flanked by Sl20.1 and Sl20.0, with complete 5' and 3' UTRs. Upstream of the Sl20.0 shsp, and within the shsp gene cluster, resides a box C/D snoRNA cluster made of SlsnoR12.1 and SlU24a. Characteristic C and D, and C' and D', boxes are conserved in SlsnoR12.1 and SlU24a while the upstream flanking region of SlsnoR12.1 carries TATA box 1, homol-E and homol-D box-like cis sequences, TM6 promoter, and an uncharacterized tomato EST. Molecular phylogenetic analysis revealed that this particular arrangement of shsps is conserved in tomato genome but is distinct from other species. The intronless genomic sequence is decorated with cis elements previously shown to be responsive to cues from plant hormones, dehydration, cold, heat, and MYC/MYB and WRKY71 transcription factors. Chromosomal mapping localized the tomato genomic sequence on the short arm of chromosome 6 in the introgression line (IL) 6-3. Quantitative polymerase chain reaction analysis of gene cluster members revealed differential expression during ripening of tomato fruit, and relatively different abundances in other plant parts.

Nitric oxide and KLF4 protein epigenetically modify class II transactivator to repress Major histocompatibility complex II expression during Mycobacterium bovis Bacillus Calmette-Guerin infection

Pathogenic mycobacteria employ several immune evasion strategies such as inhibition of class II transactivator (CIITA) and MHC-II expression, to survive and persist in host macrophages. However, precise roles for specific signaling components executing down-regulation of CIITA/MHC-II have not been adequately addressed. Here, we demonstrate that Mycobacterium bovis bacillus Calmette-Guerin (BCG)-mediated TLR2 signaling-induced iNOS/NO expression is obligatory for the suppression of IFN-gamma-induced CIITA/MHC-II functions. Significantly, NOTCH/PKC/MAPK-triggered signaling cross-talk was found critical for iNOS/NO production. NO responsive recruitment of a bifunctional transcription factor, KLF4, to the promoter of CIITA during M. bovis BCG infection of macrophages was essential to orchestrate the epigenetic modifications mediated by histone methyltransferase EZH2 or miR-150 and thus calibrate CIITA/MHC-II expression. NO-dependent KLF4 regulated the processing and presentation of ovalbumin by infected macrophages to reactive T cells. Altogether, our study delineates a novel role for iNOS/NO/KLF4 in dictating the mycobacterial capacity to inhibit CIITA/MHC-II-mediated antigen presentation by infected macrophages and thereby elude immune surveillance.