Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Power Minimization for CDMA under Colored Noise

Rate-constrained power minimization (PMIN) over a code division multiple-access (CDMA) channel with correlated noise is studied. PMIN is. shown to be an instance of a separable convex optimization problem subject to linear ascending constraints. PMIN is further reduced to a dual problem of sum-rate maximization (RMAX). The results highlight the underlying unity between PMIN, RMAX, and a problem closely related to PMIN but with linear receiver constraints. Subsequently, conceptually simple sequence design algorithms are proposed to explicitly identify an assignment of sequences and powers that solve PMIN. The algorithms yield an upper bound of 2N - 1 on the number of distinct sequences where N is the processing gain. The sequences generated using the proposed algorithms are in general real-valued. If a rate-splitting and multi-dimensional CDMA approach is allowed, the upper bound reduces to N distinct sequences, in which case the sequences can form an orthogonal set and be binary +/- 1-valued.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

Two-level k-means clustering algorithm for k-tau relationship establishment and linear-time classification

Partitional clustering algorithms, which partition the dataset into a pre-defined number of clusters, can be broadly classified into two types: algorithms which explicitly take the number of clusters as input and algorithms that take the expected size of a cluster as input. In this paper, we propose a variant of the k-means algorithm and prove that it is more efficient than standard k-means algorithms. An important contribution of this paper is the establishment of a relation between the number of clusters and the size of the clusters in a dataset through the analysis of our algorithm. We also demonstrate that the integration of this algorithm as a pre-processing step in classification algorithms reduces their running-time complexity.

Membrane modifying linear polypeptide antibiotics

Peptides Possessing antibiotic activity isolated from microbial sources have been the subject of intensive structural and biological investigation over the past two decades. Perhaps, the discovery and widespread use of penicillin, a molecule biosynthetically derived from a tripeptide precursor, as a strong antibacterial agent, has provided the necessary impetus for the detailed study of microbial peptides. While many of these peptides have not been used clinically, They show unique metal binding properties and often possess the ability to modify the electrical properties or ion permeabilities of artificial lipid membranes. Hence, these peptides have been used extensively to study transmembrane ion transport processes in model and natural systems like mitochondria, chloroplasts and plasma membranes.

Formation of linear plasmid multimers promoted by the phage lambda Red-system in lon mutants of Escherichia coli

We report here the formation of plasmid linear multimers promoted by the Red-system of phage lambda using a multicopy plasmid comprised of lambda red alpha and red beta genes, under the control of the lambda cI857 repressor. Our observations have revealed that the multimerization of plasmid DNA is dependent on the red beta and recA genes, suggesting a concerted role for these functions in the formation of plasmid multimers. The formation of multimers occurred in a recBCD+ sbcB+ xthA+ lon genetic background at a higher frequency than in the isogenic lon+ host cells. The multimers comprised tandem repeats of monomer plasmid DNA. Treatment of purified plasmid DNA with exonuclease III revealed the presence of free double-chain ends in the molecules. Determination of the size of multimeric DNA, by pulse field gel electrophoresis, revealed that the bulk of the DNA was in the range 50-240 kb, representing approximately 5-24 unit lengths of monomeric plasmid DNA. We provide a conceptual framework for Red-system-promoted formation and enhanced accumulation of plasmid linear multimers in lon mutants of E. coli.

Homologous pairing between nucleosome cores on a linear duplex DNA and nucleoprotein filaments of RecA protein-single stranded DNA

The ability of E coli recA protein to promote homologous pairing with linear duplex DNA bound to HU protein (Nucleosome cores) was found to be differentially affected. The formation of paranemic joint molecules was not affected whereas the formation of plectomic joint molecules was inhibited from the start of the reaction. The formation of paranemic joint molecules between nucleoprotein filaments of recA protein-circular single stranded DNA and closed circular duplex DNA is believed to generate positive supercoiling in the duplex DNA. We found that the positively superhelical duplex DNA was inert in the formation of joint molecules but could be converted into an active substrate, in situ, by the action of wheat germ topoisomerase I. These observations initiate an understanding of the structural features of E coli chromosome such as DNA supercoiling and nucleosome-like structures in homologous recombination.

A Kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data

The problem of identification of stiffness, mass and damping properties of linear structural systems, based on multiple sets of measurement data originating from static and dynamic tests is considered. A strategy, within the framework of Kalman filter based dynamic state estimation, is proposed to tackle this problem. The static tests consists of measurement of response of the structure to slowly moving loads, and to static loads whose magnitude are varied incrementally; the dynamic tests involve measurement of a few elements of the frequency response function (FRF) matrix. These measurements are taken to be contaminated by additive Gaussian noise. An artificial independent variable τ, that simultaneously parameterizes the point of application of the moving load, the magnitude of the incrementally varied static load and the driving frequency in the FRFs, is introduced. The state vector is taken to consist of system parameters to be identified. The fact that these parameters are independent of the variable τ is taken to constitute the set of ‘process’ equations. The measurement equations are derived based on the mechanics of the problem and, quantities, such as displacements and/or strains, are taken to be measured. A recursive algorithm that employs a linearization strategy based on Neumann’s expansion of structural static and dynamic stiffness matrices, and, which provides posterior estimates of the mean and covariance of the unknown system parameters, is developed. The satisfactory performance of the proposed approach is illustrated by considering the problem of the identification of the dynamic properties of an inhomogeneous beam and the axial rigidities of members of a truss structure.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions

We deal with a single conservation law with discontinuous convex-concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine-Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine-Hugoniot condition by a generalized Rankine-Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in L-1. Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. (C) 2006 Elsevier B.V. All rights reserved.

Kernels for large margin time-series classification

In this paper we propose a novel family of kernels for multivariate time-series classification problems. Each time-series is approximated by a linear combination of piecewise polynomial functions in a Reproducing Kernel Hilbert Space by a novel kernel interpolation technique. Using the associated kernel function a large margin classification formulation is proposed which can discriminate between two classes. The formulation leads to kernels, between two multivariate time-series, which can be efficiently computed. The kernels have been successfully applied to writer independent handwritten character recognition.

Enantioselective syntheses of cis, syn, cis- and cis, anti, cis-linear triquinanes

Enantioselective syntheses of both cis, syn, cis- and cis, anti, cis-linear triquinanes, starting from the readily available (S)-campholenaldehyde, employing an RCM reaction-based cyclopentannulation strategy, are described.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

Cluster based training for scaling non-linear support vector machines

Support Vector Machines(SVMs) are hyperplane classifiers defined in a kernel induced feature space. The data size dependent training time complexity of SVMs usually prohibits its use in applications involving more than a few thousands of data points. In this paper we propose a novel kernel based incremental data clustering approach and its use for scaling Non-linear Support Vector Machines to handle large data sets. The clustering method introduced can find cluster abstractions of the training data in a kernel induced feature space. These cluster abstractions are then used for selective sampling based training of Support Vector Machines to reduce the training time without compromising the generalization performance. Experiments done with real world datasets show that this approach gives good generalization performance at reasonable computational expense.