Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

Two dimensional weak pseudomanifolds on seven vertices

In this article we have explicitly determined all the 2-dimensional weak pseudomanifolds on 7 vertices. We have proved that there are (up to isomorphism) 13 such weak pseudomanifolds. The geometric carriers of them are 6 topological spaces, three of which are not manifolds.

Topological analysis of general linear networks

A new method of network analysis, a generalization in several different senses of existing methods and applicable to all networks for which a branch-admittance (or impedance) matrix can be formed, is presented. The treatment of network determinants is very general and essentially four terminal rather than three terminal, and leads to simple expressions based on trees of a simple graph associated with the network and matrix, and involving products of low-order, usually(2 times 2)determinants of tree-branch admittances, in addition to tree-branch products as in existing methods. By comparison with existing methods, the total number of trees and of tree pairs is usually considerably reduced, and this fact, together with an easy method of tree-pair sign determination which is also presented, makes the new method simpler in general. The method can be very easily adapted, by the use of infinite parameters, to accommodate ideal transformers, operational amplifiers, and other forms of network constraint; in fact, is thought to be applicable to all linear networks.

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

A Team of Continuous-Action Learning Automata for Noise-Tolerant Learning of Half-Spaces

Learning automata are adaptive decision making devices that are found useful in a variety of machine learning and pattern recognition applications. Although most learning automata methods deal with the case of finitely many actions for the automaton, there are also models of continuous-action-set learning automata (CALA). A team of such CALA can be useful in stochastic optimization problems where one has access only to noise-corrupted values of the objective function. In this paper, we present a novel formulation for noise-tolerant learning of linear classifiers using a CALA team. We consider the general case of nonuniform noise, where the probability that the class label of an example is wrong may be a function of the feature vector of the example. The objective is to learn the underlying separating hyperplane given only such noisy examples. We present an algorithm employing a team of CALA and prove, under some conditions on the class conditional densities, that the algorithm achieves noise-tolerant learning as long as the probability of wrong label for any example is less than 0.5. We also present some empirical results to illustrate the effectiveness of the algorithm.

Bond-order wave phase, spin solitons, and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet

The linear spin-1/2 Heisenberg antiferromagnet with exchanges J(1) and J(2) between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J(2)/J(1)=0.2411 and is particularly simple at J(2)/J(1)=1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry, and a finite-energy gap E-m to the lowest-triplet state. The interval 0.4 < J(2)/J(1) < 1.0 has large E-m and small finite-size corrections. Exact solutions are presented up to N = 28 spins with either periodic or open boundary conditions and for thermodynamics up to N = 18. The elementary excitations of the BOW phase with large E-m are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility chi(M)(T) is exponentially small for T << E-m and increases nearly linearly with T to a broad maximum. J(1) and J(2) spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-tetracyanoquinodimethane salts.

A systolic evaluator for linear, quadratic, and cubic expressions

High-speed evaluation of a large number of linear, quadratic, and cubic expressions is very important for the modeling and real-time display of objects in computer graphics. Using VLSI techniques, chips called pixel planes have actually been built by H. Fuchs and his group to evaluate linear expressions. In this paper, we describe a topological variant of Fuchs' pixel planes which can evaluate linear, quadratic, cubic, and higher-order polynomials. In our design, we make use of local interconnections only, i.e., interconnections between neighboring processing cells. This leads to the concept of tiling the processing cells for VLSI implementation.

On the relation between rotation increments in different tangent spaces

In computational mechanics, finite rotations are often represented by rotation vectors. Rotation vector increments corresponding to different tangent: spaces are generally related by a linear operator, known as the tangential transformation T. In this note, we derive the higher order terms that are usually left out in linear relation. The exact nonlinear relation is also presented. Errors via the linearized T are numerically estimated. While the concept of T arises out of the nonlinear characteristics of the rotation manifold, it has been derived via tensor analysis in the context of computational mechanics (Cardona and Geradin, 1988). We investigate the operator T from a Lie group perspective, which provides a better insight and a 1-1 correspondence between approaches based on tensor analysis and the standard matrix Lie group theory. (C) 2010 Elsevier Ltd. All rights reserved.

Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z(2) invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent nu being different in different sectors. Copyright (C) EPLA, 2010

State estimation in power systems using linear model infinity norm-based trust region approach

State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.

Constrained Linear Spectral Unmixing Technique for Regional Land Cover Mapping Using MODIS Data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up-to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat-TM/ETM+, IRS-ICID LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (similar to 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 in), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end-members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications. Index Terms-Remote sensing, digital

A new load distribution strategy for linear network with communication delays

In this paper, we propose a new load distribution strategy called `send-and-receive' for scheduling divisible loads, in a linear network of processors with communication delay. This strategy is designed to optimally utilize the network resources and thereby minimizes the processing time of entire processing load. A closed-form expression for optimal size of load fractions and processing time are derived when the processing load originates at processor located in boundary and interior of the network. A condition on processor and link speed is also derived to ensure that the processors are continuously engaged in load distributions. This paper also presents a parallel implementation of `digital watermarking problem' on a personal computer-based Pentium Linear Network (PLN) topology. Experiments are carried out to study the performance of the proposed strategy and results are compared with other strategies found in literature.

Conformation-activity correlations for chemotactic tripeptide analogs incorporating dialkyl residues with linear and cyclic alkyl sidechains at position 2

Five stereochemically constrained analogs of the chemotactic tripeptide incorporating 1-aminocycloalkane-1-carboxylic acid (Ac(n)c) and alpha,alpha-dialkylglycines (Deg, diethylglycine; Dpg, n,n-dipropylglycine and Dbg, n,n-dibutylglycine) at position 2 have been synthesized. NMR studies of peptides For-Met-Xxx-Phe-OMe (Xxx = Ac(7)c, I; Ac(8)c, II; Deg, III; Dpg, IV and Dbg, V; For, formyl) establish that peptides with cycloalkyl residues, I and II, adopt folded beta-turn conformations in CDCl3 and (CD3)(2)SO. In contrast, analogs with linear alkyl sidechains, III-V, favour fully extended (C-5) conformations in solution. Peptides I-V exhibit high activity in inducing beta-glucosaminidase release from rabbit neutrophils, with ED(50) values ranging from 1.4-8.0 x 10(-11)M. In human neutrophils the Dxg peptides III-V have ED(50) values ranging from 2.3 x 10(-8) to 5.9 x 10(-10) M, with the activity order being V > IV > III. While peptides I-IV are less active than the parent. For-Met-Leu-Phe-OH, in stimulating histamine release from human basophils, the Dbg peptide V is appreciably more potent, suggesting its potential utility as a probe for formyl peptide receptors.

An Efficient Load Distribution Strategy for a Distributed Linear Network of Processors with Communication Delays

In this paper, we present an improved load distribution strategy, for arbitrarily divisible processing loads, to minimize the processing time in a distributed linear network of communicating processors by an efficient utilization of their front-ends. Closed-form solutions are derived, with the processing load originating at the boundary and at the interior of the network, under some important conditions on the arrangement of processors and links in the network. Asymptotic analysis is carried out to explore the ultimate performance limits of such networks. Two important theorems are stated regarding the optimal load sequence and the optimal load origination point. Comparative study of this new strategy with an earlier strategy is also presented.

Topological mimicry and epitope duplication in the guanylyl cyclase C receptor

Guanylyl cyclase C (GCC) is the receptor for the gastrointestinal hormones, guanylin, and uroguanylin, in addition to the bacterial heat-stable enterotoxins, which are one of the major causes of watery diarrhea the world over. GCC is expressed in intestinal cells, colorectal tumor tissue and tumors originating from metastasis of the colorectal carcinoma. We have earlier generated a monoclonal antibody to human GCC, GCC:B10, which was useful for the immunohistochemical localization of the receptor in the rat intestine (Nandi A et al., 1997, J Cell Biochem 66:500-511), and identified its epitope to a 63-amino acid stretch in the intracellular domain of GCC. In view of the potential that this antibody has for the identification of colorectal tumors, we have characterized the epitope for GCC:B10 in this study. Overlapping peptide synthesis indicated that the epitope was contained in the sequence HIPPENIFPLE. This sequence was unique to GCC, and despite a short stretch of homology with serum amyloid protein and pertussis toxin, no cross reactivity was detected. The core epitope was delineated using a random hexameric phage display library, and two categories of sequences were identified, containing either a single, or two adjacent proline residues. No sequence identified by phage display was identical to the epitope present in GCC, indicating that phage sequences represented mimotopes of the native epitope. Alignment of these sequences with HIPPENIFPLE suggested duplication of the recognition motif, which was confirmed by peptide synthesis. These studies allowed us not only to define the requirements of epitope recognition by GCC:B10 monoclonal antibody, but also to describe a novel means of epitope recognition involving topological mimicry and probable duplication of the cognate epitope in the native guanylyl cyclase C receptor sequence.