Concise row-pruning algorithm to invert a matrix

Presented here, in a vector formulation, is an O(mn2) direct concise algorithm that prunes/identifies the linearly dependent (ld) rows of an arbitrary m X n matrix A and computes its reflexive type minimum norm inverse A(mr)-, which will be the true inverse A-1 if A is nonsingular and the Moore-Penrose inverse A+ if A is full row-rank. The algorithm, without any additional computation, produces the projection operator P = (I - A(mr)- A) that provides a means to compute any of the solutions of the consistent linear equation Ax = b since the general solution may be expressed as x = A(mr)+b + Pz, where z is an arbitrary vector. The rank r of A will also be produced in the process. Some of the salient features of this algorithm are that (i) the algorithm is concise, (ii) the minimum norm least squares solution for consistent/inconsistent equations is readily computable when A is full row-rank (else, a minimum norm solution for consistent equations is obtainable), (iii) the algorithm identifies ld rows, if any, and reduces concerned computation and improves accuracy of the result, (iv) error-bounds for the inverse as well as the solution x for Ax = b are readily computable, (v) error-free computation of the inverse, solution vector, rank, and projection operator and its inherent parallel implementation are straightforward, (vi) it is suitable for vector (pipeline) machines, and (vii) the inverse produced by the algorithm can be used to solve under-/overdetermined linear systems.

Magnetism, exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS3 is a layered antiferromagnet (T N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate5 T 2g ground state of the Fe2+ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ?=?i [?(L iz 2 ?2)+|?|L i .S i ]?? ij J ij S i .S j . The crystal field trigonal distortion parameter ?, the spin-orbit coupling ? and the isotropic Heisenberg exchange,J ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for ?/k=215.5 K; ?/k=166.5 K;J nn k=27.7 K; andJ nnn k=?2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT N=122 K for FePS3, which is remarkably close to the observed value of theT N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS3, for which the high temperature series expansion susceptibility is available.

Moments estimation in Radon space

In this paper, we show a method of obtaining general and orthogonal moments, specifically Legendre and Zernicke moments, from the Radon Transform data of a two-dimensional function. The regular or geometric moments are first evaluated directly from the projection data and the orthogonal moments are derived from these regular moments.

Raman phase conjugator

We have developed a multipurpose high pressure gas cell which can be used to generate phase conjugate beams using various stimulated scattering processes. This high pressure cell can also be used as a tunable laser source using the process of stimulated Raman scattering. The phase conjugate nature of backward scattered Raman signals was investigated through distortion correction studies.

Receiver-Only Optimized Vector Quantization for Noisy Channels

This paper considers the design and analysis of a filter at the receiver of a source coding system to mitigate the excess Mean-Squared Error (MSE) distortion caused due to channel errors. It is assumed that the source encoder is channel-agnostic, i.e., that a Vector Quantization (VQ) based compression designed for a noiseless channel is employed. The index output by the source encoder is sent over a noisy memoryless discrete symmetric channel, and the possibly incorrect received index is decoded by the corresponding VQ decoder. The output of the VQ decoder is processed by a receive filter to obtain an estimate of the source instantiation. In the sequel, the optimum linear receive filter structure to minimize the overall MSE is derived, and shown to have a minimum-mean squared error receiver type structure. Further, expressions are derived for the resulting high-rate MSE performance. The performance is compared with the MSE obtained using conventional VQ as well as the channel optimized VQ. The accuracy of the expressions is demonstrated through Monte Carlo simulations.

Additive Spanners and (alpha, beta)-Spanners

An (alpha, beta)-spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of a and an additive term beta. It is well known that any graph contains a (multiplicative) (2k - 1, 0)-spanner of size O(n(1+1/k)) and an (additive) (1, 2)-spanner of size O(n(3/2)). However no other additive spanners are known to exist. In this article we develop a couple of new techniques for constructing (alpha, beta)-spanners. Our first result is an additive (1, 6)-spanner of size O(n(4/3)). The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well approximated by paths already purchased. We show that this path buying algorithm can be parameterized in different ways to yield other sparseness-distortion tradeoffs. Our second result addresses the problem of which (alpha, beta)-spanners can be computed efficiently, ideally in linear time. We show that, for any k, a (k, k - 1)-spanner with size O(kn(1+1/k)) can be found in linear time, and, further, that in a distributed network the algorithm terminates in a constant number of rounds. Previous spanner constructions with similar performance had roughly twice the multiplicative distortion.

Solvation dynamics, energy distribution and trapping of a light solute ion

In the theoretical treatments of the dynamics of solvation of a newly created ion in a dipolar solvent, the self-motion of the solute is usually ignored. Recently, it has been shown that for a light ion the translational motion of the ion can significantly enhance its own rate of solvation. Therefore, solvation itself may not be the rate determining step in the equilibration. Instead, the rate determining step is the search of the low energy configuration which serves to localize the light ion. In this article a microscopic calculation of the probability distribution of the interaction energy of the nascent charge with the dipolar solvent molecules is presented in order to address this problem of solute trapping. It is found that to a good approximation, this distribution is Gaussian and the second moment of this distribution is exactly equal to the half of its own solvation energy. It is shown that this is in excellent agreement with the simulation results that are available for the model Brownian dipolar lattice and for liquid acetonitrile. If the distortion of the solvent by the ion is negligible then the same relation gives the energy distribution for the solvated ion, with the average centered at the final equilibrium solvation energy. These results are expected to be useful in understanding various chemical processes in dipolar liquids. Another interesting outcome of the present study is a simple dynamic argument that supports Onsager's ''inverse snow-ball'' conjecture of solvation of a light ion. A simple derivation of the semi-phenomenological relation between the solvation time correlation function and the single particle orientation, reported recently by Maroncelli et al. (J. Phys. Chem. 97 (1993) 13), is also presented.

Robust/Optimal Temperature Profile Control of a High-Speed Aerospace Vehicle Using Neural Networks

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A I-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

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.

Code design casing deterministic annealing

We address the problem of designing codes for specific applications using deterministic annealing. Designing a block code over any finite dimensional space may be thought of as forming the corresponding number of clusters over the particular dimensional space. We have shown that the total distortion incurred in encoding a training set is related to the probability of correct reception over a symmetric channel. While conventional deterministic annealing make use of the Euclidean squared error distance measure, we have developed an algorithm that can be used for clustering with Hamming distance as the distance measure, which is required in the error correcting, scenario.

Experimental studies of a distorted turbulent spot in a three-dimensional flow

We report here on the results of a series of experiments carried out on a turbulent spot in a distorted duct to study the effects of a divergence with straight streamlines preceded by a short stretch of transverse streamline curvature, both in the absence of any pressure gradient. It is found that the distortion produces substantial asymmetry in the spot: the angles at which the spot cuts across the local streamlines are altered dramatically (in contradiction of a hypothesis commonly made in transition zone modelling), and the Tollmien-Schlichting waves that accompany the wing tips of the spot are much stronger on the outside of the bend than on the inside. However there is no strong effect on the internal structure of the spot and the eddies therein, or on such propagation characteristics as overall spread rate and the celerities of the leading and trailing edges. Both lateral streamline curvature and non-homogeneity of the laminar boundary layer into which the spot propagates are shown to be strong factors responsible for the observed asymmetry. It is concluded that these factors produce chiefly a geometric distortion of the coherent structure in the spot, but do not otherwise affect its dynamics in any significant way.

Mössbauer effect and electron paramagnetic resonance studies on zinc borate glasses containing transition metal oxides

Studies have been carried out in glasses containing Fe2O3, V2O5, and Fe2O3 + V2O5. Mossbauer studies in the ZnO-B2O3-Fe2O3 system show that iron is present as Fe3+ with tetrahedral coordination and that the isomer shift and the quadrupole splitting decrease with increase of Fe2O3 Content; similarly, the isomer shift and quadrupole splitting are also found to decrease with increasing ZnO. On the other hand, in the Na2O-ZnO-B2O3-Fe2O3 system, the isomer shift increases with Na2O or ZnO while the quadrupole splitting is fairly insensitive. Electron paramagnetic resonance in the ZnO-B2O3-Fe2O3 system shows signals at g = 4.20 and 2.0, whose intensity and linewidth show strong dependence on Fe2O3 content. In the ZnO-B2O3-V2O5 system, electron paramagnetic resonance shows that vanadium is present as the vanadyl complex, and the hyperfine coupling constants, A(parallel-to) and A(perpendicular-to) decrease with increasing V2O5 content; on the other hand, g(parallel-to) decreases and g(perpendicular-to) increases slightly, indicating an increase in tetragonal distortion. Zinc borate glasses containing Fe2O3 + V2O5 do not show the hyperfine structure of V4+ due to the interaction between Fe3+ and V4+

Image reconstruction from incomplete projections data: A multiresolution modeling approach

Computerized tomography is an imaging technique which produces cross sectional map of an object from its line integrals. Image reconstruction algorithms require collection of line integrals covering the whole measurement range. However, in many practical situations part of projection data is inaccurately measured or not measured at all. In such incomplete projection data situations, conventional image reconstruction algorithms like the convolution back projection algorithm (CBP) and the Fourier reconstruction algorithm, assuming the projection data to be complete, produce degraded images. In this paper, a multiresolution multiscale modeling using the wavelet transform coefficients of projections is proposed for projection completion. The missing coefficients are then predicted based on these models at each scale followed by inverse wavelet transform to obtain the estimated projection data.

Finite element simulation of wedge indentation

A finite element simulation of frictionless wedge indentation of a copper strip has been carried out under plane strain conditions. The problem was first modelled using an one-pass contact algorithm. The difficulties associated with using this method to model wedge indentation problems are explained. An alternative procedure which alleviates some of the problems associated with the one-pass contact algorithm is proposed for modelling frictionless wedge indentation. Also, a re-meshing procedure which has to be carried out when the distortion of the elements around the indenter becomes significant, is discussed. A sample problem involving indentation of a 4 mm copper strip by a rigid wedge indenter has been modelled and the results are compared with experimental and theoretical results.