Construction of inverses with prescribed zero minors and applications to decentralized stabilization

We examine the following question: Suppose R is a principal ideal domain, and that F is an n × m matrix with elements in R, with n>m. When does there exist an m × n matrix G such that GF = Im, and such that certain prescribed minors of G equal zero? We show that there is a simple necessary condition for the existence of such a G, but that this condition is not sufficient in general. However, if the set of minors of G that are required to be zero has a certain pattern, then the condition is necessary as well as sufficient. We then show that the pattern mentioned above arises naturally in connection with the question of the existence of decentralized stabilizing controllers for a given plant. Hence our result allows us to derive an extremely simple proof of the fact that a necessary and sufficient condition for the existence of decentralized stabilizing controllers is the absence of unstable decentralized fixed modes, as well as to derive a very clean expression for these fixed modes. In addition to the application to decentralized stabilization, we believe that the result is of independent interest.

Discrete parameter simulation optimization algorithms with applications to admission control with dependent service times

We propose certain discrete parameter variants of well known simulation optimization algorithms. Two of these algorithms are based on the smoothed functional (SF) technique while two others are based on the simultaneous perturbation stochastic approximation (SPSA) method. They differ from each other in the way perturbations are obtained and also the manner in which projections and parameter updates are performed. All our algorithms use two simulations and two-timescale stochastic approximation. As an application setting, we consider the important problem of admission control of packets in communication networks under dependent service times. We consider a discrete time slotted queueing model of the system and consider two different scenarios - one where the service times have a dependence on the system state and the other where they depend on the number of arrivals in a time slot. Under our settings, the simulated objective function appears ill-behaved with multiple local minima and a unique global minimum characterized by a sharp dip in the objective function in a small region of the parameter space. We compare the performance of our algorithms on these settings and observe that the two SF algorithms show the best results overall. In fact, in many cases studied, SF algorithms converge to the global minimum.

Studies of electronic structure by x-ray Raman and emission spectroscopy: applications to MgB2 superconductors and high pressure physics

X-ray Raman scattering and x-ray emission spectroscopies were used to study the electronic properties and phase transitions in several condensed matter systems. The experimental work, carried out at the European Synchrotron Radiation Facility, was complemented by theoretical calculations of the x-ray spectra and of the electronic structure. The electronic structure of MgB2 at the Fermi level is dominated by the boron σ and π bands. The high density of states provided by these bands is the key feature of the electronic structure contributing to the high critical temperature of superconductivity in MgB2. The electronic structure of MgB2 can be modified by atomic substitutions, which introduce extra electrons or holes into the bands. X ray Raman scattering was used to probe the interesting σ and π band hole states in pure and aluminum substituted MgB2. A method for determining the final state density of electron states from experimental x-ray Raman scattering spectra was examined and applied to the experimental data on both pure MgB2 and on Mg(0.83)Al(0.17)B2. The extracted final state density of electron states for the pure and aluminum substituted samples revealed clear substitution induced changes in the σ and π bands. The experimental work was supported by theoretical calculations of the electronic structure and x-ray Raman spectra. X-ray emission at the metal Kβ line was applied to the studies of pressure and temperature induced spin state transitions in transition metal oxides. The experimental studies were complemented by cluster multiplet calculations of the electronic structure and emission spectra. In LaCoO3 evidence for the appearance of an intermediate spin state was found and the presence of a pressure induced spin transition was confirmed. Pressure induced changes in the electronic structure of transition metal monoxides were studied experimentally and were analyzed using the cluster multiplet approach. The effects of hybridization, bandwidth and crystal field splitting in stabilizing the high pressure spin state were discussed. Emission spectroscopy at the Kβ line was also applied to FeCO3 and a pressure induced iron spin state transition was discovered.

Detection of multiple source locations using a glowworm metaphor with applications to collective robotics

This paper presents a glowworm swarm based algorithm that finds solutions to optimization of multiple optima continuous functions. The algorithm is a variant of a well known ant-colony optimization (ACO) technique, but with several significant modifications. Similar to how each moving region in the ACO technique is associated with a pheromone value, the agents in our algorithm carry a luminescence quantity along with them. Agents are thought of as glowworms that emit a light whose intensity is proportional to the associated luminescence and have a circular sensor range. The glowworms depend on a local-decision domain to compute their movements. Simulations demonstrate the efficacy of the proposed glowworm based algorithm in capturing multiple optima of a multimodal function. The above optimization scenario solves problems where a collection of autonomous robots is used to form a mobile sensor network. In particular, we address the problem of detecting multiple sources of a general nutrient profile that is distributed spatially on a two dimensional workspace using multiple robots.

Emerging trends at the interface of chemistry and biology: Applications to the design of human therapeutics

This article describes recent developments in the design and implementation of various strategies towards the development of novel therapeutics using first principles from biology and chemistry. Strategies for multi-target therapeutics and network analysis with a focus on cancer and HIV are discussed. Methods for gene and siRNA delivery are presented along with challenges and opportunities for siRNA therapeutics. Advances in protein design methodology and screening are described, with a focus on their application to the design of antibody based therapeutics. Future advances in this area relevant to vaccine design are also mentioned.

Multicriterion differential games with applications to combat problems

In this paper a theory for two-person zero sum multicriterion differential games is presented. Various solution concepts based upon the notions of Pareto optimality (efficiency), security and equilibrium are defined. These are shown to have interesting applications in the formulation and analysis of two target or combat differential games. The methods for obtaining outcome regions in the state space, feedback strategies for the players and the mode of play has been discussed in the framework of bicriterion zero sum differential games. The treatment is conceptual rather than rigorous.

The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Novel geodesic splitting on paraboloid of revolution with applications to ray-theoretic analysis

Computer simulations have shown a novel geodesic splitting on the paraboloid of revolution leading to a multiplicity of surface ray paths. Such a phenomenon would have wide ramifications for wave propagation problems in general, besides applications in target-detection problems and the computational requirements of ray-theoretic formulations such as the UTD, in computing the antenna characteristics in the high-frequency domain.

Methods for making prisms with submultiple or half angles: applications to the measurement of the angles of Pechan and Pellin-Broca prisms

A simple technique is devised for making prisms with submultiple or half angles. As an application of these prisms, methods are suggested to measure the angles of the Pechan and Pellin-Broca prisms without using expensive spectrometers, autocollimators, and angle gauges. (C) 2002 Society of Photo-Optical Instrumentation Engineers.

The Co Cr S ternary diagram at 1223 K and applications to corrosion

Ternary phase relations in the Co-Cr-S system at 1223 K were determined using microprobe analysis of quenched samples. The results are consistent with the data available on the binary systems. A complete solid solution exists between cobalt monosulfide and chromium monosulfide. The CoCr2S4 thiospinel is the only ternary compound formed. A sulfur potential diagram was constructed for the region involving equilibrium between alloy and monosulfide based on thermodynamic data on the Co-Cr, Co-S, and Cr-S binary systems and the ternary information obtained in this study. The sulfidation behavior of Co-Cr alloys reported in the literature is discussed in light of the sulfur potential diagram.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.

Halogen bonds in some dihalogenated phenols: applications to crystal engineering

3,4-Dichlorophenol (1) crystallizes in the tetragonal space group I4(1)/a with a short axis of 3.7926 (9) angstrom. The structure is unique in that both type I and type II Cl.....Cl interactions are present, these contact types being distinguished by the angle ranges of the respective C-Cl....Cl angles. The present study shows that these two types of contacts are utterly different. The crystal structures of 4-bromo-3-chlorophenol (2) and 3-bromo-4-chlorophenol (3) have been determined. The crystal structure of (2) is isomorphous to that of (1) with the Br atom in the 4-position participating in a type II interaction. However, the monoclinic P2(1)/c packing of compound (3) is different; while the structure still has O-H....O hydrogen bonds, the tetramer O-H.....O synthon seen in (1) and (2) is not seen. Rather than a type I Br....Br interaction which would have been mandated if (3) were isomorphous to (1) and (2), Br forms a Br....O contact wherein its electrophilic character is clearly evident. Crystal structures of the related compounds 4-chloro-3-iodophenol (4) and 3,5-dibromophenol (5) were also determined. A computational survey of the structural landscape was undertaken for (1), (2) and (3), using a crystal structure prediction protocol in space groups P2(1)/c and I4(1)/a with the COMPASS26 force field. While both tetragonal and monoclinic structures are energetically reasonable for all compounds, the fact that (3) takes the latter structure indicates that Br prefers type II over type I contacts. In order to differentiate further between type I and type II halogen contacts, which being chemically distinct are expected to have different distance fall-off properties, a variable-temperature crystallography study was performed on compounds (1), (2) and (4). Length variations with temperature are greater for type II contacts compared with type I. The type II Br....Br interaction in (2) is stronger than the corresponding type II Cl....Cl interaction in (1), leading to elastic bending of the former upon application of mechanical stress, which contrasts with the plastic deformation of (1). The observation of elastic deformation in (2) is noteworthy; in that it finds an explanation based on the strengths of the respective halogen bonds, it could also be taken as a good starting model for future property design. Cl/Br isostructurality is studied with the Cambridge Structural Database and it is indicated that this isostructurality is based on shape and size similarity of Cl and Br, rather than arising from any chemical resemblance.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.