Formal description, compression and transformation of digital pictures

This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression. In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation. This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.

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.

Ion pairs in non-redundant protein structures

Ion pairs contribute to several functions including the activity of catalytic triads, fusion of viral membranes, stability in thermophilic proteins and solvent-protein interactions. Furthermore, they have the ability to affect the stability of protein structures and are also a part of the forces that act to hold monomers together. This paper deals with the possible ion pair combinations and networks in 25% and 90% non-redundant protein chains. Different types of ion pairs present in various secondary structural elements are analysed. The ion pairs existing between different subunits of multisubunit protein structures are also computed and the results of various analyses are presented in detail. The protein structures used in the analysis are solved using X-ray crystallography, whose resolution is better than or equal to 1.5 angstrom and R-factor better than or equal to 20%. This study can, therefore, be useful for analyses of many protein functions. It also provides insights into the better understanding of the architecture of protein structure.

Formal Verification of Full-Wave Rectifier: A Case Study

We present a case study of formal verification of full-wave rectifier for analog and mixed signal designs. We have used the Checkmate tool from CMU [1], which is a public domain formal verification tool for hybrid systems. Due to the restriction imposed by Checkmate it necessitates to make the changes in the Checkmate implementation to implement the complex and non-linear system. Full-wave rectifier has been implemented by using the Checkmate custom blocks and the Simulink blocks from MATLAB from Math works. After establishing the required changes in the Checkmate implementation we are able to efficiently verify, the safety properties of the full-wave rectifier.

Interaction of water molecules in non-identical protein structures

The interaction of the protein atoms with the surrounding water oxygen atoms has been computed for 392 protein chains from 369 protein structures belonging to 90% non-homologous high resolution (<= 1.5 angstrom) protein Structures with a crystallographic R-factor <= 20%. The percentage composition of the polar atoms is found to be 36.3%. An average of 82.55% of water oxygen atoms are found to be in the primary hydration shell and 15.12% in the secondary hydration shell. The average Percentage of interactions of water oxygen atoms with the polar atoms of the main chain and side chain are 54% and 46%. respectively. The interaction of the acidic residues, aspartate and glutamate, with the water oxygen atoms is more when compared to that of the other residues.

Enantiodivergent Formal Total Synthesis of Aspercyclide C from L-(+)-Tartaric Acid

The enantiodivergent formal syntheses of both enantiomers of aspercyclide C is accomplished. Starting from L-(+)-tartaric acid, the key protected allylic alcohol, (3R,4R)-4-(methoxy-methoxy) non-1-en-3-ol is prepared, and is then elaborated into both enantiomers of 3-(4-methoxybenzyl)oxy]non-1-en-4-ol via Mitsunobu inversion. Esterification with a known biaryl acid, followed by ring-closing metathesis and deprotection completes the syntheses.

V-Transform: “An Enhanced Polynomial Coefficient Based DC Test for Non-linear Analog Circuits

Abstract—DC testing of parametric faults in non-linear analog circuits based on a new transformation, entitled, V-Transform acting on polynomial coefficient expansion of the circuit function is presented. V-Transform serves the dual purpose of monotonizing polynomial coefficients of circuit function expansion and increasing the sensitivity of these coefficients to circuit parameters. The sensitivity of V-Transform Coefficients (VTC) to circuit parameters is up to 3x-5x more than sensitivity of polynomial coefficients. As a case study, we consider a benchmark elliptic filter to validate our method. The technique is shown to uncover hitherto untestable parametric faults whose sizes are smaller than 10 % of the nominal values. I.

Performance Modeling based on Multidimensional Surface Learning for Performance Predictions of Parallel Applications in Non-Dedicated Environments

Modeling the performance behavior of parallel applications to predict the execution times of the applications for larger problem sizes and number of processors has been an active area of research for several years. The existing curve fitting strategies for performance modeling utilize data from experiments that are conducted under uniform loading conditions. Hence the accuracy of these models degrade when the load conditions on the machines and network change. In this paper, we analyze a curve fitting model that attempts to predict execution times for any load conditions that may exist on the systems during application execution. Based on the experiments conducted with the model for a parallel eigenvalue problem, we propose a multi-dimensional curve-fitting model based on rational polynomials for performance predictions of parallel applications in non-dedicated environments. We used the rational polynomial based model to predict execution times for 2 other parallel applications on systems with large load dynamics. In all the cases, the model gave good predictions of execution times with average percentage prediction errors of less than 20%

Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-alpha method

Biochemical pathways involving chemical kinetics in medium concentrations (i.e., at mesoscale) of the reacting molecules can be approximated as chemical Langevin equations (CLE) systems. We address the physically consistent non-negative simulation of the CLE sample paths as well as the issue of non-Lipschitz diffusion coefficients when a species approaches depletion and any stiffness due to faster reactions. The non-negative Fully Implicit Stochastic alpha (FIS alpha) method in which stopped reaction channels due to depleted reactants are deleted until a reactant concentration rises again, for non-negativity preservation and in which a positive definite Jacobian is maintained to deal with possible stiffness, is proposed and analysed. The method is illustrated with the computation of active Protein Kinase C response in the Protein Kinase C pathway. (C) 2011 Elsevier Inc. All rights reserved.

Towards formal verification of analog mixed signal designs using SPICE circuit simulation traces

An extension to a formal verification approach of hybrid systems is proposed to verify analog and mixed signal (AMS) designs. AMS designs can be formally modeled as hybrid systems and therefore lend themselves to the formal analysis and verification techniques applied to hybrid systems. The proposed approach employs simulation traces obtained from an actual design implementation of AMS circuit blocks (for example, in the form of SPICE netlists) to carry out formal analysis and verification. This enables the same platform used for formally validating an abstract model of an AMS design, to be also used for validating its different refinements and design implementation; thereby, providing a simple route to formal verification at different levels of implementation. The feasibility of the proposed approach is demonstrated with a case study based on a tunnel diode oscillator. Since the device characteristic of a tunnel diode is highly non-linear with a negative resistance region, dynamic behavior of circuits in which it is employed as an element is difficult to model, analyze and verify within a general hybrid system formal verification tool. In the case study presented the formal model and the proposed computational techniques have been incorporated into CheckMate, a formal verification tool based on MATLAB and Simulink-Stateflow Framework from MathWorks.

Radiative and non-radiative effects of a substrate on localized plasmon resonance of particles

Experiments have shown strong effects of some substrates on the localized plasmons of metallic nano particles but they are inconclusive on the affecting parameters. Here, we have used discrete dipole approximation in conjunction with Sommerfeld integral relations to explain the effect of the substrates as a function of the parameters of incident radiation. The radiative coupling can both quench and enhance the resonance and its dependence on the angle and polarization of incident radiation with respect to the surface is shown. Non-radiative interaction with the substrate enhances the plasmon resonance of the particles and can shift the resonances from their free-space energies significantly. The non-radiative interaction of the substrate is sensitive to the shape of particles and polarization of incident radiation with respect to substrate. Our results show that the plasmon resonances in coupled and single particles can be significantly altered from their free-space resonances and are quenched or enhanced by the choice of substrate and polarization of incident radiation. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4736544]

Do we see what we should see? Describing non-covalent interactions in protein structures including precision

The power of X-ray crystal structure analysis as a technique is to `see where the atoms are'. The results are extensively used by a wide variety of research communities. However, this `seeing where the atoms are' can give a false sense of security unless the precision of the placement of the atoms has been taken into account. Indeed, the presentation of bond distances and angles to a false precision (i.e. to too many decimal places) is commonplace. This article has three themes. Firstly, a basis for a proper representation of protein crystal structure results is detailed and demonstrated with respect to analyses of Protein Data Bank entries. The basis for establishing the precision of placement of each atom in a protein crystal structure is non-trivial. Secondly, a knowledge base harnessing such a descriptor of precision is presented. It is applied here to the case of salt bridges, i.e. ion pairs, in protein structures; this is the most fundamental place to start with such structure-precision representations since salt bridges are one of the tenets of protein structure stability. Ion pairs also play a central role in protein oligomerization, molecular recognition of ligands and substrates, allosteric regulation, domain motion and alpha-helix capping. A new knowledge base, SBPS (Salt Bridges in Protein Structures), takes these structural precisions into account and is the first of its kind. The third theme of the article is to indicate natural extensions of the need for such a description of precision, such as those involving metalloproteins and the determination of the protonation states of ionizable amino acids. Overall, it is also noted that this work and these examples are also relevant to protein three-dimensional structure molecular graphics software.

Modeling of the non-isothermal liquid droplet impact on a heated solid substrate with heterogeneous wettability

A comprehensive numerical investigation on the impingement and spreading of a non-isothermal liquid droplet on a solid substrate with heterogeneous wettability is presented in this work. The time-dependent incompressible Navier-Stokes equations are used to describe the fluid flow in the liquid droplet, whereas the heat transfer in the moving droplet and in the solid substrate is described by the energy equation. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the time-dependent incompressible Navier-Stokes equation and the energy equation in the time-dependent moving domain. Moreover, the Marangoni convection is included in the variational form of the Navier-Stokes equations without calculating the partial derivatives of the temperature on the free surface. The heterogeneous wettability is incorporated into the numerical model by defining a space-dependent contact angle. An array of simulations for droplet impingement on a heated solid substrate with circular patterned heterogeneous wettability are presented. The numerical study includes the influence of wettability contrast, pattern diameter, Reynolds number and Weber number on the confinement of the spreading droplet within the inner region, which is more wettable than the outer region. Also, the influence of these parameters on the total heat transfer from the solid substrate to the liquid droplet is examined. We observe that the equilibrium position depends on the wettability contrast and the diameter of the inner surface. Consequently. the heat transfer is more when the wettability contrast is small and/or the diameter of inner region is large. The influence of the Weber number on the total heat transfer is more compared to the Reynolds number, and the total heat transfer increases when the Weber number increases. (C) 2015 Elsevier Ltd. All rights reserved.

Joint Bilateral Filtering based Non-local Means Image Denoising

This paper proposes a denoising algorithm which performs non-local means bilateral filtering. As existing literature suggests, non-local means (NLM) is one of the widely used denoising techniques, but has a critical drawback of smoothing of edges. In order to improve this, we perform fast and efficient NLM using Approximate Nearest Neighbour Fields and improve the edge content in denoising by formulating a joint-bilateral filter. Using the proposed joint bilateral, we are able to denoise smooth regions using the NLM approach and efficient edge reconstruction is obtained from the bilateral filter. Furthermore, to avoid tedious parameter selection, we carry out a noise estimation before performing joint bilateral filtering. The proposed approach is observed to perform well on high noise images.