A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems

Using a Girsanov change of measures, we propose novel variations within a particle-filtering algorithm, as applied to the inverse problem of state and parameter estimations of nonlinear dynamical systems of engineering interest, toward weakly correcting for the linearization or integration errors that almost invariably occur whilst numerically propagating the process dynamics, typically governed by nonlinear stochastic differential equations (SDEs). Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated within the evolving flow in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, which is directly computable, is accounted for via two different schemes, one employing resampling and the other using a gain-weighted innovation term added to the drift field of the process dynamics thereby overcoming the problem of sample dispersion posed by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates vis-a-vis those obtained through the parent-filtering schemes.

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Fragment-based real-time object tracking: a sparse representation approach

Real-time object tracking is a critical task in many computer vision applications. Achieving rapid and robust tracking while handling changes in object pose and size, varying illumination and partial occlusion, is a challenging task given the limited amount of computational resources. In this paper we propose a real-time object tracker in l(1) framework addressing these issues. In the proposed approach, dictionaries containing templates of overlapping object fragments are created. The candidate fragments are sparsely represented in the dictionary fragment space by solving the l(1) regularized least squares problem. The non zero coefficients indicate the relative motion between the target and candidate fragments along with a fidelity measure. The final object motion is obtained by fusing the reliable motion information. The dictionary is updated based on the object likelihood map. The proposed tracking algorithm is tested on various challenging videos and found to outperform earlier approach.

Fast and accurate quantification using Genetic Algorithm optimized H-1-C-13 refocused constant-time INEPT

Using Genetic Algorithm, a global optimization method inspired by nature's evolutionary process, we have improved the quantitative refocused constant-time INEPT experiment (Q-INEPT-CT) of Makela et al. (JMR 204 (2010) 124-130) with various optimization constraints. The improved `average polarization transfer' and `min-max difference' of new delay sets effectively reduces the experimental time by a factor of two (compared with Q-INEPT-CT, Makela et al.) without compromising on accuracy. We also discuss a quantitative spectral editing technique based on average polarization transfer. (C) 2013 Elsevier Inc. All rights reserved.

Classification, representation, and automatic extraction of deformation features in sheet metal parts

This paper presents classification, representation and extraction of deformation features in sheet-metal parts. The thickness is constant for these shape features and hence these are also referred to as constant thickness features. The deformation feature is represented as a set of faces with a characteristic arrangement among the faces. Deformation of the base-sheet or forming of material creates Bends and Walls with respect to a base-sheet or a reference plane. These are referred to as Basic Deformation Features (BDFs). Compound deformation features having two or more BDFs are defined as characteristic combinations of Bends and Walls and represented as a graph called Basic Deformation Features Graph (BDFG). The graph, therefore, represents a compound deformation feature uniquely. The characteristic arrangement of the faces and type of bends belonging to the feature decide the type and nature of the deformation feature. Algorithms have been developed to extract and identify deformation features from a CAD model of sheet-metal parts. The proposed algorithm does not require folding and unfolding of the part as intermediate steps to recognize deformation features. Representations of typical features are illustrated and results of extracting these deformation features from typical sheet metal parts are presented and discussed. (C) 2013 Elsevier Ltd. All rights reserved.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

An automated approach to network features of protein structure ensembles

Network theory applied to protein structures provides insights into numerous problems of biological relevance. The explosion in structural data available from PDB and simulations establishes a need to introduce a standalone-efficient program that assembles network concepts/parameters under one hood in an automated manner. Herein, we discuss the development/application of an exhaustive, user-friendly, standalone program package named PSN-Ensemble, which can handle structural ensembles generated through molecular dynamics (MD) simulation/NMR studies or from multiple X-ray structures. The novelty in network construction lies in the explicit consideration of side-chain interactions among amino acids. The program evaluates network parameters dealing with topological organization and long-range allosteric communication. The introduction of a flexible weighing scheme in terms of residue pairwise cross-correlation/interaction energy in PSN-Ensemble brings in dynamical/chemical knowledge into the network representation. Also, the results are mapped on a graphical display of the structure, allowing an easy access of network analysis to a general biological community. The potential of PSN-Ensemble toward examining structural ensemble is exemplified using MD trajectories of an ubiquitin-conjugating enzyme (UbcH5b). Furthermore, insights derived from network parameters evaluated using PSN-Ensemble for single-static structures of active/inactive states of 2-adrenergic receptor and the ternary tRNA complexes of tyrosyl tRNA synthetases (from organisms across kingdoms) are discussed. PSN-Ensemble is freely available from http://vishgraph.mbu.iisc.ernet.in/PSN-Ensemble/psn_index.html.

Delay optimized zero-forcing channel shortening algorithm for wireless communication

In Orthogonal Frequency Division Multiplexing and Discrete Multitone transceivers, a guard interval called Cyclic Prefix (CP) is inserted to avoid inter-symbol interference. The length of the CP is usually greater than the impulse response of the channel resulting in a loss of useful data carriers. In order to avoid long CP, a time domain equalizer is used to shorten the channel. In this paper, we propose a method to include a delay in the zero-forcing equalizer and obtain an optimal value of the delay, based on the location of zeros of the channel. The performance of the algorithms is studied using numerical simulations.

Burst error correction using partial fourier matrices and block sparse representation

There is a strong relation between sparse signal recovery and error control coding. It is known that burst errors are block sparse in nature. So, here we attempt to solve burst error correction problem using block sparse signal recovery methods. We construct partial Fourier based encoding and decoding matrices using results on difference sets. These constructions offer guaranteed and efficient error correction when used in conjunction with reconstruction algorithms which exploit block sparsity.

Solvent Sensitivity of Protein Unfolding: Dynamical Study of Chicken Villin Headpiece Subdomain in Water Ethanol Binary Mixture

We carry out a series of long atomistic molecular dynamics simulations to study the unfolding of a small protein, chicken villin headpiece (HP-36), in water-ethanol (EtOH) binary mixture. The prime objective of this work is to explore the sensitivity of protein unfolding dynamics toward increasing concentration of the cosolvent and unravel essential features of intermediates formed in search of a dynamical pathway toward unfolding. In water ethanol binary mixtures, HP-36 is found to unfold partially, under ambient conditions, that otherwise requires temperature as high as similar to 600 K to denature in pure aqueous solvent. However, an interesting course of pathway is observed to be followed in the process, guided by the formation of unique intermediates. The first step of unfolding is essentially the separation of the cluster formed by three hydrophobic (phenylalanine) residues, namely, Phe-7, Phe-11, and Phe-18, which constitute the hydrophobic core, thereby initiating melting of helix-2 of the protein. The initial steps are similar to temperature-induced unfolding as well as chemical unfolding using DMSO as cosolvent. Subsequent unfolding steps follow a unique path. As water-ethanol shows composition-dependent anomalies, so do the details of unfolding dynamics. With an increase in cosolvent concentration, different partially unfolded intermediates are found to be formed. This is reflected in a remarkable nonmonotonic composition dependence of several order parameters, including fraction of native contacts and protein-solvent interaction energy. The emergence of such partially unfolded states can be attributed to the preferential solvation of the hydrophobic residues by the ethyl groups of ethanol. We further quantify the local dynamics of unfolding by using a Marcus-type theory.

A NEAR OPTIMAL PROJECTION FOR SPARSE REPRESENTATION BASED CLASSIFICATION

Sparse representation based classification (SRC) is one of the most successful methods that has been developed in recent times for face recognition. Optimal projection for Sparse representation based classification (OPSRC)1] provides a dimensionality reduction map that is supposed to give optimum performance for SRC framework. However, the computational complexity involved in this method is too high. Here, we propose a new projection technique using the data scatter matrix which is computationally superior to the optimal projection method with comparable classification accuracy with respect OPSRC. The performance of the proposed approach is benchmarked with various publicly available face database.

A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter. (C) 2013 Elsevier B.V. All rights reserved.

High Throughput, Low Latency, Memory Optimized 64K Point FFT Architecture using Novel Radix-4 Butterfly Unit

In this paper we propose a fully parallel 64K point radix-4(4) FFT processor. The radix-4(4) parallel unrolled architecture uses a novel radix-4 butterfly unit which takes all four inputs in parallel and can selectively produce one out of the four outputs. The radix-4(4) block can take all 256 inputs in parallel and can use the select control signals to generate one out of the 256 outputs. The resultant 64K point FFT processor shows significant reduction in intermediate memory but with increased hardware complexity. Compared to the state-of-art implementation 5], our architecture shows reduced latency with comparable throughput and area. The 64K point FFT architecture was synthesized using a 130nm CMOS technology which resulted in a throughput of 1.4 GSPS and latency of 47.7 mu s with a maximum clock frequency of 350MHz. When compared to 5], the latency is reduced by 303 mu s with 50.8% reduction in area.

Dynamical localization in a chain of hard core bosons under periodic driving

We study the dynamics of a one-dimensional lattice model of hard core bosons which is initially in a superfluid phase with a current being induced by applying a twist at the boundary. Subsequently, the twist is removed, and the system is subjected to periodic delta-function kicks in the staggered on-site potential. We present analytical expressions for the current and work done in the limit of an infinite number of kicks. Using these, we show that the current (work done) exhibits a number of dips (peaks) as a function of the driving frequency and eventually saturates to zero (a finite value) in the limit of large frequency. The vanishing of the current (and the saturation of the work done) can be attributed to a dynamic localization of the hard core bosons occurring as a consequence of the periodic driving. Remarkably, we show that for some specific values of the driving amplitude, the localization occurs for any value of the driving frequency. Moreover, starting from a half-filled lattice of hard core bosons with the particles localized in the central region, we show that the spreading of the particles occurs in a light-cone-like region with a group velocity that vanishes when the system is dynamically localized.