Fienup Algorithm With Sparsity Constraints: Application to Frequency-Domain Optical-Coherence Tomography

We address the problem of reconstructing a sparse signal from its DFT magnitude. We refer to this problem as the sparse phase retrieval (SPR) problem, which finds applications in tomography, digital holography, electron microscopy, etc. We develop a Fienup-type iterative algorithm, referred to as the Max-K algorithm, to enforce sparsity and successively refine the estimate of phase. We show that the Max-K algorithm possesses Cauchy convergence properties under certain conditions, that is, the MSE of reconstruction does not increase with iterations. We also formulate the problem of SPR as a feasibility problem, where the goal is to find a signal that is sparse in a known basis and whose Fourier transform magnitude is consistent with the measurement. Subsequently, we interpret the Max-K algorithm as alternating projections onto the object-domain and measurement-domain constraint sets and generalize it to a parameterized relaxation, known as the relaxed averaged alternating reflections (RAAR) algorithm. On the application front, we work with measurements acquired using a frequency-domain optical-coherence tomography (FDOCT) experimental setup. Experimental results on measured data show that the proposed algorithms exhibit good reconstruction performance compared with the direct inversion technique, homomorphic technique, and the classical Fienup algorithm without sparsity constraint; specifically, the autocorrelation artifacts and background noise are suppressed to a significant extent. We also demonstrate that the RAAR algorithm offers a broader framework for FDOCT reconstruction, of which the direct inversion technique and the proposed Max-K algorithm become special instances corresponding to specific values of the relaxation parameter.

Frequency-domain stimulated and spontaneous light emission signals at molecular junctions

Using a diagrammatic superoperator formalism we calculate optical signals at molecular junctions where a single molecule is coupled to two metal leads which are held at different chemical potentials. The molecule starts in a nonequilibrium steady state whereby it continuously exchanges electrons with the leads with a constant electron flux. Expressions for frequency domain optical signals measured in response to continuous laser fields are derived by expanding the molecular correlation functions in terms of its many-body states. The nonunitary evolution of molecular states is described by the quantum master equation. (C) 2014 AIP Publishing LLC.

The Non-catalytic ``Cap Domain'' of a Mycobacterial Metallophosphoesterase Regulates Its Expression and Localization in the Cell

Despite highly conserved core catalytic domains, members of the metallophosphoesterase (MPE) superfamily perform diverse and crucial functions ranging from nucleotide and nucleic acid metabolism to phospholipid hydrolysis. Unique structural elements outside of the catalytic core called ``cap domains'' are thought to provide specialization to these enzymes; however, no directed study has been performed to substantiate this. The cap domain of Rv0805, an MPE from Mycobacterium tuberculosis, is located C-terminal to its catalytic domain and is dispensable for the catalytic activity of this enzyme in vitro. We show here that this C-terminal extension (CTE) mediates in vivo localization of the protein to the cell membrane and cell wall as well as modulates expression levels of Rv0805 in mycobacteria. We also demonstrate that Rv0805 interacts with the cell wall of mycobacteria, possibly with the mycolyl-arabinogalactan-peptidoglycan complex, by virtue of its C terminus, a hitherto unknown property of this MPE. Using a panel of mutant proteins, we identify interactions between active site residues of Rv0805 and the CTE that determine its association with the cell wall. Finally, we show that Rv0805 and a truncated mutant devoid of the CTE produce different phenotypic effects when expressed in mycobacteria. Our study thus provides a detailed dissection of the functions of the cap domain of an MPE and suggests that the repertoire of cellular functions of MPEs cannot be understood without exploring the modulatory effects of these subdomains.

Super-Resolution Reconstruction in Frequency-Domain Optical-Coherence Tomography Using the Finite-Rate-of-Innovation Principle

The standard approach to signal reconstruction in frequency-domain optical-coherence tomography (FDOCT) is to apply the inverse Fourier transform to the measurements. This technique offers limited resolution (due to Heisenberg's uncertainty principle). We propose a new super-resolution reconstruction method based on a parametric representation. We consider multilayer specimens, wherein each layer has a constant refractive index and show that the backscattered signal from such a specimen fits accurately in to the framework of finite-rate-of-innovation (FRI) signal model and is represented by a finite number of free parameters. We deploy the high-resolution Prony method and show that high-quality, super-resolved reconstruction is possible with fewer measurements (about one-fourth of the number required for the standard Fourier technique). To further improve robustness to noise in practical scenarios, we take advantage of an iterated singular-value decomposition algorithm (Cadzow denoiser). We present results of Monte Carlo analyses, and assess statistical efficiency of the reconstruction techniques by comparing their performance against the Cramer-Rao bound. Reconstruction results on experimental data obtained from technical as well as biological specimens show a distinct improvement in resolution and signal-to-reconstruction noise offered by the proposed method in comparison with the standard approach.

Time-Domain Approach to Estimate Series Capacitance of an Isolated Phase Winding of a Transformer

Information available in frequency response data is equivalently available in the time domain as a response due to an impulse excitation. The idea to pursue this equivalence to estimate series capacitance is linked to the well-known fact that under impulse excitation, the line/neutral current in a transformer has three distinct components, of which, the initial capacitive component is the first to manifest, followed by the oscillatory and inductive components. Of these, the capacitive component is temporally well separated from the rest-a crucial feature permitting its direct access and analysis. Further, the winding initially behaves as a pure capacitive network, so the initial component must obviously originate from only the (series and shunt) capacitances. With this logic, it should therefore be possible to estimate series capacitance, just by measuring the initial capacitive component of line current and the total shunt capacitance. The principle of the method and details of its implementation on two actual isolated transformerwindings (uniformly wound) are presented. For implementation, a low-voltage recurrent surge generator, a current probe, and a digital oscilloscope are all that is needed. The method is simple and requires no programming and needs least user intervention, thus paving the way for its widespread use.

Structure, interactions and evolutionary implications of a domain-swapped lectin dimer from Mycobacterium smegmatis

Crystal structure determination of the lectin domain of MSMEG_3662 from Mycobacterium smegmatis and its complexes with mannose and methyl-alpha-mannose, the first effort of its kind on a mycobacterial lectin, reveals a structure very similar to beta-prism II fold lectins from plant sources, but with extensive unprecedented domain swapping in dimer formation. The two subunits in a dimer often show small differences in structure, but the two domains, not always related by 2-fold symmetry, have the same structure. Each domain carries three sugar-binding sites, similar to those in plant lectins, one on each Greek key motif. The occurrence of beta-prism II fold lectins in bacteria, with characteristics similar to those from plants, indicates that this family of lectins is of ancient origin and had evolved into a mature system before bacteria and plants diverged. In plants, the number of binding sites per domain varies between one and three, whereas the number is two in the recently reported lectin domains from Pseudomonas putida and Pseudomonas aeruginosa. An analysis of the sequences of the lectins and the lectin domains shows that the level of sequence similarity among the three Greek keys in each domain has a correlation with the number of binding sites in it. Furthermore, sequence conservation among the lectins from different species is the highest for that Greek key which carries a binding site in all of them. Thus, it would appear that carbohydrate binding influences the course of the evolution of the lectin.

Grain and the concomitant ferroelectric domain size dependent physical properties of Ba0.85Ca0.15Zr0.1Ti0.9O3 ceramics fabricated using powders derived from oxalate precursor route

Fine powders comprising nanocrystallites of Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT) were synthesized via oxalate precursor method, which facilitated to obtain homogenous and large grain sized ceramics at a lower sintering temperature. The compacted powders were sintered at various temperatures in the range of 1200 degrees C-1500 degrees C for an optimized duration of 10 h. Interestingly the one that was sintered at 1450 degrees C/10 h exhibited well resolved Morphotrophic Phase Boundary. The average grain size associated with this sample was 30 mu m accompanied by higher domain density mostly with 90 degrees twinning. These were believed to have significant contribution towards obtaining large strain of about 0.2% and piezoelectric coefficient as high as 563 pC/N. The maximum force that was generated by BCZT ceramic (having 30 mu m grain size) was found to be 161 MPa, which is much higher than that of known actuator materials such as PZT (40MPa) and NKN-5-LT (7 MPa). (C) 2014 AIP Publishing LLC.

CLAP: A web-server for automatic classification of proteins with special reference to multi-domain proteins

Background: The function of a protein can be deciphered with higher accuracy from its structure than from its amino acid sequence. Due to the huge gap in the available protein sequence and structural space, tools that can generate functionally homogeneous clusters using only the sequence information, hold great importance. For this, traditional alignment-based tools work well in most cases and clustering is performed on the basis of sequence similarity. But, in the case of multi-domain proteins, the alignment quality might be poor due to varied lengths of the proteins, domain shuffling or circular permutations. Multi-domain proteins are ubiquitous in nature, hence alignment-free tools, which overcome the shortcomings of alignment-based protein comparison methods, are required. Further, existing tools classify proteins using only domain-level information and hence miss out on the information encoded in the tethered regions or accessory domains. Our method, on the other hand, takes into account the full-length sequence of a protein, consolidating the complete sequence information to understand a given protein better. Results: Our web-server, CLAP (Classification of Proteins), is one such alignment-free software for automatic classification of protein sequences. It utilizes a pattern-matching algorithm that assigns local matching scores (LMS) to residues that are a part of the matched patterns between two sequences being compared. CLAP works on full-length sequences and does not require prior domain definitions. Pilot studies undertaken previously on protein kinases and immunoglobulins have shown that CLAP yields clusters, which have high functional and domain architectural similarity. Moreover, parsing at a statistically determined cut-off resulted in clusters that corroborated with the sub-family level classification of that particular domain family. Conclusions: CLAP is a useful protein-clustering tool, independent of domain assignment, domain order, sequence length and domain diversity. Our method can be used for any set of protein sequences, yielding functionally relevant clusters with high domain architectural homogeneity. The CLAP web server is freely available for academic use at http://nslab.mbu.iisc.ernet.in/clap/.

A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, nu of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrodinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and nonseparable integrable billiards, nu satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of m mod kn, given a particular k, for a set of quantum numbers, m, n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. (C) 2014 Elsevier Inc. All rights reserved.

Interaction of Sesbania mosaic virus (SeMV) RNA-dependent RNA polymerase (RdRp) with the p10 domain of polyprotein 2a and its implications in SeMV replication

Identification of viral encoded proteins that interact with RNA-dependent RNA polymerase (RdRp) is an important step towards unraveling the mechanism of replication. Sesbania mosaic virus (SeMV) RdRp was shown to interact strongly with p10 domain of polyprotein 2a and moderately with the protease domain. Mutational analysis suggested that the C-terminal disordered domain of RdRp is involved in the interaction with p10. Coexpression of full length RdRp and p10 resulted in formation of RdRp-p10 complex which showed significantly higher polymerase activity than RdRp alone. Interestingly, C Delta 43 RdRp also showed a similar increase in activity. Thus, p10 acts as a positive regulator of RdRp by interacting with the C-terminal disordered domain of RdRp. (C) 2014 The Authors. Published by Elsevier B.V.

Domain size correlated magnetic properties and electrical impedance of size dependent nickel ferrite nanoparticles

We report here the investigations on the size dependent variation of magnetic properties of nickel ferrite nanoparticles. Nickel ferrite nanoparticles of different sizes (14 to 22 nm) were prepared by the sol-gel route at different annealing temperatures. They are characterized by TGA-DTA, XRD, SEM, TEM and Raman spectroscopy techniques for the confirmation of the temperature of phase formation, thermal stability, crystallinity, morphology and structural status of the nickel ferrite nanoparticles. The magnetization studies revealed that the saturation magnetization (M-s), retentivity (M-r) increase, while coercivity (H-c) and anisotropy (K-eff) decrease as the particle size increases. The observed value of M-s is found to be relatively higher for a particle size of 22 nm. In addition, we have estimated the magnetic domain size using magnetic data and correlated to the average particle size. The calculated magnetic domain size is closely matching with the particle size estimated from XRD. Impedance spectroscopy was employed to study the samples in an equivalent circuit to understand their transport phenomena. It shows that nickel ferrite nanoparticles exhibit a non-Debye behavior with increasing particle size due to the influence of increasing disorders, surface effects, grain size and grain boundaries, etc. (C) 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Faster computation of the Karhunen-Loeve expansion using its domain independence property

The goal of this work is to reduce the cost of computing the coefficients in the Karhunen-Loeve (KL) expansion. The KL expansion serves as a useful and efficient tool for discretizing second-order stochastic processes with known covariance function. Its applications in engineering mechanics include discretizing random field models for elastic moduli, fluid properties, and structural response. The main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel. Mathematically this is a homogeneous Fredholm equation of second type. One widely used method for solving this integral eigenvalue problem is to use finite element (FE) bases for discretizing the eigenfunctions, followed by a Galerkin projection. This method is computationally expensive. In the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using KL expansion, although the individual KL terms are affected. Based on this domain independence property, a numerical integration based scheme accompanied by a modification of the domain, is proposed. In addition to presenting mathematical arguments to establish the domain independence, numerical studies are also conducted to demonstrate and test the proposed method. Numerically it is demonstrated that compared to the Galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example, and of one to two orders of magnitude for a three dimensional example, while retaining the same level of accuracy. It is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved. Both normal and lognormal fields are considered in the numerical studies. (c) 2014 Elsevier B.V. All rights reserved.

Crowd Flow Segmentation based on Motion Vectors in H.264 Compressed Domain

In this work, we have explored the prospect of segmenting crowd flow in H. 264 compressed videos by merely using motion vectors. The motion vectors are extracted by partially decoding the corresponding video sequence in the H. 264 compressed domain. The region of interest ie., crowd flow region is extracted and the motion vectors that spans the region of interest is preprocessed and a collective representation of the motion vectors for the entire video is obtained. The obtained motion vectors for the corresponding video is then clustered by using EM algorithm. Finally, the clusters which converges to a single flow are merged together based on the bhattacharya distance measure between the histogram of the of the orientation of the motion vectors at the boundaries of the clusters. We had implemented our proposed approach on the complex crowd flow dataset provided by 1] and compared our results by using Jaccard measure. Since we are performing crowd flow segmentation in the compressed domain using only motion vectors, our proposed approach performs much faster compared to other pixel domain counterparts still retaining better accuracy.

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ``energy-like measure'' in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate ``high-frequency'' dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacement-based and hybrid approaches against analytical solutions.

Typical and atypical domain combinations in human protein kinases: functions, disease causing mutations and conservation in other primates

Ser/Thr and Tyr protein kinases orchestrate many signalling pathways and hence loss in this balance leads to many disease phenotypes. Due to their high abundance, diversity and importance, efforts have been made in the past to classify kinases and annotate their functions at both gross and fine levels. These kinases are conventionally classified into subfamilies based on the sequences of catalytic domains. Usually the domain architecture of a full-length kinase is consistent with the subfamily classification made based on the sequence of kinase domain. Important contributions of modular domains to the overall function of the kinase are well known. Recently occurrence of two kinds of outlier kinases-''Hybrid'' and ``Rogue'' has been reported. These show considerable deviations in their domain architectures from the typical domain architecture known for the classical kinase subfamilies. This article provides an overview of the different subfamilies of human kinases and the role of non-kinase domains in functions and diseases. Importantly this article provides analysis of hybrid and rogue kinases encoded in the human genome and highlights their conservation in closely related primate species. These kinases are examples of elegant rewiring to bring about subtle functional differences compared to canonical variants.