Polynomial time and parameterized approximation algorithms for boxicity

The boxicity (cubicity) of a graph G, denoted by box(G) (respectively cub(G)), is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (cubes) in ℝ k . The problem of computing boxicity (cubicity) is known to be inapproximable in polynomial time even for graph classes like bipartite, co-bipartite and split graphs, within an O(n 0.5 − ε ) factor for any ε > 0, unless NP = ZPP. We prove that if a graph G on n vertices has a clique on n − k vertices, then box(G) can be computed in time n22O(k2logk) . Using this fact, various FPT approximation algorithms for boxicity are derived. The parameter used is the vertex (or edge) edit distance of the input graph from certain graph families of bounded boxicity - like interval graphs and planar graphs. Using the same fact, we also derive an O(nloglogn√logn√) factor approximation algorithm for computing boxicity, which, to our knowledge, is the first o(n) factor approximation algorithm for the problem. We also present an FPT approximation algorithm for computing the cubicity of graphs, with vertex cover number as the parameter.

Maximum likelihood algorithms for joint estimation of synchronisation impairments and channel in multiple input multiple output-orthogonal frequency division multiplexing system

Maximum likelihood (ML) algorithms, for the joint estimation of synchronisation impairments and channel in multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system, are investigated in this work. A system model that takes into account the effects of carrier frequency offset, sampling frequency offset, symbol timing error and channel impulse response is formulated. Cramer-Rao lower bounds for the estimation of continuous parameters are derived, which show the coupling effect among different impairments and the significance of the joint estimation. The authors propose an ML algorithm for the estimation of synchronisation impairments and channel together, using the grid search method. To reduce the complexity of the joint grid search in the ML algorithm, a modified ML (MML) algorithm with multiple one-dimensional searches is also proposed. Further, a stage-wise ML (SML) algorithm using existing algorithms, which estimate less number of parameters, is also proposed. Performance of the estimation algorithms is studied through numerical simulations and it is found that the proposed ML and MML algorithms exhibit better performance than SML algorithm.

Sustaining cooperation on networks: an analytical study based on evolutionary game theory

We analytically study the role played by the network topology in sustaining cooperation in a society of myopic agents in an evolutionary setting. In our model, each agent plays the Prisoner's Dilemma (PD) game with its neighbors, as specified by a network. Cooperation is the incumbent strategy, whereas defectors are the mutants. Starting with a population of cooperators, some agents are switched to defection. The agents then play the PD game with their neighbors and compute their fitness. After this, an evolutionary rule, or imitation dynamic is used to update the agent strategy. A defector switches back to cooperation if it has a cooperator neighbor with higher fitness. The network is said to sustain cooperation if almost all defectors switch to cooperation. Earlier work on the sustenance of cooperation has largely consisted of simulation studies, and we seek to complement this body of work by providing analytical insight for the same. We find that in order to sustain cooperation, a network should satisfy some properties such as small average diameter, densification, and irregularity. Real-world networks have been empirically shown to exhibit these properties, and are thus candidates for the sustenance of cooperation. We also analyze some specific graphs to determine whether or not they sustain cooperation. In particular, we find that scale-free graphs belonging to a certain family sustain cooperation, whereas Erdos-Renyi random graphs do not. To the best of our knowledge, ours is the first analytical attempt to determine which networks sustain cooperation in a population of myopic agents in an evolutionary setting.

FUSION OF ALGORITHMS FOR COMPRESSED SENSING

Numerous algorithms have been proposed recently for sparse signal recovery in Compressed Sensing (CS). In practice, the number of measurements can be very limited due to the nature of the problem and/or the underlying statistical distribution of the non-zero elements of the sparse signal may not be known a priori. It has been observed that the performance of any sparse signal recovery algorithm depends on these factors, which makes the selection of a suitable sparse recovery algorithm difficult. To take advantage in such situations, we propose to use a fusion framework using which we employ multiple sparse signal recovery algorithms and fuse their estimates to get a better estimate. Theoretical results justifying the performance improvement are shown. The efficacy of the proposed scheme is demonstrated by Monte Carlo simulations using synthetic sparse signals and ECG signals selected from MIT-BIH database.

Progressive fusion of reconstruction algorithms for low latency applications in compressed sensing

Recently, it has been shown that fusion of the estimates of a set of sparse recovery algorithms result in an estimate better than the best estimate in the set, especially when the number of measurements is very limited. Though these schemes provide better sparse signal recovery performance, the higher computational requirement makes it less attractive for low latency applications. To alleviate this drawback, in this paper, we develop a progressive fusion based scheme for low latency applications in compressed sensing. In progressive fusion, the estimates of the participating algorithms are fused progressively according to the availability of estimates. The availability of estimates depends on computational complexity of the participating algorithms, in turn on their latency requirement. Unlike the other fusion algorithms, the proposed progressive fusion algorithm provides quick interim results and successive refinements during the fusion process, which is highly desirable in low latency applications. We analyse the developed scheme by providing sufficient conditions for improvement of CS reconstruction quality and show the practical efficacy by numerical experiments using synthetic and real-world data. (C) 2013 Elsevier B.V. All rights reserved.

Performance evaluation of typical approximation algorithms for nonconvex l(p)-minimization in diffuse optical tomography

The sparse estimation methods that utilize the l(p)-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These l(p)-norm-based regularizations make the optimization function nonconvex, and algorithms that implement l(p)-norm minimization utilize approximations to the original l(p)-norm function. In this work, three such typical methods for implementing the l(p)-norm were considered, namely, iteratively reweighted l(1)-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of l(p)-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images. (C) 2014 Optical Society of America

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a-p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and beta-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.

Bi-Domain Protein Tyrosine Phosphatases Reveal an Evolutionary Adaptation to Optimize Signal Transduction

Significance: The bi-domain protein tyrosine phosphatases (PTPs) exemplify functional evolution in signaling proteins for optimal spatiotemporal signal transduction. Bi-domain PTPs are products of gene duplication. The catalytic activity, however, is often localized to one PTP domain. The inactive PTP domain adopts multiple functional roles. These include modulation of catalytic activity, substrate specificity, and stability of the bi-domain enzyme. In some cases, the inactive PTP domain is a receptor for redox stimuli. Since multiple bi-domain PTPs are concurrently active in related cellular pathways, a stringent regulatory mechanism and selective cross-talk is essential to ensure fidelity in signal transduction. Recent Advances: The inactive PTP domain is an activator for the catalytic PTP domain in some cases, whereas it reduces catalytic activity in other bi-domain PTPs. The relative orientation of the two domains provides a conformational rationale for this regulatory mechanism. Recent structural and biochemical data reveal that these PTP domains participate in substrate recruitment. The inactive PTP domain has also been demonstrated to undergo substantial conformational rearrangement and oligomerization under oxidative stress. Critical Issues and Future Directions: The role of the inactive PTP domain in coupling environmental stimuli with catalytic activity needs to be further examined. Another aspect that merits attention is the role of this domain in substrate recruitment. These aspects have been poorly characterized in vivo. These lacunae currently restrict our understanding of neo-functionalization of the inactive PTP domain in the bi-domain enzyme. It appears likely that more data from these research themes could form the basis for understanding the fidelity in intracellular signal transduction.

Accurate prediction of interfacial residues in two-domain proteins using evolutionary information: Implications for three-dimensional modeling

With the preponderance of multidomain proteins in eukaryotic genomes, it is essential to recognize the constituent domains and their functions. Often function involves communications across the domain interfaces, and the knowledge of the interacting sites is essential to our understanding of the structure-function relationship. Using evolutionary information extracted from homologous domains in at least two diverse domain architectures (single and multidomain), we predict the interface residues corresponding to domains from the two-domain proteins. We also use information from the three-dimensional structures of individual domains of two-domain proteins to train naive Bayes classifier model to predict the interfacial residues. Our predictions are highly accurate (approximate to 85%) and specific (approximate to 95%) to the domain-domain interfaces. This method is specific to multidomain proteins which contain domains in at least more than one protein architectural context. Using predicted residues to constrain domain-domain interaction, rigid-body docking was able to provide us with accurate full-length protein structures with correct orientation of domains. We believe that these results can be of considerable interest toward rational protein and interaction design, apart from providing us with valuable information on the nature of interactions. Proteins 2014; 82:1219-1234. (c) 2013 Wiley Periodicals, Inc.

Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of an XY spin chain

Precise experimental implementation of unitary operators is one of the most important tasks for quantum information processing. Numerical optimization techniques are widely used to find optimized control fields to realize a desired unitary operator. However, finding high-fidelity control pulses to realize an arbitrary unitary operator in larger spin systems is still a difficult task. In this work, we demonstrate that a combination of the GRAPE algorithm, which is a numerical pulse optimization technique, and a unitary operator decomposition algorithm Ajoy et al., Phys. Rev. A 85, 030303 (2012)] can realize unitary operators with high experimental fidelity. This is illustrated by simulating the mirror-inversion propagator of an XY spin chain in a five-spin dipolar coupled nuclear spin system. Further, this simulation has been used to demonstrate the transfer of entangled states from one end of the spin chain to the other end.

Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.

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.

Parameterized Algorithms for MAX COLORABLE INDUCED SUBGRAPH Problem on Perfect Graphs

We address the parameterized complexity ofMaxColorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril IPL 1987] showed that this problem is NP-complete even on split graphs if q is part of input, but gave a n(O(q)) algorithm on chordal graphs. We first observe that the problem is W2]-hard parameterized by q, even on split graphs. However, when parameterized by l, the number of vertices in the solution, we give two fixed-parameter tractable algorithms. The first algorithm runs in time 5.44(l) (n+#alpha(G))(O(1)) where #alpha(G) is the number of maximal independent sets of the input graph. The second algorithm runs in time q(l+o()l())n(O(1))T(alpha) where T-alpha is the time required to find a maximum independent set in any induced subgraph of G. The first algorithm is efficient when the input graph contains only polynomially many maximal independent sets; for example split graphs and co-chordal graphs. The running time of the second algorithm is FPT in l alone (whenever T-alpha is a polynomial in n), since q <= l for all non-trivial situations. Finally, we show that (under standard complexitytheoretic assumptions) the problem does not admit a polynomial kernel on split and perfect graphs in the following sense: (a) On split graphs, we do not expect a polynomial kernel if q is a part of the input. (b) On perfect graphs, we do not expect a polynomial kernel even for fixed values of q >= 2.

Newton-based stochastic optimization using q-Gaussian smoothed functional algorithms

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar, Dukkipati, & Bhatnagar, 2014), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on SF algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of q-values, in comparison to Newton SF algorithms with the Gaussian and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms. (C) 2014 Elsevier Ltd. All rights reserved.