Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending-torsion coupled, geometrically non-linear building frame under earthquake support motions. (C) 2015 Elsevier Ltd. All rights reserved.

WNT-Inflammasome Signaling Mediates NOD2-Induced Development of Acute Arthritis in Mice

In addition to its role in innate immunity, the intracellular pathogen sensor nucleotide-binding oligomerization domain 2 (NOD2) has been implicated in various inflammatory disorders, including the development of acute arthritis. However, the molecular mechanisms involved in the development of NOD2-responsive acute arthritis are not clear. In this study, we demonstrate that NOD2 signals to a cellular protein, Ly6/PLAUR domain-containing protein 6, in a receptor-interacting protein kinase 2-TGF-beta-activated kinase 1-independent manner to activate the WNT signaling cascade. Gain- or loss-of-function of the WNT signaling pathway in an in vivo experimental mouse arthritis model or in vitro systems established the role for WNT-responsive X-linked inhibitor of apoptosis during the development of acute arthritis. Importantly, WNT-stimulated X-linked inhibitor of apoptosis mediates the activation of inflammasomes. The subsequent caspase-1 activation and IL-1 beta secretion together contribute to the phenotypic character of the inflammatory condition of acute arthritis. Thus, identification of a role for WNT-mediated inflammasome activation during NOD2 stimulation serves as a paradigm to understand NOD2-associated inflammatory disorders and develop novel therapeutics.

Modified Greedy Pursuits for Improving Sparse Recovery

Compressive Sensing (CS) theory combines the signal sampling and compression for sparse signals resulting in reduction in sampling rate. In recent years, many recovery algorithms have been proposed to reconstruct the signal efficiently. Subspace Pursuit and Compressive Sampling Matching Pursuit are some of the popular greedy methods. Also, Fusion of Algorithms for Compressed Sensing is a recently proposed method where several CS reconstruction algorithms participate and the final estimate of the underlying sparse signal is determined by fusing the estimates obtained from the participating algorithms. All these methods involve solving a least squares problem which may be ill-conditioned, especially in the low dimension measurement regime. In this paper, we propose a step prior to least squares to ensure the well-conditioning of the least squares problem. Using Monte Carlo simulations, we show that in low dimension measurement scenario, this modification improves the reconstruction capability of the algorithm in clean as well as noisy measurement cases.

Modified Einstein's gravity as a possible missing link between sub- and super-Chandrasekhar type Ia supernovae

We explore the effect of modification to Einstein's gravity in white dwarfs for the first time in the literature, to the best of our knowledge. This leads to significantly sub- and super-Chandrasekhar limiting masses of white dwarfs, determined by a single model parameter. On the other hand, type Ia supernovae (SNeIa), a key to unravel the evolutionary history of the universe, are believed to be triggered in white dwarfs having mass close to the Chandrasekhar limit. However, observations of several peculiar, under- and over-luminous SNeIa argue for exploding masses widely different from this limit. We argue that explosions of the modified gravity induced sub- and super-Chandrasekhar limiting mass white dwarfs result in under- and over-luminous SNeIa respectively, thus unifying these two apparently disjoint sub-classes and, hence, serving as a missing link. Our discovery raises two fundamental questions. Is the Chandrasekhar limit unique? Is Einstein's gravity the ultimate theory for understanding astronomical phenomena? Both the answers appear to be no!