Belief propagation for minimum weight many-to-one matchings in the random complete graph

In a complete bipartite graph with vertex sets of cardinalities n and n', assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as n -> infinity, with n' = n/alpha] for any fixed alpha > 1, the minimum weight of many-to-one matchings converges to a constant (depending on alpha). Many-to-one matching arises as an optimization step in an algorithm for genome sequencing and as a measure of distance between finite sets. We prove that a belief propagation (BP) algorithm converges asymptotically to the optimal solution. We use the objective method of Aldous to prove our results. We build on previous works on minimum weight matching and minimum weight edge cover problems to extend the objective method and to further the applicability of belief propagation to random combinatorial optimization problems.

Engineering a nanostructured ``super surface'' with superhydrophobic and superkilling properties

We present a nanostructured ``super surface'' fabricated using a simple recipe based on deep reactive ion etching of a silicon wafer. The topography of the surface is inspired by the surface topographical features of dragonfly wings. The super surface is comprised of nanopillars 4 mm in height and 220 nm in diameter with random inter-pillar spacing. The surface exhibited superhydrophobicity with a static water contact angle of 154.0 degrees and contact angle hysteresis of 8.3 degrees. Bacterial studies revealed the bactericidal property of the surface against both gram negative (Escherichia coli) and gram positive (Staphylococcus aureus) strains through mechanical rupture of the cells by the sharp nanopillars. The cell viability on these nanostructured surfaces was nearly six-fold lower than on the unmodified silicon wafer. The nanostructured surface also killed mammalian cells (mouse osteoblasts) through mechanical rupture of the cell membrane. Thus, such nanostructured super surfaces could find applications for designing selfcleaning and anti-bacterial surfaces in diverse applications such as microfluidics, surgical instruments, pipelines and food packaging.

Identification of dominant modes in random dynamical and aeroelastic systems

Identification of dominant modes is an important step in studying linearly vibrating systems, including flow-induced vibrations. In the presence of uncertainty, when some of the system parameters and the external excitation are modeled as random quantities, this step becomes more difficult. This work is aimed at giving a systematic treatment to this end. The ability to capture the time averaged kinetic energy is chosen as the primary criterion for selection of modes. Accordingly, a methodology is proposed based on the overlap of probability density functions (pdf) of the natural and excitation frequencies, proximity of the natural frequencies of the mean or baseline system, modal participation factor, and stochastic variation of mode shapes in terms of the modes of the baseline system - termed here as statistical modal overlapping. The probabilistic descriptors of the natural frequencies and mode shapes are found by solving a random eigenvalue problem. Three distinct vibration scenarios are considered: (i) undamped arid damped free vibrations of a bladed disk assembly, (ii) forced vibration of a building, and (iii) flutter of a bridge model. Through numerical studies, it is observed that the proposed methodology gives an accurate selection of modes. (C) 2015 Elsevier Ltd. All rights reserved.

Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

We study the dynamical behaviors of two types of spiral-and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling G(j) and (2) the number N-f of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) G(j) is large or (b) the maximum possible number of fibroblasts per myocyte N-f(max) is large. We also observe that the minimum value of G(j), for the transition from the ST to the RS state, decreases as N-f(max) increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) G(j) increases, with fixed N-f(max), and (2) N-f(max) increases, with fixed G(j). We obtain the boundary between ST and RS stability regions in the N-f(max)-G(j) plane. In particular, for low values of N-f(max), the value of G(j), at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N-f(max) increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral-and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

SPEECH ENHANCEMENT USING DISCRIMINATIVE RANDOM FIELDS

Speech enhancement in stationary noise is addressed using the ideal channel selection framework. In order to estimate the binary mask, we propose to classify each time-frequency (T-F) bin of the noisy signal as speech or noise using Discriminative Random Fields (DRF). The DRF function contains two terms - an enhancement function and a smoothing term. On each T-F bin, we propose to use an enhancement function based on likelihood ratio test for speech presence, while Ising model is used as smoothing function for spectro-temporal continuity in the estimated binary mask. The effect of the smoothing function over successive iterations is found to reduce musical noise as opposed to using only enhancement function. The binary mask is inferred from the noisy signal using Iterated Conditional Modes (ICM) algorithm. Sentences from NOIZEUS corpus are evaluated from 0 dB to 15 dB Signal to Noise Ratio (SNR) in 4 kinds of additive noise settings: additive white Gaussian noise, car noise, street noise and pink noise. The reconstructed speech using the proposed technique is evaluated in terms of average segmental SNR, Perceptual Evaluation of Speech Quality (PESQ) and Mean opinion Score (MOS).

Autoregressive cascades on random networks

A network cascade model that captures many real-life correlated node failures in large networks via load redistribution is studied. The considered model is well suited for networks where physical quantities are transmitted, e.g., studying large scale outages in electrical power grids, gridlocks in road networks, and connectivity breakdown in communication networks, etc. For this model, a phase transition is established, i.e., existence of critical thresholds above or below which a small number of node failures lead to a global cascade of network failures or not. Theoretical bounds are obtained for the phase transition on the critical capacity parameter that determines the threshold above and below which cascade appears or disappears, respectively, that are shown to closely follow numerical simulation results. (C) 2015 Elsevier B.V. All rights reserved.

Autoregressive cascades on random networks

A network cascade model that captures many real-life correlated node failures in large networks via load redistribution is studied. The considered model is well suited for networks where physical quantities are transmitted, e.g., studying large scale outages in electrical power grids, gridlocks in road networks, and connectivity breakdown in communication networks, etc. For this model, a phase transition is established, i.e., existence of critical thresholds above or below which a small number of node failures lead to a global cascade of network failures or not. Theoretical bounds are obtained for the phase transition on the critical capacity parameter that determines the threshold above and below which cascade appears or disappears, respectively, that are shown to closely follow numerical simulation results. (C) 2015 Elsevier B.V. All rights reserved.

A strategy to achieve enhanced electromagnetic interference shielding at ultra-low concentration of multiwall carbon nanotubes in P alpha MSAN/PMMA blends in the presence of a random copolymer PS-r-PMMA

A unique strategy was adopted to achieve an ultra-low electrical percolation threshold of multiwall carbon nanotubes (MWNTs) (0.25 wt%) in a classical partially miscible blend of poly-alpha-methylstyrene-co-acrylonitrile and poly(methyl methacrylate) (P alpha MSAN/PMMA), with a lower critical solution temperature. The polymer blend nanocomposite was prepared by standard melt-mixing followed by annealing above the phase separation temperature. In a two-step mixing protocol, MWNTs were initially melt-mixed with a random PS-r-PMMA copolymer and subsequently diluted with 85/15 P alpha MSAN/PMMA blends in the next mixing step. Mediated by the PS-r-PMMA, the MWNTs were mostly localized at the interface and bridged the PMMA droplets. This strategy led to enhanced electromagnetic interference (EMI) shielding effectiveness at 0.25 wt% MWNTs through multiple scattering from MWNT-covered droplets, as compared to the blends without the copolymer, which were transparent to electromagnetic radiation.