Secure Communication in Amplify-and-Forward Networks with Multiple Eavesdroppers: Decoding with SNR Thresholds

The problem of secure unicast communication over a two hop Amplify-and-Forward wireless relay network with multiple eavesdroppers is considered. Assuming that a receiver (destination or eavesdropper) can decode a message only if the received SNR is above a predefined threshold, we consider this problem in two scenarios. In the first scenario, we maximize the SNR at the legitimate destination, subject to the condition that the received SNR at each eavesdropper is below the target threshold. Due to the non-convex nature of the objective function and eavesdroppers' constraints, we transform variables and obtain a quadratically constrained quadratic program (QCQP) with convex constraints, which can be solved efficiently. When the constraints are not convex, we consider a semidefinite relaxation (SDR) to obtain computationally efficient approximate solution. In the second scenario, we minimize the total power consumed by all relay nodes, subject to the condition that the received SNR at the legitimate destination is above the threshold and at every eavesdropper, it is below the corresponding threshold. We propose a semidefinite relaxation of the problem in this scenario and also provide an analytical lower bound.

Global response sensitivity analysis of uncertain structures

The problem of characterizing global sensitivity indices of structural response when system uncertainties are represented using probabilistic and (or) non-probabilistic modeling frameworks (which include intervals, convex functions, and fuzzy variables) is considered. These indices are characterized in terms of distance measures between a fiducial model in which uncertainties in all the pertinent variables are taken into account and a family of hypothetical models in which uncertainty in one or more selected variables are suppressed. The distance measures considered include various probability distance measures (Hellinger,l(2), and the Kantorovich metrics, and the Kullback-Leibler divergence) and Hausdorff distance measure as applied to intervals and fuzzy variables. Illustrations include studies on an uncertainly parametered building frame carrying uncertain loads. (C) 2015 Elsevier Ltd. All rights reserved.

COMPLEX GEODESICS, THEIR BOUNDARY REGULARITY, AND A HARDY-LITTLEWOOD-TYPE LEMMA

We begin by giving an example of a smoothly bounded convex domain that has complex geodesics that do not extend continuously up to partial derivative D. This example suggests that continuity at the boundary of the complex geodesics of a convex domain Omega (sic) C-n, n >= 2, is affected by the extent to which partial derivative Omega curves or bends at each boundary point. We provide a sufficient condition to this effect (on C-1-smoothly bounded convex domains), which admits domains having boundary points at which the boundary is infinitely flat. Along the way, we establish a Hardy-Littlewood-type lemma that might be of independent interest.

Full current statistics for a disordered open exclusion process

We consider the nonabelian sandpile model defined on directed trees by Ayyer et al. (2015 Commun. Math. Phys. 335 1065). and restrict it to the special case of a one-dimensional lattice of n sites which has open boundaries and disordered hopping rates. We focus on the joint distribution of the integrated currents across each bond simultaneously, and calculate its cumulant generating function exactly. Surprisingly, the process conditioned on seeing specified currents across each bond turns out to be a renormalised version of the same process. We also remark on a duality property of the large deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the tilted generator are determined.

Maximum Spreading of Liquid Drops Impacting on Groove-Textured Surfaces: Effect of Surface Texture

Maximum, spreading of liquid drops impacting on solid surfaces textured with unidirectional parallel grooves is studied for drop Weber number in the range 1-100 focusing on the role of texture geometry and wettability. The maximum spread factor of impacting drops measured perpendicular to grooves; beta(m,perpendicular to) is seen to be less than, that:measured parallel to grooves, beta(m,perpendicular to).The difference between beta(m,perpendicular to), and beta(m,parallel to) increases with drop impact velocity. This deviation of beta(m,perpendicular to) from beta(m,parallel to) is analyzed by considering the possible mechanisms, correspond, ing to experimental observations (1) impregnation of drop into the grooves, (2) convex shape of liquid vapor interface near contact line at maximum spreading, and (3) contact line pinning of spreading drop at the pillar edges by incorporating them into an energy conservation-based model. The analysis reveals that contact line pinning offers a physically meaningful justification of the observed: deviation of beta(m,perpendicular to) from beta(m,parallel to) compared to other possible candidates. A unified model, incorporating all the above-mentioned mechanisms, is formulated, which predicts beta(m,perpendicular to) on several groove-textured surfaces made of intrinsically hydrophilic and hydrophobic materials with an average error of 8.3%. The effect of groove-texture geometrical parameters,on maximum drop spreading is explained using this unified model. A special case of the unified model, with contact line pinning, absent, predicts beta(m,parallel to) with an average error of 6.3%.

Advancing Edge Speeds of Epithelial Monolayers Depend on Their Initial Confining Geometry

Collective cell migrations are essential in several physiological processes and are driven by both chemical and mechanical cues. The roles of substrate stiffness and confinement on collective migrations have been investigated in recent years, however few studies have addressed how geometric shapes influence collective cell migrations. Here, we address the hypothesis that the relative position of a cell within the confinement influences its motility. Monolayers of two types of epithelial cells-MCF7, a breast epithelial cancer cell line, and MDCK, a control epithelial cell line-were confined within circular, square, and cross-shaped stencils and their migration velocities were quantified upon release of the constraint using particle image velocimetry. The choice of stencil geometry allowed us to investigate individual cell motility within convex, straight and concave boundaries. Cells located in sharp, convex boundaries migrated at slower rates than those in concave or straight edges in both cell types. The overall cluster migration occurred in three phases: an initial linear increase with time, followed by a plateau region and a subsequent decrease in cluster speeds. An acto-myosin contractile ring, present in the MDCK but absent in MCF7 monolayer, was a prominent feature in the emergence of leader cells from the MDCK clusters which occurred every similar to 125 mu m from the vertex of the cross. Further, coordinated cell movements displayed vorticity patterns in MDCK which were absent in MCF7 clusters. We also used cytoskeletal inhibitors to show the importance of acto-myosin bounding cables in collective migrations through translation of local movements to create long range coordinated movements and the creation of leader cells within ensembles. To our knowledge, this is the first demonstration of how bounding shapes influence long-term migratory behaviours of epithelial cell monolayers. These results are important for tissue engineering and may also enhance our understanding of cell movements during developmental patterning and cancer metastasis.