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.

Chemical Shifts to Metabolic Pathways: Identifying Metabolic Pathways Directly from a Single 2D NMR Spectrum

Identifying cellular processes in terms of metabolic pathways is one of the avowed goals of metabolomics studies. Currently, this is done after relevant metabolites are identified to allow their mapping onto specific pathways. This task is daunting due to the complex nature of cellular processes and the difficulty in establishing the identity of individual metabolites. We propose here a new method: ChemSMP (Chemical Shifts to Metabolic Pathways), which facilitates rapid analysis by identifying the active metabolic pathways directly from chemical shifts obtained from a single two-dimensional (2D) C-13-H-1] correlation NMR spectrum without the need for identification and assignment of individual metabolites. ChemSMP uses a novel indexing and scoring system comprised of a ``uniqueness score'' and a ``coverage score''. Our method is demonstrated on metabolic pathways data from the Small Molecule Pathway Database (SMPDB) and chemical shifts from the Human Metabolome Database (HMDB). Benchmarks show that ChemSMP has a positive prediction rate of >90% in the presence of deduttered data and can sustain the same at 60-70% even in the presence of noise, such as deletions of peaks and chemical shift deviations. The method tested on NMR data acquired for a mixture of 20 amino acids shows a success rate of 93% in correct recovery of pathways. When used on data obtained from the cell lysate of an unexplored oncogenic cell line, it revealed active metabolic pathways responsible for regulating energy homeostasis of cancer cells. Our unique tool is thus expected to significantly enhance analysis of NMIR-based metabolomics data by reducing existing impediments.

A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

BIOCARDS AND LEVEL OF ABSTRACTION

Biocards are formal descriptions of biological phenomena and their underlying functional principles. They are used in bioinspired design to document search results and to communicate the findings for use in the further design process. The present study explored the effect of abstraction level used in biocards. This was done in two workshops conducted with design students in Denmark and India. Students were given a design assignment and instructions for how to perform the BID ideation work. Half of the students were given biocards with abstract descriptions while the other half got biocards with concrete descriptions. The novelty of found solutions was evaluated by the students by rating novelty of each solution on a scale from 1 to 5. Mean values for abstract descriptions were 0,3 higher than for concrete descriptions indicating that more innovative solutions were found when students used biocards with abstract descriptions compared to concrete descriptions. The difference in mean value is significant with a confidence level better than 1%. It seems likely that more abstract descriptions in biocards helps avoiding design fixation in biomimetic design work.

Rayleigh-Taylor instability in a thermocline based thermal storage tank

Numerical simulations are performed to study the stability characteristics of a molten salt thermocline storage unit. Perturbations are introduced into a stable flow field in such a way as to make the top-fluid heavier than the fluid at the bottom, thereby causing a possible instability in the system. The evolution pattern of the various disturbances are examined in detail. Disturbances applied for short duration get decayed before they could reach the thermocline, whereas medium and long duration disturbances evolve into a ``falling spike'' or ``stalactite-like'' structure and destabilize the thermocline. Rayleigh Taylor instability is observed inside the storage tank. The effect of the duration, velocity and temperature of the disturbance on thermocline thickness and penetration length are studied. A quadratic time dependence of penetration length was observed. New perspectives on thermocline breakdown phenomena are obtained from the numerical flow field. (C) 2015 Elsevier Masson SAS. All rights reserved.

Beyond Schur's Conjecture

Schur 4] conjectured that the maximum length N of consecutive quadratic nonresidues modulo a prime p is less than root p if p is large enough. This was proved by Hummel in 2003. In this note, we outline a clear improvement over Hummel's bound for p > 23.

Beyond Schur's Conjecture

Schur 4] conjectured that the maximum length N of consecutive quadratic nonresidues modulo a prime p is less than root p if p is large enough. This was proved by Hummel in 2003. In this note, we outline a clear improvement over Hummel's bound for p > 23.

Efficient simulation and rendering of realistic motion of one-dimensional flexible objects

In gross motion of flexible one-dimensional (1D) objects such as cables, ropes, chains, ribbons and hair, the assumption of constant length is realistic and reasonable. The motion of the object also appears more natural if the motion or disturbance given at one end attenuates along the length of the object. In an earlier work, variational calculus was used to derive natural and length-preserving transformation of planar and spatial curves and implemented for flexible 1D objects discretized with a large number of straight segments. This paper proposes a novel idea to reduce computational effort and enable real-time and realistic simulation of the motion of flexible 1D objects. The key idea is to represent the flexible 1D object as a spline and move the underlying control polygon with much smaller number of segments. To preserve the length of the curve to within a prescribed tolerance as the control polygon is moved, the control polygon is adaptively modified by subdivision and merging. New theoretical results relating the length of the curve and the angle between the adjacent segments of the control polygon are derived for quadratic and cubic splines. Depending on the prescribed tolerance on length error, the theoretical results are used to obtain threshold angles for subdivision and merging. Simulation results for arbitrarily chosen planar and spatial curves whose one end is subjected to generic input motions are provided to illustrate the approach. (C) 2016 Elsevier Ltd. All rights reserved.