Interference and Outage in Clustered Wireless Ad Hoc Networks

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson clustered process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its CCDF. We consider the probability of successful transmission in an interference limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds.We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes and the Campbell-Mecke theorem.Comment: Submitted to IEEE Transactions on Information Theor

Closure Operators on Complete Almost Distributive Lattices-III

In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ(L) to be complemented.This research is supported by the U.G.C, Major Research Project Ref. No.41783/2012(SR) 17-07-2012

Antieigenvalues and antisingularvalues of a matrix and applications to problems in statistics

Let A be p × p positive definite matrix. A p-vector x such that Ax = x is called an eigenvector with the associated with eigenvalue . Equivalent characterizations are: (i) cos = 1, where is the angle between x and Ax. (ii) (x0Ax)−1 = xA−1x. (iii) cos = 1, where is the angle between A1/2x and A−1/2x. We ask the question what is x such that cos as defined in (i) is a minimum or the angle of separation between x and Ax is a maximum. Such a vector is called an anti-eigenvector and cos an anti-eigenvalue of A. This is the basis of operator trigonometry developed by K. Gustafson and P.D.K.M. Rao (1997), Numerical Range: The Field of Values of Linear Operators and Matrices, Springer. We may define a measure of departure from condition (ii) as min[(x0Ax)(x0A−1x)]−1 which gives the same anti-eigenvalue. The same result holds if the maximum of the angle between A1/2x and A−1/2x as in condition (iii) is sought. We define a hierarchical series of anti-eigenvalues, and also consider optimization problems associated with measures of separation between an r(< p) dimensional subspace S and its transform AS. Similar problems are considered for a general matrix A and its singular values leading to anti-singular values. Other possible definitions of anti-eigen and anti-singular values, and applications to problems in statistics will be presented

Synthesis through Unification

Given a specification and a set of candidate programs (program space), the program synthesis problem is to find a candidate program that satisfies the specification. We present the synthesis through unification (STUN) approach, which is an extension of the counter-example guided inductive synthesis (CEGIS) approach. In CEGIS, the synthesizer maintains a subset S of inputs and a candidate program Prog that is correct for S. The synthesizer repeatedly checks if there exists a counter-example input c such that the execution of Prog is incorrect on c. If so, the synthesizer enlarges S to include c, and picks a program from the program space that is correct for the new set S. The STUN approach extends CEGIS with the idea that given a program Prog that is correct for a subset of inputs, the synthesizer can try to find a program Prog' that is correct for the rest of the inputs. If Prog and Prog' can be unified into a program in the program space, then a solution has been found. We present a generic synthesis procedure based on the STUN approach and specialize it for three different domains by providing the appropriate unification operators. We implemented these specializations in prototype tools, and we show that our tools often per- forms significantly better on standard benchmarks than a tool based on a pure CEGIS approach

Food consumption and nutritional status in India: Emerging trends and perspectives

The paper reviews the trends over three decades in the consumption of cereals, calories and micronutrients and nutritional status based on anthropometric measures using the data sets of NSS, NNMB and NFHS. It provides an explanation for the slow growth of nutrient intake and slow reduction in malnutrition. The paper demonstrates that multiple factors influence the nutritional well-being of a child and argues that besides improving the income of a household, there is a need to improve the health and educational status of mothers.

Design automation based on fluid dynamics

This article was accepted and presented at the 9th International Workshop on Bio-Design Automation, Pittsburgh, Pennsylvania (2017).Microfluidic devices provide researchers with numerous advantages such as high throughput, increased sensitivity and accuracy, lower cost, and reduced reaction time. However, design, fabrication, and running a microfluidic device are still heavily reliant on expertise. Recent studies suggest micro-milling can be a semi-automatic, inexpensive, and simple alternative to common fabrication methods. Micro-milling does not require a clean-room, mask aligner, spin-coater, and Plasma bonder, thus cutting down the cost and time of fabrication significantly. Moreover, through this protocol researchers can easily fabricate microfluidic devices in an automated fashion eschewing levels of expertise required for typical fabrication methods, such as photolithography, soft-lithography, and etching. However, designing a microfluidic chip that meets a certain set of requirements is still heavily dependent on a microfluidic expert, several days of simulation, and numerous experiments to reach the required performance. To address this, studies have reported random automated design of microfluidic devices based on numerical simulations for micro-mixing. However, random design generation is heavily reliant on time-consuming simulations carried out beforehand, and is prone to error due to the accuracy limitations of the numerical method. On the other hand, by using micro-milling for ultra-fast and inexpensive fabrication of microfluidic devices and Taguchi design of experiments for state-space exploration of all of the geometric parameters, we are able to generate a database of geometries, flow rates, and flow properties required for a single primitive to carry out a specified microfluidic task