Epidemic Thresholds with External Agents

We study the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents - sources unconstrained by the graph, but possessing a limited infection rate or virulence. Such a model captures many existing models of externally aided epidemics, and finds use in many settings - epidemiology, marketing and advertising, network robustness, etc. We provide a detailed characterization of the impact of external agents on epidemic thresholds. In particular, for the SIS model, we show that any external infection strategy with constant virulence either fails to significantly affect the lifetime of an epidemic, or at best, sustains the epidemic for a lifetime which is polynomial in the number of nodes. On the other hand, a random external-infection strategy, with rate increasing linearly in the number of infected nodes, succeeds under some conditions to sustain an exponential epidemic lifetime. We obtain similar sharp thresholds for the SIR model, and discuss the relevance of our results in a variety of settings.Comment: 12 pages, 2 figures (to appear in INFOCOM 2014

Explicit feedback synthesis for nonlinear robust model predictive control driven by quasi-interpolation

We present QuIFS (Quasi-Interpolation driven Feedback Synthesis): an offline feedback synthesis algorithm for explicit nonlinear robust minmax model predictive control (MPC) problems with guaranteed quality of approximation. The underlying technique is driven by a particular type of grid-based quasi-interpolation scheme. The QuIFS algorithm departs drastically from conventional approximation algorithms that are employed in the MPC industry (in particular, it is neither based on multi-parametric programming tools and nor does it involve kernel methods), and the essence of its point of departure is encoded in the following challenge-answer approach: Given an error margin $\varepsilon>0$, compute in a single stroke a feasible feedback policy that is uniformly $\varepsilon$-close to the optimal MPC feedback policy for a given nonlinear system subjected to constraints and bounded uncertainties. Closed-loop stability and recursive feasibility under the approximate feedback policy are also established. We provide a library of numerical examples to illustrate our results.Comment: 31 Page

Towards a theory of cache-efficient algorithms

We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O model, enables us to establish useful relationships between the cache complexity and the I/O complexity of computations. As a corollary, we obtain cache-optimal algorithms for some fundamental problems like sorting, FFT, and an important subclass of permutations in the single-level cache model. We also show that ignoring associativity concerns could lead to inferior performance, by analyzing the average-case cache behavior of mergesort. We further extend our model to multiple levels of cache with limited associativity and present optimal algorithms for matrix transpose and sorting. Our techniques may be used for systematic exploitation of the memory hierarchy starting from the algorithm design stage, and dealing with the hitherto unresolved problem of limited associativity

Manufacturing extremism: political consequences of profit-seeking media

We analyze the consequences of a monopolistic, non-partisan, profit-maximizing media on policy divergence. The media undertakes costly coverage that may reveal the quality of an office-seeking political challenger only if quality-conscious voters pay an access fee. Voters are ideologically homogenous and the incumbent politican is a populist with known quality. We show that while media absence implies a populist challenger, media presence yields platform extremism: it creates demand for information about quality and provides incentives to the media to invest in coverage that are exploited by high-quality challengers to signal strength. JEL Classifiers: C72, D72, D8

Role of latent female genital tuberculosis in recurrent early pregnancy loss: A retrospective analysis

Background: Latent Female Genital tuberculosis (FGTB) or tubercular infestation is prevalent in Southeast Asia and even the presence of tubercular bacilli in the genital tract is becoming an important factor for reproductive failure. An immature endometrium becomes non-receptive, preventing implantation or rejection of implanted embryo in early months, resulting in recurrent pregnancy loss (RPL) in association with other factors. Objective: To detect the underlying causes of RPL in addition to the proven causes like uterine cavity defects, thrombophilia, chromosomal abnormalities, etc. Materials and Methods: 317 women with RPL, enrolled over a period of 60 months (January 2014 to December 2018) conducted at Calcutta Fertility Mission in the present study. They were grouped in A, B, and C and undergone routine tests for the same along with the PCR test with an endometrial aspirate. Results: Patients with only latent FGTB (Group A), patients with FGTB and associated factors (Group B), and patients with other causes of RPL (other than latent FGTB) (Group C) were34.4%, 42.3%, and 23.3% respectively. About 29.36%, 47.01%, and 21.62%of the patients had achieved pregnancy in Group A, B, and C, respectively. The rate of miscarriage was high in both Groups A and B, affected with latent FGTB, and live-birth was higher (75%) in Group C that did not have tubercular involvement of the genital tract. Conclusion: The tubercular infestation or latent FGTB as per our study appears to be a very important cause of RPL in patients with recurrent “unexplained” miscarriage. It should be treated adequately at an early stage to prevent permanent damage to pelvic organs and restore reproductive health in women. Key words: Female genital tuberculosis, Recurrent pregnancy loss, Endometrium, Implantation

Towards continuous-time MPC: a novel trajectory optimization algorithm

This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying optimal control problem (OCP) are a linear time-invariant system, quadratic instantaneous and terminal cost functions, and convex path constraints. The thrust of the method involves finitely parameterizing the admissible space of control trajectories and solving the OCP satisfying the given constraints at every time instant in a tractable manner without explicit time-discretization. The ensuing OCP turns out to be a convex semi-infinite program (SIP), and some recently developed results are employed to obtain an optimal solution to this convex SIP. Numerical illustrations on some benchmark models are included to show the efficacy of the algorithm.Comment: Accepted in IEEE Conference on Decision and Control (CDC), 202

A discrete-time Pontryagin maximum principle under rate constraints

Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the global behavior of their paths. While the problem of actuator saturation has been studied extensively, little attention has been devoted to the problem of actuators having limited bandwidth. While attempts have been made in the direction of incorporating frequency constraints on state-action trajectories before, rate constraints on the control at the design stage have not been studied extensively in the discrete-time regime. This article contributes toward filling this lacuna. In particular, we establish a new discrete-time Pontryagin maximum principle with rate constraints being imposed on the control trajectories, and derive first-order necessary conditions for optimality. A brief discussion on the existence of optimal control is included, and numerical examples are provided to illustrate the results

Design of Delta Sigma Modulators for Integrated Sensor Applications

The paper presents and explores the implementation of Delta Sigma Modulators for Integrated sensor applications. Elaborate design procedures and trade-offs faced have been presented. Starting at the block and topology level, comparisons of various feasible choices have been presented, along with the suited applications. Circuit level comparisons and trade-offs such as OTA and comparator design have also been presented. Finally, simulations have been shown for a modulator designed as per above criteria for integrated accelerometer applications. Keywords: MEMS, Delta Sigma Modulators, Dynamic Range, Integrated sensor