Optimal one-dimensional coverage by unreliable sensors

This paper regards the problem of optimally placing unreliable sensors in a one-dimensional environment. We assume that sensors can fail with a certain probability and we minimize the expected maximum distance from any point in the environment to the closest active sensor. We provide a computational method to find the optimal placement and we estimate the relative quality of equispaced and random placements. We prove that the former is asymptotically equivalent to the optimal placement when the number of sensors goes to infinity, with a cost ratio converging to 1, while the cost of the latter remains strictly larger.Comment: 21 pages 2 figure

Asymptotic Analysis of the LMS Algorithm with Momentum

A widely studied filtering algorithm in signal processing is the least mean square (LMS) method, due to B. Widrow and T. Hoff, 1960. A popular extension of the LMS algorithm, which is also important in deep learning, is the LMS method with momentum, originated by S. Roy and J.J. Shynk back in 1988. This is a fixed gain (or constant step-size) version of the LMS method modified by an additional momentum term that is proportional to the last correction term. Recently, a certain equivalence of the two methods has been rigorously established by K. Yuan, B. Ying and A.H. Sayed, assuming martingale difference gradient noise. The purpose of this paper is to present the outline of a significantly simpler and more transparent asymptotic analysis of the LMS algorithm with momentum under the assumption of stationary, ergodic and mixing signals

The Mitochondrial Targets of Neuroprotective Drug Vinpocetine on Primary Neuron Cultures, Brain Capillary Endothelial Cells, Synaptosomes, and Brain Mitochondria

Vinpocetine is considered as neuroprotectant drug and used for treatment of brain ischemia and cognitive deficiencies for decades. A number of enzymes, channels and receptors can bind vinpocetine, however the mechanisms of many effects' are still not clear. The present study investigated the effects of vinpocetine from the mitochondrial bioenergetic aspects. In primary brain capillary endothelial cells the purinergic receptor-stimulated mitochondrial Ca2+ uptake and efflux were studied. Vinpocetine exerted a partial inhibition on the mitochondrial calcium efflux. In rodent brain synaptosomes vinpocetine (30 μM) inhibited respiration in uncoupler stimulated synaptosomes and decreased H2O2 release from the nerve terminals in resting and in complex I inhibited conditions, respectively. In isolated rat brain mitochondria using either complex I or complex II substrates leak respiration was stimulated, but ADP-induced respiration was inhibited by vinpocetine. The stimulation of oxidation was associated with a small extent of membrane depolarization. Mitochondrial H2O2 production was inhibited by vinpocetine under all conditions investigated. The most pronounced effects were detected with the complex II substrate succinate. Vinpocetine also mitigated both Ca2+-induced mitochondrial Ca2+-release and Ca2+-induced mitochondrial swelling. It lowered the rate of mitochondrial ATP synthesis, while increasing ATPase activity. These results indicate more than a single mitochondrial target of this vinca alkaloid. The relevance of the affected mitochondrial mechanisms in the anti ischemic effect of vinpocetine is discussed

Push sum with transmission failures

The push-sum algorithm allows distributed computing of the average on a directed graph, and is particularly relevant when one is restricted to one-way and/or asynchronous communications. We investigate its behavior in the presence of unreliable communication channels where messages can be lost. We show that exponential convergence still holds and deduce fundamental properties that implicitly describe the distribution of the final value obtained. We analyze the error of the final common value we get for the essential case of two nodes, both theoretically and numerically. We provide performance comparison with a standard consensus algorithm

Trajectory convergence from coordinate-wise decrease of quadratic energy functions, and applications to platoons

We consider trajectories where the sign of the derivative of each entry is opposite to that of the corresponding entry in the gradient of an energy function. We show that this condition guarantees convergence when the energy function is quadratic and positive definite and partly extend that result to some classes of positive semi-definite quadratic functions including those defined using a graph Laplacian. We show how this condition allows establishing the convergence of a platoon application in which it naturally appears, due to deadzones in the control laws designed to avoid instabilities caused by inconsistent measurements of the same distance by different agent

A complexity analysis of Policy Iteration through combinatorial matrices arising from Unique Sink Orientations

Unique Sink Orientations (USOs) are an appealing abstraction of several major optimization problems of applied mathematics such as Linear Programming (LP), Markov Decision Processes (MDPs) or 2-player Turn Based Stochastic Games (2TBSGs). A polynomial time algorithm to find the sink of a USO would translate into a strongly polynomial time algorithm to solve the aforementioned problems—a major quest for all three cases. In the case of an acyclic USO of a cube, a situation that captures both MDPs and 2TBSGs, one can apply the well-known Policy Iteration (PI) algorithm. The study of its complexity is the object of this work. Despite its exponential worst case complexity, the principle of PI is a powerful source of inspiration for other methods. In 2012, Hansen and Zwick introduced a new combinatorial relaxation of the complexity problem for PI resulting in what we call Order-Regular (OR) matrices. They conjectured that the maximum number of rows of such matrices—an upper bound on the number of steps of PI—should follow the Fibonacci sequence. As our first contribution, we disprove the lower bound part of Hansen and Zwick's conjecture. Then, for our second contribution, we (exponentially) improve the Ω(1.4142n) lower bound on the number of steps of PI from Schurr and Szabó in the case of OR matrices and obtain an Ω(1.4269n) bound

Improved bound on the worst case complexity of Policy Iteration

Solving Markov Decision Processes is a recurrent task in engineering which can be performed efficiently in practice using the Policy Iteration algorithm. Regarding its complexity, both lower and upper bounds are known to be exponential (but far apart) in the size of the problem. In this work, we provide the first improvement over the now standard upper bound from Mansour and Singh (1999). We also show that this bound is tight for a natural relaxation of the problem