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In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of <i>N</i> independent, identically distributed measurements of an <i>M</i> dimensional random vector the maximum likelihood estimate is the sample covariance matrix. Here we consider(More)
—This work explains how to analyze the aggregate electricity consumption of many consumers, and extract key components such as heating, ventilation and air conditioning (HVAC), residential lighting, and street lighting consumption from the total consumption. To avoid explicit modeling of dependencies on time of day and on working versus non-working days,(More)
—This work presents a two-stage model for the data analysis of electricity consumption. The first stage divides the consumption in two parts: weather-and illumination-related, and residual consumption, where weather-related consumption refers to heating, ventilation, and air conditioning (HVAC). Given the hourly total consumption, we obtain the hourly(More)
This paper centers on the limit eigenvalue distribution for random Vandermonde matrices with unit magnitude complex entries. The phases of the entries are chosen independently and identically distributed from the interval [-&#x03C0;,&#x03C0;] . Various types of distribution for the phase are considered and we establish the existence of the empirical(More)
In this work we study the asymptotic traffic behaviour for Gromov's hyperbolic networks as the size of the network increases. We prove that under certain mild hypothesis the traffic in a large hyperbolic network tends to pass through a finite set of highly congested nodes. These nodes will be called the " core " of the network. We provide a formal(More)
In this work we study the asymptotic traffic behaviour in Gromov's hyperbolic spaces when the traffic decays exponentially with the distance. We prove that under general conditions, there exist a phase transition between local and global traffic. More specifically, assume that the traffic rate between two nodes u and v is given by R(u, v) = β −d(u,v) where(More)
We study how the electric vehicles (EVs) of today would perform in meeting the driving needs of vehicle owners, and propose an optimization model to find locations for charging stations needed to support EV usage. We take publicly available data from travel surveys that are person oriented and construct vehicle centric datasets. Chicago and Seattle(More)
In this work we study the asymptotic traffic flow in Gromov hyperbolic graphs when the traffic decays exponentially with the distance. We prove that under general conditions, there exists a phase transition between local and global traffic. More specifically, assume that the traffic rate between two nodes u and v is given by R(u, v) = &#x03B2;<sup>-d(u,(More)
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