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Consider measuring a vector x ∈ R n through the inner product with several measurement vectors, a1, a2,. .. , am. It is common in both signal processing and statistics to assume the linear response model yi = ai, x + εi, where εi is a noise term. However, in practice the precise relationship between the signal x and the observations yi may not follow the(More)
INTRODUCTION Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics and quantum field theory. In this letter Dedekind made the following observation: take the(More)
We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools; mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the(More)
We consider large-scale service systems with multiple customer classes and multiple server pools; interarrival and service times are exponentially distributed, and mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing choices) form a tree (in the graph with vertices being both customer(More)
Electric vehicles represent a promising technology for reducing emissions and dependence on fossil fuels and have started entering different automotive markets. In order to bolster their adoption by consumers and hence enhance their penetration rate, a charging station infrastructure needs to be deployed. This paper studies decentralized policies that(More)
We formulate an analytically tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand, and order cancellation is not a prominent feature. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are(More)
We formulate a simplified model of a limit order book, in which the arrival process is independent of the current state. We prove a phase transition result: there exist prices κ b and κa such that, for any > 0, only finitely many bid (ask) departures occur at prices below κ b − (above κa +), while the interval (κ b + , κa −) infinitely often contains no(More)
— We consider large-scale service systems with several customer classes and several server pools. Mean service time of a customer depends both on the customer class and the server type. The routing is restricted to a fixed set of " activities, " i.e. (customer-class, server-type) pairs. We assume that the bipartite graph with vertices being customer-classes(More)