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)
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 analyse the steady-state behaviour of two different models with collaborating queues: that is, models in which " customers " can be served by many types of " servers " , and " servers " can process many types of " customers ". The first example is a large-scale service system, such as a call centre. Collaboration is the result of cross-trained staff… (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)
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… (More)
1 Introduction The field of dynamical systems studies the long-term behavior of a system that evolves under the repeated application of some transformation. For example, consider the solar system: its time evolution is approximated by Newtonian mechanics and laws of gravitation. The modern theory of dynamical systems originated at the end of the 19th… (More)
We generalize the methods of Pierce of counting solutions to the congruence X a ≡ Y b mod D  and the square sieve method of counting squares in the sequence f (X) + g(Y)  to the function field setting.