8,567 research outputs found
Branching processes, the max-plus algebra and network calculus
Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory
Dynamical instability of a spin spiral in an interacting Fermi gas as a probe of the Stoner transition
We propose an experiment to probe ferromagnetic phenomena in an ultracold
Fermi gas, while alleviating the sensitivity to three-body loss and competing
many-body instabilities. The system is initialized in a small pitch spin
spiral, which becomes unstable in the presence of repulsive interactions. To
linear order the exponentially growing collective modes exhibit critical
slowing down close to the Stoner transition point. Also, to this order, the
dynamics are identical on the paramagnetic and ferromagnetic sides of the
transition. However, we show that scattering off the exponentially growing
modes qualitatively alters the collective mode structure. The critical slowing
down is eliminated and in its place a new unstable branch develops at large
wave vectors. Furthermore, long-wavelength instabilities are quenched on the
paramagnetic side of the transition. We study the experimental observation of
the instabilities, specifically addressing the trapping geometry and how
phase-contrast imaging will reveal the emerging domain structure. These probes
of the dynamical phenomena could allow experiments to detect the transition
point and distinguish between the paramagnetic and ferromagnetic regimes
From an insulating to a superfluid pair-bond liquid
We study an exchange coupled system of itinerant electrons and localized
fermion pairs resulting in a resonant pairing formation. This system inherently
contains resonating fermion pairs on bonds which lead to a superconducting
phase provided that long range phase coherence between their constituents can
be established. The prerequisite is that the resonating fermion pairs can
become itinerant. This is rendered possible through the emergence of two kinds
of bond-fermions: individual and composite fermions made of one individual
electron attached to a bound pair on a bond. If the strength of the exchange
coupling exceeds a certain value, the superconducting ground state undergoes a
quantum phase transition into an insulating pair-bond liquid state. The gap of
the superfluid phase thereby goes over continuously into a charge gap of the
insulator. The change-over from the superconducting to the insulating phase is
accompanied by a corresponding qualitative modification of the dispersion of
the two kinds of fermionic excitations. Using a bond operator formalism, we
derive the phase diagram of such a scenario together with the elementary
excitations characterizing the various phases as a function of the exchange
coupling and the temperature.Comment: 10 pages, 5 figure
Constrained Cost-Coupled Stochastic Games with Independent State Processes
We consider a non-cooperative constrained stochastic games with N players
with the following special structure. With each player there is an associated
controlled Markov chain. The transition probabilities of the i-th Markov chain
depend only on the state and actions of controller i. The information structure
that we consider is such that each player knows the state of its own MDP and
its own actions. It does not know the states of, and the actions taken by other
players. Finally, each player wishes to minimize a time-average cost function,
and has constraints over other time-avrage cost functions. Both the cost that
is minimized as well as those defining the constraints depend on the state and
actions of all players. We study in this paper the existence of a Nash
equilirium. Examples in power control in wireless communications are given.Comment: 7 pages, submitted in september 2006 to Operations Research Letter
Brownian Dynamics of a Sphere Between Parallel Walls
We describe direct imaging measurements of a colloidal sphere's diffusion
between two parallel surfaces. The dynamics of this deceptively simple
hydrodynamically coupled system have proved difficult to analyze. Comparison
with approximate formulations of a confined sphere's hydrodynamic mobility
reveals good agreement with both a leading-order superposition approximation as
well as a more general all-images stokeslet analysis.Comment: 4 pages, 3 figures, REVTeX with PostScript figure
Backpropagation training in adaptive quantum networks
We introduce a robust, error-tolerant adaptive training algorithm for
generalized learning paradigms in high-dimensional superposed quantum networks,
or \emph{adaptive quantum networks}. The formalized procedure applies standard
backpropagation training across a coherent ensemble of discrete topological
configurations of individual neural networks, each of which is formally merged
into appropriate linear superposition within a predefined, decoherence-free
subspace. Quantum parallelism facilitates simultaneous training and revision of
the system within this coherent state space, resulting in accelerated
convergence to a stable network attractor under consequent iteration of the
implemented backpropagation algorithm. Parallel evolution of linear superposed
networks incorporating backpropagation training provides quantitative,
numerical indications for optimization of both single-neuron activation
functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan
Analysis of two competing TCP/IP connections
Many mathematical models exist for describing the behavior of TCP/IP under an exogenous loss process that does not depend on the window size. The goal of this paper is to present a mathematical analysis of two asymmetric competing TCP connections where loss probabilities are directly related to their instantaneous window size, and occur when the sum of throughputs attains a given level. We obtain bounds for the stationary throughput of each connection, as well as an exact expression for symmetric connections. This allows us to further study the fairness as a function of the different round trip times. We avoid the simplifying artificial synchronization assumption that has frequently been used in the past to study similar problems, according to which whenever one connection looses a packet, the other one looses a packet as well
State-dependent M/G/1 type queueing analysis for congestion control in data networks
We study a TCP-like linear-increase multiplicative-decrease flow control mechanism. We consider congestion signals that arrive in batches according to a Poisson process. We focus on the case when the transmission rate cannot exceed a certain maximum value. The distribution of the transmission rate in steady state as well as its moments are determined. Our model is particularly useful to study the behavior of TCP, the congestion control mechanism in the Internet. Burstiness of packet losses is captured by allowing congestion signals to arrive in batches. By a simple transformation, the problem can be reformulated in terms of an equivalent M/G/1 queue, where the transmission rate in the original model corresponds to the workload in the `dual' queue. The service times in the queueing model are not i.i.d., and they depend on the workload in the system
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