1,960 research outputs found
Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue
This paper contains an asymptotic analysis of a fluid model for a heavily
loaded processor sharing queue. Specifically, we consider the behavior of
solutions of critical fluid models as time approaches \infty. The main theorems
of the paper provide sufficient conditions for a fluid model solution to
converge to an invariant state and, under slightly more restrictive
assumptions, provide a rate of convergence. These results are used in a related
work by Gromoll for establishing a heavy traffic diffusion approximation for a
processor sharing queue
Constraints on Area Variables in Regge Calculus
We describe a general method of obtaining the constraints between area
variables in one approach to area Regge calculus, and illustrate it with a
simple example. The simplicial complex is the simplest tessellation of the
4-sphere. The number of independent constraints on the variations of the
triangle areas is shown to equal the difference between the numbers of
triangles and edges, and a general method of choosing independent constraints
is described. The constraints chosen by using our method are shown to imply the
Regge equations of motion in our example.Comment: Typographical errors correcte
HJB equations for certain singularly controlled diffusions
Given a closed, bounded convex set with
nonempty interior, we consider a control problem in which the state process
and the control process satisfy where is a
standard, multi-dimensional Brownian motion, , is a fixed matrix, and . The
process is locally of bounded variation and has increments in a given
closed convex cone . Given , , and , consider the
objective that is to minimize the cost
over the
admissible controls . Both and () may
take positive and negative values. This paper studies the corresponding dynamic
programming equation (DPE), a second-order degenerate elliptic partial
differential equation of HJB-type with a state constraint boundary condition.
Under the controllability condition and the
finiteness of , , where ,
we show that the cost, that involves an improper integral, is well defined. We
establish the following: (i) the value function for the control problem
satisfies the DPE (in the viscosity sense), and (ii) the condition
is necessary and sufficient for
uniqueness of solutions to the DPE. The existence and uniqueness of solutions
are shown to be connected to an intuitive ``no arbitrage'' condition. Our
results apply to Brownian control problems that represent formal diffusion
approximations to control problems associated with stochastic processing
networks.Comment: Published in at http://dx.doi.org/10.1214/07-AAP443 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Anisotropic simplicial minisuperspace model
The computation of the simplicial minisuperspace wavefunction in the case of
anisotropic universes with a scalar matter field predicts the existence of a
large classical Lorentzian universe like our own at late timesComment: 19 pages, Latex, 6 figure
Simplicial minisuperspace models in the presence of a massive scalar field with arbitrary scalar coupling
We extend previous simplicial minisuperspace models to account for arbitrary
scalar coupling \eta R\phi^2.Comment: 24 pages and 9 figures. Accepted for publication by Classical and
Quantum Gravit
Lens Spaces and Handlebodies in 3D Quantum Gravity
We calculate partition functions for lens spaces L_{p,q} up to p=8 and for
genus 1 and 2 handlebodies H_1, H_2 in the Turaev-Viro framework. These can be
interpreted as transition amplitudes in 3D quantum gravity. In the case of lens
spaces L_{p,q} these are vacuum-to-vacuum amplitudes \O -> \O, whereas for
the 1- and 2-handlebodies H_1, H_2 they represent genuinely topological
transition amplitudes \O -> T^2 and \O -> T^2 # T^2, respectively.Comment: 14 pages, LaTeX, 5 figures, uses eps
Fluid limits for networks with bandwidth sharing and general document size distributions
We consider a stochastic model of Internet congestion control, introduced by
Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that
represents the randomly varying number of flows in a network where bandwidth is
shared among document transfers. In contrast to an earlier work by Kelly and
Williams [Ann. Appl. Probab. 14 (2004) 1055--1083], the present paper allows
interarrival times and document sizes to be generally distributed, rather than
exponentially distributed. Furthermore, we allow a fairly general class of
bandwidth sharing policies that includes the weighted -fair policies of
Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567], as well
as certain other utility based scheduling policies. To describe the evolution
of the system, measure valued processes are used to keep track of the residual
document sizes of all flows through the network. We propose a fluid model (or
formal functional law of large numbers approximation) associated with the
stochastic flow level model. Under mild conditions, we show that the
appropriately rescaled measure valued processes corresponding to a sequence of
such models (with fixed network structure) are tight, and that any weak limit
point of the sequence is almost surely a fluid model solution. For the special
case of weighted -fair policies, we also characterize the invariant
states of the fluid model.Comment: Published in at http://dx.doi.org/10.1214/08-AAP541 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Mutant glycyl-tRNA synthetase (Gars) ameliorates SOD1G93A motor neuron degeneration phenotype but has little affect on Loa dynein heavy chain mutant mice
Background:
In humans, mutations in the enzyme glycyl-tRNA synthetase (GARS) cause motor and sensory axon loss in the peripheral nervous system, and clinical phenotypes ranging from Charcot-Marie-Tooth neuropathy to a severe infantile form of spinal muscular atrophy. GARS is ubiquitously expressed and may have functions in addition to its canonical role in protein synthesis through catalyzing the addition of glycine to cognate tRNAs.
Methodology/Principal findings:
We have recently described a new mouse model with a point mutation in the Gars gene resulting in a cysteine to arginine change at residue 201. Heterozygous Gars^{C201R/+} mice have locomotor and sensory deficits. In an investigation of genetic mutations that lead to death of motor and sensory neurons, we have crossed the Gars^{C201R/+} mice to two other mutants: the TgSOD1^{G93A} model of human amyotrophic lateral sclerosis and the Legs at odd angles mouse (Dync1h1^{Loa}) which has a defect in the heavy chain of the dynein complex. We found the Dync1h1^{Loa/+}; Gars^{C201R/+} double heterozygous mice are more impaired than either parent, and this is may be an additive effect of both mutations. Surprisingly, the Gars^{C201R} mutation significantly delayed disease onset in the SOD1^{G93A}; Gars^{C201R/+} double heterozygous mutant mice and increased lifespan by 29% on the genetic background investigated.
Conclusions/Significance:
These findings raise intriguing possibilities for the study of pathogenetic mechanisms in all three mouse mutant strains
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