862 research outputs found
Heavy Tails, Importance Sampling and Cross-Entropy
We consider the problem of estimating P (Y1+ ... +Yn > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a tool for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y1+ ... +Yn > x,) n-1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some parametric examples (Pareto and Weibull) how this leads to precise answers, which as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/1 and GI/G/1 queues are also discussed
Low latency via redundancy
Low latency is critical for interactive networked applications. But while we
know how to scale systems to increase capacity, reducing latency --- especially
the tail of the latency distribution --- can be much more difficult. In this
paper, we argue that the use of redundancy is an effective way to convert extra
capacity into reduced latency. By initiating redundant operations across
diverse resources and using the first result which completes, redundancy
improves a system's latency even under exceptional conditions. We study the
tradeoff with added system utilization, characterizing the situations in which
replicating all tasks reduces mean latency. We then demonstrate empirically
that replicating all operations can result in significant mean and tail latency
reduction in real-world systems including DNS queries, database servers, and
packet forwarding within networks
On the infimum attained by a reflected L\'evy process
This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected
at 0), and focuses on the distribution of , that is, the minimal value
attained in an interval of length (where it is assumed that the queue is in
stationarity at the beginning of the interval). The first contribution is an
explicit characterization of this distribution, in terms of Laplace transforms,
for spectrally one-sided L\'evy processes (i.e., either only positive jumps or
only negative jumps). The second contribution concerns the asymptotics of
\prob{M(T_u)> u} (for different classes of functions and large);
here we have to distinguish between heavy-tailed and light-tailed scenarios
Self-Organized Branching Processes: A Mean-Field Theory for Avalanches
We discuss mean-field theories for self-organized criticality and the
connection with the general theory of branching processes. We point out that
the nature of the self-organization is not addressed properly by the previously
proposed mean-field theories. We introduce a new mean-field model that
explicitly takes the boundary conditions into account; in this way, the local
dynamical rules are coupled to a global equation that drives the control
parameter to its critical value. We study the model numerically, and
analytically we compute the avalanche distributions.Comment: 4 pages + 4 ps figure
Therapy with recombinant human antithrombin, heparin and tissue plasminogen activator improves survival and reduces ventilation days in a long-term ovine model of cutaneous burn and smoke inhalation injury
Single-crossover dynamics: finite versus infinite populations
Populations evolving under the joint influence of recombination and
resampling (traditionally known as genetic drift) are investigated. First, we
summarise and adapt a deterministic approach, as valid for infinite
populations, which assumes continuous time and single crossover events. The
corresponding nonlinear system of differential equations permits a closed
solution, both in terms of the type frequencies and via linkage disequilibria
of all orders. To include stochastic effects, we then consider the
corresponding finite-population model, the Moran model with single crossovers,
and examine it both analytically and by means of simulations. Particular
emphasis is on the connection with the deterministic solution. If there is only
recombination and every pair of recombined offspring replaces their pair of
parents (i.e., there is no resampling), then the {\em expected} type
frequencies in the finite population, of arbitrary size, equal the type
frequencies in the infinite population. If resampling is included, the
stochastic process converges, in the infinite-population limit, to the
deterministic dynamics, which turns out to be a good approximation already for
populations of moderate size.Comment: 21 pages, 4 figure
A mathematical model for fibro-proliferative wound healing disorders
The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable.
In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsenet al., J. theor. Biol. 177, 113–128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay.
Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states—a central property of the model, which is evident from stability and bifurcation analyses.
The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders
Systemic Risk and Default Clustering for Large Financial Systems
As it is known in the finance risk and macroeconomics literature,
risk-sharing in large portfolios may increase the probability of creation of
default clusters and of systemic risk. We review recent developments on
mathematical and computational tools for the quantification of such phenomena.
Limiting analysis such as law of large numbers and central limit theorems allow
to approximate the distribution in large systems and study quantities such as
the loss distribution in large portfolios. Large deviations analysis allow us
to study the tail of the loss distribution and to identify pathways to default
clustering. Sensitivity analysis allows to understand the most likely ways in
which different effects, such as contagion and systematic risks, combine to
lead to large default rates. Such results could give useful insights into how
to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P.
Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer
Proceedings in Mathematics and Statistics, Vol. 110 2015
An approximation approach for the deviation matrix of continuous-time Markov processes with application to Markov decision theory
We present an update formula that allows the expression of the deviation matrix of a continuous-time Markov process with denumerable state space having generator matrix Q* through a continuous-time Markov process with generator matrix Q. We show that under suitable stability conditions the algorithm converges at a geometric rate. By applying the concept to three different examples, namely, the M/M/1 queue with vacations, the M/G/1 queue, and a tandem network, we illustrate the broad applicability of our approach. For a problem in admission control, we apply our approximation algorithm toMarkov decision theory for computing the optimal control policy. Numerical examples are presented to highlight the efficiency of the proposed algorithm. © 2010 INFORMS
Fluid Models of Many-server Queues with Abandonment
We study many-server queues with abandonment in which customers have general
service and patience time distributions. The dynamics of the system are modeled
using measure- valued processes, to keep track of the residual service and
patience times of each customer. Deterministic fluid models are established to
provide first-order approximation for this model. The fluid model solution,
which is proved to uniquely exists, serves as the fluid limit of the
many-server queue, as the number of servers becomes large. Based on the fluid
model solution, first-order approximations for various performance quantities
are proposed
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