18,656 research outputs found
Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks
In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the 'optimal' state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the 'optimal' state-dependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies
Responding to Morally Flawed Historical Philosophers and Philosophies
Many historically-influential philosophers had profoundly wrong moral views or behaved very badly. Aristotle thought women were “deformed men” and that some people were slaves “by nature.” Descartes had disturbing views about non-human animals. Hume and Kant were racists. Hegel disparaged Africans. Nietzsche despised sick people. Mill condoned colonialism. Fanon was homophobic. Frege was anti-Semitic; Heidegger was a Nazi. Schopenhauer was sexist. Rousseau abandoned his children. Wittgenstein beat his young students. Unfortunately, these examples are just a start.
These philosophers are famous for their intellectual accomplishments, yet they display serious moral or intellectual flaws in their beliefs or actions. At least, some of their views were false, ultimately unjustified and, perhaps, harmful.
How should we respond to brilliant-but-flawed philosophers from the past? Here we explore the issues, asking questions and offering few answers. Any insights gained here might be applicable to contemporary imperfect philosophers, scholars in other fields, and people in general
Tail asymptotics for the maximum of perturbed random walk
Consider a random walk that is ``perturbed'' by a
stationary sequence to produce the process
. This paper is concerned with computing the distribution
of the all-time maximum of perturbed
random walk with a negative drift. Such a maximum arises in several different
applications settings, including production systems, communications networks
and insurance risk. Our main results describe asymptotics for
as . The tail asymptotics depend greatly
on whether the 's are light-tailed or heavy-tailed. In the light-tailed
setting, the tail asymptotic is closely related to the Cram\'{e}r--Lundberg
asymptotic for standard random walk.Comment: Published at http://dx.doi.org/10.1214/105051606000000268 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Core congestion is inherent in hyperbolic networks
We investigate the impact the negative curvature has on the traffic
congestion in large-scale networks. We prove that every Gromov hyperbolic
network admits a core, thus answering in the positive a conjecture by
Jonckheere, Lou, Bonahon, and Baryshnikov, Internet Mathematics, 7 (2011) which
is based on the experimental observation by Narayan and Saniee, Physical Review
E, 84 (2011) that real-world networks with small hyperbolicity have a core
congestion. Namely, we prove that for every subset of vertices of a
-hyperbolic graph there exists a vertex of such that the
disk of radius centered at intercepts at least
one half of the total flow between all pairs of vertices of , where the flow
between two vertices is carried by geodesic (or quasi-geodesic)
-paths. A set intercepts the flow between two nodes and if
intersect every shortest path between and . Differently from what
was conjectured by Jonckheere et al., we show that is not (and cannot be)
the center of mass of but is a node close to the median of in the
so-called injective hull of . In case of non-uniform traffic between nodes
of (in this case, the unit flow exists only between certain pairs of nodes
of defined by a commodity graph ), we prove a primal-dual result showing
that for any the size of a -multi-core (i.e., the number
of disks of radius ) intercepting all pairs of is upper bounded by
the maximum number of pairwise -apart pairs of
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