3,105 research outputs found
Writing for Reading
For some time concern about the writing ability of students has matched the attention given to their reading development. Teachers of all subjects are urged to require their students to write more, and suggestions for helping students improve their writing abound. At the same time we see additional justification for stressing writing; improvement in writing might well lead to improvement in reading
A Simply Exponential Upper Bound on the Maximum Number of Stable Matchings
Stable matching is a classical combinatorial problem that has been the
subject of intense theoretical and empirical study since its introduction in
1962 in a seminal paper by Gale and Shapley. In this paper, we provide a new
upper bound on , the maximum number of stable matchings that a stable
matching instance with men and women can have. It has been a
long-standing open problem to understand the asymptotic behavior of as
, first posed by Donald Knuth in the 1970s. Until now the best
lower bound was approximately , and the best upper bound was . In this paper, we show that for all , for some
universal constant . This matches the lower bound up to the base of the
exponent. Our proof is based on a reduction to counting the number of downsets
of a family of posets that we call "mixing". The latter might be of independent
interest
Approaching Utopia: Strong Truthfulness and Externality-Resistant Mechanisms
We introduce and study strongly truthful mechanisms and their applications.
We use strongly truthful mechanisms as a tool for implementation in undominated
strategies for several problems,including the design of externality resistant
auctions and a variant of multi-dimensional scheduling
Automated design of minimum drag light aircraft fuselages and nacelles
The constrained minimization algorithm of Vanderplaats is applied to the problem of designing minimum drag faired bodies such as fuselages and nacelles. Body drag is computed by a variation of the Hess-Smith code. This variation includes a boundary layer computation. The encased payload provides arbitrary geometric constraints, specified a priori by the designer, below which the fairing cannot shrink. The optimization may include engine cooling air flows entering and exhausting through specific port locations on the body
Stability of Service under Time-of-Use Pricing
We consider "time-of-use" pricing as a technique for matching supply and
demand of temporal resources with the goal of maximizing social welfare.
Relevant examples include energy, computing resources on a cloud computing
platform, and charging stations for electric vehicles, among many others. A
client/job in this setting has a window of time during which he needs service,
and a particular value for obtaining it. We assume a stochastic model for
demand, where each job materializes with some probability via an independent
Bernoulli trial. Given a per-time-unit pricing of resources, any realized job
will first try to get served by the cheapest available resource in its window
and, failing that, will try to find service at the next cheapest available
resource, and so on. Thus, the natural stochastic fluctuations in demand have
the potential to lead to cascading overload events. Our main result shows that
setting prices so as to optimally handle the {\em expected} demand works well:
with high probability, when the actual demand is instantiated, the system is
stable and the expected value of the jobs served is very close to that of the
optimal offline algorithm.Comment: To appear in STOC'1
Early appraisal of the fixation probability in directed networks
In evolutionary dynamics, the probability that a mutation spreads through the
whole population, having arisen in a single individual, is known as the
fixation probability. In general, it is not possible to find the fixation
probability analytically given the mutant's fitness and the topological
constraints that govern the spread of the mutation, so one resorts to
simulations instead. Depending on the topology in use, a great number of
evolutionary steps may be needed in each of the simulation events, particularly
in those that end with the population containing mutants only. We introduce two
techniques to accelerate the determination of the fixation probability. The
first one skips all evolutionary steps in which the number of mutants does not
change and thereby reduces the number of steps per simulation event
considerably. This technique is computationally advantageous for some of the
so-called layered networks. The second technique, which is not restricted to
layered networks, consists of aborting any simulation event in which the number
of mutants has grown beyond a certain threshold value, and counting that event
as having led to a total spread of the mutation. For large populations, and
regardless of the network's topology, we demonstrate, both analytically and by
means of simulations, that using a threshold of about 100 mutants leads to an
estimate of the fixation probability that deviates in no significant way from
that obtained from the full-fledged simulations. We have observed speedups of
two orders of magnitude for layered networks with 10000 nodes
A Solvable Sequence Evolution Model and Genomic Correlations
We study a minimal model for genome evolution whose elementary processes are
single site mutation, duplication and deletion of sequence regions and
insertion of random segments. These processes are found to generate long-range
correlations in the composition of letters as long as the sequence length is
growing, i.e., the combined rates of duplications and insertions are higher
than the deletion rate. For constant sequence length, on the other hand, all
initial correlations decay exponentially. These results are obtained
analytically and by simulations. They are compared with the long-range
correlations observed in genomic DNA, and the implications for genome evolution
are discussed.Comment: 4 pages, 4 figure
Exit times in non-Markovian drifting continuous-time random walk processes
By appealing to renewal theory we determine the equations that the mean exit
time of a continuous-time random walk with drift satisfies both when the
present coincides with a jump instant or when it does not. Particular attention
is paid to the corrections ensuing from the non-Markovian nature of the
process. We show that when drift and jumps have the same sign the relevant
integral equations can be solved in closed form. The case when holding times
have the classical Erlang distribution is considered in detail.Comment: 9 pages, 3 color plots, two-column revtex 4; new Appendix and
references adde
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