9,065 research outputs found
Detecting Robust Patterns in the Spread of Epidemics: A Case Study of Influenza in the United States and France
In this paper, the authors develop a method of detecting correlations between
epidemic patterns in different regions that are due to human movement and
introduce a null model in which the travel-induced correlations are cancelled.
They apply this method to the well-documented cases of seasonal influenza
outbreaks in the United States and France. In the United States (using data for
1972-2002), the authors observed strong short-range correlations between
several states and their immediate neighbors, as well as robust long-range
spreading patterns resulting from large domestic air-traffic flows. The
stability of these results over time allowed the authors to draw conclusions
about the possible impact of travel restrictions on epidemic spread. The
authors also applied this method to the case of France (1984-2004) and found
that on the regional scale, there was no transportation mode that clearly
dominated disease spread. The simplicity and robustness of this method suggest
that it could be a useful tool for detecting transmission channels in the
spread of epidemics.Comment: 8 pages, 7 figures, 3 table
Formal proof for delayed finite field arithmetic using floating point operators
Formal proof checkers such as Coq are capable of validating proofs of
correction of algorithms for finite field arithmetics but they require
extensive training from potential users. The delayed solution of a triangular
system over a finite field mixes operations on integers and operations on
floating point numbers. We focus in this report on verifying proof obligations
that state that no round off error occurred on any of the floating point
operations. We use a tool named Gappa that can be learned in a matter of
minutes to generate proofs related to floating point arithmetic and hide
technicalities of formal proof checkers. We found that three facilities are
missing from existing tools. The first one is the ability to use in Gappa new
lemmas that cannot be easily expressed as rewriting rules. We coined the second
one ``variable interchange'' as it would be required to validate loop
interchanges. The third facility handles massive loop unrolling and argument
instantiation by generating traces of execution for a large number of cases. We
hope that these facilities may sometime in the future be integrated into
mainstream code validation.Comment: 8th Conference on Real Numbers and Computers, Saint Jacques de
Compostelle : Espagne (2008
A General Framework for the Derivation of Regular Expressions
The aim of this paper is to design a theoretical framework that allows us to
perform the computation of regular expression derivatives through a space of
generic structures. Thanks to this formalism, the main properties of regular
expression derivation, such as the finiteness of the set of derivatives, need
only be stated and proved one time, at the top level. Moreover, it is shown how
to construct an alternating automaton associated with the derivation of a
regular expression in this general framework. Finally, Brzozowski's derivation
and Antimirov's derivation turn out to be a particular case of this general
scheme and it is shown how to construct a DFA, a NFA and an AFA for both of
these derivations.Comment: 22 page
Graphical Models for Optimal Power Flow
Optimal power flow (OPF) is the central optimization problem in electric
power grids. Although solved routinely in the course of power grid operations,
it is known to be strongly NP-hard in general, and weakly NP-hard over tree
networks. In this paper, we formulate the optimal power flow problem over tree
networks as an inference problem over a tree-structured graphical model where
the nodal variables are low-dimensional vectors. We adapt the standard dynamic
programming algorithm for inference over a tree-structured graphical model to
the OPF problem. Combining this with an interval discretization of the nodal
variables, we develop an approximation algorithm for the OPF problem. Further,
we use techniques from constraint programming (CP) to perform interval
computations and adaptive bound propagation to obtain practically efficient
algorithms. Compared to previous algorithms that solve OPF with optimality
guarantees using convex relaxations, our approach is able to work for arbitrary
distribution networks and handle mixed-integer optimization problems. Further,
it can be implemented in a distributed message-passing fashion that is scalable
and is suitable for "smart grid" applications like control of distributed
energy resources. We evaluate our technique numerically on several benchmark
networks and show that practical OPF problems can be solved effectively using
this approach.Comment: To appear in Proceedings of the 22nd International Conference on
Principles and Practice of Constraint Programming (CP 2016
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