37,056 research outputs found
On Approximating the Sum-Rate for Multiple-Unicasts
We study upper bounds on the sum-rate of multiple-unicasts. We approximate
the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts
network coding problem with independent sources. Our approximation
algorithm runs in polynomial time and yields an upper bound on the joint source
entropy rate, which is within an factor from the GNS cut. It
further yields a vector-linear network code that achieves joint source entropy
rate within an factor from the GNS cut, but \emph{not} with
independent sources: the code induces a correlation pattern among the sources.
Our second contribution is establishing a separation result for vector-linear
network codes: for any given field there exist networks for which
the optimum sum-rate supported by vector-linear codes over for
independent sources can be multiplicatively separated by a factor of
, for any constant , from the optimum joint entropy
rate supported by a code that allows correlation between sources. Finally, we
establish a similar separation result for the asymmetric optimum vector-linear
sum-rates achieved over two distinct fields and
for independent sources, revealing that the choice of field
can heavily impact the performance of a linear network code.Comment: 10 pages; Shorter version appeared at ISIT (International Symposium
on Information Theory) 2015; some typos correcte
Thermodynamics of Thermoelectric Phenomena and Applications
Fifty years ago, the optimization of thermoelectric devices was analyzed by considering the relation between optimal performances and local entropy production. Entropy is produced by the irreversible processes in thermoelectric devices. If these processes could be eliminated, entropy production would be reduced to zero, and the limiting Carnot efficiency or coefficient of performance would be obtained. In the present review, we start with some fundamental thermodynamic considerations relevant for thermoelectrics. Based on a historical overview, we reconsider the interrelation between optimal performances and local entropy production by using the compatibility approach together with the thermodynamic arguments. Using the relative current density and the thermoelectric potential, we show that minimum entropy production can be obtained when the thermoelectric potential is a specific, optimal value
“Constructal Theory: From Engineering to Physics, and How Flow Systems Develop Shape and Structure”
Constructal theory and its applications to various fields ranging from engineering to
natural living and inanimate systems, and to social organization and economics, are
reviewed in this paper. The constructal law states that if a system has freedom to morph
it develops in time the flow architecture that provides easier access to the currents that
flow through it. It is shown how constructal theory provides a unifying picture for the
development of flow architectures in systems with internal flows (e.g., mass, heat, electricity,
goods, and people). Early and recent works on constructal theory by various
authors covering the fields of heat and mass transfer in engineered systems, inanimate
flow structures (river basins, global circulations) living structures, social organization,
and economics are reviewed. The relation between the constructal law and the thermodynamic
optimization method of entropy generation minimization is outlined. The constructal
law is a self-standing principle, which is distinct from the Second Law of Thermodynamics.
The place of the constructal law among other fundamental principles, such
as the Second Law, the principle of least action and the principles of symmetry and
invariance is also presented. The review ends with the epistemological and philosophical
implications of the constructal law
Explicit probabilistic models for databases and networks
Recent work in data mining and related areas has highlighted the importance
of the statistical assessment of data mining results. Crucial to this endeavour
is the choice of a non-trivial null model for the data, to which the found
patterns can be contrasted. The most influential null models proposed so far
are defined in terms of invariants of the null distribution. Such null models
can be used by computation intensive randomization approaches in estimating the
statistical significance of data mining results.
Here, we introduce a methodology to construct non-trivial probabilistic
models based on the maximum entropy (MaxEnt) principle. We show how MaxEnt
models allow for the natural incorporation of prior information. Furthermore,
they satisfy a number of desirable properties of previously introduced
randomization approaches. Lastly, they also have the benefit that they can be
represented explicitly. We argue that our approach can be used for a variety of
data types. However, for concreteness, we have chosen to demonstrate it in
particular for databases and networks.Comment: Submitte
Particle algorithms for optimization on binary spaces
We discuss a unified approach to stochastic optimization of pseudo-Boolean
objective functions based on particle methods, including the cross-entropy
method and simulated annealing as special cases. We point out the need for
auxiliary sampling distributions, that is parametric families on binary spaces,
which are able to reproduce complex dependency structures, and illustrate their
usefulness in our numerical experiments. We provide numerical evidence that
particle-driven optimization algorithms based on parametric families yield
superior results on strongly multi-modal optimization problems while local
search heuristics outperform them on easier problems
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