41,174 research outputs found
Positive decomposition of transfer functions with multiple poles
We present new results on decomposing the transfer function t(z) of a linear, asymptotically stable, discrete-time SISO system as a difference t(z) = t(1)(z) - t(2)(z) of two positive linear systems. We extend the results of [4] to a class of transfer functions t(z) with multiple poles. One of the appearing positive systems is always 1-dimensional, while the other has dimension corresponding to the location and order of the poles of t(z). Recently, in [11], a universal approach was found, providing a decomposition for any asymptotically stable t(z). Our approach here gives lower dimensions than [11] in certain cases but, unfortunately, at present it can only be applied to a relatively small class of transfer functions, and it does not yield a general algorithm
Algorithm for positive realization of transfer functions
The aim of this brief is to present a finite-step algorithm for the positive realization of a rational
transfer function H(z). In comparision with previously described algorithms we emphasize that we do
not make an a priori assumption on (but, instead, include a finite step procedure for checking) the non-
negativity of the impulse response sequence of H(z). For primitive transfer functions a new method for
reducing the pole order of the dominant pole is also proposed
Neighborly inscribed polytopes and Delaunay triangulations
We construct a large family of neighborly polytopes that can be realized with
all the vertices on the boundary of any smooth strictly convex body. In
particular, we show that there are superexponentially many combinatorially
distinct neighborly polytopes that admit realizations inscribed on the sphere.
These are the first examples of inscribable neighborly polytopes that are not
cyclic polytopes, and provide the current best lower bound for the number of
combinatorial types of inscribable polytopes (which coincides with the current
best lower bound for the number of combinatorial types of polytopes). Via
stereographic projections, this translates into a superexponential lower bound
for the number of combinatorial types of (neighborly) Delaunay triangulations.Comment: 15 pages, 2 figures. We extended our results to arbitrary smooth
strictly convex bodie
Non-asymptotic confidence bounds for the optimal value of a stochastic program
We discuss a general approach to building non-asymptotic confidence bounds
for stochastic optimization problems. Our principal contribution is the
observation that a Sample Average Approximation of a problem supplies upper and
lower bounds for the optimal value of the problem which are essentially better
than the quality of the corresponding optimal solutions. At the same time, such
bounds are more reliable than "standard" confidence bounds obtained through the
asymptotic approach. We also discuss bounding the optimal value of MinMax
Stochastic Optimization and stochastically constrained problems. We conclude
with a simulation study illustrating the numerical behavior of the proposed
bounds
Diversity in the Tail of the Intersecting Brane Landscape
Techniques are developed for exploring the complete space of intersecting
brane models on an orientifold. The classification of all solutions for the
widely-studied T^6/Z_2 x Z_2 orientifold is made possible by computing all
combinations of branes with negative tadpole contributions. This provides the
necessary information to systematically and efficiently identify all models in
this class with specific characteristics. In particular, all ways in which a
desired group G can be realized by a system of intersecting branes can be
enumerated in polynomial time. We identify all distinct brane realizations of
the gauge groups SU(3) x SU(2) and SU(3) x SU(2) x U(1) which can be embedded
in any model which is compatible with the tadpole and SUSY constraints. We
compute the distribution of the number of generations of "quarks" and find that
3 is neither suppressed nor particularly enhanced compared to other odd
generation numbers. The overall distribution of models is found to have a long
tail. Despite disproportionate suppression of models in the tail by K-theory
constraints, the tail in the distribution contains much of the diversity of
low-energy physics structure.Comment: 48 pages, 8 figure
Synchronization of networks with prescribed degree distributions
We show that the degree distributions of graphs do not suffice to
characterize the synchronization of systems evolving on them. We prove that,
for any given degree sequence satisfying certain conditions, there exists a
connected graph having that degree sequence for which the first nontrivial
eigenvalue of the graph Laplacian is arbitrarily close to zero. Consequently,
complex dynamical systems defined on such graphs have poor synchronization
properties. The result holds under quite mild assumptions, and shows that there
exists classes of random, scale-free, regular, small-world, and other common
network architectures which impede synchronization. The proof is based on a
construction that also serves as an algorithm for building non-synchronizing
networks having a prescribed degree distribution.Comment: v2: A new theorem and a numerical example added. To appear in IEEE
Trans. Circuits and Systems I: Fundamental Theory and Application
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