308 research outputs found
Highly synchronized noise-driven oscillatory behavior of a FitzHugh-Nagumo ring with phase-repulsive coupling
We investigate a ring of FitzHugh--Nagumo elements coupled in
\emph{phase-repulsive} fashion and submitted to a (subthreshold) common
oscillatory signal and independent Gaussian white noises. This system can be
regarded as a reduced version of the one studied in [Phys. Rev. E \textbf{64},
041912 (2001)], although externally forced and submitted to noise. The
noise-sustained synchronization of the system with the external signal is
characterized.Comment: 7 pages, 15 figures, uses aipproc.cls, aip-6s.clo and aipxfm.sty.
"Cooperative Behavior in Neural Systems: Ninth Granada Lectures'', edited by
J. Marro, P. L. Garrido, and J. J. Torre
Algorithms for Colourful Simplicial Depth and Medians in the Plane
The colourful simplicial depth of a point x in the plane relative to a
configuration of n points in k colour classes is exactly the number of closed
simplices (triangles) with vertices from 3 different colour classes that
contain x in their convex hull. We consider the problems of efficiently
computing the colourful simplicial depth of a point x, and of finding a point,
called a median, that maximizes colourful simplicial depth.
For computing the colourful simplicial depth of x, our algorithm runs in time
O(n log(n) + k n) in general, and O(kn) if the points are sorted around x. For
finding the colourful median, we get a time of O(n^4). For comparison, the
running times of the best known algorithm for the monochrome version of these
problems are O(n log(n)) in general, improving to O(n) if the points are sorted
around x for monochrome depth, and O(n^4) for finding a monochrome median.Comment: 17 pages, 8 figure
Central Path Curvature and Iteration-Complexity for Redundant Klee—Minty Cubes
We consider a family of linear optimization problems over the n-dimensional Klee—Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This is achieved by carefully adding an exponential number of redundant constraints that forces the central path to take at least 2n − 2 sharp turns. This fact sug-gests that any feasible path-following interior-point method will take at least O(2n) iterations to solve this problem, whereas in practice typically only a few iterations (e.g., 50) suffices to obtain a high-quality solution. Thus, the construction potentially exhibits the worst-case iteration-complexity known to date which almost matches the theoretical iteration-complexity bound for this type of methods. In addition, this construction gives a counterexample to a conjecture that the total central path curvature is O(n)
Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability
We recently presented a constructive solution to the N-representability
problem of the two-electron reduced density matrix (2-RDM)---a systematic
approach to constructing complete conditions to ensure that the 2-RDM
represents a realistic N-electron quantum system [D. A. Mazziotti, Phys. Rev.
Lett. 108, 263002 (2012)]. In this paper we provide additional details and
derive further N-representability conditions on the 2-RDM that follow from the
constructive solution. The resulting conditions can be classified into a
hierarchy of constraints, known as the (2,q)-positivity conditions where the q
indicates their derivation from the nonnegativity of q-body operators. In
addition to the known T1 and T2 conditions, we derive a new class of
(2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity
conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of
(2,6)-positivity conditions. The constraints obtained can be divided into two
general types: (i) lifting conditions, that is conditions which arise from
lifting lower (2,q)-positivity conditions to higher (2,q+1)-positivity
conditions and (ii) pure conditions, that is conditions which cannot be derived
from a simple lifting of the lower conditions. All of the lifting conditions
and the pure (2,q)-positivity conditions for q>3 require tensor decompositions
of the coefficients in the model Hamiltonians. Subsets of the new
N-representability conditions can be employed with the previously known
conditions to achieve polynomially scaling calculations of ground-state
energies and 2-RDMs of many-electron quantum systems even in the presence of
strong electron correlation
Bounds on Quantum Correlations in Bell Inequality Experiments
Bell inequality violation is one of the most widely known manifestations of
entanglement in quantum mechanics; indicating that experiments on physically
separated quantum mechanical systems cannot be given a local realistic
description. However, despite the importance of Bell inequalities, it is not
known in general how to determine whether a given entangled state will violate
a Bell inequality. This is because one can choose to make many different
measurements on a quantum system to test any given Bell inequality and the
optimization over measurements is a high-dimensional variational problem. In
order to better understand this problem we present algorithms that provide, for
a given quantum state, both a lower bound and an upper bound on the maximal
expectation value of a Bell operator. Both bounds apply techniques from convex
optimization and the methodology for creating upper bounds allows them to be
systematically improved. In many cases these bounds determine measurements that
would demonstrate violation of the Bell inequality or provide a bound that
rules out the possibility of a violation. Examples are given to illustrate how
these algorithms can be used to conclude definitively if some quantum states
violate a given Bell inequality.Comment: 13 pages, 1 table, 2 figures. Updated version as published in PR
Acquired Cold Urticaria: Clinical Features, Particular Phenotypes, and Disease Course in a Tertiary Care Center Cohort
BACKGROUND: Data about special phenotypes, natural course, and prognostic variables of patients with acquired cold urticaria (ACU) are scarce.
OBJECTIVES: We sought to describe the clinical features and disease course of patients with ACU, with special attention paid to particular phenotypes, and to examine possible parameters that could predict the evolution of the disease.
METHODS: This study was a retrospective chart review of 74 patients with ACU who visited a tertiary referral center of urticaria between 2005 and 2015.
RESULTS: Fourteen patients (18.9%) presented with life-threatening reactions after cold exposure, and 21 (28.4%) showed negative results after cold stimulation tests (classified as atypical ACU). Nineteen patients (25.7%) achieved complete symptoms resolution at the end of the surveillance period and had no subsequent recurrences. Higher rates of atypical ACU along with a lower likelihood of achieving complete symptom resolution was observed in patients who had an onset of symptoms during childhood (P < .05). In patients with atypical ACU, shorter disease duration and lower doses of antihistamines required for achieving disease control were detected (P < .05). Age at disease onset, symptom severity, and cold urticaria threshold values were found to be related to disease evolution (P < .05).
LIMITATIONS: This study was limited by its retrospective nature.
CONCLUSIONS: The knowledge of the clinical predictors of the disease evolution along with the clinical features of ACU phenotypes would allow for the establishment of an early and proper therapeutic strategy
An update on the Hirsch conjecture
The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to
George Dantzig. It states that the graph of a d-dimensional polytope with n
facets cannot have diameter greater than n - d.
Despite being one of the most fundamental, basic and old problems in polytope
theory, what we know is quite scarce. Most notably, no polynomial upper bound
is known for the diameters that are conjectured to be linear. In contrast, very
few polytopes are known where the bound is attained. This paper collects
known results and remarks both on the positive and on the negative side of the
conjecture. Some proofs are included, but only those that we hope are
accessible to a general mathematical audience without introducing too many
technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2
and put into the appendix arXiv:0912.423
Metric trees of generalized roundness one
Every finite metric tree has generalized roundness strictly greater than one.
On the other hand, some countable metric trees have generalized roundness
precisely one. The purpose of this paper is to identify some large classes of
countable metric trees that have generalized roundness precisely one.
At the outset we consider spherically symmetric trees endowed with the usual
combinatorial metric (SSTs). Using a simple geometric argument we show how to
determine decent upper bounds on the generalized roundness of finite SSTs that
depend only on the downward degree sequence of the tree in question. By
considering limits it follows that if the downward degree sequence of a SST satisfies , then has generalized roundness one. Included among the
trees that satisfy this condition are all complete -ary trees of depth
(), all -regular trees () and inductive limits
of Cantor trees.
The remainder of the paper deals with two classes of countable metric trees
of generalized roundness one whose members are not, in general, spherically
symmetric. The first such class of trees are merely required to spread out at a
sufficient rate (with a restriction on the number of leaves) and the second
such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table
Universality-class dependence of energy distributions in spin glasses
We study the probability distribution function of the ground-state energies
of the disordered one-dimensional Ising spin chain with power-law interactions
using a combination of parallel tempering Monte Carlo and branch, cut, and
price algorithms. By tuning the exponent of the power-law interactions we are
able to scan several universality classes. Our results suggest that mean-field
models have a non-Gaussian limiting distribution of the ground-state energies,
whereas non-mean-field models have a Gaussian limiting distribution. We compare
the results of the disordered one-dimensional Ising chain to results for a
disordered two-leg ladder, for which large system sizes can be studied, and
find a qualitative agreement between the disordered one-dimensional Ising chain
in the short-range universality class and the disordered two-leg ladder. We
show that the mean and the standard deviation of the ground-state energy
distributions scale with a power of the system size. In the mean-field
universality class the skewness does not follow a power-law behavior and
converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick
model seem to be acceptably well fitted by a modified Gumbel distribution.
Finally, we discuss the distribution of the internal energy of the
Sherrington-Kirkpatrick model at finite temperatures and show that it behaves
similar to the ground-state energy of the system if the temperature is smaller
than the critical temperature.Comment: 15 pages, 20 figures, 1 tabl
Lassoing and corraling rooted phylogenetic trees
The construction of a dendogram on a set of individuals is a key component of
a genomewide association study. However even with modern sequencing
technologies the distances on the individuals required for the construction of
such a structure may not always be reliable making it tempting to exclude them
from an analysis. This, in turn, results in an input set for dendogram
construction that consists of only partial distance information which raises
the following fundamental question. For what subset of its leaf set can we
reconstruct uniquely the dendogram from the distances that it induces on that
subset. By formalizing a dendogram in terms of an edge-weighted, rooted
phylogenetic tree on a pre-given finite set X with |X|>2 whose edge-weighting
is equidistant and a set of partial distances on X in terms of a set L of
2-subsets of X, we investigate this problem in terms of when such a tree is
lassoed, that is, uniquely determined by the elements in L. For this we
consider four different formalizations of the idea of "uniquely determining"
giving rise to four distinct types of lassos. We present characterizations for
all of them in terms of the child-edge graphs of the interior vertices of such
a tree. Our characterizations imply in particular that in case the tree in
question is binary then all four types of lasso must coincide
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