714 research outputs found
Poisson smooth structures on stratified symplectic spaces
In this paper we introduce the notion of a smooth structure on a stratified
space, the notion of a Poisson smooth structure and the notion of a weakly
symplectic smooth structure on a stratified symplectic space, refining the
concept of a stratified symplectic Poisson algebra introduced by Sjamaar and
Lerman. We show that these smooth spaces possess several important properties,
e.g. the existence of smooth partitions of unity. Furthermore, under mild
conditions many properties of a symplectic manifold can be extended to a
symplectic stratified space provided with a smooth Poisson structure, e.g. the
existence and uniqueness of a Hamiltonian flow, the isomorphism between the
Brylinski-Poisson homology and the de Rham homology, the existence of a
Leftschetz decomposition on a symplectic stratified space. We give many
examples of stratified symplectic spaces possessing a Poisson smooth structure
which is also weakly symplectic.Comment: 21 page, final version, to appear in the Proceedings of the 6-th
World Conference on 21st Century Mathematic
Pairing correlations in N~Z pf-shell nuclei
We perform Shell Model Monte Carlo calculations to study pair correlations in
the ground states of nuclei with masses A=48-60. We find that ,
proton-neutron correlations play an important, and even dominant
role, in the ground states of odd-odd nuclei, in agreement with
experiment. By studying pairing in the ground states of Fe, we
observe that the isovector proton-neutron correlations decrease rapidly with
increasing neutron excess. In contrast, both the proton, and trivially the
neutron correlations increase as neutrons are added.
We also study the thermal properties and the temperature dependence of pair
correlations for Mn and Fe as exemplars of odd-odd and even-even
nuclei. While for Fe results are similar to those obtained for
other even-even nuclei in this mass range, the properties of Mn at low
temperatures are strongly influenced by isovector neutron-proton pairing. In
coexistence with these isovector pair correlations, our calculations also
indicate an excess of isoscalar proton-neutron pairing over the mean-field
values. The isovector neutron-proton correlations rapidly decrease with
temperatures and vanish for temperatures above keV, while the isovector
correlations among like nucleons persist to higher temperatures. Related to the
quenching of the isovector proton-neutron correlations, the average isospin
decreases from 1, appropriate for the ground state, to 0 as the temperature
increases
SIMULATION IN PRACTICE: THE BALANCING INTERCEPT
Simulation is an important tool within epidemiology for both learning and developing new methodology (1–5). Unfortunately, few epidemiology training programs teach basic simulation methods. Briefly, when conducting a simulation experiment, we generally follow the same basic steps. We first decide which variables to include, as well as their distributions and associations—often aided by a causal diagram. We then generate those variables by sampling from their specified distributions and estimate whatever target parameter is of interest (e.g., sample average or causal effect). We finally repeat the processmultiple times, building a distribution for the target parameter from the estimates obtained in each replicate
Isovector and isoscalar superfluid phases in rotating nuclei
The subtle interplay between the two nuclear superfluids, isovector T=1 and
isoscalar T=0 phases, are investigated in an exactly soluble model. It is shown
that T=1 and T=0 pair-modes decouple in the exact calculations with the T=1
pair-energy being independent of the T=0 pair-strength and vice-versa. In the
rotating-field, the isoscalar correlations remain constant in contrast to the
well known quenching of isovector pairing. An increase of the isoscalar (J=1,
T=0) pair-field results in a delay of the bandcrossing frequency. This
behaviour is shown to be present only near the N=Z line and its experimental
confirmation would imply a strong signature for isoscalar pairing collectivity.
The solutions of the exact model are also discussed in the
Hartree-Fock-Bogoliubov approximation.Comment: 5 pages, 4 figures, submitted to PR
Ergodicity, Decisions, and Partial Information
In the simplest sequential decision problem for an ergodic stochastic process
X, at each time n a decision u_n is made as a function of past observations
X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is
known that one may choose (under a mild integrability assumption) a decision
strategy whose pathwise time-average loss is asymptotically smaller than that
of any other strategy. The corresponding problem in the case of partial
information proves to be much more delicate, however: if the process X is not
observable, but decisions must be based on the observation of a different
process Y, the existence of pathwise optimal strategies is not guaranteed.
The aim of this paper is to exhibit connections between pathwise optimal
strategies and notions from ergodic theory. The sequential decision problem is
developed in the general setting of an ergodic dynamical system (\Omega,B,P,T)
with partial information Y\subseteq B. The existence of pathwise optimal
strategies grounded in two basic properties: the conditional ergodic theory of
the dynamical system, and the complexity of the loss function. When the loss
function is not too complex, a general sufficient condition for the existence
of pathwise optimal strategies is that the dynamical system is a conditional
K-automorphism relative to the past observations \bigvee_n T^n Y. If the
conditional ergodicity assumption is strengthened, the complexity assumption
can be weakened. Several examples demonstrate the interplay between complexity
and ergodicity, which does not arise in the case of full information. Our
results also yield a decision-theoretic characterization of weak mixing in
ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page
String theory and the Kauffman polynomial
We propose a new, precise integrality conjecture for the colored Kauffman
polynomial of knots and links inspired by large N dualities and the structure
of topological string theory on orientifolds. According to this conjecture, the
natural knot invariant in an unoriented theory involves both the colored
Kauffman polynomial and the colored HOMFLY polynomial for composite
representations, i.e. it involves the full HOMFLY skein of the annulus. The
conjecture sheds new light on the relationship between the Kauffman and the
HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide
various non-trivial tests of the conjecture and we sketch the string theory
arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos
corrected, final version to appear in CM
Emerging therapies for right ventricular dysfunction and failure
Therapeutic options for right ventricular (RV) dysfunction and failure are strongly limited. Right heart failure (RHF) has been mostly addressed in the context of pulmonary arterial hypertension (PAH), where it is not possible to discern pulmonary vascular- and RV-directed effects of therapeutic approaches. In part, opposing pathomechanisms in RV and pulmonary vasculature, i.e., regarding apoptosis, angiogenesis and proliferation, complicate addressing RHF in PAH. Therapy effective for left heart failure is not applicable to RHF, e.g., inhibition of adrenoceptor signaling and of the renin-angiotensin system had no or only limited success. A number of experimental studies employing animal models for PAH or RV dysfunction or failure have identified beneficial effects of novel pharmacological agents, with most promising results obtained with modulators of metabolism and reactive oxygen species or inflammation, respectively. In addition, established PAH agents, in particular phosphodiesterase-5 inhibitors and soluble guanylate cyclase stimulators, may directly address RV integrity. Promising results are furthermore derived with microRNA (miRNA) and long non-coding RNA (lncRNA) blocking or mimetic strategies, which can target microvascular rarefaction, inflammation, metabolism or fibrotic and hypertrophic remodeling in the dysfunctional RV. Likewise, pre-clinical data demonstrate that cell-based therapies using stem or progenitor cells have beneficial effects on the RV, mainly by improving the microvascular system, however clinical success will largely depend on delivery routes. A particular option for PAH is targeted denervation of the pulmonary vasculature, given the sympathetic overdrive in PAH patients. Finally, acute and durable mechanical circulatory support are available for the right heart, which however has been tested mostly in RHF with concomitant left heart disease. Here, we aim to review current pharmacological, RNA- and cell-based therapeutic options and their potential to directly target the RV and to review available data for pulmonary artery denervation and mechanical circulatory support
How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation
This paper addresses two questions in the context of neuronal networks
dynamics, using methods from dynamical systems theory and statistical physics:
(i) How to characterize the statistical properties of sequences of action
potentials ("spike trains") produced by neuronal networks ? and; (ii) what are
the effects of synaptic plasticity on these statistics ? We introduce a
framework in which spike trains are associated to a coding of membrane
potential trajectories, and actually, constitute a symbolic coding in important
explicit examples (the so-called gIF models). On this basis, we use the
thermodynamic formalism from ergodic theory to show how Gibbs distributions are
natural probability measures to describe the statistics of spike trains, given
the empirical averages of prescribed quantities. As a second result, we show
that Gibbs distributions naturally arise when considering "slow" synaptic
plasticity rules where the characteristic time for synapse adaptation is quite
longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure
Experimental Study of the Shortest Reset Word of Random Automata
In this paper we describe an approach to finding the shortest reset word of a
finite synchronizing automaton by using a SAT solver. We use this approach to
perform an experimental study of the length of the shortest reset word of a
finite synchronizing automaton. The largest automata we considered had 100
states. The results of the experiments allow us to formulate a hypothesis that
the length of the shortest reset word of a random finite automaton with
states and 2 input letters with high probability is sublinear with respect to
and can be estimated as $1.95 n^{0.55}.
Two-proton correlations from 158 AGeV Pb+Pb central collisions
The two-proton correlation function at midrapidity from Pb+Pb central
collisions at 158 AGeV has been measured by the NA49 experiment. The results
are compared to model predictions from static thermal Gaussian proton source
distributions and transport models RQMD and VENUS. An effective proton source
size is determined by minimizing CHI-square/ndf between the correlation
functions of the data and those calculated for the Gaussian sources, yielding
3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are
consistent with the data within the error in the correlation peak region.Comment: RevTeX style, 6 pages, 4 figures, 1 table. More discussion are added
about the structure on the tail of the correlation function. The systematic
error is revised. To appear in Phys. Lett.
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