40 research outputs found
Kochen-Specker Sets and Generalized Orthoarguesian Equations
Every set (finite or infinite) of quantum vectors (states) satisfies
generalized orthoarguesian equations (OA). We consider two 3-dim
Kochen-Specker (KS) sets of vectors and show how each of them should be
represented by means of a Hasse diagram---a lattice, an algebra of subspaces of
a Hilbert space--that contains rays and planes determined by the vectors so as
to satisfy OA. That also shows why they cannot be represented by a special
kind of Hasse diagram called a Greechie diagram, as has been erroneously done
in the literature. One of the KS sets (Peres') is an example of a lattice in
which 6OA pass and 7OA fails, and that closes an open question of whether the
7oa class of lattices properly contains the 6oa class. This result is important
because it provides additional evidence that our previously given proof of noa
=< (n+1)oa can be extended to proper inclusion noa < (n+1)oa and that nOA form
an infinite sequence of successively stronger equations.Comment: 16 pages and 5 figure
Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices
We study the fluctuations of the matrix entries of regular functions of
Wigner random matrices in the limit when the matrix size goes to infinity. In
the case of the Gaussian ensembles (GOE and GUE) this problem was considered by
A.Lytova and L.Pastur in J. Stat. Phys., v.134, 147-159 (2009). Our results are
valid provided the off-diagonal matrix entries have finite fourth moment, the
diagonal matrix entries have finite second moment, and the test functions have
four continuous derivatives in a neighborhood of the support of the Wigner
semicircle law.Comment: minor corrections; the manuscript will appear in the Journal of
Statistical Physic
Type-Decomposition of a Pseudo-Effect Algebra
The theory of direct decomposition of a centrally orthocomplete effect
algebra into direct summands of various types utilizes the notion of a
type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly)
noncommutative version of an effect algebra. In this article we develop the
basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set
to PEAs, and show that TD sets induce decompositions of centrally orthocomplete
PEAs into direct summands.Comment: 18 page
ARFIMA-GARCH modeling of HRV: Clinical application in acute brain injury
In the last decade, several HRV based novel methodologies for describing and assessing heart rate dynamics have been proposed in the literature with the aim of risk assessment. Such methodologies attempt to describe the non-linear and complex characteristics of HRV, and hereby the focus is in two of these characteristics, namely long memory and heteroscedasticity with variance clustering. The ARFIMA-GARCH modeling considered here allows the quantification of long range correlations and time-varying volatility. ARFIMA-GARCH HRV analysis is integrated with multimodal brain monitoring in several acute cerebral phenomena such as intracranial hypertension, decompressive craniectomy and brain death. The results indicate that ARFIMA-GARCH modeling appears to reflect changes in Heart Rate Variability (HRV) dynamics related both with the Acute Brain Injury (ABI) and the medical treatments effects. (c) 2017, Springer International Publishing AG
Convergence of stochastic empirical measures
Let Pn be a random probability measure on a metric space S. Let P^n be the empirical measure of kn iid random variables, each distributed according to Pn. Our main theorem asserts that if {Pn} converges in distribution, as random probability measures on S, then so does {P^n}. Applications of the result to the study of bootstrap and other stochastic procedures are given.random probability measure stochastic empirical measure bootstrap triangular array convergence in distribution