3,004 research outputs found
Random Matrix Theory Analysis of Cross Correlations in Financial Markets
We confirm universal behaviors such as eigenvalue distribution and spacings
predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the
daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been
reported for New York Stock Exchange in previous studies. It is shown that the
random part of the eigenvalue distribution of the cross correlation matrix is
stable even when deterministic correlations are present. Some deviations in the
small eigenvalue statistics outside the bounds of the universality class of RMT
are not completely explained with the deterministic correlations as proposed in
previous studies. We study the effect of randomness on deterministic
correlations and find that randomness causes a repulsion between deterministic
eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of
``level repulsion'' in RMT and explains some deviations from the previous
studies observed in the market data. We also study correlated groups of issues
in these markets and propose a refined method to identify correlated groups
based on RMT. Some characteristic differences between properties of Tokyo Stock
Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure
Histopathological evaluation of placentas after diagnosis of maternal SARS-CoV-2 infection.
Background:The impact of maternal SARS-CoV-2 infection on placental histopathology is not well known. Objectives:To determine if significant placental histopathological changes occur after diagnosis of SARS-CoV-2 infection in pregnancy and whether these changes are correlated with the presence or absence of symptoms associated with infection. Study Design:Retrospective cohort study of women diagnosed with SARS-CoV-2 infection who delivered at a single center from April 9th to April 27th, 2020, and had placental specimens reviewed by pathology. Women with singleton gestations and laboratory-confirmed SARS-CoV-2 infection were eligible for inclusion. Historical controls selected from a cohort of women who delivered 6 months prior to the study period were matched in a 1:1 fashion by week of gestation at delivery. Histopathological characteristics were evaluated in each placenta and the incidence of these findings were compared between placentas after diagnosis of maternal SARS-CoV-2 infection and historical controls, as well as between placentas from patients with or without typical symptoms related to infection. Statistical analysis included use of Wilcoxon rank sum test and Fisher\u27s exact test for comparison of categorical and continuous variables. Statistical significance was defined as P value \u3c 0.05. Results:A total of 50 placentas after diagnosis of maternal SARS-CoV-2 infection and 50 historical controls were analyzed. Among placentas from patients diagnosed with SARS-CoV-2 infection, 3 (6%) were preterm (33 3/7, 34 6/7 and 36 6/7 weeks of gestation), 16 (32%) were from patients with typical symptoms related to infection and 34 (68%) were from patients without typical symptoms related to the infection. All patients had diagnosis of SARS-CoV-2 infection in the third trimester. Decidual vasculopathy was not visualized in any of the placentas from patients diagnosed with SARS-CoV-2 infection. There was no statistically significant difference in placental histopathological characteristics between the groups. SARS-CoV-2 testing for all neonates at 24 hours of life was negative. Conclusions:Based on our data, there are no significant placental histopathological changes that occur after diagnosis of SARS-CoV-2 infection in the third trimester of pregnancy compared to a gestational age-matched historical control group. Similar incidences of histopathological findings were also discovered when comparing placentas from patients with SARS-CoV-2 infection with or without the presence of symptoms typically related to infection
Stochastic Budget Optimization in Internet Advertising
Internet advertising is a sophisticated game in which the many advertisers
"play" to optimize their return on investment. There are many "targets" for the
advertisements, and each "target" has a collection of games with a potentially
different set of players involved. In this paper, we study the problem of how
advertisers allocate their budget across these "targets". In particular, we
focus on formulating their best response strategy as an optimization problem.
Advertisers have a set of keywords ("targets") and some stochastic information
about the future, namely a probability distribution over scenarios of cost vs
click combinations. This summarizes the potential states of the world assuming
that the strategies of other players are fixed. Then, the best response can be
abstracted as stochastic budget optimization problems to figure out how to
spread a given budget across these keywords to maximize the expected number of
clicks.
We present the first known non-trivial poly-logarithmic approximation for
these problems as well as the first known hardness results of getting better
than logarithmic approximation ratios in the various parameters involved. We
also identify several special cases of these problems of practical interest,
such as with fixed number of scenarios or with polynomial-sized parameters
related to cost, which are solvable either in polynomial time or with improved
approximation ratios. Stochastic budget optimization with scenarios has
sophisticated technical structure. Our approximation and hardness results come
from relating these problems to a special type of (0/1, bipartite) quadratic
programs inherent in them. Our research answers some open problems raised by
the authors in (Stochastic Models for Budget Optimization in Search-Based
Advertising, Algorithmica, 58 (4), 1022-1044, 2010).Comment: FINAL versio
Reflectance Fluctuations in an Absorbing Random Waveguide
We study the statistics of the reflectance (the ratio of reflected and
incident intensities) of an -mode disordered waveguide with weak absorption
per mean free path. Two distinct regimes are identified. The regime
shows universal fluctuations.
With increasing length of the waveguide, the variance of the reflectance
changes from the value , characteristic for universal conductance
fluctuations in disordered wires, to another value , characteristic
for chaotic cavities. The weak-localization correction to the average
reflectance performs a similar crossover from the value to . In
the regime , the large- distribution of the reflectance
becomes very wide and asymmetric, for .Comment: 7 pages, RevTeX, 2 postscript figure
Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture
In the framework of a random matrix description of chaotic quantum scattering
the positions of matrix poles are given by complex eigenvalues of an
effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture
on statistics of for systems with broken time-reversal invariance and
verify that it allows to reproduce statistical characteristics of Wigner time
delays known from independent calculations. We analyze the ensuing two-point
statistical measures as e.g. spectral form factor and the number variance. In
addition we find the density of complex eigenvalues of real asymmetric matrices
generalizing the recent result by Efetov\cite{Efnh}.Comment: 4 page
Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach
We determine the asymptotic level spacing distribution for the Laguerre
Ensemble in a single scaled interval, , containing no levels,
E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the
Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by
both Edelman and Forrester, while for , the leading terms of
, found by Tracy and Widom, are reproduced without the use of the
Bessel kernel and the associated Painlev\'e transcendent. In the same
approximation, the next leading term, due to a ``finite temperature''
perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe
Correlations between zeros of a random polynomial
We obtain exact analytical expressions for correlations between real zeros of
the Kac random polynomial. We show that the zeros in the interval are
asymptotically independent of the zeros outside of this interval, and that the
straightened zeros have the same limit translation invariant correlations. Then
we calculate the correlations between the straightened zeros of the SO(2)
random polynomial.Comment: 31 pages, 2 figures; a revised version of the J. Stat. Phys. pape
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