53,581 research outputs found
Anderson transition for Google matrix eigenstates
We introduce a number of random matrix models describing the Google matrix G
of directed networks. The properties of their spectra and eigenstates are
analyzed by numerical matrix diagonalization. We show that for certain models
it is possible to have an algebraic decay of PageRank vector with the exponent
similar to real directed networks. At the same time the spectrum has no
spectral gap and a broad distribution of eigenvalues in the complex plain. The
eigenstates of G are characterized by the Anderson transition from localized to
delocalized states and a mobility edge curve in the complex plane of
eigenvalues.Comment: 9 pages, 12 figs, revte
Invasion waves in the presence of a mutualist
This paper studies invasion waves in the diffusive
Competitor-Competitor-Mutualist model generalizing the 2-species Lotka-Volterra
model studied by Weinberger et al. The mutualist may benefit the invading or
the resident species producing two different types of invasions. Sufficient
conditions for linear determinacy are derived in both cases, and when they
hold, explicit formulas for linear spreading speeds of the invasions are
obtained by linearizing the model. While in the first case the linear speed is
increased by the mutualist, it is unaffected in the second case. Mathematical
methods are based on converting the model into a cooperative reaction-diffusion
system.Comment: 21 pages, 4 figure
Scaling near the upper critical dimensionality in the localization theory
The phenomenon of upper critical dimensionality d_c2 has been studied from
the viewpoint of the scaling concepts. The Thouless number g(L) is not the only
essential variable in scale transformations, because there is the second
parameter connected with the off-diagonal disorder. The investigation of the
resulting two-parameter scaling has revealed two scenarios, and the switching
from one to another scenario determines the upper critical dimensionality. The
first scenario corresponds to the conventional one-parameter scaling and is
characterized by the parameter g(L) invariant under scale transformations when
the system is at the critical point. In the second scenario, the Thouless
number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation
of the Wegner relation s=\nu(d-2) between the critical exponents for
conductivity (s) and for localization radius (\nu), which takes the form
s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the
symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous
version of Mott's argument concerning localization due topological disorder has
been proposed.Comment: PDF, 7 pages, 6 figure
Stochastic approximation of score functions for Gaussian processes
We discuss the statistical properties of a recently introduced unbiased
stochastic approximation to the score equations for maximum likelihood
calculation for Gaussian processes. Under certain conditions, including bounded
condition number of the covariance matrix, the approach achieves storage
and nearly computational effort per optimization step, where is the
number of data sites. Here, we prove that if the condition number of the
covariance matrix is bounded, then the approximate score equations are nearly
optimal in a well-defined sense. Therefore, not only is the approximation
efficient to compute, but it also has comparable statistical properties to the
exact maximum likelihood estimates. We discuss a modification of the stochastic
approximation in which design elements of the stochastic terms mimic patterns
from a factorial design. We prove these designs are always at least as
good as the unstructured design, and we demonstrate through simulation that
they can produce a substantial improvement over random designs. Our findings
are validated by numerical experiments on simulated data sets of up to 1
million observations. We apply the approach to fit a space-time model to over
80,000 observations of total column ozone contained in the latitude band
-N during April 2012.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS627 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamical entanglement purification using chains of atoms and optical cavities
In the framework of cavity QED, we propose a practical scheme to purify
dynamically a bipartite entangled state using short chains of atoms coupled to
high-finesse optical cavities. In contrast to conventional entanglement
purification protocols, we avoid CNOT gates, thus reducing complicated pulse
sequences and superfluous qubit operations. Our interaction scheme works in a
deterministic way, and together with entanglement distribution and swapping,
opens a route towards efficient quantum repeaters for long-distance quantum
communication.Comment: 13 pages, 6 figures, revised version with incorporated erratu
Wealth-driven Selection in a Financial Market with Heterogeneous Agents
We study the co-evolution of asset prices and individual wealth in a financial market populated by an arbitrary number of heterogeneous boundedly rational investors. Using wealth dynamics as a selection device we are able to characterize the long run market outcomes, i.e. asset returns and wealth distributions, for a general class of investment behaviors. Our investigation illustrates that market interaction and wealth dynamics pose certain limits on the outcome of agents' interactions even within the ``wilderness of bounded rationality''. As an application we consider the case of heterogenous mean-variance optimizers and provide insights into the results of the simulation model introduced in Levy, Levy and Solomon (1994).Heterogeneous agents, Asset pricing model, Bounded rationality, CRRA framework, Levy-Levy-Solomon model, Evolutionary Finance.
The macroeconomy and the yield curve: a nonstructural analysis
We estimate a model with latent factors that summarize the yield curve (namely, level, slope, and curvature) as well as observable macroeconomic variables (real activity, inflation, and the stance of monetary policy). Our goal is to provide a characterization of the dynamic interactions between the macroeconomy and the yield curve. We find strong evidence of the effects of macro variables on future movements in the yield curve and much weaker evidence for a reverse influence. We also relate our results to a traditional macroeconomic approach based on the expectations hypothesis
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