4,218 research outputs found
Schulman Replies
This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896
(2000)) on PRL 83, 5419 (1999).
The suitability of the particlar two-time boundary value problem used in the
earlier PRL is argued
Causal connectivity of evolved neural networks during behavior
To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics
Granger causality and transfer entropy are equivalent for Gaussian variables
Granger causality is a statistical notion of causal influence based on
prediction via vector autoregression. Developed originally in the field of
econometrics, it has since found application in a broader arena, particularly
in neuroscience. More recently transfer entropy, an information-theoretic
measure of time-directed information transfer between jointly dependent
processes, has gained traction in a similarly wide field. While it has been
recognized that the two concepts must be related, the exact relationship has
until now not been formally described. Here we show that for Gaussian
variables, Granger causality and transfer entropy are entirely equivalent, thus
bridging autoregressive and information-theoretic approaches to data-driven
causal inference.Comment: In review, Phys. Rev. Lett., Nov. 200
Shot-noise limited monitoring and phase locking of the motion of a single trapped ion
We perform high-resolution real-time read-out of the motion of a single
trapped and laser-cooled Ba ion. By using an interferometric setup we
demonstrate shot-noise limited measurement of thermal oscillations with
resolution of 4 times the standard quantum limit. We apply the real-time
monitoring for phase control of the ion motion through a feedback loop,
suppressing the photon recoil-induced phase diffusion. Due to the spectral
narrowing in phase-locked mode, the coherent ion oscillation is measured with
resolution of about 0.3 times the standard quantum limit
Time-Domain Measurement of Broadband Coherent Cherenkov Radiation
We report on further analysis of coherent microwave Cherenkov impulses
emitted via the Askaryan mechanism from high-energy electromagnetic showers
produced at the Stanford Linear Accelerator Center (SLAC). In this report, the
time-domain based analysis of the measurements made with a broadband (nominally
1-18 GHz) log periodic dipole array antenna is described. The theory of a
transmit-receive antenna system based on time-dependent effective height
operator is summarized and applied to fully characterize the measurement
antenna system and to reconstruct the electric field induced via the Askaryan
process. The observed radiation intensity and phase as functions of frequency
were found to agree with expectations from 0.75-11.5 GHz within experimental
errors on the normalized electric field magnitude and the relative phase; 0.039
microV/MHz/TeV and 17 deg, respectively. This is the first time this agreement
has been observed over such a broad bandwidth, and the first measurement of the
relative phase variation of an Askaryan pulse. The importance of validation of
the Askaryan mechanism is significant since it is viewed as the most promising
way to detect cosmogenic neutrino fluxes at E > 10^15 eV.Comment: 10 pages, 9 figures, accepted by Phys. Rev.
Fractional Quantum Mechanics
A path integral approach to quantum physics has been developed. Fractional
path integrals over the paths of the L\'evy flights are defined. It is shown
that if the fractality of the Brownian trajectories leads to standard quantum
and statistical mechanics, then the fractality of the L\'evy paths leads to
fractional quantum mechanics and fractional statistical mechanics. The
fractional quantum and statistical mechanics have been developed via our
fractional path integral approach. A fractional generalization of the
Schr\"odinger equation has been found. A relationship between the energy and
the momentum of the nonrelativistic quantum-mechanical particle has been
established. The equation for the fractional plane wave function has been
obtained. We have derived a free particle quantum-mechanical kernel using Fox's
H function. A fractional generalization of the Heisenberg uncertainty relation
has been established. Fractional statistical mechanics has been developed via
the path integral approach. A fractional generalization of the motion equation
for the density matrix has been found. The density matrix of a free particle
has been expressed in terms of the Fox's H function. We also discuss the
relationships between fractional and the well-known Feynman path integral
approaches to quantum and statistical mechanics.Comment: 27 page
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These
versions are applicable to Laplace transforms of Schwartz distributions. We
apply these Tauberian results to deduce a number of Tauberian theorems for
power series where Ces\`{a}ro summability follows from Abel summability. We
also use our general results to give a new simple proof of the classical
Littlewood one-sided Tauberian theorem for power series.Comment: 15 page
Relativistic diffusion processes and random walk models
The nonrelativistic standard model for a continuous, one-parameter diffusion
process in position space is the Wiener process. As well-known, the Gaussian
transition probability density function (PDF) of this process is in conflict
with special relativity, as it permits particles to propagate faster than the
speed of light. A frequently considered alternative is provided by the
telegraph equation, whose solutions avoid superluminal propagation speeds but
suffer from singular (non-continuous) diffusion fronts on the light cone, which
are unlikely to exist for massive particles. It is therefore advisable to
explore other alternatives as well. In this paper, a generalized Wiener process
is proposed that is continuous, avoids superluminal propagation, and reduces to
the standard Wiener process in the non-relativistic limit. The corresponding
relativistic diffusion propagator is obtained directly from the nonrelativistic
Wiener propagator, by rewriting the latter in terms of an integral over
actions. The resulting relativistic process is non-Markovian, in accordance
with the known fact that nontrivial continuous, relativistic Markov processes
in position space cannot exist. Hence, the proposed process defines a
consistent relativistic diffusion model for massive particles and provides a
viable alternative to the solutions of the telegraph equation.Comment: v3: final, shortened version to appear in Phys. Rev.
Isotropic Conductivity of Two-Dimensional Three-Component Symmetric Composites
The effective dc-conductivity problem of isotropic, two-dimensional (2D),
three-component, symmetric, regular composites is considered. A simple cubic
equation with one free parameter for
is suggested whose solutions automatically have all the exactly known
properties of that function. Numerical calculations on four different
symmetric, isotropic, 2D, three-component, regular structures show a
non-universal behavior of with an
essential dependence on micro-structural details, in contrast with the
analogous two-component problem. The applicability of the cubic equation to
these structures is discussed. An extension of that equation to the description
of other types of 2D three-component structures is suggested, including the
case of random structures.
Pacs: 72.15.Eb, 72.80.Tm, 61.50.AhComment: 8 pages (two columns), 8 figures. J. Phys. A - submitte
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