7,376 research outputs found
Pulsar State Switching from Markov Transitions and Stochastic Resonance
Markov processes are shown to be consistent with metastable states seen in
pulsar phenomena, including intensity nulling, pulse-shape mode changes,
subpulse drift rates, spindown rates, and X-ray emission, based on the
typically broad and monotonic distributions of state lifetimes. Markovianity
implies a nonlinear magnetospheric system in which state changes occur
stochastically, corresponding to transitions between local minima in an
effective potential. State durations (though not transition times) are thus
largely decoupled from the characteristic time scales of various magnetospheric
processes. Dyadic states are common but some objects show at least four states
with some transitions forbidden. Another case is the long-term intermittent
pulsar B1931+24 that has binary radio-emission and torque states with wide, but
non-monotonic duration distributions. It also shows a quasi-period of
days in a 13-yr time sequence, suggesting stochastic resonance in a Markov
system with a forcing function that could be strictly periodic or
quasi-periodic. Nonlinear phenomena are associated with time-dependent activity
in the acceleration region near each magnetic polar cap. The polar-cap diode is
altered by feedback from the outer magnetosphere and by return currents from an
equatorial disk that may also cause the neutron star to episodically charge and
discharge. Orbital perturbations in the disk provide a natural periodicity for
the forcing function in the stochastic resonance interpretation of B1931+24.
Disk dynamics may introduce additional time scales in observed phenomena.
Future work can test the Markov interpretation, identify which pulsar types
have a propensity for state changes, and clarify the role of selection effects.Comment: 25 pages, 6 figures, submitted to the Astrophysical Journa
Optical computing by injection-locked lasers
A programmable optical computer has remained an elusive concept. To construct
a practical computing primitive equivalent to an electronic Boolean logic, one
should find a nonlinear phenomenon that overcomes weaknesses present in many
optical processing schemes. Ideally, the nonlinearity should provide a
functionally complete set of logic operations, enable ultrafast all-optical
programmability, and allow cascaded operations without a change in the
operating wavelength or in the signal encoding format. Here we demonstrate a
programmable logic gate using an injection-locked Vertical-Cavity
Surface-Emitting Laser (VCSEL). The gate program is switched between the AND
and the OR operations at the rate of 1 GHz with Bit Error Ratio (BER) of 10e-6
without changes in the wavelength or in the signal encoding format. The scheme
is based on nonlinearity of normalization operations, which can be used to
construct any continuous complex function or operation, Boolean or otherwise.Comment: 47 pages, 7 figures in total, 2 tables. Intended for submission to
Nature Physics within the next two week
Aggregation and Control of Populations of Thermostatically Controlled Loads by Formal Abstractions
This work discusses a two-step procedure, based on formal abstractions, to
generate a finite-space stochastic dynamical model as an aggregation of the
continuous temperature dynamics of a homogeneous population of Thermostatically
Controlled Loads (TCL). The temperature of a single TCL is described by a
stochastic difference equation and the TCL status (ON, OFF) by a deterministic
switching mechanism. The procedure is formal as it allows the exact
quantification of the error introduced by the abstraction -- as such it builds
and improves on a known, earlier approximation technique in the literature.
Further, the contribution discusses the extension to the case of a
heterogeneous population of TCL by means of two approaches resulting in the
notion of approximate abstractions. It moreover investigates the problem of
global (population-level) regulation and load balancing for the case of TCL
that are dependent on a control input. The procedure is tested on a case study
and benchmarked against the mentioned alternative approach in the literature.Comment: 40 pages, 21 figures; the paper generalizes the result of conference
publication: S. Esmaeil Zadeh Soudjani and A. Abate, "Aggregation of
Thermostatically Controlled Loads by Formal Abstractions," Proceedings of the
European Control Conference 2013, pp. 4232-4237. version 2: added references
for section
Critical Market Crashes
This review is a partial synthesis of the book ``Why stock market crash''
(Princeton University Press, January 2003), which presents a general theory of
financial crashes and of stock market instabilities that his co-workers and the
author have developed over the past seven years. The study of the frequency
distribution of drawdowns, or runs of successive losses shows that large
financial crashes are ``outliers'': they form a class of their own as can be
seen from their statistical signatures. If large financial crashes are
``outliers'', they are special and thus require a special explanation, a
specific model, a theory of their own. In addition, their special properties
may perhaps be used for their prediction. The main mechanisms leading to
positive feedbacks, i.e., self-reinforcement, such as imitative behavior and
herding between investors are reviewed with many references provided to the
relevant literature outside the confine of Physics. Positive feedbacks provide
the fuel for the development of speculative bubbles, preparing the instability
for a major crash. We demonstrate several detailed mathematical models of
speculative bubbles and crashes. The most important message is the discovery of
robust and universal signatures of the approach to crashes. These precursory
patterns have been documented for essentially all crashes on developed as well
as emergent stock markets, on currency markets, on company stocks, and so on.
The concept of an ``anti-bubble'' is also summarized, with two forward
predictions on the Japanese stock market starting in 1999 and on the USA stock
market still running. We conclude by presenting our view of the organization of
financial markets.Comment: Latex 89 pages and 38 figures, in press in Physics Report
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