6,892 research outputs found
A Note on Effective String Theory
Motivated by the possibility of an effective string description for the
infrared limit of pure Yang-Mills theory, we present a toy model for an
effective theory of random surfaces propagating in a target space of . We
show that the scaling exponents for the fixed area partition function of the
theory are apparently well behaved. We make some observations regarding the
usefulness of this toy model.Comment: 17 pages, LATEX, UTTG-21-9
A semiclassical theory of quantum noise in open chaotic systems
We consider the quantum evolution of classically chaotic systems in contact
with surroundings. Based on -scaling of an equation for time evolution
of the Wigner's quasi-probability distribution function in presence of
dissipation and thermal diffusion we derive a semiclassical equation for
quantum fluctuations. This identifies an early regime of evolution dominated by
fluctuations in the curvature of the potential due to classical chaos and
dissipation. A stochastic treatment of this classical fluctuations leads us to
a Fokker-Planck equation which is reminiscent of Kramers' equation for
thermally activated processes. This reveals an interplay of three aspects of
evolution of quantum noise in weakly dissipative open systems; the reversible
Liouville flow, the irreversible chaotic diffusion which is characteristic of
the system itself, and irreversible dissipation induced by the external
reservoir. It has been demonstrated that in the dissipation-free case a
competition between Liouville flow in the contracting direction of phase space
and chaotic diffusion sets a critical width in the Wigner function for quantum
fluctuations. We also show how the initial quantum noise gets amplified by
classical chaos and ultimately equilibrated under the influence of dissipation.
We establish that there exists a critical limit to the expansion of phase
space. The limit is determined by chaotic diffusion and dissipation. Making use
of appropriate quantum-classical correspondence we verify the semiclassical
analysis by the fully quantum simulation in a chaotic quartic oscillator.Comment: Plain Latex, 27 pages, 6 ps figure, To appear in Physica
Reversing the Stein Effect
The Reverse Stein Effect is identified and illustrated: A statistician who
shrinks his/her data toward a point chosen without reliable knowledge about the
underlying value of the parameter to be estimated but based instead upon the
observed data will not be protected by the minimax property of shrinkage
estimators such as that of James and Stein, but instead will likely incur a
greater error than if shrinkage were not used.Comment: Published in at http://dx.doi.org/10.1214/09-STS278 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips
We show using computer simulations and mean field theory that a system of
particles in two dimensions, when confined laterally by a pair of parallel hard
walls within a quasi one dimensional channel, possesses several anomalous
structural and mechanical properties not observed in the bulk. Depending on the
density and the distance between the walls , the system shows
structural characteristics analogous to a weakly modulated liquid, a strongly
modulated smectic, a triangular solid or a buckled phase. At fixed , a
change in leads to many reentrant discontinuous transitions involving
changes in the number of layers parallel to the confining walls depending
crucially on the commensurability of inter-layer spacing with . The solid
shows resistance to elongation but not to shear. When strained beyond the
elastic limit it fails undergoing plastic deformation but surprisingly, as the
strain is reversed, the material recovers completely and returns to its
original undeformed state. We obtain the phase diagram from mean field theory
and finite size simulations and discuss the effect of fluctuations.Comment: 14 pages, 13 figures; revised version, accepted in J. Chem. Phy
Remarkable thermal stability of BF3-doped polyaniline
We show that the recently synthesized BF3-doped polyaniline (PANI) exhibits
remarkable stability against thermal ageing. Unlike the protonated PANI, which
shows rapid degradation of the conductivity on heating in air, BF3-doped PANI
shows more than an order of magnitude improvement in conductivity. We employ
x-ray photoelectron spectroscopy (XPS), fourier transform infra-red (FTIR)
spectroscopy, and x-ray diffraction (XRD) to understand this unexpected
phenomenon.Comment: 4 pages and 3 figures. To appear in Applied Physics Letters, Sept.
200
A critical analysis of air shower structure functions and size spectrum measurements with the NBU air shower array
A total of 11,000 showers in the size range 10 to the 4 to 10 to the 6 particles so far detected by the NBU air shower array has been analyzed using five different structure functions. A comparison of structure functions in terms: (1) of shower size; and (2) electron density at various core distances has been discussed to indicate the present status of structure functions in air shower analysis
Decay and Decoupling of heavy Right-handed Majorana Neutrinos in the L-R model
Heavy right-handed neutrinos are of current interest. The interactions and
decay of such neutrinos determine their decoupling epoch during the evolution
of the universe. This in turn affects various observable features like the
energy density, nucleosynthesis, CMBR spectrum, galaxy formation, and
baryogenesis. Here, we consider reduction of right-handed electron-type
Majorana neutrinos, in the left-right symmetric model, by the WR+ - WR- channel
and the channel originating from an anomaly, involving the SU(2)R gauge group,
as well as decay of such neutrinos. We study the reduction of these neutrinos
for different ranges of left-right model parameters, and find that, if the
neutrino mass exceeds the right-handed gauge boson mass, then the neutrinos
never decouple for realistic values of the parameters, but, rather, decay in
equilibrium. Because there is no out-of-equilibrium decay, no mass bounds can
be set for the neutrinos.Comment: Latex, 16 pages, No figures. Some additions in the text and
references. Conclusions unaffected. To appear in Eur. Phys. J.
Learning from Data with Heterogeneous Noise using SGD
We consider learning from data of variable quality that may be obtained from
different heterogeneous sources. Addressing learning from heterogeneous data in
its full generality is a challenging problem. In this paper, we adopt instead a
model in which data is observed through heterogeneous noise, where the noise
level reflects the quality of the data source. We study how to use stochastic
gradient algorithms to learn in this model. Our study is motivated by two
concrete examples where this problem arises naturally: learning with local
differential privacy based on data from multiple sources with different privacy
requirements, and learning from data with labels of variable quality.
The main contribution of this paper is to identify how heterogeneous noise
impacts performance. We show that given two datasets with heterogeneous noise,
the order in which to use them in standard SGD depends on the learning rate. We
propose a method for changing the learning rate as a function of the
heterogeneity, and prove new regret bounds for our method in two cases of
interest. Experiments on real data show that our method performs better than
using a single learning rate and using only the less noisy of the two datasets
when the noise level is low to moderate
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