2,185 research outputs found
Signal Decomposition Using Masked Proximal Operators
We consider the well-studied problem of decomposing a vector time series
signal into components with different characteristics, such as smooth,
periodic, nonnegative, or sparse. We describe a simple and general framework in
which the components are defined by loss functions (which include constraints),
and the signal decomposition is carried out by minimizing the sum of losses of
the components (subject to the constraints). When each loss function is the
negative log-likelihood of a density for the signal component, this framework
coincides with maximum a posteriori probability (MAP) estimation; but it also
includes many other interesting cases. Summarizing and clarifying prior
results, we give two distributed optimization methods for computing the
decomposition, which find the optimal decomposition when the component class
loss functions are convex, and are good heuristics when they are not. Both
methods require only the masked proximal operator of each of the component loss
functions, a generalization of the well-known proximal operator that handles
missing entries in its argument. Both methods are distributed, i.e., handle
each component separately. We derive tractable methods for evaluating the
masked proximal operators of some loss functions that, to our knowledge, have
not appeared in the literature.Comment: The manuscript has 61 pages, 22 figures and 2 tables. Also hosted at
https://web.stanford.edu/~boyd/papers/sig_decomp_mprox.html. For code, see
https://github.com/cvxgrp/signal-decompositio
Gravitational-Wave Stochastic Background Detection with Resonant-Mass Detectors
In this paper we discuss how the standard optimal Wiener filter theory can be
applied, within a linear approximation, to the detection of an isotropic
stochastic gravitational-wave background with two or more detectors. We apply
then the method to the AURIGA-NAUTILUS pair of ultra low temperature bar
detectors, near to operate in coincidence in Italy, obtaining an estimate for
the sensitivity to the background spectral density of $\simeq 10^{-49}\
Hz^{-1}\simeq 8\times10^{-5}\times\rho_c\rho_c\simeq1.9 \times 10^{-26}\
kg/m^3\simeq 6
\times10^{-5}\times\rho_c\simeq 2\times10^{-5}\times
\rho_c\simeq 2 \times10^{-6}\rho_c$.Comment: 32 pages, postscript file, also available at
http://axln01.lnl.infn.it/reports/stoch.htm
A Comprehensive Archival Search for Counterparts to Ultra-Compact High Velocity Clouds: Five Local Volume Dwarf Galaxies
We report five Local Volume dwarf galaxies (two of which are presented here
for the first time) uncovered during a comprehensive archival search for
optical counterparts to ultra-compact high velocity clouds (UCHVCs). The UCHVC
population of HI clouds are thought to be candidate gas-rich, low mass halos at
the edge of the Local Group and beyond, but no comprehensive search for stellar
counterparts to these systems has been presented. Careful visual inspection of
all publicly available optical and ultraviolet imaging at the position of the
UCHVCs revealed six blue, diffuse counterparts with a morphology consistent
with a faint dwarf galaxy beyond the Local Group. Optical spectroscopy of all
six candidate dwarf counterparts show that five have an H-derived
velocity consistent with the coincident HI cloud, confirming their association,
the sixth diffuse counterpart is likely a background object. The size and
luminosity of the UCHVC dwarfs is consistent with other known Local Volume
dwarf irregular galaxies. The gas fraction () of the five
dwarfs are generally consistent with that of dwarf irregular galaxies in the
Local Volume, although ALFALFA-Dw1 (associated with ALFALFA UCHVC
HVC274.68+74.70123) has a very high 40. Despite the
heterogenous nature of our search, we demonstrate that the current dwarf
companions to UCHVCs are at the edge of detectability due to their low surface
brightness, and that deeper searches are likely to find more stellar systems.
If more sensitive searches do not reveal further stellar counterparts to
UCHVCs, then the dearth of such systems around the Local Group may be in
conflict with CDM simulations.Comment: 18 pages, 4 tables, 4 figures, ApJ Accepte
Using of small-scale quantum computers in cryptography with many-qubit entangled states
We propose a new cryptographic protocol. It is suggested to encode
information in ordinary binary form into many-qubit entangled states with the
help of a quantum computer. A state of qubits (realized, e.g., with photons) is
transmitted through a quantum channel to the addressee, who applies a quantum
computer tuned to realize the inverse unitary transformation decoding of the
message. Different ways of eavesdropping are considered, and an estimate of the
time needed for determining the secret unitary transformation is given. It is
shown that using even small quantum computers can serve as a basis for very
efficient cryptographic protocols. For a suggested cryptographic protocol, the
time scale on which communication can be considered secure is exponential in
the number of qubits in the entangled states and in the number of gates used to
construct the quantum network
Gravitational Lensing Signature of Long Cosmic Strings
The gravitational lensing by long, wiggly cosmic strings is shown to produce
a large number of lensed images of a background source. In addition to pairs of
images on either side of the string, a number of small images outline the
string due to small-scale structure on the string. This image pattern could
provide a highly distinctive signature of cosmic strings. Since the optical
depth for multiple imaging of distant quasar sources by long strings may be
comparable to that by galaxies, these image patterns should be clearly
observable in the next generation of redshift surveys such as the Sloan Digital
Sky Survey.Comment: 4 pages, revtex with 3 postscript figures include
Scaling Property of the global string in the radiation dominated universe
We investigate the evolution of the global string network in the radiation
dominated universe by use of numerical simulations in 3+1 dimensions. We find
that the global string network settles down to the scaling regime where the
energy density of global strings, , is given by with the string tension per unit length and the scaling parameter,
, irrespective of the cosmic time. We also find that the
loop distribution function can be fitted with that predicted by the so-called
one scale model. Concretely, the number density, , of the loop with
the length, , is given by
where and is related with the Nambu-Goldstone(NG)
boson radiation power from global strings, , as with
. Therefore, the loop production function also scales and
the typical scale of produced loops is nearly the horizon distance. Thus, the
evolution of the global string network in the radiation dominated universe can
be well described by the one scale model in contrast with that of the local
string network.Comment: 18 pages, 9 figures, to appear in Phys. Rev.
Entanglement of electrons in interacting molecules
Quantum entanglement is a concept commonly used with reference to the
existence of certain correlations in quantum systems that have no classical
interpretation. It is a useful resource to enhance the mutual information of
memory channels or to accelerate some quantum processes as, for example, the
factorization in Shor's Algorithm. Moreover, entanglement is a physical
observable directly measured by the von Neumann entropy of the system. We have
used this concept in order to give a physical meaning to the electron
correlation energy in systems of interacting electrons. The electronic
correlation is not directly observable, since it is defined as the difference
between the exact ground state energy of the many--electrons Schroedinger
equation and the Hartree--Fock energy. We have calculated the correlation
energy and compared with the entanglement, as functions of the nucleus--nucleus
separation using, for the hydrogen molecule, the Configuration Interaction
method. Then, in the same spirit, we have analyzed a dimer of ethylene, which
represents the simplest organic conjugate system, changing the relative
orientation and distance of the molecules, in order to obtain the configuration
corresponding to maximum entanglement.Comment: 15 pages, 7 figures, standard late
Evolution of a global string network in a matter dominated universe
We evolve the network of global strings in the matter-dominated universe by
means of numerical simulations. The existence of the scaling solution is
confirmed as in the radiation-dominated universe but the scaling parameter
takes a slightly smaller value, , which is
defined as with the energy density of
global strings and the string tension per unit length. The change of
from the radiation to the matter-dominated universe is consistent with
that obtained by Albrecht and Turok by use of the one-scale model. We also
study the loop distribution function and find that it can be well fitted with
that predicted by the one-scale model, where the number density of
the loop with the length is given by with and . Thus, the evolution of the
global string network in the matter-dominated universe can be well described by
the one-scale model as in the radiation-dominated universe.Comment: 10 pages, 5 figure
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