12,778 research outputs found
Torsion as a dynamic degree of freedom of quantum gravity
The gauge approach to gravity based on the local Lorentz group with a general
independent affine connection A_{\mu cd} is developed. We consider SO(1,3)
gauge theory with a Lagrangian quadratic in curvature as a simple model of
quantum gravity. The torsion is proposed to represent a dynamic degree of
freedom of quantum gravity at scales above the Planckian energy. The
Einstein-Hilbert theory is induced as an effective theory due to quantum
corrections of torsion via generating a stable gravito-magnetic condensate. We
conjecture that torsion possesses an intrinsic quantum nature and can be
confined. A minimal Abelian projection for the Lorentz gauge model has been
constructed, and an effective theory of the cosmic knot at the Planckian scale
is proposed.Comment: 13 pages, reduced final versio
Magic polarization for optical trapping of atoms without Stark-induced dephasing
We demonstrate that the differential ac-Stark shift of a ground-state
hyperfine transition in an optical trap can be eliminated by using properly
polarized trapping light. We use the vector polarizability of an alkali-metal
atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman
shift. We study a transition from the |2S1/2,F=2,mF=-2> to the
|2S1/2,F=1,mF=-1> state of 7Li to observe 0.59+-0.02 Hz linewidth with
interrogation time of 2 s and 0.82+-0.06 s coherence time of a superposition
state. Implications of the narrow linewidth and the long coherence time for
precision spectroscopy and quantum information processing using atoms in an
optical lattice are discussed
Disorder dependence of the ferromagnetic quantum phase transition
We quantitatively discuss the influence of quenched disorder on the
ferromagnetic quantum phase transition in metals, using a theory that describes
the coupling of the magnetization to gapless fermionic excitations. In clean
systems, the transition is first order below a tricritical temperature T_tc.
Quenched disorder is predicted to suppress T_tc until it vanishes for residual
resistivities rho_0 on the order of several microOhmcm for typical quantum
ferromagnets. We discuss experiments that allow to distinguish the mechanism
considered from other possible realizations of a first-order transition.Comment: 5pp, 1 figure; additional reference
JOBS: Joint-Sparse Optimization from Bootstrap Samples
Classical signal recovery based on minimization solves the least
squares problem with all available measurements via sparsity-promoting
regularization. In practice, it is often the case that not all measurements are
available or required for recovery. Measurements might be corrupted/missing or
they arrive sequentially in streaming fashion. In this paper, we propose a
global sparse recovery strategy based on subsets of measurements, named JOBS,
in which multiple measurements vectors are generated from the original pool of
measurements via bootstrapping, and then a joint-sparse constraint is enforced
to ensure support consistency among multiple predictors. The final estimate is
obtained by averaging over the predictors. The performance limits
associated with different choices of number of bootstrap samples and number
of estimates is analyzed theoretically. Simulation results validate some of
the theoretical analysis, and show that the proposed method yields
state-of-the-art recovery performance, outperforming minimization and
a few other existing bootstrap-based techniques in the challenging case of low
levels of measurements and is preferable over other bagging-based methods in
the streaming setting since it performs better with small and for
data-sets with large sizes
Reducing Sampling Ratios Improves Bagging in Sparse Regression
Bagging, a powerful ensemble method from machine learning, improves the
performance of unstable predictors. Although the power of Bagging has been
shown mostly in classification problems, we demonstrate the success of
employing Bagging in sparse regression over the baseline method (L1
minimization). The framework employs the generalized version of the original
Bagging with various bootstrap ratios. The performance limits associated with
different choices of bootstrap sampling ratio L/m and number of estimates K is
analyzed theoretically. Simulation shows that the proposed method yields
state-of-the-art recovery performance, outperforming L1 minimization and
Bolasso in the challenging case of low levels of measurements. A lower L/m
ratio (60% - 90%) leads to better performance, especially with a small number
of measurements. With the reduced sampling rate, SNR improves over the original
Bagging by up to 24%. With a properly chosen sampling ratio, a reasonably small
number of estimates K = 30 gives satisfying result, even though increasing K is
discovered to always improve or at least maintain the performance.Comment: arXiv admin note: substantial text overlap with arXiv:1810.0374
Combinatorial Proofs of Two Overpartition Theorems Connected by a Universal Mock Theta Function
In 2015, Bringmann, Lovejoy and Mahlburg considered certain kinds
overpartitions, which can been seen as the overpartition analogue of Schur's
partition. The motivation of their work is that the difference between the
generating function of Schur's classical partitions and the generating
functions of the partitions in which the smallest part is excluded. The
difference between the two generating functions of partitions is a
specialization of the "universal" mock theta function g_3 which introduced by
Hickerson. To give an analogue of this, by using another universal mock theta
function g_2 instead of g_3, Bringmann Lovejoy and Mahlburg introduced two
kinds of overpartitions, which satisfy certain congruence conditions and
difference conditions with the smallest parts different. They prove these
theorems by using the q-differential equations. In this paper, we will give the
generating functions of these two kinds of overpartitions by combinatorial
technique.Comment: 12pages. arXiv admin note: text overlap with arXiv:1311.5483 by other
author
Benchmarking strong-field ionisation with atomic hydrogen
As the simplest atomic system, the hydrogen atom plays a key benchmarking
role in laser and quantum physics. Atomic hydrogen is a widely used atomic test
system for theoretical calculations of strong-field ionization, since
approximate theories can be directly compared to numerical solutions of the
time-dependent Schr\"odinger equation. However, relatively little experimental
data is available for comparison to these calculations, since atomic hydrogen
sources are difficult to construct and use. We review the existing experimental
results on strong-field ionization of atomic hydrogen in multi-cycle and
few-cycle laser pulses. Quantitative agreement has been achieved between
experiment and theoretical predictions at the 10% uncertainty level, and has
been used to develop an intensity calibration method with 1% uncertainty. Such
quantitative agreement can be used to certify experimental techniques as being
free from systematic errors, guaranteeing the accuracy of data obtained on
species other than H. We review the experimental and theoretical techniques
that enable these results.Comment: invited revie
Parity Considerations in Rogers-Ramanujan-Gordon Type Overpartitions
In 2010, Andrews considers a variety of parity questions connected to
classical partition identities of Euler, Rogers, Ramanujan and Gordon. As a
large part in his paper, Andrews considered the partitions by restricting the
parity of occurrences of even numbers or odd numbers in the
Rogers-Ramanujan-Gordon type. The Rogers-Ramanujan-Gordon type partition was
defined by Gordon in 1961 as a combinatorial generalization of the
Rogers-Ramaujan identities with odd moduli.
In 1974, Andrews derived an identity which can be considered as the
generating function counterpart of the Rogers-Ramanujan-Gordon theorem, and
since then it has been called the Andrews--Gordon identity. By revisting the
Andrews--Gordon identity Andrews extended his results by considering some
additional restrictions involving parities to obtain some
Rogers-Ramanujan-Gordon type theorems and Andrews--Gordon type identities. In
the end of Andrews' paper, he posed open problems. Most of Andrews'
open problems have been settled, but the th that "extend the parity indices
to overpartitions in a manner" has not. In 2013, Chen, Sang and Shi, derived
the overpartition analogues of the Rogers-Ramanujan-Gordon theorem and the
Andrews-Gordon identity. In this paper, we post some parity restrictions on
these overpartitions analogues to get some Rogers-Ramanujan-Gordon type
overpartition theorems
Congruences modulo for Rogers--Ramanujan--Gordon type overpartitions
In a recent work, Andrews defined the singular overpartitions with the goal
of presenting an overpartition analogue to the theorems of Rogers--Ramanujan
type for ordinary partitions with restricted successive ranks. As a small part
of his work, Andrews noted two congruences modulo for the number of
singular overpartitions prescribed by parameters and . It should be
noticed that this number equals the number of the Rogers--Ramanujan--Gordon
type overpartitions with which come from the overpartition analogue of
Gordon's Rogers--Ramanujan partition theorem introduced by Chen, Sang and Shi.
In this paper, we derive numbers of congruence identities modulo for the
number of Rogers--Ramanujan--Gordon type overpartitions
Mesoscale analyses of fungal networks as an approach for quantifying phenotypic traits
We investigate the application of mesoscopic response functions (MRFs) to
characterize a large set of networks of fungi and slime moulds grown under a
wide variety of different experimental treatments, including inter-species
competition and attack by fungivores. We construct 'structural networks' by
estimating cord conductances (which yield edge weights) from the experimental
data, and we construct 'functional networks' by calculating edge weights based
on how much nutrient traffic is predicted to occur along each edge. Both types
of networks have the same topology, and we compute MRFs for both families of
networks to illustrate two different ways of constructing taxonomies to group
the networks into clusters of related fungi and slime moulds. Although both
network taxonomies generate intuitively sensible groupings of networks across
species, treatments and laboratories, we find that clustering using the
functional-network measure appears to give groups with lower intra-group
variation in species or treatments. We argue that MRFs provide a useful
quantitative analysis of network behaviour that can (1) help summarize an
expanding set of increasingly complex biological networks and (2) help extract
information that captures subtle changes in intra- and inter-specific
phenotypic traits that are integral to a mechanistic understanding of fungal
behaviour and ecology. As an accompaniment to our paper, we also make a large
data set of fungal networks available in the public domain.Comment: 16 pages, 3 figures, 1 tabl
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