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arxiv_dataset-81001701.04592 | Regular black holes from semi-classical down to Planckian size
hep-th gr-qc hep-ph
In this paper we review various models of curvature singularity free black
holes. In the first part of the review we describe semi-classical solutions of
the Einstein equations which, however, contains a "quantum" input through the
matter source. We start by reviewing the early model by Bardeen where the
metric is regularized by-hand through a short-distance cut-off, which is
justified in terms of non-linear electro-dynamical effects. This a toy-model
model useful to point-out the common features shared by all regular
semi-classical black holes. Then, we solve Einstein equations with a Gaussian
source encoding the quantum spread of an elementary particle. We identify, the
a priori arbitrary, Gaussian width with the Compton wavelength of the quantum
particle. This Compton-Gauss model leads to the estimate of a terminal density
that a gravitationally collapsed object can achieve. We identify this density
to be the Planck density, and reformulate the Gaussian model assuming this as
its peak density. All these models, are physically reliable as long as the
black hole mass is big enough with respect to the Planck mass. In the truly
Planckian regime, the semi-classical approximation breaks down. In this case, a
fully quantum black hole description is needed. In the last part of this paper,
we propose a non-geometrical quantum model of Planckian black hole implementing
the Holographic Principle and realizing the "classicalization" scenario
recently introduced by Dvali and collaborators. The classical relation between
the mass and radius of the black hole emerges only in the classical limit, far
away from the Planck scale.
| arxiv topic:hep-th gr-qc hep-ph |
arxiv_dataset-81011701.04692 | A Gentle Introduction to a Beautiful Theorem of Molien
math.GM
The purpose of this note is to give an accessible proof of Moliens Theorem in
Invariant Theory, in the language of today's Linear Algebra and Group Theory,
in order to prevent this beautiful theorem from being forgotten.
| arxiv topic:math.GM |
arxiv_dataset-81021701.04792 | Performance of Step Network Using Simulation Tool
cs.NI
Nowadays distributed computing approach has become very popular due to
several advantages over the centralized computing approach as it also offers
high performance computing at a very low cost. Each router implements some
queuing mechanism for resources allocation in a best possible optimize manner
and governs with packet transmission and buffer mechanism. In this paper,
different types of queuing disciplines have been implemented for packet
transmission when the bandwidth is allocated as well as packet dropping occurs
due to buffer overflow. This gives result in latency in packet transmission, as
the packet has to wait in a queue which is to be transmitted again. Some common
queuing mechanisms are first in first out, priority queue and weighted fair
queuing, etc. This targets simulation in heterogeneous environment through
simulator tool to improve the quality of services by evaluating the performance
of said queuing disciplines. This is demonstrated by interconnecting
heterogeneous devices through step topology. In this paper, authors compared
data packet, voice and video traffic by analyzing the performance based on
packet dropped rate, delay variation, end to end delay and queuing delay and
how the different queuing discipline effects the applications and utilization
of network resources at the routers. Before evaluating the performance of the
connected devices, a Unified Modeling Language class diagram is designed to
represent the static model for evaluating the performance of step topology.
Results are described by taking the various case studies.
| arxiv topic:cs.NI |
arxiv_dataset-81031701.04892 | The Effect of Protoplanetary Disk Cooling Times on the Formation of Gas
Giant Planets by Gravitational Instability
astro-ph.EP
Observational evidence exists for the formation of gas giant planets on wide
orbits around young stars by disk gravitational instability, but the roles of
disk instability and core accretion for forming gas giants on shorter period
orbits are less clear. The controversy extends to population synthesis models
of exoplanet demographics and to hydrodynamical models of the fragmentation
process. The latter refers largely to the handling of radiative transfer in
three dimensional (3D) hydrodynamical models, which controls heating and
cooling processes in gravitationally unstable disks, and hence dense clump
formation. A suite of models using the $\beta$ cooling approximation is
presented here. The initial disks have masses of 0.091 $M_\odot$ and extend
from 4 to 20 AU around a 1 $M_\odot$ protostar. The initial minimum Toomre
$Q_i$ values range from 1.3 to 2.7, while $\beta$ ranges from 1 to 100. We show
that the choice of $Q_i$ is equal in importance to the $\beta$ value assumed:
high $Q_i$ disks can be stable for small $\beta$, when the initial disk
temperature is taken as a lower bound, while low $Q_i$ disks can fragment for
high $\beta$. These results imply that the evolution of disks toward low $Q_i$
must be taken into account in assessing disk fragmentation possibilities, at
least in the inner disk, i.e., inside about 20 AU. The models suggest that if
low $Q_i$ disks can form, there should be an as yet largely undetected
population of gas giants orbiting G dwarfs between about 6 AU and 16 AU.
| arxiv topic:astro-ph.EP |
arxiv_dataset-81041701.04992 | An improved derivation of the Smarr Formula for Lorentz-breaking gravity
gr-qc
Thermodynamical properties of black holes in gravitational theories without
Local Lorentz invariance have been subject to intense investigation in the past
years due to the presence of universal horizons, which are strong causal
barriers even for superluminal signals. Here we present a novel general method
for deriving the Smarr formula for this class of theories: in particular we
show that the Smarr formulae for Einstein-Aether theory and infrared Horava
gravity follow from scale invariance. We not only reproduce straightforwardly
previous findings for static black hole solutions, but we are also able to
generalise them to the case of stationary rotating black holes. Finally, we
apply our results to the rotating black holes with universal horizon as found
in three dimensions, from which we shall draw some lessons on the viability of
black hole thermodynamics for black hole solutions endowed with universal
horizons.
| arxiv topic:gr-qc |
arxiv_dataset-81051701.05092 | Two types of spurious damping forces potentially modeled in numerical
seismic nonlinear response history analysis
physics.geo-ph
The purpose of this paper is to provide practitioners with further insight
into spurious damping forces that can be generated in nonlinear seismic
response history analyses (RHA). The term 'spurious' is used to refer to
damping forces that are not present in an elastic system and appear as
nonlinearities develop: such damping forces are not necessarily intended and
appear as a result of modifications in the structural properties as it yields
or damages due to the seismic action. In this paper, two types of spurious
damping forces are characterized. Each type has often been treated separately
in the literature, but each has been qualified as 'spurious', somehow blurring
their differences. Consequently, in an effort to clarify the consequences of
choosing a particular viscous damping model for nonlinear RHA, this paper shows
that damping models that avoid spurious damping forces of one type do not
necessarily avoid damping forces of the other type.
| arxiv topic:physics.geo-ph |
arxiv_dataset-81061701.05192 | Observational calibration of the projection factor of Cepheids - III.
The long-period Galactic Cepheid RS Puppis
astro-ph.SR
The projection factor (p-factor) is an essential component of the classical
Baade-Wesselink (BW) technique, that is commonly used to determine the
distances to pulsating stars. It is a multiplicative parameter used to convert
radial velocities into pulsational velocities. As the BW distances are linearly
proportional to the p-factor, its accurate calibration for Cepheids is of
critical importance for the reliability of their distance scale. We focus on
the observational determination of the p-factor of the long-period Cepheid RS
Pup (P = 41.5 days). This star is particularly important as this is one of the
brightest Cepheids in the Galaxy and an analog of the Cepheids used to
determine extragalactic distances. An accurate distance of 1910 +/- 80 pc (+/-
4.2%) has recently been determined for RS Pup using the light echoes
propagating in its circumstellar nebula. We combine this distance with new
VLTI/PIONIER interferometric angular diameters, photometry and radial
velocities to derive the p-factor of RS Pup using the code
Spectro-Photo-Interferometry of Pulsating Stars (SPIPS). We obtain p = 1.250
+/- 0.064 (+/-5.1%), defined for cross-correlation radial velocities. Together
with measurements from the literature, the p-factor of RS Pup confirms the good
agreement of a constant p = 1.293 +/- 0.039 (+/-3.0%) model with the
observations. We conclude that the p-factor of Cepheids is constant or mildly
variable over a broad range of periods (3.7 to 41.5 days).
| arxiv topic:astro-ph.SR |
arxiv_dataset-81071701.05292 | Relativistic full-potential multiple scattering theory: An ab initio
method and its applications
cond-mat.mtrl-sci
The Green function plays an essential role in the Kohn-Korringa-Rostocker
(KKR) multiple scattering method. In practice, it is constructed from the
regular and irregular solutions of the local Kohn-Sham equation and robust
methods exist for spherical potentials. However, when applied to a
non-spherical potential, numerical errors from the irregular solutions give
rise to pathological behaviors of the charge density at small radius. Here we
present a full-potential implementation of the relativistic KKR method to
perform \textit{ab initio} self-consistent calculation by directly solving the
Dirac differential equations. The pathology around the origin is completely
eliminated with the help of an efficient pole-searching technique. This method
is utilized to investigate the crystal structures of polonium and their bulk
properties. The noble metals are also calculated, both as a test of our method
and to study the relativistic effects.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-81081701.05392 | On Optimal Online Algorithms for Energy Harvesting Systems with
Continuous Energy and Data Arrivals
cs.IT math.IT
Energy harvesting (EH) has been developed to extend the lifetimes of
energy-limited communication systems. In this letter, we consider a single-user
EH communication system, in which both of the arrival data and the harvested
energy curves are modeled as general functions. Unlike most of the works in the
field, we investigate the online algorithms which only acquire the causal
information of the arrival data and the harvested energy processes. We study
how well the optimal online algorithm works compared with the optimal offline
algorithm, and thus our goal is to find the lower and upper bounds for the
ratio of the completion time in the optimal online algorithm to the optimal
offline algorithm. We propose two online algorithms which achieve the upper
bound of 2 on this ratio. Also, we show that this ratio is 2 for the optimal
online algorithm.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-81091701.05492 | Perfect phylogenies via branchings in acyclic digraphs and a
generalization of Dilworth's theorem
cs.DM cs.CC cs.DS math.CO q-bio.PE
Motivated by applications in cancer genomics and following the work of
Hajirasouliha and Raphael (WABI 2014), Hujdurovi\'c et al. (IEEE TCBB, to
appear) introduced the minimum conflict-free row split (MCRS) problem: split
each row of a given binary matrix into a bitwise OR of a set of rows so that
the resulting matrix corresponds to a perfect phylogeny and has the minimum
possible number of rows among all matrices with this property. Hajirasouliha
and Raphael also proposed the study of a similar problem, in which the task is
to minimize the number of distinct rows of the resulting matrix. Hujdurovi\'c
et al. proved that both problems are NP-hard, gave a related characterization
of transitively orientable graphs, and proposed a polynomial-time heuristic
algorithm for the MCRS problem based on coloring cocomparability graphs.
We give new, more transparent formulations of the two problems, showing that
the problems are equivalent to two optimization problems on branchings in a
derived directed acyclic graph. Building on these formulations, we obtain new
results on the two problems, including: (i) a strengthening of the heuristic by
Hujdurovi\'c et al. via a new min-max result in digraphs generalizing
Dilworth's theorem, which may be of independent interest, (ii) APX-hardness
results for both problems, (iii) approximation algorithms, and (iv)
exponential-time algorithms solving the two problems to optimality faster than
the na\"ive brute-force approach. Our work relates to several well studied
notions in combinatorial optimization: chain partitions in partially ordered
sets, laminar hypergraphs, and (classical and weighted) colorings of graphs.
| arxiv topic:cs.DM cs.CC cs.DS math.CO q-bio.PE |
arxiv_dataset-81101701.05592 | Invariants of Cohen-Macaulay rings associated to their canonical ideals
math.AC
The purpose of this paper is to introduce new invariants of Cohen-Macaulay
local rings. Our focus is the class of Cohen-Macaulay local rings that admit a
canonical ideal. Attached to each such ring R with a canonical ideal C, there
are integers--the type of R, the reduction number of C--that provide valuable
metrics to express the deviation of R from being a Gorenstein ring. We enlarge
this list with other integers--the roots of R and several canonical degrees.
The latter are multiplicity based functions of the Rees algebra of C.
| arxiv topic:math.AC |
arxiv_dataset-81111701.05692 | Finiteness theorems for holomorphic mappings from products of hyperbolic
Riemann surfaces
math.CV
We prove that the space of dominant/non-constant holomorphic mappings from a
product of hyperbolic Riemann surfaces of finite type into certain hyperbolic
manifolds with universal cover a bounded domain is a finite set.
| arxiv topic:math.CV |
arxiv_dataset-81121701.05792 | Analysis of Proportional Fair Scheduling Under Bursty On-Off Traffic
cs.IT cs.NI math.IT
Proportional fair scheduling (PFS) has been adopted as a standard solution
for fair resource allocation in modern wireless cellular networks. With the
emergence of heterogeneous networks with widely varying user loads, it is of
great importance to characterize the performance of PFS under bursty traffic,
which is the case in most wireless streaming and data transfer services. In
this letter, we provide the first analytical solution to the performance of PFS
under bursty on-off traffic load. We use the Gaussian approximation model to
derive a closed-form expression of the achievable user data rates. In order to
further improve the accuracy of our baseline analytical solution for multi-cell
networks, we design a hybrid approximation by employing multi-interference
analysis. The simulation results verify that our model guarantees extremely low
data rate estimation error, which is further insensitive to changes in session
duration, traffic load and user density.
| arxiv topic:cs.IT cs.NI math.IT |
arxiv_dataset-81131701.05892 | Bayesian Static Parameter Estimation for Partially Observed Diffusions
via Multilevel Monte Carlo
stat.CO math.PR
In this article we consider static Bayesian parameter estimation for
partially observed diffusions that are discretely observed. We work under the
assumption that one must resort to discretizing the underlying diffusion
process, for instance using the Euler-Maruyama method. Given this assumption,
we show how one can use Markov chain Monte Carlo (MCMC) and particularly
particle MCMC [Andrieu, C., Doucet, A. and Holenstein, R. (2010). Particle
Markov chain Monte Carlo methods (with discussion). J. R. Statist. Soc. Ser. B,
72, 269--342] to implement a new approximation of the multilevel (ML) Monte
Carlo (MC) collapsing sum identity. Our approach comprises constructing an
approximate coupling of the posterior density of the joint distribution over
parameter and hidden variables at two different discretization levels and then
correcting by an importance sampling method. The variance of the weights are
independent of the length of the observed data set. The utility of such a
method is that, for a prescribed level of mean square error, the cost of this
MLMC method is provably less than i.i.d. sampling from the posterior associated
to the most precise discretization. However the method here comprises using
only known and efficient simulation methodologies. The theoretical results are
illustrated by inference of the parameters of two prototypical processes given
noisy partial observations of the process: the first is an Ornstein Uhlenbeck
process and the second is a more general Langevin equation.
| arxiv topic:stat.CO math.PR |
arxiv_dataset-81141701.05992 | Some Open Problems on Locally Finite or Locally Nilpotent Derivations
and ${\mathcal E}$-Derivations
math.RA math.AC
Let $R$ be a commutative ring and $\mathcal A$ an $R$-algebra. An
$R$-$\mathcal E$-derivation of $\mathcal A$ is an $R$-linear map of the form
$\operatorname{I}-\phi$ for some $R$-algebra endomorphism $\phi$ of $\mathcal
A$, where $\operatorname{I}$ denotes the identity map of $\mathcal A$. In this
paper we discuss some open problems on whether or not the image of a locally
finite $R$-derivation or $R$-$\mathcal E$-derivation of $\mathcal A$ is a
Mathieu subspace [Z2, Z3] of $\mathcal A$, and whether or not a locally
nilpotent $R$-derivation or $R$-$\mathcal E$-derivation of $\mathcal A$ maps
every ideal of $\mathcal A$ to a Mathieu subspace of $\mathcal A$. We propose
and discuss two conjectures which state that both questions above have positive
answers if the base ring $R$ is a field of characteristic zero. We give some
examples to show the necessity of the conditions of the two conjectures, and
discuss some positive cases known in the literature. We also show some cases of
the two conjectures. In particular, both the conjectures are proved for locally
finite or locally nilpotent algebraic derivations and $\mathcal E$-derivations
of integral domains of characteristic zero.
| arxiv topic:math.RA math.AC |
arxiv_dataset-81151701.06092 | Level set shape and topology optimization of finite strain bilateral
contact problems
math.OC
This paper presents a method for the optimization of multi-component
structures comprised of two and three materials considering large motion
sliding contact and separation along interfaces. The structural geometry is
defined by an explicit level set method, which allows for both shape and
topology changes. The mechanical model assumes finite strains, a nonlinear
elastic material behavior, and a quasi-static response. Identification of
overlapping surface position is handled by a coupled parametric representation
of contact surfaces. A stabilized Lagrange method and an active set strategy
are used to model frictionless contact and separation. The mechanical model is
discretized by the extended finite element method which maintains a clear
definition of geometry. Face-oriented ghost penalization and dynamic relaxation
are implemented to improve the stability of the physical response prediction. A
nonlinear programming scheme is used to solve the optimization problem, which
is regularized by introducing a perimeter penalty into the objective function.
Sensitivities are determined by the adjoint method. The main characteristics of
the proposed method are studied by numerical examples in two dimensions. The
numerical results demonstrate improved design performance when compared to
models optimized with a small strain assumption. Additionally, examples with
load path dependent objectives display non-intuitive designs.
| arxiv topic:math.OC |
arxiv_dataset-81161701.06192 | Multiplicative Energy of Shifted Subgroups and Bounds On Exponential
Sums with Trinomials in Finite Fields
math.NT
We give a new bound on colinear triples in subgroups of prime finite fields
and use it to give some new bounds on exponential sums with trinomials.
| arxiv topic:math.NT |
arxiv_dataset-81171701.06292 | Spin $q$-Whittaker polynomials
math.CO cond-mat.stat-mech math-ph math.MP
We introduce and study a one-parameter generalization of the q-Whittaker
symmetric functions. This is a family of multivariate symmetric polynomials,
whose construction may be viewed as an application of the procedure of fusion
from integrable lattice models to a vertex model interpretation of a
one-parameter generalization of Hall-Littlewood polynomials from [Bor17, BP16a,
BP16b].
We prove branching and Pieri rules, standard and dual (skew) Cauchy summation
identities, and an integral representation for the new polynomials.
| arxiv topic:math.CO cond-mat.stat-mech math-ph math.MP |
arxiv_dataset-81181701.06392 | Rare radiative charm decays within the standard model and beyond
hep-ph hep-ex
We present standard model (SM) estimates for exclusive $c \to u \gamma$
processes in heavy quark and hybrid frameworks. Measured branching ratios
${\cal{B}}(D^0 \to (\phi, \bar K^{*0}) \gamma)$ are at or somewhat exceeding
the upper range of the SM and suggest slow convergence of the $1/m_D,
\alpha_s$-expansion. Model-independent constraints on $|\Delta C|=|\Delta U|=1$
dipole operators from ${\cal{B}}(D^0 \to \rho^0 \gamma)$ data are obtained.
Predictions and implications for leptoquark models are worked out. While
branching ratios are SM-like CP asymmetries $\lesssim 10 \%$ can be induced. In
SUSY deviations from the SM can be even larger with CP asymmetries of $O(0.1)$.
If $\Lambda_c$-baryons are produced polarized, such as at the $Z$-pole, an
angular asymmetry in $\Lambda_c \to p \gamma$ decays can be studied that is
sensitive to chirality-flipped contributions.
| arxiv topic:hep-ph hep-ex |
arxiv_dataset-81191701.06492 | Binding energies: new values and impact on the efficiency of chemical
desorption
astro-ph.GA
Recent laboratory measurements have confirmed that chemical desorption
(desorption of products due to exothermic surface reactions) can be an
efficient process. The impact of including this process into gas-grain chemical
models entirely depends on the formalism used and the associated parameters.
Among these parameters, binding energies are probably the most uncertain ones
for the moment. We propose a new model to compute binding energy of species to
water ice surfaces. We have also compared the model results using either the
new chemical desorption model proposed by Minissale et al. (2016) or the one of
Garrod et al. (2007). The new binding energies have a strong impact on the
formation of complex organic molecules. In addition, the new chemical
desorption model from Minissale produces a much smaller desorption of these
species and also of methanol. Combining the two effects, the abundances of
CH3OH and COMs observed in cold cores cannot be reproduced by astrochemical
models anymore.
| arxiv topic:astro-ph.GA |
arxiv_dataset-81201701.06592 | Limit linear series and ranks of multiplication maps
math.AG
We develop a new technique for studying ranks of multiplication maps for
linear series via limit linear series and degenerations to chains of genus-1
curves. We use this approach to prove a purely elementary criterion for proving
cases of the Maximal Rank Conjecture, and then apply the criterion to several
ranges of cases, giving a new proof of the case of quadrics, and also treating
several families in the case of cubics. Our proofs do not require restrictions
on direction of approach, so we recover new information on the locus in the
moduli space of curves on which the maximal rank condition fails.
| arxiv topic:math.AG |
arxiv_dataset-81211701.06692 | A geometric approach to cut-generating functions
math.OC math.CO math.FA math.MG
The cutting-plane approach to integer programming was initiated more that 40
years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed
integer set in tableau form and Balas introduced intersection cuts for the
corner polyhedron. This line of research was left dormant for several decades
until relatively recently, when a paper of Andersen, Louveaux, Weismantel and
Wolsey generated renewed interest in the corner polyhedron and intersection
cuts. Recent developments rely on tools drawn from convex analysis, geometry
and number theory, and constitute an elegant bridge between these areas and
integer programming. We survey these results and highlight recent breakthroughs
in this area.
| arxiv topic:math.OC math.CO math.FA math.MG |
arxiv_dataset-81221701.06792 | Ultra-High-Energy Cosmic Rays from Radio Galaxies
astro-ph.HE
Radio galaxies are intensively discussed as the sources of cosmic rays
observed above about $3\,{\times}\,10^{18}\,\text{eV}$, called ultra-high
energy cosmic rays (UHECRs). We present a first, systematic approach that takes
the individual characteristics of these sources into account, as well as the
impact of the extragalactic magnetic-field structures up to a distance of 120
Mpc. We use a mixed simulation setup, based on 3D simulations of UHECRs ejected
by observed, individual radio galaxies taken out to a distance of 120 Mpc, and
on 1D simulations over a continuous source distribution contributing from
beyond 120 Mpc. Additionally, we include the ultra-luminous radio galaxy Cygnus
A at a distance of about $250\,$Mpc, as its contribution is so strong that it
must be considered as an individual point source. The implementation of the
UHECR ejection in our simulation setup is based on a detailed consideration of
the physics of radio jets and standard first-order Fermi acceleration. We show
that the average contribution of radio galaxies taken over a very large volume
cannot explain the observed features of UHECRs measured at Earth. However, we
obtain excellent agreement with the spectrum, composition, and
arrival-direction distribution of UHECRs measured by the Pierre Auger
Observatory, if we assume that most UHECRs observed arise from only two
sources: The ultra-luminous radio galaxy Cygnus A, providing a mostly light
composition of nuclear species dominating up to about
$6\,{\times}\,10^{19}\,$eV, and the nearest radio galaxy Centaurus A, providing
a heavy composition dominating above $6\,{\times}\,10^{19}\,$eV. Here we have
to assume that extragalactic magnetic fields out to 250 Mpc, which we did not
include in the simulation, are able to isotropize the UHECR events at about 8
EeV arriving from Cygnus A.
| arxiv topic:astro-ph.HE |
arxiv_dataset-81231701.06892 | Reconstruction of Scalar Potentials in $f(R,R_{\alpha\beta}
R^{\alpha\beta},\phi)$ theory of gravity
gr-qc
In this paper, we explore the nature of scalar field potential in $f(R,
R_{\alpha\beta} R^{\alpha\beta},\phi)$ gravity using a well-motivated
reconstruction scheme for flat FRW geometry. The beauty of this scheme lies in
the assumption that the Hubble parameter can be expressed in terms of scalar
field and vice versa. Firstly, we develop field equations in this gravity and
present some general explicit forms of scalar field potential via this
technique. In the first case, we take De Sitter universe model and construct
some field potentials by taking different cases for coupling function. In the
second case, we derive some field potentials using power law model in the
presence of different matter sources like barotropic fluid, cosmological
constant and Chaplygin gas for some coupling functions. From graphical
analysis, it is concluded that using some specific values of the involved
parameters, the reconstructed scalar field potentials are cosmologically viable
in both cases.
| arxiv topic:gr-qc |
arxiv_dataset-81241701.06992 | Reconstructing CMB fluctuations and the mean reionization optical depth
astro-ph.CO hep-ph
The Thomson optical depth from reionization is a limiting factor in measuring
the amplitude of primordial fluctuations, and hence in measuring physics that
affects the low-redshift amplitude, such as the neutrino masses. Current
constraints on the optical depth, based on directly measuring large-scale
cosmic microwave background (CMB) polarization, are challenging due to
foregrounds and systematic effects. Here, we consider an indirect measurement
of large-scale polarization, using observed maps of small-scale polarization
together with maps of fields that distort the CMB, such as CMB lensing and
patchy reionization. We find that very futuristic CMB surveys will be able to
reconstruct large-scale polarization, and thus the mean optical depth, using
only measurements on small scales.
| arxiv topic:astro-ph.CO hep-ph |
arxiv_dataset-81251701.07092 | Inverting the Kasteleyn matrix for holey hexagons
math.CO math-ph math.MP
Consider a semi-regular hexagon on the triangular lattice (that is, the
lattice consisting of unit equilateral triangles, drawn so that one family of
lines is vertical). Rhombus (or lozenge) tilings of this region may be
represented in at least two very different ways: as families of
non-intersecting lattice paths; or alternatively as perfect matchings of a
certain sub-graph of the hexagonal lattice. In this article we show how the
lattice path representation of tilings may be utilised in order to calculate
the entries of the inverse Kasteleyn matrix that arises from interpreting
tilings as perfect matchings. Our main result gives precisely the inverse
Kasteleyn matrix (up to a possible change in sign) for a semi-regular hexagon
of side lengths $a,b,c,a,b,c$ (going clockwise from the south-west side). Not
only does this theorem generalise a number of known results regarding tilings
of hexagons that contain punctures, but it also provides a new formulation
through which we may attack problems in statistical physics such as Ciucu's
electrostatic conjecture.
| arxiv topic:math.CO math-ph math.MP |
arxiv_dataset-81261701.07192 | Minimal bi-ideals in regular and completely regular ordered semigroups
math.RA
Here we characterize regular and completely regular ordered semigroups by
their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a
minimal right ideal and a minimal left ideal. Furthermore, we show that every
bi-ideal in a completely regular ordered semigroup is minimal and hence a
regular ordered semigroup S is completely regular if and only if S is union its
of minimal bi-ideals.
| arxiv topic:math.RA |
arxiv_dataset-81271701.07292 | The bubble algebras at roots of unity
math.RT
We introduce multi-colour partition algebras $P_{n,m}(\delta_0, ...,
\delta_{m-1})$, which are generalization of both bubble algebras and partition
algebras, then define the bubble algebra $T_{n,m}(\delta_0, ..., \delta_{m-1})$
as a sub-algebra of the algebra $P_{n,m}(\delta_0, ..., \delta_{m-1})$. We
present general techniques to determine the structure of the bubble algebra
over the complex field in the non-semisimple case.
| arxiv topic:math.RT |
arxiv_dataset-81281701.07392 | Generation of Broadband Mid-IR and UV Light in Gas-Filled Single-Ring
Hollow-Core PCF
physics.optics
We report generation of an ultrafast supercontinuum extending into the mid-
infrared in gas-filled single-ring hollow-core photonic crystal fiber (SR-PCF)
pumped by 1.7 $\mu$m light from an optical parametric amplifier. The simple
fiber structure offers shallow dispersion and flat transmission in the near and
mid-infrared, enabling the generation of broadband spectra extending from 300
nm to 3.1 $\mu$m, with a total energy of a few $\mu$J. In addition, we report
the emission of ultraviolet dispersive waves whose frequency can be tuned
simply by adjusting the pump wavelength. SR-PCF also provides an effective
means of compressing and delivering tunable ultrafast pulses in the near and
mid-infrared spectral regions.
| arxiv topic:physics.optics |
arxiv_dataset-81291701.07492 | Path abstraction
math.CO
Given the set of paths through a digraph, the result of uniformly deleting
some vertices and identifying others along each path is coherent in such a way
as to yield the set of paths through another digraph, called a \emph{path
abstraction} of the original digraph. The construction of path abstractions is
detailed and relevant basic results are established; generalizations are also
discussed. Connections with random digraphs are also illustrated.
| arxiv topic:math.CO |
arxiv_dataset-81301701.07592 | Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$
math.GT
We classify up to diffeomorphism all smooth manifolds homeomorphic to the
complex projective m-space $\mathbb{C}P^{m}$ for $m = 5, 6, 7$ and $8$. As an
application, for $m = 7$ and $8$, we compute the smooth tangential structure
set of $\mathbb{C}P^{m}$ and obtain a bound on the number of smooth homotopy
complex projective m-spaces with given Pontryagin classes up to
orientation-preserving diffeomorphism. We also show that there exists a smooth
manifold which is tangentially homotopy equivalent but not homeomorphic to
$\mathbb{C}P^{8}$.
| arxiv topic:math.GT |
arxiv_dataset-81311701.07692 | Two regimes of interaction of a Hot Jupiter's escaping atmosphere with
the stellar wind and generation of energized atomic hydrogen corona
astro-ph.EP astro-ph.SR
The interaction of escaping upper atmosphere of a hydrogen rich
non-magnetized analog of HD209458b with a stellar wind of its host G-type star
at different orbital distances is simulated with a 2D axisymmetric multi-fluid
hydrodynamic model. A realistic sun-like spectrum of XUV radiation which
ionizes and heats the planetary atmosphere, hydrogen photo-chemistry, as well
as stellar-planetary tidal interaction are taken into account to generate
self-consistently an atmospheric hydrodynamic outflow. Two different regimes of
the planetary and stellar winds interaction have been modelled. These are: 1)
the "captured by the star" regime, when the tidal force and pressure gradient
drive the planetary material beyond the Roche lobe towards the star, and 2) the
"blown by the wind" regime, when sufficiently strong stellar wind confines the
escaping planetary atmosphere and channels it into the tail. The model
simulates in details the hydrodynamic interaction between the planetary atoms,
protons and the stellar wind, as well as the production of energetic neutral
atoms (ENAs) around the planet due to charge-exchange between planetary atoms
and stellar protons. The revealed location and shape of the ENA cloud either as
a paraboloid shell between ionopause and bowshock (for the "blown by the wind"
regime), or a turbulent layer at the contact boundary between the planetary
stream and stellar wind (for the "captured by the star" regime) are of
importance for the interpretation of Ly{\alpha} absorption features in
exoplanetary transit spectra and characterization of the plasma environments.
| arxiv topic:astro-ph.EP astro-ph.SR |
arxiv_dataset-81321701.07792 | On Lattice Calculation of Electric Dipole Moments and Form Factors of
the Nucleon
hep-lat nucl-th
We analyze commonly used expressions for computing the nucleon electric
dipole form factors (EDFF) $F_3$ and moments (EDM) on a lattice and find that
they lead to spurious contributions from the Pauli form factor $F_2$ due to
inadequate definition of these form factors when parity mixing of lattice
nucleon fields is involved. Using chirally symmetric domain wall fermions, we
calculate the proton and the neutron EDFF induced by the CP-violating quark
chromo-EDM interaction using the corrected expression. In addition, we
calculate the electric dipole moment of the neutron using background electric
field that respects time translation invariance and boundary conditions, and
find that it decidedly agrees with the new formula but not the old formula for
$F_3$. Finally, we analyze some selected lattice results for the nucleon EDM
and observe that after the correction is applied, they either agree with zero
or are substantially reduced in magnitude, thus reconciling their difference
from phenomenological estimates of the nucleon EDM.
| arxiv topic:hep-lat nucl-th |
arxiv_dataset-81331701.07892 | SDSS J105754.25+275947.5: a period-bounce eclipsing cataclysmic variable
with the lowest-mass donor yet measured
astro-ph.SR
We present high-speed, multicolour photometry of the faint, eclipsing
cataclysmic variable (CV) SDSS J105754.25+275947.5. The light from this system
is dominated by the white dwarf. Nonetheless, averaging many eclipses reveals
additional features from the eclipse of the bright spot. This enables the
fitting of a parameterised eclipse model to these average light curves,
allowing the precise measurement of system parameters. We find a mass ratio of
q = 0.0546 $\pm$ 0.0020 and inclination i = 85.74 $\pm$ 0.21$^{\circ}$. The
white dwarf and donor masses were found to be M$_{\mathrm{w}}$ = 0.800 $\pm$
0.015 M$_{\odot}$ and M$_{\mathrm{d}}$ = 0.0436 $\pm$ 0.0020 M$_{\odot}$,
respectively. A temperature T$_{\mathrm{w}}$ = 13300 $\pm$ 1100 K and distance
d = 367 $\pm$ 26 pc of the white dwarf were estimated through fitting model
atmosphere predictions to multicolour fluxes. The mass of the white dwarf in
SDSS 105754.25+275947.5 is close to the average for CV white dwarfs, while the
donor has the lowest mass yet measured in an eclipsing CV. A low-mass donor and
an orbital period (90.44 min) significantly longer than the period minimum
strongly suggest that this is a bona fide period-bounce system, although
formation from a white dwarf/brown dwarf binary cannot be ruled out. Very few
period-minimum/period-bounce systems with precise system parameters are
currently known, and as a consequence the evolution of CVs in this regime is
not yet fully understood.
| arxiv topic:astro-ph.SR |
arxiv_dataset-81341701.07992 | HJB equations in infinite dimension and optimal control of stochastic
evolution equations via generalized Fukushima decomposition
math.PR
A stochastic optimal control problem driven by an abstract evolution equation
in a separable Hilbert space is considered. Thanks to the identification of the
mild solution of the state equation as $\nu$-weak Dirichlet process, the value
processes is proved to be a real weak Dirichlet process. The uniqueness of the
corresponding decomposition is used to prove a verification theorem. Through
that technique several of the required assumptions are milder than those
employed in previous contributions about non-regular solutions of
Hamilton-Jacobi-Bellman equations.
| arxiv topic:math.PR |
arxiv_dataset-81351701.08092 | Double-sided probing by map of Asplund's distances using Logarithmic
Image Processing in the framework of Mathematical Morphology
cs.CV math.NA
We establish the link between Mathematical Morphology and the map of
Asplund's distances between a probe and a grey scale function, using the
Logarithmic Image Processing scalar multiplication. We demonstrate that the map
is the logarithm of the ratio between a dilation and an erosion of the function
by a structuring function: the probe. The dilations and erosions are mappings
from the lattice of the images into the lattice of the positive functions.
Using a flat structuring element, the expression of the map of Asplund's
distances can be simplified with a dilation and an erosion of the image; these
mappings stays in the lattice of the images. We illustrate our approach by an
example of pattern matching with a non-flat structuring function.
| arxiv topic:cs.CV math.NA |
arxiv_dataset-81361701.08192 | A construction of hyperk\"ahler metrics through Riemann-Hilbert problems
II
math.CA
We develop the theory of Riemann-Hilbert problems necessary for the results
in part one of this series of papers. In particular, we obtain solutions for a
family of non-linear Riemann-Hilbert problems through classical contraction
principles and saddle-point estimates. We use compactness arguments to obtain
the required smoothness property on solutions. We also consider limit cases of
these Riemann-Hilbert problems where the jump function develops discontinuities
of the first kind together with zeroes of a specific order at isolated points
in the contour. Solutions through Cauchy integrals are still possible and they
have at worst a branch singularity at points where the jump function is
discontinuous and a zero for points where the jump vanishes.
| arxiv topic:math.CA |
arxiv_dataset-81371701.08292 | Kneser ranks of random graphs and minimum difference representations
math.CO
Every graph $G=(V,E)$ is an induced subgraph of some Kneser graph of rank
$k$, i.e., there is an assignment of (distinct) $k$-sets $v \mapsto A_v$ to the
vertices $v\in V$ such that $A_u$ and $A_v$ are disjoint if and only if $uv\in
E$. The smallest such $k$ is called the Kneser rank of $G$ and denoted by
$f_{\rm Kneser}(G)$. As an application of a result of Frieze and Reed
concerning the clique cover number of random graphs we show that for constant
$0< p< 1$ there exist constants $c_i=c_i(p)>0$, $i=1,2$ such that with high
probability \[ c_1 n/(\log n)< f_{\rm Kneser}(G) < c_2 n/(\log n). \] We apply
this for other graph representations defined by Boros, Gurvich and Meshulam. A
{\em $k$-min-difference representation} of a graph $G$ is an assignment of a
set $A_i$ to each vertex $i\in V(G)$ such that \[ ij\in E(G) \,\,
\Leftrightarrow \, \, \min \{|A_i\setminus A_j|,|A_j\setminus A_i| \}\geq k. \]
The smallest $k$ such that there exists a $k$-min-difference representation of
$G$ is denoted by $f_{\min}(G)$. Balogh and Prince proved in 2009 that for
every $k$ there is a graph $G$ with $f_{\min}(G)\geq k$. We prove that there
are constants $c''_1, c''_2>0$ such that $c''_1 n/(\log n)< f_{\min}(G) <
c''_2n/(\log n)$ holds for almost all bipartite graphs $G$ on $n+n$ vertices.
| arxiv topic:math.CO |
arxiv_dataset-81381701.08392 | On optimal control of forward backward stochastic differential equations
math.OC math.PR
We consider a control problem where the system is driven by a decoupled as
well as a coupled forward-backward stochastic differential equation. We prove
the existence of an optimal control in the class of relaxed controls, which are
measure-valued processes, generalizing the usual strict controls. The proof is
based on some tightness properties and weak convergence on the space D of
c\`adl\`ag functions, endowed with the Jakubowsky S-topology. Moreover, under
some convexity assumptions, we show that the relaxed optimal control is
realized by a strict control.
| arxiv topic:math.OC math.PR |
arxiv_dataset-81391701.08492 | On Zero Error Capacity of Nearest Neighbor Error Channels with
Multilevel Alphabet
cs.IT math.IT
This paper studies the zero error capacity of the Nearest Neighbor Error
(NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted
symbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumed
that only one element error to a nearest neighbor element in a transmitted
symbol can occur. The NNE channels can be considered as a special type of
limited magnitude error channels, and it is closely related to error models for
flash memories. In this paper, we derive a lower bound of the zero error
capacity of the NNE channels based on a result of the perfect Lee codes. An
upper bound of the zero error capacity of the NNE channels is also derived from
a feasible solution of a linear programming problem defined based on the
confusion graphs of the NNE channels. As a result, a concise formula of the
zero error capacity is obtained using the lower and upper bounds.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-81401701.08592 | Global solvability and convergence of the Euler-Poincar\'e
regularization of the two-dimensional Euler equations
math.AP
We study the Euler-Poincar\'e equations that are the regularized Euler
equations derived from the Euler-Poincar\'e framework. It is noteworthy to
remark that the Euler-Poincar\'e equations are a generalization of two
well-known regularizations, the vortex blob method and the Euler-$\alpha$
equations. We show the global existence of a unique weak solution for the
two-dimensional (2D) Euler-Poincar\'e equations with the initial vorticity in
the space of Radon measure. This is a remarkable feature of these equations
since the existence of weak solutions with the Radon measure initial vorticity
has not been established in general for the 2D Euler equations. We also show
that weak solutions of the 2D Euler-Poincar\'e equations converge to those of
the 2D Euler equations in the limit of the regularization parameter when the
initial vorticity belongs to the space of integrable and bounded functions.
| arxiv topic:math.AP |
arxiv_dataset-81411701.08692 | Coarse-Grained Incompressible Magnetohydrodynamics: analyzing the
turbulent cascades
astro-ph.SR astro-ph.GA physics.flu-dyn physics.plasm-ph
We formulate a coarse-graining approach to the dynamics of
magnetohydrodynamic (MHD) fluids at a continuum of length-scales. In this
methodology, effective equations are derived for the observable velocity and
magnetic fields spatially-averaged at an arbitrary scale of resolution. The
microscopic equations for the bare velocity and magnetic fields are
renormalized by coarse-graining to yield macroscopic effective equations that
contain both a subscale stress and a subscale electromotive force (EMF)
generated by nonlinear interaction of eliminated fields and plasma motions. At
large coarse-graining length-scales, the direct dissipation of invariants by
microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is
shown to be negligible. The balance at large scales is dominated instead by the
subscale nonlinear terms, which can transfer invariants across scales, and are
interpreted in terms of work concepts for energy and in terms of topological
flux-linkage for the two helicities. An important application of this approach
is to MHD turbulence, where the coarse-graining length $\ell$ lies in the
inertial cascade range. We show that in the case of sufficiently rough velocity
and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and
can persist to arbitrarily small scales. Although closed expressions are not
available for subscale stress and subscale EMF, we derive rigorous upper bounds
on the effective dissipation they produce in terms of scaling exponents of the
velocity and magnetic fields. These bounds provide exact constraints on
phenomenological theories of MHD turbulence in order to allow the nonlinear
cascade of energy and cross-helicity. On the other hand, we show that the
forward cascade of magnetic helicity to asymptotically small scales is
impossible unless 3rd-order moments of either velocity or magnetic field become
infinite.
| arxiv topic:astro-ph.SR astro-ph.GA physics.flu-dyn physics.plasm-ph |
arxiv_dataset-81421701.08792 | On slowly rotating magnetized white dwarfs
astro-ph.HE
Rotating magnetized white dwarfs are studied within the framework of general
relativity using Hartle's formalism. Matter inside magnetized white dwarfs is
described by an equation of state of particles under the action of a constant
magnetic field which introduces anisotropic pressures. Our study is done for
values of magnetic field below $10^{13}$ G -a threshold of the maximum magnetic
field obtained by the cylindrical metric solution- and typical densities of
WDs. The effects of the rotation and magnetic field combined are discussed, we
compute relevant magnitudes such as the moment of inertia, quadrupole moment
and eccentricity.
| arxiv topic:astro-ph.HE |
arxiv_dataset-81431701.08892 | Reshetnyak rigidity for Riemannian manifolds
math.DG math.AP
We prove two rigidity theorems for maps between Riemannian manifolds. First,
we prove that a Lipschitz map $f:M\to N$ between two oriented Riemannian
manifolds, whose differential is almost everywhere an orientation-preserving
isometry, is an isometric immersion. This theorem was previously proved using
regularity theory for conformal maps; we give a new, simple proof, by
generalizing the Piola identity for the cofactor operator. Second, we prove
that if there exists a sequence of mapping $f_n:M\to N$, whose differentials
converge in $L^p$ to the set of orientation-preserving isometries, then there
exists a subsequence converging to an isometric immersion. These results are
generalizations of celebrated rigidity theorems by Liouville (1850) and
Reshetnyak (1967) from Euclidean to Riemannian settings. Finally, we describe
applications of these theorems to non-Euclidean elasticity and to convergence
notions of manifolds.
| arxiv topic:math.DG math.AP |
arxiv_dataset-81441701.08992 | Spectrum and mass anomalous dimension of SU(2) gauge theories with
fermions in the adjoint representation: from $N_f=1/2$ to $N_f=2$
hep-lat
We summarize our results concerning the spectrum and mass anomalous dimension
of SU(2) gauge theories with various numbers of fermions in the adjoint
representation, where each Majorana fermion corresponds effectively to half a
Dirac flavour $N_f$. The most relevant examples for extensions of the standard
model are supersymmetric Yang-Mills theory ($N_f=1/2$) and Minimal Walking
Technicolour ($N_f=2$). In addition to these theories we will also consider the
cases of $N_f=1$ and $N_f=3/2$. The results comprise the particle spectrum of
glueballs, triplet and singlet mesons, and possible fractionally charged spin
half particles. In addition we will discuss our recent results for the mass
anomalous dimension.
| arxiv topic:hep-lat |
arxiv_dataset-81451701.09092 | Hadron Spectroscopy in Double Pomeron Exchange Experiments
hep-ex hep-ph
Central exclusive production in hadron-hadron collisions at high energies,
for example p + p -> p + X + p, where the "+" represents a large rapidity gap,
is a valuable process for spectroscopy of mesonic states X. At collider
energies the gaps can be large enough to be dominated by pomeron exchange, and
then the quantum numbers of the state X are restricted. Isoscalar JPC = 0++ and
2++ mesons are selected, and our understanding of these spectra is incomplete.
In particular, soft pomeron exchanges favor gluon-dominated states such as
glueballs, which are expected in QCD but not yet well established. I will
review some published data.
| arxiv topic:hep-ex hep-ph |
arxiv_dataset-81461702.00006 | Optical Random Riemann Waves in Integrable Turbulence
nlin.PS nlin.SI physics.optics
We examine integrable turbulence (IT) in the framework of the defocusing
cubic one-dimensional nonlinear Schr\"{o}dinger equation. This is done
theoretically and experimentally, by realizing an optical fiber experiment in
which the defocusing Kerr nonlinearity strongly dominates linear dispersive
effects. Using a dispersive-hydrodynamic approach, we show that the development
of IT can be divided into two distinct stages, the initial, pre-breaking stage
being described by a system of interacting random Riemann waves. We explain the
low-tailed statistics of the wave intensity in IT and show that the Riemann
invariants of the asymptotic nonlinear geometric optics system represent the
observable quantities that provide new insight into statistical features of the
initial stage of the IT development by exhibiting stationary probability
density functions.
| arxiv topic:nlin.PS nlin.SI physics.optics |
arxiv_dataset-81471702.00106 | HAT-P-67b: An Extremely Low Density Saturn Transiting an F-Subgiant
Confirmed via Doppler Tomography
astro-ph.EP
We report the discovery of HAT-P-67b, a hot-Saturn transiting a rapidly
rotating F-subgiant. HAT-P-67b has a radius of Rp = 2.085 -0.071/+0.096 RJ,,
orbiting a M* = 1.642 -0.072/+0.155 Msun, R* = 2.546 -0.084/+0.099 Rsun host
star in a ~4.81-day period orbit. We place an upper limit on the mass of the
planet via radial velocity measurements to be Mp < 0.59 MJ, and lower limit of
> 0.056 MJ by limitations on Roche lobe overflow. Despite being a subgiant, the
host star still exhibits relatively rapid rotation, with a projected rotational
velocity of v sin I* = 35.8 +/- 1.1 km/s, making it difficult to precisely
determine the mass of the planet using radial velocities. We validated
HAT-P-67b via two Doppler tomographic detections of the planetary transit,
which eliminated potential eclipsing binary blend scenarios. The Doppler
tomographic observations also confirmed that HAT-P-67b has an orbit that is
aligned to within 12 degrees, in projection, with the spin of its host star.
HAT-P-67b receives strong UV irradiation, and is amongst the one of the lowest
density planets known, making it a good candidate for future UV transit
observations to search for an extended hydrogen exosphere.
| arxiv topic:astro-ph.EP |
arxiv_dataset-81481702.00206 | Non-standard hierarchies of the runnings of the spectral index in
inflation
astro-ph.CO gr-qc hep-ph
Recent analyses of cosmic microwave background surveys have revealed hints
that there may be a non-trivial running of the running of the spectral index.
If future experiments were to confirm these hints, it would prove a powerful
discriminator of inflationary models, ruling out simple single field models. We
discuss how isocurvature perturbations in multi-field models can be invoked to
generate large runnings in a non-standard hierarchy, and find that a minimal
model capable of practically realising this would be a two-field model with a
non-canonical kinetic structure. We also consider alternative scenarios such as
variable speed of light models and canonical quantum gravity effects and their
implications for runnings of the spectral index.
| arxiv topic:astro-ph.CO gr-qc hep-ph |
arxiv_dataset-81491702.00306 | Inflationary $\alpha$-attractor cosmology: A global dynamical systems
perspective
gr-qc astro-ph.CO hep-th math-ph math.MP
We study flat FLRW $\alpha$-attractor $\mathrm{E}$- and $\mathrm{T}$-models
by introducing a dynamical systems framework that yields regularized
unconstrained field equations on two-dimensional compact state spaces. This
results in both illustrative figures and a complete description of the entire
solution spaces of these models, including asymptotics. In particular, it is
shown that observational viability, which requires a sufficient number of
$e$-folds, is associated with a solution given by a one-dimensional center
manifold of a past asymptotic de Sitter state, where the center manifold
structure also explains why nearby solutions are attracted to this
`inflationary attractor solution.' A center manifold expansion yields a
description of the inflationary regime with arbitrary analytic accuracy, where
the slow-roll approximation asymptotically describes the tangency condition of
the center manifold at the asymptotic de Sitter state.
| arxiv topic:gr-qc astro-ph.CO hep-th math-ph math.MP |
arxiv_dataset-81501702.00406 | Models of the strongly lensed quasar DES J0408-5354
astro-ph.GA astro-ph.CO
We present gravitational lens models of the multiply imaged quasar DES
J0408-5354, recently discovered in the Dark Energy Survey (DES) footprint, with
the aim of interpreting its remarkable quad-like configuration. We first model
the DES single-epoch $grizY$ images as a superposition of a lens galaxy and
four point-like objects, obtaining spectral energy distributions (SEDs) and
relative positions for the objects. Three of the point sources (A,B,D) have
SEDs compatible with the discovery quasar spectra, while the faintest
point-like image (G2/C) shows significant reddening and a `grey' dimming of
$\approx0.8$mag. In order to understand the lens configuration, we fit
different models to the relative positions of A,B,D. Models with just a single
deflector predict a fourth image at the location of G2/C but considerably
brighter and bluer. The addition of a small satellite galaxy ($R_{\rm
E}\approx0.2$") in the lens plane near the position of G2/C suppresses the flux
of the fourth image and can explain both the reddening and grey dimming. All
models predict a main deflector with Einstein radius between $1.7"$ and $2.0",$
velocity dispersion $267-280$km/s and enclosed mass $\approx
6\times10^{11}M_{\odot},$ even though higher resolution imaging data are needed
to break residual degeneracies in model parameters. The longest time-delay
(B-A) is estimated as $\approx 85$ (resp. $\approx125$) days by models with
(resp. without) a perturber near G2/C. The configuration and predicted
time-delays of J0408-5354 make it an excellent target for follow-up aimed at
understanding the source quasar host galaxy and substructure in the lens, and
measuring cosmological parameters. We also discuss some lessons learnt from
J0408-5354 on lensed quasar finding strategies, due to its chromaticity and
morphology.
| arxiv topic:astro-ph.GA astro-ph.CO |
arxiv_dataset-81511702.00506 | Solving Uncalibrated Photometric Stereo Using Fewer Images by Jointly
Optimizing Low-rank Matrix Completion and Integrability
cs.CV
We introduce a new, integrated approach to uncalibrated photometric stereo.
We perform 3D reconstruction of Lambertian objects using multiple images
produced by unknown, directional light sources. We show how to formulate a
single optimization that includes rank and integrability constraints, allowing
also for missing data. We then solve this optimization using the Alternate
Direction Method of Multipliers (ADMM). We conduct extensive experimental
evaluation on real and synthetic data sets. Our integrated approach is
particularly valuable when performing photometric stereo using as few as 4-6
images, since the integrability constraint is capable of improving estimation
of the linear subspace of possible solutions. We show good improvements over
prior work in these cases.
| arxiv topic:cs.CV |
arxiv_dataset-81521702.00606 | Joint Offloading and Computing Optimization in Wireless Powered
Mobile-Edge Computing Systems
cs.IT math.IT
Mobile-edge computing (MEC) and wireless power transfer (WPT) have been
recognized as promising techniques in the Internet of Things (IoT) era to
provide massive low-power wireless devices with enhanced computation capability
and sustainable energy supply. In this paper, we propose a unified MEC-WPT
design by considering a wireless powered multiuser MEC system, where a
multi-antenna access point (AP) (integrated with an MEC server) broadcasts
wireless power to charge multiple users and each user node relies on the
harvested energy to execute computation tasks. With MEC, these users can
execute their respective tasks locally by themselves or offload all or part of
them to the AP based on a time division multiple access (TDMA) protocol.
Building on the proposed model, we develop an innovative framework to improve
the MEC performance, by jointly optimizing the energy transmit beamformer at
the AP, the central processing unit (CPU) frequencies and the numbers of
offloaded bits at the users, as well as the time allocation among users. Under
this framework, we address a practical scenario where latency-limited
computation is required. In this case, we develop an optimal resource
allocation scheme that minimizes the AP's total energy consumption subject to
the users' individual computation latency constraints. Leveraging the
state-of-the-art optimization techniques, we derive the optimal solution in a
semi-closed form. Numerical results demonstrate the merits of the proposed
design over alternative benchmark schemes.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-81531702.00706 | The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance
patterns, and zero mode generators
cond-mat.str-el quant-ph
We analyze general zero mode properties of the parent Hamiltonian of the
unprojected Jain-2/5 state. We characterize the zero mode condition associated
to this Hamiltonian via projection onto a four-dimensional two-particle
subspace for given pair angular momentum, for the disk and similarly for the
spherical geometry. Earlier numerical claims in the literature about ground
state uniqueness on the sphere are substantiated on analytic grounds, and
related results are derived. Preference is given to second quantized methods,
where zero mode properties are derived not from given analytic wave functions,
but from a "lattice" Hamiltonian and associated zero mode conditions. This
method reveals new insights into the guiding-center structure of the
unprojected Jain-2/5 state, in particular a system of dominance patterns
following a "generalized Pauli principle", which establishes a complete
one-to-one correspondence with the edge mode counting. We also identify
one-body operators that function as generators of zero modes.
| arxiv topic:cond-mat.str-el quant-ph |
arxiv_dataset-81541702.00806 | Diamond-colored distributive lattices, move-minimizing games, and
fundamental Weyl symmetric functions: The type $\mathsf{A}$ case
math.CO
We present some elementary but foundational results concerning
diamond-colored modular and distributive lattices and connect these structures
to certain one-player combinatorial "move-minimizing games," in particular, a
so-called "domino game." The objective of this game is to find, if possible,
the least number of "domino moves" to get from one partition to another, where
a domino move is, with one exception, the addition or removal of a
domino-shaped pair of tiles. We solve this domino game by demonstrating the
somewhat surprising fact that the associated "game graphs" coincide with a
well-known family of diamond-colored distributive lattices which shall be
referred to as the "type $\mathsf{A}$ fundamental lattices." These lattices
arise as supporting graphs for the fundamental representations of the special
linear Lie algebras and as splitting posets for type $\mathsf{A}$ fundamental
symmetric functions, connections which are further explored in sequel papers
for types $\mathsf{A}$, $\mathsf{C}$, and $\mathsf{B}$. In this paper, this
connection affords a solution to the proposed domino game as well as new
descriptions of the type $\mathsf{A}$ fundamental lattices.
| arxiv topic:math.CO |
arxiv_dataset-81551702.00906 | Attenuated Coupled Cluster: A Heuristic Polynomial Similarity
Transformation Incorporating Spin Symmetry Projection Into Traditional
Coupled Cluster Theory
physics.chem-ph cond-mat.str-el
In electronic structure theory, restricted single-reference coupled cluster
(CC) captures weak correlation but fails catastrophically under strong
correlation. Spin-projected unrestricted Hartree-Fock (SUHF), on the other
hand, misses weak correlation but captures a large portion of strong
correlation. The theoretical description of many important processes, e.g.
molecular dissociation, requires a method capable of accurately capturing both
weak- and strong correlation simultaneously, and would likely benefit from a
combined CC-SUHF approach. Based on what we have recently learned about SUHF
written as particle-hole excitations out of a symmetry-adapted reference
determinant, we here propose a heuristic coupled cluster doubles model to
attenuate the dominant spin collective channel of the quadratic terms in the
coupled cluster equations. Proof of principle results presented here are
encouraging and point to several paths forward for improving the method
further.
| arxiv topic:physics.chem-ph cond-mat.str-el |
arxiv_dataset-81561702.01006 | Near optimal neural network estimator for spectral x-ray photon counting
data with pileup
physics.med-ph
-Purpose: A neural network estimator to process x-ray spectral measurements
from photon counting detectors with pileup. The estimator is used with an
expansion of the attenuation coefficient as a linear combination of functions
of energy multiplied by coefficients that depend on the material composition at
points within the object [R.E. Alvarez and A. Macovski, Phys. Med. Biol., 1976,
733-744]. The estimator computes the line integrals of the coefficients from
measurements with different spectra. Neural network estimators are trained with
measurements of a calibration phantom with the clinical x-ray system. One
estimator uses low noise training data and another network is trained with data
computed by adding random noise to the low noise data. The performance of the
estimators is compared to each other and to the Cramer-Rao lower bound (CRLB).
Methods: The estimator performance is measured using a Monte Carlo simulation
with an idealized model of a photon counting detector that includes only pileup
and quantum noise. Transmitted x-ray spectra are computed for a calibration
phantom. The transmitted spectra are used to compute random data for photon
counting detectors with pileup. Detectors with small and large dead times are
considered. Neural network training data with extremely low noise are computed
by averaging the random detected data with pileup for a large numbers of
exposures of the phantom. Each exposure is equivalent to a projection image or
one projection of a computed tomography scan. Training data with high noise are
computed by using data from one exposure. Finally, training data are computed
by adding random data to the low noise data. The added random data are
multivariate normal with zero mean and covariance equal to the sample
covariance of data for an object with properly chosen attenuation. To test the
estimators, random data are computed for different thicknesses of three test
objects with different compositions. These are used as inputs to the neural
network estimators. The mean squared errors (MSE), variance and square of the
bias of the neural networks' outputs with the random object data are each
compared to the CRLB. Results: The MSE for a network trained with low noise
data and added noise is close to the CRLB for both the low and high pileup
cases. Networks trained with very low noise data have low bias but large
variance for both pileup cases. ralvarez@aprendtech.com Networks trained with
high noise data have both large bias and large variance. Conclusion: With a
properly chosen level of added training data noise, a neural network estimator
for photon counting data with pileup can have variance close to the CRLB with
negligible bias.
| arxiv topic:physics.med-ph |
arxiv_dataset-81571702.01106 | grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories
astro-ph.IM astro-ph.HE
Hot, diffuse, relativistic plasmas such as sub-Eddington black hole accretion
flows are expected to be collisionless, yet are commonly modeled as a fluid
using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative
effects such as heat conduction and viscosity can be important in a
collisionless plasma and will potentially alter the dynamics and radiative
properties of the flow from that in ideal fluid models; we refer to models that
include these processes as Extended GRMHD. Here we describe a new conservative
code, grim, that enables all the above and additional physics to be efficiently
incorporated. grim combines time evolution and primitive variable inversion
needed for conservative schemes into a single step using an algorithm that only
requires the residuals of the governing equations as inputs. This algorithm
enables the code to be physics agnostic as well as flexibility regarding
time-stepping schemes. grim runs on CPUs, as well as on GPUs, using the same
code. We formulate a performance model, and use it to show that our
implementation runs optimally on both architectures. grim correctly captures
classical GRMHD test problems as well as a new suite of linear and nonlinear
test problems with anisotropic conduction and viscosity in special and general
relativity. As tests and example applications, we resolve the shock
substructure due to the presence of dissipation, and report on relativistic
versions of the magneto-thermal instability and heat flux driven buoyancy
instability, which arise due to anisotropic heat conduction, and of the
firehose instability, which occurs due to anisotropic pressure (i.e.
viscosity). Finally, we show an example integration of an accretion flow around
a Kerr black hole, using Extended GRMHD.
| arxiv topic:astro-ph.IM astro-ph.HE |
arxiv_dataset-81581702.01206 | Adaptation of the visibility graph algorithm to find the time lag
between hydrogeological time series
stat.AP
Estimating the time lag between two hydrogeologic time series (e.g.
precipitation and water levels in an aquifer) is of significance for a
hydrogeologist-modeler. In this paper, we present a method to quantify such
lags by adapting the visibility graph algorithm, which converts time series
into a mathematical graph. We present simulation results to assess the
performance of the method. We also illustrate the utility of our approach using
a real world hydrogeologic dataset.
| arxiv topic:stat.AP |
arxiv_dataset-81591702.01306 | Birth of isolated nested cylinders and limit cycles in 3D piecewise
smooth vector fields with symmetry
math.DS
Our start point is a 3D piecewise smooth vector field defined in two zones
and presenting a shared fold curve for the two smooth vector fields considered.
Moreover, these smooth vector fields are symmetric relative to the fold curve,
giving raise to a continuum of nested topological cylinders such that each
orthogonal section of these cylinders is filled by centers. First we prove that
the normal form considered represents a whole class of piecewise smooth vector
fields. After we perturb the initial model in order to obtain exactly
$\mathcal{L}$ invariant planes containing centers. A second perturbation of the
initial model also is considered in order to obtain exactly $k$ isolated
cylinders filled by periodic orbits. Finally, joining the two previous
bifurcations we are able to exhibit a model, preserving the symmetry relative
to the fold curve, and having exactly $k.\mathcal{L}$ limit cycles.
| arxiv topic:math.DS |
arxiv_dataset-81601702.01406 | A conservative scheme for electromagnetic simulation of magnetized
plasmas with kinetic electrons
physics.plasm-ph
A conservative scheme has been formulated and verified for gyrokinetic
particle simulations of electromagnetic waves and instabilities in magnetized
plasmas. An electron continuity equation derived from drift kinetic equation is
used to time advance electron density perturbation by using the perturbed
mechanical flow calculated from the parallel vector potential, and the parallel
vector potential is solved by using the perturbed canonical flow from the
perturbed distribution function. In gyrokinetic particle simulations using this
new scheme, shear Alfv\'en wave dispersion relation in shearless slab and
continuum damping in sheared cylinder have been recovered. The new scheme
overcomes the stringent requirement in conventional perturbative simulation
method that perpendicular grid size needs to be as small as electron
collisionless skin depth even for the long wavelength Alfv\'en waves. The new
scheme also avoids the problem in conventional method that an unphysically
large parallel electric field arises due to the inconsistency between
electrostatic potential calculated from the perturbed density and vector
potential calculated from the perturbed canonical flow. Finally, the
gyrokinetic particle simulations of the Alfv\'en waves in sheared cylinder have
superior numerical properties compared with the fluid simulations, which suffer
from numerical difficulties associated with singular mode structures.
| arxiv topic:physics.plasm-ph |
arxiv_dataset-81611702.01506 | A data assimilation algorithm: the paradigm of the 3D Leray-alpha model
of turbulence
math.AP physics.ao-ph physics.geo-ph
In this paper we survey the various implementations of a new data
assimilation (downscaling) algorithm based on spatial coarse mesh measurements.
As a paradigm, we demonstrate the application of this algorithm to the 3D
Leray-$\alpha$ subgrid scale turbulence model. Most importantly, we use this
paradigm to show that it is not always necessary that one has to collect coarse
mesh measurements of all the state variables, that are involved in the
underlying evolutionary system, in order to recover the corresponding exact
reference solution. Specifically, we show that in the case of the 3D
Leray$-\alpha$ model of turbulence the solutions of the algorithm, constructed
using only coarse mesh observations of any two components of the
three-dimensional velocity field, and without any information of the third
component, converge, at an exponential rate in time, to the corresponding exact
reference solution of the 3D Leray$-\alpha$ model. This study serves as an
addendum to our recent work on abridged continuous data assimilation for the 2D
Navier-Stokes equations. Notably, similar results have also been recently
established for the 3D viscous Planetary Geostrophic circulation model in which
we show that coarse mesh measurements of the temperature alone are sufficient
for recovering, through our data assimilation algorithm, the full solution;
viz. the three components of velocity vector field and the temperature.
Consequently, this proves the Charney conjecture for the 3D Planetary
Geostrophic model; namely, that the history of the large spatial scales of
temperature is sufficient for determining all the other quantities (state
variables) of the model.
| arxiv topic:math.AP physics.ao-ph physics.geo-ph |
arxiv_dataset-81621702.01606 | An Operational Semantics for the Cognitive Architecture ACT-R and its
Translation to Constraint Handling Rules
cs.LO
Computational psychology has the aim to explain human cognition by
computational models of cognitive processes. The cognitive architecture ACT-R
is popular to develop such models. Although ACT-R has a well-defined
psychological theory and has been used to explain many cognitive processes,
there are two problems that make it hard to reason formally about its cognitive
models: First, ACT-R lacks a formalization of its underlying production rule
system and secondly, there are many different implementations and extensions of
ACT-R with technical artifacts complicating formal reasoning even more.
This paper describes a formal operational semantics - the very abstract
semantics - that abstracts from as many technical details as possible keeping
it open to extensions and different implementations of the ACT-R theory. In a
second step, this semantics is refined to define some of its abstract features
that are found in many implementations of ACT-R - the abstract semantics. It
concentrates on the procedural core of ACT-R and is suitable for analysis of
the transition system since it still abstracts from details like timing, the
sub-symbolic layer or conflict resolution.
Furthermore, a translation of ACT-R models to the programming language
Constraint Handling Rules (CHR) is defined. This makes the abstract semantics
an executable specification of ACT-R. CHR has been used successfully to embed
other rule-based formalisms like graph transformation systems or functional
programming. There are many results and tools that support formal reasoning
about and analysis of CHR programs. The translation of ACT-R models to CHR is
proven sound and complete w.r.t. the abstract operational semantics of ACT-R.
This paves the way to analysis of ACT-R models through CHR. Therefore, to the
best of our knowledge, our abstract semantics is the first formulation of ACT-R
suitable for both analysis and execution.
| arxiv topic:cs.LO |
arxiv_dataset-81631702.01706 | Existence of a Radner equilibrium in a model with transaction costs
q-fin.MF
We prove the existence of a Radner equilibrium in a model with proportional
transaction costs on an infinite time horizon and analyze the effect of
transaction costs on the endogenously determined interest rate. Two agents
receive exogenous, unspanned income and choose between consumption and
investing into an annuity. After establishing the existence of a discrete-time
equilibrium, we show that the discrete-time equilibrium converges to a
continuous-time equilibrium model. The continuous-time equilibrium provides an
explicit formula for the equilibrium interest rate in terms of the transaction
cost parameter. We analyze the impact of transaction costs on the equilibrium
interest rate and welfare levels.
| arxiv topic:q-fin.MF |
arxiv_dataset-81641702.01806 | Beam Search Strategies for Neural Machine Translation
cs.CL
The basic concept in Neural Machine Translation (NMT) is to train a large
Neural Network that maximizes the translation performance on a given parallel
corpus. NMT is then using a simple left-to-right beam-search decoder to
generate new translations that approximately maximize the trained conditional
probability. The current beam search strategy generates the target sentence
word by word from left-to- right while keeping a fixed amount of active
candidates at each time step. First, this simple search is less adaptive as it
also expands candidates whose scores are much worse than the current best.
Secondly, it does not expand hypotheses if they are not within the best scoring
candidates, even if their scores are close to the best one. The latter one can
be avoided by increasing the beam size until no performance improvement can be
observed. While you can reach better performance, this has the draw- back of a
slower decoding speed. In this paper, we concentrate on speeding up the decoder
by applying a more flexible beam search strategy whose candidate size may vary
at each time step depending on the candidate scores. We speed up the original
decoder by up to 43% for the two language pairs German-English and
Chinese-English without losing any translation quality.
| arxiv topic:cs.CL |
arxiv_dataset-81651702.01906 | Affiliation networks with an increasing degree sequence
stat.ME math.ST stat.TH
Affiliation network is one kind of two-mode social network with two different
sets of nodes (namely, a set of actors and a set of social events) and edges
representing the affiliation of the actors with the social events. Although a
number of statistical models are proposed to analyze affiliation networks, the
asymptotic behaviors of the estimator are still unknown or have not been
properly explored. In this paper, we study an affiliation model with the degree
sequence as the exclusively natural sufficient statistic in the exponential
family distributions. We establish the uniform consistency and asymptotic
normality of the maximum likelihood estimator when the numbers of actors and
events both go to infinity. Simulation studies and a real data example
demonstrate our theoretical results.
| arxiv topic:stat.ME math.ST stat.TH |
arxiv_dataset-81661702.02006 | Phase diagram of the triangular-lattice Potts antiferromagnet
cond-mat.stat-mech
We study the phase diagram of the triangular-lattice $Q$-state Potts model in
the real $(Q,v)$-plane, where $v=e^J-1$ is the temperature variable. Our first
goal is to provide an obviously missing feature of this diagram: the position
of the antiferromagnetic critical curve. This curve turns out to possess a
bifurcation point with two branches emerging from it, entailing important
consequences for the global phase diagram. We have obtained accurate numerical
estimates for the position of this curve by combining the transfer-matrix
approach for strip graphs with toroidal boundary conditions and the recent
method of critical polynomials. The second goal of this work is to study the
corresponding $A_{p-1}$ RSOS model on the torus, for integer $p=4,5,\ldots,8$.
We clarify its relation to the corresponding Potts model, in particular
concerning the role of boundary conditions. For certain values of $p$, we
identify several new critical points and regimes for the RSOS model and we
initiate the study of the flows between the corresponding field theories.
| arxiv topic:cond-mat.stat-mech |
arxiv_dataset-81671702.02106 | Oseen Flow in Paint Marbling
physics.flu-dyn
Paint marbling refers to techniques for creating intricate designs in colored
paints floating on a liquid surface. If the marbling motions are executed
slowly, then this layer of paints can be modeled as a two-dimensional
incompressible Newtonian fluid.
In this highly constrained model many marbling techniques can be exactly
represented by closed form homeomorphisms. Homeomorphisms can be composed and
compute the composite mapping at any resolution. Computing homeomorphisms
directly is orders of magnitude faster than finite-element methods in solving
paint marbling flows.
Most marbling patterns involve drawing rakes from one side of the tank to the
other; and these can be modeled by exact closed form homeomorphisms. But
pictorial designs for flowers and animals use short strokes of a single stylus;
presented is an exact velocity field for Oseen fluid flow and its application
to creating short stroke marbling homeomorphisms.
| arxiv topic:physics.flu-dyn |
arxiv_dataset-81681702.02206 | Semi-Supervised QA with Generative Domain-Adaptive Nets
cs.CL cs.LG
We study the problem of semi-supervised question answering----utilizing
unlabeled text to boost the performance of question answering models. We
propose a novel training framework, the Generative Domain-Adaptive Nets. In
this framework, we train a generative model to generate questions based on the
unlabeled text, and combine model-generated questions with human-generated
questions for training question answering models. We develop novel domain
adaptation algorithms, based on reinforcement learning, to alleviate the
discrepancy between the model-generated data distribution and the
human-generated data distribution. Experiments show that our proposed framework
obtains substantial improvement from unlabeled text.
| arxiv topic:cs.CL cs.LG |
arxiv_dataset-81691702.02306 | Period-luminosity relations of fast-rotating B-type stars in the young
open cluster NGC3766
astro-ph.SR
We study the pulsational properties of rapidly rotating main-sequence B-type
stars using linear non-adiabatic analysis of non-radial low-frequency modes
taking into account the effect of rotation. We compare the properties of
prograde sectoral $g$ and retrograde $r$ modes excited by the $\kappa$
mechanism at the Fe opacity peak with the newly discovered period-luminosity
relation that is obeyed by a group of fast-rotating B-type stars in the young
open cluster NGC 3766. The observed relation consists of two sequences in the
period versus magnitude diagram, at periods shorter than 0.5 days. We find that
this property is consistent with similar period-luminosity relations predicted
for excited sectoral prograde $g$-modes of azimuthal orders $m=-1$ and $m=-2$
in fast-rotating stars along an isochrone. We further show that some of the
rapidly rotating stars that have photometric variability with periods longer
than a day may be caused by $r$-mode pulsation predicted to be excited in these
stars. One fast-rotating star, in particular, shows both short and long periods
that can be explained by the simultaneous excitation of $g$- and $r$-mode
pulsations in models of fast-rotating stars.
| arxiv topic:astro-ph.SR |
arxiv_dataset-81701702.02406 | SEA: String Executability Analysis by Abstract Interpretation
cs.PL
Dynamic languages often employ reflection primitives to turn dynamically
generated text into executable code at run-time. These features make standard
static analysis extremely hard if not impossible because its essential data
structures, i.e., the control-flow graph and the system of recursive equations
associated with the program to analyse, are themselves dynamically mutating
objects. We introduce SEA, an abstract interpreter for automatic sound string
executability analysis of dynamic languages employing bounded (i.e, finitely
nested) reflection and dynamic code generation. Strings are statically
approximated in an abstract domain of finite state automata with basic
operations implemented as symbolic transducers. SEA combines standard program
analysis together with string executability analysis. The analysis of a call to
reflection determines a call to the same abstract interpreter over a code which
is synthesised directly from the result of the static string executability
analysis at that program point. The use of regular languages for approximating
dynamically generated code structures allows SEA to soundly approximate safety
properties of self modifying programs yet maintaining efficiency. Soundness
here means that the semantics of the code synthesised by the analyser to
resolve reflection over-approximates the semantics of the code dynamically
built at run-rime by the program at that point.
| arxiv topic:cs.PL |
arxiv_dataset-81711702.02506 | Nichols algebras that are quantum planes
math.QA math.RA
We compute all Nichols algebras of rigid vector spaces of dimension 2 that
admit a non-trivial quadratic relation.
| arxiv topic:math.QA math.RA |
arxiv_dataset-81721702.02606 | Third nearest neighbor parameterized tight biding model for graphene
nano-ribbons
cond-mat.mes-hall
The ab initio band structure of 2D graphene sheet is well reproduced by the
third nearest neighbor tight binding model proposed by Reich et al [Phys. Rev.
B 66, 035412]. For ribbon structures, the existing sets of tight binding
parameters can successfully explain semi-conducting behavior of all armchair
ribbon structures. However, they are still failing in describing accurately the
slope of the bands while this feature is directly associated to the group
velocity and the effective mass of electrons. In this work, both density
functional theory and tight binding calculations were performed and a new set
of tight binding parameters up to the third nearest neighbors including overlap
terms is introduced. The results obtained with this model offer excellent
agreement with the predictions of the density functional theory in most cases
of ribbon structures, even in the high-energy region. Moreover, this set can
induce electron-hole asymmetry as manifested in density functional theory.
Relevant outcomes are also demonstrated for armchair ribbons of various widths
as well as for zigzag structures, thus opening a route for multi-scale
simulations.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-81731702.02706 | Semi-Supervised Deep Learning for Monocular Depth Map Prediction
cs.CV
Supervised deep learning often suffers from the lack of sufficient training
data. Specifically in the context of monocular depth map prediction, it is
barely possible to determine dense ground truth depth images in realistic
dynamic outdoor environments. When using LiDAR sensors, for instance, noise is
present in the distance measurements, the calibration between sensors cannot be
perfect, and the measurements are typically much sparser than the camera
images. In this paper, we propose a novel approach to depth map prediction from
monocular images that learns in a semi-supervised way. While we use sparse
ground-truth depth for supervised learning, we also enforce our deep network to
produce photoconsistent dense depth maps in a stereo setup using a direct image
alignment loss. In experiments we demonstrate superior performance in depth map
prediction from single images compared to the state-of-the-art methods.
| arxiv topic:cs.CV |
arxiv_dataset-81741702.02806 | de Sitter spacetime with a Becchi-Rouet-Stora quartet
hep-th gr-qc
We generalize the topological model recently proposed and investigate the
cosmological perturbations of the model. The model has an exact de Sitter
background solution associated with a Becchi-Rouet-Stora(BRS) quartet terms
which are regarded as a Lagrangian density of the topological field theory. The
de Sitter solution can be selected without spontaneously breaking the BRS
symmetry, and be interpreted as a gauge fixing of de Sitter spacetime. The BRS
symmetry is preserved for the perturbations around the de Sitter background
before we solve the constraints of general relativity. We derive action to the
second order of the perturbations and confirm that even after solving the
constraints, we have the BRS symmetry at least for the second order action. We
construct the cosmological perturbation theory involving the BRS sector, and
obtain the two point correlation functions for the curvature perturbation and
the isocurvature perturbations which compose the BRS sector. Our result gives a
new description for de Sitter spacetime and the quantum field theory in de
Sitter spacetime.
| arxiv topic:hep-th gr-qc |
arxiv_dataset-81751702.02906 | Switching EEG Headsets Made Easy: Reducing Offline Calibration Effort
Using Active Weighted Adaptation Regularization
cs.LG cs.HC
Electroencephalography (EEG) headsets are the most commonly used sensing
devices for Brain-Computer Interface. In real-world applications, there are
advantages to extrapolating data from one user session to another. However,
these advantages are limited if the data arise from different hardware systems,
which often vary between application spaces. Currently, this creates a need to
recalibrate classifiers, which negatively affects people's interest in using
such systems. In this paper, we employ active weighted adaptation
regularization (AwAR), which integrates weighted adaptation regularization
(wAR) and active learning, to expedite the calibration process. wAR makes use
of labeled data from the previous headset and handles class-imbalance, and
active learning selects the most informative samples from the new headset to
label. Experiments on single-trial event-related potential classification show
that AwAR can significantly increase the classification accuracy, given the
same number of labeled samples from the new headset. In other words, AwAR can
effectively reduce the number of labeled samples required from the new headset,
given a desired classification accuracy, suggesting value in collating data for
use in wide scale transfer-learning applications.
| arxiv topic:cs.LG cs.HC |
arxiv_dataset-81761702.03006 | Multi-step Off-policy Learning Without Importance Sampling Ratios
cs.LG
To estimate the value functions of policies from exploratory data, most
model-free off-policy algorithms rely on importance sampling, where the use of
importance sampling ratios often leads to estimates with severe variance. It is
thus desirable to learn off-policy without using the ratios. However, such an
algorithm does not exist for multi-step learning with function approximation.
In this paper, we introduce the first such algorithm based on
temporal-difference (TD) learning updates. We show that an explicit use of
importance sampling ratios can be eliminated by varying the amount of
bootstrapping in TD updates in an action-dependent manner. Our new algorithm
achieves stability using a two-timescale gradient-based TD update. A prior
algorithm based on lookup table representation called Tree Backup can also be
retrieved using action-dependent bootstrapping, becoming a special case of our
algorithm. In two challenging off-policy tasks, we demonstrate that our
algorithm is stable, effectively avoids the large variance issue, and can
perform substantially better than its state-of-the-art counterpart.
| arxiv topic:cs.LG |
arxiv_dataset-81771702.03106 | A Las Vegas approximation algorithm for metric $1$-median selection
cs.DS
Given an $n$-point metric space, consider the problem of finding a point with
the minimum sum of distances to all points. We show that this problem has a
randomized algorithm that {\em always} outputs a $(2+\epsilon)$-approximate
solution in an expected $O(n/\epsilon^2)$ time for each constant $\epsilon>0$.
Inheriting Indyk's algorithm, our algorithm outputs a
$(1+\epsilon)$-approximate $1$-median in $O(n/\epsilon^2)$ time with
probability $\Omega(1)$.
| arxiv topic:cs.DS |
arxiv_dataset-81781702.03206 | A near/mid infrared search for ultra-bright submillimetre galaxies:
Searching for Cosmic Eyelash Analogues
astro-ph.GA
We present results from a near/mid IR search for submillimetre galaxies over
a region of 6230 sq deg. of the southern sky. We used a cross-correlation of
the VISTA Hemispheric Survey (VHS) and the WISE database to identify bright
galaxies (K_s <= 18.2) with near/mid IR colours similar to those of the high
redshift lensed sub-mm galaxy SMM J2135-0102. We find 7 galaxies which fulfill
all five adopted near/mid IR colour (NMIRQC) criteria and resemble the SED of
the reference galaxy at these wavelengths. For these galaxies, which are
broadly distributed in the sky, we determined photometric redshifts in the
range z=1.6-3.2. We searched the VHS for clusters of galaxies, which may be
acting as gravitational lenses, and found that 6 out of the 7 galaxies are
located within 3.5 arcmin of a cluster/group of galaxies. Using the J-K_s vs J
sequences we determine photometric redshifts for these clusters/groups in the
range z=0.2-0.9. We propose the newly identified sources are ultra-bright high
redshift lensed SMG candidates. Follow-up observations in the sub-mm and mm are
key to determine the ultimate nature of these objects.
| arxiv topic:astro-ph.GA |
arxiv_dataset-81791702.03306 | Nahm transformation for parabolic integrable connections on the
projective line -- case of generic regular graded residues
math.AG
We give a de Rham interpretation of Nahm's transform for certain parabolic
harmonic bundles on the projective line and compare it to minimal
Fourier--Laplace transform of $\mathcal{D}$-modules. We give an algebraic
definition of a parabolic structure on the transformed bundle and show that it
is compatible with the transformed harmonic metric.
| arxiv topic:math.AG |
arxiv_dataset-81801702.03406 | Recombination of open-f-shell tungsten ions
physics.atom-ph
We review experimental and theoretical efforts aimed at a detailed
understanding of the recombination of electrons with highly-charged tungsten
ions characterised by an open 4f sub-shell. Highly-charged tungsten occurs as a
plasma contaminant in ITER-like tokamak experiments, where it acts as an
unwanted cooling agent. Modelling of the charge state populations in a plasma
requires reliable thermal rate coefficients for charge-changing electron
collisions. The electron recombination of medium-charged tungsten species with
open 4f sub-shells is especially challenging to compute reliably. Storage-ring
experiments have been conducted that yielded recombination rate coefficients at
high energy resolution and well-understood systematics. Significant deviations
compared to simplified, but prevalent, computational models have been found. A
new class of ab-initio numerical calculations has been developed that provides
reliable predictions of the total plasma recombination rate coefficients for
these ions.
| arxiv topic:physics.atom-ph |
arxiv_dataset-81811702.03506 | Stabilization of prethermal Floquet steady states in a periodically
driven dissipative Bose-Hubbard model
cond-mat.stat-mech cond-mat.mes-hall cond-mat.quant-gas
We discuss the effect of dissipation on heating which occurs in periodically
driven quantum many body systems. We especially focus on a periodically driven
Bose-Hubbard model coupled to an energy and particle reservoir. Without
dissipation, this model is known to undergo parametric instabilities which can
be considered as an initial stage of heating. By taking the weak on-site
interaction limit as well as the weak system-reservoir coupling limit, we find
that parametric instabilities are suppressed if the dissipation is stronger
than the on-site interaction strength and stable steady states appear. Our
results demonstrate that periodically-driven systems can emit energy, which is
absorbed from external drivings, to the reservoir so that they can avoid
heating.
| arxiv topic:cond-mat.stat-mech cond-mat.mes-hall cond-mat.quant-gas |
arxiv_dataset-81821702.03606 | Sphere geometry and invariants
math.GN cs.DM math.RA
A finite abstract simplicial complex G defines two finite simple graphs: the
Barycentric refinement G1, connecting two simplices if one is a subset of the
other and the connection graph G', connecting two simplices if they intersect.
We prove that the Poincare-Hopf value i(x)=1-X(S(x)), where X is Euler
characteristics and S(x) is the unit sphere of a vertex x in G1, agrees with
the Green function value g(x,x),the diagonal element of the inverse of (1+A'),
where A' is the adjacency matrix of G'. By unimodularity, det(1+A') is the
product of parities (-1)^dim(x) of simplices in G, the Fredholm matrix 1+A' is
in GL(n,Z), where n is the number of simplices in G. We show that the set of
possible unit sphere topologies in G1 is a combinatorial invariant of the
complex G. So, also the Green function range of G is a combinatorial invariant.
To prove the invariance of the unit sphere topology we use that all unit
spheres in G1 decompose as a join of a stable and unstable part. The join
operation + renders the category X of simplicial complexes into a monoid, where
the empty complex is the 0 element and the cone construction adds 1. The
augmented Grothendieck group (X,+,0) contains the graph and sphere monoids
(Graphs, +,0) and (Spheres,+,0). The Poincare-Hopf functionals i(G) as well as
the volume are multiplicative functions on (X,+). For the sphere group, both
i(G) as well as Fredholm characteristic are characters. The join + can be
augmented with a product * so that we have a commutative ring (X,+,0,*,1)for
which there are both additive and multiplicative primes and which contains as a
subring of signed complete complexes isomorphic to the integers (Z,+,0,*,1). We
also look at the spectrum of the Laplacian of the join of two graphs. Both for
addition + and multiplication *, one can ask whether unique prime factorization
holds.
| arxiv topic:math.GN cs.DM math.RA |
arxiv_dataset-81831702.03706 | Multitask Learning with Deep Neural Networks for Community Question
Answering
cs.CL
In this paper, we developed a deep neural network (DNN) that learns to solve
simultaneously the three tasks of the cQA challenge proposed by the
SemEval-2016 Task 3, i.e., question-comment similarity, question-question
similarity and new question-comment similarity. The latter is the main task,
which can exploit the previous two for achieving better results. Our DNN is
trained jointly on all the three cQA tasks and learns to encode questions and
comments into a single vector representation shared across the multiple tasks.
The results on the official challenge test set show that our approach produces
higher accuracy and faster convergence rates than the individual neural
networks. Additionally, our method, which does not use any manual feature
engineering, approaches the state of the art established with methods that make
heavy use of it.
| arxiv topic:cs.CL |
arxiv_dataset-81841702.03806 | Algebras of bounded noncommutative analytic functions on subvarieties of
the noncommutative unit ball
math.OA
We study algebras of bounded, noncommutative (nc) analytic functions on nc
subvarieties of the nc unit ball. Given a nc variety $\mathfrak{V}$ in the nc
unit ball $\mathfrak{B}_d$, we identify the algebra of bounded analytic
functions on $\mathfrak{V}$ --- denoted $H^\infty(\mathfrak{V})$ --- as the
multiplier algebra $\operatorname{Mult} \mathcal{H}_{\mathfrak{V}}$ of a
certain reproducing kernel Hilbert space $\mathcal{H}_{\mathfrak{V}}$
consisting of nc functions on $\mathfrak{V}$. We find that every such algebra
$H^\infty(\mathfrak{V})$ is completely isometrically isomorphic to the quotient
$H^\infty(\mathfrak{B}_d)/ \mathcal{J}_{\mathfrak{V}}$ of the algebra of
bounded nc holomorphic functions on the ball by the ideal
$\mathcal{J}_{\mathfrak{V}}$ of bounded nc holomorphic functions which vanish
on $\mathfrak{V}$.
We investigate the problem of when two algebras $H^\infty(\mathfrak{V})$ and
$H^\infty(\mathfrak{W})$ are isometrically isomorphic. If the variety
$\mathfrak{W}$ is the image of $\mathfrak{V}$ under a nc analytic automorphism
of $\mathfrak{B}_d$, then $H^\infty(\mathfrak{V})$ and $H^\infty(\mathfrak{W})$
are (completely) isometrically isometric. We prove that the converse holds in
the case where the varieties are homogeneous; in general we can only show that
if the algebras are isometrically isomorphic, then there must be nc holomorphic
maps between the varieties.
Along the way we are led to consider some interesting problems on function
theory in the nc unit ball. For example, we study various versions of the
Nullstellensatz (that is, the problem of to what extent an ideal is determined
by its zero set), and we obtain perfect Nullstellensatz in both the homogeneous
as well as the commutative cases. We also consider similar problems regarding
the bounded analytic functions that extend continuously to the boundary of
$\mathfrak{B}_d$.
| arxiv topic:math.OA |
arxiv_dataset-81851702.03906 | Statically Checking Web API Requests in JavaScript
cs.SE
Many JavaScript applications perform HTTP requests to web APIs, relying on
the request URL, HTTP method, and request data to be constructed correctly by
string operations. Traditional compile-time error checking, such as calling a
non-existent method in Java, are not available for checking whether such
requests comply with the requirements of a web API. In this paper, we propose
an approach to statically check web API requests in JavaScript. Our approach
first extracts a request's URL string, HTTP method, and the corresponding
request data using an inter-procedural string analysis, and then checks whether
the request conforms to given web API specifications. We evaluated our approach
by checking whether web API requests in JavaScript files mined from GitHub are
consistent or inconsistent with publicly available API specifications. From the
6575 requests in scope, our approach determined whether the request's URL and
HTTP method was consistent or inconsistent with web API specifications with a
precision of 96.0%. Our approach also correctly determined whether extracted
request data was consistent or inconsistent with the data requirements with a
precision of 87.9% for payload data and 99.9% for query data. In a systematic
analysis of the inconsistent cases, we found that many of them were due to
errors in the client code. The here proposed checker can be integrated with
code editors or with continuous integration tools to warn programmers about
code containing potentially erroneous requests.
| arxiv topic:cs.SE |
arxiv_dataset-81861702.04006 | Gamma-ray Blazars Within the First 2 Billion Years
astro-ph.HE
The detection of high-redshift ($z>$3) blazars enables the study of the
evolution of the most luminous relativistic jets over cosmic time. More
importantly, high-redshift blazars tend to host massive black holes and can be
used to constrain the space density of heavy black holes in the early Universe.
Here, we report the first detection with the \fermi-Large Area Telescope of
five \gm-ray emitting blazars beyond $z=3.1$, more distant than any blazars
previously detected in $\gamma$-rays. Among these five objects, NVSS
J151002+570243 is now the most distant known \gm-ray emitting blazar at
$z=4.31$. These objects have steeply falling \gm-ray spectral energy
distributions (SEDs) and, those that have been observed in X-rays, a very hard
X-ray spectrum, both typical of powerful blazars. Their Compton dominance
(ratio of the inverse Compton to synchrotron peak luminosities) is also very
large ($>20$). All of these properties place these objects among the most
extreme members of the blazar population. Their optical spectra and the
modeling of their optical-UV SEDs confirm that these objects harbor massive
black holes ($M_{\rm BH} \sim 10^{8-10} {\rm M}_{\odot}$). We find that, at
$z\approx4$, the space density of $>10^{9} {\rm M}_{\odot}$ black holes hosted
in radio-loud and radio-quiet active galactic nuclei are similar, implying that
radio-loudness may play a key role in rapid black hole growth in the early
Universe.
| arxiv topic:astro-ph.HE |
arxiv_dataset-81871702.04106 | Newly observed $\Lambda_c(2860)^+$ at LHCb and its \emph{D}-wave
partners $\Lambda_c(2880)^+$, $\Xi_c(3055)^+$ and $\Xi_c(3080)^+$
hep-ph hep-ex
New resonance $\Lambda_c(2860)^+$, reported by LHCb, is a key to establish
\emph{D}-wave charmed and charmed-strange baryon families. In this work, we
first carry out an analysis of mass spectra of the $\lambda$-mode excited
charmed and charmed-strange baryon states, which may reveal the relation of
$\Lambda_c(2860)^+$, $\Lambda_c(2880)^+$, $\Xi_c(3055)^+$ and $\Xi_c(3080)^+$,
$i.e.$, $\Lambda_c(2860)^+$ and $\Lambda_c(2880)^+$ can form a \emph{D}-wave
doublet $[3/2^+,5/2^+]$ while $\Xi_c(3055)^+$ and $\Xi_c(3080)^+$ are the
strange partners of $\Lambda_c(2860)^+$ and $\Lambda_c(2880)^+$, respectively.
Further study of their two-body Okubo-Zweig-Iizuka-allowed decays supports
$\Lambda_c(2860)^+$ and $\Xi_c(3055)^+$ as the \emph{D}-wave charmed and
charmed-strange baryons, respectively, with $J^P=3/2^+$. For
$\Lambda_c(2880)^+$ and $\Xi_c(3080)^+$, however, there exist some difficulties
under the \emph{D}-wave assignment with $J^P=5/2^+$ since the experimental
widths and some ratios of partial width of $\Lambda_c(2880)^+$ and
$\Xi_c(3080)^+$ cannot be reproduced in our calculation.
| arxiv topic:hep-ph hep-ex |
arxiv_dataset-81881702.04206 | Representations of regular trees and invariants of AR-components for
generalized Kronecker quivers
math.RT
We investigate the generalized Kronecker algebra $\mathcal{K}_r = k\Gamma_r$
with $r \geq 3$ arrows. Given a regular component $\mathcal{C}$ of the
Auslander-Reiten quiver of $\mathcal{K}_r$, we show that the quasi-rank
$rk(\mathcal{C}) \in \mathbb{Z}_{\leq 1}$ can be described almost exactly as
the distance $\mathcal{W}(\mathcal{C}) \in \mathbb{N}_0$ between two
non-intersecting cones in $\mathcal{C}$, given by modules with the equal images
and the equal kernels property; more precisley, we show that the two numbers
are linked by the inequality \[ -\mathcal{W}(\mathcal{C}) \leq rk(\mathcal{C})
\leq - \mathcal{W}(\mathcal{C}) + 3.\] Utilizing covering theory, we construct
for each $n \in \mathbb{N}_0$ a bijection $\varphi_n$ between the field $k$ and
$\{ \mathcal{C} \mid \mathcal{C} \ \text{regular component}, \
\mathcal{W}(\mathcal{C}) = n \}$. As a consequence, we get new results about
the number of regular components of a fixed quasi-rank.
| arxiv topic:math.RT |
arxiv_dataset-81891702.04306 | Full Electroresistance Modulation in a Mixed-Phase Metallic Alloy
cond-mat.mtrl-sci
We report a giant, ~22%, electroresistance modulation for a metallic alloy
above room temperature. It is achieved by a small electric field of 2 kV/cm via
piezoelectric strain-mediated magnetoelectric coupling and the resulting
magnetic phase transition in epitaxial FeRh/BaTiO3 heterostructures. This work
presents detailed experimental evidence for an isothermal magnetic phase
transition driven by tetragonality modulation in FeRh thin films, which is in
contrast to the large volume expansion in the conventional temperature-driven
magnetic phase transition in FeRh. Moreover, all the experimental results in
this work illustrate FeRh as a mixed-phase model system well similar to
phase-separated colossal magnetoresistance systems with phase instability
therein.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-81901702.04406 | Quantum corrections of the truncated Wigner approximation applied to an
exciton transport model
quant-ph
We modify the path integral representation of exciton transport in open
quantum systems such that an exact description of the quantum fluctuations
around the classical evolution of the system is possible. As a consequence, the
time evolution of the system observables is obtained by calculating the average
of a stochastic difference equation which is weighted with a product of
pseudo-probability density functions. From the exact equation of motion one can
clearly identify the terms that are also present if we apply the truncated
Wigner approximation. This description of the problem is used as a basis for
the derivation of a new approximation, whose validity goes beyond the truncated
Wigner approximation. To demonstrate this we apply the formalism to a
donor-acceptor transport model.
| arxiv topic:quant-ph |
arxiv_dataset-81911702.04506 | Localization of light in three dimensions: a mobility edge in the
imaginary axis in non-Hermitian Hamiltonians
cond-mat.mes-hall
Searching for Anderson localization of light in three dimensions has
challenged experimental and theoretical research for the last decades. Here the
problem is analyzed through large scale numerical simulations, using a
radiative Hamiltonian i.e. a non-Hermitian long-range hopping Hamiltonian, well
suited to model light-matter interaction in cold atomic clouds. Light
interaction in atomic clouds is considered in presence of positional and
diagonal disorder. Due to the interplay of disorder and cooperative effects
(sub- and super-radiance) a novel type of localization transition is shown to
emerge, differing in several aspects from standard localization transitions
which occur along the real energy axis. The localization transition discussed
here is characterized by a mobility edge along the imaginary energy axis of the
eigenvalues which is mostly independent from the real energy value of the
eigenmodes. Differently from usual mobility edges it separates extended states
from hybrid localized states and it manifest itself in the large moments of the
participation ratio of the eigenstates. Our prediction of a mobility edge in
the imaginary axis, i.e. depending on the eigenmode lifetime, paves the way to
achieve control both in the time and space domain of open quantum systems.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-81921702.04606 | H{\alpha} imaging for BeXRBs in the Small Magellanic Cloud
astro-ph.SR astro-ph.GA astro-ph.HE
The Small Magellanic Cloud (SMC) hosts a large number of high-mass X-ray
binaries, and in particular of Be/X-ray Binaries (BeXRBs; neutron stars
orbiting OBe-type stars), offering a unique laboratory to address the effect of
metalicity. One key property of their optical companion is H{\alpha} in
emission, which makes them bright sources when observed through a narrow-band
H{\alpha} filter. We performed a survey of the SMC Bar and Wing regions using
wide-field cameras (WFI@MPG/ESO and MOSAIC@CTIO/Blanco) in order to identify
the counterparts of the sources detected in our XMM-Newton survey of the same
area. We obtained broad-band R and narrow-band H{\alpha} photometry, and
identified ~10000 H{\alpha} emission sources down to a sensitivity limit of
18.7 mag (equivalent to ~B8 type Main Sequence stars). We find the fraction of
OBe/OB stars to be 13% down to this limit, and by investigating this fraction
as a function of the brightness of the stars we deduce that H{\alpha} excess
peaks at the O9-B2 spectral range. Using the most up-to-date numbers of SMC
BeXRBs we find their fraction over their parent population to be ~0.002-0.025
BeXRBs/OBe, a direct measurement of their formation rate.
| arxiv topic:astro-ph.SR astro-ph.GA astro-ph.HE |
arxiv_dataset-81931702.04706 | Parity and Time Reversal Symmetry in Hanbury Brown-Twiss Effect
cond-mat.mes-hall quant-ph
The current manuscript employs the parity and time reversal symmetry in the
Hanbury Brown-Twiss experiment. For this purpose, we develop a general
scattering matrix framework founded on the concatenation of many individual
compounded scattering processes on the setup. In this way, we derive the
general scattering matrix of a parity and time reversal symmetric Hanbury
Brown-Twiss experiment (HBT-PT). Within such scattering formulation, we propose
a theoretical framework which provides how to measure the symmetry of the
system through the correlation function of a pair of particles transmitted
through the leads. The correlation function naturally reveal the quantum
statistics of both bosons and fermions and demonstrate a very preponderant role
of PT symmetry on the HBT experiment. We indicate the formation of both quantum
and classical universal Turing machine depending on controllable parameters of
the apparatus.
| arxiv topic:cond-mat.mes-hall quant-ph |
arxiv_dataset-81941702.04806 | Analysis of Tsallis' classical partition function's poles
cond-mat.stat-mech physics.class-ph
When one integrates the q-exponential function of Tsallis' so as to get the
partition function $Z$, a gamma function inevitably emerges. Consequently,
poles arise. We investigate here here the thermodynamic significance of these
poles in the case of $n$ classical harmonic oscillators (HO). Given that this
is an exceedingly well known system, any new feature that may arise can safely
be attributed to the poles' effect. We appeal to the mathematical tools used in
[EPJB 89, 150 (2016) and arXiv:1702.03535 (2017)], and obtain both bound and
unbound states. In the first case, we are then faced with a classical Einstein
crystal. We also detect what might be interpreted as pseudo gravitational
effects.
| arxiv topic:cond-mat.stat-mech physics.class-ph |
arxiv_dataset-81951702.04906 | Simply split SIMPs
hep-ph
Dark Matter which interacts strongly with itself, but only feebly with the
Standard Model is a possibility that has been entertained to solve apparent
small-scale structure problems that are pertinent to the non-interacting cold
Dark Matter paradigm. In this paper, we study the simple case in which the
self-scattering rate today is regulated by kinematics and/or the abundance
ratio, through the mass-splitting of nearly degenerate pseudo-Dirac fermions
$\chi_1$ and $\chi_2$ or real scalars $\phi_1$ and $\phi_2$. We calculate the
relic density of these states in a scenario where self-scattering proceeds
through off-diagonal couplings with a vector particle $V$ (Dark Photon) and
where the abundance is set through number-depleting 4-to-2 reactions in the
hidden sector, or, alternatively, via freeze-in. We study the implications of
the considered models and their prospect of solving astrophysical small-scale
structure problems. We also show how the introduction of the (meta-)stable
heavier state may be probed in future dark matter searches.
| arxiv topic:hep-ph |
arxiv_dataset-81961702.05006 | Time crystal behavior of excited eigenstates
quant-ph cond-mat.mes-hall cond-mat.quant-gas
In analogy to spontaneous breaking of continuous space translation symmetry
in the process of space crystal formation, it was proposed that spontaneous
breaking of continuous time translation symmetry could lead to time crystal
formation. In other words, a time-independent system prepared in the energy
ground state is expected to reveal periodic motion under infinitely weak
perturbation. In the case of the system proposed originally by Frank Wilczek,
spontaneous breaking of time translation symmetry can not be observed if one
starts with the ground state. We point out that the symmetry breaking can take
place if the system is prepared in an excited eigenstate. The latter can be
realized experimentally in ultra-cold atomic gases. We simulate the process of
the spontaneous symmetry breaking due to measurements of particle positions and
analyze the lifetime of the resulting symmetry broken state.
| arxiv topic:quant-ph cond-mat.mes-hall cond-mat.quant-gas |
arxiv_dataset-81971702.05106 | On new physics searches with multidimensional differential shapes
hep-ph
In the context of upcoming new physics searches at the LHC, we investigate
the impact of multidimensional differential rates in typical LHC analyses. We
discuss the properties of shape information, and argue that multidimensional
rates bring limited information in the scope of a discovery, but can have a
large impact on model discrimination. We also point out subtleties about
systematic uncertainties cancellations and the Cauchy-Schwarz bound on
interference terms.
| arxiv topic:hep-ph |
arxiv_dataset-81981702.05206 | Notes on Multiple Higher Category Theory
math.CT math.KT
These notes follows the articles \cite{kamel, Cam, cam-cubique} which show
how powerful can be the method of \textit{Stretchings} initiated with the
\textit{Globular Geometry} by Jacques Penon in \cite{penon} , to weakened
\textit{strict higher structures}. Here we adapt this method to weakened strict
multiple $\infty$-categories, strict multiple $(\infty,m)$-categories, and in
particular we obtain algebraic models of weak multiple $\infty$-groupoids.
| arxiv topic:math.CT math.KT |
arxiv_dataset-81991702.05306 | The mapping class groups of reducible Heegaard splittings of genus two
math.GT
The manifold which admits a genus-$2$ reducible Heegaard splitting is one of
the $3$-sphere, $\mathbb{S}^2 \times \mathbb{S}^1$, lens spaces and their
connected sums. For each of those manifolds except most lens spaces, the
mapping class group of the genus-$2$ splitting was shown to be finitely
presented. In this work, we study the remaining generic lens spaces, and show
that the mapping class group of the genus-$2$ Heegaard splitting is finitely
presented for any lens space by giving its explicit presentation. As an
application, we show that the fundamental groups of the spaces of the genus-$2$
Heegaard splittings of lens spaces are all finitely presented.
| arxiv topic:math.GT |
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