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arxiv_dataset-77001609.04522 | Tensor Graphical Model: Non-convex Optimization and Statistical
Inference
stat.ML stat.ME
We consider the estimation and inference of graphical models that
characterize the dependency structure of high-dimensional tensor-valued data.
To facilitate the estimation of the precision matrix corresponding to each way
of the tensor, we assume the data follow a tensor normal distribution whose
covariance has a Kronecker product structure. A critical challenge in the
estimation and inference of this model is the fact that its penalized maximum
likelihood estimation involves minimizing a non-convex objective function. To
address it, this paper makes two contributions: (i) In spite of the
non-convexity of this estimation problem, we prove that an alternating
minimization algorithm, which iteratively estimates each sparse precision
matrix while fixing the others, attains an estimator with an optimal
statistical rate of convergence. (ii) We propose a de-biased statistical
inference procedure for testing hypotheses on the true support of the sparse
precision matrices, and employ it for testing a growing number of hypothesis
with false discovery rate (FDR) control. The asymptotic normality of our test
statistic and the consistency of FDR control procedure are established. Our
theoretical results are backed up by thorough numerical studies and our real
applications on neuroimaging studies of Autism spectrum disorder and users'
advertising click analysis bring new scientific findings and business insights.
The proposed methods are encoded into a publicly available R package Tlasso.
| arxiv topic:stat.ML stat.ME |
arxiv_dataset-77011609.04622 | Algebraic models of homotopy types and the homotopy hypothesis
math.CT math.AT
We introduce and study a notion of cylinder coherator similar to the notion
of Grothendieck coherator which define more flexible notion of weak infinity
groupoids. We show that each such cylinder coherator produces a combinatorial
semi-model category of weak infinity groupoids, whose objects are all fibrant
and which is in a precise sense "freely generated by an object". We show that
all those semi model categories are Quillen equivalent together and Quillen to
the model category of spaces. A general procedure is given to produce such
coherator, and several explicit examples are presented: one which is simplicial
in nature and allows the comparison to the model category for spaces. A second
example can be describe as the category of globular sets endowed with "all the
operations that can be defined within a weak type theory". This second notion
seem to provide a definition of weak infinity groupoids which can be defined
internally within type theory and which is classically equivalent to homotopy
types. Finally, the category of Grothendieck infinity groupoids for a fixed
Grothendieck coherator would be an example of this formalism under a seemingly
simple conjecture whose validity is shown to imply Grothendieck homotopy
hypothesis. This conjecture seem to sum up what needs to be proved at a
technical level to ensure that the theory of Grothendieck weak infinity
groupoid is well behaved.
| arxiv topic:math.CT math.AT |
arxiv_dataset-77021609.04722 | Concordance and the Smallest Covering Set of Preference Orderings
cs.AI cs.DS cs.GT cs.IT math.IT
Preference orderings are orderings of a set of items according to the
preferences (of judges). Such orderings arise in a variety of domains,
including group decision making, consumer marketing, voting and machine
learning. Measuring the mutual information and extracting the common patterns
in a set of preference orderings are key to these areas. In this paper we deal
with the representation of sets of preference orderings, the quantification of
the degree to which judges agree on their ordering of the items (i.e. the
concordance), and the efficient, meaningful description of such sets.
We propose to represent the orderings in a subsequence-based feature space
and present a new algorithm to calculate the size of the set of all common
subsequences - the basis of a quantification of concordance, not only for pairs
of orderings but also for sets of orderings. The new algorithm is fast and
storage efficient with a time complexity of only $O(Nn^2)$ for the orderings of
$n$ items by $N$ judges and a space complexity of only $O(\min\{Nn,n^2\})$.
Also, we propose to represent the set of all $N$ orderings through a smallest
set of covering preferences and present an algorithm to construct this smallest
covering set.
The source code for the algorithms is available at
https://github.com/zhiweiuu/secs
| arxiv topic:cs.AI cs.DS cs.GT cs.IT math.IT |
arxiv_dataset-77031609.04822 | A free-form lensing model of A370 revealing stellar mass dominated BCGs,
in Hubble Frontier Fields images
astro-ph.GA astro-ph.CO
We derive a free-form mass distribution for the unrelaxed cluster A370
(z=0.375), using the latest Hubble Frontier Fields images and GLASS
spectroscopy. Starting from a reliable set of 10 multiply lensed systems we
produce a free-form lens model that identifies ~ 80 multiple-images. Good
consistency is found between models using independent subsamples of these
lensed systems, with detailed agreement for the well resolved arcs. The mass
distribution has two very similar concentrations centred on the two prominent
Brightest Cluster Galaxies (or BCGs), with mass profiles that are accurately
constrained by a uniquely useful system of long radially lensed images centred
on both BCGs. We show that the lensing mass profiles of these BCGs are mainly
accounted for by their stellar mass profiles, with a modest contribution from
dark matter within r<100 kpc of each BCG. This conclusion may favour a cooled
cluster gas origin for BCGs, rather than via mergers of normal galaxies for
which dark matter should dominate over stars. Growth via merging between BCGs
is, however, consistent with this finding, so that stars still dominate over
dark matter .
| arxiv topic:astro-ph.GA astro-ph.CO |
arxiv_dataset-77041609.04922 | Optically assisted trapping with high-permittivity dielectric rings:
Towards optical aerosol filtration
cond-mat.mtrl-sci physics.optics
Controlling the transport, trapping, and filtering of nanoparticles is
important for many applications. By virtue of their weak response to gravity
and their thermal motion, various physical mechanisms can be exploited for such
operations on nanoparticles. However, the manipulation based on optical forces
is potentially most appealing since it constitutes a highly deterministic
approach. Plasmonic nanostructures have been suggested for this purpose, but
they possess the disadvantages of locally generating heat and trapping the
nanoparticles directly on surface. Here, we propose the use of dielectric rings
made of high permittivity materials for trapping nanoparticles. Thanks to their
ability to strongly localize the field in space, nanoparticles can be trapped
without contact. We use a semi-analytical method to study the ability of these
rings to trap nanoparticles. Results are supported by full-wave simulations.
Application of the trapping concept to nanoparticle filtration is suggested.
| arxiv topic:cond-mat.mtrl-sci physics.optics |
arxiv_dataset-77051609.05022 | A double copy for ${\cal N}=2$ supergravity: a linearised tale told
on-shell
hep-th
We construct the on-shell double copy for linearised four-dimensional ${\cal
N}=2$ supergravity coupled to one vector multiplet with a quadratic
prepotential. We apply this dictionary to the weak-field approximation of
dyonic BPS black holes in this theory.
| arxiv topic:hep-th |
arxiv_dataset-77061609.05122 | Search for anomalous electroweak production of $WW/WZ$ in association
with a high-mass dijet system in $pp$ collisions at $\sqrt{s}=8$ TeV with the
ATLAS detector
hep-ex
A search is presented for anomalous quartic gauge boson couplings in
vector-boson scattering. The data for the analysis correspond to $20.2$
fb$^{-1}$ of $\sqrt{s}=8$ TeV $pp$ collisions, and were collected in 2012 by
the ATLAS experiment at the Large Hadron Collider. The search looks for the
production of $WW$ or $WZ$ boson pairs accompanied by a high-mass dijet system,
with one $W$ decaying leptonically, and a $W$ or $Z$ decaying hadronically. The
hadronically decaying $W/Z$ is reconstructed as either two small-radius jets or
one large-radius jet using jet substructure techniques. Constraints on the
anomalous quartic gauge boson coupling parameters $\alpha_4$ and $\alpha_5$ are
set by fitting the transverse mass of the diboson system, and the resulting 95%
confidence intervals are $-0.024<\alpha_4<0.030$ and $-0.028<\alpha_5<0.033$.
| arxiv topic:hep-ex |
arxiv_dataset-77071609.05222 | What prevents gravitational collapse in string theory?
hep-th gr-qc
It is conventionally believed that if a ball of matter of mass $M$ has a
radius close to $2GM$ then it must collapse to a black hole. But string theory
microstates (fuzzballs) have no horizon or singularity, and they do {\it not}
collapse. We consider two simple examples from classical gravity to illustrate
how this violation of our intuition happens. In each case the `matter' arises
from an extra compact dimension, but the topology of this extra dimension is
not trivial. The pressure and density of this matter diverge at various points,
but this is only an artifact of dimensional reduction; thus we bypass results
like Buchadahl's theorem. Such microstates give the entropy of black holes, so
these topologically nontrivial constructions dominate the state space of
quantum gravity.
| arxiv topic:hep-th gr-qc |
arxiv_dataset-77081609.05322 | Signal Transmissibility in Marginal Granular Materials
cond-mat.soft
We examine the "transmissibility" of a simulated two-dimensional pack of
frictionless disks formed by confining dilute disks in a shrinking, periodic
box to the point of mechanical stability. Two opposite boundaries are then
removed, thus allowing a set of free motions. Small free displacements on one
boundary then induce proportional displacements on the opposite boundary.
Transmissibility is the ability to distinguish different perturbations by their
distant responses. We assess transmissibility by successively identifying free
orthonormal modes of motion that have the {\em smallest} distant responses. The
last modes to be identified in this "pessimistic" basis are the most
transmissive. The transmitted amplitudes of these most transmissive modes fall
off exponentially with mode number. Similar exponential falloff is seen in a
simple elastic medium, though the responsible modes differ greatly in structure
in the two systems. Thus the marginal pack's transmissibility is qualitatively
similar to that of a simple elastic medium. We compare our results with recent
findings based on the projection of the space of free motion onto interior
sites.
| arxiv topic:cond-mat.soft |
arxiv_dataset-77091609.05422 | Large deviations for Gibbs measures with singular Hamiltonians and
emergence of Kahler-Einstein metrics
math-ph math.CV math.DG math.MP
In the present paper and the companion paper [9] a probabilistic
(statistical-mechanical) approach to the construction of canonical metrics on a
complex algebraic varieties X is introduced, by sampling "temperature deformed"
determinantal point processes. The main new ingredient is a large deviation
principle for Gibbs measures with singular Hamiltonians, which is proved in the
present paper. As an application we show that the unique Kahler-Einstein metric
with negative Ricci curvature on a canonically polarized algebraic manifold X
emerges in the many particle limit of the canonical point processes on X. In
the companion paper [9] the extension to algebraic varieties X with positive
Kodaira dimension is given and a conjectural picture relating negative
temperature states to the existence problem for Kahler-Einstein metrics with
positive Ricci curvature is developed.
| arxiv topic:math-ph math.CV math.DG math.MP |
arxiv_dataset-77101609.05522 | Learning camera viewpoint using CNN to improve 3D body pose estimation
cs.CV
The objective of this work is to estimate 3D human pose from a single RGB
image. Extracting image representations which incorporate both spatial relation
of body parts and their relative depth plays an essential role in accurate3D
pose reconstruction. In this paper, for the first time, we show that camera
viewpoint in combination to 2D joint lo-cations significantly improves 3D pose
accuracy without the explicit use of perspective geometry mathematical
models.To this end, we train a deep Convolutional Neural Net-work (CNN) to
learn categorical camera viewpoint. To make the network robust against clothing
and body shape of the subject in the image, we utilized 3D computer rendering
to synthesize additional training images. We test our framework on the largest
3D pose estimation bench-mark, Human3.6m, and achieve up to 20% error reduction
compared to the state-of-the-art approaches that do not use body part
segmentation.
| arxiv topic:cs.CV |
arxiv_dataset-77111609.05622 | Patterns of cooperation during collective emergencies in the
help-or-escape social dilemma
physics.soc-ph
Although cooperation is central to the organisation of many social systems,
relatively little is known about cooperation in situations of collective
emergency. When groups of people flee from a danger such as a burning building
or a terrorist attack, the collective benefit of cooperation is important, but
the cost of helping is high and the temptation to defect is strong. To explore
the degree of cooperation in emergencies, we develop a new social game, the
help-or-escape social dilemma. Under time and monetary pressure, players decide
how much risk they are willing to take in order to help others. Results
indicated that players took as much risk to help others during emergencies as
they did under normal conditions. In both conditions, most players applied an
egalitarian heuristic and helped others until their chance of success equalled
that of the group. This strategy is less efficient during emergencies, however,
because the increased time pressure results in fewer people helped.
Furthermore, emergencies tend to amplify participants initial tendency to
cooperate, with prosocials becoming even more cooperative and individualists
becoming even more selfish. Our framework offers new opportunities to study
human cooperation and could help authorities to better manage crowd behaviours
during mass emergencies.
| arxiv topic:physics.soc-ph |
arxiv_dataset-77121609.05722 | Poisson Noise Reduction with Higher-order Natural Image Prior Model
cs.CV
Poisson denoising is an essential issue for various imaging applications,
such as night vision, medical imaging and microscopy. State-of-the-art
approaches are clearly dominated by patch-based non-local methods in recent
years. In this paper, we aim to propose a local Poisson denoising model with
both structure simplicity and good performance. To this end, we consider a
variational modeling to integrate the so-called Fields of Experts (FoE) image
prior, that has proven an effective higher-order Markov Random Fields (MRF)
model for many classic image restoration problems. We exploit several feasible
variational variants for this task. We start with a direct modeling in the
original image domain by taking into account the Poisson noise statistics,
which performs generally well for the cases of high SNR. However, this strategy
encounters problem in cases of low SNR. Then we turn to an alternative modeling
strategy by using the Anscombe transform and Gaussian statistics derived data
term. We retrain the FoE prior model directly in the transform domain. With the
newly trained FoE model, we end up with a local variational model providing
strongly competitive results against state-of-the-art non-local approaches,
meanwhile bearing the property of simple structure. Furthermore, our proposed
model comes along with an additional advantage, that the inference is very
efficient as it is well-suited for parallel computation on GPUs. For images of
size $512 \times 512$, our GPU implementation takes less than 1 second to
produce state-of-the-art Poisson denoising performance.
| arxiv topic:cs.CV |
arxiv_dataset-77131609.05822 | Selectively (a)-spaces from almost disjoint families are necessarily
countable under a certain parametrized weak diamond principle
math.GN math.LO
The second author has recently shown ([20]) that any selectively (a) almost
disjoint family must have cardinality strictly less than $2^{\alpeh_0}$, so
under the Continuum Hypothesis such a family is necessarily countable. However,
it is also shown in the same paper that $2^{\alpeh_0} < 2^{\alpeh_1}$ alone
does not avoid the existence of uncountable selectively (a) almost disjoint
families. We show in this paper that a certain effective parametrized weak
diamond principle is enough to ensure countability of the almost disjoint
family in this context. We also discuss the deductive strength of this specific
weak diamond principle (which is consistent with the negation of the Continuum
Hypothesis, apart from other features).
| arxiv topic:math.GN math.LO |
arxiv_dataset-77141609.05922 | The RG-improved Twin Higgs effective potential at NNLL
hep-ph
We present the Renormalization Group improvement of the Twin Higgs effective
potential at cubic order in logarithmic accuracy. We first introduce a
model-independent low-energy effective Lagrangian that captures both the
pseudo-Nambu-Goldstone boson nature of the Higgs field and the twin light
degrees of freedom charged under a copy of the Standard Model. We then apply
the background field method to systematically re-sum all the one loop diagrams
contributing to the potential. We show how this technique can be efficient to
implicitly renormalize the higher-dimensional operators in the twin sector
without classifying all of them. A prediction for the Higgs mass in the Twin
Higgs model is derived and found to be of the order of $M_H \sim 120
~\text{GeV}$ with an ultraviolet cut-off $m_*\sim 10-20 ~\text{TeV}$.
Irrespective of any possible ultraviolet completion of the low-energy
Lagrangian, the infrared degrees of freedom alone are therefore enough to
account for the observed value of the Higgs mass through running effects.
| arxiv topic:hep-ph |
arxiv_dataset-77151609.06022 | Spectral properties of the Cayley Graphs of split metacyclic groups
math.CO
Let $\Gamma(G,S)$ denote the Cayley graph of a group $G$ with respect to a
set $S \subset G$. In this paper, we analyze the spectral properties of the
Cayley graphs $\mathcal{T}_{m,n,k} = \Gamma(\mathbb{Z}_m \ltimes_k
\mathbb{Z}_n, \{(\pm 1,0),(0,\pm 1)\})$, where $m,n \geq 3$ and $k^m \equiv 1
\pmod{n}$. We show that the adjacency matrix of $\mathcal{T}_{m,n,k}$, upto
relabeling, is a block circulant matrix, and we also obtain an explicit
description of these blocks. By extending a result due to Walker-Mieghem to
Hermitian matrices, we show that $\mathcal{T}_{m,n,k}$ is not Ramanujan, when
either $m > 8$, or $n \geq 400$.
| arxiv topic:math.CO |
arxiv_dataset-77161609.06122 | Fluorescence via Reverse Intersystem Crossing from Higher Triplet States
in a Bisanthracene Derivative
cond-mat.mtrl-sci physics.chem-ph
To elucidate the high external quantum efficiency observed for organic
light-emitting diodes using a bisanthracene derivative, BD1, as the emitting
molecule, off-diagonal vibronic coupling constants (VCCs) between the excited
states of BD1, which govern non-radiative transition rates, were calculated
employing time-dependent density functional theory. The VCCs were analysed
based on the concept of vibronic coupling density. The VCC calculations suggest
a fluorescence via higher triplets (FvHT) mechanism, which entails the
conversion of a T$_4$ exciton generated during electrical excitation into an
S$_2$ exciton via reverse intersystem crossing (RISC); moreover, the S$_2$
exciton relaxes to a fluorescent S$_1$ exciton because of large vibronic
coupling between S$_2$ and S$_1$. This mechanism is valid as long as the
relaxation of triplet states higher than T$_1$ to lower states is suppressed.
The symmetry-controlled thermally activated delayed fluorescence (SC-TADF) and
inverted singlet and triplet (iST) structure, which have been proposed in our
previous studies, are the special examples of the FvHT mechanism that need high
molecular symmetry. However, BD1 achieves the FvHT mechanism in spite of its
asymmetrical structure. A general condition for the suppression of radiative
and non-radiative transitions in molecules with pseudo-degenerate electronic
structures such as BD1 is discussed. A superordinate concept, fluorescence via
RISC, which includes TADF, SC-TADF, iST structure, and FvHT is also proposed.
| arxiv topic:cond-mat.mtrl-sci physics.chem-ph |
arxiv_dataset-77171609.06222 | Collisional broadening of angular correlations in a multiphase transport
model
nucl-th nucl-ex
Systematic comparisons of jetlike correlation data to radiative and
collisional energy loss model calculations are essential to extract transport
properties of the quark-gluon medium created in relativistic heavy ion
collisions. This paper presents a transport study of collisional broadening of
jetlike correlations, by following parton-parton collision history in a
multiphase transport (AMPT) model. The correlation shape is studied as a
function of the number of parton-parton collisions suffered by a high
transverse momentum probe parton ($N_{\rm coll}$) and the azimuth of the probe
relative to the reaction plane ($\phi_{\rm fin.}^{\rm probe}$). Correlation is
found to broaden with increasing $N_{\rm coll}$ and $\phi_{\rm fin.}^{\rm
probe}$ from in- to out-of-plane direction. This study provides a transport
model reference for future jet-medium interaction studies.
| arxiv topic:nucl-th nucl-ex |
arxiv_dataset-77181609.06322 | Cosmic ray heating in cool core clusters - II. Self-regulation cycle and
non-thermal emission
astro-ph.GA astro-ph.CO astro-ph.HE
Self-regulated feedback by active galactic nuclei (AGNs) appears to be
critical in balancing radiative cooling of the low-entropy gas at the centres
of galaxy clusters and in regulating star formation in central galaxies. In a
companion paper, we found steady-state solutions of the hydrodynamic equations
that are coupled to the CR energy equation for a large cluster sample. In those
solutions, radiative cooling in the central region is balanced by streaming CRs
through the generation and dissipation of resonantly generated Alfv{\'e}n waves
and by thermal conduction at large radii. Here we demonstrate that the
predicted non-thermal emission resulting from hadronic CR interactions in the
intra-cluster medium exceeds observational radio (and gamma-ray) data in a
subsample of clusters that host radio mini halos (RMHs). In contrast, the
predicted non-thermal emission is well below observational data in cooling
galaxy clusters without RMHs. These are characterised by exceptionally large
AGN radio fluxes, indicating high CR yields and associated CR heating rates. We
suggest a self-regulation cycle of AGN feedback in which non-RMH clusters are
heated by streaming CRs homogeneously throughout the central cooling region. We
predict {\em radio micro halos} surrounding the AGNs of these CR-heated
clusters in which the primary emission may predominate the hadronically
generated emission. Once the CR population has streamed sufficiently far and
lost enough energy, the cooling rate increases, which explains the increased
star formation rates in clusters hosting RMHs. Those could be powered
hadronically by CRs that have previously heated the cluster core.
| arxiv topic:astro-ph.GA astro-ph.CO astro-ph.HE |
arxiv_dataset-77191609.06422 | Combined effects of f(R) gravity and conformally invariant Maxwell field
on the extended phase space thermodynamics of higher-dimensional black holes
gr-qc
In this paper, we investigate the thermodynamics of higher-dimensional $f(R)$
black holes in the extended phase space. Both the analytic expressions and
numerical results for the possible critical physical quantities are obtained.
It is proved that meaningful critical specific volume only exists when $p$ is
odd. This unique phenomenon may be attributed to the combined effect of $f(R)$
gravity and conformally invariant Maxwell field. It is also shown that the
ratio $P_cv_c/T_c$ differs from that of higher dimensional charged AdS black
holes in Einstein gravity. However, the ratio for four-dimensional $f(R)$ black
holes is the same as that of four-dimensional RN-AdS black holes, implying that
$f(R)$ gravity does not influence the ratio. So the ratio may be related to
conformally invariant Maxwell field. To probe the phase transition, we derive
the explicit expression of the Gibbs free energy with its graph plotted. Phase
transition analogous to the van der Waals liquid-gas system take place between
the small black hole and the large black hole. Classical swallow tail behavior,
characteristic of first order phase transition, can also be observed in the
Gibbs free energy graph. Critical exponents are also calculated. It is shown
that these exponents are exactly the same as those of other AdS black holes,
implying that neither $f(R)$ gravity nor conformally invariant Maxwell field
influence the critical exponents. Since the investigated black hole solution
depends on the form of the function $f(R)$, we discuss in detail how our
results put constraint on the form of the function $f(R)$ and we also present a
simple example.
| arxiv topic:gr-qc |
arxiv_dataset-77201609.06522 | Computing Vertex-Disjoint Paths using MAOs
cs.DM cs.DS
Let G be a graph with minimum degree $\delta$. It is well-known that maximal
adjacency orderings (MAOs) compute a vertex set S such that every pair of S is
connected by at least $\delta$ internally vertex-disjoint paths in G.
We present an algorithm that, given any pair of S, computes these $\delta$
paths in linear time O(n+m). This improves the previously best solutions for
these special vertex pairs, which were flow-based. Our algorithm simplifies a
proof about pendant pairs of Mader and makes a purely existential proof of
Nagamochi algorithmic.
| arxiv topic:cs.DM cs.DS |
arxiv_dataset-77211609.06622 | An Analysis of Introductory Programming Courses at UK Universities
cs.CY cs.PL
Context: In the context of exploring the art, science and engineering of
programming, the question of which programming languages should be taught first
has been fiercely debated since computer science teaching started in
universities. Failure to grasp programming readily almost certainly implies
failure to progress in computer science. Inquiry: What first programming
languages are being taught? There have been regular national-scale surveys in
Australia and New Zealand, with the only US survey reporting on a small subset
of universities. This the first such national survey of universities in the UK.
Approach: We report the results of the first survey of introductory programming
courses (N=80) taught at UK universities as part of their first year computer
science (or related) degree programmes, conducted in the first half of 2016. We
report on student numbers, programming paradigm, programming languages and
environment/tools used, as well as the underpinning rationale for these
choices. Knowledge: The results in this first UK survey indicate a dominance of
Java at a time when universities are still generally teaching students who are
new to programming (and computer science), despite the fact that Python is
perceived, by the same respondents, to be both easier to teach as well as to
learn. Grounding: We compare the results of this survey with a related survey
conducted since 2010 (as well as earlier surveys from 2001 and 2003) in
Australia and New Zealand. Importance: This survey provides a starting point
for valuable pedagogic baseline data for the analysis of the art, science and
engineering of programming, in the context of substantial computer science
curriculum reform in UK schools, as well as increasing scrutiny of teaching
excellence and graduate employability for UK universities.
| arxiv topic:cs.CY cs.PL |
arxiv_dataset-77221609.06722 | On the pi pi continuum in the nucleon form factors and the proton radius
puzzle
hep-ph hep-lat nucl-ex nucl-th physics.atom-ph
We present an improved determination of the $\pi\pi$ continuum contribution
to the isovector spectral functions of the nucleon electromagnetic form
factors. Our analysis includes the most up-to-date results for the
$\pi\pi\to\bar N N$ partial waves extracted from Roy-Steiner equations,
consistent input for the pion vector form factor, and a thorough discussion of
isospin-violating effects and uncertainty estimates. As an application, we
consider the $\pi\pi$ contribution to the isovector electric and magnetic radii
by means of sum rules, which, in combination with the accurately known neutron
electric radius, are found to slightly prefer a small proton charge radius.
| arxiv topic:hep-ph hep-lat nucl-ex nucl-th physics.atom-ph |
arxiv_dataset-77231609.06822 | Effect of adding nanometre-sized heterogeneities on the structural
dynamics and the excess wing of a molecular glass former
cond-mat.dis-nn cond-mat.soft
We present the relaxation dynamics of glass-forming glycerol mixed with 1.1
nm sized polyhedral oligomeric silsesquioxane (POSS) molecules using dielectric
spectroscopy (DS) and two different neutron scattering (NS) techniques. Both,
the reorientational dynamics as measured by DS and the density fluctuations
detected by NS reveal a broadening of the alpha relaxation when POSS molecules
are added. Moreover, we find a significant slowing down of the alpha-relaxation
time. These effects are in accord with the heterogeneity scenario considered
for the dynamics of glasses and supercooled liquids. The addition of POSS also
affects the excess wing in glycerol arising from a secondary relaxation
process, which seems to exhibit a dramatic increase in relative strength
compared to the alpha-relaxation.
| arxiv topic:cond-mat.dis-nn cond-mat.soft |
arxiv_dataset-77241609.06922 | Constraints on galaxy formation models from the galaxy stellar mass
function and its evolution
astro-ph.GA
We explore the parameter space of the semi-analytic galaxy formation model
GALFORM, studying the constraints imposed by measurements of the galaxy stellar
mass function (GSMF) and its evolution. We use the Bayesian Emulator method to
quickly eliminate vast implausible volumes of the parameter space and zoom in
on the most interesting regions, allowing us to identify a set of models that
match the observational data within model uncertainties. We find that the GSMF
strongly constrains parameters related to quiescent star formation in discs,
stellar and AGN feedback and threshold for disc instabilities, but weakly
restricts other parameters. Constraining the model using local data alone does
not usually select models that match the evolution of the GSMF well.
Nevertheless, we show that a small subset of models provides acceptable match
to GSMF data out to redshift 1.5. We explore the physical significance of the
parameters of these models, in particular exploring whether the model provides
a better description if the mass loading of the galactic winds generated by
starbursts ($\beta_{0,\text{burst}}$) and quiescent disks
($\beta_{0,\text{disc}}$) is different. Performing a principal component
analysis of the plausible volume of the parameter space, we write a set of
relations between parameters obeyed by plausible models with respect to GSMF
evolution. We find that while $\beta_{0,\text{disc}}$ is strongly constrained
by GSMF evolution data, constraints on $\beta_{0,\text{burst}}$ are weak.
Although it is possible to find plausible models for which
$\beta_{0,\text{burst}} = \beta_{0,\text{disc}}$, most plausible models have
$\beta_{0,\text{burst}}>\beta_{0,\text{disc}}$, implying - for these - larger
SN feedback efficiency at higher redshifts.
| arxiv topic:astro-ph.GA |
arxiv_dataset-77251609.07022 | Competing turbulent cascades and eddy-wave interactions in shallow water
equilibria
physics.flu-dyn cond-mat.stat-mech
In recent work, Renaud, Venaille, and Bouchet (RVB) revisit the equilibrium
statistical mechanics theory of the shallow water equations, within a
microcanonical approach, focusing on a more careful treatment of the energy
partition between inertial gravity wave and eddy motions in the equilibrium
state, and deriving joint probability distributions for the corresponding
dynamical degrees of freedom. The authors derive a Liouville theorem that
determines the underlying phase space statistical measure, but then, through
some physical arguments, actually compute the equilibrium statistics using a
measure that \emph{violates} this theorem. Here, using a more convenient, but
essentially equivalent, grand canonical approach, the full statistical theory
consistent with the Liouville theorem is derived. The results reveal several
significant differences from the previous results: (1) The microscale wave
motions lead to a strongly fluctuating thermodynamics, including long-ranged
correlations, in contrast to the mean-field-like behavior found by RVB. The
final effective model is equivalent to that of an elastic membrane with a
nonlinear wave-renormalized surface tension. (2) Even when a mean field
approximation is made, a rather more complex joint probability distribution is
revealed. Alternative physical arguments fully support the consistency of the
results. Of course, the true fluid final steady state relies on dissipative
processes not included in the shallow water equations, such as wave breaking
and viscous effects, but it is argued that the current theory provides a more
mathematically consistent starting point for future work aimed at assessing
their impacts.
| arxiv topic:physics.flu-dyn cond-mat.stat-mech |
arxiv_dataset-77261609.07122 | UV complete composite Higgs models
hep-ph
We study confining gauge theories with fermions vectorial under the SM that
produce a Higgs doublet as a Nambu-Goldstone boson. The vacuum misalignment
required to break the electro-weak symmetry is induced by an elementary Higgs
doublet with Yukawa couplings to the new fermions. The physical Higgs is a
linear combination of elementary and composite Higgses while the SM fermions
remain elementary. The full theory is renormalizable and the SM Yukawa
couplings are generated from the ones of the elementary Higgs allowing to
eliminate all flavour problems but with interesting effects for Electric Dipole
Moments of SM particles. We also discuss how ideas on the relaxation of the
electro-weak scale could be realised within this framework.
| arxiv topic:hep-ph |
arxiv_dataset-77271609.07222 | Deep Multi-Task Learning with Shared Memory
cs.CL
Neural network based models have achieved impressive results on various
specific tasks. However, in previous works, most models are learned separately
based on single-task supervised objectives, which often suffer from
insufficient training data. In this paper, we propose two deep architectures
which can be trained jointly on multiple related tasks. More specifically, we
augment neural model with an external memory, which is shared by several tasks.
Experiments on two groups of text classification tasks show that our proposed
architectures can improve the performance of a task with the help of other
related tasks.
| arxiv topic:cs.CL |
arxiv_dataset-77281609.07322 | On Gravitational Chirality as the Genesis of Astrophysical Jets
gr-qc astro-ph.GA physics.space-ph
It has been suggested that single and double jets observed emanating from
certain astrophysical objects may have a purely gravitational origin. We
discuss new classes of plane-fronted and pulsed gravitational wave solutions to
the equation for perturbations of Ricci-flat spacetimes around Minkowski
metrics, as models for the genesis of such phenomena. These solutions are
classified in terms of their chirality and generate a family of non-stationary
spacetime metrics. Particular members of these families are used as backgrounds
in analysing time-like solutions to the geodesic equation for test particles.
They are found numerically to exhibit both single and double jet-like features
with dimensionless aspect ratios suggesting that it may be profitable to
include such backgrounds in simulations of astrophysical jet dynamics from
rotating accretion discs involving electromagnetic fields.
| arxiv topic:gr-qc astro-ph.GA physics.space-ph |
arxiv_dataset-77291609.07422 | Heavy quark fragmentation functions at next-to-leading perturbative QCD
hep-ph nucl-th
It is well-known that the dominant mechanism to produce hadronic bound states
with large transverse momentum is fragmentation. This mechanism is described by
the fragmentation functions (FFs) which are the universal and
process-independent functions. Here, we review the perturbative FFs formalism
as an appropriate tool for studying these hadronization processes and detail
the extension of this formalism at next-to-leading order (NLO). Using the
Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to
fragment into a S-wave heavy meson at NLO. As an example, we study the LO and
NLO FFs for a charm quark to split into the S-wave $D$-meson and compare our
analytic results both with experimental data and well-known phenomenological
models.
| arxiv topic:hep-ph nucl-th |
arxiv_dataset-77301609.07522 | Interpreting formulas of divisible lattice ordered abelian groups
math.LO
We show that a large class of divisible abelian $\ell$-groups (lattice
ordered groups) of continuous functions is interpretable (in a certain sense)
in the lattice of the zero sets of these functions. This has various
applications to the model theory of these $\ell$-groups, including decidability
results.
| arxiv topic:math.LO |
arxiv_dataset-77311609.07622 | Asymptotic homogenization of hygro-thermo-mechanical properties of
fibrous networks
cond-mat.soft cond-mat.mtrl-sci
The hygro-thermo-expansive response of fibrous networks involves deformation
phenomena at multiple length scales. The moisture or temperature induced
expansion of individual fibres is transmitted in the network through the
inter-fibre bonds; particularly in the case of anisotropic fibres, this
substantially influences the resulting overall deformation. This paper presents
a methodology to predict the effective properties of bonded fibrous networks.
The distinctive features of the work are i) the focus on the
hygro-thermo-mechanical response, whereas in the literature generally only the
mechanical properties are addressed; ii) the adoption of asymptotic
homogenization to model fibrous networks. Asymptotic homogenization is an
efficient and versatile multi-scale technique that allows to obtain within a
rigorous setting the effective material response, even for complex
micro-structural geometries. The fibrous networks considered in this
investigation are generated by random deposition of the fibres within a planar
region according to an orientation probability density function. Most of the
available network descriptions model the fibres essentially as uni-axial
elements, thereby not explicitly considering the role of the bonds. In this
paper, the fibres are treated as two dimensional ribbon-like elements; this
allows to naturally include the contribution of the bonding regions to the
effective expansion. The efficacy of the proposed study is illustrated by
investigating the effective response for several network realizations,
incorporating the influence of different micro-scale parameters, such as fibre
hygro-thermo-elastic properties, orientation, geometry, areal coverage.
| arxiv topic:cond-mat.soft cond-mat.mtrl-sci |
arxiv_dataset-77321609.07722 | Sooner than Expected: Hitting the Wall of Complexity in Evolution
cs.NE
In evolutionary robotics an encoding of the control software, which maps
sensor data (input) to motor control values (output), is shaped by stochastic
optimization methods to complete a predefined task. This approach is assumed to
be beneficial compared to standard methods of controller design in those cases
where no a-priori model is available that could help to optimize performance.
Also for robots that have to operate in unpredictable environments, an
evolutionary robotics approach is favorable. We demonstrate here that such a
model-free approach is not a free lunch, as already simple tasks can represent
unsolvable barriers for fully open-ended uninformed evolutionary computation
techniques. We propose here the 'Wankelmut' task as an objective for an
evolutionary approach that starts from scratch without pre-shaped controller
software or any other informed approach that would force the behavior to be
evolved in a desired way. Our focal claim is that 'Wankelmut' represents the
simplest set of problems that makes plain-vanilla evolutionary computation
fail. We demonstrate this by a series of simple standard evolutionary
approaches using different fitness functions and standard artificial neural
networks as well as continuous-time recurrent neural networks. All our tested
approaches failed. We claim that any other evolutionary approach will also fail
that does per-se not favor or enforce modularity and does not freeze or protect
already evolved functionalities. Thus we propose a hard-to-pass benchmark and
make a strong statement for self-complexifying and generative approaches in
evolutionary computation. We anticipate that defining such a 'simplest task to
fail' is a valuable benchmark for promoting future development in the field of
artificial intelligence, evolutionary robotics and artificial life.
| arxiv topic:cs.NE |
arxiv_dataset-77331609.07822 | Disorder effect on chiral edge modes and anomalous Hall conductance in
Weyl semimetals
cond-mat.mes-hall
Typical Weyl semimetals host chiral surface states and hence show an
anomalous Hall response. Although a Weyl semimetal phase is known to be robust
against weak disorder, the influence of disorder on chiral states is not fully
clarified so far. We study the behavior of such chiral states in the presence
of disorder and its consequences on an anomalous Hall response, focusing on a
thin slab of Weyl semimetal with chiral surface states along its edge. It is
shown that weak disorder does not disrupt chiral edge states but crucially
affects them owing to the renormalization of a mass parameter: the number of
chiral edge states changes depending on the strength of disorder. It is also
shown that the Hall conductance is quantized when the Fermi level is located
near Weyl nodes within a finite-size gap. This quantization of the Hall
conductance collapses once the strength of disorder exceeds a critical value,
suggesting that it serves as a probe to distinguish a Weyl semimetal phase from
a diffusive anomalous Hall metal phase.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-77341609.07922 | It wasn't me! Plausible Deniability in Web Search
cs.CR cs.CY
Our ability to control the flow of sensitive personal information to online
systems is key to trust in personal privacy on the internet. We ask how to
detect, assess and defend user privacy in the face of search engine
personalisation? We develop practical and scalable tools allowing a user to
detect, assess and defend against threats to plausible deniability. We show
that threats to plausible deniability of interest are readily detectable for
all topics tested in an extensive testing program. We show this remains the
case when attempting to disrupt search engine learning through noise query
injection and click obfuscation are used. We use our model we design a defence
technique exploiting uninteresting, proxy topics and show that it provides
amore effective defence of plausible deniability in our experiments.
| arxiv topic:cs.CR cs.CY |
arxiv_dataset-77351609.08022 | Correlation based passive imaging with a white noise source
math.AP math.PR
Passive imaging refers to problems where waves generated by unknown sources
are recorded and used to image the medium through which they travel. The
sources are typically modelled as a random variable and it is assumed that some
statistical information is available. In this paper we study the stochastic
wave equation $\partial_t^2 u - \Delta_g u = \chi W$, where $W$ is a random
variable with the white noise statistics on ${\mathbb R}^{1+n}$, $n \ge 3$,
$\chi$ is a smooth function vanishing for negative times and outside a compact
set in space, and $\Delta_g$ is the Laplace-Beltrami operator associated to a
smooth non-trapping Riemannian metric tensor $g$ on ${\mathbb R}^n$. The metric
tensor $g$ models the medium to be imaged, and we assume that it coincides with
the Euclidean metric outside a compact set. We consider the empirical
correlations on an open set $\mathcal X \subset {\mathbb R}^n$, $$ C_T(t_1,
x_1, t_2, x_2) = \frac 1 T \int_0^T u(t_1+s,x_1) u(t_2+s,x_2) ds, \quad
t_1,t_2>0,\ x_1,x_2\in \mathcal X, $$ for $T>0$. Supposing that $\chi$ is
non-zero on $\mathcal X$ and constant in time after $t > 1$, we show that in
the limit $T \to \infty$, the data $C_T$ becomes statistically stable, that is,
independent of the realization of $W$. Our main result is that, with
probability one, this limit determines the Riemannian manifold $({\mathbb
R}^n,g)$ up to an isometry. To our knowledge, this is the first result showing
that a medium can be determined in a passive imaging setting, without assuming
a separation of scales.
| arxiv topic:math.AP math.PR |
arxiv_dataset-77361609.08122 | On Shahidi local coefficients matrix
math.NT
In these notes we define and study the Shahidi local coefficients matrix
associated with a genuine principal series representation I({\sigma}) of an
n-fold cover of p-adic SL(2,F) and an additive character {\psi}. The conjugacy
class of this matrix is an invariant of the inducing representation {\sigma}
and {\psi} and its entries are linear combinations of Tate or Tate type
{\gamma}-factors. We relate these entries to functional equations associated
with linear maps defined on the dual of the space of Schwartz functions. As an
application we give new formulas for the Plancherel measure and use these to
relate principal series representations of different coverings of SL(2,F).
While we do not assume that the residual characteristic of F is relatively
prime to n we do assume that n is not divisible by 4.
| arxiv topic:math.NT |
arxiv_dataset-77371609.08222 | Transport gap engineering by contact geometry in graphene nanoribbons:
Experimental and theoretical studies on artificial materials
cond-mat.mes-hall
Electron transport in small graphene nanoribbons is studied by microwave
emulation experiments and tight-binding calculations. In particular, it is
investigated under which conditions a transport gap can be observed. Our
experiments provide evidence that armchair ribbons of width $3m+2$ with integer
$m$ are metallic and otherwise semiconducting, whereas zigzag ribbons are
metallic independent of their width. The contact geometry, defining to which
atoms at the ribbon edges the source and drain leads are attached, has strong
effects on the transport. If leads are attached only to the inner atoms of
zigzag edges, broad transport gaps can be observed in all armchair ribbons as
well as in rhomboid-shaped zigzag ribbons. All experimental results agree
qualitatively with tight-binding calculations using the nonequilibrium Green's
function method.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-77381609.08322 | On L.G. Kov\`acs' problem
math.GR
"Kourovka notebook" contains the question due to L.G. Kov\`acs (Problem
8.23): If the dihedral group $D$ of order 18 is a section of a direct product
$X\times Y$, must at least one of $X$ and $Y$ have a section isomorphic to $D$?
The goal of our short paper is to give the positive answer to this question
provided that $X$ and $Y$ are locally finite. In fact, we prove even more: If a
non-trivial semidirect product $D=A\rtimes B$ of a cyclic $p$-group $A$ and a
group $B$ of order $q$, where $p$ and $q$ are distinct primes, lies in a
locally finite variety generated by a set $\mathfrak{X}$ of groups, then $D$ is
a section of a group from $\mathfrak{X}$.
| arxiv topic:math.GR |
arxiv_dataset-77391609.08422 | Optimizing the placement of tap positions and guess and determine
cryptanalysis with variable sampling
cs.IT math.IT
In this article an optimal selection of tap positions for certain LFSR-based
encryption schemes is investigated from both design and cryptanalytic
perspective. Two novel algorithms towards an optimal selection of tap positions
are given which can be satisfactorily used to provide (sub)optimal resistance
to some generic cryptanalytic techniques applicable to these schemes. It is
demonstrated that certain real-life ciphers (e.g. SOBER-t32, SFINKS and
Grain-128), employing some standard criteria for tap selection such as the
concept of full difference set, are not fully optimized with respect to these
attacks. These standard design criteria are quite insufficient and the proposed
algorithms appear to be the only generic method for the purpose of (sub)optimal
selection of tap positions. We also extend the framework of a generic
cryptanalytic method called Generalized Filter State Guessing Attacks (GFSGA),
introduced in [26] as a generalization of the FSGA method, by applying a
variable sampling of the keystream bits in order to retrieve as much
information about the secret state bits as possible. Two different modes that
use a variable sampling of keystream blocks are presented and it is shown that
in many cases these modes may outperform the standard GFSGA mode. We also
demonstrate the possibility of employing GFSGA-like attacks to other design
strategies such as NFSR-based ciphers (Grain family for instance) and filter
generators outputting a single bit each time the cipher is clocked. In
particular, when the latter scenario is considered, the idea of combining GFSGA
technique and algebraic attacks appears to be a promising unified cryptanalytic
method against NFSR-based stream ciphers.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-77401609.08522 | Phaseless super-resolution in the continuous domain
cs.IT math.IT
Phaseless super-resolution refers to the problem of superresolving a signal
from only its low-frequency Fourier magnitude measurements. In this paper, we
consider the phaseless super-resolution problem of recovering a sum of sparse
Dirac delta functions which can be located anywhere in the continuous
time-domain. For such signals in the continuous domain, we propose a novel
Semidefinite Programming (SDP) based signal recovery method to achieve the
phaseless superresolution. This work extends the recent work of Jaganathan et
al. [1], which considered phaseless super-resolution for discrete signals on
the grid.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-77411609.08622 | The dust content of galaxies from z = 0 to z = 9
astro-ph.GA astro-ph.CO
We study the dust content of galaxies from $z=0$ to $z=9$ in semi-analytic
models of galaxy formation that include new recipes to track the production and
destruction of dust. We include condensation of dust in stellar ejecta, the
growth of dust in the interstellar medium (ISM), the destruction of dust by
supernovae and in the hot halo, and dusty winds and inflows. The rate of dust
growth in the ISM depends on the metallicity and density of molecular clouds.
Our fiducial model reproduces the relation between dust mass and stellar mass
from $z=0$ to $z=7$, the number density of galaxies with dust masses less than
$10^{8.3}\,\rm{M}_\odot$, and the cosmic density of dust at $z=0$. The model
accounts for the double power-law trend between dust-to-gas (DTG) ratio and
gas-phase metallicity of local galaxies and the relation between DTG ratio and
stellar mass. The dominant mode of dust formation is dust growth in the ISM,
except for galaxies with $M_*<10^7\,\rm{M}_\odot$, where condensation of dust
in supernova ejecta dominates. The dust-to-metal ratio of galaxies depends on
the gas-phase metallicity, unlike what is typically assumed in cosmological
simulations. Model variants including higher condensation efficiencies, a fixed
timescale for dust growth in the ISM, or no growth at all reproduce some of the
observed constraints, but fail to simultaneously reproduce the shape of dust
scaling relations and the dust mass of high-redshift galaxies.
| arxiv topic:astro-ph.GA astro-ph.CO |
arxiv_dataset-77421609.08722 | Solving polynomial systems via homotopy continuation and monodromy
math.AG cs.MS
We study methods for finding the solution set of a generic system in a family
of polynomial systems with parametric coefficients. We present a framework for
describing monodromy based solvers in terms of decorated graphs. Under the
theoretical assumption that monodromy actions are generated uniformly, we show
that the expected number of homotopy paths tracked by an algorithm following
this framework is linear in the number of solutions. We demonstrate that our
software implementation is competitive with the existing state-of-the-art
methods implemented in other software packages.
| arxiv topic:math.AG cs.MS |
arxiv_dataset-77431609.08822 | Quantitative separation of the anisotropic magnetothermopower and planar
Nernst effect by the rotation of an in-plane thermal gradient
cond-mat.mes-hall cond-mat.mtrl-sci
A thermal gradient as the driving force for spin currents plays a key role in
spin caloritronics. In this field the spin Seebeck effect (SSE) is of major
interest and was investigated in terms of in-plane thermal gradients inducing
perpendicular spin currents (transverse SSE) and out-of-plane thermal gradients
generating parallel spin currents (longitudinal SSE). Up to now all spincaloric
experiments employ a spatially fixed thermal gradient. Thus anisotropic
measurements with respect to well defined crystallographic directions were not
possible. Here we introduce a new experiment that allows not only the in-plane
rotation of the external magnetic field, but also the rotation of an in-plane
thermal gradient controlled by optical temperature detection. As a consequence,
the anisotropic magnetothermopower and the planar Nernst effect in a permalloy
thin film can be measured simultaneously and reveal a phase shift, that allows
the quantitative separation of the thermopower, the anisotropic
magnetothermopower and the planar Nernst effect.
| arxiv topic:cond-mat.mes-hall cond-mat.mtrl-sci |
arxiv_dataset-77441609.08922 | The CP-odd sector and $\theta$ dynamics in holographic QCD
hep-ph hep-lat hep-th
The holographic model of V-QCD is used to analyze the physics of QCD in the
Veneziano large-N limit. An unprecedented analysis of the CP-odd physics is
performed going beyond the level of effective field theories. The structure of
holographic saddle-points at finite $\theta$ is determined, as well as its
interplay with chiral symmetry breaking. Many observables (vacuum energy and
higher-order susceptibilities, singlet and non-singlet masses and mixings) are
computed as functions of $\theta$ and the quark mass $m$. Wherever applicable
the results are compared to those of chiral Lagrangians, finding agreement. In
particular, we recover the Witten-Veneziano formula in the small $x\to 0$
limit, we compute the $\theta$-dependence of the pion mass and we derive the
hyperscaling relation for the topological susceptibility in the conformal
window in terms of the quark mass.
| arxiv topic:hep-ph hep-lat hep-th |
arxiv_dataset-77451609.09022 | Eigenvector Statistics of Sparse Random Matrices
math.PR
We prove that the bulk eigenvectors of sparse random matrices, i.e. the
adjacency matrices of Erd\H{o}s-R\'enyi graphs or random regular graphs, are
asymptotically jointly normal, provided the averaged degree increases with the
size of the graphs. Our methodology follows [6] by analyzing the eigenvector
flow under Dyson Brownian motion, combining with an isotropic local law for
Green's function. As an auxiliary result, we prove that for the eigenvector
flow of Dyson Brownian motion with general initial data, the eigenvectors are
asymptotically jointly normal in the direction $q$ after time $\eta_*\ll t\ll
r$, if in a window of size $r$, the initial density of states is bounded below
and above down to the scale $\eta_*$, and the initial eigenvectors are
delocalized in the direction $q$ down to the scale $\eta_*$.
| arxiv topic:math.PR |
arxiv_dataset-77461609.09122 | Sharp Dirac's Theorem for DP-Critical Graphs
math.CO
Correspondence coloring, or DP-coloring, is a generalization of list coloring
introduced recently by Dvo\v{r}\'{a}k and Postle. In this paper we establish a
version of Dirac's theorem on the minimum number of edges in critical graphs in
the framework of DP-colorings. A corollary of our main result answers a
question posed by Kostochka and Stiebitz on classifying list-critical graphs
that satisfy Dirac's bound with equality.
| arxiv topic:math.CO |
arxiv_dataset-77471609.09222 | Dimension reduction for systems with slow relaxation
cond-mat.stat-mech math.PR physics.data-an
We develop reduced, stochastic models for high dimensional, dissipative
dynamical systems that relax very slowly to equilibrium and can encode long
term memory. We present a variety of empirical and first principles approaches
for model reduction, and build a mathematical framework for analyzing the
reduced models. We introduce the notions of universal and asymptotic filters to
characterize `optimal' model reductions for sloppy linear models. We illustrate
our methods by applying them to the practically important problem of modeling
evaporation in oil spills.
| arxiv topic:cond-mat.stat-mech math.PR physics.data-an |
arxiv_dataset-77481609.09322 | Modified viscosity in accretion disks. Application to Galactic black
hole binaries, intermediate mass black holes and AGN
astro-ph.HE
Black holes (BHs) surrounded by accretion disks are present in the Universe
at different scales of masses, from microquasars up to the active galactic
nuclei (AGNs). The current picture remains ad hoc due to the complexity of the
magnetic field action. In addition, accretion disks at high Eddington rates can
be radiation-pressure dominated and, according to some of the heating
prescriptions, thermally unstable. The observational verification of their
resulting variability patterns may shed light on both the role of radiation
pressure and magnetic fields. We compute the structure and time evolution of an
accretion disk, using the code GLADIS (which models the global accretion disk
instability). We supplement this model with a modified viscosity prescription,
which can to some extent describe the magnetisation of the disk. We study the
results for a large grid of models, to cover the whole parameter space, and we
derive conclusions separately for different scales of black hole masses, which
are characteristic for various types of cosmic sources. We show the
dependencies between the flare or outburst duration, its amplitude, and period,
on the accretion rate and viscosity scaling. We show that if the heating rate
in the accretion disk grows more rapidly with the total pressure and
temperature, the instability results in longer and sharper flares. In general,
we confirm that the disks around the supermassive black holes are more
radiation-pressure dominated and present relatively brighter bursts. Our method
can also be used as an independent tool for the black hole mass determination,
which we confront now for the intermediate black hole in the source HLX-1.
| arxiv topic:astro-ph.HE |
arxiv_dataset-77491609.09422 | Jet formation in solar atmosphere due to magnetic reconnection
astro-ph.SR
Using numerical simulations, we show that jets with features of type II
spicules and cold coronal jets corresponding to temperatures $10^{4}$ K can be
formed due to magnetic reconnection in a scenario in presence of magnetic
resistivity. For this we model the low chromosphere-corona region using the C7
equilibrium solar atmosphere model and assuming Resistive MHD rules the
dynamics of the plasma. The magnetic filed configurations we analyze correspond
to two neighboring loops with opposite polarity. The separation of the loops'
feet determines the thickness of a current sheet that triggers a magnetic
reconnection process, and the further formation of a high speed and sharp
structure. We analyze the cases where the magnetic filed strength of the two
loops is equal and different. In the first case, with a symmetric configuration
the spicules raise vertically whereas in an asymmetric configuration the
structure shows an inclination. With a number of simulations carried out under
a 2.5D approach, we explore various properties of excited jets, namely, the
morphology, inclination and velocity. The parameter space involves magnetic
field strength between 20 and 40 G, and the resistivity is assumed to be
uniform with a constant value of the order $10^{-2}\Omega\cdot m$
| arxiv topic:astro-ph.SR |
arxiv_dataset-77501609.09522 | Charged Point Normalization: An Efficient Solution to the Saddle Point
Problem
cs.LG
Recently, the problem of local minima in very high dimensional non-convex
optimization has been challenged and the problem of saddle points has been
introduced. This paper introduces a dynamic type of normalization that forces
the system to escape saddle points. Unlike other saddle point escaping
algorithms, second order information is not utilized, and the system can be
trained with an arbitrary gradient descent learner. The system drastically
improves learning in a range of deep neural networks on various data-sets in
comparison to non-CPN neural networks.
| arxiv topic:cs.LG |
arxiv_dataset-77511609.09622 | Inhibiting decoherence of two-level atom in thermal bath by presence of
boundaries
quant-ph
We study, in the paradigm of open quantum systems, the dynamics of quantum
coherence of a static polarizable two-level atom which is coupled with a
thermal bath of fluctuating electromagnetic field in the absence and presence
of boundaries. The purpose is to find the conditions under which the
decoherence can be inhibited effectively. We find that without boundaries,
quantum coherence of the two-level atom inevitably decreases due to the effect
of thermal bath. However, the quantum decoherence, in the presence of a
boundary, could be effectively inhibited when the atom is transversely
polarizable and near this boundary. In particular, we find that in the case of
two parallel reflecting boundaries, the atom with a parallel dipole
polarization at arbitrary location between these two boundaries will be never
subjected to decoherence provided we take some special distances for the two
boundaries.
| arxiv topic:quant-ph |
arxiv_dataset-77521609.09722 | Photoionisation of Cl$^+$ from the $3s^23p^4\;^3P_{2,1,0}$ and
the$3s^23p^4\;^1D_2, ^1S_0$ states in the energy range 19 - 28 eV
physics.atom-ph astro-ph.EP
Absolute photoionisation cross sections for the Cl$^+$ ion in its ground and
the metastable states; $3s^2 3p^4\; ^3P_{2,1,0}$, and $3s^2 3p^4\; ^1D_2,\;
^1S_0$, were measured recently at the Advanced Light Source ALS) at Lawrence
Berkeley National Laboratory using the merged beams photon-ion technique at an
photon energy resolution of 15 meV in the energy range 19 -- 28 eV. These
measurements are compared with large-scale Dirac Coulomb {\it R}-matrix
calculations in the same energy range. Photoionisation of this sulphur-like
chlorine ion is characterized by multiple Rydberg series of autoionizing
resonances superimposed on a direct photoionisation continuum. A wealth of
resonance features observed in the experimental spectra are spectroscopically
assigned and their resonance parameters tabulated and compared with the recent
measurements. Metastable fractions in the parent ion beam are determined from
the present study. Theoretical resonance energies and quantum defects of the
prominent Rydberg series $3s^2 3p^3 nd$, identified in the spectra as
$3p\rightarrow nd$ transitions are compared with the available measurements
made on this element. Weaker Rydberg series $3s^2 3p^3 ns$, identified as $3p
\rightarrow ns$ transitions and window resonances $3s3p^4 (^4P)np$ features,
due to $3s \rightarrow np$ transitions are also found in the spectra.
| arxiv topic:physics.atom-ph astro-ph.EP |
arxiv_dataset-77531609.09822 | Stepping Stabilization Using a Combination of DCM Tracking and Step
Adjustment
cs.RO
In this paper, a method for stabilizing biped robots stepping by a
combination of Divergent Component of Motion (DCM) tracking and step adjustment
is proposed. In this method, the DCM trajectory is generated, consistent with
the predefined footprints. Furthermore, a swing foot trajectory modification
strategy is proposed to adapt the landing point, using DCM measurement. In
order to apply the generated trajectories to the full robot, a Hierarchical
Inverse Dynamics (HID) is employed. The HID enables us to use different
combinations of the DCM tracking and step adjustment for stabilizing different
biped robots. Simulation experiments on two scenarios for two different
simulated robots, one with active ankles and the other with passive ankles, are
carried out. Simulation results demonstrate the effectiveness of the proposed
method for robots with both active and passive ankles.
| arxiv topic:cs.RO |
arxiv_dataset-77541610.00053 | Superconducting optoelectronic circuits for neuromorphic computing
cs.NE cond-mat.supr-con physics.optics
Neural networks have proven effective for solving many difficult
computational problems. Implementing complex neural networks in software is
very computationally expensive. To explore the limits of information
processing, it will be necessary to implement new hardware platforms with large
numbers of neurons, each with a large number of connections to other neurons.
Here we propose a hybrid semiconductor-superconductor hardware platform for the
implementation of neural networks and large-scale neuromorphic computing. The
platform combines semiconducting few-photon light-emitting diodes with
superconducting-nanowire single-photon detectors to behave as spiking neurons.
These processing units are connected via a network of optical waveguides, and
variable weights of connection can be implemented using several approaches. The
use of light as a signaling mechanism overcomes fanout and parasitic
constraints on electrical signals while simultaneously introducing physical
degrees of freedom which can be employed for computation. The use of
supercurrents achieves the low power density necessary to scale to systems with
enormous entropy. The proposed processing units can operate at speeds of at
least $20$ MHz with fully asynchronous activity, light-speed-limited latency,
and power densities on the order of 1 mW/cm$^2$ for neurons with 700
connections operating at full speed at 2 K. The processing units achieve an
energy efficiency of $\approx 20$ aJ per synapse event. By leveraging
multilayer photonics with deposited waveguides and superconductors with feature
sizes $>$ 100 nm, this approach could scale to systems with massive
interconnectivity and complexity for advanced computing as well as explorations
of information processing capacity in systems with an enormous number of
information-bearing microstates.
| arxiv topic:cs.NE cond-mat.supr-con physics.optics |
arxiv_dataset-77551610.00153 | Study of the lowest tensor and scalar resonances in the $\tau \to
\pi\pi\pi \nu_\tau$ decay
hep-ph
In this note we present a new parametrization of the hadronic current for the
decay $\tau \to \pi\pi\pi \nu_\tau$ derived from the chiral lagrangian with
explicit inclusion of resonances. We have included both scalar, vector and
axial-vector resonances. For the first time, the lowest tensor resonance
($f_2(1270)$) is included as well. Both single and double-resonance
contributions to the hadronic form factors are taken into account. To satisfy
the correct high energy behaviour of the hadronic form factors, constraints on
numerical values of the vertex constants are obtained.
| arxiv topic:hep-ph |
arxiv_dataset-77561610.00253 | Asynchronous Distributed Execution Of Fixpoint-Based Computational
Fields
cs.LO
Coordination is essential for dynamic distributed systems whose components
exhibit interactive and autonomous behaviors. Spatially distributed, locally
interacting, propagating computational fields are particularly appealing for
allowing components to join and leave with little or no overhead. Computational
fields are a key ingredient of aggregate programming, a promising software
engineering methodology particularly relevant for the Internet of Things. In
our approach, space topology is represented by a fixed graph-shaped field,
namely a network with attributes on both nodes and arcs, where arcs represent
interaction capabilities between nodes. We propose a SMuC calculus where
mu-calculus- like modal formulas represent how the values stored in neighbor
nodes should be combined to update the present node. Fixpoint operations can be
understood globally as recursive definitions, or locally as asynchronous
converging propagation processes. We present a distributed implementation of
our calculus. The translation is first done mapping SMuC programs into normal
form, purely iterative programs and then into distributed programs. Some key
results are presented that show convergence of fixpoint computations under fair
asynchrony and under reinitialization of nodes. The first result allows nodes
to proceed at different speeds, while the second one provides robustness
against certain kinds of failure. We illustrate our approach with a case study
based on a disaster recovery scenario, implemented in a prototype simulator
that we use to evaluate the performance of a recovery strategy.
| arxiv topic:cs.LO |
arxiv_dataset-77571610.00353 | $O(m^9)$ network flow LP model of the Assignment Problem polytope with
applications to hard combinatorial optimization problems
cs.DS cs.CC cs.DM math.CO math.OC
In this paper, we present a new, network flow LP model of the standard
Assignment Problem (AP) polytope. The model is not meant to be competitive with
existing standard procedures for solving the AP, as its complexity order of
size is $O(m^9)$, where m is the number of assignments. However, it allows for
hard combinatorial optimization problems (COPs) to be solved as Assignment
Problems (APs), including, in particular, the Quadratic, Cubic, Quartic,
Quintic, and Sextic Assignment Problems, as well as the Traveling Salesman
Problem and many of its variations. Hence, in particular, the model re-affirms
"P = NP." Illustrations are provided for the Linear Assignment (LAP), Quadratic
Assignment (QAP), and Traveling Salesman (TSP) problems. Issues pertaining to
the extended formulations "barriers" for the LP modeling of hard COPs are not
discussed in this paper because the developments are focused on the Assignment
Problem polytope only, and also the applicability/non-applicability of those
"barriers" are thoroughly addressed in a separate paper* in which it is shown
that, in an optimization context, these "barriers" have no pertinence for a
model which projects to the AP polytope, provided appropriate costs can be
attached to the non-superfluous variables of the model. Hence, the issues of
the "barriers" are left out of this paper essentially for the sake of space.
*: Diaby, M., M. Karwan, and L. Sun [2024]. On modeling NP-Complete problems
as polynomial-sized linear programs: Escaping/Side-stepping the "barriers."
Available at: arXiv:2304.07716 [cc.CC].
| arxiv topic:cs.DS cs.CC cs.DM math.CO math.OC |
arxiv_dataset-77581610.00453 | Estimating thermodynamic expectations and free energies in expanded
ensemble simulations: systematic variance reduction through conditioning
cond-mat.stat-mech
Markov chain Monte Carlo methods are primarily used for sampling from a given
probability distribution and estimating multi-dimensional integrals based on
the information contained in the generated samples. Whenever it is possible,
more accurate estimates are obtained by combining Monte Carlo integration and
integration by numerical quadrature along particular coordinates. We show that
this variance reduction technique, referred to as conditioning in probability
theory, can be advantageously implemented in \emph{expanded ensemble}
simulations. These simulations aim at estimating thermodynamic expectations as
a function of an external parameter that is sampled like an additional
coordinate. Conditioning therein entails integrating along the external
coordinate by numerical quadrature. We prove variance reduction with respect to
alternative standard estimators and demonstrate the practical efficiency of the
technique by estimating free energies and characterizing a structural phase
transition between two solid phases.
| arxiv topic:cond-mat.stat-mech |
arxiv_dataset-77591610.00553 | A general theory of linear cosmological perturbations: bimetric theories
gr-qc astro-ph.CO hep-th
We implement the method developed in [1] to construct the most general
parametrised action for linear cosmological perturbations of bimetric theories
of gravity. Specifically, we consider perturbations around a homogeneous and
isotropic background, and identify the complete form of the action invariant
under diffeomorphism transformations, as well as the number of free parameters
characterising this cosmological class of theories. We discuss, in detail, the
case without derivative interactions, and compare our results with those found
in massive bigravity.
| arxiv topic:gr-qc astro-ph.CO hep-th |
arxiv_dataset-77601610.00653 | Phase transitions in distributed control systems with multiplicative
noise
cond-mat.stat-mech cond-mat.dis-nn cs.SY math.OC
Contemporary technological challenges often involve many degrees of freedom
in a distributed or networked setting. Three aspects are notable: the variables
are usually associated with the nodes of a graph with limited communication
resources, hindering centralized control; the communication is subjected to
noise; and the number of variables can be very large. These three aspects make
tools and techniques from statistical physics particularly suitable for the
performance analysis of such networked systems in the limit of many variables
(analogous to the thermodynamic limit in statistical physics). Perhaps not
surprisingly, phase-transition like phenomena appear in these systems, where a
sharp change in performance can be observed with a smooth parameter variation,
with the change becoming discontinuous or singular in the limit of infinite
system size. In this paper we analyze the so called network consensus problem,
prototypical of the above considerations, that has been previously analyzed
mostly in the context of additive noise. We show that qualitatively new
phase-transition like phenomena appear for this problem in the presence of
multiplicative noise. Depending on dimensions and on the presence or absence of
a conservation law, the system performance shows a discontinuous change at a
threshold value of the multiplicative noise strength. In the absence of the
conservation law, and for graph spectral dimension less than two, the
multiplicative noise threshold (the stability margin of the control problem) is
zero. This is reminiscent of the absence of robust controllers for certain
classes of centralized control problems. Although our study involves a toy
model we believe that the qualitative features are generic, with implication
for the robust stability of distributed control systems, as well as the effect
of roundoff errors and communication noise on distributed algorithms.
| arxiv topic:cond-mat.stat-mech cond-mat.dis-nn cs.SY math.OC |
arxiv_dataset-77611610.00753 | Maxwell's equations as a special case of deformation of a solid lattice
in Euler's coordinates
physics.gen-ph
It is shown that the set of equations known as Maxwell's equations perfectly
describe two very different systems: (1) the usual electromagnetic phenomena in
vacuum or in the matter and (2) the deformation of isotropic solid lattices,
containing topological defects as dislocations and disclinations, in the case
of constant and homogenous expansion. The analogy between these two physical
systems is complete, as it is not restricted to one of the two Maxwell's
equation couples in the vacuum, but generalized to the two equation couples as
well as to the diverse phenomena of dielectric polarization and magnetization
of matter, just as to the electrical charges and the electrical currents. The
eulerian approach of the solid lattice developed here includes Maxwell's
equations as a special case, since it stems from a tensor theory, which is
reduced to a vector one by contraction on the tensor indices. Considering the
tensor aspect of the eulerian solid lattice deformation theory, the analogy can
be extended to other physical phenomena than electromagnetism, a point which is
shortly discussed at the end of the paper.
| arxiv topic:physics.gen-ph |
arxiv_dataset-77621610.00853 | Constrained Hitting Set and Steiner Tree in $SC_k$ and $2K_2$-free
Graphs
math.CO cs.DM
\emph{Strictly Chordality-$k$ graphs ($SC_k$)} are graphs which are either
cycle-free or every induced cycle is of length exactly $k, k \geq 3$. Strictly
chordality-3 and strictly chordality-4 graphs are well known chordal and
chordal bipartite graphs, respectively. For $k\geq 5$, the study has been
recently initiated in \cite{sadagopan} and various structural and algorithmic
results are reported. In this paper, we show that maximum independent set
(MIS), minimum vertex cover, minimum dominating set, feedback vertex set (FVS),
odd cycle transversal (OCT), even cycle transversal (ECT) and Steiner tree
problem are polynomial time solvable on $SC_k$ graphs, $k\geq 5$. We next
consider $2K_2$-free graphs and show that FVS, OCT, ECT, Steiner tree problem
are polynomial time solvable on subclasses of $2K_2$-free graphs.
| arxiv topic:math.CO cs.DM |
arxiv_dataset-77631610.00953 | Fast and Reliable Primary Frequency Reserves From Refrigerators with
Decentralized Stochastic Control
math.OC cs.SY
Due to increasing shares of renewable energy sources, more frequency reserves
are required to maintain power system stability. In this paper, we present a
decentralized control scheme that allows a large aggregation of refrigerators
to provide Primary Frequency Control (PFC) reserves to the grid based on local
frequency measurements and without communication.
The control is based on stochastic switching of refrigerators depending on
the frequency deviation. We develop methods to account for typical lockout
constraints of compressors and increased power consumption during the startup
phase. In addition, we propose a procedure to dynamically reset the thermostat
temperature limits in order to provide reliable PFC reserves, as well as a
corrective temperature feedback loop to build robustness to biased frequency
deviations. Furthermore, we introduce an additional randomization layer in the
controller to account for thermostat resolution limitations, and finally, we
modify the control design to account for refrigerator door openings.
Extensive simulations with actual frequency signal data and with different
aggregation sizes, load characteristics, and control parameters, demonstrate
that the proposed controller outperforms a relevant state-of-the-art
controller.
| arxiv topic:math.OC cs.SY |
arxiv_dataset-77641610.01053 | Magnetic state of Nb(1-7nm)/Cu$_{30}$Ni$_{70}$(6nm) superlattices
revealed by Polarized Neutron Reflectometry and SQUID magnetometry
cond-mat.mes-hall
We report results of a magnetic characterization of
[Cu$_{30}$Ni$_{70}$(6nm)]$_{20}$ (x=1-7nm) superlattices using Polarized
Neutron Reflectometry (PNR) and SQUID magnetometry. The study has shown that
the magnetic moment of the structures growths almost linearly from H = 0 to
H$_{sat}$ = 1.3kOe which is an indirect evidence of antiferromagnetic (AF)
coupling of the magnetic moments in neighbouring layers. PNR, however, did not
detect any in-plane AF coupling. Taking into account the out-of-plane easy axis
of the Cu$_{30}$Ni$_{70}$ layers, this may mean that only the out-of-plane
component of the magnetic moments are AF coupled.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-77651610.01153 | Integration of higher IT education in Ukraine in the global
IT-educational space
cs.CY
The article presents the results of a study of the current state of higher IT
education system in Ukraine. The problems of reforming higher IT education
system of Ukraine in accordance with the commitments made by Ukraine in
connection with the ratification of the EU-Ukraine Agreement Law of Ukraine N
1678-VII of September 16, 2014. An indicator of the presence or absence of a
real reform of the system of higher IT education in Ukraine is detected. A
comparative analysis of lists of IT-specialties of higher education in Ukraine
in 2005 and 2015 with similar lists adopted by the international system of
higher IT education is made. A discrepancy between the list of IT-specialties
in Ukraine and international list of IT specialties are identified. The
conclusion about the need for immediate correction of the list of higher
education in Ukraine IT-specialties in order to bring it into line with
international standards. It recommended a series of actions that will lead to
the solution of the problem.
| arxiv topic:cs.CY |
arxiv_dataset-77661610.01253 | Some bivariate stochastic models arising from group representation
theory
math.PR math.CA
The aim of this paper is to study some continuous-time bivariate Markov
processes arising from group representation theory. The first component (level)
can be either discrete (quasi-birth-and-death processes) or continuous
(switching diffusion processes), while the second component (phase) will always
be discrete and finite. The infinitesimal operators of these processes will be
now matrix-valued (either a block tridiagonal matrix or a matrix-valued
second-order differential operator). The matrix-valued spherical functions
associated to the compact symmetric pair $(\mathrm{SU}(2)\times \mathrm{SU}(2),
\mathrm{diag} \, \mathrm{SU}(2))$ will be eigenfunctions of these infinitesimal
operators, so we can perform spectral analysis and study directly some
probabilistic aspects of these processes. Among the models we study there will
be rational extensions of the one-server queue and Wright-Fisher models
involving only mutation effects.
| arxiv topic:math.PR math.CA |
arxiv_dataset-77671610.01353 | Confidence regions for high-dimensional generalized linear models under
sparsity
stat.ME math.ST stat.TH
We study asymptotically normal estimation and confidence regions for
low-dimensional parameters in high-dimensional sparse models. Our approach is
based on the $\ell_1$-penalized M-estimator which is used for construction of a
bias corrected estimator. We show that the proposed estimator is asymptotically
normal, under a sparsity assumption on the high-dimensional parameter,
smoothness conditions on the expected loss and an entropy condition. This leads
to uniformly valid confidence regions and hypothesis testing for
low-dimensional parameters. The present approach is different in that it allows
for treatment of loss functions that we not sufficiently differentiable, such
as quantile loss, Huber loss or hinge loss functions. We also provide new
results for estimation of the inverse Fisher information matrix, which is
necessary for the construction of the proposed estimator. We formulate our
results for general models under high-level conditions, but investigate these
conditions in detail for generalized linear models and provide mild sufficient
conditions. As particular examples, we investigate the case of quantile loss
and Huber loss in linear regression and demonstrate the performance of the
estimators in a simulation study and on real datasets from genome-wide
association studies. We further investigate the case of logistic regression and
illustrate the performance of the estimator on simulated and real data.
| arxiv topic:stat.ME math.ST stat.TH |
arxiv_dataset-77681610.01453 | Gravitational Baryogenesis in Running Vacuum models
gr-qc astro-ph.CO
We study the gravitational baryogenesis mechanism for generating baryon
asymmetry in the context of running vacuum models. Regardless if these models
can produce a viable cosmological evolution, we demonstrate that they produce a
non-zero baryon-to-entropy ratio even if the universe is filled with conformal
matter. This is a sound difference between the running vacuum gravitational
baryogenesis and the Einstein-Hilbert one, since in the latter case, the
predicted baryon-to-entropy ratio is zero. We consider two well known and most
used running vacuum models and show that the resulting baryon-to-entropy ratio
is compatible with the observational data. Moreover, we also show that the
mechanism of gravitational baryogenesis may constrain the running vacuum
models.
| arxiv topic:gr-qc astro-ph.CO |
arxiv_dataset-77691610.01553 | Coordination of Heterogeneous Nonlinear Multi-Agent Systems with
Prescribed Behaviors
math.OC
In this paper, we consider a coordination problem for a class of
heterogeneous nonlinear multi-agent systems with a prescribed input-output
behavior which was represented by another input-driven system. In contrast to
most existing multi-agent coordination results with an autonomous (virtual)
leader, this formulation takes possible control inputs of the leader into
consideration. First, the coordination was achieved by utilizing a group of
distributed observers based on conventional assumptions of model matching
problem. Then, a fully distributed adaptive extension was proposed without
using the input of this input-output behavior. An example was given to verify
their effectiveness.
| arxiv topic:math.OC |
arxiv_dataset-77701610.01653 | Decay Properties of Solutions to a 4-parameter Family of Wave Equations
math.AP
In this paper, persistence properties of solutions are investigated for a
4-parameter family ($k-abc$ equation) of evolution equations having
$(k+1)$-degree non-linearities and containing as its integrable members the
Camassa-Holm, the Degasperis-Procesi, Novikov and Fokas-Olver-Rosenau-Qiao
equations. These properties will imply that strong solutions of the $k-abc$
equation will decay at infinity in the spatial variable provided that the
initial data does. Furthermore, it is shown that the equation exhibits unique
continuation for appropriate values of the parameters $k$, $a$, $b$, and $c$.
| arxiv topic:math.AP |
arxiv_dataset-77711610.01753 | A general lower bound for collaborative tree exploration
cs.DM cs.DS
We consider collaborative graph exploration with a set of $k$ agents. All
agents start at a common vertex of an initially unknown graph and need to
collectively visit all other vertices. We assume agents are deterministic,
vertices are distinguishable, moves are simultaneous, and we allow agents to
communicate globally. For this setting, we give the first non-trivial lower
bounds that bridge the gap between small ($k \leq \sqrt n$) and large ($k \geq
n$) teams of agents. Remarkably, our bounds tightly connect to existing results
in both domains.
First, we significantly extend a lower bound of $\Omega(\log k / \log\log k)$
by Dynia et al. on the competitive ratio of a collaborative tree exploration
strategy to the range $k \leq n \log^c n$ for any $c \in \mathbb{N}$. Second,
we provide a tight lower bound on the number of agents needed for any
competitive exploration algorithm. In particular, we show that any
collaborative tree exploration algorithm with $k = Dn^{1+o(1)}$ agents has a
competitive ratio of $\omega(1)$, while Dereniowski et al. gave an algorithm
with $k = Dn^{1+\varepsilon}$ agents and competitive ratio $O(1)$, for any
$\varepsilon > 0$ and with $D$ denoting the diameter of the graph. Lastly, we
show that, for any exploration algorithm using $k = n$ agents, there exist
trees of arbitrarily large height $D$ that require $\Omega(D^2)$ rounds, and we
provide a simple algorithm that matches this bound for all trees.
| arxiv topic:cs.DM cs.DS |
arxiv_dataset-77721610.01853 | $GW$100: a plane wave perspective for small molecules
cond-mat.mtrl-sci
In a recent work, van Setten and coworkers have presented a carefully
converged $G_0W_0$ study of 100 closed shell molecules [J. Chem. Theory Comput.
11, 5665 (2015)]. For two different codes they found excellent agreement to
within few 10 meV if identical Gaussian basis sets were used. We inspect the
same set of molecules using the projector augmented wave method and the Vienna
ab initio simulation package (VASP). For the ionization potential, the basis
set extrapolated plane wave results agree very well with the Gaussian basis
sets, often reaching better than 50 meV agreement. In order to achieve this
agreement, we correct for finite basis set errors as well as errors introduced
by periodically repeated images. For electron affinities below the vacuum level
differences between Gaussian basis sets and VASP are slightly larger. We
attribute this to larger basis set extrapolation errors for the Gaussian basis
sets. For quasi particle (QP) resonances above the vacuum level, differences
between VASP and Gaussian basis sets are, however, found to be substantial.
This is tentatively explained by insufficient basis set convergence of the
Gaussian type orbital calculations as exemplified for selected test cases.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-77731610.01953 | The Future Internet of Things and Security of its Control Systems
cs.CY cs.CR
We consider the future cyber security of industrial control systems. As best
as we can see, much of this future unfolds in the context of the Internet of
Things (IoT). In fact, we envision that all industrial and infrastructure
environments, and cyber-physical systems in general, will take the form
reminiscent of what today is referred to as the IoT. IoT is envisioned as
multitude of heterogeneous devices densely interconnected and communicating
with the objective of accomplishing a diverse range of objectives, often
collaboratively. One can argue that in the relatively near future, the IoT
construct will subsume industrial plants, infrastructures, housing and other
systems that today are controlled by ICS and SCADA systems. In the IoT
environments, cybersecurity will derive largely from system agility,
moving-target defenses, cybermaneuvering, and other autonomous or
semi-autonomous behaviors. Cyber security of IoT may also benefit from new
design methods for mixed-trusted systems; and from big data analytics --
predictive and autonomous.
| arxiv topic:cs.CY cs.CR |
arxiv_dataset-77741610.02053 | Biorthogonal projected energies of a Gutzwiller similarity transformed
Hamiltonian
cond-mat.str-el
We present a method incorporating biorthogonal orbital-optimization, symmetry
projection, and double-occupancy screening with a non-unitary similarity
transformation generated by the Gutzwiller factor $
n_{i\uparrow}n_{i\downarrow}$, and apply it to the Hubbard model. Energies are
calculated with mean-field computational scaling with high-quality results
comparable to coupled cluster singles and doubles. This builds on previous work
performing similarity transformations with more general, two-body Jastrow-style
correlators. The theory is tested on two-dimensional lattices ranging from
small systems into the thermodynamic limit and is compared to available
reference data.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-77751610.02153 | Distribution of singular values of random band matrices;
Marchenko-Pastur law and more
math.PR
We consider the limiting spectral distribution of matrices of the form
$\frac{1}{2b_{n}+1} (R + X)(R + X)^{*}$, where $X$ is an $n\times n$ band
matrix of bandwidth $b_{n}$ and $R$ is a non random band matrix of bandwidth
$b_{n}$. We show that the Stieltjes transform of ESD of such matrices converges
to the Stieltjes transform of a non-random measure. And the limiting Stieltjes
transform satisfies an integral equation. For $R=0$, the integral equation
yields the Stieltjes transform of the Marchenko-Pastur law.
| arxiv topic:math.PR |
arxiv_dataset-77761610.02253 | Performance analysis of multi-dimensional ESPRIT-type algorithms for
arbitrary and strictly non-circular sources with spatial smoothing
cs.IT math.IT
Spatial smoothing is a widely used preprocessing scheme to improve the
performance of high-resolution parameter estimation algorithms in case of
coherent signals or if only a small number of snapshots is available. In this
paper, we present a first-order performance analysis of the spatially smoothed
versions of R-D Standard ESPRIT and R-D Unitary ESPRIT for sources with
arbitrary signal constellations as well as R-D NC Standard ESPRIT and R-D NC
Unitary ESPRIT for strictly second-order (SO) non-circular (NC) sources. The
derived expressions are asymptotic in the effective signal-to-noise ratio
(SNR), i.e., the approximations become exact for either high SNRs or a large
sample size. Moreover, no assumptions on the noise statistics are required
apart from a zero-mean and finite SO moments. We show that both R-D NC
ESPRIT-type algorithms with spatial smoothing perform asymptotically identical
in the high effective SNR regime. Generally, the performance of spatial
smoothing based algorithms depends on the number of subarrays, which is a
design parameter and needs to be chosen beforehand. In order to gain more
insights into the optimal choice of the number of subarrays, we simplify the
derived analytical R-D mean square error (MSE) expressions for the special case
of a single source. The obtained MSE expression explicitly depends on the
number of subarrays in each dimension, which allows us to analytically find the
optimal number of subarrays for spatial smoothing. Based on this result, we
additionally derive the maximum asymptotic gain from spatial smoothing and
explicitly compute the asymptotic efficiency for this special case. All the
analytical results are verified by simulations.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-77771610.02353 | Phonon Optimized Potentials
cond-mat.mtrl-sci
Molecular dynamics (MD) simulations have been extensively used to study
phonons and gain insight, but direct comparisons to experimental data are often
difficult, due to a lack of empirical interatomic potentials (EIPs) for
different systems. As a result, this issue has become a major barrier to
realizing the promise associated with advanced atomistic level modeling
techniques. Here, we present a general method for specifically optimizing EIPs
from ab initio inputs for the study of phonon transport properties, thereby
resulting in phonon optimized potentials (POPs). The method uses a genetic
algorithm (GA) to directly fit to the key properties that determine whether or
not the atomic level dynamics and most notably the phonon transport are
described properly.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-77781610.02453 | A construction of certain weak colimits and an exactness property of the
2-category of categories
math.CT
Given a 2-category $\mathcal{A}$, a $2$-functor $\mathcal{A} \overset {F}
{\longrightarrow} \mathcal{C}at$ and a distinguished 1-subcategory $\Sigma
\subset \mathcal{A}$ containing all the objects, a $\sigma$-cone for $F$ (with
respect to $\Sigma$) is a lax cone such that the structural $2$-cells
corresponding to the arrows of $\Sigma$ are invertible. The conical
$\sigma$-limit is the universal (up to isomorphism) $\sigma$-cone. The notion
of $\sigma$-limit generalises the well known notions of pseudo and lax limit.
We consider the fundamental notion of $\sigma$-filtered} pair $(\mathcal{A}, \,
\Sigma)$ which generalises the notion of 2-filtered 2-category. We give an
explicit construction of $\sigma$-filtered $\sigma$-colimits of categories,
construction which allows computations with these colimits. We then state and
prove a basic exactness property of the 2-category of categories, namely, that
$\sigma$-filtered $\sigma$-colimits commute with finite weighted pseudo (or bi)
limits. An important corollary of this result is that a $\sigma$-filtered
$\sigma$-colimit of exact category valued 2-functors is exact. This corollary
is essential in the 2-dimensional theory of flat and pro-representable
2-functors, that we develop elsewhere.
| arxiv topic:math.CT |
arxiv_dataset-77791610.02553 | Regularization by noise and flows of solutions for a stochastic heat
equation
math.PR
Motivated by the regularization by noise phenomenon for SDEs we prove
existence and uniqueness of the flow of solutions for the non-Lipschitz
stochastic heat equation $$\frac{\partial u}{\partial
t}=\frac12\frac{\partial^2 u}{\partial z^2} + b(u(t,z)) + \dot{W}(t,z), $$
where $\dot W$ is a space-time white noise on $\mathbb{R}_+\times\mathbb{R}$
and $b$ is a bounded measurable function on $\mathbb{R}$. As a byproduct of our
proof we also establish the so-called path--by--path uniqueness for any initial
condition in a certain class on the same set of probability one. This extends
recent results of Davie (2007) to the context of stochastic partial
differential equations.
| arxiv topic:math.PR |
arxiv_dataset-77801610.02653 | Lasso-based forecast combinations for forecasting realized variances
stat.AP
Volatility forecasts are key inputs in financial analysis. While lasso based
forecasts have shown to perform well in many applications, their use to obtain
volatility forecasts has not yet received much attention in the literature.
Lasso estimators produce parsimonious forecast models. Our forecast combination
approach hedges against the risk of selecting a wrong degree of model
parsimony. Apart from the standard lasso, we consider several lasso extensions
that account for the dynamic nature of the forecast model. We apply forecast
combined lasso estimators in a comprehensive forecasting exercise using
realized variance time series of ten major international stock market indices.
We find the lasso extended "ordered lasso" to give the most accurate realized
variance forecasts. Multivariate forecast models, accounting for volatility
spillovers between different stock markets, outperform univariate forecast
models for longer forecast horizons.
| arxiv topic:stat.AP |
arxiv_dataset-77811610.02753 | Local M-estimation with Discontinuous Criterion for Dependent and
Limited Observations
math.ST stat.ME stat.TH
This paper examines asymptotic properties of local M-estimators under three
sets of high-level conditions. These conditions are sufficiently general to
cover the minimum volume predictive region, conditional maximum score estimator
for a panel data discrete choice model, and many other widely used estimators
in statistics and econometrics. Specifically, they allow for discontinuous
criterion functions of weakly dependent observations, which may be localized by
kernel smoothing and contain nuisance parameters whose dimension may grow to
infinity. Furthermore, the localization can occur around parameter values
rather than around a fixed point and the observation may take limited values,
which leads to set estimators. Our theory produces three different
nonparametric cube root rates and enables valid inference for the local
M-estimators, building on novel maximal inequalities for weakly dependent data.
Our results include the standard cube root asymptotics as a special case. To
illustrate the usefulness of our results, we verify our conditions for various
examples such as the Hough transform estimator with diminishing bandwidth,
maximum score-type set estimator, and many others.
| arxiv topic:math.ST stat.ME stat.TH |
arxiv_dataset-77821610.02853 | Minimal energy solutions to the fractional Lane-Emden system, I:
Existence and singularity formation
math.AP
This is the first of two papers which study asymptotic behavior of minimal
energy solutions to the fractional Lane-Emden system in a smooth bounded domain
$\Omega$ \[(-\Delta)^s u = v^p, \quad (-\Delta)^s v = u^q \text{ in } \Omega
\quad \text{and} \quad u = v = 0 \text{ on } \pa \Omega \quad \text{for } 0 < s
< 1\] under the assumption that the subcritical pair $(p,q)$ approaches to the
critical Sobolev hyperbola. If $p = 1$, the above problem is reduced to the
subcritical higher-order fractional Lane-Emden equation with the Navier
boundary condition \[(-\Delta)^s u = u^{\frac{n+2s}{n-2s}-\ep} \text{ in }
\Omega \quad \text{and} \quad u = (-\Delta)^{s \over 2} u = 0 \quad \text{for }
1 < s < 2.\] The main objective of this paper is to deduce the existence of
minimal energy solutions, and to examine their (normalized) pointwise limits
provided that $\Omega$ is convex. As a by-product of our study, a new approach
for the existence of an extremal function for the Hardy-Littlewood-Sobolev
inequality is provided.
| arxiv topic:math.AP |
arxiv_dataset-77831610.02953 | Comments on Dumitrescu's "A Selectable Sloppy Heap"
cs.DS
Dumitrescu [arXiv:1607.07673] describes a data structure referred to as a
Selectable Sloppy Heap. We present a simplified approach, and also point out
aspects of Dumitrescu's exposition that require scrutiny.
| arxiv topic:cs.DS |
arxiv_dataset-77841610.03053 | Solid-state neutron detectors based on thickness scalable hexagonal
boron nitride
physics.ins-det
This paper reports on the device processing and characterization of hexagonal
boron nitride (hBN) based solid-state thermal neutron detectors, where hBN
thickness varied from 2.5 to 15 microns. These natural hBN epilayers (with
19.9% B-10) were grown by a low pressure chemical vapor deposition process.
Complete dry processing was adopted for the fabrication of these
metal-semiconductor-metal (MSM) configuration detectors. These detectors showed
intrinsic thermal neutron detection efficiency values of 0.86%, 2.4%, 3.15%,
and 4.71% for natural hBN thickness values of 2.5, 7.5, 10, and 15 microns,
respectively. Measured efficiencies are very close (more than 92%) to the
theoretical maximum efficiencies for corresponding hBN thickness values for
these detectors. This clearly shows the hBN thickness scalability of these
detectors. A 15-micron thick hBN based MSM detector is expected to yield an
efficiency of 21.4%, if enriched hBN (with ~100% B-10) is used instead of
natural hBN. These results demonstrate that the fabrication of hBN thickness
scalable highly efficient thermal neutron detectors is possible.
| arxiv topic:physics.ins-det |
arxiv_dataset-77851610.03153 | Determination of a structural break in a mean-reverting process
math.ST stat.TH
Determining accurately when regime and structural changes occur in various
time-series data is critical in many social and natural sciences. We develop
and show further the equivalence of two consistent estimation techniques in
locating the change point under the framework of a generalised version of the
Ornstein-Uhlehnbeck process. Our methods are based on the least sum of squared
error and the maximum log-likelihood approaches. The case where both the
existence and the location of the change point are unknown is investigated and
an informational methodology is employed to address these issues. Numerical
illustrations are presented to assess the performance of the methods.
| arxiv topic:math.ST stat.TH |
arxiv_dataset-77861610.03253 | A quantum spectrum analyzer enhanced by a nuclear spin memory
quant-ph cond-mat.mes-hall
We realize a two-qubit sensor designed for achieving high spectral resolution
in quantum sensing experiments. Our sensor consists of an active "sensing
qubit" and a long-lived "memory qubit", implemented by the electronic and the
nitrogen-15 nuclear spins of a nitrogen-vacancy center in diamond,
respectively. Using state storage times of up to 45 ms, we demonstrate
spectroscopy of external ac signals with a line width of 19 Hz (~2.9 ppm) and
of carbon-13 nuclear magnetic resonance (NMR) signals with a line width of 190
Hz (~ 74 ppm). This represents an up to 100-fold improvement in spectral
resolution compared to measurements without nuclear memory.
| arxiv topic:quant-ph cond-mat.mes-hall |
arxiv_dataset-77871610.03353 | Heegaard Floer invariants in codimension one
math.GT
Using Heegaard Floer homology, we construct a numerical invariant for any
smooth, oriented $4$-manifold $X$ with the homology of $S^1 \times S^3$.
Specifically, we show that for any smoothly embedded $3$-manifold $Y$
representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer
$d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism
invariant of $X$. We show how this invariant can be used to obstruct embeddings
of certain types of $3$-manifolds, including those obtained as a connected sum
of a rational homology $3$-sphere and any number of copies of $S^1 \times S^2$.
We also give similar obstructions to embeddings in certain open $4$-manifolds,
including exotic $\mathbb{R}^4$s.
| arxiv topic:math.GT |
arxiv_dataset-77881610.03453 | High Energy QCD at NLO: from light-cone wave function to JIMWLK
evolution
hep-ph hep-th nucl-th
Soft components of the light cone wave-function of a fast moving projectile
hadron is computed in perturbation theory to third order in QCD coupling
constant. At this order, the Fock space of the soft modes consists of
one-gluon, two-gluon, and a quark-antiquark states. The hard component of the
wave-function acts as a non-Abelian background field for the soft modes and is
represented by a valence charge distribution that accounts for non-linear
density effects in the projectile. When scattered off a dense target, the
diagonal element of the S-matrix reveals the Hamiltonian of high energy
evolution, the JIMWLK Hamiltonian. This way we provide a new direct derivation
of the JIMWLK Hamiltonian at the Next-to-Leading Order.
| arxiv topic:hep-ph hep-th nucl-th |
arxiv_dataset-77891610.03553 | Long Term Sunspot Cycle Phase Coherence with Periodic Phase Disruptions
astro-ph.SR
In 1965 Paul D. Jose published his discovery that both the motion of the Sun
about the center of mass of the solar system and periods comprised of eight
Hale magnetic sunspot cycles with a mean period of ~22.37 years have a matching
periodicity of ~179 years. We have investigated the implied link between solar
barycentric torque cycles and sunspot cycles and have found that the unsigned
solar torque values from 1610 to 2057 are consistently phase and magnitude
coherent in ~179 year Jose Cycles. We are able to show that there is also a
surprisingly high degree of sunspot cycle phase coherence for times of minima
in addition to magnitude correlation of peaks between the nine Schwabe sunspot
cycles of 1878.8 to 1976.1 (SC12 through SC20) and those of 1699 to 1798.3
(SC[-5] through SC4). We further show that the remaining seven Schwabe cycles
in each ~179 year cycle are non-coherent. In addition we have analyzed the
empirical solar motion triggers of both sunspot cycle phase coherence and phase
disruption, from which we conclude that sunspot cycles SC28 through SC35 (2057
to 2143) will be phase coherent at times of minima and amplitude correlated at
maxima with SC12 through SC19 (1878.8-1964.8). The resulting predicted start
times +/- 0.9 year, 1 sigma, of future sunspot cycles SC28 to SC36 are
tabulated.
| arxiv topic:astro-ph.SR |
arxiv_dataset-77901610.03653 | Dynamic patterns of overexploitation in fisheries
q-bio.PE
Understanding overfishing phenomenon and regulating fishing quotas is a major
global challenge for the 21st Century both in terms of providing food for
humankind and to preserve the oceans ecosystems. However, fishing is a complex
economic activity, affected not just by overfishing but also by such factors as
pollution, technology, financial factors and more. For this reason, it is often
difficult to state with complete certainty that overfishing is the cause of the
decline of a fishery. In this study, we developed a simple dynamic model based
on the earlier, well-known Lotka-Volterra model or Prey-Predator model. To
describe exploitation patterns, we assume that the fish stock and the fishing
industry are coupled stock variables in the model and they dynamically affect
each other, with the fishing yield proportional to both the fishing capital and
the fish stock. The model is based on the concept that the fishing industry
acts as the predator of the resource and that its growth and subsequent decline
is directly related to the abundance of the fish stock. If the model can be fit
historical data relative to specific fisheries, then it is a strong indication
that the fishing industry is strongly affected by the magnitude of the fish
stock and that, in particular, the decline of the yield and the decline of the
stock are linked to each other. The model does not pretend to be a general
description of the fishing industry in all its varied forms; however, the data
reported here show that the model can indeed qualitatively describe several
historical case of the collapse of fisheries. The model can also be used as a
qualitative guide to understand the behavior of several other fisheries. These
result indicate that one of the main factors causing the present crisis of the
world's fisheries is the overexploitation of the fish stocks.
| arxiv topic:q-bio.PE |
arxiv_dataset-77911610.03753 | Evidence for a spinon Fermi surface in the triangular S=1 quantum spin
liquid Ba$_3$NiSb$_2$O$_9$
cond-mat.str-el
Inelastic neutron scattering is used to study the low-energy magnetic
excitations in the spin-1 triangular lattice of the 6H-B phase of
Ba$_3$NiSb$_2$O$_9$. We study two powder samples: Ba$_3$NiSb$_2$O$_9$
synthesized under high pressure and Ba$_{2.5}$Sr$_{0.5}$NiSb$_2$O$_9$ in which
chemical pressure stabilizes the 6H-B structure. The measured excitation
spectra show broad gapless and nondispersive continua at characteristic wave
vectors. Our data rules out most theoretical scenarios that have previously
been proposed for this phase, and we find that it is well described by an
exotic quantum spin liquid with three flavors of unpaired fermionic spinons,
forming a large spinon Fermi surface.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-77921610.03853 | IMF and [Na/Fe] abundance ratios from optical and NIR Spectral Features
in Early-type Galaxies
astro-ph.GA
We present a joint analysis of the four most prominent sodium-sensitive
features (NaD, NaI8190, NaI1.14, and NaI2.21), in the optical and Near-Infrared
spectral range, of two nearby, massive (sigma~300km/s), early-type galaxies
(named XSG1 and XSG2). Our analysis relies on deep VLT/X-Shooter long-slit
spectra, along with newly developed stellar population models, allowing for
[Na/Fe] variations, up to 1.2dex, over a wide range of age, total metallicity,
and IMF slope. The new models show that the response of the Na-dependent
spectral indices to [Na/Fe] is stronger when the IMF is bottom heavier. For the
first time, we are able to match all four Na features in the central regions of
massive early-type galaxies, finding an overabundance of [Na/Fe], in the range
0.5-0.7dex, and a bottom-heavy IMF. Therefore, individual abundance variations
cannot be fully responsible for the trends of gravity-sensitive indices,
strengthening the case towards a non-universal IMF. Given current limitations
of theoretical atmosphere models, our [Na/Fe] estimates should be taken as
upper limits. For XSG1, where line strengths are measured out to 0.8Re, the
radial trend of [Na/Fe] is similar to [Mg/Fe] and [C/Fe], being constant out to
0.5Re, and decreasing by 0.2-0.3dex at 0.8Re, without any clear correlation
with local metallicity. Such a result seems to be in contrast with the
predicted increase of Na nucleosynthetic yields from AGB stars and TypeII SNe.
For XSG1, the Na-inferred IMF radial profile is consistent, within the errors,
with that derived from TiO features and the Wing-Ford band, presented in a
recent paper.
| arxiv topic:astro-ph.GA |
arxiv_dataset-77931610.03953 | Excitons in solids from time-dependent density-functional theory:
Assessing the Tamm-Dancoff approximation
cond-mat.mtrl-sci
Excitonic effects in solids can be calculated using the Bethe-Salpeter
equation (BSE) or the Casida equation of time-dependent density-functional
theory (TDDFT). In both methods, the Tamm-Dancoff approximation (TDA), which
decouples excitations and de-excitations, is widely used to reduce
computational cost. Here, we study the effect of the TDA on exciton binding
energies of solids obtained from the Casida equation using long-range corrected
(LRC) exchange-correlation kernels. We find that the TDA underestimates
TDDFT-LRC exciton binding energies of semiconductors slightly, but those of
insulators significantly (i.e., by more than 100%), and thus it is essential to
solve the full Casida equation to describe strongly bound excitons. These
findings are relevant in the ongoing search for accurate and efficient TDDFT
approaches for excitons.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-77941610.04053 | Relaxation of charge in monolayer graphene: fast non-linear diffusion vs
Coulomb effects
cond-mat.mes-hall
Pristine monolayer graphene exhibits very poor screening because the density
of states vanishes at the Dirac point. As a result, charge relaxation is
controlled by the effects of zero-point motion (rather than by the Coulomb
interaction) over a wide range of parameters. Combined with the fact that
graphene possesses finite intrinsic conductivity, this leads to a regime of
relaxation described by a non-linear diffusion equation with a diffusion
coefficient that diverges at zero charge density. Some consequences of this
fast diffusion are self-similar superdiffusive regimes of relaxation, the
development of a charge depleted region at the interface between electron- and
hole-rich regions, and finite extinction times for periodic charge profiles.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-77951610.04153 | Aminated TiO2 nanotube as a Photoelectrochemical Water Splitting
photoanode
cond-mat.mtrl-sci
The present work reports on the enhancement of TiO2 nanotubes
photoelectrochemical water splitting rate by decorating the nanostructure with
an amine layer in a hydrothermal process using diethylenetriamine (DETA). The
aminate coated TiO2 tubes show a stable improvement of the photoresponse in
both UV and visible light spectrum and under hydrothermal conditions, 4-fold
increase of the photoelectrochemical water splitting rate is observed. From
intensity modulated photocurrent spectroscopy (IMPS) measurements significantly
faster electron transport times are observed indicating a surface passivating
effect of the N-decoration.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-77961610.04253 | On Near Perfect Numbers
math.NT
The study of perfect numbers (numbers which equal the sum of their proper
divisors) goes back to antiquity, and is responsible for some of the oldest and
most popular conjectures in number theory. We investigate a generalization
introduced by Pollack and Shevelev: $k$-near-perfect numbers. These are
examples to the well-known pseudoperfect numbers first defined by Sierpi\'nski,
and are numbers such that the sum of all but at most $k$ of its proper divisors
equals the number. We establish their asymptotic order for all integers $k\ge
4$, as well as some properties of related quantities.
| arxiv topic:math.NT |
arxiv_dataset-77971610.04353 | Products of Ideals and Jet Schemes
math.AC math.AG
In the present paper, we give a full description of the jet schemes of the
polynomial ideal $\left( x_1\ldots x_n \right) \in k[x_1, \ldots, x_n]$ over a
field of zero characteristic. We use this description to answer questions about
products and intersections of ideals emerged recently in algorithmic studies of
algebraic differential equations.
| arxiv topic:math.AC math.AG |
arxiv_dataset-77981610.04453 | Note on recursion relations for the $\mathcal{Q}$-cut representation
hep-th
In this note, we study the $\mathcal{Q}$-cut representation by combining it
with BCFW deformation. As a consequence, the one-loop integrand is expressed in
terms of a recursion relation, i.e., $n$-point one-loop integrand is
constructed using tree-level amplitudes and $m$-point one-loop integrands with
$m\leq n-1$. By giving explicit examples, we show that the integrand from the
recursion relation is equivalent to that from Feynman diagrams or the original
$\mathcal{Q}$-cut construction, up to scale free terms.
| arxiv topic:hep-th |
arxiv_dataset-77991610.04553 | Optical phase conjugation with less than a photon per degree of freedom
physics.optics
We demonstrate experimentally that optical phase conjugation can be used to
focus light through strongly scattering media even when far less than a photon
per optical degree of freedom is detected. We found that the best achievable
intensity contrast is equal to the total number of detected photons, as long as
the resolution of the system is high enough. Our results demonstrate that phase
conjugation can be used even when the photon budget is extremely low, such as
in high-speed focusing through dynamic media, or imaging deep inside tissue.
| arxiv topic:physics.optics |
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