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arxiv_dataset-107001901.00453 | Spectral asymptotics of radial solutions and nonradial bifurcation for
the H\'enon equation
math.AP
We study the spectral asymptotics of nodal (i.e., sign-changing) solutions of
the problem
\begin{equation*} (H) \qquad \qquad \left \{
\begin{aligned}
-\Delta u &=|x|^\alpha |u|^{p-2}u&&\qquad \text{in ${\bf B}$,} \\
u&=0&&\qquad \text{on $\partial {\bf B}$,}
\end{aligned}
\right.
\end{equation*}
in the unit ball ${\bf B} \subset \mathbb{R}^N,N\geq 3$, $p>2$ in the limit
$\alpha \to +\infty$. More precisely, for a given positive integer $K$, we
derive asymptotic $C^1$-expansions for the negative eigenvalues of the
linearization of the unique radial solution $u_\alpha$ of $(H)$ with precisely
$K$ nodal domains and $u_\alpha(0)>0$. As an application, we derive the
existence of an unbounded sequence of bifurcation points on the radial solution
branch $\alpha \mapsto (\alpha,u_\alpha)$ which all give rise to bifurcation of
nonradial solutions whose nodal sets remain homeomorphic to a disjoint union of
concentric spheres.
| arxiv topic:math.AP |
arxiv_dataset-107011901.00553 | An adaptive stigmergy-based system for evaluating technological
indicator dynamics in the context of smart specialization
cs.AI cs.CY
Regional innovation is more and more considered an important enabler of
welfare. It is no coincidence that the European Commission has started looking
at regional peculiarities and dynamics, in order to focus Research and
Innovation Strategies for Smart Specialization towards effective investment
policies. In this context, this work aims to support policy makers in the
analysis of innovation-relevant trends. We exploit a European database of the
regional patent application to determine the dynamics of a set of technological
innovation indicators. For this purpose, we design and develop a software
system for assessing unfolding trends in such indicators. In contrast with
conventional knowledge-based design, our approach is biologically-inspired and
based on self-organization of information. This means that a functional
structure, called track, appears and stays spontaneous at runtime when local
dynamism in data occurs. A further prototyping of tracks allows a better
distinction of the critical phenomena during unfolding events, with a better
assessment of the progressing levels. The proposed mechanism works if
structural parameters are correctly tuned for the given historical context.
Determining such correct parameters is not a simple task since different
indicators may have different dynamics. For this purpose, we adopt an
adaptation mechanism based on differential evolution. The study includes the
problem statement and its characterization in the literature, as well as the
proposed solving approach, experimental setting and results.
| arxiv topic:cs.AI cs.CY |
arxiv_dataset-107021901.00653 | A space-consistent version of the minimum-contrast estimator for linear
stochastic evolution equations
math.PR
A new modification of the minimum-contrast estimator (the weighted MCE) of
drift parameter in a linear stochastic evolution equation with additive
fractional noise is introduced in the setting of the spectral approach (Fourier
coordinates of the solution are observed). The reweighing technique, which
utilizes the self-similarity property, achieves strong consistency and
asymptotic normality of the estimator as number of coordinates increases and
time horizon is fixed (the space consistency). In this respect, this
modification outperforms the standard (non-weighted) minimum-contrast
estimator. Compared to other drift estimators studied within spectral approach
(eg. maximum likelihood, trajectory fitting), the weighted MCE is rather
universal. It covers discrete time as well as continuous time observations and
it is applicable to processes with any value of Hurst index $H \in (0,1)$. To
the author's best knowledge, this is so far the first space-consistent
estimator studied for $H < 1/2$.
| arxiv topic:math.PR |
arxiv_dataset-107031901.00753 | Experimental demonstration of spectrally-broadband Huygens sources using
low-index spheres
physics.class-ph physics.optics
Manipulating the excitation of resonant electric and magnetic multipole
moments in structured dielectric media has unlocked many sophisticated
electromagnetic functionalities. This article demonstrates the experimental
realization of a broadband Huygens' source. This Huygens' source consists of a
spherical particle that exhibits a well-defined forward-scattering pattern
across more than an octave-spanning spectral band at GHz frequencies, where the
scattering in the entire backward hemisphere is suppressed. Two different
low-index nonmagnetic spheres are studied that differ in their permittivity.
This causes them to offer a different shape for the forward-scattering pattern.
The theoretical understanding of this broadband feature is based on the
approximate equality of the resonant electric and magnetic multipole moments in
both amplitude and phase in low permittivity spheres. This is a key condition
to approximate the electromagnetic duality symmetry which, together with the
spherical symmetry, suppresses the backscattering. With such a configuration,
broadband Huygens' sources can be designed even if magnetic materials are
unavailable. This article provides guidelines for designing broadband Huygens'
sources using low-index spheres that could be valuable to a plethora of
applications.
| arxiv topic:physics.class-ph physics.optics |
arxiv_dataset-107041901.00853 | Experimental investigation of majorization uncertainty relations in the
high-dimensional systems
quant-ph
Uncertainty relation is not only of fundamental importance to quantum
mechanics, but also crucial to the quantum information technology. Recently,
majorization formulation of uncertainty relations (MURs) have been widely
studied, ranging from two measurements to multiple measurements. Here, for the
first time, we experimentally investigate MURs for two measurements and
multiple measurements in the high-dimensional systems, and study the intrinsic
distinction between direct-product MURs and direct-sum MURs. The experimental
results reveal that by taking different nonnegative Schur-concave functions as
uncertainty measure, the two types of MURs have their own particular
advantages, and also verify that there exists certain case where
three-measurement majorization uncertainty relation is much stronger than the
one obtained by summing pairwise two-measurement uncertainty relations. Our
work not only fills the gap of experimental studies of majorization uncertainty
relations, but also represents an advance in quantitatively understanding and
experimental verification of majorization uncertainty relations which are
universal and capture the essence of uncertainty in quantum theory.
| arxiv topic:quant-ph |
arxiv_dataset-107051901.00953 | Unified view of nonlinear wave structures associated with whistler-mode
chorus
physics.space-ph astro-ph.SR physics.plasm-ph
A range of nonlinear wave structures, including Langmuir waves, unipolar
electric fields and bipolar electric fields, are often observed in association
with whistler-mode chorus waves in the near-Earth space. We demonstrate that
the three seemingly different nonlinear wave structures originate from the same
nonlinear electron trapping process by whistler-mode chorus waves. The ratio of
the Landau resonant velocity to the electron thermal velocity controls the type
of nonlinear wave structures that will be generated.
| arxiv topic:physics.space-ph astro-ph.SR physics.plasm-ph |
arxiv_dataset-107061901.01053 | Cyber Security Challenges and Solutions for V2X Communications: A Survey
cs.IT math.IT
In recent years, vehicles became able to establish connections with other
vehicles and infrastructure units that are located in the roadside. In the near
future, the vehicular network will be expanded to include the communication
between vehicles and any smart devices in the roadside which is called
Vehicle-to-Everything (V2X) communication. The vehicular network causes many
challenges due to heterogeneous nodes, various speeds and intermittent
connection, where traditional security methods are not always efficacious. As a
result, an extensive variety of research works has been done on optimizing
security solutions whilst considering network requirements. In this paper, we
present a comprehensive survey and taxonomy of the existing security solutions
for V2X communication technology. Then, we provide discussions and comparisons
with regard to some pertinent criteria. Also, we present a threat analysis for
V2X enabling technologies. Finally, we point out the research challenges and
some future directions.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-107071901.01153 | Demystifying Multi-Faceted Video Summarization: Tradeoff Between
Diversity,Representation, Coverage and Importance
cs.CV
This paper addresses automatic summarization of videos in a unified manner.
In particular, we propose a framework for multi-faceted summarization for
extractive, query base and entity summarization (summarization at the level of
entities like objects, scenes, humans and faces in the video). We investigate
several summarization models which capture notions of diversity, coverage,
representation and importance, and argue the utility of these different models
depending on the application. While most of the prior work on submodular
summarization approaches has focused oncombining several models and learning
weighted mixtures, we focus on the explainability of different models and
featurizations, and how they apply to different domains. We also provide
implementation details on summarization systems and the different modalities
involved. We hope that the study from this paper will give insights into
practitioners to appropriately choose the right summarization models for the
problems at hand.
| arxiv topic:cs.CV |
arxiv_dataset-107081901.01253 | Towards Constraining Parity-Violations in Gravity with Satellite
Gradiometry
gr-qc
Parity violation in gravity, if existed, could have important implications,
and it is meaningful to search and test the possible observational effects.
Chern-Simons modified gravity serves as a natural model for gravitational
parity-violations. Especially, considering extensions to Einstein-Hilbert
action up to second order curvature terms, it is known that theories of
gravitational parity-violation will reduce to the dynamical Chern-Simons
gravity. In this letter, we outline the theoretical principles of testing the
dynamical Chern-Simons gravity with orbiting gravity gradiometers, which could
be naturally incorporated into future satellite gravity missions. The secular
gravity gradient signals, due to the Mashhoon-Theiss (anomaly) effect, in
dynamical Chern-Simons gravity are worked out, which can improve the constraint
of the corresponding Chern-Simons length scale $\xi^{\frac{1}{4}}_{cs}$
obtained from such measurement scheme. For orbiting superconducting
gradiometers or gradiometers with optical readout, a bound
$\xi^{\frac{1}{4}}_{cs}\leq 10^6 \ km$ (or even better) could in principle be
obtained, which will be at least 2 orders of magnitude stronger than the
current one based on the observations from the GP-B mission and the LAGEOS I,
II satellites.
| arxiv topic:gr-qc |
arxiv_dataset-107091901.01353 | Observations of A Fast-Expanding and UV-Bright Type Ia Supernova SN
2013gs
astro-ph.HE astro-ph.SR
In this paper, we present extensive optical and ultraviolet (UV) observations
of the type Ia supernova (SN Ia) 2013gs discovered during the Tsinghua-NAOC
Transient Survey. The photometric observations in the optical show that the
light curves of SN 2013gs is similar to that of normal SNe Ia, with an absolute
peak magnitude of $M_{B}$ = $-$19.25 $\pm$ 0.15 mag and a post-maximum decline
rate $\Delta$m$_{15}$(B) = 1.00 $ \pm $ 0.05 mag. \emph{Gehrels Swift} UVOT
observations indicate that SN 2013gs shows unusually strong UV emission
(especially in the $uvw1$ band) at around the maximum light (M$_{uvw1}$ $\sim$
$-$18.9 mag). The SN is characterized by relatively weak Fe~{\sc ii} {\sc iii}
absorptions at $\sim$ 5000{\AA} in the early spectra and a larger expansion
velocity ($v_{Si}$ $\sim$ 13,000 km s$^{-1}$ around the maximum light) than the
normal-velocity SNe Ia. We discuss the relation between the $uvw1-v$ color and
some observables, including Si~{\sc ii} velocity, line strength of Si~{\sc ii}
$\lambda$6355, Fe~{\sc ii}/{\sc iii} lines and $\Delta m_{15}$(B). Compared to
other fast-expanding SNe Ia, SN 2013gs exhibits Si and Fe absorption lines with
similar strength and bluer $uvw1-v$ color. We briefly discussed the origin of
the observed UV dispersion of SNe Ia.
| arxiv topic:astro-ph.HE astro-ph.SR |
arxiv_dataset-107101901.01453 | Metrics on triangulated categories
math.CT math.AG math.AT math.RT
In this survey we explain the results of the recent article arXiv:1806.06471.
Following a 1973 article by Lawvere one can define metrics on categories, and
following Kelly's 1982 book one can complete a category with respect to its
metric. We specialize these general constructions to triangulated categories,
and restrict our attention to "good metrics". And the remarkable new theorem is
that, when we start with a triangulated category $\mathcal S$ with a good
metric, its completion $\mathfrak{L}(\mathcal{S})$ contains an interesting
subcategory $\mathfrak{S}(\mathcal{S})$ which is always triangulated.
As special cases we obtain $\mathcal{H}^0(\mathrm{Perf}(X))$ and
$D^b_{\mathrm{coh}}(X)$ from each other. We also give a couple of other
examples.
| arxiv topic:math.CT math.AG math.AT math.RT |
arxiv_dataset-107111901.01553 | Search for dark matter produced in association with a single top quark
or a top quark pair in proton-proton collisions at $\sqrt{s} =$ 13 TeV
hep-ex
A search for dark matter produced in association with top quarks in
proton-proton collisions at a center-of-mass energy of 13 TeV is presented. The
data set used corresponds to an integrated luminosity of 35.9 fb$^{-1}$
recorded with the CMS detector at the LHC. Whereas previous searches for
neutral scalar or pseudoscalar mediators considered dark matter production in
association with a top quark pair only, this analysis also includes production
modes with a single top quark. The results are derived from the combination of
multiple selection categories that are defined to target either the single top
quark or the top quark pair signature. No significant deviations with respect
to the standard model predictions are observed. The results are interpreted in
the context of a simplified model in which a scalar or pseudoscalar mediator
particle couples to a top quark and subsequently decays into dark matter
particles. Scalar and pseudoscalar mediator particles with masses below 290 and
300 GeV, respectively, are excluded at 95% confidence level, assuming a dark
matter particle mass of 1 GeV and mediator couplings to fermions and dark
matter particles equal to unity.
| arxiv topic:hep-ex |
arxiv_dataset-107121901.01653 | Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems
quant-ph cs.LG cs.SY eess.SY
In this paper, we develop a theory of learning nonlinear input-output maps
with fading memory by dissipative quantum systems, as a quantum counterpart of
the theory of approximating such maps using classical dynamical systems. The
theory identifies the properties required for a class of dissipative quantum
systems to be {\em universal}, in that any input-output map with fading memory
can be approximated arbitrarily closely by an element of this class. We then
introduce an example class of dissipative quantum systems that is provably
universal. Numerical experiments illustrate that with a small number of qubits,
this class can achieve comparable performance to classical learning schemes
with a large number of tunable parameters. Further numerical analysis suggests
that the exponentially increasing Hilbert space presents a potential resource
for dissipative quantum systems to surpass classical learning schemes for
input-output maps.
| arxiv topic:quant-ph cs.LG cs.SY eess.SY |
arxiv_dataset-107131901.01753 | Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly
Complex and Diverse Learning Environments and Their Solutions
cs.NE
While the history of machine learning so far largely encompasses a series of
problems posed by researchers and algorithms that learn their solutions, an
important question is whether the problems themselves can be generated by the
algorithm at the same time as they are being solved. Such a process would in
effect build its own diverse and expanding curricula, and the solutions to
problems at various stages would become stepping stones towards solving even
more challenging problems later in the process. The Paired Open-Ended
Trailblazer (POET) algorithm introduced in this paper does just that: it pairs
the generation of environmental challenges and the optimization of agents to
solve those challenges. It simultaneously explores many different paths through
the space of possible problems and solutions and, critically, allows these
stepping-stone solutions to transfer between problems if better, catalyzing
innovation. The term open-ended signifies the intriguing potential for
algorithms like POET to continue to create novel and increasingly complex
capabilities without bound. Our results show that POET produces a diverse range
of sophisticated behaviors that solve a wide range of environmental challenges,
many of which cannot be solved by direct optimization alone, or even through a
direct-path curriculum-building control algorithm introduced to highlight the
critical role of open-endedness in solving ambitious challenges. The ability to
transfer solutions from one environment to another proves essential to
unlocking the full potential of the system as a whole, demonstrating the
unpredictable nature of fortuitous stepping stones. We hope that POET will
inspire a new push towards open-ended discovery across many domains, where
algorithms like POET can blaze a trail through their interesting possible
manifestations and solutions.
| arxiv topic:cs.NE |
arxiv_dataset-107141901.01853 | Primes in Beatty sequence
math.NT
For a polynomial $g(x)$ of deg $k \geq 2$ with integer coefficients and
positive integer leading coefficient, we prove an upper bound for the least
prime $p$ such that $g(p)$ is in non-homogeneous Beatty sequence $\lbrace
\lfloor \alpha n+\beta\rfloor : n=1,2,3, \dots \rbrace$, where $\alpha, \beta
\in \mathbb{R}$ with $\alpha >1$ is irrational and we prove an asymptotic
formula for the number of primes $p$ such that $g(p)=\lfloor \alpha n+\beta
\rfloor.$ Next we obtain an asymptotic formula for number of primes $p$ of the
form $p=\lfloor \alpha n+\beta \rfloor$ which also satisfies $p \equiv f \pmod
d$ where $f, d$ are integers with $1\leq f < d$ and $(f,d)=1$.
| arxiv topic:math.NT |
arxiv_dataset-107151901.01953 | Modified Reynolds equation for steady flow through a curved pipe
math-ph math.AP math.MP
A modified Reynolds equation governing the steady flow of a fluid with low
Reynolds number through a curvilinear, narrow tube, with its derivation from
Stokes equations through asymptotic methods is presented. The channel
considered may have large curvature and torsion. Approximations of the velocity
and the pressure of the fluid inside the channel are constructed by
artificially imposing appropriate boundary conditions at the inlet and the
outlet. A justification for the approximations is provided along with a
comparison with a simpler case.
| arxiv topic:math-ph math.AP math.MP |
arxiv_dataset-107161901.02053 | Detecting the Trend in Musical Taste over the Decade -- A Novel Feature
Extraction Algorithm to Classify Musical Content with Simple Features
cs.IR cs.LG cs.SD eess.AS
This work proposes a novel feature selection algorithm to classify Songs into
different groups. Classification of musical content is often a non-trivial job
and still relatively less explored area. The main idea conveyed in this article
is to come up with a new feature selection scheme that does the classification
job elegantly and with high accuracy but with simpler but wisely chosen small
number of features thus being less prone to over-fitting. This uses a very
basic general idea about the structure of the audio signal which is generally
in the shape of a trapezium. So, using this general idea of the Musical
Community we propose three frames to be considered and analyzed for feature
extraction for each of the audio signal -- opening, stanzas and closing -- and
it has been established with the help of a lot of experiments that this scheme
leads to much efficient classification with less complex features in a low
dimensional feature space thus is also a computationally less expensive method.
Step by step analysis of feature extraction, feature ranking, dimensionality
reduction using PCA has been carried in this article. Sequential Forward
selection (SFS) algorithm is used to explore the most significant features both
with the raw Fisher Discriminant Ratio (FDR) and also with the significant
eigen-values after PCA. Also during classification extensive validation and
cross validation has been done in a monte-carlo manner to ensure validity of
the claims.
| arxiv topic:cs.IR cs.LG cs.SD eess.AS |
arxiv_dataset-107171901.02153 | Audio Captcha Recognition Using RastaPLP Features by SVM
cs.LG cs.SD eess.AS stat.ML
Nowadays, CAPTCHAs are computer generated tests that human can pass but
current computer systems can not. They have common usage in various web
services in order to be able to detect a human from computer programs
autonomously. In this way, owners can protect their web services from bots. In
addition to visual CAPTCHAs which consist of distorted images, mostly test
images, that a user must write some description about that image, there are a
significant amount of audio CAPTCHAs as well. Briefly, audio CAPTCHAs are sound
files which consist of human sound under heavy noise where the speaker
pronounces a bunch of digits consecutively. Generally, in those sound files,
there are some periodic and non-periodic noises to get difficult to recognize
them with a program but not for a human listener. We gathered numerous randomly
collected audio file to train and then test them using our SVM algorithm to be
able to extract digits out of each conversation.
| arxiv topic:cs.LG cs.SD eess.AS stat.ML |
arxiv_dataset-107181901.02253 | Thrust distribution in Higgs decays at the next-to-leading order and
beyond
hep-ph
We present predictions for the thrust distribution in hadronic decays of the
Higgs boson at the next-to-leading order and the approximate
next-to-next-to-leading order. The approximate NNLO corrections are derived
from a factorization formula in the soft/collinear phase-space regions. We find
large corrections, especially for the gluon channel. The scale variations at
the lowest orders tend to underestimate the genuine higher order contributions.
The results of this paper is therefore necessary to control the perturbative
uncertainties of the theoretical predictions. We also discuss on possible
improvements to our results, such as a soft-gluon resummation for the 2-jets
limit, and an exact next-to-next-to-leading order calculation for the
multi-jets region.
| arxiv topic:hep-ph |
arxiv_dataset-107191901.02353 | On neighbourhood degree sequences of complex networks
cs.SI physics.soc-ph
Network topology is a fundamental aspect of network science that allows us to
gather insights into the complicated relational architectures of the world we
inhabit. We provide a first specific study of neighbourhood degree sequences in
complex networks. We consider how to explicitly characterise important physical
concepts such as similarity, heterogeneity and organisation in these sequences,
as well as updating the notion of hierarchical complexity to reflect previously
unnoticed organisational principles. We also point out that neighbourhood
degree sequences are related to a powerful subtree kernel for unlabelled graph
classification. We study these newly defined sequence properties in a
comprehensive array of graph models and over 200 real-world networks. We find
that these indices are neither highly correlated with each other nor with
classical network indices. Importantly, the sequences of a wide variety of real
world networks are found to have greater similarity and organisation than is
expected for networks of their given degree distributions. Notably, while
biological, social and technological networks all showed consistently large
neighbourhood similarity and organisation, hierarchical complexity was not a
consistent feature of real world networks. Neighbourhood degree sequences are
an interesting tool for describing unique and important characteristics of
complex networks.
| arxiv topic:cs.SI physics.soc-ph |
arxiv_dataset-107201901.02453 | Neural Inverse Rendering of an Indoor Scene from a Single Image
cs.CV
Inverse rendering aims to estimate physical attributes of a scene, e.g.,
reflectance, geometry, and lighting, from image(s). Inverse rendering has been
studied primarily for single objects or with methods that solve for only one of
the scene attributes. We propose the first learning-based approach that jointly
estimates albedo, normals, and lighting of an indoor scene from a single image.
Our key contribution is the Residual Appearance Renderer (RAR), which can be
trained to synthesize complex appearance effects (e.g., inter-reflection, cast
shadows, near-field illumination, and realistic shading), which would be
neglected otherwise. This enables us to perform self-supervised learning on
real data using a reconstruction loss, based on re-synthesizing the input image
from the estimated components. We finetune with real data after pretraining
with synthetic data. To this end, we use physically-based rendering to create a
large-scale synthetic dataset, which is a significant improvement over prior
datasets. Experimental results show that our approach outperforms
state-of-the-art methods that estimate one or more scene attributes.
| arxiv topic:cs.CV |
arxiv_dataset-107211901.02553 | The second RIT binary black hole simulations catalog and its application
to gravitational waves parameter estimation
gr-qc astro-ph.HE
The RIT numerical relativity group is releasing the second public catalog of
black-hole-binary waveforms \url{http://ccrg.rit.edu/~RITCatalog}. This release
consists of 320 accurate simulations that include 46 precessing and 274
nonprecessing binary systems with mass ratios $q=m_1/m_2$ in the range $1/6\leq
q\leq1$ and individual spins up to $s/m^2=0.95$. The new catalog contains
search and ordering tools for the waveforms based on initial parameters of the
binary, trajectory information, peak radiation, and final remnant black hole
properties. The final black hole remnant properties provided here can be used
to model the merger of black-hole binaries from its initial configurations. The
waveforms are extrapolated to infinite observer location and can be used to
independently interpret gravitational wave signals from laser interferometric
detectors. As an application of this waveform catalog we reanalyze the signal
of GW150914 implementing parameter estimation techniques that make use of only
numerical waveforms without any reference to information from phenomenological
models.
| arxiv topic:gr-qc astro-ph.HE |
arxiv_dataset-107221901.02653 | A new proof of Jacquet-Rallis's fundamental lemma
math.NT math.RT
We give a new proof of the so-called Lie algebra version of Jacquet-Rallis's
fundamental lemma for local non-Archimedean fields of characteristic zero. This
proof is local and based on a previous result of W. Zhang on the compatibility
of smooth transfer with a (partial) Fourier transform.
| arxiv topic:math.NT math.RT |
arxiv_dataset-107231901.02753 | Diagrammatic Coupled Cluster Monte Carlo
physics.chem-ph physics.comp-ph
We propose a modified coupled cluster Monte Carlo algorithm that
stochastically samples connected terms within the truncated
Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian
by construction of coupled cluster diagrams on the fly. Our new approach --
diagCCMC -- allows propagation to be performed using only the connected
components of the similarity-transformed Hamiltonian, greatly reducing the
memory cost associated with the stochastic solution of the coupled cluster
equations. We show that for perfectly local, noninteracting systems, diagCCMC
is able to represent the coupled cluster wavefunction with a memory cost that
scales linearly with system size. The favorable memory cost is observed with
the only assumption of fixed stochastic granularity and is valid for arbitrary
levels of coupled cluster theory. Significant reduction in memory cost is also
shown to smoothly appear with dissociation of a finite chain of helium atoms.
This approach is also shown not to break down in the presence of strong
correlation through the example of a stretched nitrogen molecule. Our novel
methodology moves the theoretical basis of coupled cluster Monte Carlo closer
to deterministic approaches.
| arxiv topic:physics.chem-ph physics.comp-ph |
arxiv_dataset-107241901.02853 | Lambda Calculus and Probabilistic Computation
cs.LO
We introduce two extensions of the $\lambda$-calculus with a probabilistic
choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling
respectively call-by-value and call-by-name probabilistic computation. We prove
that both enjoys confluence and standardization, in an extended way: we revisit
these two fundamental notions to take into account the asymptotic behaviour of
terms.
The common root of the two calculi is a further calculus based on Linear
Logic, $\Lambda_\oplus^!$, which allows for a fine control of the interaction
between choice and copying, and which allows us to develop a unified, modular
approach.
| arxiv topic:cs.LO |
arxiv_dataset-107251901.02953 | Black hole scalarisation from the breakdown of scale-invariance
gr-qc hep-th
Electro-vacuum black holes are scale-invariant; their energy-momentum tensor
is traceless. Quantum corrections of various sorts, however, can often produce
a trace anomaly and a breakdown of scale-invariance. The (quantum-corrected)
black hole solutions of the corresponding gravitational effective field theory
(EFT) have a non-vanishing Ricci scalar. Then, the presence of a scalar field
with the standard non-minimal coupling $\xi \phi^2 R$ naturally triggers a
spontaneous scalarisation of the corresponding black holes. This scalarisation
phenomenon occurs for an (infinite) discrete set of $\xi$. We illustrate the
occurrence of this phenomenon for two examples of static, spherically
symmetric, asymptotically flat black hole solution of EFTs. In one example the
trace anomaly comes from the matter sector -- a novel, closed form,
generalisation of the Reissner-Nordstr\"om solution with an $F^4$ correction --
whereas in the other example it comes from the geometry sector -- a
noncommutative geometry generalization of the Schwarzschild black hole. For
comparison, we also consider the scalarisation of a black hole surrounded by
(non-conformally invariant) classical matter (Einstein-Maxwell-dilaton black
holes). We find that the scalarised solutions are, generically, entropically
favoured.
| arxiv topic:gr-qc hep-th |
arxiv_dataset-107261901.03053 | Vibration isolation system with a compact damping system for power
recycling mirrors of KAGRA
physics.ins-det gr-qc
A vibration isolation system called Type-Bp system used for power recycling
mirrors has been developed for KAGRA, the interferometric gravitational-wave
observatory in Japan. A suspension of the Type-Bp system passively isolates an
optic from seismic vibration using three main pendulum stages equipped with two
vertical vibration isolation systems. A compact reaction mass around each of
the main stages allows for achieving sufficient damping performance with a
simple feedback as well as vibration isolation ratio. Three Type-Bp systems
were installed in KAGRA, and were proved to satisfy the requirements on the
damping performance, and also on estimated residual displacement of the optics.
| arxiv topic:physics.ins-det gr-qc |
arxiv_dataset-107271901.03153 | Optimal mean value estimates beyond Vinogradov's mean value theorem
math.NT
We establish improved mean value estimates associated with the number of
integer solutions of certain systems of diagonal equations, in some instances
attaining the sharpest conjectured conclusions. This is the first occasion on
which bounds of this quality have been attained for Diophantine systems not of
Vinogradov type. As a consequence of this progress, whenever $u \ge 3v$ we
obtain the Hasse principle for systems consisting of $v$ cubic and $u$
quadratic diagonal equations in $6v+4u+1$ variables, thus attaining the
convexity barrier for this problem.
| arxiv topic:math.NT |
arxiv_dataset-107281901.03253 | Reverse-Engineering Satire, or "Paper on Computational Humor Accepted
Despite Making Serious Advances"
cs.AI cs.CL
Humor is an essential human trait. Efforts to understand humor have called
out links between humor and the foundations of cognition, as well as the
importance of humor in social engagement. As such, it is a promising and
important subject of study, with relevance for artificial intelligence and
human-computer interaction. Previous computational work on humor has mostly
operated at a coarse level of granularity, e.g., predicting whether an entire
sentence, paragraph, document, etc., is humorous. As a step toward deep
understanding of humor, we seek fine-grained models of attributes that make a
given text humorous. Starting from the observation that satirical news
headlines tend to resemble serious news headlines, we build and analyze a
corpus of satirical headlines paired with nearly identical but serious
headlines. The corpus is constructed via Unfun.me, an online game that
incentivizes players to make minimal edits to satirical headlines with the goal
of making other players believe the results are serious headlines. The edit
operations used to successfully remove humor pinpoint the words and concepts
that play a key role in making the original, satirical headline funny. Our
analysis reveals that the humor tends to reside toward the end of headlines,
and primarily in noun phrases, and that most satirical headlines follow a
certain logical pattern, which we term false analogy. Overall, this paper
deepens our understanding of the syntactic and semantic structure of satirical
news headlines and provides insights for building humor-producing systems.
| arxiv topic:cs.AI cs.CL |
arxiv_dataset-107291901.03353 | RetinaMask: Learning to predict masks improves state-of-the-art
single-shot detection for free
cs.CV
Recently two-stage detectors have surged ahead of single-shot detectors in
the accuracy-vs-speed trade-off. Nevertheless single-shot detectors are
immensely popular in embedded vision applications. This paper brings
single-shot detectors up to the same level as current two-stage techniques. We
do this by improving training for the state-of-the-art single-shot detector,
RetinaNet, in three ways: integrating instance mask prediction for the first
time, making the loss function adaptive and more stable, and including
additional hard examples in training. We call the resulting augmented network
RetinaMask. The detection component of RetinaMask has the same computational
cost as the original RetinaNet, but is more accurate. COCO test-dev results are
up to 41.4 mAP for RetinaMask-101 vs 39.1mAP for RetinaNet-101, while the
runtime is the same during evaluation. Adding Group Normalization increases the
performance of RetinaMask-101 to 41.7 mAP. Code is
at:https://github.com/chengyangfu/retinamask
| arxiv topic:cs.CV |
arxiv_dataset-107301901.03453 | The Fourier extension method and discrete orthogonal polynomials on an
arc of the circle
math.NA cs.NA
The Fourier extension method, also known as the Fourier continuation method,
is a method for approximating non-periodic functions on an interval using
truncated Fourier series with period larger than the interval on which the
function is defined. When the function being approximated is known at only
finitely many points, the approximation is constructed as a projection based on
this discrete set of points. In this paper we address the issue of estimating
the absolute error in the approximation. The error can be expressed in terms of
a system of discrete orthogonal polynomials on an arc of the unit circle, and
these polynomials are then evaluated asymptotically using Riemann--Hilbert
methods.
| arxiv topic:math.NA cs.NA |
arxiv_dataset-107311901.03553 | DIVE: A spatiotemporal progression model of brain pathology in
neurodegenerative disorders
cs.CV cs.LG q-bio.NC q-bio.QM stat.ML
Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is
an image-based disease progression model with single-vertex resolution,
designed to reconstruct long-term patterns of brain pathology from short-term
longitudinal data sets. DIVE clusters vertex-wise biomarker measurements on the
cortical surface that have similar temporal dynamics across a patient
population, and concurrently estimates an average trajectory of vertex
measurements in each cluster. DIVE uniquely outputs a parcellation of the
cortex into areas with common progression patterns, leading to a new signature
for individual diseases. DIVE further estimates the disease stage and
progression speed for every visit of every subject, potentially enhancing
stratification for clinical trials or management. On simulated data, DIVE can
recover ground truth clusters and their underlying trajectory, provided the
average trajectories are sufficiently different between clusters. We
demonstrate DIVE on data from two cohorts: the Alzheimer's Disease Neuroimaging
Initiative (ADNI) and the Dementia Research Centre (DRC), UK, containing
patients with Posterior Cortical Atrophy (PCA) as well as typical Alzheimer's
disease (tAD). DIVE finds similar spatial patterns of atrophy for tAD subjects
in the two independent datasets (ADNI and DRC), and further reveals distinct
patterns of pathology in different diseases (tAD vs PCA) and for distinct types
of biomarker data: cortical thickness from Magnetic Resonance Imaging (MRI) vs
amyloid load from Positron Emission Tomography (PET). Finally, DIVE can be used
to estimate a fine-grained spatial distribution of pathology in the brain using
any kind of voxelwise or vertexwise measures including Jacobian compression
maps, fractional anisotropy (FA) maps from diffusion imaging or other PET
measures. DIVE source code is available online:
https://github.com/mrazvan22/dive
| arxiv topic:cs.CV cs.LG q-bio.NC q-bio.QM stat.ML |
arxiv_dataset-107321901.03653 | Cubefree Trinomial Discriminants
math.NT
The discriminant of a polynomial of the form $\pm x^n \pm x^m \pm 1$ has the
form $n^n \pm m^m(n-m)^{n-m}$ when $n,m$ are relatively prime. We investigate
when these discriminants have prime power divisors. We explain several
symmetries that appear in the classification of these values of $n,m$. We prove
that there are infinitely many pairs of integers $n,m$ for which this
discriminant has no prime cube divisors. This result is extended to show that
for infinitely many fixed $m$, there are infinitely many $n$ for which the
discriminant has no prime cube divisor.
| arxiv topic:math.NT |
arxiv_dataset-107331901.03753 | Analysis of the Frequency and Detectability of Objects Resembling
Nuclear/Radiological Threats in Commercial Cargo
physics.soc-ph physics.ins-det
The threat of smuggled nuclear/radiological weapons and material in
commercial containerized cargo remains a significant threat to global security
more than a decade after the enactment of laws in the United States and
elsewhere mandating interdiction efforts. While significant progress has been
made towards deploying passive radiation detection systems in maritime ports,
such systems are incapable of detecting shielded threats or even certain
scenarios in which material is unshielded. Research efforts towards developing
systems for detecting such threats have typically focused on the development of
systems that are highly-specific to nuclear/radiological threats and no such
systems have been widely deployed. While most existing commercially-available
cargo radiography systems are not specifically designed for this interdiction
task, if items resembling nuclear/radiological threats are sufficiently rare in
cargo radiographs to limit false alarms to an acceptably low frequency, then a
smuggling interdiction scheme based on existing technology may be feasible.
This analysis characterizes the relevant nuclear and radiological threats that
may evade detection by passive monitors, and utilizes a dataset of 122,500
stream-of-commerce cargo container images from a 6 MeV endpoint gamma
radiography system to determine the frequency at which objects of similar size
and density to such threats occur in containers. It is found that for a broad
class of threats, including assembled fission devices, gamma radiography is
sufficient to flag threats in this cargo stream at false positive rates of
$\lesssim$2%.
| arxiv topic:physics.soc-ph physics.ins-det |
arxiv_dataset-107341901.03853 | Caristi-Kirk and Oettli-Th\'era Ball Spaces and applications
math.FA
Based on the theory of ball spaces introduced by Kuhlmann and Kuhlmann we
introduce and study Caristi-Kirk and Oettli-Th\'era ball spaces. We show that
if the underlying metric space is complete, then these have a very strong
property: every ball contains a singleton ball. This fact provides quick proofs
for several results which are equivalent to the Caristi-Kirk Fixed Point
Theorem, namely Ekeland's Variational Principles, the Oettli-Th\'era Theorem,
Takahashi's Theorem and the Flower Petal Theorem.
| arxiv topic:math.FA |
arxiv_dataset-107351901.03953 | Light-Field for RF
eess.IV cs.CV
Most computer vision systems and computational photography systems are
visible light based which is a small fraction of the electromagnetic (EM)
spectrum. In recent years radio frequency (RF) hardware has become more widely
available, for example, many cars are equipped with a RADAR, and almost every
home has a WiFi device. In the context of imaging, RF spectrum holds many
advantages compared to visible light systems. In particular, in this regime, EM
energy effectively interacts in different ways with matter. This property
allows for many novel applications such as privacy preserving computer vision
and imaging through absorbing and scattering materials in visible light such as
walls. Here, we expand many of the concepts in computational photography in
visible light to RF cameras. The main limitation of imaging with RF is the
large wavelength that limits the imaging resolution when compared to visible
light. However, the output of RF cameras is usually processed by computer
vision and perception algorithms which would benefit from multi-modal sensing
of the environment, and from sensing in situations in which visible light
systems fail. To bridge the gap between computational photography and RF
imaging, we expand the concept of light-field to RF. This work paves the way to
novel computational sensing systems with RF.
| arxiv topic:eess.IV cs.CV |
arxiv_dataset-107361901.04053 | Moonshots for aging
q-bio.OT
As the global population ages, there is increased interest in living longer
and improving one's quality of life in later years. However, studying aging -
the decline in body function - is expensive and time-consuming. And despite
research success to make model organisms live longer, there still aren't really
any feasible solutions for delaying aging in humans. With space travel,
scientists couldn't know what it would take to get to the moon. They had to
extrapolate from theory and shorter-range tests. Perhaps with aging, we need a
similar moonshot philosophy. And though "shot" might imply medicine, perhaps we
need to think beyond biological interventions. Like the moon, we seem a long
way away from provable therapies to increase human healthspan (the healthy
period of one's life) or lifespan (how long one lives). This review therefore
focuses on radical proposals. We hope it might stimulate discussion on what we
might consider doing significantly differently than ongoing aging research.
| arxiv topic:q-bio.OT |
arxiv_dataset-107371901.04153 | Optimal Strategies of Blotto Games: Beyond Convexity
cs.GT
The Colonel Blotto game, first introduced by Borel in 1921, is a well-studied
game theory classic. Two colonels each have a pool of troops that they divide
simultaneously among a set of battlefields. The winner of each battlefield is
the colonel who puts more troops in it and the overall utility of each colonel
is the sum of weights of the battlefields that s/he wins. Over the past
century, the Colonel Blotto game has found applications in many different forms
of competition from advertisements to politics to sports.
Two main objectives have been proposed for this game in the literature: (i)
maximizing the guaranteed expected payoff, and (ii) maximizing the probability
of obtaining a minimum payoff $u$. The former corresponds to the conventional
utility maximization and the latter concerns scenarios such as elections where
the candidates' goal is to maximize the probability of getting at least half of
the votes (rather than the expected number of votes). In this paper, we
consider both of these objectives and show how it is possible to obtain
(almost) optimal solutions that have few strategies in their support.
One of the main technical challenges in obtaining bounded support strategies
for the Colonel Blotto game is that the solution space becomes non-convex. This
prevents us from using convex programming techniques in finding optimal
strategies which are essentially the main tools that are used in the
literature. However, we show through a set of structural results that the
solution space can, interestingly, be partitioned into polynomially many
disjoint convex polytopes that can be considered independently. Coupled with a
number of other combinatorial observations, this leads to polynomial time
approximation schemes for both of the aforementioned objectives.
| arxiv topic:cs.GT |
arxiv_dataset-107381901.04253 | Ruprecht 147: a paradigm of dissolving star cluster
astro-ph.GA
We employed recent Gaia/DR2 data to investigate the dynamical status of the
nearby (300 pc), old (2.5 Gyr) open cluster Ruprecht~147. We found prominent
leading and trailing tails of stars along the cluster orbit, which demonstrates
that Ruprecht~147 is losing stars at fast pace. Star counts indicate the
cluster has a core radius of 33.3 arcmin, and a tidal radius of 137.5 arcmin.
The cluster also possesses an extended corona, which cannot be reproduced by a
simple King model. We computed the present-day cluster mass using its
luminosity and mass function, and derived an estimate of 234$\pm$52
$M_{\odot}$. We also estimated the cluster original mass using available
recipes extracted from N-body simulations obtaining a mass at birth of
50000$\pm$6500 $M_{\odot}$. Therefore dynamical mass loss, mostly caused by
tidal interaction with the Milky Way, reduced the cluster mass by about 99\%.
We then conclude that Ruprecht~147 is rapidly dissolving into the general
Galactic disc.
| arxiv topic:astro-ph.GA |
arxiv_dataset-107391901.04353 | Distribution of solutions of the fastest apparent convergence condition
in optimized perturbation theory and its relation to anti-Stokes lines
hep-th hep-ph math-ph math.MP
We discuss fundamental properties of the fastest apparent convergence (FAC)
condition which is used as a variational criterion in optimized perturbation
theory (OPT). We examine an integral representation of the FAC condition and a
distribution of the zeros of the integral in a complex artificial parameter
space on the basis of theory of Lefschetz thimbles. We find that the zeros
accumulate on a certain line segment so-called anti-Stokes line in the limit $K
\to \infty$, where $K$ is a truncation order of a perturbation series. This
phenomenon gives an underlying mechanism that physical quantities calculated by
OPT can be insensitive to the choice of the artificial parameter.
| arxiv topic:hep-th hep-ph math-ph math.MP |
arxiv_dataset-107401901.04453 | The geometry of involutions in ranked groups with a TI-subgroup
math.LO math.GR
We revisit the geometry of involutions in groups of finite Morley rank. Our
approach unifies and generalises numerous results, both old and recent, that
have exploited this geometry; though in fact, we prove much more. We also
conjecture that this path leads to a new identification theorem for
$\operatorname{PGL}_2(\mathbb{K})$.
| arxiv topic:math.LO math.GR |
arxiv_dataset-107411901.04553 | Reactor neutrino oscillations as constraints on Effective Field Theory
hep-ph hep-ex
We study constraints on the Standard Model Effective Field Theory (SMEFT)
from neutrino oscillations in short-baseline reactor experiments. We calculate
the survival probability of reactors antineutrinos at the leading order in the
SMEFT expansion, that is including linear effects of dimension-6 operators. It
is shown that, at this order, reactor experiments alone cannot probe
charged-current contact interactions between leptons and quarks that are of the
(pseudo)vector (V$\pm$A) or pseudo-scalar type. We also note that
flavor-diagonal (pseudo)vector coefficients do not have observable effects in
oscillation experiments. In this we reach novel or different conclusions than
prior analyses of non-standard neutrino interactions. On the other hand,
reactor experiments offer a unique opportunity to probe tensor and scalar SMEFT
operators that are off-diagonal in the lepton-flavor space. We derive
constraints on the corresponding SMEFT parameters using the most recent data
from the Daya Bay and RENO experiments.
| arxiv topic:hep-ph hep-ex |
arxiv_dataset-107421901.04653 | Normalized Flat Minima: Exploring Scale Invariant Definition of Flat
Minima for Neural Networks using PAC-Bayesian Analysis
stat.ML cs.LG
The notion of flat minima has played a key role in the generalization studies
of deep learning models. However, existing definitions of the flatness are
known to be sensitive to the rescaling of parameters. The issue suggests that
the previous definitions of the flatness might not be a good measure of
generalization, because generalization is invariant to such rescalings. In this
paper, from the PAC-Bayesian perspective, we scrutinize the discussion
concerning the flat minima and introduce the notion of normalized flat minima,
which is free from the known scale dependence issues. Additionally, we
highlight the scale dependence of existing matrix-norm based generalization
error bounds similar to the existing flat minima definitions. Our modified
notion of the flatness does not suffer from the insufficiency, either,
suggesting it might provide better hierarchy in the hypothesis class.
| arxiv topic:stat.ML cs.LG |
arxiv_dataset-107431901.04753 | The generality of transient compartmentalization and its associated
error thresholds
q-bio.PE cond-mat.soft physics.bio-ph
Can prelife proceed without cell division? A recently proposed mechanism
suggests that transient compartmentalization could have preceded cell division
in prebiotic scenarios. Here, we study transient compartmentalization dynamics
in the presence of mutations and noise in replication, as both can be
detrimental the survival of compartments. Our study comprises situations where
compartments contain uncoupled autocatalytic reactions feeding on a common
resource, and systems based on RNA molecules copied by replicases, following a
recent experimental study.
Using the theory of branching processes, we show analytically that two
regimes are possible. In the diffusion-limited regime, replication is
asynchronous which leads to a large variability in the composition of
compartments. In contrast, in a replication-limited regime, the growth is
synchronous and thus the compositional variability is low. Typically, simple
autocatalysts are in the former regime, while polymeric replicators can access
the latter.
For deterministic growth dynamics, we introduce mutations that turn
functional replicators into parasites. We derive the phase boundary separating
coexistence or parasite dominance as a function of relative growth, inoculation
size and mutation rate. We show that transient compartmentalization allows
coexistence beyond the classical error threshold, above which the parasite
dominates. Our findings invite to revisit major prebiotic transitions, notably
the transitions towards cooperation, complex polymers and cell division.
| arxiv topic:q-bio.PE cond-mat.soft physics.bio-ph |
arxiv_dataset-107441901.04853 | Search for Anderson localization of light by cold atoms in a static
electric field
cond-mat.dis-nn physics.atom-ph
We explore the potential of a static electric field to induce Anderson
localization of light in a large three-dimensional (3D) cloud of randomly
distributed, immobile atoms with a degenerate ground state (total angular
momentum $J_g = 0$) and a three-fold degenerate excited state ($J_e = 1$). We
study both the spatial structure of quasimodes of the atomic cloud and the
scaling of the Thouless number with the size of the cloud. Our results indicate
that unlike the static magnetic field, the electric field does not induce
Anderson localization of light by atoms. We explain this conclusion by the
incomplete removal of degeneracy of the excited atomic state by the field and
the relatively strong residual dipole-dipole coupling between atoms which is
weaker than in the absence of external fields but stronger than in the presence
of a static magnetic field. A joint analysis of these results together with our
previous results concerning Anderson localization of scalar waves and light
suggests the existence of a critical strength of dipole-dipole interactions
that should not be surpassed for Anderson localization to be possible in 3D.
| arxiv topic:cond-mat.dis-nn physics.atom-ph |
arxiv_dataset-107451901.04953 | A forgotten Theorem of Schoenberg on one-sided integral averages
math.CA math.ST stat.TH
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a function for which we want to
take local averages. Assuming we cannot look into the future, the 'average' at
time $t$ can only use $f(s)$ for $s \leq t$. A natural way to do so is via a
weight $\phi$ and $$ g(t) = \int_{0}^{\infty}{f(t-s) \phi(s) ds}.$$ We would
like that (1) constant functions, $f(t) \equiv \mbox{const}$, are mapped to
themselves and (2) $\phi$ to be monotonically decreasing (the more recent past
should weigh more heavily than the distant past). Moreover, we want that (3) if
$f(t)$ crosses a certain threshold $n$ times, then $g(t)$ should not cross the
same threshold more than $n$ times (if $f(t)$ is the outside wind speed and
crosses the Tornado threshold at two points in time, we would like the averaged
wind speed to cross the Tornado threshold at most twice). A Theorem implicit in
the work of Schonberg is that these three conditions characterize a unique
weight that is given by the exponential distribution $$ \phi(s) = \lambda^{}
e^{-\lambda s} \qquad \mbox{for some} \quad \lambda > 0.$$
| arxiv topic:math.CA math.ST stat.TH |
arxiv_dataset-107461901.05053 | An Agent-Based Model to Explain the Emergence of Stylised Facts in Log
Returns
q-fin.TR
This paper outlines an agent-based model of a simple financial market in
which a single asset is available for trade by three different types of
traders. The model was first introduced in the PhD thesis of one of the
authors, see reference [1]. The simulated log returns are examined for the
presence of the stylised facts of financial data. The features of
leptokurtosis, volatility clustering and aggregational Gaussianity are
especially highlighted and studied in detail. The following ingredients are
found to be essential for the production of these stylised facts: the memory of
noise traders who make random trade decisions; the inclusion of technical
traders that trade in line with trends in the price and the inclusion of
fundamental traders who know the "fundamental value" of the stock and trade
accordingly. When these three basic types of traders are included log returns
are produced with a leptokurtic distribution and volatility clustering as well
as some further statistical features of empirical data. This enhances and
broadens our understanding of the fundamental processes involved in the
production of empirical data by the market.
| arxiv topic:q-fin.TR |
arxiv_dataset-107471901.05153 | Channel Conditions for the Optimality of Interference Decoding Schemes
for K-user Gaussian Interference Channels
cs.IT math.IT
The Han-Kobayashi (HK) scheme achieves the best known achievable rate region
for the K user interference channel (IC). Simple HK schemes are HK schemes with
Gaussian signaling, no time sharing, and no private-common power splitting. The
class of simple HK schemes includes the treating interference as noise (TIN)
scheme and schemes that involve various levels of interference decoding and
cancellation at each receiver. We derive conditions under which simple HK
schemes achieve sum capacity for general K user Gaussian ICs. These results
generalize existing sum capacity results for the TIN scheme to the class of
simple HK schemes.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-107481901.05253 | OxH2x+1+ Clusters: A New Series of Non-Metallic Superalkali Cations by
Trapping H3O+ into Water
physics.chem-ph
The term superalkali refers to the clusters with lower ionization energy than
alkali atoms. Typical superalkali cations include a central electronegative
core with excess metal ligands, OLi3+, for instance, which mimic the properties
of alkali metal ions. We report a new series of non-metallic superalkali
cations, OxH2x+1+ (x = 1-5) using ab initio MP2/6-311++G(d,p) level. These
cations are designed by successive replacement of H-ligands of hydronium cation
(OH3+) by ammonium (OH3) moieties followed by their geometry optimization. The
resulting OxH2x+1 + clusters, which can be expressed in the form of OH3 +
(x-1)H2O complexes, possess a number of electrostatic as well as partially
covalent H-bonds, with the interacting energy in the range 5.2-29.3 kcal/mol as
revealed by quantum theory of atoms in molecules analyses. These cations are
found to be stable against deprotonation as well as dehydration pathways, and
their stability increases with the increase in x. Interestingly, the vertical
electron affinities (EAv) of OxH2x+1 + clusters decreases rapidly from 5.16 eV
for x = 1 to 2.67 eV for x = 5, which suggest their superalkali nature. It is
also possible to continue this series of non-metallic superalkali cations for x
> 5 with even lower EAv, down to an approximated limit of 1.85 eV, which is
obtained for OH3 + trapped into water cavity implicitly using polarizable
continuum model. The findings of this study will not only provide new insights
into structure and interactions of OxH2x+1 + clusters but also reveal their
novel properties, which can be exploited their interesting applications.
| arxiv topic:physics.chem-ph |
arxiv_dataset-107491901.05353 | A Primer on PAC-Bayesian Learning
stat.ML cs.LG
Generalised Bayesian learning algorithms are increasingly popular in machine
learning, due to their PAC generalisation properties and flexibility. The
present paper aims at providing a self-contained survey on the resulting
PAC-Bayes framework and some of its main theoretical and algorithmic
developments.
| arxiv topic:stat.ML cs.LG |
arxiv_dataset-107501901.05453 | A Study of Charge Radii and Neutron Skin Thickness near Nuclear Drip
Lines
nucl-th
We studied the charge radius, rms radius and neutron skin thickness $\Delta
r_{np}$ in even-even isotopes of Si, S, Ar and Ca and isotones of N =20, 28, 50
and 82. The $\Delta r_{np}$ in doubly-magic $^{48}$Ca, $^{68}$Ni,
$^{120,132}$Sn and $^{208}$Pb nuclei has also been calculated. Theoretical
calculations are done with the Hartree-Fock-Bogoliubov theory with the
effective Skyrme interactions. Calculated theoretical estimates are in good
agreement with the recently available experimental data. The charge radii for
Si, S, Ar and Ca isotopes is observed to be minimum at neutron number N =14.
The theoretically computed results with UNEDF0 model parameterization of
functional are reasonably reproducing the experimental data for $\Delta r_{np}$
in $^{48}$Ca, $^{68}$Ni and $^{120,132}$Sn. The energy density functional of
UNEDF1 model provides much improved result of $\Delta r_{np}$ for $^{208}$Pb.
| arxiv topic:nucl-th |
arxiv_dataset-107511901.05553 | Truly Generalizable Radiograph Segmentation with Conditional Domain
Adaptation
cs.CV
Digitization techniques for biomedical images yield different visual patterns
in radiological exams. These differences may hamper the use of data-driven
approaches for inference over these images, such as Deep Neural Networks.
Another noticeable difficulty in this field is the lack of labeled data, even
though in many cases there is an abundance of unlabeled data available.
Therefore an important step in improving the generalization capabilities of
these methods is to perform Unsupervised and Semi-Supervised Domain Adaptation
between different datasets of biomedical images. In order to tackle this
problem, in this work we propose an Unsupervised and Semi-Supervised Domain
Adaptation method for segmentation of biomedical images using Generative
Adversarial Networks for Unsupervised Image Translation. We merge these
unsupervised networks with supervised deep semantic segmentation architectures
in order to create a semi-supervised method capable of learning from both
unlabeled and labeled data, whenever labeling is available. We compare our
method using several domains, datasets, segmentation tasks and traditional
baselines, such as unsupervised distance-based methods and reusing pretrained
models both with and without Fine-tuning. We perform both quantitative and
qualitative analysis of the proposed method and baselines in the distinct
scenarios considered in our experimental evaluation. The proposed method shows
consistently better results than the baselines in scarce labeled data
scenarios, achieving Jaccard values greater than 0.9 and good segmentation
quality in most tasks. Unsupervised Domain Adaptation results were observed to
be close to the Fully Supervised Domain Adaptation used in the traditional
procedure of Fine-tuning pretrained networks.
| arxiv topic:cs.CV |
arxiv_dataset-107521901.05653 | Protoperads i: Combinatorics and definitions
math.AT
This paper is the first of two articles which develop the notion of
protoperads. In this one, we construct a new monoidal product on the category
of reduced S-modules. We study the associated monoids, called protoperads,
which are a generalization of operads. As operads encode algebraic operations
with several inputs and one outputs, protoperads encode algebraic operations
with the same number of inputs and outputs. We describe the underlying
combinatorics of protoperads, and show that there exists a notion of free
protoperad. We also show that the monoidal product introduced here is related
to Vallette's one on the category of S-bimodules, via the induction functor.
| arxiv topic:math.AT |
arxiv_dataset-107531901.05753 | Spin transport parameters of NbN thin films characterised by spin
pumping experiments
cond-mat.mtrl-sci cond-mat.mes-hall
We present measurements of ferromagnetic-resonance - driven spin pumping and
inverse spin-Hall effect in NbN/Y3Fe5O12 (YIG) bilayers. A clear enhancement of
the (effective) Gilbert damping constant of the thin-film YIG was observed due
to the presence of the NbN spin sink. By varying the NbN thickness and
employing spin-diffusion theory, we have estimated the room temperature values
of the spin diffusion length and the spin Hall angle in NbN to be 14 nm and
-1.1 10-2, respectively. Furthermore, we have determined the spin-mixing
conductance of the NbN/YIG interface to be 10 nm-2. The experimental
quantification of these spin transport parameters is an important step towards
the development of superconducting spintronic devices involving NbN thin films.
| arxiv topic:cond-mat.mtrl-sci cond-mat.mes-hall |
arxiv_dataset-107541901.05853 | Nuclear dimension of simple C*-algebras
math.OA
We compute the nuclear dimension of separable, simple, unital, nuclear,
Z-stable C*-algebras. This makes classification accessible from Z-stability and
in particular brings large classes of C*-algebras associated to free and
minimal actions of amenable groups on finite dimensional spaces within the
scope of the Elliott classification programme.
| arxiv topic:math.OA |
arxiv_dataset-107551901.05953 | Outline for a quantum theory of gravity
gr-qc hep-th quant-ph
By invoking an asymmetric metric tensor, and borrowing ideas from
non-commutative geometry, string theory, and trace dynamics, we propose an
action function for quantum gravity. The action is proportional to the four
dimensional non-commutative curvature scalar (which is torsion dependent) that
is sourced by the Nambu-Goto world-sheet action for a string, plus the
Kalb-Ramond string action. This `quantum gravity' is actually a non-commutative
{\it classical} matrix dynamics, and the only two fundamental constants in the
theory are the square of Planck length and the speed of light. By treating the
entity described by this action as a microstate, one constructs the statistical
thermodynamics of a large number of such microstates, in the spirit of trace
dynamics. Quantum field theory (and $\hbar$) and quantum general relativity
(and $G$) emerge from the underlying matrix dynamics in the thermodynamic
limit. The statistical fluctuations that are inevitably present about
equilibrium, are the source for spontaneous localisation, which drives
macroscopic quantum gravitational systems to the classical general relativistic
limit. While the mathematical formalism governing these ideas remains to be
developed, we hope here to highlight the deep connection between quantum
foundations, and the sought for quantum theory of gravity. In the sense
described in this article, ongoing experimental tests of spontaneous collapse
theories are in fact also tests of string theory!
| arxiv topic:gr-qc hep-th quant-ph |
arxiv_dataset-107561901.06053 | A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural
Networks
cs.LG stat.ML
The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is
often considered to be Gaussian in the large data regime by assuming that the
classical central limit theorem (CLT) kicks in. This assumption is often made
for mathematical convenience, since it enables SGD to be analyzed as a
stochastic differential equation (SDE) driven by a Brownian motion. We argue
that the Gaussianity assumption might fail to hold in deep learning settings
and hence render the Brownian motion-based analyses inappropriate. Inspired by
non-Gaussian natural phenomena, we consider the GN in a more general context
and invoke the generalized CLT (GCLT), which suggests that the GN converges to
a heavy-tailed $\alpha$-stable random variable. Accordingly, we propose to
analyze SGD as an SDE driven by a L\'{e}vy motion. Such SDEs can incur `jumps',
which force the SDE transition from narrow minima to wider minima, as proven by
existing metastability theory. To validate the $\alpha$-stable assumption, we
conduct extensive experiments on common deep learning architectures and show
that in all settings, the GN is highly non-Gaussian and admits heavy-tails. We
further investigate the tail behavior in varying network architectures and
sizes, loss functions, and datasets. Our results open up a different
perspective and shed more light on the belief that SGD prefers wide minima.
| arxiv topic:cs.LG stat.ML |
arxiv_dataset-107571901.06153 | Infeasibility and structural bias in Differential Evolution
cs.NE
This paper thoroughly investigates a range of popular DE configurations to
identify components responsible for the emergence of structural bias - recently
identified tendency of the algorithm to prefer some regions of the search space
for reasons directly unrelated to the objective function values. Such tendency
was already studied in GA and PSO where a connection was established between
the strength of structural bias and population sizes and potential weaknesses
of these algorithms was highlighted. For DE, this study goes further and
extends the range of aspects that can contribute to presence of structural bias
by including algorithmic component which is usually overlooked - constraint
handling technique. A wide range of DE configurations were subjected to the
protocol for testing for bias. Results suggest that triggering mechanism for
the bias in DE differs to the one previously found for GA and PSO - no clear
dependency on population size exists. Setting of DE parameters is based on a
separate study which on its own leads to interesting directions of new
research. Overall, DE turned out to be robust against structural bias - only
DE/current-to-best/1/bin is clearly biased but this effect is mitigated by the
use of penalty constraint handling technique.
| arxiv topic:cs.NE |
arxiv_dataset-107581901.06253 | CONet: A Cognitive Ocean Network
cs.CY cs.AI
The scientific and technological revolution of the Internet of Things has
begun in the area of oceanography. Historically, humans have observed the ocean
from an external viewpoint in order to study it. In recent years, however,
changes have occurred in the ocean, and laboratories have been built on the
seafloor. Approximately 70.8% of the Earth's surface is covered by oceans and
rivers. The Ocean of Things is expected to be important for disaster
prevention, ocean-resource exploration, and underwater environmental
monitoring. Unlike traditional wireless sensor networks, the Ocean Network has
its own unique features, such as low reliability and narrow bandwidth. These
features will be great challenges for the Ocean Network. Furthermore, the
integration of the Ocean Network with artificial intelligence has become a
topic of increasing interest for oceanology researchers. The Cognitive Ocean
Network (CONet) will become the mainstream of future ocean science and
engineering developments. In this article, we define the CONet. The
contributions of the paper are as follows: (1) a CONet architecture is proposed
and described in detail; (2) important and useful demonstration applications of
the CONet are proposed; and (3) future trends in CONet research are presented.
| arxiv topic:cs.CY cs.AI |
arxiv_dataset-107591901.06353 | Spectra of biperiodic planar networks
math.CO math.AG
A biperiodic planar network is a pair $(G,c)$ where $G$ is a graph embedded
on the torus and $c$ is a function from the edges of $G$ to non-zero complex
numbers. Associated to the discrete Laplacian on a biperiodic planar network is
its spectrum: a triple $(C,S,\nu)$, where $C$ is a curve and $S$ is a divisor
on it. We give a complete classification of networks (modulo a natural
equivalence) in terms of their spectral data. The space of networks has a large
group of cluster automorphisms arising from the $Y-\Delta$ transformations. We
show that the spectrum provides action-angle coordinates for the discrete
cluster integrable systems defined by these automorphisms.
| arxiv topic:math.CO math.AG |
arxiv_dataset-107601901.06453 | Holographic Phase Retrieval and Reference Design
cs.IT cs.NA eess.SP math.IT math.NA math.OC
A general mathematical framework and recovery algorithm is presented for the
holographic phase retrieval problem. In this problem, which arises in
holographic coherent diffraction imaging, a "reference" portion of the signal
to be recovered via phase retrieval is a priori known from experimental design.
A generic formula is also derived for the expected recovery error when the
measurement data is corrupted by Poisson shot noise. This facilitates an
optimization perspective towards reference design and analysis. We employ this
optimization perspective towards quantifying the performance of various
reference choices.
| arxiv topic:cs.IT cs.NA eess.SP math.IT math.NA math.OC |
arxiv_dataset-107611901.06553 | Neuroflight: Next Generation Flight Control Firmware
cs.RO
Little innovation has been made to low-level attitude flight control used by
uncrewed aerial vehicles (UAVs), which still predominantly uses the classical
PID controller. In this work we introduce Neuroflight, the first open source
neuro-flight controller firmware. We present our toolchain for training a
neural network in simulation and compiling it to run on embedded hardware.
Challenges faced jumping from simulation to reality are discussed along with
our solutions. Our evaluation shows the neural network can execute at over
2.67kHz on an Arm Cortex-M7 processor and flight tests demonstrate a quadcopter
running Neuroflight can achieve stable flight and execute aerobatic maneuvers.
| arxiv topic:cs.RO |
arxiv_dataset-107621901.06653 | Fast algorithms at low temperatures via Markov chains
cs.DS math.CO math.PR
We define a discrete-time Markov chain for abstract polymer models and show
that under sufficient decay of the polymer weights, this chain mixes rapidly.
We apply this Markov chain to polymer models derived from the hard-core and
ferromagnetic Potts models on bounded-degree (bipartite) expander graphs. In
this setting, Jenssen, Keevash and Perkins (2019) recently gave an FPTAS and an
efficient sampling algorithm at sufficiently high fugacity and low temperature
respectively. Their method is based on using the cluster expansion to obtain a
complex zero-free region for the partition function of a polymer model, and
then approximating this partition function using the polynomial interpolation
method of Barvinok.
Our approach via the polymer model Markov chain circumvents the zero-free
analysis and the generalization to complex parameters, and leads to a sampling
algorithm with a fast running time of $O(n \log n)$ for the Potts model and
$O(n^2 \log n)$ for the hard-core model, in contrast to typical running times
of $n^{O(\log \Delta)}$ for algorithms based on Barvinok's polynomial
interpolation method on graphs of maximum degree $\Delta$. We finally combine
our results for the hard-core and ferromagnetic Potts models with standard
Markov chain comparison tools to obtain polynomial mixing time for the usual
spin Glauber dynamics restricted to even and odd or `red' dominant portions of
the respective state spaces.
| arxiv topic:cs.DS math.CO math.PR |
arxiv_dataset-107631901.06753 | Thermofield Theory for Finite-Temperature Quantum Chemistry
physics.chem-ph cond-mat.str-el
Thermofield dynamics has proven to be a very useful theory in high-energy
physics, particularly since it permits the treatment of both time- and
temperature-dependence on an equal footing. We here show that it also has an
excellent potential for studying thermal properties of electronic systems in
physics and chemistry. We describe a general framework for constructing finite
temperature correlated wave function methods typical of ground state methods.
We then introduce two distinct approaches to the resulting imaginary time
Schrodinger equation, which we refer to as fixed-reference and covariant
methods. As an example, we derive the two corresponding versions of thermal
configuration interaction theory, and apply them to the Hubbard model, while
comparing with exact benchmark results.
| arxiv topic:physics.chem-ph cond-mat.str-el |
arxiv_dataset-107641901.06853 | Schubert Derivations on the Infinite Wedge Power
math.AG math-ph math.CO math.MP math.RT
The {\em Schubert derivation} is a distinguished Hasse-Schmidt derivation on
the exterior algebra of a free abelian group, encoding the formalism of
Schubert calculus for all Grassmannians at once. The purpose of this paper is
to extend the Schubert derivation to the infinite exterior power of a free
${\mathbb Z}$-module of infinite rank (fermionic Fock space). Classical vertex
operators naturally arise from the {\em integration by parts formula}, that
also recovers the generating function occurring in the {\em bosonic vertex
representation} of the Lie algebra $gl_\infty({\mathbb Z})$, due to Date,
Jimbo, Kashiwara and Miwa (DJKM). In the present framework, the DJKM result
will be interpreted as a limit case of the following general observation: the
singular cohomology of the complex Grassmannian $G(r,n)$ is an irreducible
representation of the Lie algebra of $n\times n$ square matrices.}
| arxiv topic:math.AG math-ph math.CO math.MP math.RT |
arxiv_dataset-107651901.06953 | Edelstein effects, spin-transfer torque, and spin pumping caused by
pristine surface states of topological insulators
cond-mat.mes-hall
The Edelstein effect caused by the pristine surface states of
three-dimensional topological insulators is investigated by means of a
semiclassical approach. The combined effect of random impurity scattering and
the spin-momentum locking of the gapless Dirac cone yields a current-induced
surface spin accumulation independent from chemical potential and temperature.
In a nearby ferromagnet that does not make direct contact with the topological
insulator, the bound state nature of the pristine surface state causes a
spin-transfer torque that is entirely field-like, whose magnitude is highly
influenced by the interface cleanliness and the quantum well state of the
ferromagnet. Through incorporating quantum tunneling into Bloch equation, the
spin pumping mediated by the pristine surface state is shown to be described by
the same spin mixing conductance as the spin-transfer torque, and a
semiclassical approach is proposed to explain the inverse Edelstein effect that
converts the spin pumping spin current into a charge current. Consistency of
these results with various experiments will be elaborated in detail.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-107661901.07053 | Concave power solutions of the Dominative $p$-Laplace equation
math.AP
In this paper, we study properties of solutions of the Dominative $p$-Laplace
equation with homogeneous Dirichlet boundary conditions in a bounded convex
domain $\Omega$. For the equation $-\mathcal{D}_p u= 1$, we show that
$\sqrt{u}$ is concave, and for the eigenvalue problem $\mathcal{D}_p u +
\lambda u=0$, we show that $\log {u}$ is concave.
| arxiv topic:math.AP |
arxiv_dataset-107671901.07153 | Convergence of $p$-Stable Random Fractional Wavelet Series and Some of
its Properties
math.FA
For appropriate orthonormal wavelet basis $\{\psi_{j\,k}^e
\}_{j\in\mathbb{Z}\,k\in\mathbb{Z}^d\,e\in\{0,1\}^d}$, constants $p$ and
$\gamma$, if $\mathcal{I}_{\gamma}$ denotes the Riesz fractional integral
operator of order $\gamma$ and $(\eta_{j\,k\,e})_{j\in\mathbb{Z}
k\in\mathbb{Z}^d \,e\in\{0,1\}^d}$ a sequence of independent identically
distributed symmetric $p$-stable random variables, we investigate the
convergence of the series $\sum\limits_{j\,k\,e} \eta_{j\,k\,e}
\mathcal{I}_{\gamma} \psi_{j\,k\,}^e$. Similar results are also studied for
modified fractional integral operators. Finally, some geometric properties
related to self similarity are studied.
| arxiv topic:math.FA |
arxiv_dataset-107681901.07253 | Direct and inverse approximation theorems of functions in the Orlicz
type spaces S_M
math.CA
In the Orlicz type spaces ${\mathcal S}_{M}$, we prove direct and inverse
approximation theorems in terms of the best approximations of functions and
moduli of smoothness of fractional order. We also show the equivalence between
moduli of smoothness and Peetre $K$-functionals in the spaces ${\mathcal
S}_{M}$.
| arxiv topic:math.CA |
arxiv_dataset-107691901.07353 | Small-Angle Scattering
physics.ins-det
Small-Angle Scattering (SAS) investigates structures in samples that
generally range from approximately 0.5 nm to a few 100 nm. This can both be
done for isotropic samples such as blends and liquids, as well as anisotropic
samples such as quasi-crystals. In order to obtain data about that size regime
scattered intensity, mostly of x-rays or neutrons, is investigated at angles
from close to zero, still in the region of the primary beam up to 10\deg ,
depending on the wavelength of the incoming radiation. The two primary sources
for SAS experiments are x-ray (small-angle x-ray scattering, SAXS) sources and
neutron (small-angle neutron scattering, SANS) sources, which shall be the two
cases discussed here. Also scattering with electrons or other particle waves is
possible, but not the main use case for the purpose of this manuscript. For
most small-angle scattering instruments, both SAXS and SANS, the science case
covers the investigation of self-assembled polymeric and biological systems,
multi-scale systems with large size distribution of the contained particles,
solutions of (nano-)particles and soft-matter systems, protein solutions, and
material science investigations. In the case of SANS this is augmented by the
possibility to also investigate the spin state of the sample and hence perform
investigations of the magnetic structure of the sample. In the following
sections the general setup of both SAXS and SANS instruments shall be
discussed, as well as data acquisition and evaluation and preparation of the
sample and the experiment in general. The information contained herein should
provide sufficient information for planning and performing a SAS experiment and
evaluate the gathered data.
| arxiv topic:physics.ins-det |
arxiv_dataset-107701901.07453 | Orbital Angular Momentum at Small $x$
hep-ph nucl-ex nucl-th
We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital
angular momentum (OAM) distributions in the proton in the double-logarithmic
approximation (DLA), which resums powers of $\alpha_s \ln^2 (1/x)$ with
$\alpha_s$ the strong coupling constant. Starting with the operator definitions
for the quark and gluon OAM, we simplify them at small $x$, relating them,
respectively, to the polarized dipole amplitudes for the quark and gluon
helicities defined in our earlier works. Using the small-$x$ evolution
equations derived for these polarized dipole amplitudes earlier we arrive at
the following small-$x$ asymptotics of the quark and gluon OAM distributions in
the large-$N_c$ limit:
\begin{align}
L_{q + \bar{q}} (x, Q^2) = - \Delta \Sigma (x, Q^2) \sim
\left(\frac{1}{x}\right)^{\frac{4}{\sqrt{3}} \, \sqrt{\frac{\alpha_s
\, N_c}{2 \pi}} }, \ \ \ \ \
L_G (x, Q^2) \sim \Delta G (x, Q^2) \sim
\left(\frac{1}{x}\right)^{\frac{13}{4 \sqrt{3}} \, \sqrt{\frac{\alpha_s
\, N_c}{2 \pi}}} . \end{align}
| arxiv topic:hep-ph nucl-ex nucl-th |
arxiv_dataset-107711901.07553 | Specification of additional information for solving stochastic inverse
problems
math.NA cs.NA math.PR
Methods have been developed to identify the probability distribution of a
random vector $Z$ from information consisting of its bounded range and the
probability density function or moments of a quantity of interest, $Q(Z)$. The
mapping from $Z$ to $Q(Z)$ may arise from a stochastic differential equation
whose coefficients depend on $Z$. This problem differs from Bayesian inverse
problems as the latter is primarily driven by observation noise. We motivate
this work by demonstrating that additional information on $Z$ is required to
recover its true law. Our objective is to identify what additional information
on $Z$ is needed and propose methods to recover the law of $Z$ under such
information. These methods employ tools such as Bayes' theorem, principle of
maximum entropy, and forward uncertainty quantification to obtain solutions to
the inverse problem that are consistent with information on $Z$ and $Q(Z)$. The
additional information on $Z$ may include its moments or its family of
distributions. We justify our objective by considering the capabilities of
solutions to this inverse problem to predict the probability law of unobserved
quantities of interest.
| arxiv topic:math.NA cs.NA math.PR |
arxiv_dataset-107721901.07653 | Determining eigenstates and thermal states on a quantum computer using
quantum imaginary time evolution
quant-ph
The accurate computation of Hamiltonian ground, excited, and thermal states
on quantum computers stands to impact many problems in the physical and
computer sciences, from quantum simulation to machine learning. Given the
challenges posed in constructing large-scale quantum computers, these tasks
should be carried out in a resource-efficient way. In this regard, existing
techniques based on phase estimation or variational algorithms display
potential disadvantages; phase estimation requires deep circuits with ancillae,
that are hard to execute reliably without error correction, while variational
algorithms, while flexible with respect to circuit depth, entail additional
high-dimensional classical optimization. Here, we introduce the quantum
imaginary time evolution and quantum Lanczos algorithms, which are analogues of
classical algorithms for finding ground and excited states. Compared to their
classical counterparts, they require exponentially less space and time per
iteration, and can be implemented without deep circuits and ancillae, or
high-dimensional optimization. We furthermore discuss quantum imaginary time
evolution as a subroutine to generate Gibbs averages through an analog of
minimally entangled typical thermal states. Finally, we demonstrate the
potential of these algorithms via an implementation using exact classical
emulation as well as through prototype circuits on the Rigetti quantum virtual
machine and Aspen-1 quantum processing unit.
| arxiv topic:quant-ph |
arxiv_dataset-107731901.07753 | Construction of Liouville Brownian motion via Dirichlet form theory
math.PR
The Liouville Brownian motion which was introduced in \cite{GRV} is a natural
diffusion process associated with a random metric in two dimensional Liouville
quantum gravity. In this paper we construct the Liouville Brownian motion via
Dirichlet form theory. By showing that the Liouville measure is smooth in the
strict sense, the positive continuous additive functional $(F_t)_{t \ge 0}$ of
the Liouville measure in the strict sense w.r.t. the planar Brownian motion
$(B_t)_{t \ge 0}$ is obtained. Then the Liouville Brownian motion can be
defined as a time changed process of the planar Brownian motion $B_{F_t^{-1}}$.
| arxiv topic:math.PR |
arxiv_dataset-107741901.07853 | Synthesis and investigation of the properties of organic-inorganic
perovskite films with non-contact optical methods
physics.app-ph cond-mat.mtrl-sci
Presented in this work are the results of our study of the photoelectric
properties of perovskite $CH_3NH_3PbI_{2.98}Cl_{0.02}$ films deposited on a
glass substrate using the spin-coating method. The unit cell parameters of the
perovskite are determined using x-ray diffractometry. It is shown that the film
morphology represents a net of non-oriented needle-like structures with
significant roughness and porosity. In order to investigate the properties of
the films obtained, non-contact methods were used, such as transmission and
reflection measurements and the measurements of the spectral characteristics of
the small-signal surface photovoltage. The method of spectral characteristics
of the low-signal surface photovoltage and the transmission method reveal
information about the external quantum yield in the films studied and about the
diffusion length of minority carriers in the perovskite films. As a result of
this analysis, it has been established that the films obtained are naturally
textured, and their bandgap is 1.59 eV. It is shown that in order to correctly
determine absorption coefficient and the bandgap values, Urbach effect should
be accounted for. Minority carriers' diffusion length is longer than the film
thickness, which is equal to 400 nm. The films obtained are promising materials
for solar cells.
| arxiv topic:physics.app-ph cond-mat.mtrl-sci |
arxiv_dataset-107751901.07953 | Direct Reconstruction of Distorted Signals and Images Using Shifts
Methods
eess.SP
Mathematical methods of step-by-step and combined shifts are proposed for
experimental data processing to reconstruct the measuring system impulse
response distorted by shift-invariant blur. Proposed methods base on direct
non-blind deconvolution without using approximations and integral transforms.
Methods are fast and effective for accurate data reconstruction, which gives a
possibility of increasing the effective resolution of measuring systems by
mathematical methods up to physical limits without solving the expensive and
quite difficult scientific and technical problems. Step-by-step and combined
shifts methods supplement each other in data reconstruction at different
distortions of signals, noise levels and data volumes. Methods may be adapted
for reconstruction of multi-dimensional data. There are considered the
restorations of 2D images blurred by uniform motion and distorted by functions,
which may be factored, such as Gaussian-like functions. The comparative
analysis of step-by-step and combined shifts methods is presented.
Reconstruction inaccuracies are estimated. Examples of signal reconstructions
and image restorations at different distortions are considered.
| arxiv topic:eess.SP |
arxiv_dataset-107761901.08053 | Quantum States of a Time-Asymmetric Universe: Wave Function, Density
Matrix, and Empirical Equivalence
quant-ph hep-th physics.hist-ph
What is the quantum state of the universe? Although there have been several
interesting suggestions, the question remains open. In this paper, I consider a
natural choice for the universal quantum state arising from the Past
Hypothesis, a boundary condition that accounts for the time-asymmetry of the
universe. The natural choice is given not by a wave function (representing a
pure state) but by a density matrix (representing a mixed state).
I begin by classifying quantum theories into two types: theories with a
fundamental wave function and theories with a fundamental density matrix. The
Past Hypothesis is compatible with infinitely many initial wave functions, none
of which seems to be particularly natural. However, once we turn to density
matrices, the Past Hypothesis provides a natural choice---the normalized
projection onto the Past Hypothesis subspace in the Hilbert space.
Nevertheless, the two types of theories can be empirically equivalent. To
provide a concrete understanding of the empirical equivalence, I provide a
novel subsystem analysis in the context of Bohmian theories. Given the
empirical equivalence, it seems empirically underdetermined whether the
universe is in a pure state or a mixed state. Finally, I discuss some
theoretical payoffs of the density-matrix theories and present some open
problems for future research.
| arxiv topic:quant-ph hep-th physics.hist-ph |
arxiv_dataset-107771901.08153 | Robust 3D Surface Recovery by Applying a Focus Criterion in White Light
Scanning Interference Microscopy
physics.optics
White light scanning interference (WLSI) microscopes provide an accurate
surface topography of engineered surfaces. However, the measurement accuracy is
substantially reduced in surfaces with low-reflectivity regions or high
roughness, like a surface affected by corrosion. An alternative technique
called shape from focus (SFF) takes advantage of the surface texture to recover
the 3D surface by using a focus metric through a vertical scan. In this work,
we propose a technique called SFF-WLSI, which consists of recovering the 3D
surface of an object by applying the Tenegrad Variance (TENV) focus metric to
WLSI images. Extensive simulation results show that the proposed technique
yields accurate measurements under different surface roughness and surface
reflectivity, outperforming the conventional WLSI and the SFF techniques. We
validated the simulation results on two real objects with a Mirau-type
microscope. The first was a flat lapping specimen with Ra = 0.05 {\mu}m for
which we measured an average value of Ra = 0.055 {\mu}m and standard deviation
{\sigma} = 0.008 {\mu}m. The second was a metallic sphere with corrosion, which
we reconstructed with WLSI versus the proposed SFF-WLSI technique, producing a
better 3D reconstruction with less undefined depth values.
| arxiv topic:physics.optics |
arxiv_dataset-107781901.08253 | Gas flow around a planet embedded in a protoplanetary disc: the
dependence on the planetary mass
astro-ph.EP
The three-dimensional structure of the gas flow around a planet is thought to
influence the accretion of both gas and solid materials. In particular, the
outflow in the mid-plane region may prevent the accretion of the solid
materials and delay the formation of super-Earths' cores. However, it is not
yet understood how the nature of the flow field and outflow speed change as a
function of the planetary mass. In this study, we investigate the dependence of
gas flow around a planet embedded in a protoplanetary disc on the planetary
mass. Assuming an isothermal, inviscid gas disc, we perform three-dimensional
hydrodynamical simulations on the spherical polar grid, which has a planet
located at its centre. We find that gas enters the Bondi or Hill sphere at high
latitudes and exits through the mid-plane region of the disc regardless of the
assumed dimensionless planetary mass $m=R_{\rm Bondi}/H$, where $R_{\rm Bondi}$
and $H$ are the Bondi radius of the planet and disc scale height, respectively.
The altitude from where gas predominantly enters the envelope varies with the
planetary mass. The outflow speed can be expressed as $|u_{\rm
out}|=\sqrt{3/2}mc_{\rm s}$ $(R_{\rm Bondi}\leq R_{\rm Hill})$ or $|u_{\rm
out}|=\sqrt{3/2}(m/3)^{1/3} c_{\rm s}$ ($R_{\rm Bondi}\geq R_{\rm Hill}$),
where $c_{\rm s}$ is the isothermal sound speed and $R_{\rm Hill}$ is the Hill
radius. The outflow around a planet may reduce the accretion of dust and
pebbles onto the planet when $m\gtrsim\sqrt{\rm St}$, where St is the Stokes
number. Our results suggest that the flow around proto-cores of super-Earths
may delay their growth and, consequently, help them to avoid runaway gas
accretion within the lifetime of the gas disc.
| arxiv topic:astro-ph.EP |
arxiv_dataset-107791901.08353 | Stabilizing Scheduling Policies for Networked Control Systems
eess.SY cs.SY
This paper deals with the problem of allocating communication resources for
Networked Control Systems (NCSs). We consider an NCS consisting of a set of
discrete-time LTI plants whose stabilizing feedback loops are closed through a
shared communication channel. Due to a limited communication capacity of the
channel, not all plants can exchange information with their controllers at any
instant of time. We propose a method to find periodic scheduling policies under
which global asymptotic stability of each plant in the NCS is preserved. The
individual plants are represented as switched systems, and the NCS is expressed
as a weighted directed graph. We construct stabilizing scheduling policies by
employing cycles on the underlying weighted directed graph of the NCS that
satisfy appropriate contractivity conditions. We also discuss algorithmic
design of these cycles.
| arxiv topic:eess.SY cs.SY |
arxiv_dataset-107801901.08453 | Computational Modular Character Theory
math.RT
This book describes some computational methods to deal with modular
characters of finite groups. It is the theoretical background of the MOC system
of the same authors. This system was, and is still used, to compute the modular
character tables of sporadic simple groups.
| arxiv topic:math.RT |
arxiv_dataset-107811901.08553 | Data Interpolations in Deep Generative Models under Non-Simply-Connected
Manifold Topology
cs.LG stat.ML
Exploiting the deep generative model's remarkable ability of learning the
data-manifold structure, some recent researches proposed a geometric data
interpolation method based on the geodesic curves on the learned data-manifold.
However, this interpolation method often gives poor results due to a
topological difference between the model and the dataset. The model defines a
family of simply-connected manifolds, whereas the dataset generally contains
disconnected regions or holes that make them non-simply-connected. To
compensate this difference, we propose a novel density regularizer that make
the interpolation path circumvent the holes denoted by low probability density.
We confirm that our method gives consistently better interpolation results from
the experiments with real-world image datasets.
| arxiv topic:cs.LG stat.ML |
arxiv_dataset-107821901.08653 | An Identity for Vertically Aligned Entries in Pascal's Triangle
math.CO math.NT
The classic way to write down Pascal's triangle leads to entries in
alternating rows being vertically aligned. In this paper, we prove a linear
dependence on vertically aligned entries in Pascal's triangle. Furthermore, we
give an application of this dependence to morphisms between hyperelliptic
curves.
| arxiv topic:math.CO math.NT |
arxiv_dataset-107831901.08753 | On Output Activation Functions for Adversarial Losses: A Theoretical
Analysis via Variational Divergence Minimization and An Empirical Study on
MNIST Classification
cs.LG stat.ML
Recent years have seen adversarial losses been applied to many fields. Their
applications extend beyond the originally proposed generative modeling to
conditional generative and discriminative settings. While prior work has
proposed various output activation functions and regularization approaches,
some open questions still remain unanswered. In this paper, we aim to study the
following two research questions: 1) What types of output activation functions
form a well-behaved adversarial loss? 2) How different combinations of output
activation functions and regularization approaches perform empirically against
one another? To answer the first question, we adopt the perspective of
variational divergence minimization and consider an adversarial loss
well-behaved if it behaves as a divergence-like measure between the data and
model distributions. Using a generalized formulation for adversarial losses, we
derive the necessary and sufficient conditions of a well-behaved adversarial
loss. Our analysis reveals a large class of theoretically valid adversarial
losses. For the second question, we propose a simple comparative framework for
adversarial losses using discriminative adversarial networks. The proposed
framework allows us to efficiently evaluate adversarial losses using a standard
evaluation metric such as the classification accuracy. With the proposed
framework, we evaluate a comprehensive set of 168 combinations of twelve output
activation functions and fourteen regularization approaches on the handwritten
digit classification problem to decouple their effects. Our empirical findings
suggest that there is no single winning combination of output activation
functions and regularization approaches across all settings. Our theoretical
and empirical results may together serve as a reference for choosing or
designing adversarial losses in future research.
| arxiv topic:cs.LG stat.ML |
arxiv_dataset-107841901.08853 | Spin-phonon coupling in hole-doped pyrochlore iridates
Y$_2$(Ir$_{1-x}$Ru$_x$)$_2$O$_7$: A Raman scattering study
cond-mat.str-el
Temperature dependent Raman scattering measurements have been performed to
explore unusual coupling between magnetism and crystal structure in doped
pyrochlore iridate Y$_2$(Ir$_{1-x}$Ru$_x$)$_2$O$_7$ with $x$ = 0.0, 0.05 and
0.2. The parent Y$_2$Ir$_2$O$_7$ shows an onset of magnetic ordering around
$\sim$ 160 K ($T_{N}$) which monotonically decreases with Ru doping. Further,
magnetic moment also decreases with progressive substitution of Ru.
Substitution of Ru$^{4+}$ (4$d^4$) for Ir$^{4+}$ (5$d^5$) does not introduce
significant modification in structural parameters, however, the magnetic
transition temperature decreases systematically with doping. Raman scattering
data show an anomalous change in $A_{1g}$ and $P_3$ Raman mode frequency and
line-width across $T_{N}$ of individual samples. We further show that the
shifting of Raman mode frequency with temperature exhibits a strong deviation
from anharmonic decay around and below the $T_{N}$ of respective samples which
underlines a spin-phonon coupling in these materials.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-107851901.08953 | Indecomposable objects determined by their index in Higher Homological
Algebra
math.RT
Let $\mathscr{C}$ be a 2-Calabi-Yau triangulated category, and let
$\mathscr{T}$ be a cluster tilting subcategory of $\mathscr{C}$. An important
result from Dehy and Keller tells us that a rigid object $c \in \mathscr{C}$ is
uniquely defined by its index with respect to $\mathscr{T}$.
The notion of triangulated categories extends to the notion of
$(d+2)$-angulated categories. Thanks to a paper by Oppermann and Thomas, we now
have a definition for cluster tilting subcategories in higher dimensions. This
paper proves that under a technical assumption, an indecomposable object in a
$(d+2)$-angulated category is uniquely defined by its index with respect to a
higher dimensional cluster tilting subcategory. We also demonstrate an
application of this result in higher dimensional cluster categories.
| arxiv topic:math.RT |
arxiv_dataset-107861901.09053 | Seeds for Generalized Taxicab Numbers
math.NT
The generalized taxicab number $T(n,m,t)$ is equal to the smallest number
that is the sum of $n$ positive $m$th powers in $t$ ways. This definition is
inspired by Ramanujan's observation that $1729 = 1^3+ 12^3 =9^3 + 10^3 $ is the
smallest number that is the sum of two cubes in two ways and thus $1729=
T(2,3,2)$. In this paper we prove that for any given positive integers $m$ and
$t$, there exists a number $s$ such $T(s+k,m,t) =T(s,m,t) +k$ for every $k \geq
0$. The smallest such $s$ is termed the seed for the generalized taxicab
number. Furthermore, we find explicit expressions for this seed number when the
number of ways $t$ is 2 or 3 and present a conjecture for $t \geq 4$ ways.
| arxiv topic:math.NT |
arxiv_dataset-107871901.09153 | Transverse bifurcation of viscous slow MHD shocks
math.AP
We study by a combination of analytical and numerical Evans function
techniques multi-D viscous and inviscid stability and associated transverse
bifurcation of planar slow Lax MHD shocks in a channel with periodic boundary
conditions. Notably, this includes the first multi-D numerical Evans function
study for viscous MHD. Our results suggest that, rather than a planar shock, a
nonplanar traveling wave with the same normal velocity is the typical mode of
propagation in the slow Lax mode. Moreover, viscous and inviscid stability
transitions appear to agree, answering (for this particular model and setting)
an open question of Zumbrun and Serre.
| arxiv topic:math.AP |
arxiv_dataset-107881901.09253 | On Deriving Probabilistic Models for Adsorption Energy on Transition
Metals using Multi-level Ab initio and Experimental Data
physics.data-an physics.comp-ph
In this paper, we apply multi-task Gaussian Process (MT-GP) to show that the
adsorption energy of small adsorbates on transition metal surfaces can be
modeled to a high level of fidelity using data from multiple sources, taking
advantage of the relatively abundant ''low fidelity" data (such as from density
functional theory computations) and small amounts of ''high fidelity"
computational (e.g. using the random phase approximation) or experimental data.
To fully explore the performance of MT-GP, we perform two case studies - one
using purely computational datasets and the other using a combination of
experimental and computational datasets. In both cases, the performance of
MT-GPs is significantly better than single-task models built on a single data
source. This method can be used to learn improved models from fused datasets,
and thereby build accurate models under tight computational and experimental
budget.
| arxiv topic:physics.data-an physics.comp-ph |
arxiv_dataset-107891901.09353 | Subsumption of Weakly Well-Designed SPARQL Patterns is Undecidable
cs.DB
Weakly well-designed SPARQL patterns is a recent generalisation of
well-designed patterns, which preserve good computational properties but also
capture almost all patterns that appear in practice. Subsumption is one of
static analysis problems for SPARQL, along with equivalence and containment. In
this paper we show that subsumption is undecidable for weakly well-designed
patterns, which is in stark contrast to well-designed patterns, and to
equivalence and containment.
| arxiv topic:cs.DB |
arxiv_dataset-107901901.09453 | On Learning Invariant Representation for Domain Adaptation
cs.LG cs.AI stat.ML
Due to the ability of deep neural nets to learn rich representations, recent
advances in unsupervised domain adaptation have focused on learning
domain-invariant features that achieve a small error on the source domain. The
hope is that the learnt representation, together with the hypothesis learnt
from the source domain, can generalize to the target domain. In this paper, we
first construct a simple counterexample showing that, contrary to common
belief, the above conditions are not sufficient to guarantee successful domain
adaptation. In particular, the counterexample exhibits \emph{conditional
shift}: the class-conditional distributions of input features change between
source and target domains. To give a sufficient condition for domain
adaptation, we propose a natural and interpretable generalization upper bound
that explicitly takes into account the aforementioned shift. Moreover, we shed
new light on the problem by proving an information-theoretic lower bound on the
joint error of \emph{any} domain adaptation method that attempts to learn
invariant representations. Our result characterizes a fundamental tradeoff
between learning invariant representations and achieving small joint error on
both domains when the marginal label distributions differ from source to
target. Finally, we conduct experiments on real-world datasets that corroborate
our theoretical findings. We believe these insights are helpful in guiding the
future design of domain adaptation and representation learning algorithms.
| arxiv topic:cs.LG cs.AI stat.ML |
arxiv_dataset-107911901.09553 | On the dynamics of reaction coordinates in classical, time-dependent,
many-body processes
cond-mat.stat-mech
Complex microscopic many-body processes are often interpreted in terms of
so-called `reaction coordinates', i.e. in terms of the evolution of a small set
of coarse-grained observables. A rigorous method to produce the equation of
motion of such observables is to use projection operator techniques, which
split the dynamics of the observables into a main contribution and a marginal
one. The basis of any derivation in this framework is the classical (or
quantum) Heisenberg equation for an observable. If the Hamiltonian of the
underlying microscopic dynamics and the observable under study do not
explicitly depend on time, this equation is obtained by a straight-forward
derivation. However, the problem is more complicated if one considers
Hamiltonians which depend on time explicitly as e.g. in systems under external
driving, or if the observable of interest has an explicit dependence on time.
We use an analogy to fluid dynamics to derive the classical Heisenberg picture
and then apply a projection operator formalism to derive the non-stationary
generalized Langevin equation for a coarse-grained variable. We show, in
particular, that the results presented for time-independent Hamiltonians and
observables in J. Chem. Phys. 147, 214110 (2017) can be generalized to the
time-dependent case.
| arxiv topic:cond-mat.stat-mech |
arxiv_dataset-107921901.09653 | Optimal inflow control penalizing undersupply in transport systems with
uncertain demands
math.OC
We are concerned with optimal control strategies subject to uncertain
demands. An Ornstein-Uhlenbeck process describes the uncertain demand. The
transport within the supply system is modeled by the linear advection equation.
We consider different approaches to control the produced amount at a given time
to meet the stochastic demand in an optimal way. In particular, we introduce an
undersupply penalty and analyze its effect on the optimal output in a numerical
simulation study.
| arxiv topic:math.OC |
arxiv_dataset-107931901.09753 | On maximum of Gaussian process with unique maximum point of its variance
math.PR
Gaussian random processes which variances reach theirs maximum values at
unique points are considered. Exact asymptotic behaviors of probabilities of
large absolute maximums of theirs trajectories have been evaluated using Double
Sum Method under the widest possible conditions.
| arxiv topic:math.PR |
arxiv_dataset-107941901.09853 | Universal four-dimensional representation of $H \to \gamma \gamma$ at
two loops through the Loop-Tree Duality
hep-ph hep-th
We extend useful properties of the $H\to\gamma\gamma$ unintegrated dual
amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism.
In particular, we show that the universality of the functional form --
regardless of the nature of the internal particle -- still holds at this order.
We also present an algorithmic way to renormalise two-loop amplitudes, by
locally cancelling the ultraviolet singularities at integrand level, thus
allowing a full four-dimensional numerical implementation of the method. Our
results are compared with analytic expressions already available in the
literature, finding a perfect numerical agreement. The success of this
computation plays a crucial role for the development of a fully local
four-dimensional framework to compute physical observables at Next-to-Next-to
Leading order and beyond.
| arxiv topic:hep-ph hep-th |
arxiv_dataset-107951901.09953 | TGAN: Deep Tensor Generative Adversarial Nets for Large Image Generation
cs.CV cs.LG
Deep generative models have been successfully applied to many applications.
However, existing works experience limitations when generating large images
(the literature usually generates small images, e.g. 32 * 32 or 128 * 128). In
this paper, we propose a novel scheme, called deep tensor adversarial
generative nets (TGAN), that generates large high-quality images by exploring
tensor structures. Essentially, the adversarial process of TGAN takes place in
a tensor space. First, we impose tensor structures for concise image
representation, which is superior in capturing the pixel proximity information
and the spatial patterns of elementary objects in images, over the
vectorization preprocess in existing works. Secondly, we propose TGAN that
integrates deep convolutional generative adversarial networks and tensor
super-resolution in a cascading manner, to generate high-quality images from
random distributions. More specifically, we design a tensor super-resolution
process that consists of tensor dictionary learning and tensor coefficients
learning. Finally, on three datasets, the proposed TGAN generates images with
more realistic textures, compared with state-of-the-art adversarial
autoencoders. The size of the generated images is increased by over 8.5 times,
namely 374 * 374 in PASCAL2.
| arxiv topic:cs.CV cs.LG |
arxiv_dataset-107961901.10053 | Towards Fair Deep Clustering With Multi-State Protected Variables
cs.LG stat.ML
Fair clustering under the disparate impact doctrine requires that population
of each protected group should be approximately equal in every cluster.
Previous work investigated a difficult-to-scale pre-processing step for
$k$-center and $k$-median style algorithms for the special case of this problem
when the number of protected groups is two. In this work, we consider a more
general and practical setting where there can be many protected groups. To this
end, we propose Deep Fair Clustering, which learns a discriminative but fair
cluster assignment function. The experimental results on three public datasets
with different types of protected attribute show that our approach can steadily
improve the degree of fairness while only having minor loss in terms of
clustering quality.
| arxiv topic:cs.LG stat.ML |
arxiv_dataset-107971901.10153 | Simultaneous prediction of multiple outcomes using revised stacking
algorithms
q-bio.QM cs.LG stat.ML
Motivation: HIV is difficult to treat because its virus mutates at a high
rate and mutated viruses easily develop resistance to existing drugs. If the
relationships between mutations and drug resistances can be determined from
historical data, patients can be provided personalized treatment according to
their own mutation information. The HIV Drug Resistance Database was built to
investigate the relationships. Our goal is to build a model using data in this
database, which simultaneously predicts the resistance of multiple drugs using
mutation information from sequences of viruses for any new patient.
Results: We propose two variations of a stacking algorithm which borrow
information among multiple prediction tasks to improve multivariate prediction
performance. The most attractive feature of our proposed methods is the
flexibility with which complex multivariate prediction models can be
constructed using any univariate prediction models. Using cross-validation
studies, we show that our proposed methods outperform other popular
multivariate prediction methods.
Availability: An R package will be made available.
| arxiv topic:q-bio.QM cs.LG stat.ML |
arxiv_dataset-107981901.10253 | Dynamic Inverse Wave Problems - Part II: Operator Identification and
Applications
math.AP
We present a framework which enables the analysis of dynamic inverse problems
for wave phenomena that are modeled through second-order hyperbolic PDEs. This
includes well-posedness and regularity results for the forward operator in an
abstract setting, where the operators in an evolution equation represent the
unknowns. We also prove Fr\'echet-differentiability and local ill-posedness for
this problem. We then demonstrate how to apply this theory to actual problems
by two example equations motivated by linear elasticity and electrodynamics.
For these problems it is even possible to obtain a simple characterization of
the adjoint of the Fr\'echet-derivative of the forward operator, which is of
particular interest for the application of regularization schemes.
| arxiv topic:math.AP |
arxiv_dataset-107991901.10353 | Discovery of kilogauss magnetic fields on the nearby white dwarfs
WD1105-340 and WD2150+591
astro-ph.SR
Magnetic fields are present in roughly 10% of white dwarfs. These fields
affect the structure and evolution of such stars, and may provide clues about
their earlier evolution history. Particularly important for statistical studies
is the collection of high-precision spectropolarimetric observations of (1)
complete magnitude-limited samples and (2) complete volume-limited samples of
white dwarfs. In the course of one of our surveys we have discovered previously
unknown kG-level magnetic fields on two nearby white dwarfs, WD1105-340 and
WD2150+591. Both stars are brighter than m_V = 15. WD2150+591 is within the
20-pc volume around the Sun, while WD1105-340 is just beyond 25 pc in distance.
These discoveries increase the small sample of such weak-field white dwarfs
from 21 to 23 stars. Our data appear consistent with roughly dipolar field
topology, but it also appears that the surface field structure may be more
complex on the older star than on the younger one, a result similar to one
found earlier in our study of the weak-field stars WD2034+372 and WD2359-434.
This encourages further efforts to uncover a clear link between magnetic
morphology and stellar evolution.
| arxiv topic:astro-ph.SR |
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