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arxiv_dataset-51001403.5101 | Evidence for a tricritical point coinciding with the triple point in
(Pb0.94Sr0.06)(ZrxTi1-x)O3 : A combined synchrotron x-ray diffraction,
dielectric and Landau theory study
cond-mat.mtrl-sci
We present here results of high resolution synchrotron x-ray diffraction
(SXRD) and dielectric studies in conjunction with Landau theory considerations
on (Pb0.94Sr0.06)(ZrxTi1-x)O3 compositions in the vicinity of the morphotropic
phase boundary (MPB) to find evidence for the flattening of the free energy
surface at the MPB proposed in recent ab-initio studies on strongly
piezoelectric ceramics. SXRD results reveal that the tetragonal and
pseudorhombohedral monoclinic compositions with x=0.515 and 0.550 transform
directly into the cubic paraelectric phase, whereas for 0.520<x<0.545, the
pseudotetragonal as well as pseudorhombohedral monoclinic compositions first
transform to the tetragonal phase and then to the cubic phase. Our results
reveal the existence of a triple point at x~0.550. It is shown that the
tetragonal to cubic transition, irrespective of the composition, upto x~0.545
is accompanied with a discontinuous change in the unit cell volume and thermal
hysteresis confirming first order nature of this transition. The
pseudorhombohedral monoclinic composition for x=0.550, on the other hand,
transforms directly into the cubic phase in a second order manner. Our
experimental results thus reveal a crossover from first order to second order
phase transition through a tricritical point around x=0.550. Landau theory
calculations also confirm gradual flattening of the free energy surface on
approaching the tricritical composition x=0.550. We conclude that the triple
point in the PZT phase diagram is indeed a tricritical point.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-51011403.5201 | Minkowski content and fractal curvatures of self-similar tilings and
generator formulas for self-similar sets
math.MG
We study Minkowski contents and fractal curvatures of arbitrary self-similar
tilings (constructed on a feasible open set of an IFS) and the general
relations to the corresponding functionals for self-similar sets. In
particular, we characterize the situation, when these functionals coincide. In
this case, the Minkowski content and the fractal curvatures of a self-similar
set can be expressed completely in terms of the volume function or curvature
data, respectively, of the generator of the tiling. In special cases such
formulas have been obtained recently using tube formulas and complex dimensions
or as a corollary to results on self-conformal sets. Our approach based on the
classical Renewal Theorem is simpler and works for a much larger class of
self-similar sets and tilings. In fact, generator type formulas are obtained
for essentially all self-similar sets, when suitable volume functions (and
curvature functions, respectively) related to the generator are used. We also
strengthen known results on the Minkowski measurability of self-similar sets,
in particular on the question of non-measurability in the lattice case.
| arxiv topic:math.MG |
arxiv_dataset-51021403.5301 | Revealing the high-density equation of state through binary neutron star
mergers
astro-ph.SR gr-qc nucl-th
We present a novel method for revealing the equation of state of high-density
neutron star matter through gravitational waves emitted during the postmerger
phase of a binary neutron star system. The method relies on a small number of
detections of the peak frequency in the postmerger phase for binaries of
different (relatively low) masses, in the most likely range of expected
detections. From such observations, one can construct the derivative of the
peak frequency versus the binary mass, in this mass range. Through a detailed
study of binary neutron star mergers for a large sample of equations of state,
we show that one can extrapolate the above information to the highest possible
mass (the threshold mass for black hole formation in a binary neutron star
merger). In turn, this allows for an empirical determination of the maximum
mass of cold, nonrotating neutron stars to within 0.1 M_sun, while the
corresponding radius is determined to within a few percent. Combining this with
the determination of the radius of cold, nonrotating neutron stars of 1.6 M_sun
(to within a few percent, as was demonstrated in Bauswein et al., PRD, 86,
063001, 2012), allows for a clear distinction of a particular candidate
equation of state among a large set of other candidates. Our method is
particularly appealing because it reveals simultaneously the moderate and very
high-density parts of the equation of state, enabling the distinction of
mass-radius relations even if they are similar at typical neutron star masses.
Furthermore, our method also allows to deduce the maximum central energy
density and maximum central rest-mass density of cold, nonrotating neutron
stars with an accuracy of a few per cent.
| arxiv topic:astro-ph.SR gr-qc nucl-th |
arxiv_dataset-51031403.5401 | Exploring Indonesian Web Based Career Center Discrepancy of Web
Popularity and Type of Services
cs.CY
Utilization of the Internet in higher education focus on the learning process
or the provision of academic information for students. The subject of this
research is in the form of web-based management alumnus Career Center with
specific sub domain. Colleges that already have a Career Center only 34 of the
264 colleges as sample. Type the service the most are information jobs, while
others are still rarely available as a forum of alumni and career consultation.
Ownership Career Center contributed to the popularity of college website.
Providing services such as communication and consultation career impact on the
popularity of the Career Center website.
| arxiv topic:cs.CY |
arxiv_dataset-51041403.5501 | K-12 Teaching and Physics Enrollment
physics.ed-ph physics.soc-ph
We have collected and analyzed the relevant data from public schools in
greater Houston area of Texas. Based and analyzed. Since the data is only
limited to a few school, we are still working on getting more data so that we
can compare and contrast the results adequately and understand the core of the
enrollment issue at the national level. However, based on the raw data and
partial analysis, we propose a few recommendations towards the improvement of
science education in Texas Schools, in general, and greater Houston area
schools in particular. Our results indicate that the quality of science
education can be improved significantly if we focus on the improvement of high
school education or even intermediate schools when students are first time
exposed to science in a little technical way. Simply organizing teacher
training programs at K-12 level as school education plays a pivotal role in the
decrease in physics enrollment at the higher level. Similar analysis can
actually be generalized to other states to find out the best way to increase
the physics enrollment.
| arxiv topic:physics.ed-ph physics.soc-ph |
arxiv_dataset-51051403.5601 | CIR Modulation of the X-ray Flux from the O7.5 III(n)((f)) Star xi
Persei?
astro-ph.SR
We analyze a 162 ks HETG Chandra observation of the O7.5 III(n)((f)) star xi
Per, together with contemporaneous H alpha observations. The X-ray spectrum of
this star is similar to other single O stars, and not pathological in any way.
Its UV wind lines are known to display cyclical time variability, with a period
of 2.086 days, which is thought to be associated with co-rotating interaction
regions (CIRs). We examine the Chandra and H alpha data for variability on this
time scale. We find that the X-rays vary by about 15% over the course of the
observations and that this variability is out of phase with variable absorption
on the blue wing of the H alpha profiles (assumed to be a surrogate for the UV
absorption associated with CIRs). While not conclusive, both sets of data are
consistent with models where the CIRs are either a source of X-rays or modulate
them.
| arxiv topic:astro-ph.SR |
arxiv_dataset-51061403.5701 | Cortex simulation system proposal using distributed computer network
environments
cs.AI
In the dawn of computer science and the eve of neuroscience we participate in
rebirth of neuroscience due to new technology that allows us to deeply and
precisely explore whole new world that dwells in our brains.
| arxiv topic:cs.AI |
arxiv_dataset-51071403.5801 | Applicability of Well-Established Memristive Models for Simulations of
Resistive Switching Devices
cs.ET
Highly accurate and predictive models of resistive switching devices are
needed to enable future memory and logic design. Widely used is the memristive
modeling approach considering resistive switches as dynamical systems. Here we
introduce three evaluation criteria for memristor models, checking for
plausibility of the I-V characteristics, the presence of a sufficiently
non-linearity of the switching kinetics, and the feasibility of predicting the
behavior of two anti-serially connected devices correctly. We analyzed two
classes of models: the first class comprises common linear memristor models and
the second class widely used non-linear memristive models. The linear memristor
models are based on Strukovs initial memristor model extended by different
window functions, while the non-linear models include Picketts physics-based
memristor model and models derived thereof. This study reveals lacking
predictivity of the first class of models, independent of the applied window
function. Only the physics-based model is able to fulfill most of the basic
evaluation criteria.
| arxiv topic:cs.ET |
arxiv_dataset-51081403.5901 | Finding the largest low-rank clusters with Ky Fan $2$-$k$-norm and
$\ell_1$-norm
math.OC
We propose a convex optimization formulation with the Ky Fan $2$-$k$-norm and
$\ell_1$-norm to find $k$ largest approximately rank-one submatrix blocks of a
given nonnegative matrix that has low-rank block diagonal structure with noise.
We analyze low-rank and sparsity structures of the optimal solutions using
properties of these two matrix norms. We show that, under certain hypotheses,
with high probability, the approach can recover rank-one submatrix blocks even
when they are corrupted with random noise and inserted into a much larger
matrix with other random noise blocks.
| arxiv topic:math.OC |
arxiv_dataset-51091403.6001 | Outlier eigenvalues for deformed i.i.d. random matrices
math.PR
We consider a square random matrix of size N of the form A + Y where A is
deterministic and Y has iid entries with variance 1/N. Under mild assumptions,
as N grows, the empirical distribution of the eigenvalues of A+Y converges
weakly to a limit probability measure \beta on the complex plane. This work is
devoted to the study of the outlier eigenvalues, i.e. eigenvalues in the
complement of the support of \beta. Even in the simplest cases, a variety of
interesting phenomena can occur. As in earlier works, we give a sufficient
condition to guarantee that outliers are stable and provide examples where
their fluctuations vary with the particular distribution of the entries of Y or
the Jordan decomposition of A. We also exhibit concrete examples where the
outlier eigenvalues converge in distribution to the zeros of a Gaussian
analytic function.
| arxiv topic:math.PR |
arxiv_dataset-51101403.6101 | Homotopy theory of G-diagrams and equivariant excision
math.AT
Let $G$ be a finite group acting on a small category $I$. We study functors
$X \colon I \to \mathscr{C}$ equipped with families of compatible natural
transformations that give a kind of generalized $G$-action on $X$. Such objects
are called $G$-diagrams. When $\mathscr{C}$ is a sufficiently nice model
category we define a model structure on the category of $G$-diagrams in
$\mathscr{C}$. There are natural $G$-actions on Bousfield-Kan style homotopy
limits and colimits of $G$-diagrams. We prove that weak equivalences between
point-wise (co)fibrant $G$-diagrams induce weak $G$-equivalences on homotopy
(co)limits. A case of particular interest is when the indexing category is a
cube. We use homotopy limits and colimits over such diagrams to produce loop
and suspension spaces with respect to permutation representations of $G$. We go
on to develop a theory of enriched equivariant homotopy functors and give an
equivariant "linearity" condition in terms of cubical $G$-diagrams. In the case
of $G$-topological spaces we prove that this condition is equivalent to
Blumberg's notion of $G$-linearity. In particular we show that the
Wirthm\"{u}ller isomorphism theorem is a direct consequence of the equivariant
linearity of the identity functor on $G$-spectra.
| arxiv topic:math.AT |
arxiv_dataset-51111403.6201 | Radiometric 81Kr dating identifies 120,000 year old ice at Taylor
Glacier, Antarctica
physics.geo-ph
We present the first successful 81Kr-Kr radiometric dating of ancient polar
ice. Krypton was extracted from the air bubbles in four ~350 kg polar ice
samples from Taylor Glacier in the McMurdo Dry Valleys, Antarctica, and dated
using Atom Trap Trace Analysis (ATTA). The 81Kr radiometric ages agree with
independent age estimates obtained from stratigraphic dating techniques with a
mean absolute age offset of 6 +/- 2.5 ka. Our experimental methods and sampling
strategy are validated by 1) 85Kr and 39Ar analyses that show the samples to be
free of modern air contamination, and 2) air content measurements that show the
ice did not experience gas loss. We estimate the error in the 81Kr ages due to
past geomagnetic variability to be below 3 ka. We show that ice from the
previous interglacial period (MIS 5e, 130-115 ka before present) can be found
in abundance near the surface of Taylor Glacier. Our study paves the way for
reliable radiometric dating of ancient ice in blue ice areas and margin sites
where large samples are available, greatly enhancing their scientific value as
archives of old ice and meteorites. At present, ATTA 81Kr analysis requires a
40-80 kg ice sample; as sample requirements continue to decrease 81Kr dating of
ice cores is a future possibility.
| arxiv topic:physics.geo-ph |
arxiv_dataset-51121403.6301 | Muon anomalous magnetic moment and positron excess at AMS-02 in a gauged
horizontal symmetric model
hep-ph
We studied an extension of the standard model with a fourth generation of
fermions to explain the discrepancy in the muon $(g-2)$ and explain the
positron excess seen in the AMS-02 experiment. We introduce a gauged
$SU(2)_{HV}$ horizontal symmetry between the muon and the 4th generation lepton
families. The 4th generation right-handed neutrino is identified as the dark
matter with mass $\sim 700$ GeV. The dark matter annihilates only to $(\mu^+
\mu^-)$ and $(\nu^c_\mu ~\nu_\mu)$ states via $SU(2)_{HV}$ gauge boson. The
$SU(2)_{HV}$ gauge boson with mass $\sim 1.4$ TeV gives an adequate
contribution to the $(g-2)$ of muon and fulfill the experimental constraint
from BNL measurement. The higgs production constraints from 4th generation
fermions is evaded by extending the higgs sector.
| arxiv topic:hep-ph |
arxiv_dataset-51131403.6401 | Spectral gaps for normally hyperbolic trapping
math.AP gr-qc
We establish a resonance free strip for codimension 2 symplectic normally
hyperbolic trapped sets with smooth incoming/outgoing tails. An important
application is wave decay on Kerr and Kerr-de Sitter black holes. We recover
the optimal size of the strip and give an $o(h^{-2})$ resolvent bound there. We
next show existence of deeper resonance free strips under the $r$-normal
hyperbolicity assumption and a pinching condition. We also give a lower bound
on the ne-sided cutoff resolvent on the real line.
| arxiv topic:math.AP gr-qc |
arxiv_dataset-51141403.6501 | Computing points of bounded height in projective space over a number
field
math.NT
We construct an algorithm for solving the following problem: given a number
field $K$, a positive integer $N$, and a positive real number $B$, determine
all points in $\mathbb P^N(K)$ having relative height at most $B$. A
theoretical analysis of the efficiency of the algorithm is provided, as well as
sample computations showing how the algorithm performs in practice. Two
variants of the method are described, and examples are given to compare their
running times. In the case $N=1$ we compare our method to an earlier algorithm
for enumerating elements of bounded height in number fields.
| arxiv topic:math.NT |
arxiv_dataset-51151403.6601 | Novalike Cataclysmic Variables in the Infrared
astro-ph.SR
Novalike cataclysmic variables have persistently high mass transfer rates and
prominent steady state accretion disks. We present an analysis of infrared
observations of twelve novalikes obtained from the Two Micron All Sky Survey,
the Spitzer Space Telescope, and the Wide-field Infrared Survey Explorer All
Sky Survey. The presence of an infrared excess at >3-5 microns over the
expectation of a theoretical steady state accretion disk is ubiquitous in our
sample. The strength of the infrared excess is not correlated with orbital
period, but shows a statistically significant correlation (but shallow trend)
with system inclination that might be partially (but not completely) linked to
the increasing view of the cooler outer accretion disk and disk rim at higher
inclinations. We discuss the possible origin of the infrared excess in terms of
emission from bremsstrahlung or circumbinary dust, with either mechanism
facilitated by the mass outflows (e.g., disk wind/corona, accretion stream
overflow, and so on) present in novalikes. Our comparison of the relative
advantages and disadvantages of either mechanism for explaining the
observations suggests that the situation is rather ambiguous, largely
circumstantial, and in need of stricter observational constraints.
| arxiv topic:astro-ph.SR |
arxiv_dataset-51161403.6701 | An intuition behind quantum measurement
quant-ph physics.hist-ph
An attempt is made to give a heuristic explanation of the distinguished role
of measurement in the quantum theory. We question the notion of "naive"
reductionism by stressing the difference between an isolated quantum and
classical object. It is argued that the transition from the micro- to the
macroscopic description should be made along some parameters not characterized
by the quantum theory.
| arxiv topic:quant-ph physics.hist-ph |
arxiv_dataset-51171403.6801 | Linking a genetic defect in migraine to spreading depression in a
computational model
q-bio.NC
Familial hemiplegic migraine (FHM) is a rare subtype of migraine with aura. A
mutation causing FHM type 3 (FHM3) has been identified in SCN1A encoding the
Nav1.1 Na$^+$ channel. This genetic defect affects the inactivation gate. While
the Na$^+$ tail currents following voltage steps are consistent with both
hyperexcitability and hypoexcitability, in this computational study, we
investigate functional consequences beyond these isolated events. Our extended
Hodgkin-Huxley framework establishes a connection between genotype and cellular
phenotype, i.e., the pathophysiological dynamics that spans over multiple time
scales and is relevant to migraine with aura. In particular, we investigate the
dynamical repertoire from normal spiking (milliseconds) to spreading depression
and anoxic depolarization (tens of seconds) and show that FHM3 mutations render
gray matter tissue more vulnerable to spreading depression despite opposing
effects associated with action potential generation. We conclude that the
classification in terms of hypoexcitability vs. hyperexcitability is too simple
a scheme. Our mathematical analysis provides further basic insight into also
previously discussed criticisms against this scheme based on psychophysical and
clinical data.
| arxiv topic:q-bio.NC |
arxiv_dataset-51181403.6901 | Automatic Segmentation of Broadcast News Audio using Self Similarity
Matrix
cs.SD cs.LG cs.MM
Generally audio news broadcast on radio is com- posed of music, commercials,
news from correspondents and recorded statements in addition to the actual news
read by the newsreader. When news transcripts are available, automatic
segmentation of audio news broadcast to time align the audio with the text
transcription to build frugal speech corpora is essential. We address the
problem of identifying segmentation in the audio news broadcast corresponding
to the news read by the newsreader so that they can be mapped to the text
transcripts. The existing techniques produce sub-optimal solutions when used to
extract newsreader read segments. In this paper, we propose a new technique
which is able to identify the acoustic change points reliably using an acoustic
Self Similarity Matrix (SSM). We describe the two pass technique in detail and
verify its performance on real audio news broadcast of All India Radio for
different languages.
| arxiv topic:cs.SD cs.LG cs.MM |
arxiv_dataset-51191403.7001 | Spaghetti prediction: A robust method for forecasting short time series
stat.ME
A novel method for predicting time series is described and demonstrated. This
method inputs time series data points and outputs multiple "spaghetti"
functions from which predictions can be made. Spaghetti prediction has
desirable properties that are not realized by classic autoregression, moving
average, spline, Gaussian process, and other methods. It is particularly
appropriate for short time series because it allows asymmetric prediction
distributions and produces prediction functions which are robust in that they
use multiple independent models.
| arxiv topic:stat.ME |
arxiv_dataset-51201403.7101 | Helical states and solitons in noncentrosymmetric superconductors
cond-mat.supr-con
We show how the two-band nature of superconductivity in noncentrosymmetric
compounds leads to a variety of novel nonuniform superconducting states induced
by a magnetic field. At low fields, a two-band helical state is realized, with
a distinctly non-BCS quasiparticle spectrum. At high fields, the
superconducting state becomes unstable towards the formation of a lattice of
topological phase solitons.
| arxiv topic:cond-mat.supr-con |
arxiv_dataset-51211403.7201 | A multi-wavelength view of the central kiloparsec region in the Luminous
Infrared Galaxy NGC1614
astro-ph.GA astro-ph.CO
The Luminous Infrared Galaxy NGC1614 hosts a prominent circumnuclear ring of
star formation. However, the nature of the dominant emitting mechanism in its
central ~100 pc is still under debate. We present sub-arcsecond angular
resolution radio, mid-infrared, Pa-alpha, optical, and X-ray observations of
NGC1614, aimed at studying in detail both the circumnuclear ring and the
nuclear region. The 8.4 GHz continuum emission traced by the Very Large Array
(VLA) and the Gemini/T-ReCS 8.7 micron emission, as well as the Pa-alpha line
emission, show remarkable morphological similarities within the star-forming
ring, suggesting that the underlying emission mechanisms are tightly related.
We used an HST/NICMOS Pa-alpha map of similar resolution to our radio maps to
disentangle the thermal free-free and non-thermal synchrotron radio emission,
from which we obtained the intrinsic synchrotron power-law for each individual
region within the central kpc of NGC1614. The radio ring surrounds a relatively
faint, steep-spectrum source at the very center of the galaxy, suggesting that
the central source is not powered by an AGN, but rather by a compact (r < 90
pc) starburst. Chandra X-ray data also show that the central kpc region is
dominated by starburst activity, without requiring the existence of an AGN. We
also used publicly available infrared data to model-fit the spectral energy
distribution of both the starburst ring and a putative AGN in NGC1614. In
summary, we conclude that there is no need to invoke an AGN to explain the
observed bolometric properties of the galaxy.
| arxiv topic:astro-ph.GA astro-ph.CO |
arxiv_dataset-51221403.7301 | $TMF_0(3)$ Characteristic classes for String bundles
math.AT
We compute the completed $TMF_0(3)$ cohomology of the 7-connective cover
$BString$ of $BO$. We use cubical structures on line bundles over elliptic
curves to construct an explicit class which together with the Pontryagin
classes freely generates the cohomology ring.
| arxiv topic:math.AT |
arxiv_dataset-51231403.7401 | Twisted Cyclic Homology And Crossed Product Algebras
math.KT
$HC_*(A \rtimes G)$ is the cyclic homology of the crossed product algebra $A
\rtimes G.$ For any $g \epsilon G$ we will define a homomorphism from
$HC_*^g(A),$ the twisted cylic homology of $A$ with respect to $g,$ to $HC_*(A
\rtimes G).$ If $G$ is the finite cyclic group generated by $g$ and $|G|=r$ is
invertible in $k,$ then $HC_*(A \rtimes G)$ will be isomorphic to a direct sum
of $r$ copies of $HC_*^g(A).$ For the case where $|G|$ is finite and $Q \subset
k$ we will generalize the Karoubi and Connes periodicity exact sequences for
$HC_*^g(A)$ to Karoubi and Connes periodicity exact sequences for $HC_*(A
\rtimes G)$ .
| arxiv topic:math.KT |
arxiv_dataset-51241403.7501 | Adams filtration and generalized Hurewicz maps for infinite loopspaces
math.AT
We study the Hurewicz map h from the homotopy groups of a spectrum X to the
R-homology of its 0th space X(0), where R is a connective commutative
S-algebra.
We prove that the decreasing filtration of the domain of h associated to an
R-based Adams resolution is compatible with the augmentation ideal filtration
of the range associated to the suspension spectrum of X(0)_+, an augmented
commutative S-algebra. The proof makes use of the interplay of this filtration
with Topological Andre Quillen Homology.
An application is a Connectivity Theorem: Localize at a prime p and suppose X
is (c-1)-connected for some positive c. If f in pi_*(X) has Adams filtration s
and |f| < cp^s, then f maps to zero in R_*(X(0)). An application of that is a
Finiteness Theorem: If the mod p cohomology of X is finitely presented as a
module over the Steenrod algebra, then the image of the mod p Hurewicz map for
X(0) is finite. We illustrate these theorems with calculations of the mod 2
Hurewicz image of BO, its connected covers, and tmf(0), and the mod p Hurewicz
image of all the spaces in the BP and BP<n> spectra. Enroute, we get new proofs
of theorems of Milnor and Wilson.
In the special case when X is a suspension spectrum and R = HZ/2, we recover
results announced by Lannes and Zarati in the 1980s (with a totally different
proof), and generalizations to all primes p. We get a chromatic version of this
for the Hurewicz map for Morava E theory and all X.
| arxiv topic:math.AT |
arxiv_dataset-51251403.7601 | Extreme Fluctuations of Current in the Symmetric Simple Exclusion
Process: a Non-Stationary Setting
cond-mat.stat-mech
We use the macroscopic fluctuation theory (MFT) to evaluate the probability
distribution P of extreme values of integrated current J at a specified time
t=T in the symmetric simple exclusion process (SSEP) on an infinite line. As
shown recently [Phys. Rev. E 89, 010101(R) (2014)], the SSEP belongs to the
elliptic universality class. Here, for very large currents, the diffusion terms
of the MFT equations can be neglected compared with the terms coming from the
shot noise. Using the hodograph transformation and an additional change of
variables, we reduce the "inviscid" MFT equations to Laplace's equation in an
extended space. This opens the way to an exact solution. Here we solve the
extreme-current problem for a flat deterministic initial density profile with
an arbitrary density 0<n<1. The solution yields the most probable density
history of the system conditional on the extreme current, and leads to a
super-Gaussian extreme-current statistics, - ln P = F(n) J^3/T, in agreement
with Derrida and Gerschenfeld [J. Stat. Phys. 137, 978 (2009)]. We calculate
the function F(n) analytically. It is symmetric with respect to the
half-filling density n=1/2, diverges as n approached 0 or 1, and exhibits a
singularity F(n) |n-1/2| at the half-filling density n=1/2.
| arxiv topic:cond-mat.stat-mech |
arxiv_dataset-51261403.7701 | The fused Kolmogorov filter: A nonparametric model-free screening method
stat.ME
A new model-free screening method called the fused Kolmogorov filter is
proposed for high-dimensional data analysis. This new method is fully
nonparametric and can work with many types of covariates and response
variables, including continuous, discrete and categorical variables. We apply
the fused Kolmogorov filter to deal with variable screening problems emerging
from a wide range of applications, such as multiclass classification,
nonparametric regression and Poisson regression, among others. It is shown that
the fused Kolmogorov filter enjoys the sure screening property under weak
regularity conditions that are much milder than those required for many
existing nonparametric screening methods. In particular, the fused Kolmogorov
filter can still be powerful when covariates are strongly dependent on each
other. We further demonstrate the superior performance of the fused Kolmogorov
filter over existing screening methods by simulations and real data examples.
| arxiv topic:stat.ME |
arxiv_dataset-51271403.7801 | Heegner points on Cartan non-split curves
math.NT
Let $E$ be an elliptic curve of conductor $N$, and let $K$ be an imaginary
quadratic field such that the root number of $E/K$ is $-1$. Let $O$ be an order
in $K$ and assume that there exists an odd prime $p$, such that $p^2 \mid\mid
N$, and $p$ is inert in $O$. Although there are no Heegner points on $X_0(N)$
attached to $O$, in this article we construct such points on Cartan non-split
curves. In order to do that we give a method to compute Fourier expansions for
forms in Cartan non-split curves, and prove that the constructed points form a
Heegner system as in the classical case.
| arxiv topic:math.NT |
arxiv_dataset-51281403.7901 | Lie-series for orbital elements -- I. The planar case
astro-ph.EP
Lie-integration is one of the most efficient algorithms for numerical
integration of ordinary differential equations if high precision is needed for
longer terms. The method is based on the computation of the Taylor-coefficients
of the solution as a set of recurrence relations. In this paper we present
these recurrence formulae for orbital elements and other integrals of motion
for the planar $N$-body problem. We show that if the reference frame is fixed
to one of the bodies -- for instance to the Sun in the case of the Solar System
--, the higher order coefficients for all orbital elements and integrals of
motion depend only on the mutual terms corresponding to the orbiting bodies.
| arxiv topic:astro-ph.EP |
arxiv_dataset-51291403.8001 | Non post-selected indistinguishable single photons generated by a
quantum dot under resonant excitation
cond-mat.mes-hall
We report on two-photon interferences from highly indistinguishable single
photons emitted by a quantum dot. Stricly resonant excitation with picosecond
laser pulses allows coherent state preparation with a signifi- cantly increased
coherence time (T2 \sim 1 ns) and reduced lifetime (T1 \sim 650 ps), as
compared to a non-resonant excitation scheme. Building-up the Hong-Ou-Mandel
dip without post-selection of the interfering photons, visi- bilities greater
than 70 % have been observed. Near-unity indistinguishable photons could be
achieved for every dot if charge noise is controlled. Indeed, the remaining
decoherence mechanism is likely due to the fluctuating electrostatic
environment of the dots.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-51301403.8101 | Electromagnetic fingerprints of the Little Bang
nucl-th hep-ph nucl-ex
Measurements of thermal photons emitted from the rapidly expanding hot and
dense medium ("Little Bang") formed in ultra relativistic heavy-ion collisions,
and their current theoretical interpretation, are reviewed.
| arxiv topic:nucl-th hep-ph nucl-ex |
arxiv_dataset-51311404.0047 | Screening Clouds and Majorana Fermions
cond-mat.str-el
Ken Wilson developed the Numerical Renormalization Group technique which
greatly enhanced our understanding of the Kondo effect and other quantum
impurity problems. Wilson's NRG also inspired Philippe Nozieres to propose the
idea of a large "Kondo screening cloud". While much theoretical evidence has
accumulated for this idea it has remained somewhat controversial and has not
yet been confirmed experimentally. Recently a new possibility for observing an
analogous crossover length scale has emerged, involving a Majorana fermion
localized at the interface between a topological superconductor quantum wire
and a normal wire. We give an overview of this topic both with and without
interactions included in the normal wire.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-51321404.0147 | On the spectra of quenched random perturbations of partially expanding
maps on the torus
math.DS
We consider quenched random perturbations of skew products of rotations on
the unit circle over uniformly expanding maps on the unit circle. It is known
that if the skew product satisfies a certain condition (shown to be generic in
the case of linear expanding maps), then the transfer operator of the skew
product has a spectral gap. Using semiclassical analysis we show that the
spectral gap is preserved under small random perturbations. This implies
exponential decay of quenched random correlation functions for smooth
observables at small noise levels.
| arxiv topic:math.DS |
arxiv_dataset-51331404.0247 | Extracting hadron masses from fixed topology simulations
hep-lat hep-th
Lattice QCD simulations tend to become stuck in a single topological sector
at fine lattice spacing or when using chirally symmetric overlap quarks. In
such cases physical observables differ from their full QCD counterparts by
finite volume corrections. These systematic errors need to be understood on a
quantitative level and possibly be removed. In this paper we extend an existing
relation from the literature between two-point correlation functions at fixed
and the corresponding hadron masses at unfixed topology by calculating all
terms proportional to $1/V^2$ and $1/V^3$, where $V$ is the spacetime volume.
Since parity is not a symmetry at fixed topology, parity mixing is
comprehensively discussed. In the second part of this work we apply our
equations to a simple model, quantum mechanics on a circle both for a free
particle and for a square-well potential, where we demonstrate in detail, how
to extract physically meaningful masses from computations or simulations at
fixed topology.
| arxiv topic:hep-lat hep-th |
arxiv_dataset-51341404.0347 | Fluctuation and dissipation in de Sitter space
hep-th gr-qc
In this paper we study some thermal properties of quantum field theories in
de Sitter space by means of holographic techniques. We focus on the static
patch of de Sitter and assume that the quantum fields are in the standard
Bunch-Davies vacuum. More specifically, we follow the stochastic motion of a
massive charged particle due to its interaction with Hawking radiation. The
process is described in terms of the theory of Brownian motion in inhomogeneous
media and its associated Langevin dynamics. At late times, we find that the
particle undergoes a regime of slow diffusion and never reaches the horizon, in
stark contrast to the usual random walk behavior at finite temperature.
Nevertheless, the fluctuation-dissipation theorem is found to hold at all
times.
| arxiv topic:hep-th gr-qc |
arxiv_dataset-51351404.0447 | PSelInv -- A Distributed Memory Parallel Algorithm for Selected
Inversion : the Symmetric Case
math.NA cs.DC cs.NA
We describe an efficient parallel implementation of the selected inversion
algorithm for distributed memory computer systems, which we call
\texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a
general sparse matrix $A$ that can be decomposed as $A = LU$, where $L$ is
lower triangular and $U$ is upper triangular. The implementation described in
this paper focuses on the case of sparse symmetric matrices. It contains an
interface that is compatible with the distributed memory parallel sparse direct
factorization \texttt{SuperLU\_DIST}. However, the underlying data structure
and design of \texttt{PSelInv} allows it to be easily combined with other
factorization routines such as \texttt{PARDISO}. We discuss general
parallelization strategies such as data and task distribution schemes. In
particular, we describe how to exploit the concurrency exposed by the
elimination tree associated with the $LU$ factorization of $A$. We demonstrate
the efficiency and accuracy of \texttt{PSelInv} by presenting a number of
numerical experiments. In particular, we show that \texttt{PSelInv} can run
efficiently on more than $4,000$ cores for a modestly sized matrix. We also
demonstrate how \texttt{PSelInv} can be used to accelerate large-scale
electronic structure calculations.
| arxiv topic:math.NA cs.DC cs.NA |
arxiv_dataset-51361404.0547 | Modelling and analysis of turbulent datasets using ARMA processes
physics.data-an physics.flu-dyn
We introduce a novel way to extract information from turbulent datasets by
applying an ARMA statistical analysis. Such analysis goes well beyond the
analysis of the mean flow and of the fluctuations and links the behavior of the
recorded time series to a discrete version of a stochastic differential
equation which is able to describe the correlation structure in the dataset. We
introduce a new intermittency parameter $\Upsilon$ that measures the difference
between the resulting analysis and the Obukhov model of turbulence, the
simplest stochastic model reproducing both Richardson law and the Kolmogorov
spectrum. We test the method on datasets measured in a von K\'arm\'an swirling
flow experiment. We found that the ARMA analysis is well correlated with
spatial structures of the flow, and can discriminate between two different
flows with comparable mean velocities, obtained by changing the forcing.
Moreover, we show that the intermittency parameter is highest in regions where
shear layer vortices are present, thereby establishing a link between
intermittency corrections and coherent structures. We show that some salient
features of the analysis are preserved when considering global instead of local
observables. Finally we analyze flow configurations with multistability
features where the ARMA technique is efficient in discriminating different
stability branches of the system.
| arxiv topic:physics.data-an physics.flu-dyn |
arxiv_dataset-51371404.0647 | Nonlinear Zeno dynamics due to atomic interactions in Bose-Einstein
condensate
cond-mat.quant-gas physics.atom-ph quant-ph
We show that nonlinear interactions induce both the Zeno and anti-Zeno
effects in the generalised Bose-Josephson model (with the on-site interactions
and the second-order tunneling) describing Bose-Einstein condensate in
double-well trap subject to particle removal from one of the wells. We find
that the on-site interactions induce \textit{only} the Zeno effect, which
appears at long evolution times, whereas the second-order tunneling leads to a
strong decay of the atomic population at short evolution times, reminiscent of
the anti-Zeno effect, and destroys the nonlinear Zeno effect due to the on-site
interactions at long times.
| arxiv topic:cond-mat.quant-gas physics.atom-ph quant-ph |
arxiv_dataset-51381404.0747 | New Dirac Delta function based methods with applications to perturbative
expansions in quantum field theory
math-ph hep-th math.MP quant-ph
We derive new all-purpose methods that involve the Dirac Delta distribution.
Some of the new methods use derivatives in the argument of the Dirac Delta. We
highlight potential avenues for applications to quantum field theory and we
also exhibit a connection to the problem of blurring/deblurring in signal
processing. We find that blurring, which can be thought of as a result of
multi-path evolution, is, in Euclidean quantum field theory without spontaneous
symmetry breaking, the strong coupling dual of the usual small coupling
expansion in terms of the sum over Feynman graphs.
| arxiv topic:math-ph hep-th math.MP quant-ph |
arxiv_dataset-51391404.0847 | Execution Time Analysis for Industrial Control Applications
cs.SE cs.SY
Estimating the execution time of software components is often mandatory when
evaluating the non-functional properties of software-intensive systems. This
particularly holds for real-time embedded systems, e.g., in the context of
industrial automation. In practice it is however very hard to obtain reliable
execution time estimates which are accurate, but not overly pessimistic with
respect to the typical behavior of the software.
This article proposes two new concepts to ease the use of execution time
analysis for industrial control applications: (1) a method based on recurring
occurrences of code sequences for automatically creating a timing model of a
given processor and (2) an interactive way to integrate execution time analysis
into the development environment, thus making timing analysis results easily
accessible for software developers. The proposed methods are validated by an
industrial case study, which shows that a significant amount of code reuse is
present in a set of representative industrial control applications.
| arxiv topic:cs.SE cs.SY |
arxiv_dataset-51401404.0947 | Theoretical study of a $d^{*}$ resonance in $^{3}G_{3}$ partial wave of
nucleon-nucleon scattering
nucl-th hep-ph
Inspired by the recent results of the WASA-at-COSY Collaboration, in which
they found a resonance pole in the coupled $^{3}D_{3}$ - $^{3}G_{3}$ partial
waves as expected from the $d^{*}$ resonance hypothesis, we calculated the
resonance structure in the coupled $^{3}D_{3}$ - $^{3}G_{3}$ partial wave phase
shifts of nucleon-nucleon scattering in the framework of two constituent quark
models: the quark delocalization color screening model and the chiral quark
model. Our results show that there is a resonance $^{7}S_{3}^{\Delta\Delta}$ in
the coupled $^{3}D_{3}^{NN}$ and $^{3}G_{3}^{NN}$ partial waves in both of
these two models, which is in accordance with the expectation from the $d^{*}$
resonance structure. The resonance shape in the $^{3}D_{3}^{NN}$ partial wave
is remarkable, whereas in the $^{3}G_{3}^{NN}$ phase shifts there is a small
rise around the resonance energy. This result is in agreement with the recent
experimental observations of WASA-at-COSY Collaboration.
| arxiv topic:nucl-th hep-ph |
arxiv_dataset-51411404.1047 | The classification of p-nilpotent restricted Lie algebras of dimension
at most 4
math.RA
In this paper we obtain the classification of $p$-nilpotent restricted Lie
algebras of dimension at most four over a perfect field of characteristic p.
| arxiv topic:math.RA |
arxiv_dataset-51421404.1147 | Error bounds for gradient density estimation computed from a finite
sample set using the method of stationary phase
stat.CO
For a twice continuously differentiable function $S$, we define the density
function of its gradient (derivative in one dimension) $s = S^{\prime}$ as a
random variable transformation of a uniformly distributed random variable using
$s$ as the transformation function. Given $N$ values of $S$ sampled at equally
spaced locations, we demonstrate using the method of stationary phase that the
approximation error between the integral of the scaled, discrete power spectrum
of the wave function
$\phi^{D}_{\tau}=\frac{1}{\sqrt{L}}\exp\left(\frac{iS}{\tau}\right)$ and the
integral of the true density function of $s$ over an arbitrarily small interval
is bounded above by $O(1/N)$ as $N \rightarrow \infty$ ($\tau \rightarrow 0$).
In addition to its easy implementation and fast computability in $O(N \log N)$
that only requires computing the discrete Fourier transform, our framework for
obtaining the derivative density does not involve any parameter selection like
the number of histogram bins, width of the histogram bins, width of the kernel
parameter, number of mixture components etc. as required by other widely
applied methods like histograms and Parzen windows.
| arxiv topic:stat.CO |
arxiv_dataset-51431404.1247 | To be or not to be oblate: the shape of the dark matter halo in the
polar ring galaxies
astro-ph.GA astro-ph.CO
With the aim to determine the spatial distribution of the dark matter halo,
we investigate two polar ring galaxies NGC 4262 and SPRC-7. For both galaxies
the stellar kinematics data for the central galaxy were obtained from optical
spectroscopy at the 6-m telescope of the Special Astrophysical Observatory of
the Russian Academy of Sciences. The information about polar gaseous components
was taken from the optical 3D-spectroscopic observations of ionized gas (for
SPRC-7) and H {\sc i} radio observations (for NGC 4262). SPRC-7 is the system
with a relative angle $\delta=73^{\circ}$ towards the central galaxy and a
quite massive stellar-gaseous polar component. Meanwhile NGC 4262 is the
classic polar case with $\delta=88^{\circ}$ where the polar ring mainly
consists of neutral gas with a negligible stellar contribution to the mass. We
are hence dealing with two different systems and the results are quite diverse
too. The observed properties of both galaxies were compared with the results of
self consistent simulations of velocity fields of the polar component along
with the rotation curve of the central lenticular galaxy. For SPRC-7 we have
found a slightly flattened halo towards the polar plane with the axis ratio
$c/a \simeq 1.7 \pm 0.2$ for the isothermal halo model and $c/a \simeq 1.5 \pm
0.2$ for the NFW model. The case of NGC 4262 is more unusual, the shape of the
dark matter distribution varies strongly with radius. Namely, the dark matter
halo is fattened in the vicinity of the galactic disc ($c/a \approx 0.4 \pm
0.1$), however it is prolate far beyond the central galaxy ($c/a \approx 1.7$
for the isothermal halo and $c/a \approx 2.3$ for NFW).
| arxiv topic:astro-ph.GA astro-ph.CO |
arxiv_dataset-51441404.1347 | The Probability Density Function of a Transformation-based
Hyperellipsoid Sampling Technique
math.ST stat.TH
Sun and Farooq [2] showed that random samples can be efficiently drawn from
an arbitrary n-dimensional hyperellipsoid by transforming samples drawn
randomly from the unit n-ball. They stated that it was a straightforward to
show that, given a uniform distribution over the n-ball, the transformation
results in a uniform distribution over the hyperellipsoid, but did not present
a full proof. This technical note presents such a proof.
| arxiv topic:math.ST stat.TH |
arxiv_dataset-51451404.1447 | Localized SiO emission triggered by the passage of the W51C SNR shock
astro-ph.GA
The region towards W51C is a convincing example of interaction between a
supernova remnant and a surrounding molecular cloud. Large electron abundances
have been reported towards the position W51C-E located in this interaction
region, and it was proposed that the enhanced ionization fraction was due to
cosmic ray particles freshly accelerated by the SNR shock. We present PdB
interferometer observations of the H$^{13}$CO$^+$(1-0) and DCO$^+$(2-1)
emission lines centered at position W51C-E. These observations confirm the
previous scenario of cosmic-ray induced ionization at this location. In
addition, SiO(2-1) emission has been successfully mapped in the close vicinity
of W51C-E, with a spatial resolution of 7". The morphology and kinematics of
the SiO emission are analyzed and strongly suggest that this emission is
produced by the passage of the SNR primary shock. Put in conjunction with the
enhanced ionization fraction in this region, we give a consistent picture in
which the W51C-E position is located downstream of the shock, where a large
reservoir of freshly accelerated particles is available.
| arxiv topic:astro-ph.GA |
arxiv_dataset-51461404.1547 | Asymptotic Behavior of Ultra-Dense Cellular Networks and Its Economic
Impact
cs.IT cs.NI math.IT
This paper investigates the relationship between base station (BS) density
and average spectral efficiency (SE) in the downlink of a cellular network.
This relationship has been well known for sparse deployment, i.e. when the
number of BSs is small compared to the number of users. In this case the SE is
independent of BS density. As BS density grows, on the other hand, it has
previously been shown that increasing the BS density increases the SE, but no
tractable form for the SE-BS density relationship has yet been derived. In this
paper we derive such a closed-form result that reveals the SE is asymptotically
a logarithmic function of BS density as the density grows. Further, we study
the impact of this result on the network operator's profit when user demand
varies, and derive the profit maximizing BS density and the optimal amount of
spectrum to be utilized in closed forms. In addition, we provide deployment
planning guidelines that will aid the operator in his decision if he should
invest in densifying his network or in acquiring more spectrum.
| arxiv topic:cs.IT cs.NI math.IT |
arxiv_dataset-51471404.1647 | Analysis of Capacity Region of Delay-Tolerant Hybrid Mobile Ad Hoc
Networks
cs.NI
Network capacity region is an important character of mobile ad hoc networks.
Using cell-partitioned model, an expression of upper bound of delay-tolerant
hybrid mobile ad hoc network is deduced regardless of coverage of base
stations, types of mobile process, scheduling and routing algorithms. The
limitation of the upper bound is derived, Analysis of the limitation of upper
bound is carried out when the steady-state follows even-distribution law. The
relationship among limitation of capacity, the node density and coverage of
base station is analyzed.
| arxiv topic:cs.NI |
arxiv_dataset-51481404.1747 | Exponential Fermi acceleration in general time-dependent billiards
nlin.CD
It is shown, that under very general conditions, a generic time-dependent
billiard, for which a phase-space of corresponding static (frozen) billiards is
of the mixed type, exhibits the exponential Fermi acceleration in the adiabatic
limit. The velocity dynamics in the adiabatic regime is represented as an
integral over a path through the abstract space of invariant components of
corresponding static billiards, where the paths are generated probabilistically
in terms of transition-probability matrices. We study the statistical
properties of possible paths and deduce the conditions for the exponential
Fermi acceleration. The exponential Fermi acceleration and theoretical concepts
presented in the paper are demonstrated numerically in four different
time-dependent billiards.
| arxiv topic:nlin.CD |
arxiv_dataset-51491404.1847 | Evaluation and Ranking of Machine Translated Output in Hindi Language
using Precision and Recall Oriented Metrics
cs.CL
Evaluation plays a crucial role in development of Machine translation
systems. In order to judge the quality of an existing MT system i.e. if the
translated output is of human translation quality or not, various automatic
metrics exist. We here present the implementation results of different metrics
when used on Hindi language along with their comparisons, illustrating how
effective are these metrics on languages like Hindi (free word order language).
| arxiv topic:cs.CL |
arxiv_dataset-51501404.1947 | Eine entscheidbare Klasse n-stelliger Horn-Pr\"adikate
cs.LO
Similar to a tree grammar, a Horn theory can be used to describe an infinite
set of terms. In this paper, we present a class of Horn theories such that the
set of definable predicates is closed wrt. conjunction and such that the
satisfiability of a predicate is decidable. This extends previous results on
Horn clauses with unary predicates.
| arxiv topic:cs.LO |
arxiv_dataset-51511404.2047 | P. Etingof's conjecture about Drinfeld associators
math.QA
We construct a family of Drinfeld associators interpolating between the
Knizhnik-Zamolodchikov associator, the Alekseev-Torossian associator and the
anti-Knizhnik-Zamolodchikov associator. We give explicit integral formul\ae\
for the family of elements of the Grothendieck-Teichm\"uller Lie algebra
tangent to the family of associators. As an application, we settle a conjecture
of Pavel Etingof about the Alekseev-Torossian associator.
Furthermore, we give explicit integral formul\ae\ for the family of stable
formality morphisms corresponding (in a precise way) to the above family of
associators, and for the family of graph cohomology classes corresponding to
the above family of elements of the Grothendieck-Teichm\"uller Lie algebra. It
follows in particular that the ``logarithmic'' Kontsevich formality morphism
corresponds to the Knizhnik-Zamolodchikov associator.
| arxiv topic:math.QA |
arxiv_dataset-51521404.2147 | Characterization of the Endemic Equilibrium and Response to Mutant
Injection in a Multi-strain Disease Model
q-bio.PE
Starting from common assumptions, we build a rate equation model for
multi-strain disease dynamics in terms of immune repertoire classes. We then
move to a strain-level description where a low-order closure reminiscent of a
pair approximation can be applied. We characterize the endemic equilibrium of
the ensuing model in the absence of mutation and discuss the presence of
degeneracy regarding the prevalence of the different strains. Finally we study
the behavior of the system under the injection of mutant strains.
| arxiv topic:q-bio.PE |
arxiv_dataset-51531404.2247 | Unusual Scaling Laws of the Band Gap and Optical Absorption of
Phosphorene Nanoribbons
cond-mat.mes-hall cond-mat.mtrl-sci physics.comp-ph
We report the electronic structure and optical absorption spectra of
monolayer black phosphorus (phosphorene) nanoribbons (PNRs) via
first-principles simulations. The band gap of PNRs is strongly enhanced by
quantum confinement. However, differently orientated PNRs exhibit distinct
scaling laws for the band gap vs the ribbon width (w). The band gaps of
armchair PNRs scale as 1/(w^2), while zigzag PNRs exhibit a 1/w behavior. These
distinct scaling laws reflect a significant implication of the band dispersion
of phosphorene: electrons and holes behave as classical particles along the
zigzag direction, but resemble relativistic particles along the armchair
direction. This unexpected merging of classical and relativistic properties in
a single material may produce novel electrical and magnetotransport properties
of few-layer black phosphorus and its ribbon structures. Finally, the
respective PNRs host electrons and holes with markedly different effective
masses and optical responses, which are suitable for a wide range of
applications.
| arxiv topic:cond-mat.mes-hall cond-mat.mtrl-sci physics.comp-ph |
arxiv_dataset-51541404.2347 | Automation Security
cs.OH
Web-based Automated Process Control systems are a new type of applications
that use the Internet to control industrial processes with the access to the
real-time data. Supervisory control and data acquisition (SCADA) networks
contain computers and applications that perform key functions in providing
essential services and commodities (e.g., electricity, natural gas, gasoline,
water, waste treatment, transportation) to all Americans. As such, they are
part of the nation s critical infrastructure and require protection from a
variety of threats that exist in cyber space today.
| arxiv topic:cs.OH |
arxiv_dataset-51551404.2447 | A class group heuristic based on the distribution of 1-eigenspaces in
matrix groups
math.NT math.GR
We propose a modification to the Cohen--Lenstra prediction for the
distribution of class groups of number fields, which should also apply when the
base field contains non-trivial roots of unity. The underlying heuristic
derives from the distribution of 1-eigenspaces in certain generalized
symplectic groups over finite rings. The motivation for that heuristic comes
from the function field case. We also give explicit formulas for the new
predictions in several important cases. These are in close accordance with
known data.
| arxiv topic:math.NT math.GR |
arxiv_dataset-51561404.2547 | Warped products and Spaces of Constant Curvature
math.DG
We will obtain the warped product decompositions of spaces of constant
curvature (with arbitrary signature) in their natural models as subsets of
pseudo-Euclidean space. This generalizes the corresponding result by S. Nolker
to arbitrary signatures, and has a similar level of detail. Although our
derivation is complete in some sense, none is proven. Motivated by
applications, we will give more information for the spaces with Euclidean and
Lorentzian signatures. This is an expository article which is intended to be
used as a reference. So we also give a review of the theory of circles and
spheres in pseudo-Riemannian manifolds.
| arxiv topic:math.DG |
arxiv_dataset-51571404.2647 | A Multilevel Stochastic Collocation Method for Partial Differential
Equations with Random Input Data
math.NA
Stochastic collocation methods for approximating the solution of partial
differential equations with random input data (e.g., coefficients and forcing
terms) suffer from the curse of dimensionality whereby increases in the
stochastic dimension cause an explosion of the computational effort. We propose
and analyze a multilevel version of the stochastic collocation method that, as
is the case for multilevel Monte Carlo (MLMC) methods, uses hierarchies of
spatial approximations to reduce the overall computational complexity. In
addition, our proposed approach utilizes, for approximation in stochastic
space, a sequence of multi-dimensional interpolants of increasing fidelity
which can then be used for approximating statistics of the solution as well as
for building high-order surrogates featuring faster convergence rates. A
rigorous convergence and computational cost analysis of the new multilevel
stochastic collocation method is provided, demonstrating its advantages
compared to standard single-level stochastic collocation approximations as well
as MLMC methods. Numerical results are provided that illustrate the theory and
the effectiveness of the new multilevel method.
| arxiv topic:math.NA |
arxiv_dataset-51581404.2747 | Two-body gravitational spin-orbit interaction at linear order in the
mass ratio
gr-qc
We analytically compute, to linear order in the mass-ratio, the "geodetic"
spin precession frequency of a small spinning body orbiting a large
(non-spinning) body to the eight-and-a-half post-Newtonian order, thereby
extending previous analytical knowledge which was limited to the third
post-Newtonian level. These results are obtained applying analytical
gravitational self-force theory to the first-derivative level generalization of
Detweiler's gauge-invariant redshift variable. We compare our analytic results
with strong-field numerical data recently obtained by S.~R.~Dolan et al.
[Phys.\ Rev.\ D {\bf 89}, 064011 (2014)]. Our new, high-post-Newtonian-order
results capture the strong-field features exhibited by the numerical data. We
argue that the spin-precession will diverge as $\approx -0.14/(1-3y)$ as the
light-ring is approached. We transcribe our kinematical spin-precession results
into a corresponding improved analytic knowledge of one of the two
(gauge-invariant) effective gyro-gravitomagnetic ratios characterizing
spin-orbit couplings within the effective-one-body formalism. We provide
simple, accurate analytic fits both for spin-precession and the effective
gyro-gravitomagnetic ratio. The latter fit predicts that the
linear-in-mass-ratio correction to the gyro-gravitomagnetic ratio changes sign
before reaching the light-ring. This strong-field prediction might be important
for improving the analytic modeling of coalescing spinning binaries.
| arxiv topic:gr-qc |
arxiv_dataset-51591404.2847 | Concircular tensors in Spaces of Constant Curvature: With Applications
to Orthogonal Separation of The Hamilton-Jacobi Equation
math-ph math.MP
We study concircular tensors in spaces of constant curvature and then apply
the results obtained to the problem of the orthogonal separation of the
Hamilton-Jacobi equation on these spaces. Any coordinates which separate the
geodesic Hamilton-Jacobi equation are called separable. Specifically for spaces
of constant curvature, we obtain canonical forms of concircular tensors modulo
the action of the isometry group, we obtain the separable coordinates induced
by irreducible concircular tensors, and we obtain warped products adapted to
reducible concircular tensors. Using these results, we show how to enumerate
the isometrically inequivalent orthogonal separable coordinates, construct the
transformation from separable to Cartesian coordinates, and execute the
Benenti-Eisenhart-Kalnins-Miller (BEKM) separation algorithm for separating
natural Hamilton-Jacobi equations.
| arxiv topic:math-ph math.MP |
arxiv_dataset-51601404.2947 | The freezing tendency towards 4-coordinated amorphous network causes
increase in heat capacity of supercooled Stillinger-Weber silicon
cond-mat.stat-mech cond-mat.soft
The supercooled liquid silicon, modeled by Stillinger-Weber potential, shows
anomalous increase in heat capacity $C_p$, with a maximum $C_p$ value close to
1060 K at zero pressure. We study equilibration and relaxation of the
supercooled SW Si, in the temperature range of 1060 K--1070 K at zero pressure.
We find that as the relaxation of the metastable supercooled liquid phase
initiates, a straight line region (SLR) is formed in cumulative potential
energy distributions. The configurational temperature corresponding to the SLR
is close to 1060 K, which was earlier identified as the freezing temperature of
4-coordinated amorphous network. The SLR is found to be tangential to the
distribution of the metastable liquid phase and thus influences the broadness
of the distribution. As the bath temperature is reduced from 1070 K to 1060 K,
the effective temperature approaches the bath temperature which results in
broadening of the metastable phase distribution. This, in turn, causes an
increase in overall fluctuations of potential energy and hence an increase of
heat capacity. We also find that during initial stages of relaxation,
4-coordinated atoms form 6-membered rings with a chair--like structure and
other structural units that indicate crystallization. Simultaneously a strong
correlation is established between the number of chair-shaped 6-membered rings
and the number of 4-coordinated atoms in the system. This shows that all
properties related to 4-coordinated particles are highly correlated as the SLR
is formed in potential energy distributions and this can be interpreted as a
consequence of `freezing' of amorphous network formed by 4-coordinated
particles.
| arxiv topic:cond-mat.stat-mech cond-mat.soft |
arxiv_dataset-51611404.3047 | Medium Effects in DIS from Polarized Nuclear Targets
hep-ph nucl-th
The behavior of the nucleon structure functions in lepton nuclei deep
inelastic scattering, both polarized and unpolarized, due to nuclear structure
effects is reanalyzed. The study is performed in two schemes: an x-rescaling
approach, and one in which there is an increase of sea quark components in the
in medium nucleon, related to the low energy N-N interaction. In view of a
recent interesting experimental proposal to study the behavior of the proton
spin structure functions in nuclei we proceed to compare these approaches in an
effort to enlighten the possible phenomenological interest of such difficult
experiment.
| arxiv topic:hep-ph nucl-th |
arxiv_dataset-51621404.3147 | A Posteriori and A Priori Error Estimates of Quadratic Finite Element
Method for Elliptic Obstacle Problem
math.NA
A residual based {\em a posteriori} error estimator is derived for a
quadratic finite element method (fem) for the elliptic obstacle problem. The
error estimator involves various residuals consisting the data of the problem,
discrete solution and a Lagrange multiplier related to the obstacle constraint.
{\em A priori} error estimates for the Lagrange multiplier have been derived
and further under an assumption that the contact set does not degenerate to a
curve in any part of the domain, optimal order {\em a priori} error estimates
have been derived whenever the data and the solution are sufficiently regular,
precisely, under the sufficient conditions required for quadratic fem in the
case of linear elliptic problem. The numerical experiments of adaptive fem for
a model problem satisfying the above condition on contact set show optimal
order convergence. This demonstrates that the quadratic fem for obstacle
problem can exhibit optimal performance.
| arxiv topic:math.NA |
arxiv_dataset-51631404.3247 | Strong Brightness Variations Signal Cloudy-to-Clear Transition of Brown
Dwarfs
astro-ph.SR
[ABRIDGED] We report the results of a $J$ band search for cloud-related
variability in the atmospheres of 62 L4-T9 dwarfs using the Du Pont 2.5-m
telescope at Las Campanas Observatory and the Canada France Hawaii Telescope on
Mauna Kea. We find 9 of 57 objects included in our final analysis to be
significantly variable with >99% confidence, 5 of which are new discoveries. In
our study, strong sinusoidal signals (peak-to-peak amplitudes >2%) are confined
to the L/T transition (4/16 objects with L9-T3.5 spectral types and 0/41
objects for all other spectral types). The probability that the observed
occurrence rates for strong variability inside and outside the L/T transition
originate from the same underlying true occurrence rate is excluded with >99.7%
confidence. These observations suggest that the settling of condensate clouds
below the photosphere in brown dwarf atmospheres does not occur in a spatially
uniform manner. Rather, the formation and sedimentation of dust grains at the
L/T transition is coupled to atmospheric dynamics, resulting in highly
contrasting regions of thick and thin clouds and/or clearings. Outside the L/T
transition we identify 5 weak variables (peak-to-peak amplitudes of 0.6%-1.6%).
Excluding L9-T3.5 spectral types, we infer that $60^{+22}_{-18}$% of targets
vary with amplitudes of 0.5%$-$1.6%, suggesting that surface heterogeneities
are common among L and T dwarfs. Our survey establishes a significant link
between strong variability and L/T transition spectral types, providing
evidence in support of the hypothesis that cloud holes contribute to the abrupt
decline in condensate opacity and 1 micron brightening observed in this regime.
More generally, fractional cloud coverage is an important model parameter for
brown dwarfs and giant planets, especially those with L/T transition spectral
types and colors.
| arxiv topic:astro-ph.SR |
arxiv_dataset-51641404.3347 | Stability and Identification with Optimal Macroprudential Policy Rules
q-fin.EC
This paper investigates the identification, the determinacy and the stability
of ad hoc, "quasi-optimal" and optimal policy rules augmented with financial
stability indicators (such as asset prices deviations from their fundamental
values) and minimizing the volatility of the policy interest rates, when the
central bank precommits to financial stability. Firstly, ad hoc and
quasi-optimal rules parameters of financial stability indicators cannot be
identified. For those rules, non zero policy rule parameters of financial
stability indicators are observationally equivalent to rule parameters set to
zero in another rule, so that they are unable to inform monetary policy.
Secondly, under controllability conditions, optimal policy rules parameters of
financial stability indicators can all be identified, along with a bounded
solution stabilizing an unstable economy as in Woodford (2003), with
determinacy of the initial conditions of non- predetermined variables.
| arxiv topic:q-fin.EC |
arxiv_dataset-51651404.3447 | Group homomorphisms as error correcting codes
cs.IT math.GR math.IT
We investigate the minimum distance of the error correcting code formed by
the homomorphisms between two finite groups $G$ and $H$. We prove some general
structural results on how the distance behaves with respect to natural group
operations, such as passing to subgroups and quotients, and taking products.
Our main result is a general formula for the distance when $G$ is solvable or
$H$ is nilpotent, in terms of the normal subgroup structure of $G$ as well as
the prime divisors of $|G|$ and $|H|$. In particular, we show that in the above
case, the distance is independent of the subgroup structure of $H$. We
complement this by showing that, in general, the distance depends on the
subgroup structure $G$.
| arxiv topic:cs.IT math.GR math.IT |
arxiv_dataset-51661404.3547 | Moving stone in the Hele-Shaw flow
physics.flu-dyn math.NA
Asymptotic analysis of the Hele-Shaw flow with a small moving obstacle is
performed. The method of solution utilises the uniform asymptotic formulas for
Green's and Neumann functions recently obtained by V. Maz'ya and A. Movchan.
Theoretical results of the paper are illustrated by the numerical simulations.
| arxiv topic:physics.flu-dyn math.NA |
arxiv_dataset-51671404.3647 | Renormalization group approach to a $p$-wave superconducting model
cond-mat.supr-con cond-mat.str-el
We present in this work an exact renormalization group (RG) treatment of a
one-dimensional $p$-wave superconductor. The model proposed by Kitaev consists
of a chain of spinless fermions with a $p$-wave gap. It is a paradigmatic model
of great actual interest since it presents a weak pairing superconducting phase
that has Majorana fermions at the ends of the chain. Those are predicted to be
useful for quantum computation. The RG allows to obtain the phase diagram of
the model and to study the quantum phase transition from the weak to the strong
pairing phase. It yields the attractors of these phases and the critical
exponents of the weak to strong pairing transition. We show that the weak
pairing phase of the model is governed by a chaotic attractor being non-trivial
from both its topological and RG properties. In the strong pairing phase the RG
flow is towards a conventional strong coupling fixed point. Finally, we propose
an alternative way for obtaining $p$-wave superconductivity in a
one-dimensional system without spin-orbit interaction.
| arxiv topic:cond-mat.supr-con cond-mat.str-el |
arxiv_dataset-51681404.3747 | Low-distance Surface Codes under Realistic Quantum Noise
quant-ph cs.ET
We study the performance of distance-three surface code layouts under
realistic multi-parameter noise models. We first calculate their thresholds
under depolarizing noise. We then compare a Pauli-twirl approximation of
amplitude and phase damping to amplitude and phase damping. We find the
approximate channel results in a pessimistic estimate of the logical error
rate, indicating the realistic threshold may be higher than previously
estimated. From Monte-Carlo simulations, we identify experimental parameters
for which these layouts admit reliable computation. Due to its low resource
cost and superior performance, we conclude that the 17-qubit layout should be
targeted in early experimental implementations of the surface code. We find
that architectures with gate times in the 5-40 ns range and T1 times of at
least 1-2 us range will exhibit improved logical error rates with a 17-qubit
surface code encoding.
| arxiv topic:quant-ph cs.ET |
arxiv_dataset-51691404.3847 | Teichmuller spaces, ergodic theory and global Torelli theorem
math.AG
A Teichm\"uller space $Teich$ is a quotient of the space of all complex
structures on a given manifold $M$ by the connected components of the group of
diffeomorphisms. The mapping class group $\Gamma$ of $M$ is the group of
connected components of the diffeomorphism group. The moduli problems can be
understood as statements about the $\Gamma$-action on $Teich$. I will describe
the mapping class group and the Teichmuller space for a hyperkahler manifold.
It turns out that this action is ergodic. We use the ergodicity to show that a
hyperkahler manifold is never Kobayashi hyperbolic.
This is my ICM submission, with review of some of my work on Teichmuller
spaces and moduli; proofs are sketched, new observations and some open problems
added.
| arxiv topic:math.AG |
arxiv_dataset-51701404.3947 | Hidden GeV-scale interactions of quarks
hep-ph
We explore quark interactions mediated by new gauge bosons of masses in the
0.3 - 50 GeV range. A tight upper limit on the gauge coupling of light Z'
bosons is imposed by the anomaly cancellation conditions in conjunction with
collider bounds on new charged fermions. Limits from quarkonium decays are
model dependent, while electroweak constraints are mild. We derive the limits
for a Z' boson coupled to baryon number, and then construct a Z' model with
relaxed constraints, allowing quark couplings as large as 0.2 for a mass of a
few GeV.
| arxiv topic:hep-ph |
arxiv_dataset-51711404.4047 | Goldstones with Extended Shift Symmetries
hep-th cond-mat.other cond-mat.supr-con hep-ph
We consider scalar field theories invariant under extended shift symmetries
consisting of higher order polynomials in the spacetime coordinates. These
generalize ordinary shift symmetries and the linear shift symmetries of the
galileons. We find Wess-Zumino Lagrangians which transform up to total
derivatives under these symmetries, and which possess fewer derivatives per
field and lower order equations of motion than the strictly invariant terms. In
the non-relativistic context, where the extended shifts are purely spatial,
these theories may describe multi-critical Goldstone bosons. In the
relativistic case, where the shifts involve the full spacetime coordinate,
these theories generally propagate extra ghostly degrees of freedom.
| arxiv topic:hep-th cond-mat.other cond-mat.supr-con hep-ph |
arxiv_dataset-51721404.4147 | Travelling times in scattering by obstacles
math-ph math.DG math.MP
The paper deals with some problems related to recovering information about an
obstacle in an Euclidean space from certain measurements of lengths of
generalized geodesics in the exterior of the obstacle. The main result is that
if two obstacles satisfy some generic regularity conditions and have (almost)
the same traveling times, then the generalized geodesic flows in their
exteriors are conjugate on the non-trapping part of their phase spaces with a
time preserving conjugacy. In the case of a union of two strictly convex
domains in the plane, a constructive algorithm is described to recover the
obstacle from traveling times.
| arxiv topic:math-ph math.DG math.MP |
arxiv_dataset-51731404.4247 | The ballistic transport instability in Saturn's rings III: numerical
simulations
astro-ph.EP
Saturn's inner B-ring and its C-ring support wavetrains of contrasting
amplitudes but with similar length scales, 100-1000 km. In addition, the inner
B-ring is punctuated by two intriguing `flat' regions between radii 93,000 km
and 98,000 km in which the waves die out, whereas the C-ring waves coexist with
a forest of plateaus, narrow ringlets, and gaps. In both regions the waves are
probably generated by a large-scale linear instability whose origin lies in the
meteoritic bombardment of the rings: the ballistic transport instability. In
this paper, the third in a series, we numerically simulate the long-term
nonlinear evolution of this instability in a convenient local model. Our C-ring
simulations confirm that the unstable system forms low-amplitude wavetrains
possessing a preferred band of wavelengths. B-ring simulations, on the other
hand, exhibit localised nonlinear wave `packets' separated by linearly stable
flat zones. Wave packets travel slowly while spreading in time, a result that
suggests the observed flat regions in Saturn's B-ring are shrinking. Finally,
we present exploratory runs of the inner B-ring edge which reproduce earlier
numerical results: ballistic transport can maintain the sharpness of a
spreading edge while building a `ramp' structure at its base. Moreover, the
ballistic transport instability can afflict the ramp region, but only in
low-viscosity runs.
| arxiv topic:astro-ph.EP |
arxiv_dataset-51741404.4347 | Complementary ab initio and X-ray nano-diffraction study of Ta2O5
cond-mat.mtrl-sci
Numerous different crystal structures of Ta2O5 are reported in literature.
Although experimentally and computationally obtained lattice parameters and
mechanical properties are in excellent agreement there is a pronounced
deviation when it comes to electronic structures of Ta2O5. Based on ab initio
studies and nano-beam X-ray diffraction of sputtered Ta2O5 thin films, we
introduce an orthorhombic basic structure with a = 0.6425, b = 0.3769, and c =
0.7706 nm, which is stabilized by flipping of an oxygen atom in neighboring
c-planes. The calculated energy of formation is with -3.209 eV/atom almost as
low as -3.259 eV/atom for the well-known Stephenson superstructure. We propose
the new structure based on the fact that it allows for a good description of
orthorhombic Ta2O5 even with a small and simple unit cell, which is especially
advantageous for computational studies.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-51751404.4447 | Entanglement in N-harmonium: bosons and fermions
quant-ph cond-mat.str-el physics.atom-ph
The ground-state entanglement of a single particle of the N-harmonium system
(i.e., a completely-integrable model of $N$ particles where both the
confinement and the two-particle interaction are harmonic) is shown to be
analytically determined in terms of $N$ and the relative interaction strength.
For bosons, we compute the von Neumann entropy of the one-body reduced density
matrix by using the corresponding natural occupation numbers. There exists a
critical number $N_c$ of particles so that below it, for positive values of the
coupling constant, the entanglement grows when the number of particles is
increasing; the opposite occurs for $N > N_c$. For fermions, we compute the
one-body reduced density matrix for the closed-shell spinned case. In the
strong coupling regime, the linear entropy of the system decreases when $N$ is
growing. For fixed $N$, the entanglement is found (a) to decrease (increase)
for negatively (positively) increasing values of the coupling constant, and (b)
to grow when the energy is increasing. Moreover, the spatial and spin
contributions to the total entanglement are found to be of comparable size.
| arxiv topic:quant-ph cond-mat.str-el physics.atom-ph |
arxiv_dataset-51761404.4547 | Control of parallel non-observable queues: asymptotic equivalence and
optimality of periodic policies
cs.PF math.OC math.PR
We consider a queueing system composed of a dispatcher that routes
deterministically jobs to a set of non-observable queues working in parallel.
In this setting, the fundamental problem is which policy should the dispatcher
implement to minimize the stationary mean waiting time of the incoming jobs. We
present a structural property that holds in the classic scaling of the system
where the network demand (arrival rate of jobs) grows proportionally with the
number of queues. Assuming that each queue of type $r$ is replicated $k$ times,
we consider a set of policies that are periodic with period $k \sum_r p_r$ and
such that exactly $p_r$ jobs are sent in a period to each queue of type $r$.
When $k\to\infty$, our main result shows that all the policies in this set are
equivalent, in the sense that they yield the same mean stationary waiting time,
and optimal, in the sense that no other policy having the same aggregate
arrival rate to \emph{all} queues of a given type can do better in minimizing
the stationary mean waiting time. This property holds in a strong probabilistic
sense. Furthermore, the limiting mean waiting time achieved by our policies is
a convex function of the arrival rate in each queue, which facilitates the
development of a further optimization aimed at solving the fundamental problem
above for large systems.
| arxiv topic:cs.PF math.OC math.PR |
arxiv_dataset-51771404.4647 | Upper bound for the Gromov width of coadjoint orbits of compact Lie
groups
math.SG
We find an upper bound for the Gromov width of coadjoint orbits of compact
Lie groups with respect to the Kirillov Kostant Souriau form by computing
certain Gromov Witten invariants, the approach presented here is closely
related to the one used by Gromov in his celebrated nonsqueezing theorem.
| arxiv topic:math.SG |
arxiv_dataset-51781404.4747 | Critical Casimir forces in a magnetic system: An experimental protocol
cond-mat.stat-mech
We numerically test an experimentally realizable method for the extraction of
the critical Casimir force based on its thermodynamic definition as the
derivative of the excess free energy with respect to system size. Free energy
differences are estimated for different system sizes by integrating the order
parameter along an isotherm. The method could be developed for experiments on
magnetic systems and could give access to the critical Casimir force for any
universality class. By choosing an applied field that opposes magnetic ordering
at the boundaries, the Casimir force is found to increase by an order of
magnitude over zero-field results.
| arxiv topic:cond-mat.stat-mech |
arxiv_dataset-51791404.4847 | Probing Lepton Asymmetry with 21 cm Fluctuations
astro-ph.CO hep-ph
We investigate the issue of how accurately we can constrain the lepton number
asymmetry xi_nu = mu_nu/T_nu in the Universe by using future observations of 21
cm line fluctuations and cosmic microwave background (CMB). We find that
combinations of the 21 cm line and the CMB observations can constrain the
lepton asymmetry better than big-bang nucleosynthesis (BBN). Additionally, we
also discuss constraints on xi_nu in the presence of some extra radiation, and
show that the 21 cm line observations can substantially improve the constraints
obtained by CMB alone, and allow us to distinguish the effects of the lepton
asymmetry from the ones of extra radiation.
| arxiv topic:astro-ph.CO hep-ph |
arxiv_dataset-51801404.4947 | Optimality of Radio Power Control via Fast-Lipschitz Optimization
math.OC
Fixed point algorithms play an important role to compute feasible solutions
to the radio power control problems in wireless networks. Although these
algorithms are shown to converge to the fixed points that give feasible problem
solutions, the solutions often lack notion of problem optimality. This paper
reconsiders well known fixed point algorithms such as those with standard and
type-II standard interference functions, and investigates the conditions under
which they give optimal power control solutions by the recently proposed
Fast-Lipschitz optimization framework. When the qualifying conditions of
Fast-Lipschitz optimization apply, it is established that the fixed points are
the optimal solutions of radio power optimization problems. The analysis is
performed by a logarithmic transformation of variables that gives problems
treatable within the Fast-Lipschitz framework. It is shown how the logarithmic
problem constraints are contractive by the standard or type-II standard
assumptions on the original power control problem, and how a set of cost
functions fulfill the Fast-Lipschitz qualifying conditions. The analysis on non
monotonic interference function allows to establish a new qualifying condition
for Fast-Lipschitz optimization. The results are illustrated by considering
power control problems with standard interference function, problems with
type-II standard interference functions, and a case of sub-homogeneous power
control problems. It is concluded that Fast-Lipschitz optimization may play an
important role in many resource allocation problems in wireless networks.
| arxiv topic:math.OC |
arxiv_dataset-51811404.5047 | Electromagnetic response of quark-gluon plasma in heavy-ion collisions
hep-ph nucl-th
We study the electromagnetic response of the quark-gluon plasma in
AA-collisions at RHIC and LHC energies for a realistic space-time evolution of
the plasma fireball. We demonstrate that for a realistic electric conductivity
the electromagnetic response of the plasma is in a quantum regime when the
induced electric current does not generate a classical electromagnetic field,
and can only lead to a rare emission of single photons.
| arxiv topic:hep-ph nucl-th |
arxiv_dataset-51821404.5147 | On the Witt vectors of perfect rings in positive characteristic
math.AC
The purpose of this article is to prove some results on the Witt vectors of
perfect $\mathbf{F}_p$-algebras. Let $A$ be a perfect $\mathbf{F}_p$-algebra
for a prime integer $p$ and assume that $A$ has the property $\mathbf{P}$. Then
does the ring of Witt vectors of $A$ also have $\mathbf{P}$? A main theorem
gives an affirmative answer for $\mathbf{P}="\mbox{integrally closed}"$ under a
very mild condition.
| arxiv topic:math.AC |
arxiv_dataset-51831404.5247 | Displacement cascades and defects annealing in tungsten, Part II: Object
kinetic Monte Carlo Simulation of Tungsten Cascade Aging
cond-mat.mtrl-sci
We describe the results of object kinetic Monte Carlo (OKMC) simulations of
the annealing of primary cascade damage in bulk tungsten using a comprehensive
database of cascades obtained from molecular dynamics [1] as a function of
primary knock-on atom (PKA) energy and direction, and temperatures of 300, 1025
and 2050 K. An increase in SIA clustering but decrease in vacancy clustering
with temperature combined with disparate mobilities of SIAs versus vacancies
causes an interesting temperature effect on cascade annealing, which is quite
different from what one would expect. The annealing efficiency (ratio of number
of defects after and before annealing) exhibits an inverse U-shape curve as a
function of temperature. In addition, we will also describe the capabilities of
our newly developed OKMC code; KSOME (kinetic simulations of microstructure
evolution) used to carryout these simulations
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-51841404.5347 | Homomorphisms between scalar Vema modules of ${\mathfrak gl}(n, {\mathbb
C})$
math.RT
In this article, we classify the homomorphisms between scalar generalized
Verma modules of ${\mathfrak gl}(n, {\mathbb C})$. In fact such homomorphisms
are compositions of elementary homomorphisms.
| arxiv topic:math.RT |
arxiv_dataset-51851404.5447 | Minimality of invariant submanifolds in Metric Contact Pair Geometry
math.DG
We study invariant submanifolds of manifolds endowed with a normal or complex
metric contact pair with decomposable endomorphism field $\phi$. For the normal
case, we prove that a $\phi$-invariant submanifold tangent to a Reeb vector
field and orthogonal to the other one is minimal. For a $\phi$-invariant
submanifold $N$ everywhere transverse to both the Reeb vector fields but not
orthogonal to them, we prove that it is minimal if and only if the angle
between the tangential component $\xi$ (with respect to $N$) of a Reeb vector
field and the Reeb vector field itself is constant along the integral curves of
$\xi$. For the complex case (when just one of the two natural almost complex
structures is supposed to be integrable), we prove that a complex submanifold
is minimal if and only if it is tangent to both the Reeb vector fields.
| arxiv topic:math.DG |
arxiv_dataset-51861404.5547 | Renormalization of myoglobin-ligand binding energetics by quantum
many-body effects
physics.chem-ph cond-mat.str-el physics.bio-ph
We carry out a first-principles atomistic study of the electronic mechanisms
of ligand binding and discrimination in the myoglobin protein. Electronic
correlation effects are taken into account using one of the most advanced
methods currently available, namely a linear-scaling density functional theory
(DFT) approach wherein the treatment of localized iron 3d electrons is further
refined using dynamical mean-field theory (DMFT). This combination of methods
explicitly accounts for dynamical and multi-reference quantum physics, such as
valence and spin fluctuations, of the 3d electrons, whilst treating a
significant proportion of the protein (more than 1000 atoms) with density
functional theory. The computed electronic structure of the myoglobin complexes
and the nature of the Fe-O2 bonding are validated against experimental
spectroscopic observables. We elucidate and solve a long standing problem
related to the quantum-mechanical description of the respiration process,
namely that DFT calculations predict a strong imbalance between O2 and CO
binding, favoring the latter to an unphysically large extent. We show that the
explicit inclusion of many body-effects induced by the Hund's coupling
mechanism results in the correct prediction of similar binding energies for
oxy- and carbonmonoxymyoglobin.
| arxiv topic:physics.chem-ph cond-mat.str-el physics.bio-ph |
arxiv_dataset-51871404.5647 | On the impossibility of $W_p^2$ estimates for elliptic equations with
piecewise constant coefficients
math.AP
In this paper, we present counterexamples showing that for any $p\in
(1,\infty)$, $p\neq 2$, there is a non-divergence form uniformly elliptic
operator with piecewise constant coefficients in $\mathbb{R}^2$ (constant on
each quadrant in $\mathbb{R}^2$) for which there is no $W^2_p$ estimate. The
corresponding examples in the divergence case are also discussed. One
implication of these examples is that the ranges of $p$ are sharp in the recent
results obtained in [4,5] for non-divergence type elliptic and parabolic
equations in a half space with the Dirichlet or Neumann boundary condition when
the coefficients do not have any regularity in a tangential direction.
| arxiv topic:math.AP |
arxiv_dataset-51881404.5747 | Vertex operator approach to semi-infinite spin chain : recent progress
nlin.SI cond-mat.stat-mech hep-th math-ph math.MP math.QA
Vertex operator approach is a powerful method to study exactly solvable
models. We review recent progress of vertex operator approach to semi-infinite
spin chain. (1) The first progress is a generalization of boundary condition.
We study $U_q(\widehat{sl}(2))$ spin chain with a triangular boundary, which
gives a generalization of diagonal boundary [Baseilhac and Belliard 2013,
Baseilhac and Kojima 2014]. We give a bosonization of the boundary vacuum
state. As an application, we derive a summation formulae of boundary
magnetization. (2) The second progress is a generalization of hidden symmetry.
We study supersymmetry $U_q(\widehat{sl}(M|N))$ spin chain with a diagonal
boundary [Kojima 2013]. By now we have studied spin chain with a boundary,
associated with symmetry $U_q(\widehat{sl}(N))$, $U_q(A_2^{(2)})$ and
$U_{q,p}(\widehat{sl}(N))$ [Furutsu-Kojima 2000, Yang-Zhang 2001, Kojima 2011,
Miwa-Weston 1997, Kojima 2011], where bosonizations of vertex operators are
realized by "monomial" . However the vertex operator for
$U_q(\widehat{sl}(M|N))$ is realized by "sum", a bosonization of boundary
vacuum state is realized by "monomial".
| arxiv topic:nlin.SI cond-mat.stat-mech hep-th math-ph math.MP math.QA |
arxiv_dataset-51891404.5847 | Thermal Infrared Observations of Asteroid (99942) Apophis with Herschel
astro-ph.EP
The near-Earth asteroid (99942) Apophis is a potentially hazardous asteroid.
We obtained far-infrared observations of this asteroid with the Herschel Space
Observatory's PACS instrument at 70, 100, and 160 micron. These were taken at
two epochs in January and March 2013 during a close Earth encounter. These
first thermal measurements of Apophis were taken at similar phase angles before
and after opposition. We performed a detailed thermophysical model analysis by
using the spin and shape model recently derived from applying a 2-period
Fourier series method to a large sample of well-calibrated photometric
observations. We find that the tumbling asteroid Apophis has an elongated shape
with a mean diameter of 375$^{+14}_{-10}$ m (of an equal volume sphere) and a
geometric V-band albedo of 0.30$^{+0.05}_{-0.06}$. We find a thermal inertia in
the range 250-800 Jm$^{-2}$s$^{-0.5}$K$^{-1}$ (best solution at 600
Jm$^{-2}$s$^{-0.5}$K$^{-1}$), which can be explained by a mixture of low
conductivity fine regolith with larger rocks and boulders of high thermal
inertia on the surface. The thermal inertia, and other similarities with
(25143) Itokawa indicate that Apophis might also have a rubble-pile structure.
If we combine the new size value with the assumption of an Itokawa-like density
and porosity we estimate a mass between 4.4 and 6.2 10$^{10}$ kg which is more
than 2-3 times larger than previous estimates. We expect that the newly derived
properties will influence impact scenario studies and influence the long-term
orbit predictions of Apophis.
| arxiv topic:astro-ph.EP |
arxiv_dataset-51901404.5947 | Emergence of the Dirac Equation in the Solitonic Source of the Kerr
Spinning Particle
gr-qc quant-ph
Gravitational and electromagnetic (EM) field of the Dirac electron is
described by the Kerr-Newman (KN) solution. We elaborate a regular source of
the KN solution which satisfies the requirement of flat space-time inside the
source and realization of the exact KN solution outside the source. This
requirement removes conflict between gravity and quantum theory and determines
many details of the source structure. In particular, we obtain that the KN
source should forms a gravitating bag model, similar to the known MIT and SLAC
bag models. As opposite to the known bag models, the self-interacting Higgs
field should be confined inside the bag, while outside the bag the gauge
symmetry should be unbroken to provide the external KN gravity. We show that
twistorial structure of the Kerr geometry (the Kerr theorem) determines
structure of the Dirac equation, resulting in a variable mass term, which is
generated inside the bag through interaction with the confined Higgs field.
Similar to the other bag models, ellipsoidal deformations of the KN bag creates
a string-like structure of the dressed electron -- circular string positioned
along perimeter of the KN bag.
| arxiv topic:gr-qc quant-ph |
arxiv_dataset-51911404.6047 | Full control of quadruple quantum dot circuit charge states in the
single electron regime
cond-mat.mes-hall
We report the realization of an array of four tunnel coupled quantum dots in
the single electron regime, which is the first required step toward a scalable
solid state spin qubit architecture. We achieve an efficient tunability of the
system but also find out that the conditions to realize spin blockade readout
are not as straightforwardly obtained as for double and triple quantum dot
circuits. We use a simple capacitive model of the series quadruple quantum dots
circuit to investigate its complex charge state diagrams and are able to find
the most suitable configurations for future Pauli spin blockade measurements.
We then experimentally realize the corresponding charge states with a good
agreement to our model.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-51921404.6147 | A spider-like outflow in Barnard 5 - IRS 1: The transition from a
collimated jet to a wide-angle outflow?
astro-ph.SR
We present line and continuum observations made with the Submillimeter Array
(SMA) of the young stellar object Barnard 5 - IRS1 located in the Perseus
molecular cloud. Our $^{12}$CO(2-1) line observations resolve the high-velocity
bipolar northeast-southwest outflow associated with this source. We find that
the outflowing gas shows different structures at three different velocity
regimes, in both lobes, resulting in a spider-like morphology. In addition to
the low-velocity, cone-like (wide-angle) lobes that have previously been
observed, we report the presence of intermediate-velocity parabolic shells
emerging very close to the Class I protostar, as well as high velocity
molecular bullets that appear to be associated to the optical/IR jet emanating
from this source. These compact high-velocity features reach radial velocities
of about 50 km s$^{-1}$ away from the cloud velocity. We interpret the peculiar
spider-like morphology is a result of the molecular material being entrained by
a wind with both a collimated jet-like component and a wide-angle component. We
suggest the outflow is in a transitional evolutionary phase between a mostly
jet-driven flow and an outflow in which the entrainment is dominated by the
wide-angle wind component. We also detect 1300 $\mu$m continuum emission at the
position of the protostar, which likely arises from the dusty envelope and disk
surrounding the protostar. Finally, we report the detection of $^{13}$CO(2-1)
and SO(6$_5$-5$_4$) emission arising from the outflow and the location of the
young stellar object.
| arxiv topic:astro-ph.SR |
arxiv_dataset-51931404.6247 | Career on the Move: Geography, Stratification, and Scientific Impact
physics.soc-ph cs.SI physics.data-an
Changing institutions is an integral part of an academic life. Yet little is
known about the mobility patterns of scientists at an institutional level and
how these career choices affect scientific outcomes. Here, we examine over
420,000 papers, to track the affiliation information of individual scientists,
allowing us to reconstruct their career trajectories over decades. We find that
career movements are not only temporally and spatially localized, but also
characterized by a high degree of stratification in institutional ranking. When
cross-group movement occurs, we find that while going from elite to lower-rank
institutions on average associates with modest decrease in scientific
performance, transitioning into elite institutions does not result in
subsequent performance gain. These results offer empirical evidence on
institutional level career choices and movements and have potential
implications for science policy.
| arxiv topic:physics.soc-ph cs.SI physics.data-an |
arxiv_dataset-51941404.6347 | To the center of cold spot with Planck
astro-ph.CO gr-qc
The structure of the cold spot, of a non-Gaussian anomaly in the cosmic
microwave background (CMB) sky first detected by Vielva et al. is studied using
the data by Planck satellite. The obtained map of the degree of stochasticity
(K-map) of CMB for the cold spot, reveals, most clearly in 100 GHz band, a
shell-type structure with a center coinciding with the minima of the
temperature distribution. The shell structure is non-Gaussian at a 4\sigma
confidence level. Such behavior of the K-map supports the void nature of the
cold spot. The applied method can be used for tracing voids that have no
signatures in redshift surveys.
| arxiv topic:astro-ph.CO gr-qc |
arxiv_dataset-51951404.6447 | Counterexamples to Cantorian Set Theory
math.GM
This paper provides some counterexamples to Cantor's contributions to the
foundations of Set Theory. The first counterexample forces Cantor's Diagonal
Method (DM) to yield one of the numbers in the target list. To study this
anomaly, and given that for the DM to work the list of numbers have to be
written down, the set of numbers that can be represented using positional
fractional notation, $\mathbb{W}$, is properly characterized. It is then shown
that $\mathbb{W}$ is not isomorphic to $\mathbb{R}$, meaning that results
obtained from the application of the DM to $\mathbb{W}$ in order to derive
properties of $\mathbb{R}$ are not valid. It is then shown that Cantor's DM for
a generic list of reals can be forced to yield one of the numbers of the list,
thus invalidating Cantor's result that infers the non-denumerability of
$\mathbb{R}$ from the application of the DM to $\mathbb{W}$. Cantor's Theorem
about the different cardinalities of a set and its power set is then
questioned, and by means of another counterexample we show that the theorem
does not actually hold for infinite sets. After analyzing all these results, it
is shown that the current notion of cardinality for infinite sets does not
depend on the size of the sets, but rather on the representation chosen for
them. Following this line of thought, the concept of model as a framework for
the construction of the representation of a set is introduced, and a theorem
showing that an infinite set can be well-ordered if there is a proper model for
it is proven. To reiterate that the cardinality of a set does not determine
whether the set can be well-ordered, a set of cardinality
$\aleph_{0}^{\aleph_{0}}$ is proven to be equipollent to the set of natural
numbers $\mathbb{N}$. The paper concludes with an analysis of the cardinality
of the ordinal numbers, for which a representation of cardinality
$\aleph_{0}^{\aleph_{0}}$ is proposed.
| arxiv topic:math.GM |
arxiv_dataset-51961404.6547 | E-books and Graphics with LaTeXML
cs.DL
Marked by the highlights of native generation of EPUB E-books and TikZ
support for creating SVG images, we present an annual report of LaTeXML
development in 2013. LaTeXML provides a reimplementation of the $\TeX$ parser,
geared towards preserving macro semantics; it supports an array of output
formats, notably HTML5, EPUB, XHTML and its own $\LaTeX$-near XML. Other
highlights include enhancing performance when used inside high-throughput
build-systems, via incorporating a native ZIP archive workflow, as well as a
simplified installation procedure that now allows to deploy LaTeXML as a cloud
service. To this end, we also introduce an official plugin-based scheme for
publishing new features that go beyond the core scope of LaTeXML, such as web
services or unconventional post-processors. The software suite has now migrated
to GitHub and we welcome forks and patches from the wider FLOSS community.
| arxiv topic:cs.DL |
arxiv_dataset-51971404.6647 | The interpolation method for random graphs with prescribed degrees
math.PR math.CO
We consider large random graphs with prescribed degrees, such as those
generated by the configuration model. In the regime where the empirical degree
distribution approaches a limit $\mu$ with finite mean, we establish the
systematic convergence of a broad class of graph parameters that includes in
particular the independence number, the maximum cut size and the log-partition
function of the antiferromagnetic Ising and Potts models. The corresponding
limits are shown to be Lipschitz and concave functions of $\mu$. Our work
extends the applicability of the celebrated interpolation method, introduced in
the context of spin glasses, and recently related to the fascinating problem of
right-convergence of sparse graphs.
| arxiv topic:math.PR math.CO |
arxiv_dataset-51981404.6747 | 10 inventions on Improving Toolbars: A TRIZ based analysis
cs.HC
Toolbar is one among the popular elements of a graphical user interface. The
other popular elements of graphical user interface are buttons, menu,
scrollbar, dialog box etc., all of which provide easy access to various
functions of a GUI System.
A toolbar often does a similar function as the menu but with certain
differences. A menu has the advantage of holding a large number of items
without needing any additional screen space. In contrast, each button on the
toolbar permanently occupies some space on the screen. It is not possible to
implement large number of functions through a toolbar, as they will occupy more
and more valuable screen space. However, the toolbar has an advantage as it
gives a single click access to any function unlike a menu system where the user
has to navigate through sub-menus to ultimate discover the item he is looking
for.
This article explores the desired features of a toolbar and the ideal
features of an advanced toolbar. The contradictions are described from a TRIZ
perspective and solutions are derived using Inventive principles. Besides the
article illustrates 10 inventions on improving Toolbars selected from US patent
database.
| arxiv topic:cs.HC |
arxiv_dataset-51991404.6847 | Pseudocalar meson and vector meson interactions and dynamically
generated axial-vector mesons
nucl-th hep-lat hep-ph
The axial-vector mesons $a_1(1260)$, $b_1(1235)$, $f_1(1285)$, $h_1(1170)$,
$h_1(1380)$, and $K_1(1270)$ are dynamically generated in the unitized chiral
perturbation theory. Such a picture has been tested extensively in the past few
years. In this work, we calculate the interaction kernel up to
$\mathcal{O}(p^2)$ and study the impact on the dynamically generated
axial-vector states. In anticipation of future lattice QCD simulations, we
calculate the scattering lengths and the pole positions as functions of the
pion mass, with the light-quark mass dependence of the kaon, the eta, and the
vector mesons determined by the $n_f=2+1$ lattice QCD simulations of the
PACS-CS Collaboration.
| arxiv topic:nucl-th hep-lat hep-ph |
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