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arxiv_dataset-67001510.06043 | Entropy-continuity for interval maps with holes
math.DS
We study the dependence of the topological entropy of piecewise monotonic
maps with holes under perturbations, for example sliding a hole of fixed size
at uniform speed or expanding a hole with uniform expansion. We show that under
suitable conditions the topological entropy varies locally Hoelder continuously
with the local Hoelder exponent depending itself on the value of the
topological entropy.
| arxiv topic:math.DS |
arxiv_dataset-67011510.06143 | High Performance Latent Variable Models
cs.LG cs.AI
Latent variable models have accumulated a considerable amount of interest
from the industry and academia for their versatility in a wide range of
applications. A large amount of effort has been made to develop systems that is
able to extend the systems to a large scale, in the hope to make use of them on
industry scale data. In this paper, we describe a system that operates at a
scale orders of magnitude higher than previous works, and an order of magnitude
faster than state-of-the-art system at the same scale, at the same time showing
more robustness and more accurate results.
Our system uses a number of advances in distributed inference: high
performance in synchronization of sufficient statistics with relaxed
consistency model; fast sampling, using the Metropolis-Hastings-Walker method
to overcome dense generative models; statistical modeling, moving beyond Latent
Dirichlet Allocation (LDA) to Pitman-Yor distributions (PDP) and Hierarchical
Dirichlet Process (HDP) models; sophisticated parameter projection schemes, to
resolve the conflicts within the constraint between parameters arising from the
relaxed consistency model.
This work significantly extends the domain of applicability of what is
commonly known as the Parameter Server. We obtain results with up to hundreds
billion oftokens, thousands of topics, and a vocabulary of a few million
token-types, using up to 60,000 processor cores operating on a production
cluster of a large Internet company. This demonstrates the feasibility to scale
to problems orders of magnitude larger than any previously published work.
| arxiv topic:cs.LG cs.AI |
arxiv_dataset-67021510.06243 | A Note on Powers in Finite Fields
math.NT
The study of solutions to polynomial equations over finite fields has a long
history in mathematics and is an interesting area of contemporary research. In
recent years the subject has found important applications in the modelling of
problems from applied mathematical fields such as signal analysis, system
theory, coding theory and cryptology. In this connection it is of interest to
know criteria for the existence of squares and other powers in arbitrary finite
fields. Making good use of polynomial division in polynomial rings over finite
fields, we have examined a classical criterion of Euler for squares in odd
prime fields, giving it a formulation which is apt for generalization to
arbitrary finite fields and powers. Our proof uses algebra rather than
classical number theory, which makes it convenient when presenting basic
methods of applied algebra in the classroom.
| arxiv topic:math.NT |
arxiv_dataset-67031510.06343 | On the coupling of regularization techniques and the boundary element
method for a hemivariational inequality modelling a delamination problem
math.NA
In this paper, we couple regularization techniques with the adaptive
$hp$-version of the boundary element method ($hp$-BEM) for the efficient
numerical solution of linear elastic problems with nonmonotone contact boundary
conditions. As a model example we treat the delamination of composite
structures with a contaminated interface layer. This problem has a weak
formulation in terms of a nonsmooth variational inequality. The resulting
hemivariational inequality (HVI) is first regularized and then, discretized by
an adaptive $hp$-BEM. We give conditions for the uniqueness of the solution and
provide an a-priori error estimate. Furthermore, we derive an a-posteriori
error estimate for the nonsmooth variational problem based on a novel
regularized mixed formulation, thus enabling $hp$-adaptivity. Various numerical
experiments illustrate the behavior, strengths and weaknesses of the proposed
high-order approximation scheme.
| arxiv topic:math.NA |
arxiv_dataset-67041510.06443 | The Representation Dimension of a Selfinjective Algebra of Euclidean
Type
math.RT math.RA
We prove that the representation dimension of a selfinjective algebra of
euclidean type is equal to three, and give an explicit construction of the
Auslander generator of its module category.
| arxiv topic:math.RT math.RA |
arxiv_dataset-67051510.06543 | Effective resonant stability of Mercury
math.DS astro-ph.EP
Mercury is the unique known planet that is situated in a 3:2 spin-orbit
resonance nowadays. Observations and models converge to the same conclusion:
the planet is presently deeply trapped in the resonance and situated at the
Cassini state $1$, or very close to it. We investigate the complete non-linear
stability of this equilibrium, with respect to several physical parameters, in
the framework of Birkhoff normal form and Nekhoroshev stability theory. We use
the same approach adopted for the 1:1 spin-orbit case with a peculiar attention
to the role of Mercury's non negligible eccentricity. The selected parameters
are the polar moment of inertia, the Mercury's inclination and eccentricity and
the precession rates of the perihelion and node. Our study produces a bound to
both the latitudinal and longitudinal librations (of 0.1 radians) for a long
but finite time (greatly exceeding the age of the solar system). This is the
so-called effective stability time. Our conclusion is that Mercury, placed
inside the 3:2 spin-orbit resonance, occupies a very stable position in the
space of these physical parameters, but not the most stable possible one.
| arxiv topic:math.DS astro-ph.EP |
arxiv_dataset-67061510.06643 | A long-period Cepheid variable in the starburst cluster VdBH222
astro-ph.SR
Galactic starburst clusters play a twin role in astrophysics, serving as
laboratories for the study of stellar physics and also delineating the
structure and recent star formation history of the Milky Way. In order to
exploit these opportunities we have undertaken a multi-epoch spectroscopic
survey of the red supergiant dominated young massive clusters thought to be
present at both near and far ends of the Galactic Bar. Significant
spectroscopic variability suggestive of radial pulsations was found for the
yellow supergiant VdBH 222 #505. Follow-up photometric investigations revealed
modulation with a period of ~23.325d; both timescale and pulsational profile
are consistent with a Cepheid classification. As a consequence #505 may be
recognised as one of the longest period Galactic cluster Cepheids identified to
date and hence of considerable use in constraining the bright end of the
period/luminosity relation at solar metallicities. In conjunction with extant
photometry we infer a distance of ~6kpc for VdBH222 and an age of ~20Myr. This
results in a moderate reduction in both integrated cluster mass (~2x10^4Msun)
and the initial stellar masses of the evolved cluster members (~10Msun). As
such, VdBH222 becomes an excellent test-bed for studying the properties of some
of the lowest mass stars observed to undergo type-II supernovae. Moreover, the
distance is in tension with a location of VdBH 222 at the far end of the
Galactic Bar. Instead a birthsite in the near 3kpc arm is suggested; providing
compelling evidence of extensive recent star formation in a region of the inner
Milky Way which has hitherto been thought to be devoid of such activity.
| arxiv topic:astro-ph.SR |
arxiv_dataset-67071510.06743 | Quantum-proof multi-source randomness extractors in the Markov model
quant-ph cs.CC cs.CR
Randomness extractors, widely used in classical and quantum cryptography and
other fields of computer science, e.g., derandomization, are functions which
generate almost uniform randomness from weak sources of randomness. In the
quantum setting one must take into account the quantum side information held by
an adversary which might be used to break the security of the extractor. In the
case of seeded extractors the presence of quantum side information has been
extensively studied. For multi-source extractors one can easily see that high
conditional min-entropy is not sufficient to guarantee security against
arbitrary side information, even in the classical case. Hence, the interesting
question is under which models of (both quantum and classical) side information
multi-source extractors remain secure. In this work we suggest a natural model
of side information, which we call the Markov model, and prove that any
multi-source extractor remains secure in the presence of quantum side
information of this type (albeit with weaker parameters). This improves on
previous results in which more restricted models were considered and the
security of only some types of extractors was shown.
| arxiv topic:quant-ph cs.CC cs.CR |
arxiv_dataset-67081510.06843 | A non-symplectic automorphism of order 21 of a K3 surface
math.AG
In this paper, we prove that, over an algebraically closed field whose
characteristic is not 2,3 nor 7, a pair of a K3 surface and a purely
non-symplectic automorphism of order 21 or 42 is unique up to isomorphism.
| arxiv topic:math.AG |
arxiv_dataset-67091510.06943 | Corrigendum: The symplectic sum formula for Gromov-Witten invariants
math.SG
We correct an error and an oversight in [IP]. The sign of the curvature in
(8.7) is wrong, requiring a new proof of Proposition 8.1. Also, several lemmas
addressed only the basic case of maps with intersection multiplicity s=1; the
general case follows by applying the pointwise estimates in [IP] with a
modified Sobolev norm. These corrections do not affect the results of the
paper.
We thank M. Tehrani and A. Zinger for pointing out these issues.
| arxiv topic:math.SG |
arxiv_dataset-67101510.07043 | Bayesian Redshift Classification of Emission-line Galaxies with
Photometric Equivalent Widths
astro-ph.IM astro-ph.CO astro-ph.GA
We present a Bayesian approach to the redshift classification of
emission-line galaxies when only a single emission line is detected
spectroscopically. We consider the case of surveys for high-redshift
Lyman-alpha-emitting galaxies (LAEs), which have traditionally been classified
via an inferred rest-frame equivalent width (EW) greater than 20 angstrom. Our
Bayesian method relies on known prior probabilities in measured emission-line
luminosity functions and equivalent width distributions for the galaxy
populations, and returns the probability that an object in question is an LAE
given the characteristics observed. This approach will be directly relevant for
the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), which seeks to
classify ~10^6 emission-line galaxies into LAEs and low-redshift [O II]
emitters. For a simulated HETDEX catalog with realistic measurement noise, our
Bayesian method recovers 86% of LAEs missed by the traditional EW > 20 angstrom
cutoff over 2 < z < 3, outperforming the EW cut in both contamination and
incompleteness. This is due to the method's ability to trade off between the
two types of binary classification error by adjusting the stringency of the
probability requirement for classifying an observed object as an LAE. In our
simulations of HETDEX, this method reduces the uncertainty in cosmological
distance measurements by 14% with respect to the EW cut, equivalent to
recovering 29% more cosmological information. Rather than using binary object
labels, this method enables the use of classification probabilities in
large-scale structure analyses. It can be applied to narrowband emission-line
surveys as well as upcoming large spectroscopic surveys including Euclid and
WFIRST.
| arxiv topic:astro-ph.IM astro-ph.CO astro-ph.GA |
arxiv_dataset-67111510.07143 | The commutators of classical groups
math.RA math.GR
In his seminal paper, half a century ago, Hyman Bass established a commutator
formula in the setting of (stable) general linear group which was the key step
in defining the K_1 group. Namely, he proved that for an associative ring A
with identity, E(A)=[E(A),E(A)]=[GL(A),GL(A)] where GL(A) is the stable general
linear group and E(A) is its elementary subgroup. Since then, various
commutator formulas have been studied in stable and non-stable settings, and
for a range of classical and algebraic like-groups, mostly in relation to
subnormal subgroups of these groups. The major classical theorems and methods
developed include some of the splendid results of the heroes of classical
algebraic K-theory; Bak, Quillen, Milnor, Suslin, Swan and Vaserstein, among
others.
One of the dominant techniques in establishing commutator type results is
localisation. In this note we describe some recent applications of localisation
methods to the study (higher/relative) commutators in the groups of points of
algebraic and algebraic-like groups, such as general linear groups, GL(n,A),
unitary groups GU(2n,A, Lambda) and Chevalley groups G(Phi,A).
We also state some of the intermediate results as well as some corollaries of
these results. This note provides a general overview of the subject and covers
the current activities. It contains complete proofs of several main results to
give the reader a self-contained source. We have borrowed some of the proofs
from our previous papers and expositions
| arxiv topic:math.RA math.GR |
arxiv_dataset-67121510.07243 | General relativistic magnetohydrodynamical simulations of the jet in M87
astro-ph.HE
(abridged) The connection between black hole, accretion disk, and radio jet
can be best constrained by fitting models to observations of nearby low
luminosity galactic nuclei, in particular the well studied sources Sgr~A* and
M87. There has been considerable progress in modeling the central engine of
active galactic nuclei by an accreting supermassive black hole coupled to a
relativistic plasma jet. However, can a single model be applied to a range of
black hole masses and accretion rates? Here we want to compare the latest
three-dimensional numerical model, originally developed for Sgr A* in the
center of the Milky Way, to radio observations of the much more powerful and
more massive black hole in M87. We postprocess three-dimensional GRMHD models
of a jet-producing radiatively inefficient accretion flow around a spinning
black hole using relativistic radiative transfer and ray-tracing to produce
model spectra and images. As a key new ingredient to these models, we allow the
proton-electron coupling in these simulations depend on the magnetic properties
of the plasma. We find that the radio emission in M87 is well described by a
combination of a two-temperature accretion flow and a hot single-temperature
jet. The model fits the basic observed characteristics of the M87 radio core.
The best fit model has a mass-accretion rate of Mdot approx 9x10^{-3} MSUN/YR
and a total jet power of P_j \sim 10^{43} erg/s. Emission at 1.3mm is produced
by the counter jet close to the event horizon. Its characteristic crescent
shape surrounding the black hole shadow could be resolved by future
millimeter-wave VLBI experiments. The model was successfully derived from one
for the supermassive black hole in center of the Milky Way by appropriately
scaling mass and accretion rate. This suggests the possibility that this model
could also apply to a larger range of low-luminosity black holes.
| arxiv topic:astro-ph.HE |
arxiv_dataset-67131510.07343 | Giant nonlinearity via breaking parity-time symmetry: a route to
low-threshold phonon diodes
cond-mat.mes-hall
Nonreciprocal devices that permit wave transmission in only one direction are
indispensible in many fields of science including, e.g., electronics, optics,
acoustics, and thermodynamics. Manipulating phonons using such nonreciprocal
devices may have a range of applications such as phonon diodes, transistors,
switches, etc. One way of achieving nonreciprocal phononic devices is to use
materials with strong nonlinear response to phonons. However, it is not easy to
obtain the required strong mechanical nonlinearity, especially for few-phonon
situations. Here, we present a general mechanism to amplify nonlinearity using
$\mathcal{PT}$-symmetric structures, and show that an on-chip micro-scale
phonon diode can be fabricated using a $\mathcal{PT}$-symmetric mechanical
system, in which a lossy mechanical-resonator with very weak mechanical
nonlinearity is coupled to a mechanical resonator with mechanical gain but no
mechanical nonlinearity. When this coupled system transits from the
$\mathcal{PT}$-symmetric regime to the broken-$\mathcal{PT}$-symmetric regime,
the mechanical nonlinearity is transferred from the lossy resonator to the one
with gain, and the effective nonlinearity of the system is significantly
enhanced. This enhanced mechanical nonlinearity is almost lossless because of
the gain-loss balance induced by the $\mathcal{PT}$-symmetric structure. Such
an enhanced lossless mechanical nonlinearity is then used to control the
direction of phonon propagation, and can greatly decrease (by over three orders
of magnitude) the threshold of the input-field intensity necessary to observe
the unidirectional phonon transport. We propose an experimentally realizable
lossless low-threshold phonon diode of this type. Our study opens up new
perspectives for constructing on-chip few-phonon devices and hybrid
phonon-photon components.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-67141510.07443 | Misfit stabilized embedded nanoparticles in metallic alloys
cond-mat.mtrl-sci
Nanoscale inhomogeneities are typical for numerous metallic alloys and
crucially important for their practical applications. At the same time,
stabilization mechanisms of such a state are poorly understood. We present a
general overview of the problem, together with a more detailed discussion of
the prototype example, namely, Guinier-Preston zones in Al-based alloys. It is
shown that coherent strain due to a misfit between inclusion and host crystal
lattices plays a decisive role in the emergence of the inhomogeneous state. We
suggest a model explaining formation of ultrathin plates (with the thickness of
a few lattice constants) typical for Al-Cu alloys. Discreteness of the array of
misfit dislocations and long-ranged elastic interactions between them are the
key ingredients of the model. This opens a way to a general understanding of
the nature of (meta)stable embedded nanoparticles in practically important
systems.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-67151510.07543 | Chemical Freeze-out Parameters via a Non-perturbative QCD Approach
hep-ph nucl-ex nucl-th
By analyzing the calculated baryon number susceptibility ratios
${\chi_{1}^{B}}/{\chi_{2}^{B}}$ and ${\chi_{3}^{B}}/{\chi_{1}^{B}}$ in
two-flavor system via the Dyson-Schwinger equation approach of QCD, we
determine the chemical freeze-out temperature and baryon chemical potential in
cases of both thermodynamic limit and finite size. We calculate the
center-of-mass energy dependence of the ${\chi_{4}^{B}}/{\chi_{2}^{B}}\,
(\kappa \sigma^{2})$ at the freeze-out line and find an excellent agreement
with experimental data in $\sqrt{S_{NN}^{}} \geq 19.6\,$GeV region when taking
into account the finite size effect. Our calculations indicate that the $\kappa
\sigma^{2}$ exhibits a non-monotonic behavior in lower collision energy region.
| arxiv topic:hep-ph nucl-ex nucl-th |
arxiv_dataset-67161510.07643 | Evolution families and maximal regularity for systems of parabolic
equations
math.AP math.FA
In this paper we prove maximal $L^p$-regularity for a system of parabolic
PDEs, where the elliptic operator $A$ has coefficients which depend on time in
a measurable way and are continuous in the space variable. The proof is based
on operator-theoretic methods and one of the main ingredients in the proof is
the construction of an evolution family on weighted $L^q$-spaces.
| arxiv topic:math.AP math.FA |
arxiv_dataset-67171510.07743 | Investigating AGN Black Hole Masses and the M-$\sigma_e$ relation for
Low Surface Brightness Galaxies
astro-ph.GA
We present an analysis of the optical nuclear spectra from the active
galactic nuclei (AGN) in a sample of low surface brightness (LSB) galaxies.
Using data from the Sloan Digital Sky Survey (SDSS), we derived the virial
black hole (BH) masses of 24 galaxies from their broad H$\alpha$ parameters. We
find that our estimates of nuclear BH masses lie in the range
$10^{5}-10^{7}~M_{\odot}$, with a median mass of 5.62 x 10$^{6}~M_{\odot}$. The
bulge stellar velocity dispersion $\sigma_{e}$ was determined from the
underlying stellar spectra. We compared our results with the existing BH mass -
velocity dispersion ($M_{BH}-\sigma_{e}$) correlations and found that the
majority of our sample lie in the low BH mass regime and below the
$M_{BH}-\sigma_{e}$ correlation. We analysed the effects of any systematic bias
in the M$_{BH}$ estimates, the effects of galaxy orientation in the measurement
of $\sigma_e$ and the increase of $\sigma_e$ due to the presence of bars and
found that these effects are insufficient to explain the observed offset in
M$_{BH}$ - $\sigma_e$ correlation. Thus the LSB galaxies tend to have low mass
BHs which probably are not in co-evolution with the host galaxy bulges. A
detailed study of the nature of the bulges and the role of dark matter in the
growth of the BHs is needed to further understand the BH-bulge co-evolution in
these poorly evolved and dark matter dominated systems.
| arxiv topic:astro-ph.GA |
arxiv_dataset-67181510.07843 | Long range interaction induced density modulated state in a
Bose-Einstein condensate
cond-mat.quant-gas
We consider a Gross-Pitaevskii model of BEC with non-local s-wave scattering
to study the density modulated state in 1D. We resort to a perturbative Taylor
series expansion for the order parameter. By perturbative calculations, we show
that under long range s-wave scattering a density modulated state is
energetically favourable as compared to the uniform density state. We obtain
density modulated state as a solution to the perturbative non-local GP
equation, rather than the conventional approach of introducing amplitude
modulations on top of the uniform density state and lowering the roton minimum.
| arxiv topic:cond-mat.quant-gas |
arxiv_dataset-67191510.07943 | Metamorphosis of the Cosmological Constant and 5D Origin of the Fiducial
Metric
hep-th
In a recently proposed theory, the cosmological constant (CC) does not curve
spacetime in our universe, but instead gets absorbed into another universe
endowed with its own dynamical metric, nonlocally coupled to ours. Thus, one
achieves a long standing goal of removing entirely any cosmological constant
from our universe. Dark energy then cannot be due to a cosmological constant,
but must be obtained via other mechanisms. Here we focus on the scenario in
which dark energy is due to massive gravity and its extensions. We show how the
metric of the other universe, that absorbs our CC, also gives rise to the
fiducial metric known to be necessary for the diffeomorphism invariant
formulation of massive gravity. This is achieved in a framework where the other
universe is described by 5D AdS gravity, while our universe lives on its
boundary and is endowed with dynamical massive gravity. A non-dynamical
pullback of the bulk AdS metric acts as the fiducial metric for massive gravity
on the boundary. This framework also removes a difficulty caused by the quantum
strongly coupled behavior of massive gravity at the Lambda3 scale: in the
present approach, the massive gravity action does not receive any loop-induced
counterterms, despite being strongly coupled.
| arxiv topic:hep-th |
arxiv_dataset-67201510.08043 | On algebraic solitons for geometric evolution equations on
three-dimensional Lie groups
math.DG
In this paper, we investigate the relationship between algebraic soliton
metrics and soliton metrics for geometric evolution equations on Lie groups.
After discussing the general relationship between algebraic soliton metrics and
soliton metrics, we investigate the cross curvature flow and the second order
renormalization group flow on simply connected three-dimensional unimodular Lie
groups, providing a complete classification of left invariant algebraic
solitons on such spaces.
| arxiv topic:math.DG |
arxiv_dataset-67211510.08143 | High dispersion spectroscopy of solar-type superflare stars with
Subaru/HDS
astro-ph.SR
We carried out spectroscopic observations with Subaru/HDS of 50 solar-type
superflare stars found from Kepler data. More than half (34 stars) of the
target stars show no evidence of the binary system, and we confirmed
atmospheric parameters of these stars are roughly in the range of solar-type
stars. We then conducted the detailed analyses for these 34 stars. First, the
value of the "$v\sin i$" (projected rotational velocity) measured from
spectroscopic results is consistent with the rotational velocity estimated from
the brightness variation. Second, there is a correlation between the amplitude
of the brightness variation and the intensity of Ca II IR triplet line. All the
targets expected to have large starspots because of their large amplitude of
the brightness variation show high chromospheric activities compared with the
Sun. These results support that the brightness variation of superflare stars is
explained by the rotation of a star with large starspots.
| arxiv topic:astro-ph.SR |
arxiv_dataset-67221510.08243 | Classical and Quantum Stochastic Models of Resistive and Memristive
Circuits
math-ph math.DS math.MP math.OC quant-ph
The purpose of this paper is to examine stochastic Markovian models for
circuits in phase space for which the drift term is equivalent to the standard
circuit equations. In particular we include dissipative components
corresponding to both a resistor and a memristor in series. We obtain a
dilation of the problem for which is canonical in the sense that the underlying
Poisson Brackets structure is preserved under the stochastic flow. We do this
first of all for standard Wiener noise, but also treat the problem using a new
concept of symplectic noise where the Poisson structure is extended to the
noise as well as the circuit variables, and in particular where we have
canonically conjugate noises. Finally we construct a dilation which describes
the quantum mechanical analogue.
| arxiv topic:math-ph math.DS math.MP math.OC quant-ph |
arxiv_dataset-67231510.08343 | Koszul Duality for Quasi-split Real Groups
math.RT math.AG
We establish a categorical version of Vogan duality for quasi-split real
groups. This proves a conjecture of Soergel in the quasi-split case.
| arxiv topic:math.RT math.AG |
arxiv_dataset-67241510.08443 | From Stringy Particle Physics to Moduli Stabilisation and Cosmology
hep-th hep-ph
Intersecting D6-branes provide a geometrically intuitive road to stringy
particle physics models, where D6-branes stuck at orbifold singularities can
lead to the stabilisation of deformation moduli, and the QCD axion can arise
from the open string sector in a very constrained way compared to pure field
theory. We demonstrate this interplay of different physical features here
through an explicit model.
| arxiv topic:hep-th hep-ph |
arxiv_dataset-67251510.08543 | Micromagnetic simulations with periodic boundary conditions: Hard-soft
nanocomposites
cond-mat.mes-hall
We developed a micromagnetic method for modeling magnetic systems with
periodic boundary conditions along an arbitrary number of dimensions. The main
feature is an adaptation of the Ewald summation technique for evaluation of
long-range dipolar interactions. The method was applied to investigate the
hysteresis process in hard-soft magnetic nanocomposites with various
geometries. The dependence of the results on different micromagnetic parameters
was studied. We found that for layered structures with an out-of-plane hard
phase easy axis the hysteretic properties are very sensitive to the strength of
the interlayer exchange coupling, as long as the spontaneous magnetization for
the hard phase is significantly smaller than for the soft phase. The origin of
this behavior was discussed. Additionally, we investigated the soft phase size
optimizing the energy product of hard-soft nanocomposites.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-67261510.08643 | Symmetries of the pseudo-diffusion equation, and its unconventional
2-sided kernel
math-ph math.MP quant-ph
We determine by two related methods the invariance algebra $\g$ of the
\emph{`pseudo-diffusion equation'} (PSDE) $$ L~Q \equiv \left[\frac
{\partial}{\partial t} -\frac 1 4 \left(\frac {\partial^2}{\partial x^2} -\frac
1 {t^2} \frac {\partial^2}{\partial p^2}\right)\right]~Q(x,p,t)=0, $$ which
describes the behavior of the $Q$ functions in the $(x,p)$-phase space as a
function of a squeeze parameter $y$, where $t=e^{2y}$. The algebra turns out to
be isomorphic to that of its constant coefficient version. Relying on this
isomorphism we construct a local point transformation which maps the factor
$t^{-2}$ to 1. We show that any generalized version $u_t-u_{xx}+ b(t) u_{yy}=0$
of PSDE has a smaller symmetry algebra than $\g$, except for $b(t)$ equals to a
constant or it is proportional to $t^{-2}$. We apply the group elements
$G_i(\ga) := \exp[\ga A_i]$ and obtain new solutions of the PSDE from simple
ones, and interpret the physics of some of the results. We make use of the
`factorization property' of the PSDE to construct its \textit{`2-sided
kernel'}, because it has to depend on two times, $t_0 < t < t_1$. We include a
detailed discussion of the identification of the Lie algebraic structure of the
symmetry algebra $\g$, and its contraction from $\su(1,1)\oplus\so(3,1)$.
| arxiv topic:math-ph math.MP quant-ph |
arxiv_dataset-67271510.08743 | Deligne--Langlands gamma factors in families
math.NT
Let F be a p-adic field, W_F its absolute Weil group, and let k be an
algebraically closed field of prime characteristic l different from p. Attached
to any l-adic representation of W_F are local epsilon- and L-factors. There are
natural notions of families of l-adic representations of W_F, such as the
theory of Galois deformations or, more generally, families over arbitrary
Noetherian W(k)-algebras. However, the epsilon and L-factors do not interpolate
well in such families. In this paper it is shown that the gamma factor, which
is the product of the epsilon factor with a ratio of L-factors, interpolates
over such families.
| arxiv topic:math.NT |
arxiv_dataset-67281510.08843 | Non-linear gauge transformations in $D=10$ SYM theory and the BCJ
duality
hep-th
Recent progress on scattering amplitudes in super Yang--Mills and superstring
theory benefitted from the use of multiparticle superfields. They universally
capture tree-level subdiagrams, and their generating series solve the
non-linear equations of ten-dimensional super Yang--Mills. We provide
simplified recursions for multiparticle superfields and relate them to earlier
representations through non-linear gauge transformations of their generating
series. In this work we discuss the gauge transformations which enforce their
Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between
color and kinematics. Another gauge transformation due to Harnad and Shnider is
shown to streamline the theta-expansion of multiparticle superfields, bypassing
the need to use their recursion relations beyond the lowest components. The
findings of this work tremendously simplify the component extraction from
kinematic factors in pure spinor superspace.
| arxiv topic:hep-th |
arxiv_dataset-67291510.08943 | MessageGuard: A Browser-based Platform for Usable, Content-Based
Encryption Research
cs.CR
This paper describes MessageGuard, a browser-based platform for research into
usable content-based encryption. MessageGuard is designed to enable
collaboration between security and usability researchers on long-standing
research questions in this area. It significantly simplifies the effort
required to work in this space and provides a place for research results to be
shared, replicated, and compared with minimal confounding factors. MessageGuard
provides ubiquitous encryption and secure cryptographic operations, enabling
research on any existing web application, with realistic usability studies on a
secure platform. We validate MessageGuard's compatibility and performance, and
we illustrate its utility with case studies for Gmail and Facebook Chat.
| arxiv topic:cs.CR |
arxiv_dataset-67301510.09043 | Nash multiplicities and resolution invariants
math.AG
The Nash multiplicity sequence was defined by M. Lejeune-Jalabert as a
non-increasing sequence of integers attached to a germ of a curve inside a germ
of a hypersurface. M. Hickel generalized this notion and described a sequence
of blow ups which allows us to compute it and study its behavior.
In this paper, we show how this sequence can be used to compute some
invariants that appear in algorithmic resolution of singularities.
| arxiv topic:math.AG |
arxiv_dataset-67311510.09143 | The rise of fully turbulent flow
physics.flu-dyn
Over a century of research into the origin of turbulence in wallbounded shear
flows has resulted in a puzzling picture in which turbulence appears in a
variety of different states competing with laminar background flow. At slightly
higher speeds the situation changes distinctly and the entire flow is
turbulent. Neither the origin of the different states encountered during
transition, nor their front dynamics, let alone the transformation to full
turbulence could be explained to date. Combining experiments, theory and
computer simulations here we uncover the bifurcation scenario organising the
route to fully turbulent pipe flow and explain the front dynamics of the
different states encountered in the process. Key to resolving this problem is
the interpretation of the flow as a bistable system with nonlinear propagation
(advection) of turbulent fronts. These findings bridge the gap between our
understanding of the onset of turbulence and fully turbulent flows.
| arxiv topic:physics.flu-dyn |
arxiv_dataset-67321511.0002 | A quadratic hypergeometric 2F1 transformation over finite fields
math.NT
In 1984, the second author conjectured a quadratic transformation formula
which relates two hypergeometric 2F1 functions over a finite field F_q. We
prove this conjecture and give an application. The proof depends on a new
linear transformation formula for pseudo hypergeometric functions over F_q.
| arxiv topic:math.NT |
arxiv_dataset-67331511.0012 | A Contraction Theory Approach for Analysis of Performance Recovery in
Dynamic Surface Control
cs.SY
Dynamic surface control (DSC) method uses high gain filters to avoid the
"explosion of complexity" issue inherent in backstepping based controller
designs. As a result, the closed loop system and filter dynamics possess time
scale separation between them. This paper attempts to design a novel
disturbance observer based dynamic surface controller using contraction
framework. In doing so the steady state error bounds are obtained in terms of
design parameters which are exploited to tune the closed loop system
performance. The results not only show that DSC technique recover the
performance of a backstepping controller for a small range of filter parameter
but also derive the maximum bound for it. Furthermore the stability bounds are
also derived in the presence of disturbances and convergence of trajectories to
a small penultimate bound is proved. The convergence results are shown to hold
for less conservative choice of filter parameter and observer gain. The
effectiveness of the proposed controller is verified through simulation
example.
| arxiv topic:cs.SY |
arxiv_dataset-67341511.0022 | Constraints on top quark flavor changing neutral currents using diphoton
events at the LHC
hep-ph
In this paper we show that the diphoton mass spectrum in proton-proton
collisions at the LHC is sensitive to the top quark flavor changing neutral
current in the vertices of $tu\gamma$ and $tc\gamma$. The diphoton mass
spectrum measured by the CMS experiment at the LHC at a center-of-mass energy
of 8 TeV and an integrated luminosity of 19.5 fb$^{-1}$ is used as an example
to set limits on these FCNC couplings. It is also shown that the angular
distribution of the diphotons is sensitive to anomalous $tu\gamma$ and
$tc\gamma$ couplings and it is a powerful tool to probe any value of the
branching fraction of top quark rare decay to an up-type quark plus a photon
down to the order of $10^{-4}$. We also show that the $tu\gamma$ FCNC coupling
has a significant contribution to the neutron electric dipole moment (EDM) and
the upper bound on neutron EDM can be used to constrain the $tu\gamma$ FCNC
coupling.
| arxiv topic:hep-ph |
arxiv_dataset-67351511.0032 | A short review on techniques for processes and process simulation of
scaffold-free tissue engineering
q-bio.QM q-bio.TO
The invention of three-dimensional printers has led to major innovations in
tissue engineering. They have enabled the printing of complex geometries such
as those that occur in natural tissues, that were not possible with traditional
manufacturing techniques. Tissue engineering in particular deals with printing
bio-compatible material that may be infused with live cells. Thus additional
complexity is incurred because the live cells can migrate and proliferate and
thus change the printed geometry. One of the important issues is the prediction
of geometry and possibly mechanical properties of the steady state tissue. In
this short review, we will provide an overview of different tissue engineering
processes that are currently available. Furthermore, we will review two
important techniques, namely, Cellular Potts Model (CPM), and Cellular Particle
Dynamics (CPD) that have been used to predict the steady state of printed
tissue.
| arxiv topic:q-bio.QM q-bio.TO |
arxiv_dataset-67361511.0042 | Bootstrapping Empirical Processes of Cluster Functionals with
Application to Extremograms
math.ST stat.ME stat.TH
In the extreme value analysis of time series, not only the tail behavior is
of interest, but also the serial dependence plays a crucial role. Drees and
Rootz\'en (2010) established limit theorems for a general class of empirical
processes of so-called cluster functionals which can be used to analyse various
aspects of the extreme value behavior of mixing time series. However, usually
the limit distribution is too complex to enable a direct construction of
confidence regions. Therefore, we suggest a multiplier block bootstrap analog
to the empirical processes of cluster functionals. It is shown that under
virtually the same conditions as used by Drees and Rootz\'en (2010),
conditionally on the data, the bootstrap processes converge to the same limit
distribution. These general results are applied to construct confidence regions
for the empirical extremogram introduced by Davis and Mikosch (2009). In a
simulation study, the confidence intervals constructed by our multiplier block
bootstrap approach compare favorably to the stationary bootstrap proposed by
Davis et al.\ (2012).
| arxiv topic:math.ST stat.ME stat.TH |
arxiv_dataset-67371511.0052 | The Strong Suslin Reciprocity Law
math.KT
We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The
Suslin reciprocity law is a generalization of the Weil reciprocity law to
higher Milnor $K-$theory. The Milnor $K-$groups can be identified with the top
cohomology groups of the polylogarithmic motivic complexes; Goncharov's
conjecture predicts the existence of a contracting homotopy underlying Suslin
reciprocity. The main ingredient of the proof is a homotopy invariance theorem
for the cohomology of the polylogarithmic motivic complexes in the "next to
Milnor" degree. We apply these results to the theory of scissors congruences of
hyperbolic polytopes. For every triple of rational functions on a compact
projective curve over $\mathbb{C}$ we construct a hyperbolic polytope (defined
up to scissors congruence). The hyperbolic volume and the Dehn invariant of
this polytope can be computed directly from the triple of rational functions on
the curve.
| arxiv topic:math.KT |
arxiv_dataset-67381511.0062 | On the so-called rogue waves in the nonlinear Schr\"odinger equation
physics.flu-dyn math-ph math.DS math.MP nlin.CD physics.ao-ph
The mechanism of a rogue water wave is still unknown. One popular conjecture
is that the Peregrine wave solution of the nonlinear Schr\"odinger equation
(NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking
the infinite spatial period limit to the homoclinic solutions. In this article,
from the perspective of the phase space structure of these homoclinic orbits in
the infinite dimensional phase space where the NLS defines a dynamical system,
we exam the observability of these homoclinic orbits (and their
approximations). Our conclusion is that these approximate homoclinic orbits are
the most observable solutions,and they should correspond to the most common
deep ocean waves rather than the rare rogue waves. We also discuss other
possibilities for the mechanism of a rogue wave: rough dependence on initial
data or finite time blow up.
| arxiv topic:physics.flu-dyn math-ph math.DS math.MP nlin.CD physics.ao-ph |
arxiv_dataset-67391511.0072 | Hypocycloidal throat for 2+1-dimensional thin-shell wormholes
gr-qc
Recently we have shown that for $2+1-$dimensional thin-shell wormholes a
non-circular throat may lead to a physical wormhole in the sense that the
energy conditions are satisfied. By the same token, herein we consider angular
dependent throat geometry embedded in a $2+1-$dimensional flat spacetime in
polar coordinates. It is shown that a generic, natural example of throat
geometry is provided remarkably by a hypocycloid. That is, two flat
$2+1-$dimensions are glued together along a hypocycloid. The energy required in
each hypocycloid increases with the frequency of the roller circle inside the
large one.
| arxiv topic:gr-qc |
arxiv_dataset-67401511.0082 | Local digital algorithms applied to Boolean models
math.PR cs.CG math.ST stat.TH
We investigate the estimation of specific intrinsic volumes of stationary
Boolean models by local digital algorithms; that is, by weighted sums of $n
\times\ldots \times n$ configuration counts. We show that asymptotically
unbiased estimators for the specific surface area or integrated mean curvature
do not exist if the dimension is at least two or three, respectively. For
3-dimensional stationary, isotropic Boolean models, we derive asymptotically
unbiased estimators for the specific surface area and integrated mean
curvature. For a Boolean model with balls as grains we even obtain an
asymptotically unbiased estimator for the specific Euler characteristic.
| arxiv topic:math.PR cs.CG math.ST stat.TH |
arxiv_dataset-67411511.0092 | A web-based IDE for IDP
cs.PL cs.AI
IDP is a knowledge base system based on first order logic. It is finding its
way to a larger public but is still facing practical challenges. Adoption of
new languages requires a newcomer-friendly way for users to interact with it.
Both an online presence to try to convince potential users to download the
system and offline availability to develop larger applications are essential.
We developed an IDE which can serve both purposes through the use of web
technology. It enables us to provide the user with a modern IDE with relatively
little effort.
| arxiv topic:cs.PL cs.AI |
arxiv_dataset-67421511.0102 | Comparing galaxy disk and star-formation properties in X-ray bright and
faint groups and clusters
astro-ph.GA
Galaxy morphologies and star-formation rates depend on environment. Galaxies
in under-dense regions are generally star-forming and disky whereas galaxies in
overdense regions tend to be early-type and not actively forming stars. The
mechanism(s) responsible for star-formation quenching and morphological
transformation remain unclear, although many processes have been proposed. We
study the dependence of star-formation and morphology on X-ray luminosity for
galaxies in Sloan Digital Sky Survey Data Release 7 (SDSS-DR7) groups and
clusters. While controlling for stellar and halo mass dependencies, we find
that galaxies in X-ray strong groups and clusters have preferentially low
star-forming and disk fractions -- with the differences being strongest at low
stellar masses. The trends that we observe do not change when considering only
galaxies found within or outside of the X-ray radius of the host group. When
considering central and satellite galaxies separately we find that this
dependence on X-ray luminosity is only present for satellites, and we show that
our results are consistent with "galaxy stangulation" as a mechanism for
quenching these satellites. We investigate the dynamics of the groups and
clusters in the sample, and find that the velocity distributions of galaxies
beyond the virial radius in low X-ray luminosity halos tend to be less Gaussian
in nature than the rest of the data set. This may be indicative of low X-ray
luminosity groups and clusters having enhanced populations of star-forming and
disk galaxies as a result of recent accretion.
| arxiv topic:astro-ph.GA |
arxiv_dataset-67431511.0112 | Metal Enrichment in the Reionization Epoch
astro-ph.GA
The presence of elements heavier than helium ("metals") is of fundamental
importance for a large number of astrophysical processes occurring in planet,
star and galaxy formation; it also affects cosmic structure formation and
evolution in several ways. Even a small amount of heavy elements can
dramatically alter the chemistry of the gas, opening the path to complex
molecules. Metals might enhance the ability of the gas to radiate away its
thermal energy, thus favoring the formation of gravitationally bound objects;
they can also condensate in a solid phase (dust grains), partly or totally
blocking radiation from luminous sources. Finally, they represent useful
tracers of energy deposition by stars and probe the physical properties of the
environment by absorption or emission lines. Last, but certainly not least,
life -- as we know it on Earth -- is tightly related to the presence of at
least some of the heavy elements. In this pedagogical review I will concentrate
on the connection between early metal enrichment and cosmic reionization. As we
will see these two processes are intimately connected and their joint study
might turn out to be fundamental in understanding the overall evolution of the
Universe during the first billion years after the Big Bang, an epoch
corresponding to redshifts z>6.
| arxiv topic:astro-ph.GA |
arxiv_dataset-67441511.0122 | Smoothing methods comparison for CMB E- and B-mode separation
astro-ph.CO
The anisotropies of the B-mode polarization in the cosmic microwave
background radiation play a crucial role for the study of the very early
Universe. However, in the real observation, the mixture of the E-mode and
B-mode can be caused by the partial sky surveys, which must be separated before
applied to the cosmological explanation. The separation method developed by
Smith (\citealt{PhysRevD.74.083002}) has been widely adopted, where the edge of
the top-hat mask should be smoothed to avoid the numerical errors. In this
paper, we compare three different smoothing methods, and investigate the
leakage residuals of the E-B mixture. We find that, if the less information
loss is needed and the smaller region is smoothed in the analysis, the
\textit{sin}- and \textit{cos}-smoothing methods are better. However, if we
need a clean constructed B-mode map, the larger region around the mask edge
should be smoothed. In this case, the \textit{Gaussian}-smoothing method
becomes much better. In addition, we find that the leakage caused by the
numerical errors in the \textit{Gaussian}-smoothing method mostly concentrates
on two bands, which is quite easy to be reduced for the further E-B
separations.
| arxiv topic:astro-ph.CO |
arxiv_dataset-67451511.0132 | Self-Induced Systems
math.DS
A minimal Cantor system is said to be self-induced whenever it is conjugate
to one of its induced systems. Substitution subshifts and some odometers are
classical examples, and we show that these are the only examples in the
equicontinuous or expansive case. Nevertheless, we exhibit a zero entropy
self-induced system that is neither equicontinuous nor expansive. We also
provide non-uniquely ergodic self-induced systems with infinite
entropy.Moreover, we give a characterization of self-induced minimal Cantor
systems in terms of substitutions on finite or infinite alphabets.
| arxiv topic:math.DS |
arxiv_dataset-67461511.0142 | Highest weight Harish-Chandra supermodules and their geometric
realizations
math.RT math-ph math.DG math.MP
In this paper we discuss the highest weight $\frak k_r$-finite
representations of the pair $(\frak g_r,\frak k_r)$ consisting of $\frak g_r$,
a real form of a complex basic Lie superalgebra of classical type $\frak g$
(${\frak g}\neq A(n,n)$), and the maximal compact subalgebra $\frak k_r$ of
$\frak g_{r,0}$, together with their geometric global realizations. These
representations occur, as in the ordinary setting, in the superspaces of
sections of holomorphic super vector bundles on the associated Hermitian
superspaces $G_r/K_r$.
| arxiv topic:math.RT math-ph math.DG math.MP |
arxiv_dataset-67471511.0152 | Reverberation Mapping with Intermediate-Band Photometry: Detection of
Broad-Line H$\alpha$ Time Lags for Quasars at $0.2<z<0.4$
astro-ph.GA
We present a reverberation mapping (RM) experiment that combines broad- and
intermediate-band photometry; it is the first such attempt targeting a sample
of 13 quasars at $0.2<z<0.9$. The quasars were selected to have strong
H$\alpha$ or H$\beta$ emission lines that are located in one of three
intermediate bands (with FWHM around 200 \AA) centered at 8045, 8505, and 9171
\AA. The imaging observations were carried out in the intermediate bands and
the broad $i$ and $z$ bands using the prime-focus imager 90Prime on the 2.3m
Bok telescope. Because of the large ($\sim$1 deg$^2$) field-of-view (FoV) of
90Prime, we were able to include the 13 quasars within only five telescope
pointings or fields. The five fields were repeatedly observed over 20--30
epochs that were unevenly distributed over a duration of 5--6 months. The
combination of the broad- and intermediate-band photometry allows us to derive
accurate light curves for both optical continuum (from the accretion disk) and
line (from the broad-line region, or BLR) emission. We detect H$\alpha$ time
lags between the continuum and line emission in 6 quasars. These quasars are at
a relatively low redshift range $0.2<z<0.4$. The measured lags are consistent
with the current BLR size-luminosity relation for H$\beta$ at $z<0.3$. While
this experiment appears successful in detecting lags of the bright H$\alpha$
line, further investigation is required to see if it can also be applied to the
fainter H$\beta$ line for quasars at higher redshifts. Finally we demonstrate
that by using a small telescope with a large FoV, intermediate-band photometric
RM can be efficiently executed for a large sample of quasars at $z>0.2$.
| arxiv topic:astro-ph.GA |
arxiv_dataset-67481511.0162 | A Method for BPS Equations of Vortices
hep-th math-ph math.MP
We develop a new method for obtaining the BPS equations of static vortices
motivated by the results of the \textit{On-Shell} method on the standard
Maxwell-Higgs model and its Born-Infeld-Higgs model~\cite{Atmaja:2014fha}. Our
method relies on the existence of what we shall call an energy function, $Q$,
which is a mere function of the (effective) fields. The total energy of BPS
vortices, $E_{BPS}$, are simply given by a difference between the boundaries
value of $Q$ at $r\to\infty$ and at $r=0$, $E_{BPS}=Q(r\to\infty)-Q(r=0)$.
Imposing a condition that these (effective) fields are independent, we may
define a BPS Lagrangian, $\mathcal{L}_{BPS}$, derived by taking integral of
differential $Q$, $\mathcal{L}_{BPS}=-\int dQ$. Matching the Lagrangian
$\mathcal{L}_{BPS}$ with the corresponding effective Lagrangian, we can extract
several equations. Solving these equations yields the desired BPS equations
and, in some cases, also constraint equations. With our method, the various
known BPS equations of vortices are derived in a relatively simple procedure.
| arxiv topic:hep-th math-ph math.MP |
arxiv_dataset-67491511.0172 | Model Based Clustering for Mixed Data: clustMD
stat.ME
A model based clustering procedure for data of mixed type, clustMD, is
developed using a latent variable model. It is proposed that a latent variable,
following a mixture of Gaussian distributions, generates the observed data of
mixed type. The observed data may be any combination of continuous, binary,
ordinal or nominal variables. clustMD employs a parsimonious covariance
structure for the latent variables, leading to a suite of six clustering models
that vary in complexity and provide an elegant and unified approach to
clustering mixed data. An expectation maximisation (EM) algorithm is used to
estimate clustMD; in the presence of nominal data a Monte Carlo EM algorithm is
required. The clustMD model is illustrated by clustering simulated mixed type
data and prostate cancer patients, on whom mixed data have been recorded.
| arxiv topic:stat.ME |
arxiv_dataset-67501511.0182 | ATP consumption of eukaryotic flagella measured at a single-cell level
physics.bio-ph cond-mat.soft q-bio.CB
The motility of cilia and flagella is driven by thousands of dynein motors
that hydrolyze adenosine triphosphate (ATP). Despite decades of genetic,
biochemical, structural and biophysical studies, some aspects of ciliary
motility remain elusive, such as the regulation of beating patterns and the
energetic efficiency of these nanomachines. Here, we introduce an experimental
method to measure ATP consumption of actively beating axonemes on a single-cell
level. We encapsulated individual sea urchin sperm with demembranated flagellum
inside water-in-oil emulsion droplets and measured the axonemes ATP consumption
by monitoring fluorescence intensity of a fluorophore-coupled reporter system
for ATP turnover in the droplet. Concomitant phase contrast imaging allowed us
to extract a linear dependence between the ATP consumption rate and the
flagellar beating frequency, with ~2.3e5 ATP molecules consumed per beat of a
demembranated flagellum. Increasing the viscosity of the aqueous medium led to
modified beating waveforms of the axonemes and to higher energy consumption per
beat cycle. Our single-cell experimental platform provides both new insights
into the beating mechanism of flagella and a powerful tool for future studies.
| arxiv topic:physics.bio-ph cond-mat.soft q-bio.CB |
arxiv_dataset-67511511.0192 | Accelerator physics and technology research toward future multi-MW
proton accelerators
physics.acc-ph
Recent P5 report indicated the accelerator-based neutrino and rare decay
physics research as a centrepiece of the US domestic HEP program. Operation,
upgrade and development of the accelerators for the near-term and longer-term
particle physics program at the Intensity Frontier face formidable challenges.
Here we discuss accelerator physics and technology research toward future
multi-MW proton accelerators.
| arxiv topic:physics.acc-ph |
arxiv_dataset-67521511.0202 | Generalized Hardy-Morrey spaces
math.FA
The generalized Morrey space was defined independetly by T. Mizuhara 1991 and
E. Nakai in 1994. Generalized Morrey space ${\mathcal M}_{p,\phi}({\mathbb
R}^n)$ is equipped with a parameter $0<p<\infty$ and a function $\phi:{\mathbb
R}^n \times (0,\infty) \to (0,\infty)$. Our experience shows that ${\mathcal
M}_{p,\phi}({\mathbb R}^n)$ is easy to handle when $1<p<\infty$. However, when
$0<p \le 1$, the function space ${\mathcal M}_{p,\phi}({\mathbb R}^n)$ is
difficult to handle as many examples show.
The aim of this paper is twofold. One of them is to propose a way to deal
with ${\mathcal M}_{p,\phi}({\mathbb R}^n)$ for $0<p \le 1$. One of them is to
propose here a way to consider the decomposition method of generalized
Hardy-Morrey spaces. We shall obtain some estimates for these spaces about the
Hardy-Littlewood maximal operator. Especially, the vector-valued estimates
obtained in the earlier papers are refined. The key tool is the weighted Hardy
operator. Much is known about the weighted Hardy operator. Another aim is to
propose here a way
to consider the decomposition method of generalized Hardy-Morrey spaces.
Generalized Hardy-Morrey spaces emerged from generalized Morrey spaces. By
means of the grand maximal operator and the norm of generalized Morrey spaces,
we can define generalized Hardy-Morrey spaces. With this culmination, we can
easily refine the existing results. In particular, our results complement the
one the 2014 paper by Iida, the third author and Tanaka; there was a mistake
there. As an application, we consider bilinear estimates, which is the \lq \lq
so-called" Olsen inequality.
| arxiv topic:math.FA |
arxiv_dataset-67531511.0212 | Classical decoherence in a nanomechanical resonator
cond-mat.mes-hall
Decoherence is an essential mechanism that defines the boundary between
classical and quantum behaviours, while imposing technological bounds for
quantum devices. Little is known about quantum coherence of mechanical systems,
as opposed to electromagnetic degrees of freedom. But decoherence can also be
thought of in a purely classical context, as the loss of phase coherence in the
classical phase space. Indeed the bridge between quantum and classical physics
is under intense investigation, using in particular classical nanomechanical
analogues of quantum phenomena. In the present work, by separating pure
dephasing from dissipation, we quantitatively model the classical decoherence
of a mechanical resonator: through the experimental control of frequency
fluctuations, we engineer artificial dephasing. Building on the fruitful
analogy introduced between spins/quantum bits and nanomechanical modes, we
report on the methods available to define pure dephasing in these systems,
while demonstrating the intrinsic almost-ideal properties of silicon-nitride
beams. These experimental and theoretical results, at the boundary between
classical nanomechanics and quantum information fields, are prerequisite in the
understanding of decoherence processes in mechanical devices, both classical
and quantum.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-67541511.0222 | Second-order cosmological perturbation theory and initial conditions for
$N$-body simulations
gr-qc astro-ph.CO
We use gauge-invariant cosmological perturbation theory to calculate the
displacement field that sets the initial conditions for $N$-body simulations.
Using first and second-order fully relativistic perturbation theory in the
synchronous-comoving gauge, allows us to go beyond the Newtonian predictions
and to calculate relativistic corrections to it. We use an Einstein--de Sitter
model, including both growing and decaying modes in our solutions. The impact
of our results should be assessed through the implementation of the featured
displacement in cosmological $N$-body simulations.
| arxiv topic:gr-qc astro-ph.CO |
arxiv_dataset-67551511.0232 | Criticality and Spin Squeezing in the Rotational Dynamics of a BEC on a
Ring Lattice
cond-mat.quant-gas
We examine the dynamics of circulating modes of a Bose-Einstein condensate
confined in toroidal lattice. Nonlinearity due to interactions leads to
criticality that separates oscillatory and self-trapped phases among
counter-propagating modes which however share the same physical space. In the
mean-field limit, the criticality is found to substantially enhance sensitivity
to rotation of the system. Analysis of the quantum dynamics reveals the
fluctuations near criticality are significant, that we explain using
spin-squeezing formalism visualized on a Bloch sphere. We utilize the squeezing
to propose a Ramsey interferometric scheme that suppresses fluctuation in the
relevant quadrature sensitive to rotation.
| arxiv topic:cond-mat.quant-gas |
arxiv_dataset-67561511.0242 | Design of an Alarm System for Isfahan Ozone Level based on Artificial
Intelligence Predictor Models
cs.AI
The ozone level prediction is an important task of air quality agencies of
modern cities. In this paper, we design an ozone level alarm system (OLP) for
Isfahan city and test it through the real word data from 1-1-2000 to 7-6-2011.
We propose a computer based system with three inputs and single output. The
inputs include three sensors of solar ultraviolet (UV), total solar radiation
(TSR) and total ozone (O3). And the output of the system is the predicted O3 of
the next day and the alarm massages. A developed artificial intelligence (AI)
algorithm is applied to determine the output, based on the inputs variables.
For this issue, AI models, including supervised brain emotional learning (BEL),
adaptive neuro-fuzzy inference system (ANFIS) and artificial neural networks
(ANNs), are compared in order to find the best model. The simulation of the
proposed system shows that it can be used successfully in prediction of major
cities ozone level.
| arxiv topic:cs.AI |
arxiv_dataset-67571511.0252 | Inertia Sets For Families of Graphs
math.CO
This paper consists of a few results, discovered and proved during the
2012-2013 research group at Eastern Oregon University. Inertia tables are a
visual representation of the possible inertias of a given graph. The inertia of
a graph counts the number of real positive and negative eigenvalues of its
corresponding adjacency matrix. The problem of studying inertia tables is
directly related to the inverse eigenvalue problem and can be used as a tool
for the minimum rank problem. This paper describes the inverse eigenvalue
problem, and tools used. We describe a number of new general formulas for
various simple undirected graphs and improved upon an established notation for
inertia tables.
| arxiv topic:math.CO |
arxiv_dataset-67581511.0262 | On the border lines between the regions of distinct solution type for
solutions of the Friedmann equation satisfying the Hubble condition
gr-qc
It is well-known that there are four distinct basic types (two Big Bang
types, Lemaitre and Big Crunch type) for solutions of the general Friedmann
equation with positive cosmological constant, where radiation and matter do not
couple (see e.g. [2, p.7]. In that paper the system of case distinction
parameters contains a "critical radiation parameter" $\sigma_{cr}$. The present
note contains the constructive description of the so-called {\em border lines}
between Big Bang/Big Crunch type and Big Bang/Lemaitre type for so-called
Hubble solutions of the Friedmann equation by two smooth function branches,
expressing the cosmological constant as unique functions of the matter and
radiation density (which is considered as a parameter). These functions satisfy
simple asymptotic relations w.r.t. the matter density. They are constructed as
the solutions of the equation $\sigma=\sigma_{cr}.
| arxiv topic:gr-qc |
arxiv_dataset-67591511.0272 | SO(10) models with flavour symmetries: Classification and examples
hep-ph
We establish the full list of flavour symmetry groups which may be enforced,
without producing any further accidental symmetry, on the Yukawa-coupling
matrices of an SO(10) Grand Unified Theory with arbitrary numbers of scalar
multiplets in the 10, $\overline{126}$, and 120 representations of SO(10). For
each of the possible discrete non-Abelian symmetry groups, we present examples
of minimal models which do not run into obvious contradiction with the
phenomenological fermion masses and mixings.
| arxiv topic:hep-ph |
arxiv_dataset-67601511.0282 | Presupernova neutrinos: realistic emissivities from stellar evolution
astro-ph.SR nucl-th
We present a new calculation of neutrino emissivities and energy spectra from
a massive star going through the advanced stages of nuclear burning
(presupernova) in the months before becoming a supernova. The contributions
from beta decay and electron capture, pair annihilation, plasmon decay, and the
photoneutrino process are modeled in detail, using updated tabulated nuclear
rates. We also use realistic conditions of temperature, density, electron
fraction and nuclear isotopic composition of the star from the state of the art
stellar evolution code MESA. Results are presented for a set of progenitor
stars with mass between 15 $M_\odot$ and 30 $M_\odot$. It is found that beta
processes contribute substantially to the neutrino emissivity above realistic
detection thresholds of few MeV, at selected positions and times in the
evolution of the star.
| arxiv topic:astro-ph.SR nucl-th |
arxiv_dataset-67611511.0292 | Enriched algebraic theories and monads for a system of arities
math.CT cs.LO math.LO
Under a minimum of assumptions, we develop in generality the basic theory of
universal algebra in a symmetric monoidal closed category $\mathcal{V}$ with
respect to a specified system of arities $j:\mathcal{J} \hookrightarrow
\mathcal{V}$. Lawvere's notion of algebraic theory generalizes to this context,
resulting in the notion of single-sorted $\mathcal{V}$-enriched
$\mathcal{J}$-cotensor theory, or $\mathcal{J}$-theory for short. For suitable
choices of $\mathcal{V}$ and $\mathcal{J}$, such $\mathcal{J}$-theories include
the enriched algebraic theories of Borceux and Day, the enriched Lawvere
theories of Power, the equational theories of Linton's 1965 work, and the
$\mathcal{V}$-theories of Dubuc, which are recovered by taking $\mathcal{J} =
\mathcal{V}$ and correspond to arbitrary $\mathcal{V}$-monads on $\mathcal{V}$.
We identify a modest condition on $j$ that entails that the
$\mathcal{V}$-category of $\mathcal{T}$-algebras exists and is monadic over
$\mathcal{V}$ for every $\mathcal{J}$-theory $\mathcal{T}$, even when
$\mathcal{T}$ is not small and $\mathcal{V}$ is neither complete nor
cocomplete. We show that $j$ satisfies this condition if and only if $j$
presents $\mathcal{V}$ as a free cocompletion of $\mathcal{J}$ with respect to
the weights for left Kan extensions along $j$, and so we call such systems of
arities eleutheric. We show that $\mathcal{J}$-theories for an eleutheric
system may be equivalently described as (i) monads in a certain one-object
bicategory of profunctors on $\mathcal{J}$, and (ii) $\mathcal{V}$-monads on
$\mathcal{V}$ satisfying a certain condition. We prove a characterization
theorem for the categories of algebras of $\mathcal{J}$-theories, considered as
$\mathcal{V}$-categories $\mathcal{A}$ equipped with a specified
$\mathcal{V}$-functor $\mathcal{A} \rightarrow \mathcal{V}$.
| arxiv topic:math.CT cs.LO math.LO |
arxiv_dataset-67621511.0302 | Co-word Maps and Topic Modeling: A Comparison Using Small and
Medium-Sized Corpora (n < 1000)
cs.DL
Induced by "big data," "topic modeling" has become an attractive alternative
to mapping co-words in terms of co-occurrences and co-absences using network
techniques. Does topic modeling provide an alternative for co-word mapping in
research practices using moderately sized document collections? We return to
the word/document matrix using first a single text with a strong argument ("The
Leiden Manifesto") and then upscale to a sample of moderate size (n = 687) to
study the pros and cons of the two approaches in terms of the resulting
possibilities for making semantic maps that can serve an argument. The results
from co-word mapping (using two different routines) versus topic modeling are
significantly uncorrelated. Whereas components in the co-word maps can easily
be designated, the topic models provide sets of words that are very differently
organized. In these samples, the topic models seem to reveal similarities other
than semantic ones (e.g., linguistic ones). In other words, topic modeling does
not replace co-word mapping in small and medium-sized sets; but the paper
leaves open the possibility that topic modeling would work well for the
semantic mapping of large sets.
| arxiv topic:cs.DL |
arxiv_dataset-67631511.0312 | The cave of Shadows. Addressing the human factor with generalized
additive mixed models
stat.AP
Generalized additive mixed models are introduced as an extension of the
generalized linear mixed model which makes it possible to deal with temporal
autocorrelational structure in experimental data. This autocorrelational
structure is likely to be a consequence of learning, fatigue, or the ebb and
flow of attention within an experiment (the `human factor'). Unlike molecules
or plots of barley, subjects in psycholinguistic experiments are intelligent
beings that depend for their survival on constant adaptation to their
environment, including the environment of an experiment. Three data sets
illustrate that the human factor may interact with predictors of interest, both
factorial and metric. We also show that, especially within the framework of the
generalized additive model, in the nonlinear world, fitting maximally complex
models that take every possible contingency into account is ill-advised as a
modeling strategy. Alternative modeling strategies are discussed for both
confirmatory and exploratory data analysis.
| arxiv topic:stat.AP |
arxiv_dataset-67641511.0322 | Di-hadron fragmentation and mapping of the nucleon structure
hep-ph hep-ex nucl-ex nucl-th
The fragmentation of a colored parton directly into a pair of colorless
hadrons is a non-perturbative mechanism that offers important insights into the
nucleon structure. Di-hadron fragmentation functions can be extracted from
semi-inclusive electron-positron annihilation data. They also appear in
observables describing the semi-inclusive production of two hadrons in
deep-inelastic scattering of leptons off nucleons or in hadron-hadron
collisions. When a target nucleon is transversely polarized, a specific
chiral-odd di-hadron fragmentation function can be used as the analyzer of the
net density of transversely polarized quarks in a transversely polarized
nucleon, the so-called transversity distribution. The latter can be extracted
through suitable single-spin asymmetries in the framework of collinear
factorization, thus in a much simpler framework with respect to the traditional
one in single-hadron fragmentation. At subleading twist, the same chiral-odd
di-hadron fragmentation function provides the cleanest access to the poorly
known twist-3 parton distribution $e(x)$, which is intimately related to the
mechanism of dynamical chiral symmetry breaking in QCD. When sensitive to
details of transverse momentum dynamics of partons, the di-hadron fragmentation
functions for a longitudinally polarized quark can be connected to the
longitudinal jet handedness to explore possible effects due to $CP-$violation
of the QCD vacuum. In this review, we outline the formalism of di-hadron
fragmentation functions, we discuss different observables where they appear and
we present measurements and future worldwide plans.
| arxiv topic:hep-ph hep-ex nucl-ex nucl-th |
arxiv_dataset-67651511.0332 | Cosmological perturbation theory with York time
gr-qc
One method to overcome the notorious problem of time in the quantisation of
gravity is the identification of a physically preferred time parameter, a
promising candidate being so-called `York time'. The dynamical equations for
matter and spatial geometry in York time may be obtained via Hamiltonian
reduction, that is, by solving the Hamiltonian constraint for the physical,
non-vanishing Hamiltonian density identified as the variable conjugate to the
chosen time parameter. Yet in general this equation cannot be solved
algebraically. Here we show how in a cosmological scenario, where one may treat
geometric and matter inhomogeneities as small perturbations, one is able to
obtain the physical Hamiltonian density by solving the constraint equation
perturbatively. By construction the Hamiltonian density is quadratic in the
perturbation variables, which makes it easily quantisable, although subtleties
arise due to the non-canonical form of the Poisson brackets and the
time-dependent coefficients. The latter are determined by the evolution of the
background variables.
| arxiv topic:gr-qc |
arxiv_dataset-67661511.0342 | Study of the ${\psi}(1S,2S)$ and ${\eta}_{c}(1S,2S)$ weak decays into
$DM$
hep-ph
Inspired by the recent measurements on the $J/{\psi}(1S)$ ${\to}$
$D_{s}{\rho}$, $D_{u}K^{\ast}$ weak decays at BESIII and the potential
prospects of the charmonium at the high-luminosity heavy-flavor experiments, we
study ${\psi}(1S,2S)$ and ${\eta}_{c}(1S,2S)$ weak decays into final states
including one charmed meson plus one light meson, considering the QCD
corrections to hadronic matrix elements with the QCD factorization. It is found
that the Cabibbo favored ${\psi}(1S,2S)$ ${\to}$ $D_{s}^{-}{\rho}^{+}$,
$D_{s}^{-}{\pi}^{+}$, $\overline{D}_{u}^{0}\overline{K}^{{\ast}0}$ decays have
branching ratios ${\gtrsim}$ $10^{-10}$, which might be accessible at the
future experiments.
| arxiv topic:hep-ph |
arxiv_dataset-67671511.0352 | Inflation with a massive vector field nonminimally coupled to gravity
gr-qc
We study the possibility that inflation is driven by a massive vector field
with SO(3) global symmetry nonminimally coupled to gravity. From an
E^3-invariant Robertson-Walker metric we propose an Ansatz for the vector
field, allowing us to study the evolution of the system. We study the behaviour
of the equations of motion using the methods of the theory of dynamical systems
and find exponential inflationary regimes.
| arxiv topic:gr-qc |
arxiv_dataset-67681511.0362 | Probing proton fluctuations with asymmetric rapidity correlations
hep-ph nucl-th
Intrinsic fluctuations of the proton saturation momentum generate asymmetric
rapidity distributions on an event-by-event basis. We argue that the asymmetric
component, $\left<a_1^2\right>$, of the orthogonal polynomial decomposition of
the two-particle rapidity correlation function is a sensitive probe to this
distribution of fluctuations. We present a simple model connecting the
experimentally measured $\left<a_1^2\right>$ to the variance, $\sigma$, of the
distribution of the logarithm of the proton saturation scale. We find that
$\sigma\approx 0. 5-1$ describes the asymmetric component of the rapidity
correlations recently measured by the ATLAS collaboration.
| arxiv topic:hep-ph nucl-th |
arxiv_dataset-67691511.0372 | A structural property of Adian inverse semigroups
math.GR
We prove that an inverse semigroup over an Adian presentation is E-unitary.
| arxiv topic:math.GR |
arxiv_dataset-67701511.0382 | Neutrino Astronomy (Rapporteur Talk)
astro-ph.HE
This report is the write-up of a rapporteur talk on neutrino astronomy given
at the 34th International Cosmic Ray Conference in The Hague, Netherlands, in
2015. Here, selected contributions on the neutrino astronomy from the total of
40 talks and 90 posters presented in NU sessions at the 34th ICRC are
summarized in the attempt of providing a status report on this rapidly glowing
new field. The field of neutrino astronomy has recently experienced a "phase
transition" since the first observation of high energy cosmic neutrinos.
Extensive efforts have been made to identify the origin of the neutrino flux
observed in the 100 TeV to PeV region, from both theoretical and experimental
perspectives. In addition, the search for neutrino fluxes beyond the observed
level has become increasingly important for further understanding the origin of
the observed cosmic-ray up to $10^{20}$ eV. Although the IceCube Neutrino
Observatory is the only experiment currently measuring this neutrino flux, its
initial measurements have been confirmed via analysis using several independent
detection channels. Further, there have been a number of developments in the
search for neutrino point sources, while no successful observations have yet
been reported. Following the IceCube observations, a large number of studies of
next-generation neutrino detectors, including up-scaled underground Cherenkov
neutrino detectors and Cherenkov radio neutrino detectors, have been reported.
| arxiv topic:astro-ph.HE |
arxiv_dataset-67711511.0392 | The Douglas-Rachford Algorithm for Weakly Convex Penalties
math.OC
The Douglas-Rachford algorithm is widely used in sparse signal processing for
minimizing a sum of two convex functions. In this paper, we consider the case
where one of the functions is weakly convex but the other is strongly convex so
that the sum is convex. We provide a condition that ensures the convergence of
the same Douglas-Rachford iterations, provided that the strongly convex
function is smooth. We also present a modified Douglas-Rachford algorithm that
does not impose a smoothness condition for the convex function. We then provide
a discussion on the convergence speed of the two types of algorithms and
demonstrate the discussion with numerical experiments.
| arxiv topic:math.OC |
arxiv_dataset-67721511.0402 | Detecting and dating structural breaks in functional data without
dimension reduction
stat.ME
Methodology is proposed to uncover structural breaks in functional data that
is "fully functional" in the sense that it does not rely on dimension reduction
techniques. A thorough asymptotic theory is developed for a fully functional
break detection procedure as well as for a break date estimator, assuming a
fixed break size and a shrinking break size. The latter result is utilized to
derive confidence intervals for the unknown break date. The main results
highlight that the fully functional procedures perform best under conditions
when analogous fPCA based estimators are at their worst, namely when the
feature of interest is orthogonal to the leading principal components of the
data. The theoretical findings are confirmed by means of a Monte Carlo
simulation study in finite samples. An application to annual temperature curves
illustrates the practical relevance of the proposed procedures.
| arxiv topic:stat.ME |
arxiv_dataset-67731511.0412 | Change Patterns for Model Creation: Investigating the Role of Nesting
Depth
cs.SE
Process model quality has been an area of considerable research efforts. In
this context, the correctness-by-construction principle of change patterns
offers a promising perspective. However, using change patterns for model
creation imposes a more structured way of modeling. While the process of
process modeling (PPM) based on change primitives has been investigated, little
is known about this process based on change patterns and factors that impact
the cognitive complexity of pattern usage. Insights from the field of cognitive
psychology as well as observations from a pilot study suggest that the nesting
depth of the model to be created has a significant impact on cognitive
complexity. This paper proposes a research design to test the impact of nesting
depth on the cognitive complexity of change pattern usage in an experiment.
| arxiv topic:cs.SE |
arxiv_dataset-67741511.0422 | Optimization techniques for multivariate least trimmed absolute
deviation estimation
math.ST stat.CO stat.TH
Given a dataset an outlier can be defined as an observation that it is
unlikely to follow the statistical properties of the majority of the data.
Computation of the location estimate of is fundamental in data analysis, and it
is well known in statistics that classical methods, such as taking the sample
average, can be greatly affected by the presence of outliers in the data. Using
the median instead of the mean can partially resolve this issue but not
completely. For the univariate case, a robust version of the median is the
Least Trimmed Absolute Deviation (LTAD) robust estimator introduced
in~\cite{Tableman1994}, which has desirable asymptotic properties such as
robustness, consistently, high breakdown and normality. There are different
generalizations of the LTAD for multivariate data, depending on the choice of
norm. In~\cite{ChaPitZiou:2015} we present such a generalization using the
Euclidean norm and propose a solution technique for the resulting combinatorial
optimization problem, based on a necessary condition, that results in a highly
convergent local search algorithm. In this subsequent work we use the $L^1$
norm to generalize the LTAD to higher dimensions, and show that the resulting
mixed integer programming problem has an integral relaxation, after applying an
appropriate data transformation. Moreover, we utilize the structure of the
problem to show that the resulting LP's can be solved efficiently using a
subgradient optimization approach. The robust statistical properties of the
proposed estimator are verified by extensive computational results.
| arxiv topic:math.ST stat.CO stat.TH |
arxiv_dataset-67751511.0432 | Standard methods for inexpensive pollen loads authentication by means of
computer vision and machine learning
cs.CV
We present a complete methodology for authenticating local bee pollen against
fraudulent samples using image processing and machine learning techniques. The
proposed standard methods do not need expensive equipment such as advanced
microscopes and can be used for a preliminary fast rejection of unknown pollen
types. The system is able to rapidly reject the non-local pollen samples with
inexpensive hardware and without the need to send the product to the
laboratory. Methods are based on the color properties of bee pollen loads
images and the use of one-class classifiers which are appropriate to reject
unknown pollen samples when there is limited data about them. The validation of
the method is carried out by authenticating Spanish bee pollen types.
Experimentation shows that the proposed methods can obtain an overall
authentication accuracy of 94%. We finally illustrate the user interaction with
the software in some practical cases by showing the developed application
prototype.
| arxiv topic:cs.CV |
arxiv_dataset-67761511.0442 | Thermodynamic resource theories, non-commutativity and maximum entropy
principles
quant-ph
We discuss some features of thermodynamics in the presence of multiple
conserved quantities. We prove a generalisation of Landauer principle
illustrating tradeoffs between the erasure costs paid in different
"currencies". We then show how the maximum entropy and complete passivity
approaches give different answers in the presence of multiple observables. We
discuss how this seems to prevent current resource theories from fully
capturing thermodynamic aspects of non-commutativity.
| arxiv topic:quant-ph |
arxiv_dataset-67771511.0452 | On Transiso Graphs of Groups of order less than 32
math.GR
Transiso graph $\Gamma_d(G)$ is defined in for a finite group $G$ and a
divisor $d$ of $|G|$. In the present paper, we have determined some finite
groups $G$ for which the graphs $\Gamma_d(G)$ are complete for each divisor $d$
of $|G|$. We have also discussed the completeness of transiso graphs for the
groups of order less than $32$.
| arxiv topic:math.GR |
arxiv_dataset-67781511.0462 | Homogenization via unfolding in domains separated by the thin layer of
the thin beams
math.AP
We consider a thin heterogeneous layer consisted of the thin beams (of radius
$r$) and we study the limit behaviour of this problem as the periodicity
$\varepsilon$, the thickness $\delta$ and the radius $r$ of the beams tend to
zero. The decomposition of the displacement field in the beams developed in
[Griso, Decompositions of displacements of thin structures, 2008] is used,
which allows to obtain a priori estimates. Two types of the unfolding operators
are introduced to deal with the different parts of the decomposition. In
conclusion we obtain the limit problem together with the transmission
conditions across the interface.
| arxiv topic:math.AP |
arxiv_dataset-67791511.0472 | On some series formed by values of the Riemann Zeta function
math.CV math.NT
The partial fraction expansion of coth($\pi$z), due to Euler, is generalized
to power series having for coefficients the Riemann zeta function evaluated at
certain arithmetic sequences. A further generalization using arbitrary
Dirichlet series is also proposed. The resulting formulas are new, as far as we
know, since they could not be found in any of the classical or recent handbooks
of formulas that were at our disposal.
| arxiv topic:math.CV math.NT |
arxiv_dataset-67801511.0482 | On the ferromagnetic ground state of SmN
cond-mat.mtrl-sci
SmN is a ferromagnetic semiconductor with the unusual property of an
orbital-dominant magnetic moment that is largely cancelled by an antiparallel
spin contribution, resulting in a near-zero net moment. However, there is a
basic gap in the understanding of the ferromagnetic ground state, with existing
density functional theory calculations providing values of the $4f$ magnetic
moments at odds with experimental data. To clarify the situation, we employ an
effective $4f$ Hamiltonian incorporating spin-orbit coupling, exchange, the
crystal field, and $J$-mixing to calculate the ground state $4f$ moments. Our
results are in excellent agreement with experimental data, revealing moderate
quenching of both spin and orbital moments to magnitudes of $\sim 2~\mu_B$ in
bulk SmN, enhanced to an average of $\sim 3~\mu_B$ in SmN layers within a
SmN/GdN superlattice. These calculations provide insight into recent studies of
SmN showing that it is an unconventional superconductor at low temperatures and
displays twisted magnetization phases in magnetic heterostructures.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-67811511.0492 | Atmospheric effects of stellar cosmic rays on Earth-like exoplanets
orbiting M-dwarfs
astro-ph.EP
M-dwarf stars are generally considered favourable for rocky planet detection.
However, such planets may be subject to extreme conditions due to possible high
stellar activity. The goal of this work is to determine the potential effect of
stellar cosmic rays on key atmospheric species of Earth-like planets orbiting
in the habitable zone of M-dwarf stars and show corresponding changes in the
planetary spectra. We build upon the cosmic rays model scheme of Grenfell et
al. (2012), who considered cosmic ray induced NOx production, by adding further
cosmic ray induced production mechanisms (e.g. for HOx) and introducing primary
protons of a wider energy range (16 MeV - 0.5 TeV). Previous studies suggested
that planets in the habitable zone that are subject to strong flaring
conditions have high atmospheric methane concentrations, while their ozone
biosignature is completely destroyed. Our current study shows, however, that
adding cosmic ray induced HOx production can cause a decrease in atmospheric
methane abundance of up to 80\%. Furthermore, the cosmic ray induced HOx
molecules react with NOx to produce HNO$_3$, which produces strong HNO$_3$
signals in the theoretical spectra and reduces NOx-induced catalytic
destruction of ozone so that more than 25\% of the ozone column remains. Hence,
an ozone signal remains visible in the theoretical spectrum (albeit with a
weaker intensity) when incorporating the new cosmic ray induced NOx and HOx
schemes, even for a constantly flaring M-star case. We also find that HNO$_3$
levels may be high enough to be potentially detectable. Since ozone
concentrations, which act as the key shield against harmful UV radiation, are
affected by cosmic rays via NOx-induced catalytic destruction of ozone, the
impact of stellar cosmic rays on surface UV fluxes is also studied.
| arxiv topic:astro-ph.EP |
arxiv_dataset-67821511.0502 | The Kelmans-Seymour conjecture I: special separations
math.CO
Seymour and, independently, Kelmans conjectured in the 1970s that every
5-connected nonplanar graph contains a subdivision of $K_5$. This conjecture
was proved by Ma and Yu for graphs containing $K_4^-$, and an important step in
their proof is to deal with a 5-separation in the graph with a planar side. In
order to establish the Kelmans-Seymour conjecture for all graphs, we need to
consider 5-separations and 6-separations with less restrictive structures. The
goal of this paper is to deal with special 5-separations and 6-separations,
including those with an apex side. Results will be used in subsequent papers to
prove the Kelmans-Seymour conjecture.
| arxiv topic:math.CO |
arxiv_dataset-67831511.0512 | Loop-Erased Random Surfaces
math.PR math-ph math.AT math.CO math.MP
Loop-erased random walk and it's scaling limit, Schramm--Loewner evolution,
have found numerous applications in mathematics and physics. We present a 2
dimensional analogue of LERW, the loop erased random surface. We do this by
defining a 2 dimensional spanning tree and declaring that LERS should have the
same relation to these 2 trees as LERW has to ordinary spanning trees.
Furthermore we present numerical evidence that the growth rate for LERS on a
$\delta$ fine grid as $\delta \to 0$ is $2.5269 \pm 0.0017$ and we hypothesize
that it has an exact value of 48/19. This suggests the possibility of a fractal
limiting object for LERS analogous to SLE for LERW.
| arxiv topic:math.PR math-ph math.AT math.CO math.MP |
arxiv_dataset-67841511.0522 | Rainbow Valley of Colored (Anti) de Sitter Gravity in Three Dimensions
hep-th gr-qc
We propose a theory of three-dimensional (anti) de Sitter gravity carrying
Chan-Paton color charges. We define the theory by Chern-Simons formulation with
the gauge algebra $(\mathfrak{gl}_{2}\oplus \mathfrak{gl}_{2})\otimes
\mathfrak{u}(N)$, obtaining a color-decorated version of interacting spin-one
and spin-two fields. We also describe the theory in metric formulation and show
that, among $N^{2}$ massless spin-two fields, only the singlet one plays the
role of metric graviton whereas the rest behave as \emph{colored spinning
matter} that strongly interacts at large $N$. Remarkably, these \emph{colored
spinning matter} acts as Higgs field and generates a non-trivial potential of
staircase shape. At each extremum labelled by $k = 0, \ldots, [\frac{N-1}2]$,
the $\mathfrak{u}(N)$ color gauge symmetry is spontaneously broken down to
$\mathfrak{u}(N-k)\oplus \mathfrak{u}(k)$ and provides different (A)dS
backgrounds with the cosmological constants
$\big(\frac{N}{N-2k}\big)^{2}\,\L$\,. When this symmetry breaking takes place,
the spin-two Goldstone modes combine with (or are eaten by) the spin-one gauge
fields to become partially-massless spin-two fields. We discuss various aspects
of this theory and highlight physical implications.
| arxiv topic:hep-th gr-qc |
arxiv_dataset-67851511.0532 | Multiple Transitions of Coupled Atom-Molecule Bosonic Mixtures in Two
Dimensions
cond-mat.quant-gas cond-mat.stat-mech
Motivated by the physics of coherently coupled, ultracold atom-molecule
mixtures, we investigate a classical model possessing the same symmetry --
namely a $U(1)\times \mathbb{Z}_2$ symmetry, associated with the mass
conservation in the mixture ($U(1)$ symmetry), times the $\mathbb{Z}_2$
symmetry in the phase relationship between atoms and molecules. In two spatial
dimensions the latter symmetry can lead to a finite-temperature Ising
transition, associated with (quasi) phase locking between the atoms and the
molecules. On the other hand, the $U(1)$ symmetry has an associated
Berezinskii-Kosterlitz-Thouless (BKT) transition towards quasi-condensation of
atoms or molecules. The existence of the two transitions is found to depend
crucially on the population imbalance (or detuning) between atoms and
molecules: when the molecules are majority in the system, their BKT
quasi-condensation transition occurs at a higher temperature than that of the
atoms; the latter has the unconventional nature of an Ising (quasi)
phase-locking transition, lacking a finite local order parameter below the
critical temperature. When the balance is gradually biased towards the atoms,
the two transitions merge together to leave out a unique BKT transition, at
which both atoms and molecules acquire quasi-long-range correlations, but only
atoms exhibit conventional BKT criticality, with binding of vortex-antivortex
pairs into short-range dipoles. The molecular vortex-antivortex excitations
bind as well, but undergo a marked crossover from a high-temperature regime in
which they are weakly bound, to a low-temperature regime of strong binding,
reminiscent of their transition in the absence of atom-molecule coupling.
| arxiv topic:cond-mat.quant-gas cond-mat.stat-mech |
arxiv_dataset-67861511.0542 | A static spherically symmetric thin shell wormhole colliding with a
spherical thin shell
gr-qc
We consider a static spherically symmetric thin shell wormhole collides with
another thin shell consisting of ordinary matter. By employing the geometrical
constraint, which leads to the conservation of energy and momentum, we show
that the state after the collision can be solved from the initial data. In the
low speed approximation, the solutions are rather simple. The shell may either
bounce back or pass through the wormhole. In either case, the wormhole shrinks
right after the collision. In the "bouncing" case, a surprising result is that
the radial speeds before and after the collision satisfy an addition law, which
is independent of the masses of the wormhole and the shell. Once the shell
passes through the wormhole, we find that the shell always expands. However,
the expansion rate is the same as its collapsing rate right before the
collision. Finally, we find out the solution for the shell moving together with
the wormhole.
| arxiv topic:gr-qc |
arxiv_dataset-67871511.0552 | Automatic Instrument Recognition in Polyphonic Music Using Convolutional
Neural Networks
cs.SD cs.IR cs.LG cs.NE
Traditional methods to tackle many music information retrieval tasks
typically follow a two-step architecture: feature engineering followed by a
simple learning algorithm. In these "shallow" architectures, feature
engineering and learning are typically disjoint and unrelated. Additionally,
feature engineering is difficult, and typically depends on extensive domain
expertise.
In this paper, we present an application of convolutional neural networks for
the task of automatic musical instrument identification. In this model, feature
extraction and learning algorithms are trained together in an end-to-end
fashion. We show that a convolutional neural network trained on raw audio can
achieve performance surpassing traditional methods that rely on hand-crafted
features.
| arxiv topic:cs.SD cs.IR cs.LG cs.NE |
arxiv_dataset-67881511.0562 | External Photoevaporation of the Solar Nebula II: Effects on Disk
Structure and Evolution with Non-Uniform Turbulent Viscosity due to the
Magnetorotational Instability
astro-ph.EP
The structure and evolution of protoplanetary disks, especially the radial
flows of gas through them, are sensitive to a number of factors. One that has
been considered only occasionally in the literature is external
photoevaporation by far-ultraviolet (FUV) radiation from nearby, massive stars,
despite the fact that nearly half of all disks will experience
photoevaporation. Another effect apparently not considered in the literature is
a spatially and temporally varying value of $\alpha$ in the disk [where the
turbulent viscosity $\nu$ is $\alpha$ times the sound speed C times the disk
scale height H]. Here we use the formulation of Bai \& Stone (2011) to relate
$\alpha$ to the ionization fraction in the disk, assuming turbulent transport
of angular momentum is due to the magnetorotational instability. We find that
disk evolution is most sensitive to the surface area of dust. Typically $\alpha
\lesssim 10^{-5}$ in the inner disk ($< 2$ AU), rising to $\sim 10^{-1}$ beyond
20 AU. This drastically alters the structure of the disk and the flow of mass
through it: while the outer disk rapidly viscously spreads, the inner disk
hardly evolves; this leads to a steep surface density profile with a slope < p
> $\approx$ 2 - 5 in the 5-30 AU region) that is made steeper by external
photoevaporation. We also find that the combination of variable $\alpha$ and
external photoevaporation eventually causes gas as close as 3 AU, previously
accreting inward, to be drawn outward to the photoevaporated outer edge of the
disk. These effects have drastic consequences for planet formation and volatile
transport in protoplanetary disks.
| arxiv topic:astro-ph.EP |
arxiv_dataset-67891511.0572 | Online learning in repeated auctions
cs.GT cs.LG stat.ML
Motivated by online advertising auctions, we consider repeated Vickrey
auctions where goods of unknown value are sold sequentially and bidders only
learn (potentially noisy) information about a good's value once it is
purchased. We adopt an online learning approach with bandit feedback to model
this problem and derive bidding strategies for two models: stochastic and
adversarial. In the stochastic model, the observed values of the goods are
random variables centered around the true value of the good. In this case,
logarithmic regret is achievable when competing against well behaved
adversaries. In the adversarial model, the goods need not be identical and we
simply compare our performance against that of the best fixed bid in hindsight.
We show that sublinear regret is also achievable in this case and prove
matching minimax lower bounds. To our knowledge, this is the first complete set
of strategies for bidders participating in auctions of this type.
| arxiv topic:cs.GT cs.LG stat.ML |
arxiv_dataset-67901511.0582 | Generalizing Coordinate Non Commutativity
physics.gen-ph
In this paper, we establish and employ a local framework to the first order
of Riemann's curvature tensor in order to develop the corresponding coordinate
non commutativity into general manifolds. We also exploit a new translation of
function at the level of quantum mechanics to show that the final correlation
result of the generalized non commutativity is a mixture of the Canonical and
Quadratic formalisms and does not consist only of the Lie algebraic formalism.
The basic premise of this article is that the geometry of a four-dimensional
pseudo Riemann manifold representing space time, is homeomorphic to Minkowski
space time.
| arxiv topic:physics.gen-ph |
arxiv_dataset-67911511.0592 | Two-body problem in general relativity: A heuristic guide for the
Einstein-Rosen bridge and EPR paradox
physics.hist-ph
Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution
and the singularity within it while working in Princeton on the unified field
theory and with his assistant Nathan Rosen, on the theory of the Einstein-Rosen
bridges. He was also occupied with quantum theory. He believed that quantum
theory was an incomplete representation of real things. Together with Rosen and
Boris Podolsky he invented the EPR paradox. I demonstrate that the two-body
problem in general relativity was a heuristic guide in Einstein's and
collaborators' 1935 work on the Einstein-Rosen bridge and EPR paradox.
| arxiv topic:physics.hist-ph |
arxiv_dataset-67921511.0602 | A First Szeg\H{o}'s Limit Theorem for a class of non-Toeplitz matrices
math.SP
We compute the limiting statistical distribution of the eigenvalues of
sequences of matrices whose entries satisfy what we call a vanishing mean
variation condition and are $\mu$-distributed for some probability measure. As
an application of our results, we extend the well-known class of
Kac-Murdock-Szeg\H{o} generalized Toeplitz matrices to sequences of matrices
whose diagonal entries are modeled by Riemann integrable functions.
| arxiv topic:math.SP |
arxiv_dataset-67931511.0612 | The Kernel Two-Sample Test for Brain Networks
stat.ML
In clinical and neuroscientific studies, systematic differences between two
populations of brain networks are investigated in order to characterize mental
diseases or processes. Those networks are usually represented as graphs built
from neuroimaging data and studied by means of graph analysis methods. The
typical machine learning approach to study these brain graphs creates a
classifier and tests its ability to discriminate the two populations. In
contrast to this approach, in this work we propose to directly test whether two
populations of graphs are different or not, by using the kernel two-sample test
(KTST), without creating the intermediate classifier. We claim that, in
general, the two approaches provides similar results and that the KTST requires
much less computation. Additionally, in the regime of low sample size, we claim
that the KTST has lower frequency of Type II error than the classification
approach. Besides providing algorithmic considerations to support these claims,
we show strong evidence through experiments and one simulation.
| arxiv topic:stat.ML |
arxiv_dataset-67941511.0622 | Numerical simulation of the transient aerodynamic phenomena induced by
passing manoeuvres
physics.flu-dyn
Several three-dimensional Unsteady Reynolds-Averaged Navier-Stokes (URANS)
simulations of the passing generic vehicles (Ahmed bodies) are presented. The
relative motion of vehicles was obtained using a combination of deforming and
sliding computational grids. The vehicle studied is an Ahmed body with an angle
of the rear end slanted surface of $30^{\circ}$. Several different relative
velocities and transversal distances between vehicles were studied. The
aerodynamic influence of the passage on the overtaken vehicle was studied. The
results of the simulations were found to agree well with the existing
experimental data. Numerical results were used to explain effects of the
overtaking manoeuvre on the main aerodynamic coefficients.
| arxiv topic:physics.flu-dyn |
arxiv_dataset-67951511.0632 | Intragroup transfers, intragroup diversification and their risk
assessment
q-fin.RM math.PR
When assessing group solvency, an important question is to what extent
intragroup transfers may be considered, as this determines to which extent
diversification can be achieved. We suggest a framework to describe the
families of admissible transfers that range from the free movement of capital
to excluding any transactions. The constraints on admissible transactions are
described as random closed sets. The paper focuses on the corresponding
solvency tests that amount to the existence of acceptable selections of the
random sets of admissible transactions.
| arxiv topic:q-fin.RM math.PR |
arxiv_dataset-67961511.0642 | Skip-Thought Memory Networks
cs.NE cs.CL cs.LG
Question Answering (QA) is fundamental to natural language processing in that
most nlp problems can be phrased as QA (Kumar et al., 2015). Current weakly
supervised memory network models that have been proposed so far struggle at
answering questions that involve relations among multiple entities (such as
facebook's bAbi qa5-three-arg-relations in (Weston et al., 2015)). To address
this problem of learning multi-argument multi-hop semantic relations for the
purpose of QA, we propose a method that combines the jointly learned long-term
read-write memory and attentive inference components of end-to-end memory
networks (MemN2N) (Sukhbaatar et al., 2015) with distributed sentence vector
representations encoded by a Skip-Thought model (Kiros et al., 2015). This
choice to append Skip-Thought Vectors to the existing MemN2N framework is
motivated by the fact that Skip-Thought Vectors have been shown to accurately
model multi-argument semantic relations (Kiros et al., 2015).
| arxiv topic:cs.NE cs.CL cs.LG |
arxiv_dataset-67971511.0652 | Asymptotic error distributions of the Euler method for continuous-time
nonlinear filtering
math.PR
We deduce the asymptotic error distribution of the Euler method for the
nonlinear filtering problem with continuous-time observations. Previous works
by several authors have shown that the error structure of the method is
characterized by conditional expectations of some functionals of multiple
stochastic integrals. Our main result is a proof of the stable convergence of a
sequence of such conditional expectations, using the technique of martingale
limit theorems in the spirit of Jacod.
| arxiv topic:math.PR |
arxiv_dataset-67981511.0662 | Use of Eigenvector Centrality to Detect Graph Isomorphism
cs.SI cs.DM cs.DS
Graph Isomorphism is one of the classical problems of graph theory for which
no deterministic polynomial-time algorithm is currently known, but has been
neither proven to be NP-complete. Several heuristic algorithms have been
proposed to determine whether or not two graphs are isomorphic (i.e.,
structurally the same). In this research, we propose to use the sequence
(either the non-decreasing or nonincreasing order) of eigenvector centrality
(EVC) values of the vertices of two graphs as a precursor step to decide
whether or not to further conduct tests for graph isomorphism. The eigenvector
centrality of a vertex in a graph is a measure of the degree of the vertex as
well as the degrees of its neighbors. We hypothesize that if the non-increasing
(or non-decreasing) order of listings of the EVC values of the vertices of two
test graphs are not the same, then the two graphs are not isomorphic. If two
test graphs have an identical non-increasing order of the EVC sequence, then
they are declared to be potentially isomorphic and confirmed through additional
heuristics. We test our hypothesis on random graphs (generated according to the
Erdos-Renyi model) and we observe the hypothesis to be indeed true: graph pairs
that have the same sequence of non-increasing order of EVC values have been
confirmed to be isomorphic using the well-known Nauty software.
| arxiv topic:cs.SI cs.DM cs.DS |
arxiv_dataset-67991511.0672 | Renormalisation group for multiple zeta values
math.NT
Calculating multiple zeta values at arguments of any sign in a way that is
compatible with both the quasi-shuffle product as well as meromorphic
continuation, is commonly referred to as the renormalisation problem for
multiple zeta values. We consider the set of all solutions to this problem and
provide a framework for comparing its elements in terms of a free and
transitive action of a particular subgroup of the group of characters of the
quasi-shuffle Hopf algebra. In particular, this provides a transparent way of
relating different solutions at non-positive values, which answers an open
question in the recent literature.
| arxiv topic:math.NT |
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