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We introduce canonical correlation forests (CCFs), a new decision tree
ensemble method for classification and regression. Individual canonical
correlation trees are binary decision trees with hyperplane splits based on
local canonical correlation coefficients calculated during training. Unlike
axis-aligned alternatives, the decision surfaces of CCFs are not restricted to
the coordinate system of the inputs features and therefore more naturally
represent data with correlated inputs. CCFs naturally accommodate multiple
outputs, provide a similar computational complexity to random forests, and
inherit their impressive robustness to the choice of input parameters. As part
of the CCF training algorithm, we also introduce projection bootstrapping, a
novel alternative to bagging for oblique decision tree ensembles which
maintains use of the full dataset in selecting split points, often leading to
improvements in predictive accuracy. Our experiments show that, even without
parameter tuning, CCFs out-perform axis-aligned random forests and other
state-of-the-art tree ensemble methods on both classification and regression
problems, delivering both improved predictive accuracy and faster training
times. We further show that they outperform all of the 179 classifiers
considered in a recent extensive survey.
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The Wu invariant is a regular homotopy invariant for immersions of oriented
3-manifolds into the 5-space. In this paper, we present new expressions and
vanishing theorems for the invariant, from the viewpoint of almost contact
structures and complex tangents. As an application, we determine the regular
homotopy classes of inclusion maps of the surface singularity links of type ADE
into the 5-sphere.
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Bribery in an election is one of the well-studied control problems in
computational social choice. In this paper, we propose and study the safe
bribery problem. Here the goal of the briber is to ask the bribed voters to
vote in such a way that the briber never prefers the original winner (of the
unbribed election) more than the new winner, even if the bribed voters do not
fully follow the briber's advice. Indeed, in many applications of bribery,
campaigning for example, the briber often has limited control on whether the
bribed voters eventually follow her recommendation and thus it is conceivable
that the bribed voters can either partially or fully ignore the briber's
recommendation. We provide a comprehensive complexity theoretic landscape of
the safe bribery problem for many common voting rules in this paper.
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We give a new conceptual proof of the classification of cuspidal modules for
the solenoidal Lie algebra. This classification was originally published by
Y.Su. Our proof is based on the theory of modules for the solenoidal Lie
algebras that admit a compatible action of the commutative algebra of functions
on a torus.
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Results of experiments on the dynamics and kinetic roughening of
one-dimensional slow-combustion fronts in three grades of paper are reported.
Extensive averaging of the data allows a detailed analysis of the spatial and
temporal development of the interface fluctuations. The asymptotic scaling
properties, on long length and time scales, are well described by the
Kardar-Parisi-Zhang (KPZ) equation with short-range, uncorrelated noise. To
obtain a more detailed picture of the strong-coupling fixed point,
characteristic of the KPZ universality class, universal amplitude ratios, and
the universal coupling constant are computed from the data and found to be in
good agreement with theory. Below the spatial and temporal scales at which a
cross-over takes place to the standard KPZ behavior, the fronts display higher
apparent exponents and apparent multiscaling. In this regime the interface
velocities are spatially and temporally correlated, and the distribution of the
magnitudes of the effective noise has a power-law tail. The relation of the
observed short-range behavior and the noise as determined from the local
velocity fluctuations is discussed.
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The Thomson effect induces heat release or absorption under the simultaneous
application of a charge current and a temperature gradient to conductors. Here,
we theoretically investigate the temperature profile due to the
Thomson-effect-induced heat release/absorption in junctionless single
conductors which can be a simple temperature modulator. We also perform
analysis of the temperature profile for realistic conductors. As a result, we
find that, for a conductor with a large Thomson coefficient, the temperature
derivative of the Seebeck coefficient, the Thomson-effect-induced heat
absorption overcomes the Joule heating, resulting in current-induced cooling in
the bulk region. We also elucidate that a feedback effect of the Thomson effect
stabilizes the system temperature to one-side of the heat bath, which reflects
the fact that the Thomson effect is dependent on the position and proportional
to the local temperature gradient. This work will be the basis for thermal
management utilizing the Thomson effect.
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Transverse momentum spectra of charged particles including pions, kaons and
(anti-)protons measured by ALICE experiment in the pT range of 0.1-2.5 GeV/c
and pseudorapidity less than 0.5 are studied in pp collisions at 900 GeV center
of mass energy using modified Hagedorn function with embedded transverse flow
velocity and are compared to the predictions of EPOS-LHC, Pythia, QGSJET and
Sibyll models. We find that the average transverse flow velocity decreases with
increasing the mass of the particle while the kinetic freeze-out temperature
extracted from the function increases with the particle's mass. The former
varies from 0.36 c to 0.25 c for pions to protons while the latter from 76 MeV
to 95 MeV respectively. The fit of the models predictions also yield the same
values for T0 and beta as the experimental data. The only difference is in the
values of n, and N0 which yields different values for different models. The
EPOS-LHC, Pythia, and QGSJET models reproduce the data in most of the pT range
for pions, EPOS-LHC and Sibyll for kaons up to 1.5 GeV/c and EPOS-LHC for
protons up to 1.6 GeV/c. The model simulations also reproduced the behavior of
increasing average transverse momentum with mass reported by the ALICE
experiment.
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LHCb Collaboration studied the resonant structure of $B_s\to
\overline{D}^0K^-\pi^+$ decays using the Dalitz plot analysis technique, based
on a data sample corresponding to an integrated luminosity of $3.0{\rm
fb}^{-1}$ of $pp$ collision. The $K^-\pi^+$ components have been analyzed in
the amplitude model, where the decay amplitude is modeled to be the resonant
contributions with respect to the intermediate resonances $K^*(892)$,
$K_0^*(1430)$ and $K_2^*(1430)$. Motivated by the experimental results, we
investigate the color-favored quasi-two-body $B \to \overline{D}^0K\pi$ decays
in the framework of the perturbative QCD (PQCD) approach. We calculate the the
branching fractions by introducing the appropriate wave functions of $K\pi$
pair. Our results are in agreement well the available data, and others can be
tested in LHCb and Belle-II experiments. Using the narrow-width-approximation,
we also extract the branching fractions of the corresponding two-body $B\to
\overline D R$ decays, which agree to the previous theoretical calculations and
the experimental data within the errors. There are no $CP$ asymmetries in these
decays in the standard model, because these decays are all governed by only the
tree operators.
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The binodals and the non-ergodicity lines of a binary mixture of hard
sphere-like particles with large size ratio are computed for studying the
interplay between dynamic arrest and phase separation in depletion-driven
colloidal mixtures. Contrarily to the case of hard core plus short range
effective attraction, physical gellation without competition with the
fluid-phase separation can occur in such mixtures. This behavior due to the
oscillations in the depletion potential should concern all simple mixtures with
non-ideal depletant, justifying further studies of their dynamic properties.
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Lately, network sampling proved as a promising tool for simplifying large
real-world networks and thus providing for their faster and more efficient
analysis. Still, understanding the changes of network structure and properties
under different sampling methods remains incomplete. In this paper, we analyze
the presence of characteristic group of nodes (i.e., communities, modules and
mixtures of the two) in social and information networks. Moreover, we observe
the changes of node group structure under two sampling methods, random node
selection based on degree and breadth-first sampling. We show that the sampled
information networks contain larger number of mixtures than original networks,
while the structure of sampled social networks exhibits stronger
characterization by communities. The results also reveal there exist no
significant differences in the behavior of both sampling methods. Accordingly,
the selection of sampling method impact on the changes of node group structure
to a much smaller extent that the type and the structure of analyzed network.
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We report the independent discovery of PSR J0027-1956 with the Murchison
Widefield Array (MWA) in the ongoing Southern-sky MWA Rapid Two-meter (SMART)
pulsar survey. J0027-1956 has a period of ~1.306 s, a dispersion measure (DM)
of ~20.869 pc cm^-3 , and a nulling fraction of ~77%. This pulsar highlights
the advantages of the survey's long dwell times (~80 min), which, when fully
searched, will be sensitive to the expected population of similarly bright,
intermittent pulsars with long nulls. A single-pulse analysis in the MWA's
140-170 MHz band also reveals a complex sub-pulse drifting behavior, including
both rapid changes of the drift rate characteristic of mode switching pulsars,
as well as a slow, consistent evolution of the drift rate within modes. In some
longer drift sequences, interruptions in the otherwise smooth drift rate
evolution occur preferentially at a particular phase, typically lasting a few
pulses. These properties make this pulsar an ideal test bed for prevailing
models of drifting behavior such as the carousel model.
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Grid-interfacing inverters act as the interface between renewable resources
and the electric grid, and have the potential to offer fast and programmable
controls compared to synchronous generators. With this flexibility there has
been significant research efforts into determining the best way to control
these inverters. Inverters are limited in their maximum current output in order
to protect semiconductor devices, presenting a nonlinear constraint that needs
to be accounted for in their control algorithms. Existing approaches either
simply saturate a controller that is designed for unconstrained systems, or
assume small perturbations and linearize a saturated system. These approaches
can lead to stability issues or limiting the control actions to be too
conservative.
In this paper, we directly focus on a nonlinear system that explicitly
accounts for the saturation of the current magnitude. We use a Lyapunov
stability approach to determine a stability condition for the system,
guaranteeing that a class of controllers would be stabilizing if they satisfy a
simple SDP condition. With this condition we fit a linear-feedback controller
by sampling the output (offline) model predictive control problems. This
learned controller has improved performances with existing designs.
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We grow strained Ge/SiGe heterostructures by reduced-pressure chemical vapor
deposition on 100 mm Ge wafers. The use of Ge wafers as substrates for epitaxy
enables high-quality Ge-rich SiGe strain-relaxed buffers with a threading
dislocation density of (6$\pm$1)$\times$10$^5$ cm$^{-2}$, nearly an order of
magnitude improvement compared to control strain-relaxed buffers on Si wafers.
The associated reduction in short-range scattering allows for a drastic
improvement of the disorder properties of the two-dimensional hole gas,
measured in several Ge/SiGe heterostructure field-effect transistors. We
measure an average low percolation density of (1.22$\pm$0.03)$\times$10$^{10}$
cm$^{-2}$, and an average maximum mobility of (3.4$\pm$0.1)$\times$10$^{6}$
cm$^2$/Vs and quantum mobility of (8.4$\pm$0.5)$\times$10$^{4}$ cm$^2$/Vs when
the hole density in the quantum well is saturated to
(1.65$\pm$0.02)$\times$10$^{11}$ cm$^{-2}$. We anticipate immediate application
of these heterostructures for next-generation, higher-performance Ge
spin-qubits and their integration into larger quantum processors.
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We study some convergence issues for a recent approach to the problem of
transparent boundary conditions for the Helmholtz equation in unbounded
domains. The approach is based on the minimization on an integral functional
which arises from an integral formulation of the radiation condition at
infinity. In this Letter, we implement a Fourier-Chebyschev collocation method
and show that this approach reduce the computational cost significantly. As a
consequence, we give numerical evidence of some convergence estimates available
in literature and we study the robustness of the algorithm at low and mid-high
frequencies.
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In this paper, given a reflexive real Banach space X and two sequentially
weakly lower semicontinuous functionals Phi, Psi on X with Psi strongly
continuous and coercive, we are mainly interested in the existence of
infinitely many local minima of the functional capital Phi + r Psi for each
sufficiently real r.
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We exploit the many-body self-consistent Green's function method to analyze
finite-temperature properties of infinite nuclear matter and to explore the
behavior of the thermal index used to simulate thermal effects in equations of
state for astrophysical applications. We show how the thermal index is both
density and temperature dependent, unlike often considered, and we provide an
error estimate based on our ${\it ab~initio}$ calculations. The inclusion of
many-body forces is found to be critical for the density dependence of the
thermal index. We also compare our results to a parametrization in terms of the
density dependence of the nucleon effective mass. Our study questions the
validity of predictions made for the gravitational-wave signal from
neutron-star merger simulations with a constant thermal index.
|
The synthesis of stoichiometric and epitaxial pyrochlore iridate thin films
presents significant challenges yet is critical for unlocking experimental
access to novel topological and magnetic states. Towards this goal, we unveil
an in-situ two-stage growth mechanism that facilitates the synthesis of
high-quality oriented pyrochlore iridate thin films. The growth starts with the
deposition of a pyrochlore titanate as an active iso-structural template,
followed by the application of an in-situ solid phase epitaxy technique in the
second stage to accomplish the formation of single crystalline, large-area
films. This novel protocol ensures the preservation of stoichiometry and
structural homogeneity, leading to a marked improvement in surface and
interface qualities over previously reported methods. The success of this
synthesis approach is attributed to the application of directional laser-heat
annealing, which effectively reorganizes the continuous random network of ions
into a crystalline structure, as evidenced by our comprehensive analysis of the
growth kinetics. This new synthesis approach advances our understanding of
pyrochlore iridate film fabrication and opens a new perspective for
investigating their unique physical properties.
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The scission kinetics of bottle-brush molecules in solution and on an
adhesive substrate is modeled by means of Molecular Dynamics simulation with
Langevin thermostat. Our macromolecules comprise a long flexible polymer
backbone with $L$ segments, consisting of breakable bonds, along with two side
chains of length $N$, tethered to each segment of the backbone. In agreement
with recent experiments and theoretical predictions, we find that bond cleavage
is significantly enhanced on a strongly attractive substrate even though the
chemical nature of the bonds remains thereby unchanged.
We find that the mean bond life time $<\tau>$ decreases upon adsorption by
more than an order of magnitude even for brush molecules with comparatively
short side chains $N=1 \div 4$. The distribution of scission probability along
the bonds of the backbone is found to be rather sensitive regarding the
interplay between length and grafting density of side chains. The life time
$<\tau>$ declines with growing contour length $L$ as $<\tau>\propto L^{-0.17}$,
and with side chain length as $<\tau>\propto N^{-0.53}$. The probability
distribution of fragment lengths at different times agrees well with
experimental observations. The variation of the mean length $L(t)$ of the
fragments with elapsed time confirms the notion of the thermal degradation
process as a first order reaction.
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Observations of Halpha emission measures and pulsar dispersion measures at
high Galactic latitude (|b| > 10 deg) provide information about the density and
distribution of the diffuse warm ionized medium (WIM). The diffuse WIM has a
lognormal distribution of EM sin |b|, which is consistent with a density
structure established by isothermal turbulence. The H+ responsible for most of
the emission along high-EM sin |b| sightlines is clumped in high density (> 0.1
cm^{-3}) regions that occupy only a few parsecs along the line of sight, while
the H+ along low-EM sightlines occupies hundreds of parsecs with considerably
lower densities.
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We present a novel optimised design for a source of cold atomic cadmium,
compatible with continuous operation and potentially quantum degenerate gas
production. The design is based on spatially segmenting the first and
second-stages of cooling with the the strong dipole-allowed $^1$S$_0$-$^1$P$_1$
transition at 229 nm and the 326 nm $^1$S$_0$-$^3$P$_1$ intercombination
transition, respectively. Cooling at 229 nm operates on an effusive atomic beam
and takes the form of a compact Zeeman slower ($\sim$5 cm) and two-dimensional
magneto-optical trap (MOT), both based on permanent magnets. This design allows
for reduced interaction time with the photoionising 229 nm photons and produces
a slow beam of atoms that can be directly loaded into a three-dimensional MOT
using the intercombination transition. The efficiency of the above process is
estimated across a broad range of experimentally feasible parameters via use of
a Monte Carlo simulation, with loading rates up to 10$^8$ atoms/s into the 326
nm MOT possible with the oven at only 100 $^\circ$C. The prospects for further
cooling in a far-off-resonance optical-dipole trap and atomic launching in a
moving optical lattice are also analysed, especially with reference to the
deployment in a proposed dual-species cadmium-strontium atom interferometer.
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The edge isoperimetric inequality in the discrete cube specifies, for each
pair of integers $m$ and $n$, the minimum size $g_n(m)$ of the edge boundary of
an $m$-element subset of $\{0,1\}^{n}$; the extremal families (up to
automorphisms of the discrete cube) are initial segments of the lexicographic
ordering on $\{0,1\}^n$. We show that for any $m$-element subset $\mathcal{F}
\subset \{0,1\}^n$ and any integer $l$, if the edge boundary of $\mathcal{F}$
has size at most $g_n(m)+l$, then there exists an extremal family $\mathcal{G}
\subset \{0,1\}^n$ such that $|\mathcal{F} \Delta \mathcal{G}| \leq Cl$, where
$C$ is an absolute constant. This is best-possible, up to the value of $C$. Our
result can be seen as a `stability' version of the edge isoperimetric
inequality in the discrete cube, and as a discrete analogue of the seminal
stability result of Fusco, Maggi and Pratelli concerning the isoperimetric
inequality in Euclidean space.
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Angular momentum evolution in low-mass stars is determined by initial
conditions during star formation, stellar structure evolution, and the
behaviour of stellar magnetic fields. Here we show that the empirical picture
of angular momentum evolution arises naturally if rotation is related to
magnetic field strength instead of to magnetic flux, and formulate a corrected
braking law based on this. Angular momentum evolution then becomes a strong
function of stellar radius, explaining the main trends observed in open
clusters and field stars at a few Gyr: the steep transition in rotation at the
boundary to full convection arises primarily from the large change in radius
across this boundary, and does not require changes in dynamo mode or field
topology. Additionally, the data suggest transient core-envelope decoupling
among solar-type stars, and field saturation at longer periods in very low-mass
stars. For solar-type stars, our model is also in good agreement with the
empirical Skumanich law. Finally, in further support of the theory, we show
that the predicted age at which low-mass stars spin down from the saturated to
unsaturated field regimes in our model corresponds remarkably well to the
observed lifetime of magnetic activity in these stars.
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We study the classical dynamics of the collinear positron-hydrogen scattering
system below the three-body breakup threshold. Observing the chaotic behavior
of scattering time signals, we in- troduce a code system appropriate to a
coarse grained description of the dynamics. And, for the purpose of systematic
analysis of the phase space structure, a surface of section is introduced being
chosen to match the code system. Partition of the surface of section leads us
to a surprising conjec- ture that the topological structure of the phase space
of the system is invariant under exchange of the dynamical variables of proton
with those of positron. It is also found that there is a finite set of
forbidden patterns of symbol sequences. And the shortest periodic orbit is
found to be stable, around which invariant tori form an island of stability in
the chaotic sea. Finally we discuss a possible quantum manifestation of the
classical phase space structure relevant to resonances in scattering cross
sections.
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We introduce a renormalized Jellium model to calculate the equation of state
for charged colloidal suspensions. An almost perfect agreement with Monte Carlo
simulations is found. Our self-consistent approach naturally allows to define
the effective charge of particles {\em at finite colloidal density}. Although
this quantity may differ significantly from its counterpart obtained from the
standard Poisson-Boltzmann cell approach, the osmotic pressures for both models
are in good agreement. We argue that by construction, the effective charge
obtained using the Jellium approximation is more appropriate to the study of
colloidal interactions. We also discuss a possibility of a fluid-fluid critical
point and show how the new equation of state can be used to shed light on the
surprising results found in recent sedimentation experiments.
|
The nitrogen-vacancy (NV) center is a promising candidate to realize
practical quantum sensors with high sensitivity and high spatial resolution,
even at room temperature and atmospheric pressure. In conventional
high-frequency AC magnetometry with NV centers, the setup requires a pulse
sequence with an appropriate time synchronization and strong microwave power.
To avoid these practical difficulties, AC magnetic field sensing using
continuous-wave opticallydetected magnetic resonance (CW-ODMR) was recently
demonstrated. That previous study utilized radio frequency (RF) dressed states
generated by the coherent interaction between the electron spin of the NV
center and the RF wave. However, the drawback of this method is that the
detectable frequency of the AC magnetic fields is fixed. Here, we propose and
demonstrate frequency-tunable magnetic field sensing based on CW-ODMR. In the
new sensing scheme, we obtain RF double-dressed states by irradiation with a RF
field at two different frequencies. One creates the RF dressed states and
changes the frequency of the target AC field. The other is a target AC field
that induces a change in the CW-ODMR spectrum by generating the RF
double-dressed states through coherent interaction with the RF dressed states.
The sensitivity of our method is estimated to be comparable to or even higher
than that of the conventional method based on a RF field with a single
frequency. The estimated bandwidth is 7.45 MHz, higher than that of the
conventional method using the RF dressed states. Our frequency-tunable magnetic
field sensor based on CW-ODMR paves the way for new applications in diamond
devices.
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In this paper, we study distributed channel triggering mechanisms for
wireless networked control systems (WNCSs) for conventional and smart sensors,
i.e., sensors without and with computational power, respectively. We first
consider the case of conventional sensors in which the state estimate is
performed based on the intermittent raw measurements received from the sensor
and we show that the priority measure is associated with the statistical
properties of the observations, as it is the case of the cost of information
loss (CoIL) [1]. Next, we consider the case of smart sensors and despite the
fact that CoIL can also be deployed, we deduce that it is more beneficial to
use the available measurements and we propose a function of the value of
information (VoI) [2], [3] that also incorporates the channel conditions as the
priority measure. The different scenarios and priority measures are discussed
and compared for simple scenarios via simulations.
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The response of oxide thin films to polar discontinuities at interfaces and
surfaces has generated an enormous activity due to the variety of interesting
effects it gives rise to. A case in point is the discovery of the electron gas
at the interface between LaAlO3 and SrTiO3, which has since been shown to be
quasi-two-dimensional, switchable, magnetic and/or superconducting. Despite
these findings, the origin of the two-dimensional electron gas is highly
debated and several possible mechanisms remain. Here we review the main
proposed mechanisms and attempt to model expected effects in a quantitative way
with the ambition of better constraining what effects can/cannot explain the
observed phenomenology. We do it in the framework of a phenomenological model
for understanding electronic and/or redox screening of the chemical charge in
oxide heterostructures. We also discuss the effect of intermixing, both
conserving and non-conserving the total stoichiometry.
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In this article we study linear complementarity problem with hidden
$Z$-matrix. We extend the results of Fiedler and Pt{\'a}k for the linear system
in complementarity problem using game theoretic approach. We establish a result
related to singular hidden $Z$-matrix. We show that for a non-degenerate
feasible basis, linear complementarity problem with hidden $Z$-matrix has
unique non-degenerate solution under some assumptions. The purpose of this
paper is to study some properties of hidden $Z$-matrix.
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Using methods from coarse topology we show that fundamental classes of closed
enlargeable manifolds map non-trivially both to the rational homology of their
fundamental groups and to the K-theory of the corresponding reduced
C*-algebras. Our proofs do not depend on the Baum--Connes conjecture and
provide independent confirmation for specific predictions derived from this
conjecture.
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Data reuse is a common practice in the social sciences. While published data
play an essential role in the production of social science research, they are
not consistently cited, which makes it difficult to assess their full scholarly
impact and give credit to the original data producers. Furthermore, it can be
challenging to understand researchers' motivations for referencing data. Like
references to academic literature, data references perform various rhetorical
functions, such as paying homage, signaling disagreement, or drawing
comparisons. This paper studies how and why researchers reference social
science data in their academic writing. We develop a typology to model
relationships between the entities that anchor data references, along with
their features (access, actions, locations, styles, types) and functions
(critique, describe, illustrate, interact, legitimize). We illustrate the use
of the typology by coding multidisciplinary research articles (n=30)
referencing social science data archived at the Inter-university Consortium for
Political and Social Research (ICPSR). We show how our typology captures
researchers' interactions with data and purposes for referencing data. Our
typology provides a systematic way to document and analyze researchers'
narratives about data use, extending our ability to give credit to data that
support research.
|
Category theory has been successfully applied in various domains of science,
shedding light on universal principles unifying diverse phenomena and thereby
enabling knowledge transfer between them. Applications to machine learning have
been pursued recently, and yet there is still a gap between abstract
mathematical foundations and concrete applications to machine learning tasks.
In this paper we introduce DisCoPyro as a categorical structure learning
framework, which combines categorical structures (such as symmetric monoidal
categories and operads) with amortized variational inference, and can be
applied, e.g., in program learning for variational autoencoders. We provide
both mathematical foundations and concrete applications together with
comparison of experimental performance with other models (e.g., neuro-symbolic
models). We speculate that DisCoPyro could ultimately contribute to the
development of artificial general intelligence.
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We prove a general result concerning cyclic orderings of the elements of a
matroid. For each matroid $M$, weight function
$\omega:E(M)\rightarrow\mathbb{N}$, and positive integer $D$, the following are
equivalent. (1) For all $A\subseteq E(M)$, we have $\sum_{a\in A}\omega(a)\le
D\cdot r(A)$. (2) There is a map $\phi$ that assigns to each element $e$ of
$E(M)$ a set $\phi(e)$ of $\omega(e)$ cyclically consecutive elements in the
cycle $(1,2,...,D)$ so that each set $\{e|i\in\phi(e)\}$, for $i=1,...,D$, is
independent.
As a first corollary we obtain the following. For each matroid $M$ so that
$|E(M)|$ and $r(M)$ are coprime, the following are equivalent. (1) For all
non-empty $A\subseteq E(M)$, we have $|A|/r(A)\le|E(M)|/r(M)$. (2) There is a
cyclic permutation of $E(M)$ in which all sets of $r(M)$ cyclically consecutive
elements are bases of $M$. A second corollary is that the circular arboricity
of a matroid is equal to its fractional arboricity.
These results generalise classical results of Edmonds, Nash-Williams and
Tutte on covering and packing matroids by bases and graphs by spanning trees.
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We prove that the volumes determined by the lengths of the non-zero vectors
$\pm\vecx$ in a random lattice L of covolume 1 define a stochastic process
that, as the dimension n tends to infinity, converges weakly to a Poisson
process on the positive real line with intensity 1/2. This generalizes earlier
results by Rogers and Schmidt.
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We perform a systematic search for long-term extreme variability quasars
(EVQs) in the overlapping Sloan Digital Sky Survey (SDSS) and 3-Year Dark
Energy Survey (DES) imaging, which provide light curves spanning more than 15
years. We identified ~1000 EVQs with a maximum g band magnitude change of more
than 1 mag over this period, about 10% of all quasars searched. The EVQs have
L_bol~10^45-10^47 erg/s and L/L_Edd~0.01-1. Accounting for selection effects,
we estimate an intrinsic EVQ fraction of ~30-50% among all g<~22 quasars over a
baseline of ~15 years. These EVQs are good candidates for so-called
"changing-look quasars", where a spectral transition between the two types of
quasars (broad-line and narrow-line) is observed between the dim and bright
states. We performed detailed multi-wavelength, spectral and variability
analyses for the EVQs and compared to their parent quasar sample. We found that
EVQs are distinct from a control sample of quasars matched in redshift and
optical luminosity: (1) their UV broad emission lines have larger equivalent
widths; (2) their Eddington ratios are systematically lower; and (3) they are
more variable on all timescales. The intrinsic difference in quasar properties
for EVQs suggest that internal processes associated with accretion are the main
driver for the observed extreme long-term variability. However, despite their
different properties, EVQs seem to be in the tail of a continuous distribution
of quasar properties, rather than standing out as a distinct population. We
speculate that EVQs are normal quasars accreting at relatively low accretion
rates, where the accretion flow is more likely to experience instabilities that
drive the factor of few changes in flux on multi-year timescales.
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A topological mechanism is a zero elastic-energy deformation of a mechanical
structure that is robust against smooth changes in system parameters. Here, we
map the nonlinear elasticity of a paradigmatic class of topological mechanisms
onto linear fermionic models using a supersymmetric field theory introduced by
Witten and Olive. Heuristically, this approach consists of taking the square
root of a non-linear Hamiltonian and generalizes the standard procedure of
obtaining two copies of Dirac equation from the square root of the linear Klein
Gordon equation. Our real space formalism goes beyond topological band theory
by incorporating non-linearities and spatial inhomogeneities, such as domain
walls, where topological states are typically localized. By viewing the two
components of the real fermionic field as site and bond displacements
respectively, we determine the relation between the supersymmetry
transformations and the Bogomolny-Prasad-Sommerfield (BPS) bound saturated by
the mechanism. We show that the mechanical constraint, which enforces a BPS
saturated kink into the system, simultaneously precludes an anti-kink. This
mechanism breaks the usual kink-antikink symmetry and can be viewed as a
manifestation of the underlying supersymmetry being half-broken.
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The paper continues previous works which study the behavior of second
correlation function of characteristic polynomials of the special case of
$n\times n$ one-dimensional Gaussian Hermitian random band matrices, when the
covariance of the elements is determined by the matrix
$J=(-W^2\triangle+1)^{-1}$. Applying the transfer matrix approach, we study the
case when the bandwidth $W$ is proportional to the threshold $\sqrt{n}$
|
A search for the decay of the Standard Model Higgs boson into a $b\bar{b}$
pair when produced in association with a $W$ or $Z$ boson is performed with the
ATLAS detector. The analysed data, corresponding to an integrated luminosity of
36.1 fb$^{-1}$, were collected in proton-proton collisions in Run 2 of the
Large Hadron Collider at a centre-of-mass energy of 13 TeV. Final states
containing zero, one and two charged leptons (electrons or muons) are
considered, targeting the decays $Z\to\nu\nu$, $W\to\ell\nu$ and
$Z\to\ell\ell$. For a Higgs boson mass of 125 GeV, an excess of events over the
expected background from other Standard Model processes is found with an
observed significance of 3.5 standard deviations, compared to an expectation of
3.0 standard deviations. This excess provides evidence for the Higgs boson
decay into $b$-quarks and for its production in association with a vector
boson. The combination of this result with that of the Run 1 analysis yields a
ratio of the measured signal events to the Standard Model expectation equal to
$0.90 \pm 0.18 \rm{(stat.)} ^{+0.21}_{-0.19} \rm{(syst.)}$. Assuming the
Standard Model production cross-section, the results are consistent with the
value of the Yukawa coupling to $b$-quarks in the Standard Model.
|
We present a modification of the standard halo model with the goal of
providing an improved description of galaxy clustering. Recent surveys, like
the Sloan Digital Sky Survey (SDSS) and the Anglo-Australian Two-degree survey
(2dF), have shown that there seems to be a correlation between the clustering
of galaxies and their properties such as metallicity and star formation rate,
which are believed to be environment-dependent. This environmental dependence
is not included in the standard halo model where the host halo mass is the only
variable specifying galaxy properties. In our approach, the halo properties
i.e., the concentration, and the Halo Occupation Distribution --HOD--
prescription, will not only depend on the halo mass (like in the standard halo
model) but also on the halo environment. We examine how different environmental
dependence of halo concentration and HOD prescription affect the correlation
function. We see that at the level of dark matter, the concentration of haloes
affects moderately the dark matter correlation function only at small scales.
However the galaxy correlation function is extremely sensitive to the HOD
details, even when only the HOD of a small fraction of haloes is modified.
|
Higher cluster categories were recently introduced as a generalization of
cluster categories.
This paper shows that in Dynkin types A and D, half of all higher cluster
categories are actually just quotients of cluster categories. The other half
can be obtained as quotients of 2-cluster categories, the "lowest" type of
higher cluster categories.
Hence, in Dynkin types A and D, all higher cluster phenomena are implicit in
cluster categories and 2-cluster categories. In contrast, the same is not true
in Dynkin type E.
|
In 1957, Hadwiger made the famous conjecture that any convex body of
$n$-dimensional Euclidean space $\mathbb{E}^n$ can be covered by $2^n$ smaller
positive homothetic copies. Up to now, this conjecture is still open for all
$n\geq 3$. Denote by $\gamma_{m}(K)$ the smallest positive number $\lambda$
such that $K$ can be covered by $m$ translations of $\lambda K$. The values of
$\gamma_m(K)$ for some particular $m$ and $K$ have been studied. In this
article, we will focus on the situation where $K$ is the unit crosspolytope of
the three-dimensional.
|
Any one measurement with polarized light makes it possible to fix the Mueller
matrices of the Lorentz type with up to four arbitrary numeric parameters (x,
u; z, w). These parameters are subject to the quadratic condition. It is
demonstrated that the quadratic form can be diagonalized; in the case of
partially polarized light four diagonal coefficients turn out to benon-zero and
positive; in the case of completely polarized light two diagonal coefficients
equal to zero.
|
In this paper we proposed two new quasi-boundary value methods for
regularizing the ill-posed backward heat conduction problems. With a standard
finite difference discretization in space and time, the obtained all-at-once
nonsymmetric sparse linear systems have the desired block $\omega$-circulant
structure, which can be utilized to design an efficient parallel-in-time (PinT)
direct solver that built upon an explicit FFT-based diagonalization of the time
discretization matrix. Convergence analysis is presented to justify the optimal
choice of the regularization parameter. Numerical examples are reported to
validate our analysis and illustrate the superior computational efficiency of
our proposed PinT methods.
|
Protein-stabilised emulsions can be seen as mixtures of unadsorbed proteins
and of protein-stabilised droplets. To identify the contributions of these two
components to the overall viscosity of sodium caseinate o/w emulsions, the
rheological behaviour of pure suspensions of proteins and droplets were
characterised, and their properties used to model the behaviour of their
mixtures. These materials are conveniently studied in the framework developed
for soft colloids. Here, the use of viscosity models for the two types of pure
suspensions facilitates the development of a semi-empirical model that relates
the viscosity of protein-stabilised emulsions to their composition.
|
Despite their exceptional performance on various tasks after fine-tuning,
pre-trained language models (PLMs) face significant challenges due to growing
privacy concerns with data in centralized training methods. We consider
federated learning (FL) to fine-tune PLMs in this paper. However, the
substantial number of parameters in PLMs poses significant difficulties for
client devices with limited communication and computational resources. One
promising solution is to exploit parameter-efficient fine-tuning (PEFT) into
FL, which trains a much smaller set of parameters than full parameter
fine-tuning (FFT). Although remarkably improving training efficiency, PEFT
methods may lead to degraded performance especially when data across different
clients are non i.i.d, as revealed by experimental results. To overcome this,
we propose FeDeRA, which extends and improves a widely used PEFT method, i.e.,
low-rank adaption (LoRA). FeDeRA follows LoRA by decomposing the weight
matrices of the PLMs into low-rank matrices, which allows for more efficient
computation and parameter updates during fine-tuning. Different from LoRA which
simply initializes these low-rank matrices by random sampling or zeros, the
proposed FeDeRA initializes these matrices by the results of performing
singular value decomposition (SVD) on the pre-trained weight matrices.
Extensive experiments across various tasks and datasets show that FeDeRA
outperforms the considered PEFT baselines and is comparable to or even
surpasses FFT method within the FL setting in terms of task performance.
Moreover, FeDeRA requires only 1% trainable paramentes compared to FFT,
significantly reducing training time costs by more than 90% to achieve the same
task performance level. The experimental results also highlight the robustness
of FeDeRA against data heterogeneity, as it maintains stable task performance
even as data heterogeneity increases.
|
We generalize the effective field theory of single clock inflation to include
dissipative effects. Working in unitary gauge we couple a set of composite
operators in the effective action which is constrained solely by invariance
under time-dependent spatial diffeomorphisms. We restrict ourselves to
situations where the degrees of freedom responsible for dissipation do no
contribute to the density perturbations at late time. The dynamics of the
perturbations is then modified by the appearance of `friction' and noise terms,
and assuming certain locality properties for the Green's functions of these
composite operators, we show that there is a regime characterized by a large
friction term \gamma >> H in which the \zeta-correlators are dominated by the
noise and the power spectrum can be significantly enhanced. We also compute the
three point function <\zeta\zeta\zeta> for a wide class of models and discuss
under which circumstances large friction leads to an increased level of
non-Gaussianities. In particular, under our assumptions, we show that strong
dissipation together with the required non-linear realization of the symmetries
implies |f_NL| ~ \gamma/(c_s^2H) >> 1. As a paradigmatic example we work out a
variation of the `trapped inflation' scenario with local response functions and
perform the matching with our effective theory. A detection of the generic type
of signatures that result from incorporating dissipative effects during
inflation, as we describe here, would teach us about the dynamics of the early
universe and also extend the parameter space of inflationary models.
|
Simplicial toric stack bundles are smooth Deligne-Mumford stacks over smooth
varieties with fibre a toric Deligne-Mumford stack. We compute the Grothendieck
$K$-theory of simplicial toric stack bundles and study the Chern character
homomorphism.
|
This note is the sequel to [A note on secondary K-theory. Algebra and Number
Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of
noncommutative motives, we prove that the canonical map from the derived Brauer
group to the secondary Grothendieck ring has the following injectivity
properties: in the case of a regular integral quasi-compact quasi-separated
scheme, it is injective; in the case of an integral normal Noetherian scheme
with a single isolated singularity, it distinguishes any two derived Brauer
classes whose difference is of infinite order. As an application, we show that
the canonical map is injective in the case of affine cones over smooth
projective plane complex curves of degree greater than or equal to four as well
as in the case of Mumford's (celebrated) singular surface.
|
Monocular depth estimation is a challenging problem on which deep neural
networks have demonstrated great potential. However, depth maps predicted by
existing deep models usually lack fine-grained details due to the convolution
operations and the down-samplings in networks. We find that increasing input
resolution is helpful to preserve more local details while the estimation at
low resolution is more accurate globally. Therefore, we propose a novel depth
map fusion module to combine the advantages of estimations with
multi-resolution inputs. Instead of merging the low- and high-resolution
estimations equally, we adopt the core idea of Poisson fusion, trying to
implant the gradient domain of high-resolution depth into the low-resolution
depth. While classic Poisson fusion requires a fusion mask as supervision, we
propose a self-supervised framework based on guided image filtering. We
demonstrate that this gradient-based composition performs much better at noisy
immunity, compared with the state-of-the-art depth map fusion method. Our
lightweight depth fusion is one-shot and runs in real-time, making our method
80X faster than a state-of-the-art depth fusion method. Quantitative
evaluations demonstrate that the proposed method can be integrated into many
fully convolutional monocular depth estimation backbones with a significant
performance boost, leading to state-of-the-art results of detail enhancement on
depth maps.
|
Evert and Helton proved that real free spectrahedra are the matrix convex
hulls of their absolute extreme points. However, this result does not extend to
complex free spectrahedra, and we examine multiple ways in which the analogous
result can fail. We also develop some local techniques to determine when matrix
convex sets are not (duals of) free spectrahedra, as part of a continued study
of minimal and maximal matrix convex sets and operator systems. These results
apply to both the real and complex cases.
|
Recently, decentralized optimization over the Stiefel manifold has attacked
tremendous attentions due to its wide range of applications in various fields.
Existing methods rely on the gradients to update variables, which are not
applicable to the objective functions with non-smooth regularizers, such as
sparse PCA. In this paper, to the best of our knowledge, we propose the first
decentralized algorithm for non-smooth optimization over Stiefel manifolds. Our
algorithm approximates the non-smooth part of objective function by its Moreau
envelope, and then existing algorithms for smooth optimization can be deployed.
We establish the convergence guarantee with the iteration complexity of
$\mathcal{O} (\epsilon^{-4})$. Numerical experiments conducted under the
decentralized setting demonstrate the effectiveness and efficiency of our
algorithm.
|
The new complete orthonormal sets of -Laguerre type polynomials (-LTP,) are
suggested. Using Schr\"odinger equation for complete orthonormal sets of
-exponential type orbitals (-ETO) introduced by the author, it is shown that
the origin of these polynomials is the centrally symmetric potential which
contains the core attraction potential and the quantum frictional potential of
the field produced by the particle itself. The quantum frictional forces are
the analog of radiation damping or frictional forces suggested by Lorentz in
classical electrodynamics. The new -LTP are complete without the inclusion of
the continuum states of hydrogen like atoms. It is shown that the nonstandard
and standard conventions of -LTP and their weight functions are the same. As an
application, the sets of infinite expansion formulas in terms of -LTP and
L-Generalized Laguerre polynomials (L-GLP) for atomic nuclear attraction
integrals of Slater type orbitals (STO) and Coulomb-Yukawa like correlated
interaction potentials (CIP) with integer and noninteger indices are obtained.
The arrange and rearranged power series of a general power function are also
investigated. The convergence of these series is tested by calculating concrete
cases for arbitrary values of parameters of orbitals and power function.
|
A stream of new theta relations is obtained. They follow from the general
Thomae formula, which is a new result giving expressions for theta derivatives
(the zero values of the lowest non-vanishing derivatives of theta functions
with singular half-period characteristics) in terms of branch points and the
period matrix of a hyperelliptic Riemann surface. The new theta relations
contain (i) linear relations on the vector space of first order theta
derivatives which are arranged in gradients, (ii) relations between second
order theta derivatives and symmetric bilinear forms on the vector space of the
gradients, (iii) relations between third order theta derivatives and symmetric
trilinear forms on the vector space of the gradients, and (iv) a conjecture
regarding higher order theta derivatives. It is shown how the Schottky identity
(in the hyperelliptic case) is derived from the obtained relations.
|
We investigate the charge-detection-induced dephasing of a charge qubit
interacting with an electronic beam collider composed of a quantum point
contact. We report that, while the qubit is dephased by the partitioned beam of
uncorrelated electrons, the interference of the qubit is fully restored when
the two inputs are identically biased so that all the electrons suffer
two-electron collision. This phenomenon is related to Fermi statistics and
illustrates the peculiar nonlocality of dephasing. We also describe detection
properties for the injection of entangled electron pairs.
|
This study introduces a new approach to power analysis in the context of
estimating a local average treatment effect (LATE), where the study subjects
exhibit noncompliance with treatment assignment. As a result of distributional
complications in the LATE context, compared to the simple ATE context, there is
currently no standard method of power analysis for the LATE. Moreover, existing
methods and commonly used substitutes - which include instrumental variable
(IV), intent-to-treat (ITT), and scaled ATE power analyses - require specifying
generally unknown variance terms and/or rely upon strong and unrealistic
assumptions, thus providing unreliable guidance on the power of tests of the
LATE. This study develops a new approach that uses standardized effect sizes to
place bounds on the power for the most commonly used estimator of the LATE, the
Wald IV estimator, whereby variance terms and distributional parameters need
not be specified nor assumed. Instead, in addition to the effect size, sample
size, and error tolerance parameters, the only other parameter that must be
specified by the researcher is the compliance rate. Additional conditions can
also be introduced to further narrow the bounds on the power calculation. The
result is a generalized approach to power analysis in the LATE context that is
simple to implement.
|
We use solvable two-dimensional gauge theories to illustrate the issues in
relating large N gauge theory to string theory. We also give an introduction to
recent mathematical work which allows constructing master fields for higher
dimensional large N theories. We illustrate this with a new derivation of the
Hopf equation governing the evolution of the spectral density in matrix quantum
mechanics. Based on lectures given at the 1994 Trieste Spring School on String
Theory, Gauge Theory and Quantum Gravity.
|
This note describes an application of the theory of generalised Burnside
rings to algebraic representation theory. Tables of marks are given explicitly
for the groups $S_4$ and $S_5$ which are of particular interest in the context
of reductive algebraic groups. As an application, the base sets for the
nilpotent element $F_4 (a_3)$ are computed.
|
Compact groups (CGs) of galaxies are defined as isolated and dense galaxy
systems that appear to be a unique site of multiple galaxy interactions.
Semi-analytical models of galaxy formation (SAMs) are a prime tool to
understand CGs. We investigate how the frequency and the three-dimensional
nature of CGs depends on the SAM and its underlying cosmological parameters.
Extracting 9 lightcones of galaxies from 5 different SAMs and selecting CGs as
in observed samples, we find that the frequency and nature of CGs depends
strongly on the cosmological parameters. Moving from the WMAP1 to the WMAP7 and
Planck cosmologies (increasing density of the Universe and decreasing
normalisation of the power spectrum), the space density of CGs is decreased by
a factor 2.5, while the fraction of CGs that are physically dense falls from 50
to 35 percent. The lower $\sigma_8$ leads to fewer dense groups, while the
higher $\Omega_{\rm m}$ causes more chance alignments. However, with increased
mass and spatial resolution, the fraction of CGs that are physically dense is
pushed back up to 50 percent. The intrinsic differences in the SAM recipes also
lead to differences in the frequency and nature of CGs, particularly those
related to how SAMs treat orphan galaxies. We find no dependence of CG
properties on the flux limit of the mock catalogues nor on the waveband in
which galaxies are selected. One should thus be cautious when interpreting a
particular SAM for the frequency and nature of CGs.
|
In this work, we provide some novel results that establish both the existence
of Henig global proper efficient points and their density in the efficient set
for vector optimization problems in arbitrary normed spaces. Our results do not
require the assumption of convexity, and in certain cases, can be applied to
unbounded sets. However, it is important to note that a weak compactness
condition on the set (or on a section of it) and a separation property between
the order cone and its conical neighborhoods remains necessary. The weak
compactness condition ensures that certain convergence properties hold. The
separation property enables the interpolation of a family of Bishop-Phelps
cones between the order cone and each of its conic neighborhoods. This
interpolation, combined with the proper handling of two distinct types of conic
neighborhoods, plays a crucial role in the proofs of our results, which include
as a particular case other results that have already been established under
more restrictive conditions.
|
Long Range (LoRa) has become a key enabler technology for low power wide area
networks. However, due to its ALOHA-based medium access scheme, LoRa has to
cope with collisions that limit the capacity and network scalability.
Collisions between randomly overlapped signals modulated with different
spreading factors (SFs) result in inter-SF interference, which increases the
packet loss likelihood when signal-to-interference ratio (SIR) is low. This
issue cannot be resolved by channel coding since the probability of error
distance is not concentrated around the adjacent symbol. In this paper, we
analytically model this interference, and propose an interference cancellation
method based on the idea of segmentation of the received signal. This scheme
has three steps. First, the SF of the interference signal is identified, then
the equivalent data symbol and complex amplitude of the interference are
estimated. Finally, the estimated interference signal is subtracted from the
received signal before demodulation. Unlike conventional serial interference
cancellation (SIC), this scheme can directly estimate and reconstruct the
non-aligned inter-SF interference without synchronization. Simulation results
show that the proposed method can significantly reduce the symbol error rate
(SER) under low SIR compared with the conventional demodulation. Moreover, it
also shows high robustness to fractional sample timing offset (STO) and carrier
frequency offset (CFO) of interference. The presented results clearly show the
effectiveness of the proposed method in terms of the SER performance.
|
In this paper, we study a generalization of twisted (groupoid) equivariant
$\mathrm{K}$-theory in the sense of Freed-Moore for $\mathbb{Z}_2$-graded
$\mathrm{C}^*$-algebras. It is defined by using Fredholm operators on Hilbert
modules with twisted representations. We compare it with another description
using odd symmetries, which is a generalization of van Daele's
$\mathrm{K}$-theory for $\mathbb{Z}_2$-graded Banach algebras. In particular,
we obtain a simple presentation of the twisted equivariant $\mathrm{K}$-group
when the $\mathrm{C}^*$-algebra is trivially graded. It is applied for the
bulk-edge correspondence of topological insulators with CT-type symmetries.
|
For popular websites most important concern is to handle incoming load
dynamically among web servers, so that they can respond to their client without
any wait or failure. Different websites use different strategies to distribute
load among web servers but most of the schemes concentrate on only one factor
that is number of requests, but none of the schemes consider the point that
different type of requests will require different level of processing efforts
to answer, status record of all the web servers that are associated with one
domain name and mechanism to handle a situation when one of the servers is not
working. Therefore, there is a fundamental need to develop strategy for dynamic
load allocation on web side. In this paper, an effort has been made to
introduce a cluster based frame work to solve load distribution problem. This
framework aims to distribute load among clusters on the basis of their
operational capabilities. Moreover, the experimental results are shown with the
help of example, algorithm and analysis of the algorithm.
|
The dynamical responses of Blume-Capel (S=1) ferromagnet to the plane
propagating (with fixed frequency and wavelength) and standing magnetic field
waves are studied sepa- rately in two dimensions by extensive Monte Carlo
simulation. Depending on the values of temperature, amplitude of the
propagating magnetic field and the strength of anisotropy, two different
dynamical phases are observed. For a fixed value of anisotropy and the
amplitude of the propagating magnetic field, the system undergoes a dynamical
phase transition from a driven spin wave propagating phase to a pinned or spin
frozen state as the system is cooled down. The time averaged magnetisation over
a full cycle of the propagating magnetic field plays the role of the dynamic
order parameter. A comprehensive phase diagram is plotted in the plane formed
by the amplitude of the propagating wave and the temperature of the system. It
is found that the phase boundary shrinks inward as the anisotropy increases.
The phase boundary, in the plane described by the strength of the anisotropy
and temperature, is also drawn. This phase boundary was observed to shrink
inward as the field amplitude increases.
|
Two quadrature-based algorithms for computing the matrix fractional power
$A^\alpha$ are presented in this paper. These algorithms are based on the
double exponential (DE) formula, which is well-known for its effectiveness in
computing improper integrals as well as in treating nearly arbitrary endpoint
singularities. The DE formula transforms a given integral into another integral
that is suited for the trapezoidal rule; in this process, the integral interval
is transformed to the infinite interval. Therefore, it is necessary to truncate
the infinite interval into an appropriate finite interval. In this paper, a
truncation method, which is based on a truncation error analysis specialized to
the computation of $A^\alpha$, is proposed. Then, two algorithms are presented
-- one computes $A^\alpha$ with a fixed number of abscissas, and the other
computes $A^\alpha$ adaptively. Subsequently, the convergence rate of the DE
formula for Hermitian positive definite matrices is analyzed. The convergence
rate analysis shows that the DE formula converges faster than the Gaussian
quadrature when $A$ is ill-conditioned and $\alpha$ is a non-unit fraction.
Numerical results show that our algorithms achieved the required accuracy and
were faster than other algorithms in several situations.
|
The noncritical $D=4$ $W_3$ string is a model of $W_3$ gravity coupled to two
free scalar fields. In this paper we discuss its BRST quantization in direct
analogy with that of the $D=2$ (Virasoro) string. In particular, we calculate
the physical spectrum as a problem in BRST cohomology. The corresponding
operator cohomology forms a BV-algebra. We model this BV-algebra on that of the
polyderivations of a commutative ring on six variables with a quadratic
constraint, or, equivalently, on the BV-algebra of (polynomial) polyvector
fields on the base affine space of $SL(3,C)$. In this paper we attempt to
present a complete summary of the progress made in these studies. [...]
|
For any factorization domain $\cal A$ and an algebra endomorphism $\sigma$ of
$\cal A$, there exists a non-associative algebra $({\cal
A},\sigma,[\cdot,\cdot])$ with multiplication satisfying skew-symmetry and
generalized (twisted) Jacobi identities, called a $\sigma$-deformed Witt
algebra. In this paper, we obtain the necessary and sufficient conditions for
the algebra $({\cal A},\sigma,[\cdot,\cdot])$ to be simple.
|
The many-body Hamiltonians and other fermionic physical observables are
expressed in terms of fermionic creation and annihilation operators, which form
the algebra of canonical anti-commutation relations (CAR). In this work we use
a canonical isomorphism between CAR and $\mathcal M_{2^\infty}$ algebras to
derive analytic matrix representations of many-fermion operators. Code-lines
implementing these matrix representations are supplied and Hubbard-type
Hamiltonians are worked out explicitly.
|
We study the production of the spin partner of the X(3872), which is a
D^{*}\bar D^{*} bound state with quantum numbers J^{PC}=2^{++} and named
X_2(4012) here, with the associated emission of a photon in electron--positron
collisions. The results show that the ideal energy region to observe the
X_2(4012) in e^+e^- annihilations is from 4.4~GeV to 4.5~GeV, due to the
presence of the S-wave \bar D^{*} D_1(2420) and \bar D^{*} D_2(2460)
thresholds, respectively. We also point out that it will be difficult to
observe the \gamma X(4012) at the e^+e^- center-of-mass energy around 4.26~GeV.
|
We present a study to detect friendship, its strength, and its change from
smartphone location data collectedamong members of a fraternity. We extract a
rich set of co-location features and build classifiers that detectfriendships
and close friendship at 30% above a random baseline. We design cross-validation
schema to testour model performance in specific application settings, finding
it robust to seeing new dyads and to temporalvariance.
|
The Hubble expansion of galaxies, the $2.73\dK$ blackbody radiation
background and the cosmic abundances of the light elements argue for a hot,
dense origin of the universe --- the standard Big Bang cosmology --- and enable
its evolution to be traced back fairly reliably to the nucleosynthesis era when
the temperature was of $\Or(1)$ MeV corresponding to an expansion age of
$\Or(1)$ sec. All particles, known and hypothetical, would have been created at
higher temperatures in the early universe and analyses of their possible
effects on the abundances of the synthesized elements enable many interesting
constraints to be obtained on particle properties. These arguments have
usefully complemented laboratory experiments in guiding attempts to extend
physics beyond the Standard $SU(3)_{\c}{\otimes}SU(2)_{\L}{\otimes}U(1)_{Y}$
Model, incorporating ideas such as supersymmetry, compositeness and
unification. We first present a pedagogical account of relativistic cosmology
and primordial nucleosynthesis, discussing both theoretical and observational
aspects, and then proceed to examine such constraints in detail, in particular
those pertaining to new massless particles and massive unstable particles.
Finally, in a section aimed at particle physicists, we illustrate applications
of such constraints to models of new physics.
|
We report on a search for direct scalar bottom quark (sbottom) pair
production in $p \bar{p}$ collisions at $\sqrt{s}=1.96$~TeV, in events with
large missing transverse energy and two jets of hadrons in the final state,
where at least one of the jets is required to be identified as originating from
a $b$ quark. The study uses a CDF Run~II data sample corresponding to
2.65~fb${}^{-1}$ of integrated luminosity. The data are in agreement with the
standard model. In an R-parity conserving minimal supersymmetric scenario, and
assuming that the sbottom decays exclusively into a bottom quark and a
neutralino, 95$\%$ confidence-level upper limits on the sbottom pair production
cross section of 0.1~pb are obtained. For neutralino masses below 70~GeV/$c^2$,
sbottom masses up to 230~GeV/$c^2$ are excluded at 95$\%$ confidence level.
|
We consider a stochastic process in which independent identically distributed
random matrices are multiplied and where the Lyapunov exponent of the product
is positive. We continue multiplying the random matrices as long as the norm,
$\epsilon$, of the product is \emph{less} than unity. If the norm is greater
than unity we reset the matrix to a multiple of the identity and then continue
the multiplication. We address the problem of determining the probability
density function of the norm, $P_\epsilon$. We argue that, in the limit as
$\epsilon\to 0$, $P_\epsilon\sim (\ln (1/\epsilon))^\mu \epsilon^\gamma$, where
$\mu $ and $\gamma$ are two real parameters.
Our motivation for analysing this \emph{matrix contraction process} is that
it serves as a model for describing the fine-structure of strange attractors,
where a dense concentration of trajectories results from the differential of
the flow being contracting in some region. We exhibit a matrix-product model
for the differential of the flow in a random velocity field, and show that
there is a phase transition, with the parameter $\mu$ changing abruptly from
$\mu=0$ to $\mu=-\frac{3}{2}$ as a parameter of the flow field model is varied.
|
Fairness in graph neural networks has been actively studied recently.
However, existing works often do not explicitly consider the role of message
passing in introducing or amplifying the bias. In this paper, we first
investigate the problem of bias amplification in message passing. We
empirically and theoretically demonstrate that message passing could amplify
the bias when the 1-hop neighbors from different demographic groups are
unbalanced. Guided by such analyses, we propose BeMap, a fair message passing
method, that leverages a balance-aware sampling strategy to balance the number
of the 1-hop neighbors of each node among different demographic groups.
Extensive experiments on node classification demonstrate the efficacy of BeMap
in mitigating bias while maintaining classification accuracy. The code is
available at https://github.com/xiaolin-cs/BeMap.
|
In this paper, we study two important metrics in multiple-input
multiple-output (MIMO) time-varying Rayleigh flat fading channels. One is the
eigen-mode, and the other is the instantaneous mutual information (IMI). Their
second-order statistics, such as the correlation coefficient, level crossing
rate (LCR), and average fade/outage duration, are investigated, assuming a
general nonisotropic scattering environment. Exact closed-form expressions are
derived and Monte Carlo simulations are provided to verify the accuracy of the
analytical results. For the eigen-modes, we found they tend to be
spatio-temporally uncorrelated in large MIMO systems. For the IMI, the results
show that its correlation coefficient can be well approximated by the squared
amplitude of the correlation coefficient of the channel, under certain
conditions. Moreover, we also found the LCR of IMI is much more sensitive to
the scattering environment than that of each eigen-mode.
|
For $f$ analytic on the unit disc let $r_t(f)(z)=f(e^{it}z)$ and
$f_r(z)=f(rz)$, rotations and dilations respectively. We show that for $f$ in
the Bergman space $A^p$ and $0<\alpha\leq 1$ the following are equivalent.
\begin{itemize} \item[(i)] $\n{r_t(f)-f}_{A^p}=\og(|t|^{\alpha}), \quad t\to
0$, \item[(ii)] $\n{(f')_r}_{A^p} =\og\left (1-r)^{\alpha-1}\right ), \quad
r\to 1^{-}$, \item[(iii)] $\n{f_r-f}_{A^p}=\og((1-r)^{\alpha}),\quad r\to
1^{-}$. \end{itemize}
The Hardy space analogues of these conditions are known to be equivalent by
results of Hardy and Littlewood and of E. Storozhenko, and in that setting they
describe the mean Lipschitz spaces $\Lambda (p, \alpha)$.
On the way, we provide an elementary proof of the equivalence of $(ii)$ and
$(iii)$ in Hardy spaces, and show that similar assertions are valid for certain
weighted mean Lipschitz spaces.
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A redshift survey has been carried out in the region of the Hubble Deep Field
North using the Low Resolution Imaging Spectrograph at the Keck Observatory.
The resulting redshift catalog, which contains 671 entries, is a compendium of
our own data together with published LRIS/Keck data. It is more than 92%
complete for objects, irrespective of morphology, to $R = 24$ mag in the HDF
itself and to $R = 23$ mag in the Flanking Fields within a diameter of 8 arcmin
centered on the HDF, an unusually high completion for a magnitude limited
survey performed with a large telescope. A median redshift $z = 1.0$ is reached
at $R \sim 23.8$.
Strong peaks in the redshift distribution, which arise when a group or poor
cluster of galaxies intersect the area surveyed, can be identified to $z \sim
1.2$ in this dataset. More than 68% of the galaxies are members of these
redshift peaks. In a few cases, closely spaced peaks in $z$ can be resolved
into separate groups of galaxies that can be distinguished in both velocity and
location on the sky.
The radial separation of these peaks in the pencil-beam survey is consistent
with a characteristic length scale for the their separation of $\approx$70 Mpc
in our adopted cosmology ($h = 0.6, \Omega_M = 0.3$, $\Lambda = 0$). Strong
galaxy clustering is in evidence at all epochs back to $z \le 1.1$. (abstract
abridged)
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From geometry and conservation we derive two nonlinear evolution equations
for sand ripples. In the case of a strong wind leading to a net erosion of the
sand bed, ripples obey the Benney equation. This leads either to order or
disorder depending on whether dispersion is strong or weak. In the most
frequent case where erosion is counterbalanced by deposition, we derive a new
one-parameter nonlinear equation. It reveals ripple structures which then
undergo a coarsening process at long times, a process which then slows down
dramatically with the growth of the ripple wavelength.
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The derivative discontinuity in the exact exchange-correlation potential of
ensemble Density Functional Theory (DFT) is investigated at the specific
integer number that corresponds to the maximum number of bound electrons,
$J_{max}$. A recently developed complex-scaled analog of DFT is extended to
fractional particle numbers and used to study ensembles of both bound and
metastable states. It is found that the exact exchange-correlation potential
experiences discontinuous jumps at integer particle numbers including
$J_{max}$. For integers below $J_{max}$ the jump is purely real because of the
real shift in the chemical potential. At $J_{max}$, the jump has a non-zero
imaginary component reflecting the finite lifetime of the $(J_{max}+1)$ state.
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We present the first observational evidence for a collimated jet in a
cataclysmic variable system; the recurrent nova T Pyxidis. Optical spectra show
bipolar components of H$\alpha$ with velocities $\sim 1400 km/s$, very similar
to those observed in the supersoft X-ray sources and in SS 433. We argue that a
key ingredient of the formation of jets in the supersoft X-ray sources and T
Pyx (in addition to an accretion disk threaded by a vertical magnetic field),
is the presence of nuclear burning on the surface of the white dwarf.
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The electrical properties of superconducting tapes and coatings in the
direction transverse to the long dimension of the composite has been rarely
studied. However, transverse dissipation can eventually determine the behavior
of a transmission line in the case of failure due to the presence of
transversal cracks, and is also fundamental in the AC regime. In this paper we
present a preliminary experimental study of the electrical transport properties
along the transverse direction of BSCCO-metal tapes, and compare them with
those measured along the long axis of the material. In spite of the fact that
the tapes under study are not multi-filamentary, our experiments suggest that
there is a measurable anisotropy of the transport properties between the
longitudinal and transverse directions.
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In the present paper, questions about a local behavior of mappings
$f:D\rightarrow \overline{{\Bbb R}^n},$ $n\ge 2,$ in $\overline{D}$ are
studied. Under some conditions on a measurable function $Q(x),$ $Q:D\rightarrow
[0, \infty],$ and boundaries of $D$ and $D^{\,\prime}=f(D),$ it is showed that
a family of open discrete map\-ping $f:D\rightarrow \overline{{\Bbb R}^n},$
$n\ge 2,$ with characteristic of quasiconformality $Q(x),$ is equicontinuous in
$\overline{D}.$
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We investigate the boson star with the self-interacting scalar field as a
model of galactic halos. The model has slightly increasing rotation curves and
allows wider ranges of the mass($m$) and coupling($\lambda$) of the halo dark
matter particle than the non-interacting model previously
suggested(ref.\cite{sin1}). Two quantities are related by
$\lambda^{\frac{1}{2}} (m_p/m)^2\st{>}{\sim} 10^{50}$.
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We present a comprehensive spectral analysis of all INTEGRAL data obtained so
far for the X-ray--bright Seyfert galaxy NGC 4151. We also use all
contemporaneous data from RXTE, XMM, Swift and Suzaku. We find a linear
correlation between the medium and hard-energy X-ray fluxes measured by
INTEGRAL, which indicates an almost constant spectral index over six years. The
majority of INTEGRAL observations were made when the source was either at a
very bright or very dim hard--X-ray state. We find that thermal Comptonization
models applied to the bright state yields the plasma temperature of 50--70 keV
and its optical depth of 1.3--2.6, depending on the assumed source geometry.
For the dim state, these parameters are in the ranges of 180--230 keV and
0.3--0.7, respectively. The Compton parameter is y = 1 for all the spectra,
indicating a stable geometry. Using this result, we can determine the
reflection effective solid angles associated with the close and distant
reprocessing media as = 0.3 x 2pi and 0.2 x 2pi, respectively. The plasma
energy balance, the weak disc reflection and a comparison of the UV fluxes
illuminating the plasma to the observed ones are all consistent with an inner
hot accretion surrounded by an outer cold disc. The disc truncation radius can
be determined from an approximate equipartition between the observed UV and
X-ray emission, and from the fitted disc blackbody model, as 15 gravitational
radii. Alternatively, our results can be explained by a mildly relativistic
coronal outflow.
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In this paper we address the problem of interpolating a spline developable
patch bounded by a given spline curve and the first and the last rulings of the
developable surface. In order to complete the boundary of the patch a second
spline curve is to be given. Up to now this interpolation problem could be
solved, but without the possibility of choosing both endpoints for the rulings.
We circumvent such difficulty here by resorting to degree elevation of the
developable surface. This is useful not only to solve this problem, but also
other problems dealing with triangular developable patches.
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Most large web-scale applications are now built by composing collections
(from a few up to 100s or 1000s) of microservices. Operators need to decide how
many resources are allocated to each microservice, and these allocations can
have a large impact on application performance. Manually determining
allocations that are both cost-efficient and meet performance requirements is
challenging, even for experienced operators. In this paper we present AutoTune,
an end-to-end tool that automatically minimizes resource utilization while
maintaining good application performance.
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We present the results of a search for pair production of scalar top quarks
in an R-parity violating supersymmetry scenario in 106 pb-1 of ppbar collisions
at $\sqrt{s} = 1.8$ TeV collected by the Collider Detector at Fermilab. In this
mode each scalar top quark decays into a tau lepton and a b quark. We search
for events with two tau's, one decaying leptonically (e or mu) and one decaying
hadronically, and two jets. No candidate events pass our final selection
criteria. We set a 95% confidence level lower limit on the scalar top quark
mass at 122 GeV/c2 for Br (stop-> tau + b) = 1.
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This paper is part of a series of articles on noncommutative geometry and
conformal geometry. In this paper, we reformulate the local index formula in
conformal geometry in such a way to take into account of the action of
conformal diffeomorphisms. We also construct and compute a whole new family of
geometric conformal invariants associated with conformal diffeomorphisms. This
includes conformal invariants associated with equivariant characteristic
classes. The approach of this paper involves using various tools from
noncommutative geometry, such as twisted spectral triples and cyclic theory. An
important step is to establish the conformal invariance of the Connes-Chern
character of the conformal Dirac spectral triple of Connes-Moscovici.
Ultimately, however, the main results of the paper are stated in a purely
differential-geometric fashion.
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This paper focuses on quantifying the outage performance of terahertz (THz)
relaying systems. In this direction, novel closed-form expressions for the
outage probability of a dual-hop relaying system, in which both the
source-relay and relay-destination links suffer from fading and stochastic beam
misalignment, are extracted. Our results reveal the importance of taking into
account the impact of beam misalignment when characterizing the outage
performance of the system as well as when selecting the transmission
frequencies.
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Radio astronomy has changed. For years it studied relatively rare sources,
which emit mostly non-thermal radiation across the entire electromagnetic
spectrum, i.e. radio quasars and radio galaxies. Now it is reaching such faint
flux densities that it detects mainly star-forming galaxies and the more common
radio-quiet active galactic nuclei. These sources make up the bulk of the
extragalactic sky, which has been studied for decades in the infrared, optical,
and X-ray bands. I follow the transformation of radio astronomy by reviewing
the main components of the radio sky at the bright and faint ends, the issue of
their proper classification, their number counts, luminosity functions, and
evolution. The overall "big picture" astrophysical implications of these
results, and their relevance for a number of hot topics in extragalactic
astronomy, are also discussed. The future prospects of the faint radio sky are
very bright, as we will soon be flooded with survey data. This review should be
useful to all extragalactic astronomers, irrespective of their favourite
electromagnetic band(s), and even stellar astronomers might find it somewhat
gratifying.
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In this work, we attempt to solve the Hit Song Science problem, which aims to
predict which songs will become chart-topping hits. We constructed a dataset
with approximately 1.8 million hit and non-hit songs and extracted their audio
features using the Spotify Web API. We test four models on our dataset. Our
best model was random forest, which was able to predict Billboard song success
with 88% accuracy.
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We report direct measurement of population dynamics in the excited state
manifold of a nitrogen-vacancy (NV) center in diamond. We quantify the
phonon-induced mixing rate and demonstrate that it can be completely suppressed
at low temperatures. Further, we measure the intersystem crossing (ISC) rate
for different excited states and develop a theoretical model that unifies the
phonon-induced mixing and ISC mechanisms. We find that our model is in
excellent agreement with experiment and that it can be used to predict unknown
elements of the NV center's electronic structure. We discuss the model's
implications for enhancing the NV center's performance as a room-temperature
sensor.
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{Results from a long-term observational project called the Araucaria Project
are presented. Based on Wide Field optical monitoring of 8 nearby galaxies,
covering a large range of metallicities, more than 500 Cepheids and a few
hundred Blue Supergiant candidates were identified. From the analysis of
Cepheid P-L relations of outstanding quality derived from our data we conclude
that the slope of these relations in the I band and Wesenheit index are not
dependent on metallicity. Comparing the I-band magnitudes of Cepheids of a
period of ten days, as computed from our P-L relations, to the I-band
magnitudes of the tip of the RGB, which is widely believed to be independent of
population effects, we cannot see any obvious dependence of the zero point of
the I-band P-L relation on metallicity. A preliminary analysis of IR follow-up
observations of sub-samples of the identified Cepheids in various galaxies of
the project show that the distances obtained from these data are systematically
shorter by about of 0.1 mag than those derived from the optical photometry. It
is likely that this effect can be attributed to the internal reddening in the
program galaxies.
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The contribution of nucleon isobar $N^*$ exchanges to backward elastic
pd-scattering is calculated on the basis of deuteron 6q-model and found to be
negligible in comparison with the neutron exchange. It is shown that the pole
amplitude of neutron pickup from the deuteron $nN^*$-component is favoured in
the reaction $pd\to dN^*$ for backward going $N^*(1440)$ and $N^*(1710)$ at
kinetic energy of incident proton of 1.5--2 GeV whereas the triangular diagram
with subprocess $pp\to d\pi^+$ related to the usual $pn-$component of deuteron
is considerable suppressed.
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Neutron stars may harbour the true ground state of matter in the form of
strange quark matter. If present, this type of matter is expected to be a color
superconductor, a consequence of quark pairing with respect to the color/flavor
degrees of freedom. The stellar magnetic field threading the quark core becomes
a color-magnetic admixture and, in the event that superconductivity is of type
II, leads to the formation of color-magnetic vortices. In this Letter we show
that the volume-averaged color-magnetic vortex tension force should naturally
lead to a significant degree of non-axisymmetry in systems like radio pulsars.
We show that gravitational radiation from such color-magnetic `mountains' in
young pulsars like the Crab and Vela could be observable by the future Einstein
Telescope, thus becoming a probe of paired quark matter in neutron stars. The
detectability threshold can be pushed up toward the sensitivity level of
Advanced LIGO if we invoke an interior magnetic field about a factor ten
stronger than the surface polar field.
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The examination of parity symmetry in gravitational interactions has drawn
increasing attention. Although Einstein's General Relativity is
parity-conserved, numerous theories of parity-violating (PV) gravity in
different frameworks have recently been proposed for different motivations. In
this review, we briefly summarize the recent progress of these theories, and
focus on the observable effects of PV terms in the gravitational waves (GWs),
which are mainly reflected in the difference between the left-hand and
right-hand polarization modes. We are primarily concerned with the implications
of these theories for GWs generated by the compact binary coalescences and the
primordial GWs generated in the early Universe. The deviation of GW waveforms
and/or primordial power spectrum can always be quantified by the energy scale
of parity violation of the theory. Applying the current and future GW
observation from laser interferometers and cosmic microwave background
radiation, the current and potential constraints on the PV energy scales are
presented, which indicates that the parity symmetry of gravity can be tested in
high energy scale in this new era of gravitational waves.
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Quasars contribute to the 21-cm signal from the Epoch of Reionization (EoR)
primarily through their ionizing UV and X-ray emission. However, their radio
continuum and Lyman-band emission also regulates the 21-cm signal in their
direct environment, potentially leaving the imprint of their duty cycle.
We develop a model for the radio and UV luminosity functions of quasars from
the EoR, and constrain it using recent observations. Our model is consistent
with the z~7.5 quasar from Banados et al 2017, and also predicts only a few
quasars suitable for 21-cm forest observations (10mJy) in the sky. We exhibit a
new effect on the 21-cm signal observed against the CMB: a radio-loud quasar
can leave the imprint of its duty cycle on the 21-cm tomography. We apply this
effect in a cosmological simulation and conclude that the effect of typical
radio-loud quasars is most likely negligible in an SKA field of view. For a
1-10mJy quasar the effect is stronger though hardly observable at SKA
resolution. Then we study the contribution of the lyman band Ly-alpha to
Ly-beta) emission of quasars to the Wouthuisen-Field coupling. The collective
effect of quasars on the 21-cm power spectrum is larger than the thermal noise
at low k, though featureless. However, a distinctive pattern around the
brightest quasars in an SKA field of view may be observable in the tomography,
encoding the duration of their duty cycle. This pattern has a high
signal-to-noise ratio for the brightest quasar in a typical SKA shallow survey.
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In federated learning (FL), a number of devices train their local models and
upload the corresponding parameters or gradients to the base station (BS) to
update the global model while protecting their data privacy. However, due to
the limited computation and communication resources, the number of local
trainings (a.k.a. local update) and that of aggregations (a.k.a. global update)
need to be carefully chosen. In this paper, we investigate and analyze the
optimal trade-off between the number of local trainings and that of global
aggregations to speed up the convergence and enhance the prediction accuracy
over the existing works. Our goal is to minimize the global loss function under
both the delay and the energy consumption constraints. In order to make the
optimization problem tractable, we derive a new and tight upper bound on the
loss function, which allows us to obtain closed-form expressions for the number
of local trainings and that of global aggregations. Simulation results show
that our proposed scheme can achieve a better performance in terms of the
prediction accuracy, and converge much faster than the baseline schemes.
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We study corotational wave maps from $(1+4)$-dimensional Minkowski space into
the $4$-sphere. We prove the stability of an explicitly known self-similar wave
map under perturbations that are small in the critical Sobolev space.
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We consider linear reaction systems with slow and fast reactions, which can
be interpreted as master equations or Kolmogorov forward equations for Markov
processes on a finite state space. We investigate their limit behavior if the
fast reaction rates tend to infinity, which leads to a coarse-grained model
where the fast reactions create microscopically equilibrated clusters, while
the exchange mass between the clusters occurs on the slow time scale.
Assuming detailed balance the reaction system can be written as a gradient
flow with respect to the relative entropy. Focusing on the physically relevant
cosh-type gradient structure we show how an effective limit gradient structure
can be rigorously derived and that the coarse-grained equation again has a
cosh-type gradient structure. We obtain the strongest version of convergence in
the sense of the Energy-Dissipation Principle (EDP), namely EDP-convergence
with tilting.
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The physics of critical phenomena in a many-body system far from thermal
equilibrium is an interesting and important issue to be addressed both
experimentally and theoretically. The trapped cold atoms have been actively
used as a clean and versatile simulator for classical and quantum-mechanical
systems, deepening understanding of the many-body physics behind. Here we
review the nonlinear and collective dynamics in a periodically modulated
magneto-optically trapped cold atoms. By temporally modulating the intensity of
the trapping lasers with the controlled phases, one can realize two kinds of
nonlinear oscillators, the parametrically driven oscillator and the resonantly
driven Duffing oscillator, which exhibit the dynamical bistable states. Cold
atoms behave not only as the single-particle nonlinear oscillators, but also as
the coupled oscillators by the light-induced inter-atomic interaction, which
leads to the phase transitions far from equilibrium in a way similar to the
phase transition in equilibrium. The parametrically driven cold atoms show the
ideal mean-field symmetry-breaking transition, and the symmetry is broken with
respect to time translation by the modulation period. Such a phase transition
results from the cooperation and competition between the inter-particle
interaction and the fluctuations, which lead to the nonlinear switching of
atoms between the vibrational states, and the experimentally measured critical
characteristics prove it as the ideal mean-field transition class. On the other
hand, the resonantly driven cold atoms that possess the coexisting periodic
attractors exhibit the kinetic phase transition analogous to the discontinuous
gas-liquid phase transition in equilibrium, and interestingly the global
interaction between atoms causes the shift of the phase-transition boundary.
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We present the fully integrated form of the two-loop four-gluon amplitude in
$\mathcal{N} = 2$ supersymmetric quantum chromodynamics with gauge group
SU$(N_c)$ and with $N_f$ massless supersymmetric quarks (hypermultiplets) in
the fundamental representation. Our result maintains full dependence on $N_c$
and $N_f$, and relies on the existence of a compact integrand representation
that exhibits the duality between color and kinematics. Specializing to the
$\mathcal{N} = 2$ superconformal theory, where $N_f = 2N_c$ , we obtain
remarkably simple amplitudes that have an analytic structure close to that of
$\mathcal{N} = 4$ super-Yang-Mills theory, except that now certain lower-weight
terms appear. We comment on the corresponding results for other gauge groups.
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Subsets and Splits