text
stringlengths 6
128k
|
|---|
We supply a detailed proof of the result by P.S. Green and T.
H$\ddot{\text{u}}$bsch that all complete intersection Calabi--Yau 3-folds in
product of projective spaces are connected through projective conifold
transitions (known as the standard web). We also introduce a subclass of small
transitions which we call primitive small transitions and study such subclass.
More precisely, given a small projective resolution $\pi : \widehat{X}
\rightarrow X$ of a Calabi--Yau 3-fold $X$, we show that if the natural closed
immersion $Def(\widehat{X}) \hookrightarrow Def(X)$ is an isomorphism then $X$
has only ODPs as singularities.
|
We replace a Hamiltonian with a modular Hamiltonian in the spectral form
factor and the level spacing distribution function. This study establishes a
connection between quantities within Quantum Entanglement and Quantum Chaos. To
have a universal study for Quantum Entanglement, we consider the Gaussian
random 2-qubit model. The maximum violation of Bell's inequality demonstrates a
positive correlation with the entanglement entropy. Thus, the violation plays
an equivalent role as Quantum Entanglement. We first provide an analytical
estimation of the relation between quantum entanglement quantities and the dip
when a subregion only has one qubit. The time of the first dip is monotone for
entanglement entropy. The dynamics in a subregion is independent of the initial
state at a late time. It is one of the signaling conditions for classical
chaos. We also extend our analysis to the Gaussian random 3-qubit state, and it
indicates a similar result. The simulation shows that the level spacing
distribution function approaches GUE at a late time. In the end, we develop a
technique within QFT to the spectral form factor for its relation to an
$n$-sheet manifold. We apply the technology to a single interval in CFT$_2$ and
the spherical entangling surface in $\mathcal{N}=4$ super Yang-Mills theory.
The result is one for both cases, but the R\'enyi entropy can depend on the
R\'enyi index. For the case of CFT$_2$, it indicates the difference between the
continuum and discrete spectrum.
|
We address an unexpectedly large rectification using a simple quantum wire
with correlated site potentials. The external electric field, associated with
voltage bias, leads to unequal charge currents for two different polarities of
external bias and this effect is further enhanced by incorporating the
asymmetry in wire-to-electrode coupling. Our calculations suggest that in some
cases almost cent percent rectification is obtained for a wide bias window.
This performance is valid against disorder configurations and thus we can
expect an experimental verification of our theoretical analysis in near future.
|
We prove that every positive semidefinite matrix over the natural numbers
that is eventually 0 in each row and column can be factored as the product of
an upper triangular matrix times a lower triangular matrix. We also extend some
known results about factorization with respect to tensor products of nest
algebras. Our proofs use the theory of reproducing kernel Hilbert spaces.
|
In this paper we give a new foundational, categorical formulation for
operations and relations and objects parameterizing them. This generalizes and
unifies the theory of operads and all their cousins including but not limited
to PROPs, modular operads, twisted (modular) operads, properads, hyperoperads,
their colored versions, as well as algebras over operads and an abundance of
other related structures, such as crossed simplicial groups, the augmented
simplicial category or FI--modules.
The usefulness of this approach is that it allows us to handle all the
classical as well as more esoteric structures under a common framework and we
can treat all the situations simultaneously. Many of the known constructions
simply become Kan extensions.
In this common framework, we also derive universal operations, such as those
underlying Deligne's conjecture, construct Hopf algebras as well as perform
resolutions, (co)bar transforms and Feynman transforms which are related to
master equations. For these applications, we construct the relevant model
category structures. This produces many new examples.
|
We first recall Solomon's relations for Welschinger's invariants counting
real curves in real symplectic fourfolds, announced in \cite{Jake2} and
established in \cite{RealWDVV}, and the WDVV-style relations for Welschinger's
invariants counting real curves in real symplectic sixfolds with some symmetry
established in \cite{RealWDVV3}. We then explicitly demonstrate that in some
important cases (projective spaces with standard conjugations, real blowups of
the projective plane, and two- and three-fold products of the one-dimensional
projective space with two involutions each), these relations provide complete
recursions determining all Welschinger's invariants from basic input. We
include extensive tables of Welschinger's invariants in low degrees obtained
from these recursions with {\it Mathematica}. These invariants provide lower
bounds for counts of real rational curves, including with curve insertions in
smooth algebraic threefolds.
|
We study vacuum structure of N=1 supersymmetric quiver gauge theories which
can be realized geometrically by D brane probes wrapping cycles of local
Calabi-Yau three-folds. In particular, we show that the A_2 quiver theory with
gauge group U(N_1) \times U(N_2) with N_1 / 2 < N_2 < 2N_1 / 3 has a regime
with an infrared free description that is partially magnetic and partially
electric. Using this dual description, we show that the model has a landscape
of inequivalent meta-stable vacua where supersymmetry is dynamically broken and
all the moduli are stabilized. Each vacuum has distinct unbroken gauge
symmetry. B-terms generated by the supersymmetry breaking give rise to gaugino
masses at one-loop, and we are left with the bosonic pure Yang-Mills theory in
the infrared. We also identify the supersymmetric vacua in this model using
their infrared free descriptions and show that the decay rates of the
supersymmetry breaking vacua into the supersymmetric vacua can be made
parametrically small.
|
The main scope of this chapter is metrics defined for coding and decoding
purposes, mainly for block codes.
|
Pion-nucleon elastic scattering in the dominant $P_{33}$ channel is examined
in the model in which the interaction is of the form $\pi + N\leftrightarrow N,
\Delta(1232)$. New expressions are found for the elastic pion-nucleon
scattering amplitude which differ from existing formula both in the kinematics
and in the treatment of the renormalization of the nucleon mass and coupling
constant. Fitting the model to the phase shifts in the $P_{33}$ channel does
not uniquely fix the parameters of the model. The cutoff for the pion-nucleon
form factor is found to lie in the range $\beta = 750\pm350$ MeV/c. The masses
of the nucleon and the $\Delta$ which would arise if there were no coupling to
mesons are found to be $m_{_N}^{(0)}= 1200\pm 200$ MeV and $m_\Delta^{(0)} =
1500\pm 200$ MeV. The difference in these bare masses, a quantity which would
be accounted for by a residual gluon interaction, is found to be $\delta
m^{(0)}=350\pm 100$ MeV.
|
Real topological phases protected by the spacetime inversion (P T) symmetry
are a current research focus. The basis is that the P T symmetry endows a real
structure in momentum space, which leads to Z2 topological classifications in
1D and 2D. Here, we provide solutions to two outstanding problems in the
diagnosis of real topology. First, based on the stable equivalence in K-theory,
we clarify that the 2D topological invariant remains well defined in the
presence of nontrivial 1D invariant, and we develop a general numerical
approach for its evaluation, which was hitherto unavailable. Second, under the
unit-cell convention, noncentered P T symmetries assume momentum dependence,
which violates the presumption in previous methods for computing the
topological invariants. We clarify the classifications for this case and
formulate the invariants by introducing a twisted Wilson-loop operator for both
1D and 2D. A simple model on a rectangular lattice is constructed to
demonstrate our theory, which can be readily realized using artificial
crystals.
|
The emerging graph Transformers have achieved impressive performance for
graph representation learning over graph neural networks (GNNs). In this work,
we regard the self-attention mechanism, the core module of graph Transformers,
as a two-step aggregation operation on a fully connected graph. Due to the
property of generating positive attention values, the self-attention mechanism
is equal to conducting a smooth operation on all nodes, preserving the
low-frequency information. However, only capturing the low-frequency
information is inefficient in learning complex relations of nodes on diverse
graphs, such as heterophily graphs where the high-frequency information is
crucial. To this end, we propose a Signed Attention-based Graph Transformer
(SignGT) to adaptively capture various frequency information from the graphs.
Specifically, SignGT develops a new signed self-attention mechanism (SignSA)
that produces signed attention values according to the semantic relevance of
node pairs. Hence, the diverse frequency information between different node
pairs could be carefully preserved. Besides, SignGT proposes a structure-aware
feed-forward network (SFFN) that introduces the neighborhood bias to preserve
the local topology information. In this way, SignGT could learn informative
node representations from both long-range dependencies and local topology
information. Extensive empirical results on both node-level and graph-level
tasks indicate the superiority of SignGT against state-of-the-art graph
Transformers as well as advanced GNNs.
|
Chiral plasmonic nanostructures will be of increasing importance for future
applications in the field of nano optics and metamaterials. Their sensitivity
to incident circularly polarized light in combination with the ability of
extreme electromagnetic field localization renders them ideal candidates for
chiral sensing and for all-optical information processing. Here, the resonant
modes of single plasmonic helices are investigated. We find that a single
plasmonic helix can be efficiently excited with circularly polarized light of
both equal and opposite handedness relative to that of the helix. An analytic
model provides resonance conditions matching the results of full-field
modeling. The underlying geometric considerations explain the mechanism of
excitation and deliver quantitative design rules for plasmonic helices being
resonant in a desired wavelength range. Based on the developed analytical
design tool, single silver helices were fabricated and optically characterized.
They show the expected strong chiroptical response to both handednesses in the
targeted visible range. With a value of 0.45 the experimentally realized
dissymmetry factor is the largest obtained for single plasmonic helices in the
visible range up to now.
|
We investigate, using mean-field theory and simulation, the effect of
asymmetry on the critical behavior and probability density of Bak-Sneppen
models. Two kinds of anisotropy are investigated: (i) different numbers of
sites to the left and right of the central (minimum) site are updated and (ii)
sites to the left and right of the central site are renewed in different ways.
Of particular interest is the crossover from symmetric to asymmetric scaling
for weakly asymmetric dynamics, and the collapse of data with different numbers
of updated sites but the same degree of asymmetry. All non-symmetric rules
studied fall, independent of the degree of asymmetry, in the same universality
class. Conversely, symmetric variants reproduce the exponents of the original
model. Our results confirm the existence of two symmetry-based universality
classes for extremal dynamics.
|
We study the extended supersymmetric quantum mechanics, with supercharges
transforming in the fundamental representation of U(N|M), as realized in
certain one-dimensional nonlinear sigma models with Kaehler manifolds as target
space. We discuss the symmetry algebra characterizing these models and, using
operatorial methods, compute the heat kernel in the limit of short propagation
time. These models are relevant for studying the quantum properties of a
certain class of higher spin field equations in first quantization.
|
The much debated issue of the transverse single spin asymmetry A_N observed
in the inclusive large P_T production of a single hadron in pp interactions,
p(transv. polarized) p --> pion X, is considered in a TMD factorization scheme.
A previous result [1,2] stating that the maximum contribution of the Collins
effect is strongly suppressed, is revisited, correcting a numerical error. New
estimates are given, adopting the Collins functions recently extracted from
SIDIS and e+e- data, and phenomenological consequences are discussed.
|
We perform for the first time a dynamical system analysis of both the
background and perturbation equations, of $\Lambda$CDM cosmology and
quintessence scenario with an exponential potential. In the former case the
perturbations do not change the stability of the late-time attractor of the
background equations, and the system still results in the dark-energy
dominated, de Sitter solution, having passed from the correct dark-matter era
with $\gamma\approx6/11$. However, in the case of quintessence the
incorporation of perturbations changes the stability and properties of the
background evolution, and the only conditionally stable points present either
an exponentially increasing matter clustering not favored by observations, or
Laplacian instabilities, and thus not physically interesting. This result is a
severe disadvantage of quintessence cosmology comparing to $\Lambda$CDM
paradigm.
|
We derive an exact expression for the tachyon $\beta$-function for the
Wess-Zumino-Witten model. We check our result up to three loops by calculating
the three-loop tachyon $\beta$-function for a general non-linear $\sigma$-model
with torsion, and then specialising to the case of the WZW model.
|
We report a photoinduced change of the coercive field, i.e., a
photocoercivity effect (PCE), under very low intensity illumination of a
low-doped (Ga,Mn)As ferromagnetic semiconductor. We find a strong correlation
between the PCE and the sample resistivity. Spatially resolved dynamics of the
magnetization reversal rule out any role of thermal heating in the origin of
this PCE, and we propose a mechanism based on the light-induced lowering of the
domain wall pinning energy. The PCE is local and reversible, allowing writing
and erasing of magnetic images using light.
|
The conformational vibrations of Z-DNA with counterions are studied in
framework of phenomenological model developed. The structure of left-handed
double helix with counterions neutralizing the negatively charged phosphate
groups of DNA is considered as the ion-phosphate lattice. The frequencies and
Raman intensities for the modes of Z-DNA with Na+ and Mg2+ ions are calculated,
and the low-frequency Raman spectra are built. At the spectra range about the
frequency 150 cm-1 new mode of ion-phosphate vibrations is found, which
characterizes the vibrations of Mg2+ counterions. The results of our
calculations show that the intensities of Z-DNA modes are sensitive to the
concentration of magnesium counterions. The obtained results describe well the
experimental Raman spectra of Z-DNA.
|
Stochastic processes wherein the size of the state space is changing as a
function of time offer models for the emergence of scale-invariant features
observed in complex systems. I consider such a sample-space reducing (SSR)
stochastic process that results in a random sequence of strictly decreasing
integers $\{x(t)\}$, $0\le t \le \tau$, with boundary conditions $x(0) = N$ and
$x(\tau)$ = 1. This model is shown to be exactly solvable:
$\mathcal{P}_N(\tau)$, the probability that the process survives for time
$\tau$ is analytically evaluated. In the limit of large $N$, the asymptotic
form of this probability distribution is Gaussian, with mean and variance both
varying logarithmically with system size: $\langle \tau \rangle \sim \ln N$ and
$\sigma_{\tau}^{2} \sim \ln N$. Correspondence can be made between survival
time statistics in the SSR process and record statistics of i.i.d. random
variables.
|
Online conversations include more than just text. Increasingly, image-based
responses such as memes and animated gifs serve as culturally recognized and
often humorous responses in conversation. However, while NLP has broadened to
multimodal models, conversational dialog systems have largely focused only on
generating text replies. Here, we introduce a new dataset of 1.56M text-gif
conversation turns and introduce a new multimodal conversational model Pepe the
King Prawn for selecting gif-based replies. We demonstrate that our model
produces relevant and high-quality gif responses and, in a large randomized
control trial of multiple models replying to real users, we show that our model
replies with gifs that are significantly better received by the community.
|
We estimate differential rapidity cross sections for $\Psi$ and $\Upsilon$
production via p-Pb collisions at 8 TeV. We use the mixed heavy quark hybrid
theory in which the $J/\Psi(1S),\Upsilon(1S),\Upsilon(2S)$ are standard mesons
while the $\Psi(2S)$ and $\Upsilon(3S)$ are mixed hybrids, approximately 50%
standard $|q \bar{q}>$ states and 50% hybrid $|q \bar{q} g>$ states. This is an
extension of previous work on heavy-quark state production via A-A collisions
at RHIC.
|
We show that any non-zero Banach space with a separable dual contains a
totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such
that every Lipschitz function on the space is Fr\'echet differentiable
somewhere in S.
|
We address the problem of identifying individual cetaceans from images
showing the trailing edge of their fins. Given the trailing edge from an
unknown individual, we produce a ranking of known individuals from a database.
The nicks and notches along the trailing edge define an individual's unique
signature. We define a representation based on integral curvature that is
robust to changes in viewpoint and pose, and captures the pattern of nicks and
notches in a local neighborhood at multiple scales. We explore two ranking
methods that use this representation. The first uses a dynamic programming
time-warping algorithm to align two representations, and interprets the
alignment cost as a measure of similarity. This algorithm also exploits learned
spatial weights to downweight matches from regions of unstable curvature. The
second interprets the representation as a feature descriptor. Feature keypoints
are defined at the local extrema of the representation. Descriptors for the set
of known individuals are stored in a tree structure, which allows us to perform
queries given the descriptors from an unknown trailing edge. We evaluate the
top-k accuracy on two real-world datasets to demonstrate the effectiveness of
the curvature representation, achieving top-1 accuracy scores of approximately
95% and 80% for bottlenose dolphins and humpback whales, respectively.
|
We mainly discuss the Wu classes $v(M)$ and the Steenrod operation $Sq$ of
the topological blow up $\tilde{M}$. The formula of the Wu class $v(\tilde{M})$
will be given as well as the formula of the Steenrod operation $Sq$. As an
application, we will use our results to describe a geometric obstruction.
|
The Reynolds-Averaged Navier-Stokes (RANS) approach remains a backbone for
turbulence modeling due to its high cost-effectiveness. Its accuracy is largely
based on a reliable Reynolds stress anisotropy tensor closure model. There has
been an amount of work aiming at improving traditional closure models, while
they are still not satisfactory to some complex flow configurations. In recent
years, advances in computing power have opened up a new way to address this
problem: the machine-learning-assisted turbulence modeling. In this paper, we
employ neural networks to fully predict the Reynolds stress anisotropy tensor
of turbulent channel flows at different friction Reynolds numbers, for both
interpolation and extrapolation scenarios. Several generic neural networks of
Multi-Layer Perceptron (MLP) type are trained with different input feature
combinations to acquire a complete grasp of the role of each parameter. The
best performance is yielded by the model with the dimensionless mean streamwise
velocity gradient $\alpha$, the dimensionless wall distance $y^+$ and the
friction Reynolds number $\mathrm{Re}_\tau$ as inputs. A deeper theoretical
insight into the Tensor Basis Neural Network (TBNN) clarifies some remaining
ambiguities found in the literature concerning its application of Pope's
general eddy viscosity model. We emphasize the sensitivity of the TBNN on the
constant tensor $\textbf{T}^{*(0)}$ upon the turbulent channel flow data set,
and newly propose a generalized $\textbf{T}^{*(0)}$, which considerably
enhances its performance. Through comparison between the MLP and the augmented
TBNN model with both $\{\alpha, y^+, \mathrm{Re}_\tau\}$ as input set, it is
concluded that the former outperforms the latter and provides excellent
interpolation and extrapolation predictions of the Reynolds stress anisotropy
tensor in the specific case of turbulent channel flow.
|
We consider a well posed SPDE$\colon dZ=(AZ+b(Z)) dt+dW(t),\,Z_0=x,
$
on a separable Hilbert space $H$, where $A\colon H\to H$ is self-adjoint,
negative and such that $A^{-1+\beta}$ is of trace class for some $\beta>0$,
$b\colon H\to H$ is Lipschitz continuous and $W$ is a cylindrical Wiener
process on $H$. We denote by $W_A(t)=\int_0^te^{(t-s)A}\,dW(s),\,t\in[0,T],$
the stochastic convolution. We prove, with the help of a formula for nonlinear
transformations of Gaussian integrals due to R. Ramer, the following identity
$$(P\circ Z_x^{-1})(\Phi) =\int_X\Phi(h+e^{\cdot A}x)\, \exp\left\{
-\tfrac12|\gamma_x(h)|^2_{ H_{Q_T}} + I(\gamma_x)(h)\right\} N_{Q_T}(dh), $$
where $ N_{Q_T}$ is the law of $W_A$ in $C([0,T],H)$, $ H_{Q_T}$ its
Cameron--Martin space, $$ [\gamma_x(k)](t)=\int_0^t e^{(t-s)A}b(k(s)+e^{sA}x)
ds,\quad t\in[0,T], \; k \in C([0,T],H)
$$
and $I(\gamma_x) $ is the It\^o integral of $\gamma_x$. Some applications are
discussed; in particular, when $b$ is dissipative we provide an explicit
formula for the law of the stationary process and the invariant measure $\nu$
of the Markov semigroup $(P_t)$.
Some concluding remarks are devoted to a similar problem with colored noise.
|
Charmless B decay modes $B \to \pi \pi, \pi K$ and $KK$ aresystematically
investigated with and without flavor SU(3) symmetry. Independent analyses on
$\pi \pi$ and $\pi K$ modes both favor a large ratio between color-suppressed
tree ($C$) and tree ($T)$ diagram, which suggests that they are more likely to
originate from long distance effects. The sizes of QCD penguin diagrams
extracted individually from $\pi\pi$, $\pi K$ and $KK$ modes are found to
follow a pattern of SU(3) breaking in agreement with the naive factorization
estimates. Global fits to these modes are done under various scenarios of
SU(3)relations. The results show good determinations of weak phase $\gamma$ in
consistency with the Standard Model (SM), but a large electro-weak penguin
$(P_{\tmop{EW}})$ relative to $T + C$ with a large relative strong phase are
favored, which requires an big enhancement of color suppressed electro-weak
penguin ($P_{\tmop{EW}}^C$) compatible in size but destructively interfering
with $P_{\tmop{EW}}$ within the SM, or implies new physics. Possibility of
sizable contributions from nonfactorizable diagrams such as $W$-exchange ($E$),
annihilation($A$) and penguin-annihilation diagrams($P_A$) are investigated.
The implications to the branching ratios and CP violations in $K K$modes are
discussed.
|
General relativistic magnetohydrodynamic (GRMHD) simulations represent a
fundamental tool to probe various underlying mechanisms at play during binary
neutron star (BNS) and neutron star (NS) - black hole (BH) mergers.
Contemporary flux-conservative GRMHD codes numerically evolve a set of
conservative equations based on `conserved' variables which then need to be
converted back into the fundamental (`primitive') variables. The corresponding
conservative-to-primitive variable recovery procedure, based on root-finding
algorithms, constitutes one of the core elements of such GRMHD codes. Recently,
a new robust, accurate and efficient recovery scheme called RePrimAnd was
introduced, which has demonstrated the ability to always converge to a unique
solution. The scheme provides fine-grained error policies to handle invalid
states caused by evolution errors, and also provides analytical bounds for the
error of all primitive variables. In this work, we describe the technical
aspects of implementing the RePrimAnd scheme into the GRMHD code Spritz. To
check our implementation as well as to assess the various features of the
scheme, we perform a number of GRMHD tests in three dimensions. Our tests,
which include critical cases such as a NS collapse to a BH as well as the early
evolution (~50 ms) of a Fishbone-Moncrief BH-accrection disk system, show that
RePrimAnd is able to support magnetized, low density environments with
magnetic-to-fluid pressure ratios as high as 10^4, in situations where the
previously used recovery scheme fails.
|
The optical trapping techniques have been extensively used in physics,
biophysics, micro-chemistry, and micro-mechanics to allow trapping and
manipulation of materials ranging from particles, cells, biological substances,
and polymers to DNA and RNA molecules. In this Letter, we present a convenient
and effective way to generate a novel phenomenon of trapping, named trap split,
in a conventional four-level double-\Lambda atomic system driven by four
femtosecond Laguerre-Gaussian laser pulses. We find that trap split can be
always achieved when atoms are trapped by such laser pulses, as compared to
Gaussian ones. This work would greatly facilitate the trapping and manipulating
the particles and generation of trap split. It may also suggest the possibility
of extension into new research fields, such as micro-machining and biophysics.
|
Graphene is a monoatomic layer of graphite with Carbon atoms arranged in a
two dimensional honeycomb lattice configuration. It has been known for more
than sixty years that the electronic structure of graphene can be modelled by
two-dimensional massless relativistic fermions. This property gives rise to
numerous applications, both in applied sciences and in theoretical physics.
Electronic circuits made out of graphene could take advantage of its high
electron mobility that is witnessed even at room temperature. In the
theoretical domain the Dirac-like behavior of graphene can simulate high energy
effects, such as the relativistic Klein paradox. Even more surprisingly,
topological effects can be encoded in graphene such as the generation of
vortices, charge fractionalization and the emergence of anyons. The impact of
the topological effects on graphene's electronic properties can be elegantly
described by the Atiyah-Singer index theorem. Here we present a pedagogical
encounter of this theorem and review its various applications to graphene. A
direct consequence of the index theorem is charge fractionalization that is
usually known from the fractional quantum Hall effect. The charge
fractionalization gives rise to the exciting possibility of realizing graphene
based anyons that unlike bosons or fermions exhibit fractional statistics.
Besides being of theoretical interest, anyons are a strong candidate for
performing error free quantum information processing.
|
We use cosmological simulations of high-redshift minihalos to investigate the
effect of dark matter annihilation (DMA) on the collapse of primordial gas. We
numerically investigate the evolution of the gas as it assembles in a
Population III stellar disk. We find that when DMA effects are neglected, the
disk undergoes multiple fragmentation events beginning at ~ 500 yr after the
appearance of the first protostar. On the other hand, DMA heating and
ionization of the gas speeds the initial collapse of gas to protostellar
densities and also affects the stability of the developing disk against
fragmentation, depending on the DM distribution. We compare the evolution when
we model the DM density with an analytical DM profile which remains centrally
peaked, and when we simulate the DM profile using N-body particles (the 'live'
DM halo). When utilizing the analytical DM profile, DMA suppresses disk
fragmentation for ~ 3500 yr after the first protostar forms, in agreement with
earlier work. However, when using a 'live' DM halo, the central DM density peak
is gradually flattened due to the mutual interaction between the DM and the
rotating gaseous disk, reducing the effects of DMA on the gas, and enabling
secondary protostars of mass ~ 1 M_sol to be formed within ~ 900 yr. These
simulations demonstrate that DMA is ineffective in suppressing gas collapse and
subsequent fragmentation, rendering the formation of long-lived dark stars
unlikely. However, DMA effects may still be significant in the early collapse
and disk formation phase of primordial gas evolution.
|
Dodona (dodona.ugent.be) is an intelligent tutoring system for computer
programming. It bridges the gap between assessment and learning by providing
real-time data and feedback to help students learn better, teachers teach
better and educational technology become more effective. We demonstrate how
Dodona can be used as a virtual co-teacher to stimulate active learning and
support challenge-based education in open and collaborative learning
environments. We also highlight some of the opportunities (automated feedback,
learning analytics, educational data mining) and challenges (scalable feedback,
open internet exams, plagiarism) we faced in practice. Dodona is free for use
and has more than 36 thousand registered users across many educational and
research institutes, of which 15 thousand new users registered last year.
Lowering the barriers for such a broad adoption was achieved by following best
practices and extensible approaches for software development, authentication,
content management, assessment, security and interoperability, and by adopting
a holistic view on computer-assisted learning and teaching that spans all
aspects of managing courses that involve programming assignments. The source
code of Dodona is available on GitHub under the permissive MIT open-source
license.
|
In spite of the large amount of existing neural models in the literature,
there is a lack of a systematic review of the possible effect of choosing
different initial conditions on the dynamic evolution of neural systems. In
this short review we intend to give insights into this topic by discussing some
published examples. First, we briefly introduce the different ingredients of a
neural dynamical model. Secondly, we introduce some concepts used to describe
the dynamic behavior of neural models, namely phase space and its portraits,
time series, spectra, multistability and bifurcations. We end with an analysis
of the irreversibility of processes and its implications on the functioning of
normal and pathological brains.
|
We prove a positive mass theorem for spin initial data sets $(M,g,k)$ that
contain an asymptotically flat end and a shield of dominant energy (a subset of
$M$ on which the dominant energy scalar $\mu-|J|$ has a positive lower bound).
In a similar vein, we show that for an asymptotically flat end $\mathcal{E}$
that violates the positive mass theorem (i.e. $\mathrm{E} < |\mathrm{P}|$),
there exists a constant $R>0$, depending only on $\mathcal{E}$, such that any
initial data set containing $\mathcal{E}$ must violate the hypotheses of
Witten's proof of the positive mass theorem in an $R$-neighborhood of
$\mathcal{E}$. This implies the positive mass theorem for spin initial data
sets with arbitrary ends, and we also prove a rigidity statement. Our proofs
are based on a modification of Witten's approach to the positive mass theorem
involving an additional independent timelike direction in the spinor bundle.
|
We give a pedagogical analysis on $K$ matrix models describing the $\pi N$
scattering amplitude, in $S_{11}$ channel at low energies. We show how the
correct use of analyticity in the $s$ channel and crossing symmetry in $t$ and
$u$ channels leads to a much improved analytic behavior in the negative $s$
region, in agreement with the prediction from chiral perturbation amplitudes in
its validity region. The analysis leads again to the conclusion that a genuine
$N^*(890)$ resonance exists.
|
Many molecular "quantum" theories, like "quantum chemistry", conceal that
they are actually quantum-classical approaches---they treat one set of
molecular degrees of freedom classically while the remaining degrees of freedom
follow the laws of quantum mechanics. We show that the prominent "frozen-nuclei
approximation", which is often used in molecular control communities, is a
further example for such theory reduction: It treats the nuclei of the molecule
as classical particles. Here, we demonstrate that the ignorance about the
quantum nature of nuclei has far-reaching consequences for the theoretical
description of molecules. We analyse the symmetry of oriented and aligned rigid
molecules with feasible permutations of identical nuclei and show: The
presumption of fixed nuclei corresponds to a localized state that is impossible
to create if the existence of stable nuclear spin isomers is a justifiable
assumption for the controlled molecule. The results of studies on molecules
containing identical nuclei have to be re-evaluated and properly
anti-symmetrised, because for such molecules the premise of frozen nuclei is
inherently wrong: Molecular wave functions have to obey the spin-statistics
theorem twice.
|
Partially observable Markov decision processes (POMDP) are a useful model for
decision-making under partial observability and stochastic actions. Partially
Observable Monte-Carlo Planning is an online algorithm for deciding on the next
action to perform, using a Monte-Carlo tree search approach, based on the UCT
(UCB applied to trees) algorithm for fully observable Markov-decision
processes. POMCP develops an action-observation tree, and at the leaves, uses a
rollout policy to provide a value estimate for the leaf. As such, POMCP is
highly dependent on the rollout policy to compute good estimates, and hence
identify good actions. Thus, many practitioners who use POMCP are required to
create strong, domain-specific heuristics.
In this paper, we model POMDPs as stochastic contingent planning problems.
This allows us to leverage domain-independent heuristics that were developed in
the planning community. We suggest two heuristics, the first is based on the
well-known h_add heuristic from classical planning, and the second is computed
in belief space, taking the value of information into account.
|
We present PhysioLLM, an interactive system that leverages large language
models (LLMs) to provide personalized health understanding and exploration by
integrating physiological data from wearables with contextual information.
Unlike commercial health apps for wearables, our system offers a comprehensive
statistical analysis component that discovers correlations and trends in user
data, allowing users to ask questions in natural language and receive generated
personalized insights, and guides them to develop actionable goals. As a case
study, we focus on improving sleep quality, given its measurability through
physiological data and its importance to general well-being. Through a user
study with 24 Fitbit watch users, we demonstrate that PhysioLLM outperforms
both the Fitbit App alone and a generic LLM chatbot in facilitating a deeper,
personalized understanding of health data and supporting actionable steps
toward personal health goals.
|
In this note, we provide a tractable example of a polyhomogeneous solution
space for electromagnetism at null infinity in four dimensions. The memory
effect for electromagnetism is then derived from the polyhomogeneous solution
space. We also comment on the connection between the electromagnetic memories
and asymptotic symmetries.
|
Double barrier GaN/AlN resonant tunneling heterostructures have been grown by
molecular beam epitaxy on the (0001) plane of commercially available bulk GaN
substrates. Resonant tunneling diodes were fabricated; room temperature
current-voltage measurements reveal the presence of a negative differential
conductance region under forward bias with peak current densities of ~6.4
$kA/cm^2$ and a peak to valley current ratio of ~1.3. Reverse bias operation
presents a characteristic turn-on threshold voltage intimately linked to the
polarization fields present in the heterostructure. An analytic electrostatic
model is developed to capture the unique features of
polar-heterostructure-based resonant tunneling diodes; both the resonant and
threshold voltages are derived as a function of the design parameters and
polarization fields. Subsequent measurements confirm the repeatability of the
negative conductance and demonstrate that III-nitride tunneling
heterostructures are capable of robust resonant transport at room temperature.
|
It has recently been pointed out by Kowalski et. al. (arxiv:0804.4142) that
there is `an unexpected brightness of the SnIa data at z>1'. We quantify this
statement by constructing a new statistic which is applicable directly on the
Type Ia Supernova (SnIa) distance moduli. This statistic is designed to pick up
systematic brightness trends of SnIa datapoints with respect to a best fit
cosmological model at high redshifts. It is based on binning the normalized
differences between the SnIa distance moduli and the corresponding best fit
values in the context of a specific cosmological model (eg LCDM). We then focus
on the highest redshift bin and extend its size towards lower redshifts until
the Binned Normalized Difference (BND) changes sign (crosses 0) at a redshift
z_c (bin size N_c). The bin size N_c of this crossing (the statistical
variable) is then compared with the corresponding crossing bin size N_{mc} for
Monte Carlo data realizations based on the best fit model. We find that the
crossing bin size N_c obtained from the Union08 and Gold06 data with respect to
the best fit LCDM model is anomalously large compared to N_{mc} of the
corresponding Monte Carlo datasets obtained from the best fit LCDM in each
case. In particular, only 2.2% of the Monte Carlo LCDM datasets are consistent
with the Gold06 value of N_c while the corresponding probability for the
Union08 value of N_c is 5.3%. Thus, according to this statistic, the
probability that the high redshift brightness bias of the Union08 and Gold06
datasets is realized in the context of a (w_0,w_1)=(-1,0) model (LCDM
cosmology) is less than 6%. The corresponding realization probability in the
context of a (w_0,w_1)=(-1.4,2) model is more than 30% for both the Union08 and
the Gold06 datasets.
|
New experimental results from photoproduction of hadrons at HERA are
reviewed.
|
We investigate the magnetic properties of archetypal transition-metal oxides
MnO, FeO, CoO and NiO under very high pressure by x-ray emission spectroscopy
at the K\beta line. We observe a strong modification of the magnetism in the
megabar range in all the samples except NiO. The results are analyzed within a
multiplet approach including charge-transfer effects. The pressure dependence
of the emission line is well accounted for by changes of the ligand field
acting on the d electrons and allows us to extract parameters like local
d-hybridization strength, O-2p bandwidth and ionic crystal field across the
magnetic transition. This approach allows a first-hand insight into the
mechanism of the pressure induced spin transition.
|
We prove various finiteness and representability results for flat cohomology
of finite flat abelian group schemes. In particular, we show that if
$f:X\rightarrow \mathrm{Spec} (k)$ is a projective scheme over a field $k$ and
$G$ is a finite flat abelian group scheme over $X$ then $R^if_*G$ is an
algebraic space for all $i$. More generally, we study the derived pushforwards
$R^if_*G$ for $f:X\rightarrow S$ a projective morphism and $G$ a finite flat
abelian group scheme over $X$. We also develop a theory of compactly supported
cohomology for finite flat abelian group schemes, describe cohomology in terms
of the cotangent complex for group schemes of height $1$, and relate the
Dieudonn\'e modules of the group schemes $R^if_*\mu _p$ to cohomology
generalizing work of Illusie. A higher categorical version of our main
representability results is also presented.
|
Over the years, Isogeometric Analysis has shown to be a successful
alternative to the Finite Element Method (FEM). However, solving the resulting
linear systems of equations efficiently remains a challenging task. In this
paper, we consider a p-multigrid method, in which coarsening is applied in the
approximation order p instead of the mesh width h. Since the use of classical
smoothers (e.g. Gauss-Seidel) results in a p-multigrid method with
deteriorating performance for higher values of p, the use of an ILUT smoother
is investigated. Numerical results and a spectral analysis indicate that the
resulting p-multigrid method exhibits convergence rates independent of h and p.
In particular, we compare both coarsening strategies (e.g. coarsening in h or
p) adopting both smoothers for a variety of two and threedimensional
benchmarks.
|
Amplitudes for the reaction $\pi^-p\to \Lambda K^0$ are reconstructed from
data on the differential cross section $d\sigma/d\Omega$, the recoil
polarization $P$, and on the spin rotation parameter $\beta$. At low energies,
no data on $\beta$ exist, resulting in ambiguities. An approximation using $S$
and $P$ waves leads only to a fair description of the data on $d\sigma/d\Omega$
and $P$; in this case, there are two sets of amplitudes. Including $D$ waves,
the data on $d\sigma/d\Omega$ and $P$ are well reproduced by the fit but now,
there are several distinct solutions which describe the data with identical
precision. In the range where the spin rotation parameter $\beta$ was measured,
a full and unambiguous reconstruction of the partial wave amplitudes is
possible. The energy-independent amplitudes are compared to the energy
dependent amplitudes which resulted from a coupled channel fit (BnGa2011-02) to
a large data set including both pion and photo-induced reactions. Significant
deviations are observed. Consistency between energy dependent and energy
independent solutions by choosing the energy independent solution which is
closest to the energy dependent solution. In a second step, the {\it known}
energy dependent solution for low (or high) partial waves is imposed and only
the high (or low) partial waves are fitted leading to smaller uncertainties.
|
Among the thriving ecosystem of cloud computing and the proliferation of
Large Language Model (LLM)-based code generation tools, there is a lack of
benchmarking for code generation in cloud-native applications. In response to
this need, we present CloudEval-YAML, a practical benchmark for cloud
configuration generation. CloudEval-YAML tackles the diversity challenge by
focusing on YAML, the de facto standard of numerous cloud-native tools. We
develop the CloudEval-YAML benchmark with practicality in mind: the dataset
consists of hand-written problems with unit tests targeting practical
scenarios. We further enhanced the dataset to meet practical needs by
rephrasing questions in a concise, abbreviated, and bilingual manner. The
dataset consists of 1011 problems that take more than 1200 human hours to
complete. To improve practicality during evaluation, we build a scalable
evaluation platform for CloudEval-YAML that achieves a 20 times speedup over a
single machine. To the best of our knowledge, the CloudEval-YAML dataset is the
first hand-written dataset targeting cloud-native applications. We present an
in-depth evaluation of 12 LLMs, leading to a deeper understanding of the
problems and LLMs, as well as effective methods to improve task performance and
reduce cost.
|
We study the diffusion and submonolayer spreading of chainlike molecules on
surfaces. Using the fluctuating bond model we extract the collective and tracer
diffusion coefficients D_c and D_t with a variety of methods. We show that
D_c(theta) has unusual behavior as a function of the coverage theta. It first
increases but after a maximum goes to zero as theta go to one. We show that the
increase is due to entropic repulsion that leads to steep density profiles for
spreading droplets seen in experiments. We also develop an analytic model for
D_c(theta) which agrees well with the simulations.
|
We investigate the metastable repulsive branch of a mobile impurity coupled
to a degenerate Fermi gas via short-range interactions. We show that the
quasiparticle lifetime of this repulsive Fermi polaron can be experimentally
probed by driving Rabi oscillations between weakly and strongly interacting
impurity states. Using a time-dependent variational approach, we find that we
can accurately model the impurity Rabi oscillations that were recently measured
for repulsive Fermi polarons in both two and three dimensions. Crucially, our
theoretical description does not include relaxation processes to the
lower-lying attractive branch. Thus, the theory-experiment agreement
demonstrates that the quasiparticle lifetime is determined by many-body
dephasing within the upper repulsive branch rather than by the metastability of
the upper branch itself. Our findings shed light on recent experimental
observations of persistent repulsive correlations, and have important
consequences for the nature and stability of the strongly repulsive Fermi gas.
|
[Abridged] Star and planet formation are the complex outcomes of
gravitational collapse and angular momentum transport mediated by protostellar
and protoplanetary disks. In this review we focus on the role of gravitational
instability in this process. We begin with a brief overview of the
observational evidence for massive disks that might be subject to gravitational
instability, and then highlight the diverse ways in which the instability
manifests itself in protostellar and protoplanetary disks: the generation of
spiral arms, small scale turbulence-like density fluctuations, and
fragmentation of the disk itself. We present the analytic theory that describes
the linear growth phase of the instability, supplemented with a survey of
numerical simulations that aim to capture the non-linear evolution. We
emphasize the role of thermodynamics and large scale infall in controlling the
outcome of the instability. Despite apparent controversies in the literature,
we show a remarkable level of agreement between analytic predictions and
numerical results. We highlight open questions related to (1) the development
of a turbulent cascade in thin disks, and (2) the role of mode-mode coupling in
setting the maximum angular momentum transport rate in thick disks.
|
Community structure analysis is a powerful tool for social networks, which
can simplify their topological and functional analysis considerably. However,
since community detection methods have random factors and real social networks
obtained from complex systems always contain error edges, evaluating the
significance of community structure partitioned is an urgent and important
question. In this paper, integrating the specific characteristics of real
society, we present a novel framework analyzing the significance of social
community specially. The dynamics of social interactions are modeled by
identifying social leaders and corresponding hierarchical structures. Instead
of a direct comparison with the average outcome of a random model, we compute
the similarity of a given node with the leader by the number of common
neighbors. To determine the membership vector, an efficient community detection
algorithm is proposed based on the position of nodes and their corresponding
leaders. Then, using log-likelihood score, the tightness of community can be
derived. Based on the distribution of community tightness, we establish a new
connection between $p$-value theory and network analysis and then get a novel
statistical form significance measure. Finally, the framework is applied to
both benchmark networks and real social networks. Experimental results show
that our work can be used in many fields, such as determining the optimal
number of communities, analyzing the social significance of a given community,
comparing the performance among various algorithms and so on.
|
A novel hybrid design based electronic voting system is proposed, implemented
and analyzed. The proposed system uses two voter verification techniques to
give better results in comparison to single identification based systems.
Finger print and facial recognition based methods are used for voter
identification. Cross verification of a voter during an election process
provides better accuracy than single parameter identification method. The
facial recognition system uses Viola-Jones algorithm along with rectangular
Haar feature selection method for detection and extraction of features to
develop a biometric template and for feature extraction during the voting
process. Cascaded machine learning based classifiers are used for comparing the
features for identity verification using GPCA (Generalized Principle Component
Analysis) and K-NN (K-Nearest Neighbor). It is accomplished through comparing
the Eigen-vectors of the extracted features with the biometric template
pre-stored in the election regulatory body database. The results of the
proposed system show that the proposed cascaded design based system performs
better than the systems using other classifiers or separate schemes i.e. facial
or finger print based schemes. The proposed system will be highly useful for
real time applications due to the reason that it has 91% accuracy under nominal
light in terms of facial recognition. with bags of paper votes. The central
station compiles and publishes the names of winners and losers through
television and radio stations. This method is useful only if the whole process
is completed in a transparent way. However, there are some drawbacks to this
system. These include higher expenses, longer time to complete the voting
process, fraudulent practices by the authorities administering elections as
well as malpractices by the voters [1]. These challenges result in manipulated
election results.
|
We develop an effective extended Hubbard model to describe the low-energy
electronic properties of the twisted bilayer graphene. By using the Bloch
states in the effective continuum model and with the aid of the maximally
localized algorithm, we construct the Wannier orbitals and obtain an effective
tight-binding model on the emergent honeycomb lattice. We found the Wannier
state takes a peculiar three-peak form in which the amplitude maxima are
located at the triangle corners surrounding the center. We estimate the direct
Coulomb interaction and the exchange interaction between the Wannier states. At
the filling of two electrons per super cell, in particular, we find an
unexpected coincidence in the direct Coulomb energy between a charge-ordered
state and a homogeneous state, which would possibly lead to an unconventional
many-body state.
|
The rapidly developing deep learning (DL) techniques have been applied in
software systems with various application scenarios. However, they could also
pose new safety threats with potentially serious consequences, especially in
safety-critical domains. DL libraries serve as the underlying foundation for DL
systems, and bugs in them can have unpredictable impacts that directly affect
the behaviors of DL systems. Previous research on fuzzing DL libraries still
has limitations in the diversity of test inputs, the construction of test
oracles, and the precision of detection. In this paper, we propose MoCo, a
novel fuzzing testing method for DL libraries via assembling code. MoCo first
disassembles the seed code file to obtain the template and code blocks, and
then employs code block mutation operators (e.g., API replacement, random
generation, and boundary checking) to generate more new code blocks adapted to
the template. By inserting context-appropriate code blocks into the template
step by step, MoCo can generate a tree of code files with intergenerational
relations. According to the derivation relations in this tree and the applied
mutation operators, we construct the test oracle based on the execution state
consistency. Since the granularity of code assembly and mutation is controlled
rather than randomly divergent, we can quickly pinpoint the lines of code where
the bugs are located and the corresponding triggering conditions. We conduct a
comprehensive experiment to evaluate the efficiency and effectiveness of MoCo
using three widely-used DL libraries (i.e., TensorFlow, PyTorch, and Jittor).
During the experiment, MoCo detects 64 new bugs of four types in three DL
libraries, where 51 bugs have been confirmed, and 13 bugs have been fixed by
developers.
|
In an intelligent transportation system, the effects and relations of traffic
flow at different points in a network are valuable features which can be
exploited for control system design and traffic forecasting. In this paper, we
define the notion of causality based on the directed information, a
well-established data-driven measure, to represent the effective connectivity
among nodes of a vehicular traffic network. This notion indicates whether the
traffic flow at any given point affects another point's flow in the future and,
more importantly, reveals the extent of this effect. In contrast with
conventional methods to express connections in a network, it is not limited to
linear models and normality conditions. In this work, directed information is
used to determine the underlying graph structure of a network, denoted directed
information graph, which expresses the causal relations among nodes in the
network. We devise an algorithm to estimate the extent of the effects in each
link and build the graph. The performance of the algorithm is then analyzed
with synthetic data and real aggregated data of vehicular traffic.
|
This paper introduces KnowHalu, a novel approach for detecting hallucinations
in text generated by large language models (LLMs), utilizing step-wise
reasoning, multi-formulation query, multi-form knowledge for factual checking,
and fusion-based detection mechanism. As LLMs are increasingly applied across
various domains, ensuring that their outputs are not hallucinated is critical.
Recognizing the limitations of existing approaches that either rely on the
self-consistency check of LLMs or perform post-hoc fact-checking without
considering the complexity of queries or the form of knowledge, KnowHalu
proposes a two-phase process for hallucination detection. In the first phase,
it identifies non-fabrication hallucinations--responses that, while factually
correct, are irrelevant or non-specific to the query. The second phase,
multi-form based factual checking, contains five key steps: reasoning and query
decomposition, knowledge retrieval, knowledge optimization, judgment
generation, and judgment aggregation. Our extensive evaluations demonstrate
that KnowHalu significantly outperforms SOTA baselines in detecting
hallucinations across diverse tasks, e.g., improving by 15.65% in QA tasks and
5.50% in summarization tasks, highlighting its effectiveness and versatility in
detecting hallucinations in LLM-generated content.
|
Astrophysical fluids under the influence of magnetic fields are often
subjected to single-fluid or two-fluid approximations. In the case of weakly
ionized plasmas however, this can be inappropriate due to distinct responses
from the multiple constituent species to both collisional and non-collisional
forces. As a result, in dense molecular clouds and proto-stellar accretion
discs for instance, the conductivity of the plasma may be highly anisotropic
leading to phenomena such as Hall and ambipolar diffusion strongly influencing
the dynamics.
Diffusive processes are known to restrict the stability of conventional
numerical schemes which are not implicit in nature. Furthermore, recent work
establishes that a large Hall term can impose an additional severe stability
limit on standard explicit schemes. Following a previous paper which presented
the one-dimensional case, we describe a fully three-dimensional method which
relaxes the normal restrictions on explicit schemes for multifluid processes.
This is achieved by applying the little known Super TimeStepping technique to
the symmetric (ambipolar) component of the evolution operator for the magnetic
field in the local plasma rest-frame, and the new Hall Diffusion Scheme to the
skew-symmetric (Hall) component.
|
If dark energy --- which drives the accelerated expansion of the universe ---
consists of a light scalar field, it might be detectable as a "fifth force"
between normal-matter objects, in potential conflict with precision tests of
gravity. Chameleon fields and other theories with screening mechanisms,
however, can evade these tests by suppressing the forces in regions of high
density, such as the laboratory. Using a cesium matter-wave interferometer near
a spherical mass in an ultra-high vacuum chamber, we reduce the screening
mechanism by probing the field with individual atoms rather than bulk matter.
Thus, we constrain a wide class of dark energy theories, including a range of
chameleon and other theories that reproduce the observed cosmic acceleration.
|
In this paper, we provide a theoretical description, and calculate, the
nonlinear frequency shift, group velocity and collionless damping rate, $\nu$,
of a driven electron plasma wave (EPW). All these quantities, whose physical
content will be discussed, are identified as terms of an envelope equation
allowing one to predict how efficiently an EPW may be externally driven. This
envelope equation is derived directly from Gauss law and from the investigation
of the nonlinear electron motion, provided that the time and space rates of
variation of the EPW amplitude, $E_p$, are small compared to the plasma
frequency or the inverse of the Debye length. $\nu$ arises within the EPW
envelope equation as more complicated an operator than a plain damping rate,
and may only be viewed as such because $(\nu E_p)/E_p$ remains nearly constant
before abruptly dropping to zero. We provide a practical analytic formula for
$\nu$ and show, without resorting to complex contour deformation, that in the
limit $E_p \to 0$, $\nu$ is nothing but the Landau damping rate. We then term
$\nu$ the "nonlinear Landau damping rate" of the driven plasma wave. As for the
nonlinear frequency shift of the EPW, it is also derived theoretically and
found to assume values significantly different from previously published ones,
assuming that the wave is freely propagating. Moreover, we find no limitation
in $k \lambda_D$, $k$ being the plasma wavenumber and $\lambda_D$ the Debye
length, for a solution to the dispertion relation to exist, and want to stress
here the importance of specifying how an EPW is generated to discuss its
properties. Our theoretical predictions are in excellent agreement with results
inferred from Vlasov simulations of stimulated Raman scattering (SRS), and an
application of our theory to the study of SRS is presented.
|
A conditionally exactly solvable potential, the supersymmetric partner of the
harmonic oscillator is investigated in the PT-symmetric setting. It is shown
that a number of properties characterizing shape-invariant and Natanzon-class
potentials generated by an imaginary coordinate shift $x-{\rm i}\epsilon$ also
hold for this potential outside the Natanzon class.
|
Over the last decade, most of the increase in computing power has been gained
by advances in accelerated many-core architectures, mainly in the form of
GPGPUs. While accelerators achieve phenomenal performances in various computing
tasks, their utilization requires code adaptations and transformations. Thus,
OpenMP, the most common standard for multi-threading in scientific computing
applications, introduced offloading capabilities between host (CPUs) and
accelerators since v4.0, with increasing support in the successive v4.5, v5.0,
v5.1, and the latest v5.2 versions. Recently, two state-of-the-art GPUs -- the
Intel Ponte Vecchio Max 1100 and the NVIDIA A100 GPUs -- were released to the
market, with the oneAPI and NVHPC compilers for offloading, correspondingly. In
this work, we present early performance results of OpenMP offloading
capabilities to these devices while specifically analyzing the portability of
advanced directives (using SOLLVE's OMPVV test suite) and the scalability of
the hardware in representative scientific mini-app (the LULESH benchmark). Our
results show that the coverage for version 4.5 is nearly complete in both
latest NVHPC and oneAPI tools. However, we observed a lack of support in
versions 5.0, 5.1, and 5.2, which is particularly noticeable when using NVHPC.
From the performance perspective, we found that the PVC1100 and A100 are
relatively comparable on the LULESH benchmark. While the A100 is slightly
better due to faster memory bandwidth, the PVC1100 reaches the next problem
size (400^3) scalably due to the larger memory size.
|
We propose and analyze surface-plasmon-driven electron spin currents in a
thin metallic film. The electron gas in the metal follows the transversally
rotating electric fields of the surface plasmons (SPs), which leads to a static
magnetization gradient. We consider herein SPs in a thin-film
insulator-metal-insulator structure and solve the spin diffusion equation in
the presence of a magnetization gradient. The results reveal that the SPs at
the metal interfaces generate spin currents in the metallic film. For thinner
film, the SPs become strongly hybridized, which increases the magnetization
gradient and enhances the spin current. We also discuss how the spin current
depends on SP wavelength and the spin-diffusion length of the metal. The
polarization of the spin current can be controlled by tuning the wavelength of
the SPs and/or the spin diffusion length.
|
Information scrambling refers to the unitary dynamics that quickly spreads
and encodes localized quantum information over an entire many-body system and
makes the information accessible from any small subsystem. While information
scrambling is the key to understanding complex quantum many-body dynamics and
is well-understood in random unitary models, it has been hardly explored in
Hamiltonian systems. In this Letter, we investigate the information recovery in
various time-independent Hamiltonian systems, including chaotic spin chains and
Sachdev-Ye-Kitaev (SYK) models. We show that information recovery is possible
in certain, but not all, chaotic models, which highlights the difference
between information recovery and quantum chaos based on the energy spectrum or
the out-of-time-ordered correlators. We also show that information recovery
probes transitions caused by the change of information-theoretic features of
the dynamics.
|
To advance the neural decoding of Portuguese, in this paper we present a
fully open Transformer-based, instruction-tuned decoder model that sets a new
state of the art in this respect. To develop this decoder, which we named
Gerv\'asio PT*, a strong LLaMA~2 7B model was used as a starting point, and its
further improvement through additional training was done over language
resources that include new instruction data sets of Portuguese prepared for
this purpose, which are also contributed in this paper. All versions of
Gerv\'asio are open source and distributed for free under an open license,
including for either research or commercial usage, and can be run on
consumer-grade hardware, thus seeking to contribute to the advancement of
research and innovation in language technology for Portuguese.
|
Radiative transfer models were developed to understand the optical
polarizations in edge-on galaxies, which are observed to occur even outside the
geometrically thin dust disk, with a scale height of ~ 0.2 kpc. In order to
reproduce the vertically extended polarization structure, we find it is
essential to include a geometrically thick dust layer in the radiative transfer
model, in addition to the commonly-known thin dust layer. The models include
polarizations due to both dust scattering and dichroic extinction which is
responsible for the observed interstellar polarization in the Milky Way. We
also find that the polarization level is enhanced if the clumpiness of the
interstellar medium, and the dichroic extinction by vertical magnetic fields in
the outer regions of the dust lane are included in the radiative transfer
model. The predicted degree of polarization outside the dust lane was found to
be consistent with that (ranging from 1% to 4%) observed in NGC 891.
|
The trade-off between optimality and complexity has been one of the most
important challenges in the field of robust Model Predictive Control (MPC). To
address the challenge, we propose a flexible robust MPC scheme by synergizing
the multi-stage and tube-based MPC approaches. The key idea is to exploit the
non-conservatism of the multi-stage MPC and the simplicity of the tube-based
MPC. The proposed scheme provides two options for the user to determine the
trade-off depending on the application: the choice of the robust horizon and
the classification of the uncertainties. Beyond the robust horizon, the
branching of the scenario-tree employed in multi-stage MPC is avoided with the
help of tubes. The growth of the problem size with respect to the number of
uncertainties is reduced by handling \emph{small} uncertainties via an
invariant tube that can be computed offline. This results in linear growth of
the problem size beyond the robust horizon and no growth of the problem size
concerning small magnitude uncertainties. The proposed approach helps to
achieve a desired trade-off between optimality and complexity compared to
existing robust MPC approaches. We show that the proposed approach is robustly
asymptotically stable. Its advantages are demonstrated for a CSTR example.
|
Large N gauge theories with adjoint matter can be numerically studied using
lattice techniques. Eguchi-Kawai reductions holds for this theory and one can
reduce the lattice model to a single site. Hybrid Monte Carlo algorithm can be
used to simulate this model. One can either perform an exact computation of the
"fermionic force" or use pseudo fermions as part of the HMC algorithm. The
former algorithm is slower than the latter but has the advantage that one can
work with any real number for the fermion flavor. Some results using both
algorithms will be presented.
|
In this article, we propose a generalized model for nonequilibrium
vibrational energy distribution functions. The model can be used, in place of
equilibrium (Boltzmann) distribution functions, when deriving reaction rate
constants for high-temperature nonequilibrium flows. The distribution model is
derived based on recent \textit{ab initio} calculations, carried out using
potential energy surfaces developed using accurate computational quantum
chemistry techniques for the purpose of studying air chemistry at high
temperatures. Immediately behind a strong shock wave, the vibrational energy
distribution is non-Boltzmann. Specifically, as the gas internal energy rapidly
excites to a high temperature, overpopulation of the high-energy tail (relative
to a corresponding Boltzmann distribution) is observed in \textit{ab initio}
simulations. As the gas excites further and begins to dissociate, a depletion
of the high-energy tail is observed, during a time-invariant quasi-steady state
(QSS). Since the probability of dissociation is exponentially related to the
vibrational energy of the dissociating molecule, the overall dissociation rate
is sensitive to the populations of these high vibrational energy states. The
non-Boltzmann effects captured by the new model either enhance or reduce the
dissociation rate relative to that obtained assuming a Boltzmann distribution.
This article proposes a simple model that is demonstrated to reproduce these
non-Boltzmann effects quantitatively when compared to \textit{ab initio}
simulations.
|
The purpose of these lectures is threefold: We first give a short survey of
the Hida white noise calculus, and in this context we introduce the
Hida-Malliavin derivative as a stochastic gradient with values in the Hida
stochastic distribution space $(\mathcal{S}% )^*$. We show that this
Hida-Malliavin derivative defined on $L^2(\mathcal{F}_T,P)$ is a natural
extension of the classical Malliavin derivative defined on the subspace
$\mathbb{D}_{1,2}$ of $L^2(P)$. The Hida-Malliavin calculus allows us to prove
new results under weaker assumptions than could be obtained by the classical
theory. In particular, we prove the following: (i) A general integration by
parts formula and duality theorem for Skorohod integrals, (ii) a generalised
fundamental theorem of stochastic calculus, and (iii) a general Clark-Ocone
theorem, valid for all $F \in L^2(\mathcal{F}_T,P)$. As applications of the
above theory we prove the following: A general representation theorem for
backward stochastic differential equations with jumps, in terms of
Hida-Malliavin derivatives; a general stochastic maximum principle for optimal
control; backward stochastic Volterra integral equations; optimal control of
stochastic Volterra integral equations and other stochastic systems.
|
We present a probabilistic generative model and efficient algorithm to model
reciprocity in directed networks. Unlike other methods that address this
problem such as exponential random graphs, it assigns latent variables as
community memberships to nodes and a reciprocity parameter to the whole network
rather than fitting order statistics. It formalizes the assumption that a
directed interaction is more likely to occur if an individual has already
observed an interaction towards her. It provides a natural framework for
relaxing the common assumption in network generative models of conditional
independence between edges, and it can be used to perform inference tasks such
as predicting the existence of an edge given the observation of an edge in the
reverse direction. Inference is performed using an efficient
expectation-maximization algorithm that exploits the sparsity of the network,
leading to an efficient and scalable implementation. We illustrate these
findings by analyzing synthetic and real data, including social networks,
academic citations and the Erasmus student exchange program. Our method
outperforms others in both predicting edges and generating networks that
reflect the reciprocity values observed in real data, while at the same time
inferring an underlying community structure. We provide an open-source
implementation of the code online.
|
In this article, we investigate four-dimensional gradient shrinking Ricci
solitons close to a K\"ahler model. The first theorem could be considered as a
rigidity result for the K\"ahler-Ricci soliton structure on $\mathbb{S}^2\times
\mathbb{R}^2$ (in the sense of Remark 1). Moreover, we show that if the
quotient of norm of the self-dual Weyl tensor and scalar curvature is close to
that on a K\"ahler metric in a specific sense, then the gradient Ricci soliton
must be either half-conformally flat or locally K\"ahler.
|
Terahertz (THz)-band communications are celebrated as a key enabling
technology for next-generation wireless systems that promises to integrate a
wide range of data-demanding and delay-sensitive applications. Following recent
advancements in optical, electronic, and plasmonic transceiver design,
integrated, adaptive, and efficient THz systems are no longer far-fetched. In
this paper, we present a progressive vision of how the traditional "THz gap"
will transform into a "THz rush" over the next few years. We posit that the
breakthrough that the THz band will introduce will not be solely driven by
achievable high data rates, but more profoundly by the interaction between THz
sensing, imaging, and localization applications. We first detail the
peculiarities of each of these applications at the THz band. Then, we
illustrate how their coalescence results in enhanced environment-aware system
performance in beyond-5G use cases. We further discuss the implementation
aspects of this merging of applications in the context of shared and dedicated
resource allocation, highlighting the role of machine learning.
|
Query workloads and database schemas in OLAP applications are becoming
increasingly complex. Moreover, the queries and the schemas have to continually
\textit{evolve} to address business requirements. During such repetitive
transitions, the \textit{order} of index deployment has to be considered while
designing the physical schemas such as indexes and MVs.
An effective index deployment ordering can produce (1) a prompt query runtime
improvement and (2) a reduced total deployment time. Both of these are
essential qualities of design tools for quickly evolving databases, but
optimizing the problem is challenging because of complex index interactions and
a factorial number of possible solutions.
We formulate the problem in a mathematical model and study several techniques
for solving the index ordering problem. We demonstrate that Constraint
Programming (CP) is a more flexible and efficient platform to solve the problem
than other methods such as mixed integer programming and A* search. In addition
to exact search techniques, we also studied local search algorithms to find
near optimal solution very quickly.
Our empirical analysis on the TPC-H dataset shows that our pruning techniques
can reduce the size of the search space by tens of orders of magnitude. Using
the TPC-DS dataset, we verify that our local search algorithm is a highly
scalable and stable method for quickly finding a near-optimal solution.
|
Izawa's gauge-fixing procedure based on BRS symmetry is applied twice to the
massive tensor field theory of Fierz-Pauli type. It is shown the second
application can remove massless singularities which remain after the first
application. Massless limit of the theory is discussed.
|
For humanoid robots to live up to their potential utility, they must be able
to robustly recover from instabilities. In this work, we propose a number of
balance enhancements to enable the robot to both achieve specific, desired
footholds in the world and adjusting the step positions and times as necessary
while leveraging ankle and hip. This includes improving the calculation of
capture regions for bipedal locomotion to better consider how step constraints
affect the ability to recover. We then explore a new strategy for performing
cross-over steps to maintain stability, which greatly enhances the variety of
tracking error from which the robot may recover. Our last contribution is a
strategy for time adaptation during the transfer phase for recovery. We then
present these results on our humanoid robot, Nadia, in both simulation and
hardware, showing the robot walking over rough terrain, recovering from
external disturbances, and taking cross-over steps to maintain balance.
|
The problem of existence of arbitrage free and monotone CDO term structure
models is studied. Conditions for positivity and monotonicity of the
corresponding Heath-Jarrow-Morton-Musiela equation for the $x$-forward rates
with the use of the Milian type result are formulated. Two state spaces are
taken into account - of square integrable functions and a Sobolev space. For
the first the regularity results concerning pointwise monotonicity are proven.
Arbitrage free and monotone models are characterized in terms of the volatility
of the model and characteristics of the driving L\'evy process.
|
In this paper, the reinforcement learning (RL)-based optimal control problem
is studied for multiplicative-noise systems, where input delay is involved and
partial system dynamics is unknown. To solve a variant of Riccati-ZXL
equations, which is a counterpart of standard Riccati equation and determines
the optimal controller, we first develop a necessary and sufficient stabilizing
condition in form of several Lyapunov-type equations, a parallelism of the
classical Lyapunov theory. Based on the condition, we provide an offline and
convergent algorithm for the variant of Riccati-ZXL equations. According to the
convergent algorithm, we propose a RL-based optimal control design approach for
solving linear quadratic regulation problem with partially unknown system
dynamics. Finally, a numerical example is used to evaluate the proposed
algorithm.
|
For a space with involutive action, there is a variant of K-theory. Motivated
by T-duality in type II orbifold string theory, we establish that a twisted
version of the variant enjoys a topological T-duality for Real circle bundles,
i.e. circle bundles with real structure.
|
The positive parity doublet bands based on the $\pi h_{11/2}\otimes\nu
h_{11/2}$ configuration in $^{126}$Cs have been investigated in the two
quasi-particles coupled with a triaxial rotor model. The energy spectra $E(I)$,
energy staggering parameter $S(I)=[E(I)-E(I-1)]/2I$, $B(M1)$ and $B(E2)$
values, intraband $B(M1)/B(E2)$ ratios,
$B(M1)_{\textrm{in}}/B(M1)_{\textrm{out}}$ ratios, and orientation of the
angular momentum for the rotor as well as the valence proton and neutron are
calculated. After including the pairing correlation, good agreement has been
obtained between the calculated results and the data available, which supports
the interpretation of this positive parity doublet bands as chiral bands.
|
Polar molecules are an emerging platform for quantum technologies based on
their long-range electric dipole-dipole interactions, which open new
possibilities for quantum information processing and the quantum simulation of
strongly correlated systems. Here, we use magnetic and microwave fields to
design a fast entangling gate with $>0.999$ fidelity and which is robust with
respect to fluctuations in the trapping and control fields and to small thermal
excitations. These results establish the feasibility to build a scalable
quantum processor with a broad range of molecular species in optical-lattice
and optical-tweezers setups.
|
New methods for $D$-decomposition analysis are presented. They are based on
topology of real algebraic varieties and computational real algebraic geometry.
The estimate of number of root invariant regions for polynomial parametric
families of polynomial and matrices is given. For the case of two parametric
family more sharp estimate is proven. Theoretic results are supported by
various numerical simulations that show higher precision of presented methods
with respect to traditional ones. The presented methods are inherently global
and could be applied for studying $D$-decomposition for the space of parameters
as a whole instead of some prescribed regions. For symbolic computations the
Maple v.14 software and its package RegularChains are used.
|
Magnetic Resonance Fingerprinting (MRF) is an efficient quantitative MRI
technique that can extract important tissue and system parameters such as T1,
T2, B0, and B1 from a single scan. This property also makes it attractive for
retrospectively synthesizing contrast-weighted images. In general,
contrast-weighted images like T1-weighted, T2-weighted, etc., can be
synthesized directly from parameter maps through spin-dynamics simulation
(i.e., Bloch or Extended Phase Graph models). However, these approaches often
exhibit artifacts due to imperfections in the mapping, the sequence modeling,
and the data acquisition. Here we propose a supervised learning-based method
that directly synthesizes contrast-weighted images from the MRF data without
going through the quantitative mapping and spin-dynamics simulation. To
implement our direct contrast synthesis (DCS) method, we deploy a conditional
Generative Adversarial Network (GAN) framework and propose a multi-branch U-Net
as the generator. The input MRF data are used to directly synthesize
T1-weighted, T2-weighted, and fluid-attenuated inversion recovery (FLAIR)
images through supervised training on paired MRF and target spin echo-based
contrast-weighted scans. In-vivo experiments demonstrate excellent image
quality compared to simulation-based contrast synthesis and previous DCS
methods, both visually as well as by quantitative metrics. We also demonstrate
cases where our trained model is able to mitigate in-flow and spiral
off-resonance artifacts that are typically seen in MRF reconstructions and thus
more faithfully represent conventional spin echo-based contrast-weighted
images.
|
It has recently been shown that the thermodynamics of a FRW universe can be
fully derived using the generalized uncertainty principle (GUP) in extra
dimensions as a primary input. There is a phenomenologically close relation
between the GUP and Modified Dispersion Relations (MDR). However, the form of
the MDR in theories with extra dimensions is as yet not known. The purpose of
this letter is to derive the MDR in extra dimensional scenarios. To achieve
this goal, we focus our attention on the thermodynamics of a FRW universe
within a proposed MDR in an extra dimensional model universe. We then compare
our results with the well-known results for the thermodynamics of a FRW
universe in an extra dimensional GUP setup. The result shows that the entropy
functionals calculated in these two approaches are the same, pointing to a
possible conclusion that these approaches are equivalent. In this way, we
derive the MDR form in a model universe with extra dimensions that would have
interesting implications on the construction of the ultimate quantum gravity
scenario.
|
We observe matterwave interference of a single cesium atom in free fall. The
interferometer is an absolute sensor of acceleration and we show that this
technique is sensitive to forces at the level of $3.2\times10^{-27}$ N with a
spatial resolution at the micron scale. We observe the build up of the
interference pattern one atom at a time in an interferometer where the mean
path separation extends far beyond the coherence length of the atom. Using the
coherence length of the atom wavepacket as a metric, we directly probe the
velocity distribution and measure the temperature of a single atom in free
fall.
|
In general a contractible complex need not be collapsible. Moreover, there
exist complexes which are collapsible but even so admit a collapsing sequence
where one "gets stuck", that is one can choose the collapses in such a way that
one arrives at a nontrivial complex which admits no collapsing moves. Here we
examine this phenomenon in the case of a simplex. In particular we characterize
all values of $n$ and $d$ so that the n-simplex may collapse to a d-complex
from which no further collapses are possible. Equivalently and in the language
of high-dimensional generalizations of trees, we construct hypertrees that are
anticollapsible, but not collapsible. Furthermore we examine anticollapsibility
in random simplicial complexes.
|
The use of complex analysis for computing one-loop scattering amplitudes is
naturally induced by generalised unitarity-cut conditions, fulfilled by complex
values of the loop variable. We report on two techniques: the cut-integration
with spinor-variables as contour integrals of rational functions; and the use
of the Discrete Fourier Transform to optimize the reduction of tensor-integrals
to master scalar integrals.
|
We investigate the thermodynamic properties of stellar self-gravitating
system arising from the Tsallis generalized entropy. In particular, physical
interpretation of the thermodynamic instability, as has been revealed by
previous paper(Taruya & Sakagami, cond-mat/0107494, Physica A 307, 185 (2002)),
is discussed in detail based on the non-extensive thermostatistics. Examining
the Clausius relation in a quasi-static experiment, we obtain the standard
result of thermodynamic relation that the physical temperature of the
equilibrium non-extensive system is identified with the inverse of the Lagrange
multiplier, $T_{phys}=1/\beta$. Using this relation, the specific heat of total
system is computed, and confirm the common feature of self-gravitating system
that the presence of negative specific heat leads to the thermodynamic
instability. In addition to the gravothermal instability discovered previously,
the specific heat shows the curious divergent behavior at the polytrope index
$n>3$, suggesting another type of thermodynamic instability. Evaluating the
second variation of free energy, we find that the marginal stability condition
indicated from the specific heat can be exactly recovered from the second
variation of free energy. Thus, the stellar polytropic system is consistently
characterized by the non-extensive thermostatistics as a plausible thermal
equilibrium state. We also clarify the non-trivial scaling behavior appeared in
specific heat and address the origin of non-extensive nature in stellar
polytrope.
|
We investigate the stochasticity in temperature fluctuations in the cosmic
microwave background (CMB) radiation data from {\it Wilkinson Microwave
Anisotropy Probe}. We show that the angular fluctuations of the temperature is
a Markov process with a {\it Markov angular scale}, $\Theta_{\rm
Markov}=1.01^{+0.09}_{-0.07}$. We characterize the complexity of the CMB
fluctuations by means of a Fokker-Planck or Langevin equation and measure the
associated Kramers-Moyal coefficients for the fluctuating temperature field
$T(\hat n)$ and its increment, $\Delta T =T(\hat n_1) - T(\hat n_2)$. Through
this method we show that temperature fluctuations in the CMB has fat tails
compared to a Gaussian distribution.
|
Kinesin-5, also known as Eg5 in vertebrates is a processive motor with 4
heads, which moves on filamentous tracks called microtubules. The basic
function of Kinesin-5 is to slide apart two anti-parallel microtubules by
simultaneously walking on both the microtubules. We develop an analytical
expression for the steady-state relative velocity of this sliding in terms of
the rates of attachments and detachments of motor heads with the ATPase sites
on the microtubules. We first analyse the motion of one pair of motor heads on
one microtubule and then couple it to the motion of the other pair of motor
heads of the same motor on the second microtubule to get the relative velocity
of sliding.
|
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.
|
It has been shown experimentally that contact interactions may influence the
migration of cancer cells. Previous works have modelized this thanks to
stochastic, discrete models (cellular automata) at the cell level. However, for
the study of the growth of real-size tumors with several millions of cells, it
is best to use a macroscopic model having the form of a partial differential
equation (PDE) for the density of cells. The difficulty is to predict the
effect, at the macroscopic scale, of contact interactions that take place at
the microscopic scale. To address this we use a multiscale approach: starting
from a very simple, yet experimentally validated, microscopic model of
migration with contact interactions, we derive a macroscopic model. We show
that a diffusion equation arises, as is often postulated in the field of glioma
modeling, but it is nonlinear because of the interactions. We give the explicit
dependence of diffusivity on the cell density and on a parameter governing
cell-cell interactions. We discuss in details the conditions of validity of the
approximations used in the derivation and we compare analytic results from our
PDE to numerical simulations and to some in vitro experiments. We notice that
the family of microscopic models we started from includes as special cases some
kinetically constrained models that were introduced for the study of the
physics of glasses, supercooled liquids and jamming systems.
|
With the ongoing debate on 'freedom of speech' vs. 'hate speech' there is an
urgent need to carefully understand the consequences of the inevitable
culmination of the two, i.e., 'freedom of hate speech' over time. An ideal
scenario to understand this would be to observe the effects of hate speech in
an (almost) unrestricted environment. Hence, we perform the first temporal
analysis of hate speech on Gab.com, a social media site with very loose
moderation policy. We first generate temporal snapshots of Gab from millions of
posts and users. Using these temporal snapshots, we compute an activity vector
based on DeGroot model to identify hateful users. The amount of hate speech in
Gab is steadily increasing and the new users are becoming hateful at an
increased and faster rate. Further, our analysis analysis reveals that the hate
users are occupying the prominent positions in the Gab network. Also, the
language used by the community as a whole seem to correlate more with that of
the hateful users as compared to the non-hateful ones. We discuss how, many
crucial design questions in CSCW open up from our work.
|
We present a method developed to actively compensate common-mode magnetic
disturbances on a multi-sensor device devoted to differential measurements. The
system uses a field-programmable-gated-array card, and operates in conjunction
with a high sensitivity magnetometer: compensating the common-mode of magnetic
disturbances results in a relevant reduction of the difference-mode noise. The
digital nature of the compensation system allows for using a numerical approach
aimed at automatically adapting the feedback loop filter response. A common
mode disturbance attenuation exceeding 50 dB is achieved, resulting in a final
improvement of the differential noise floor by a factor of 10 over the whole
spectral interval of interest.
|
The asymmetric simple exclusion process and its analysis by mode coupling
theory (MCT) is reviewed. To treat the weakly asymmetric case at large space
scale $x\varepsilon^{-1}$, %(corresponding to small Fourier momentum at scale
$p\varepsilon$), large time scale $t \varepsilon^{-\chi}$ and weak hopping bias
$b \varepsilon^{\kappa}$ in the limit $\varepsilon \to 0$ we develop a
mesoscale MCT that allows for studying the crossover at $\kappa=1/2$ and
$\chi=2$ from Kardar-Parisi-Zhang (KPZ) to Edwards-Wilkinson (EW) universality.
The dynamical structure function is shown to satisfy for all $\kappa$ an
integral equation that is independent of the microscopic model parameters and
has a solution that yields a scale-invariant function with the KPZ dynamical
exponent $z=3/2$ at scale $\chi=3/2+\kappa$ for $0\leq\kappa<1/2$ and for
$\chi=2$ the exact Gaussian EW solution with $z=2$ for $\kappa>1/2$. At the
crossover point it is a function of both scaling variables which converges at
macroscopic scale to the conventional MCT approximation of KPZ universality for
$\kappa<1/2$. This fluctuation pattern confirms long-standing conjectures for
$\kappa \leq 1/2$ and is in agreement with mathematically rigorous results for
$\kappa>1/2$ despite the numerous uncontrolled approximations on which MCT is
based.
|
Memristor-based crossbar arrays represent a promising emerging memory
technology to replace conventional memories by offering a high density and
enabling computing-in-memory (CIM) paradigms. While analog computing provides
the best performance, non-idealities and ADC/DAC conversion limit
memristor-based CIM. Logic-in-Memory (LIM) presents another flavor of CIM, in
which the memristors are used in a binary manner to implement logic gates.
Since binary neural networks (BNNs) use binary logic gates as the dominant
operation, they can benefit from the massively parallel execution of binary
operations and better resilience to variations of the memristors. Although
conventional neural networks have been thoroughly investigated, the impact of
faults on memristor-based BNNs remains unclear. Therefore, we analyze the
impact of faults on logic gates in memristor-based crossbar arrays for BNNs. We
propose a simulation framework that simulates different traditional faults to
examine the accuracy loss of BNNs on memristive crossbar arrays. In addition,
we compare different logic families based on the robustness and feasibility to
accelerate AI applications.
|
We find three characterizations for a multidimensional (n+1)-web W possessing
a reduct reducible subweb: its closed form equations, the integrability of an
invariant distribution associated with W, and the relations between the
components of its torsion tensor. In the case of codimension one, the latter
criterion establishes a relation with solutions of a system of nonlinear
second-order PDEs. Some particular cases of this system were considered by
Goursat in 1899.
|
We construct a rational $T^2$-equivariant elliptic cohomology theory for the
2-torus $T^2$, starting from an elliptic curve C over the complex numbers and a
coordinate data around the identity. The theory is defined by constructing an
object $EC_{T^2}$ in the algebraic model category $dA(T^2)$, which by Greenlees
and Shipley is Quillen-equivalent to rational $T^2$-spectra. This result is a
generalization to the 2-torus of the construction [Gre05] for the circle. The
object $EC_{T^2}$ is directly built using geometric inputs coming from the
Cousin complex of the structure sheaf of the surface CxC.
|
Elliott and Halberstam proved that $\sum_{p<n} 2^{\omega(n-p)}$ is asymptotic
to $\phi(n)$. In analogy to the Erd\H{o}s--Kac Theorem, Elliott conjectured
that if one restricts the summation to primes $p$ such that $\omega(n-p)\le 2
\log \log n+\lambda(2\log \log n)^{1/2}$ then the sum will be asymptotic to
$\phi(n)\int_{-\infty}^{\lambda} e^{-t^2/2}dt/\sqrt{2\pi}$. We show that this
conjecture follows from the Bombieri--Vinogradov Theorem. We further prove a
related result involving Poisson--Dirichlet distribution, employing deeper
lying level of distribution results of the primes.
|
Blazars, radio-loud active galactic nuclei with the relativistic jet closely
aligned with the line of sight, dominate the extragalactic sky observed at
gamma-ray energies, above 100 MeV. We discuss some of the emission properties
of these sources, focusing in particular on the "blazar sequence" and the
interpretative models of the high-energy emission of BL Lac objects.
|
Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.