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Let K be an algebraically closed field, X a K-scheme, and X(K) the set of
closed points in X. A constructible set C in X(K) is a finite union of subsets
Y(K) for finite type subschemes Y in X. A constructible function f : X(K) --> Q
has f(X(K)) finite and f^{-1}(c) constructible for all nonzero c. Write CF(X)
for the Q-vector space of constructible functions on X.
Let phi : X --> Y and psi : Y --> Z be morphisms of C-varieties. MacPherson
defined a Q-linear "pushforward" CF(phi) : CF(X) --> CF(Y) by "integration"
w.r.t. the topological Euler characteristic. It is functorial, that is, CF(psi
o phi)=CF(psi) o CF(phi). This was extended to K of characteristic zero by
Kennedy.
This paper generalizes these results to K-schemes and Artin K-stacks with
affine stabilizers. We define notions of Euler characteristic for constructible
sets in K-schemes and K-stacks, and pushforwards and pullbacks of constructible
functions, with functorial behaviour. Pushforwards and pullbacks commute in
Cartesian squares. We also define "pseudomorphisms", a generalization of
morphisms well suited to constructible functions problems.
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We determine the Seiberg-Witten-Floer homology groups of the three-manifold
which is the product of a surface of genus $g \geq 1$ times the circle,
together with its ring structure, for spin-c structures which are non-trivial
on the three-manifold. We give applications to computing Seiberg-Witten
invariants of four-manifolds which are connected sums along surfaces and also
we reprove the higher type adjunction inequalities previously obtained by
Oszv\'ath and Szab\'o.
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We study integral operators related to a regularized version of the classical
Poincar\'e path integral and the adjoint class generalizing Bogovski\u{\i}'s
integral operator, acting on differential forms in $R^n$. We prove that these
operators are pseudodifferential operators of order -1. The Poincar\'e-type
operators map polynomials to polynomials and can have applications in finite
element analysis. For a domain starlike with respect to a ball, the special
support properties of the operators imply regularity for the de Rham complex
without boundary conditions (using Poincar\'e-type operators) and with full
Dirichlet boundary conditions (using Bogovski\u{\i}-type operators). For
bounded Lipschitz domains, the same regularity results hold, and in addition we
show that the cohomology spaces can always be represented by $C^\infty$
functions.
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The yrast states of even even vibrational and transitional nuclei are inter-
preted as a rotating condensate of interacting d-bosons and the corresponding
semi-classical tidal wave concept. A simple experimental manifestation of the
anharmonicity caused by the boson interaction is found. The interpretation is
substantiated by calculations based on the Collective Model and the Cranking
Model.
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We present results of deep integral field spectroscopy observations using
high resolution optical (4150-7200 A) VIMOS VLT spectra, of NGC 4696, the
dominant galaxy in the Centaurus cluster (Abell 3526). After the Virgo cluster,
this is the second nearest (z=0.0104) example of a cool core cluster. NGC 4696
is surrounded by a vast, luminous H alpha emission line nebula (L = 2.2 \times
10^40 ergs per second). We explore the origin and excitation of the
emission-line filaments and find their origin consistent with being drawn out,
under rising radio bubbles, into the intracluster medium as in other similar
systems. Contrary to previous observations we do not observe evidence for shock
excitation of the outer filaments. Our optical spectra are consistent with the
recent particle heating excitation mechanism of Ferland et al.
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Let $ \{X_j, j\in \Z\}$ be a Gaussian stationary sequence having a spectral
function $F$ of infinite type. Then for all $n$ and $z\ge 0$,$$
\P\Big\{\sup_{j=1}^n |X_j|\le z \Big\}\le
\Big(\int_{-z/\sqrt{G(f)}}^{z/\sqrt{G(f)}} e^{-x^2/2}\frac{\dd x}{\sqrt{2\pi}}
\Big)^n,$$ where $ G(f)$ is the geometric mean of the Radon Nycodim derivative
of the absolutely continuous part $f$ of $F$. The proof uses properties of
finite Toeplitz forms. Let $ \{X(t), t\in \R\}$ be a sample continuous
stationary Gaussian process with covariance function $\g(u) $.
We also show that there exists an absolute constant $K$ such that for all
$T>0$, $a>0$ with $T\ge \e(a)$, $$\P\Big\{\sup_{0\le s,t\le T} |X(s)-X(t)|\le
a\Big\} \le \exp \Big \{-{KT \over \e(a) p(\e(a))}\Big\}
,$$ where $\e (a)= \min\big\{b>0: \d (b)\ge a\big\}$, $\d (b)=\min_{u\ge
1}\{\sqrt{2(1-\g((ub))}, u\ge 1\}$, and
$ p(b) = 1+\sum_{j=2}^\infty {|2\g (jb)-\g ((j-1)b)-\g ((j+1)b)| \over
2(1-\g(b))}$. The proof is based on some decoupling inequalities arising from
Brascamp-Lieb inequality. Both approaches are developed and compared on
examples. Several other related results are established.
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For midrapidity fragments from central 50-200 AMeV Au+Au collisions
temperatures from double ratios of isotopic yields were compared with
temperatures from particle unbound states. Temperatures from particle unbound
states with T = 4-5 MeV show with increasing beam energy an increasing
difference to temperatures from double ratios of isotopic yields, which
increase from T = 5MeV to T = 12MeV. The lower temperatures extracted from
particle unstable states can be explained by increasing cooling of the decaying
system due to expansion. This expansion is driven by the radial flow, and
freeze out of particle unstable states might depend on the dynamics of the
expanding system. Source sizes from pp-correlation functions were found to be 9
to 11 fm.
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This is a sequel to the papers [OW1], [OW2]. In [OW1], the authors introduced
a canonical affine connection on $M$ associated to the contact triad
$(M,\lambda,J)$. In [OW2], they used the connection to establish a priori
$W^{k,p}$-coercive estimates for maps $w: \dot \Sigma \to M$ satisfying
$\overline{\partial}^\pi w= 0, \, d(w^*\lambda \circ j) = 0$ \emph{without
involving symplectization}. We call such a pair $(w,j)$ a contact instanton. In
this paper, we first prove a canonical neighborhood theorem of the locus $Q$
foliated by closed Reeb orbits of a Morse-Bott contact form. Then using a
general framework of the three-interval method, we establish exponential decay
estimates for contact instantons $(w,j)$ of the triad $(M,\lambda,J)$, with
$\lambda$ a Morse-Bott contact form and $J$ a CR-almost complex structure
adapted to $Q$, under the condition that the asymptotic charge of $(w,j)$ at
the associated puncture vanishes.
We also apply the three-interval method to the symplectization case and
provide an alternative approach via tensorial calculations to exponential decay
estimates in the Morse-Bott case for the pseudoholomorphic curves on the
symplectization of contact manifolds. This was previously established by
Bourgeois [Bou] (resp. by Bao [Ba]), by using special coordinates, for the
cylindrical (resp. for the asymptotically cylindrical) ends. The exponential
decay result for the Morse-Bott case is an essential ingredient in the set-up
of the moduli space of pseudoholomorphic curves which plays a central role in
contact homology and symplectic field theory (SFT).
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Quantum theory permits interference between indistinguishable paths but, at
the same time, restricts its order. Single-particle interference, for instance,
is limited to the second order, that is, to pairs of single-particle paths. To
date, all experimental efforts to search for higher-order interferences beyond
those compatible with quantum mechanics have been based on such single-particle
schemes. However, quantum physics is not bounded to single-particle
interference. We here experimentally study many-particle higher-order
interference using a two-photon-five-slit setup. We observe nonzero
two-particle interference up to fourth order, corresponding to the interference
of two distinct two-particle paths. We further show that fifth-order
interference is restricted to $10^{-3}$ in the intensity-correlation regime and
to $10^{-2}$ in the photon-correlation regime, thus providing novel bounds on
higher-order quantum interference.
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Isolated isothermal spheres of N gravitationally interacting points with
equal mass are believed to be stable when density contrasts do not exceed 709.
That stability limit does, however, not take into consideration fluctuations of
temperature near the onset of instability. These are important when N is
finite. Here we correlate {\it global mean quadratic temperature fluctuations}
with onset of instability. We show that such fluctuations trigger instability
when the density contrast reaches a value near $709\cdot\exp(-3.3N^{-1/3})$.
These lower values of limiting density contrasts are significantly smaller than
709 when N is not very big and this suggests (i) that numerical calculations
with small N may not reflect correctly the onset of core collapse in clusters
with big N and (ii) that a greater number of globular clusters than is normally
believed may already be in an advanced stage of core collapse because most of
observed globular clusters whose parameters fit quasi-isothermal configurations
are close to marginal stability.
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We introduce an end-to-end learning framework for image-to-image composition,
aiming to plausibly compose an object represented as a cropped patch from an
object image into a background scene image. As our approach emphasizes more on
semantic and structural coherence of the composed images, rather than their
pixel-level RGB accuracies, we tailor the input and output of our network with
structure-aware features and design our network losses accordingly, with ground
truth established in a self-supervised setting through the object cropping.
Specifically, our network takes the semantic layout features from the input
scene image, features encoded from the edges and silhouette in the input object
patch, as well as a latent code as inputs, and generates a 2D spatial affine
transform defining the translation and scaling of the object patch. The learned
parameters are further fed into a differentiable spatial transformer network to
transform the object patch into the target image, where our model is trained
adversarially using an affine transform discriminator and a layout
discriminator. We evaluate our network, coined SAC-GAN, for various image
composition scenarios in terms of quality, composability, and generalizability
of the composite images. Comparisons are made to state-of-the-art alternatives,
including Instance Insertion, ST-GAN, CompGAN and PlaceNet, confirming
superiority of our method.
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Dynamic-mode atomic force microscopy (AFM) in liquid remains complicated due
to the strong viscous damping of the cantilever resonance. Here we show that a
high-quality resonance (Q>20) can be achieved in aqueous solution by attaching
a microgram-bead at the end of the nanogram-cantilever. The resulting increase
in cantilever mass causes the resonance frequency to drop significantly.
However, the force sensitivity --- as expressed via the minimum detectable
force gradient --- is hardly affected, because of the enhanced quality factor.
Via the enhancement of the quality factor, the attached bead also reduces the
relative importance of noise in the deflection detector. It can thus yield an
improved signal-to-noise ratio when this detector noise is significant. We
describe and analyze these effects for a set-up which includes magnetic
actuation of the cantilevers and which can be easily implemented in any AFM
system that is compatible with an inverted optical microscope.
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Autonomous robotic surgery has advanced significantly based on analysis of
visual and temporal cues in surgical workflow, but relational cues from domain
knowledge remain under investigation. Complex relations in surgical annotations
can be divided into intra- and inter-relations, both valuable to autonomous
systems to comprehend surgical workflows. Intra- and inter-relations describe
the relevance of various categories within a particular annotation type and the
relevance of different annotation types, respectively. This paper aims to
systematically investigate the importance of relational cues in surgery. First,
we contribute the RLLS12M dataset, a large-scale collection of robotic left
lateral sectionectomy (RLLS), by curating 50 videos of 50 patients operated by
5 surgeons and annotating a hierarchical workflow, which consists of 3 inter-
and 6 intra-relations, 6 steps, 15 tasks, and 38 activities represented as the
triplet of 11 instruments, 8 actions, and 16 objects, totaling 2,113,510 video
frames and 12,681,060 annotation entities. Correspondingly, we propose a
multi-relation purification hybrid network (MURPHY), which aptly incorporates
novel relation modules to augment the feature representation by purifying
relational features using the intra- and inter-relations embodied in
annotations. The intra-relation module leverages a R-GCN to implant visual
features in different graph relations, which are aggregated using a targeted
relation purification with affinity information measuring label consistency and
feature similarity. The inter-relation module is motivated by attention
mechanisms to regularize the influence of relational features based on the
hierarchy of annotation types from the domain knowledge. Extensive experimental
results on the curated RLLS dataset confirm the effectiveness of our approach,
demonstrating that relations matter in surgical workflow analysis.
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Authors propose a conceptual model of participation in viral diffusion
process composed of four stages: awareness, infection, engagement and action.
To verify the model it has been applied and studied in the virtual social chat
environment settings. The study investigates the behavioral paths of actions
that reflect the stages of participation in the diffusion and presents
shortcuts, that lead to the final action, i.e. the attendance in a virtual
event. The results show that the participation in each stage of the process
increases the probability of reaching the final action. Nevertheless, the
majority of users involved in the virtual event did not go through each stage
of the process but followed the shortcuts. That suggests that the viral
diffusion process is not necessarily a linear sequence of human actions but
rather a dynamic system.
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We prove the Plancherel formula for hypergeometric functions associated to a
root system in the situation when the root multiplicities are negative (but
close to 0). As a result we obtain a classification of the hypergeometric
functions that are square integrable, and we find a closed formula for their
square norm as a function of the root multiplicities.
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Simulating the dynamics and the non-equilibrium steady state of an open
quantum system are hard computational tasks on conventional computers. For the
simulation of the time evolution, several efficient quantum algorithms have
recently been developed. However, computing the non-equilibrium steady state as
the long-time limit of the system dynamics is often not a viable solution,
because of exceedingly long transient features or strong quantum correlations
in the dynamics. Here, we develop an efficient quantum algorithm for the direct
estimation of averaged expectation values of observables on the non-equilibrium
steady state, thus bypassing the time integration of the master equation. The
algorithm encodes the vectorized representation of the density matrix on a
quantum register, and makes use of quantum phase estimation to approximate the
eigenvector associated to the zero eigenvalue of the generator of the system
dynamics. We show that the output state of the algorithm allows to estimate
expectation values of observables on the steady state. Away from critical
points, where the Liouvillian gap scales as a power law of the system size, the
quantum algorithm performs with exponential advantage compared to exact
diagonalization.
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Soil temperature is one of the most significant parameters that plays a
crucial role in glacier energy, dynamics of mass balance, processes of surface
hydrological, coaction of glacier-atmosphere, nutrient cycling, ecological
stability, the management of soil, water, and field crop. In this work, we
introduce a novel approach using transformer models for the purpose of
forecasting soil temperature prediction. To the best of our knowledge, the
usage of transformer models in this work is the very first attempt to predict
soil temperature. Experiments are carried out using six different FLUXNET
stations by modeling them with five different transformer models, namely,
Vanilla Transformer, Informer, Autoformer, Reformer, and ETSformer. To
demonstrate the effectiveness of the proposed model, experiment results are
compared with both deep learning approaches and literature studies. Experiment
results show that the utilization of transformer models ensures a significant
contribution to the literature, thence determining the new state-of-the-art.
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Active motions of a biological membrane can be induced by non-thermal
fluctuations that occur in the outer environment of the membrane. We discuss
the dynamics of a membrane interacting hydrodynamically with an active wall
that exerts random velocities on the ambient fluid. Solving the hydrodynamic
equations of a bound membrane, we first derive a dynamic equation for the
membrane fluctuation amplitude in the presence of different types of walls.
Membrane two-point correlation functions are calculated for three different
cases; (i) a static wall, (ii) an active wall, and (iii) an active wall with an
intrinsic time scale. We focus on the mean squared displacement (MSD) of a
tagged membrane describing the Brownian motion of a membrane segment. For the
static wall case, there are two asymptotic regimes of MSD ($\sim t^{2/3}$ and
$\sim t^{1/3}$) when the hydrodynamic decay rate changes monotonically. In the
case of an active wall, the MSD grows linearly in time ($\sim t$) in the early
stage, which is unusual for a membrane segment. This linear-growth region of
the MSD is further extended when the active wall has a finite intrinsic time
scale.
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A useful finite-dimensional matrix representation of the derivative of
periodic functions is obtained by using some elementary facts of trigonometric
interpolation. This NxN matrix becomes a projection of the angular derivative
into polynomial subspaces of finite dimension and it can be interpreted as a
generator of discrete rotations associated to the z-component of the projection
of the angular momentum operator in such subspaces, inheriting thus some
properties of the continuum operator. The group associated to these discrete
rotations is the cyclic group of order N. Since the square of the quantum
angular momentum L^2 is associated to a partial differential boundary value
problem in the angular variables $\theta$ and $\phi$ whose solution is given in
terms of the spherical harmonics, we can project such a differential equation
to obtain an eigenvalue matrix problem of finite dimension by extending to
several variables a projection technique for solving numerically two point
boundary value problems and using the matrix representation of the angular
derivative found before. The eigenvalues of the matrix representing L^2 are
found to have the exact form n(n+1), counting the degeneracy, and the
eigenvectors are found to coincide exactly with the corresponding spherical
harmonics evaluated at a certain set of points.
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A key problem in sensor networks is to decide which sensors to query when, in
order to obtain the most useful information (e.g., for performing accurate
prediction), subject to constraints (e.g., on power and bandwidth). In many
applications the utility function is not known a priori, must be learned from
data, and can even change over time. Furthermore for large sensor networks
solving a centralized optimization problem to select sensors is not feasible,
and thus we seek a fully distributed solution. In this paper, we present
Distributed Online Greedy (DOG), an efficient, distributed algorithm for
repeatedly selecting sensors online, only receiving feedback about the utility
of the selected sensors. We prove very strong theoretical no-regret guarantees
that apply whenever the (unknown) utility function satisfies a natural
diminishing returns property called submodularity. Our algorithm has extremely
low communication requirements, and scales well to large sensor deployments. We
extend DOG to allow observation-dependent sensor selection. We empirically
demonstrate the effectiveness of our algorithm on several real-world sensing
tasks.
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We consider a typical setup of cavity QED consisting of a two-level atom
interacting strongly with a single resonant electromagnetic field mode inside a
cavity. The cavity is resonantly driven and the output undergoes continuous
homodyne measurements. We derive an explicit expression for the state of the
system conditional on a discrete photocount record. This expression takes a
particularly simple form if the system is initially in the steady state. As a
byproduct, we derive a general formula for the steady state that had been
conjectured before in the strong driving limit.
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We present the conceptual design and the physics potential of DarkSPHERE, a
proposed 3 m in diameter spherical proportional counter electroformed
underground at the Boulby Underground Laboratory. This effort builds on the R&D
performed and experience acquired by the NEWS-G Collaboration. DarkSPHERE is
primarily designed to search for nuclear recoils from light dark matter in the
0.05--10 GeV mass range. Electroforming the spherical shell and the
implementation of a shield based on pure water ensures a background level below
0.01 dru. These, combined with the proposed helium-isobutane gas mixture, will
provide sensitivity to the spin-independent nucleon cross-section of $2\times
10^{-41} (2\times 10^{-43})$ cm$^2$ for a dark matter mass of $0.1 (1)$ GeV.
The use of a hydrogen-rich gas mixture with a natural abundance of $^{13}$C
provides sensitivity to spin-dependent nucleon cross-sections more than two
orders of magnitude below existing constraints for dark matter lighter than 1
GeV. The characteristics of the detector also make it suitable for searches of
other dark matter signatures, including scattering of MeV-scale dark matter
with electrons, and super-heavy dark matter with masses around the Planck scale
that leave extended ionisation tracks in the detector.
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In a recent paper, by working in the orbifold GUT limit of the Heterotic
string, we showed how one could accommodate gauge coupling unification in the
"mini-landscape" models of Lebedev et al. Furthermore, it was shown how one of
the solutions was consistent with the decoupling of other exotics with F=0. In
this short addendum, we show that this solution is also consistent with D=0.
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Constructing charges in the covariant phase space formalism often leads to
formally divergent expressions, even when the fields satisfy physically
acceptable fall-off conditions. These expressions can be rendered finite by
corner ambiguities in the definition of the presymplectic potential, which in
some cases may be motivated by arguments involving boundary Lagrangians. We
show that the necessary corner terms are already present in the variation of
the bulk action and can be extracted in a straightforward way. Once these
corner terms are included in the presymplectic potential, charges derived from
an associated codimension-2 form are automatically finite. We illustrate the
procedure with examples in two and three dimensions, working in Bondi gauge and
obtaining integrable charges. As a by-product, actions are derived for these
theories that admit a well-defined variational principle when the fields
satisfy boundary conditions on a timelike surface with corners. An interesting
feature of our analysis is that the fields are not required to be fully
on-shell.
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Recidivism prediction provides decision makers with an assessment of the
likelihood that a criminal defendant will reoffend that can be used in
pre-trial decision-making. It can also be used for prediction of locations
where crimes most occur, profiles that are more likely to commit violent
crimes. While such instruments are gaining increasing popularity, their use is
controversial as they may present potential discriminatory bias in the risk
assessment. In this paper we propose a new fair-by-design approach to predict
recidivism. It is prototype-based, learns locally and extracts empirically the
data distribution. The results show that the proposed method is able to reduce
the bias and provide human interpretable rules to assist specialists in the
explanation of the given results.
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This paper has been withdrawn, because the result turned out to be well
known.
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Complex Event Processing (CEP) has emerged as the unifying field for
technologies that require processing and correlating distributed data sources
in real-time. CEP finds applications in diverse domains, which has resulted in
a large number of proposals for expressing and processing complex events.
However, existing CEP languages lack from a clear semantics, making them hard
to understand and generalize. Moreover, there are no general techniques for
evaluating CEP query languages with clear performance guarantees.
In this paper we embark on the task of giving a rigorous and efficient
framework to CEP. We propose a formal language for specifying complex events,
called CEL, that contains the main features used in the literature and has a
denotational and compositional semantics. We also formalize the so-called
selection strategies, which had only been presented as by-design extensions to
existing frameworks. With a well-defined semantics at hand, we study how to
efficiently evaluate CEL for processing complex events in the case of unary
filters. We start by studying the syntactical properties of CEL and propose
rewriting optimization techniques for simplifying the evaluation of formulas.
Then, we introduce a formal computational model for CEP, called complex event
automata (CEA), and study how to compile CEL formulas into CEA. Furthermore, we
provide efficient algorithms for evaluating CEA over event streams using
constant time per event followed by constant-delay enumeration of the results.
By gathering these results together, we propose a framework for efficiently
evaluating CEL with unary filters. Finally, we show experimentally that this
framework consistently outperforms the competition, and even over trivial
queries can be orders of magnitude more efficient.
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In this report, we explore the ability of language model agents to acquire
resources, create copies of themselves, and adapt to novel challenges they
encounter in the wild. We refer to this cluster of capabilities as "autonomous
replication and adaptation" or ARA. We believe that systems capable of ARA
could have wide-reaching and hard-to-anticipate consequences, and that
measuring and forecasting ARA may be useful for informing measures around
security, monitoring, and alignment. Additionally, once a system is capable of
ARA, placing bounds on a system's capabilities may become significantly more
difficult.
We construct four simple example agents that combine language models with
tools that allow them to take actions in the world. We then evaluate these
agents on 12 tasks relevant to ARA. We find that these language model agents
can only complete the easiest tasks from this list, although they make some
progress on the more challenging tasks. Unfortunately, these evaluations are
not adequate to rule out the possibility that near-future agents will be
capable of ARA. In particular, we do not think that these evaluations provide
good assurance that the ``next generation'' of language models (e.g. 100x
effective compute scaleup on existing models) will not yield agents capable of
ARA, unless intermediate evaluations are performed during pretraining.
Relatedly, we expect that fine-tuning of the existing models could produce
substantially more competent agents, even if the fine-tuning is not directly
targeted at ARA.
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This study presents an integrated approach for identifying key nodes in
information propagation networks using advanced artificial intelligence
methods. We introduce a novel technique that combines the Decision-making Trial
and Evaluation Laboratory (DEMATEL) method with the Global Structure Model
(GSM), creating a synergistic model that effectively captures both local and
global influences within a network. This method is applied across various
complex networks, such as social, transportation, and communication systems,
utilizing the Global Network Influence Dataset (GNID). Our analysis highlights
the structural dynamics and resilience of these networks, revealing insights
into node connectivity and community formation. The findings demonstrate the
effectiveness of our AI-based approach in offering a comprehensive
understanding of network behavior, contributing significantly to strategic
network analysis and optimization.
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Given a pair of positive real numbers $\alpha, \beta$ and a sesqui-analytic
function $K$ on a bounded domain $\Omega \subset \mathbb C^m$, in this paper,
we investigate the properties of the sesqui-analytic function $\mathbb
K^{(\alpha, \beta)}:= K^{\alpha+\beta}\big(\partial_i\bar{\partial}_j\log K\big
)_{i,j=1}^ m,$ taking values in $m\times m$ matrices. One of the key findings
is that $\mathbb K^{(\alpha, \beta)}$ is non-negative definite whenever
$K^\alpha$ and $K^\beta$ are non-negative definite. In this case, a realization
of the Hilbert module determined by the kernel $\mathbb K^{(\alpha,\beta)}$ is
obtained. Let $\mathcal M_i$, $i=1,2,$ be two Hilbert modules over the
polynomial ring $\mathbb C[z_1, \ldots, z_m]$. Then $\mathbb C[z_1, \ldots,
z_{2m}]$ acts naturally on the tensor product $\mathcal M_1\otimes \mathcal
M_2$. The restriction of this action to the polynomial ring $\mathbb C[z_1,
\ldots, z_m]$ obtained using the restriction map $p \mapsto p_{|\Delta}$ leads
to a natural decomposition of the tensor product $\mathcal M_1\otimes \mathcal
M_2$, which is investigated. Two of the initial pieces in this decomposition
are identified.
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The Rocket Chip Generator uses a collection of parameterized processor
components to produce RISC-V-based SoCs. It is a powerful tool that can produce
a wide variety of processor designs ranging from tiny embedded processors to
complex multi-core systems. In this paper we extend the features of the Memory
Management Unit of the Rocket Chip Generator and specifically the TLB
hierarchy. TLBs are essential in terms of performance because they mitigate the
overhead of frequent Page Table Walks, but may harm the critical path of the
processor due to their size and/or associativity. In the original Rocket Chip
implementation the L1 Instruction/Data TLB is fully-associative and the shared
L2 TLB is direct-mapped. We lift these restrictions and design and implement
configurable, set-associative L1 and L2 TLB templates that can create any
organization from direct-mapped to fully-associative to achieve the desired
ratio of performance and resource utilization, especially for larger TLBs. We
evaluate different TLB configurations and present performance, area, and
frequency results of our design using benchmarks from the SPEC2006 suite on the
Xilinx ZCU102 FPGA.
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We introduce a new variant of the weak optimal transport problem where mass
is distributed from one space to the other through unnormalized kernels. We
give sufficient conditions for primal attainment and prove a dual formula for
this transport problem. We also obtain dual attainment conditions for some
specific cost functions. As a byproduct we obtain a transport characterization
of the stochastic order defined by convex positively 1-homogenous functions, in
the spirit of Strassen theorem for convex domination.
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Lately, the three-dimensional (3D) Dirac semimetal, which possesses 3D linear
dispersion in electronic structure as a bulk analogue of graphene, has
generated widespread interests in both material science and condensed matter
physics. Very recently, crystalline Cd3As2 has been proposed and proved to be
one of 3D Dirac semimetals which can survive in atmosphere. Here, by controlled
point contact (PC) measurement, we observe the exotic superconductivity around
point contact region on the surface of Cd3As2 crystal. The observation of zero
bias conductance peak (ZBCP) and double conductance peaks (DCPs) symmetric to
zero bias further reveal p-wave like unconventional superconductivity in Cd3As2
quantum matter. Considering the topological property of the 3D Dirac semimetal,
our findings may indicate that the Cd3As2 crystal under certain conditions is a
candidate of the topological superconductor, which is predicted to support
Majorana zero modes or gapless Majorana edge/surface modes in the boundary
depending on the dimensionality of the material.
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The beneficial role of noise-injection in learning is a consolidated concept
in the field of artificial neural networks, suggesting that even biological
systems might take advantage of similar mechanisms to optimize their
performance. The training-with-noise algorithm proposed by Gardner and
collaborators is an emblematic example of a noise-injection procedure in
recurrent networks, which can be used to model biological neural systems. We
show how adding structure to noisy training data can substantially improve the
algorithm performance, allowing the network to approach perfect retrieval of
the memories and wide basins of attraction, even in the scenario of maximal
injected noise. We also prove that the so-called Hebbian Unlearning rule
coincides with the training-with-noise algorithm when noise is maximal and data
are stable fixed points of the network dynamics.
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Corporate credit ratings issued by third-party rating agencies are quantified
assessments of a company's creditworthiness. Credit Ratings highly correlate to
the likelihood of a company defaulting on its debt obligations. These ratings
play critical roles in investment decision-making as one of the key risk
factors. They are also central to the regulatory framework such as BASEL II in
calculating necessary capital for financial institutions. Being able to predict
rating changes will greatly benefit both investors and regulators alike. In
this paper, we consider the corporate credit rating migration early prediction
problem, which predicts the credit rating of an issuer will be upgraded,
unchanged, or downgraded after 12 months based on its latest financial
reporting information at the time. We investigate the effectiveness of
different standard machine learning algorithms and conclude these models
deliver inferior performance. As part of our contribution, we propose a new
Multi-task Envisioning Transformer-based Autoencoder (META) model to tackle
this challenging problem. META consists of Positional Encoding,
Transformer-based Autoencoder, and Multi-task Prediction to learn effective
representations for both migration prediction and rating prediction. This
enables META to better explore the historical data in the training stage for
one-year later prediction. Experimental results show that META outperforms all
baseline models.
|
Each node in a wireless multi-hop network can adjust the power level at which
it transmits and thus change the topology of the network to save energy by
choosing the neighbors with which it directly communicates. Many previous
algorithms for distributed topology control have assumed an ability at each
node to deduce some location-based information such as the direction and the
distance of its neighbor nodes with respect to itself. Such a deduction of
location-based information, however, cannot be relied upon in real environments
where the path loss exponents vary greatly leading to significant errors in
distance estimates. Also, multipath effects may result in different signal
paths with different loss characteristics, and none of these paths may be
line-of-sight, making it difficult to estimate the direction of a neighboring
node. In this paper, we present Step Topology Control (STC), a simple
distributed topology control algorithm which reduces energy consumption while
preserving the connectivity of a heterogeneous sensor network without use of
any location-based information. We show that the STC algorithm achieves the
same or better order of communication and computational complexity when
compared to other known algorithms that also preserve connectivity without the
use of location-based information. We also present a detailed simulation-based
comparative analysis of the energy savings and interference reduction achieved
by the algorithms. The results show that, in spite of not incurring a higher
communication or computational complexity, the STC algorithm performs better
than other algorithms in uniform wireless environments and especially better
when path loss characteristics are non-uniform.
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Mobile crowdsourcing has become easier thanks to the widespread of
smartphones capable of seamlessly collecting and pushing the desired data to
cloud services. However, the success of mobile crowdsourcing relies on
balancing the supply and demand by first accurately forecasting spatially and
temporally the supply-demand gap, and then providing efficient incentives to
encourage participant movements to maintain the desired balance. In this paper,
we propose Deep-Gap, a deep learning approach based on residual learning to
predict the gap between mobile crowdsourced service supply and demand at a
given time and space. The prediction can drive the incentive model to achieve a
geographically balanced service coverage in order to avoid the case where some
areas are over-supplied while other areas are under-supplied. This allows
anticipating the supply-demand gap and redirecting crowdsourced service
providers towards target areas. Deep-Gap relies on historical supply-demand
time series data as well as available external data such as weather conditions
and day type (e.g., weekday, weekend, holiday). First, we roll and encode the
time series of supply-demand as images using the Gramian Angular Summation
Field (GASF), Gramian Angular Difference Field (GADF) and the Recurrence Plot
(REC). These images are then used to train deep Convolutional Neural Networks
(CNN) to extract the low and high-level features and forecast the crowdsourced
services gap. We conduct comprehensive comparative study by establishing two
supply-demand gap forecasting scenarios: with and without external data.
Compared to state-of-art approaches, Deep-Gap achieves the lowest forecasting
errors in both scenarios.
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We present an algorithm that, given finite simplicial sets $X$, $A$, $Y$ with
an action of a finite group $G$, computes the set $[X,Y]^A_G$ of homotopy
classes of equivariant maps $\ell \colon X \to Y$ extending a given equivariant
map $f \colon A \to Y$ under the stability assumption $\dim X^H \leq 2
\operatorname{conn} Y^H$ and $\operatorname{conn} Y^H \geq 1$, for all
subgroups $H\leq G$. For fixed $n = \operatorname{dim} X$, the algorithm runs
in polynomial time. When the stability condition is dropped, the problem is
undecidable already in the non-equivariant setting.
The algorithm is obtained as a special case of a more general result: For
finite diagrams of simplicial sets $X$, $A$, $Y$, i.e. functors
$\mathcal{I}^\mathrm{op} \to \mathsf{sSet}$, in the stable range
$\operatorname{dim} X \leq 2 \operatorname{conn} Y$ and $\operatorname{conn} Y
> 1$, we give an algorithm that computes the set $[X, Y]^A$ of homotopy classes
of maps of diagrams $\ell \colon X \to Y$ extending a given $f \colon A \to Y$.
Again, for fixed $n = \dim X$, the running time of the algorithm is polynomial.
The algorithm can be utilized to compute homotopy invariants in the
equivariant setting -- for example, one can algorithmically compute equivariant
stable homotopy groups. Further, one can apply the result to solve problems
from computational topology, which we showcase on the following Tverberg-type
problem: Given a $k$-dimensional simplicial complex $K$, is there a map $K \to
\mathbb{R}^{d}$ without $r$-tuple intersection points? In the metastable range
of dimensions, $rd \geq (r+1)k +3$, the result of Mabillard and Wagner shows
this problem equivalent to the existence of a particular equivariant map. In
this range, our algorithm is applicable and, thus, the $r$-Tverberg problem is
algorithmically decidable (in polynomial time when $k$, $d$ and $r$ are fixed).
|
Consider a finite set $E$. Assume that each $e \in E$ has a "weight" $w
\left(e\right) \in \mathbb{R}$ assigned to it, and any two distinct $e, f \in
E$ have a "distance" $d \left(e, f\right) = d \left(f, e\right) \in \mathbb{R}$
assigned to them, such that the distances satisfy the ultrametric triangle
inequality $d(a,b)\leqslant \max \left\{d(a,c),d(b,c)\right\}$. We look for a
subset of $E$ of given size with maximum perimeter (where the perimeter is
defined by summing the weights of all elements and their pairwise distances).
We show that any such subset can be found by a greedy algorithm (which starts
with the empty set, and then adds new elements one by one, maximizing the
perimeter at each step). We use this to define numerical invariants, and also
to show that the maximum-perimeter subsets of all sizes form a strong greedoid,
and the maximum-perimeter subsets of any given size are the bases of a matroid.
This essentially generalizes the "$P$-orderings" constructed by Bhargava in
order to define his generalized factorials, and is also similar to the strong
greedoid of maximum diversity subsets in phylogenetic trees studied by Moulton,
Semple and Steel.
We further discuss some numerical invariants of $E, w, d$ stemming from this
construction, as well as an analogue where maximum-perimeter subsets are
replaced by maximum-perimeter tuples (i.e., elements can appear multiple
times).
|
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.
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We will construct a theory which can explain the dynamics toward the steady
state self-gravitating systems (SGSs) where many particles interact via the
gravitational force. Real examples of SGS in the universe are globular clusters
and galaxies. The idea is to represent an interaction by which a particle of
the system is affected from the others by a special random force. That is, we
will use a special Langevin equation, just as the normal Langevin equation can
unveil the dynamics toward the steady state described by the Maxwell-Boltzmann
distribution. However, we cannot introduce the randomness into the system
without any evidence. Then, we must confirm that each orbit is random indeed.
Of course, it is impossible to understand orbits of stars in globular clusters
from observations. Thus we use numerical simulations. From the numerical
simulations of SGS, grounds that we use the random noise become clear. The
special Langevin equation includes the additive and the multiplicative noise.
By using the random process, we derive the non-Maxwellian distribution of SGS
especially around the core. The number density can be obtained through the
steady state solution of the Fokker-Planck equation corresponding to the random
process. We exhibit that the number density becomes equal to the density
profiles around the core by adjusting the friction coefficient and the
intensity of the multiplicative noise. Moreover, we also show that our model
can be applied in the system which has a heavier particle, corresponding to the
black hole in a globular cluster.
|
Demand for Personal Protective Equipment (PPE) such as surgical masks,
gloves, and gowns has increased significantly since the onset of the COVID-19
pandemic. In hospital settings, both medical staff and patients are required to
wear PPE. As these facilities resume regular operations, staff will be required
to wear PPE at all times while additional PPE will be mandated during medical
procedures. This will put increased pressure on hospitals which have had
problems predicting PPE usage and sourcing its supply. To meet this challenge,
we propose an approach to predict demand for PPE. Specifically, we model the
admission of patients to a medical department using multiple independent
queues. Each queue represents a class of patients with similar treatment plans
and hospital length-of-stay. By estimating the total workload of each class, we
derive closed-form estimates for the expected amount of PPE required over a
specified time horizon using current PPE guidelines. We apply our approach to a
data set of 22,039 patients admitted to the general internal medicine
department at St. Michael's hospital in Toronto, Canada from April 2010 to
November 2019. We find that gloves and surgical masks represent approximately
90% of predicted PPE usage. We also find that while demand for gloves is driven
entirely by patient-practitioner interactions, 86% of the predicted demand for
surgical masks can be attributed to the requirement that medical practitioners
will need to wear them when not interacting with patients.
|
We attribute the recently discovered cosmic ray electron and cosmic ray
positron excess components and their cutoffs to the acceleration in the
supernova shock in the polar cap of exploding Wolf Rayet and Red Super Giant
stars. Considering a spherical surface at some radius around such a star, the
magnetic field is radial in the polar cap as opposed to most of 4 pi (the full
solid angle), where the magnetic field is nearly tangential. This difference
yields a flatter spectrum, and also an enhanced positron injection for the
cosmic rays accelerated in the polar cap. This reasoning naturally explains the
observations. Precise spectral measurements will be the test, as this predicts
a simple E^-2 spectrum for the new components in the source, steepened to E^-3
in observations with an E^-4 cutoff.
|
We give an alternative proof of a conjecture of Bollob\'as, Brightwell and
Leader, first proved by Peter Allen, stating that the number of boolean
functions definable by 2-SAT formulae is $(1+o(1))2^{\binom{n+1}{2}}$. One step
in the proof determines the asymptotics of the number of
"odd-blue-triangle-free" graphs on $n$ vertices.
|
Oxygen vacancies (VO's) are of paramount importance in influencing the
properties and applications of ceria (CeO2). Yet, comprehending the
distribution and nature of the VO's poses a significant challenge due to the
vast number of electronic configurations and intricate many-body interactions
among VO's and polarons (Ce3+'s). In this study, we employed a combination of
LASSO regression in machine learning, in conjunction with a cluster expansion
model and first-principles calculations to decouple the interactions among the
Ce3+'s and VO's, thereby circumventing the limitations associated with sampling
electronic configurations. By separating these interactions, we identified
specific electronic configurations characterized by the most favorable VO-Ce3+
attractions and the least Ce3+-Ce3+/VO-VO repulsions, which are crucial in
determining the stability of vacancy structures. Through more than 10^8
Metropolis Monte Carlo samplings of Vo's and Ce3+ in the near-surface of
CeO2(111), we explored potential configurations within an 8x8 supercell. Our
findings revealed that oxygen vacancies tend to aggregate and are most abundant
in the third oxygen layer, primarily due to extensive geometric relaxation-an
aspect previously overlooked. This behavior is notably dependent on the
concentration of Vo. This work introduces a novel theoretical framework for
unraveling the complex vacancy structures in metal oxides, with potential
applications in redox and catalytic chemistry.
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The number of maximal independent sets of the n-cycle graph C_n is known to
be the nth term of the Perrin sequence. The action of the automorphism group of
C_n on the family of these maximal independent sets partitions this family into
disjoint orbits, which represent the non-isomorphic (i.e., defined up to a
rotation and a reflection) maximal independent sets. We provide exact formulas
for the total number of orbits and the number of orbits having a given number
of isomorphic representatives. We also provide exact formulas for the total
number of unlabeled (i.e., defined up to a rotation) maximal independent sets
and the number of unlabeled maximal independent sets having a given number of
isomorphic representatives. It turns out that these formulas involve both
Perrin and Padovan sequences.
|
Modern time series analysis requires the ability to handle datasets that are
inherently high-dimensional; examples include applications in climatology,
where measurements from numerous sensors must be taken into account, or
inventory tracking of large shops, where the dimension is defined by the number
of tracked items. The standard way to mitigate computational issues arising
from the high dimensionality of the data is by applying some dimension
reduction technique that preserves the structural properties of the ambient
space. The dissimilarity between two time series is often measured by
``discrete'' notions of distance, e.g. the dynamic time warping or the discrete
Fr\'echet distance. Since all these distance functions are computed directly on
the points of a time series, they are sensitive to different sampling rates or
gaps. The continuous Fr\'echet distance offers a popular alternative which aims
to alleviate this by taking into account all points on the polygonal curve
obtained by linearly interpolating between any two consecutive points in a
sequence.
We study the ability of random projections \`a la Johnson and Lindenstrauss
to preserve the continuous Fr\'echet distance of polygonal curves by
effectively reducing the dimension. In particular, we show that one can reduce
the dimension to $O(\epsilon^{-2} \log N)$, where $N$ is the total number of
input points while preserving the continuous Fr\'echet distance between any two
determined polygonal curves within a factor of $1\pm \epsilon$. We conclude
with applications on clustering.
|
The concept of graph compositions is related to several number theoretic
concepts, including partitions of positive integers and the cardinality of the
power set of finite sets. This paper examines graph compositions where the
total number of components is restricted and illustrates a connection between
graph compositions and Stirling numbers of the second kind.
|
We characterize the sufficient conditions which three weight functions $u$
and $v_{1}, v_{2}$ satisfy ensure the boundedness of the Hardy operator with
variable limits on product space. The corresponding bound is explicitly worked
out. Moreover, as application, we can obtain an explicit scale of bound for the
P\'{o}lya-Knopp type operator with certain weights.
|
With a densely defined symmetric semi-bounded operator of nonzero defect
indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a
topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the
reachable sets of a dynamical system governed by the equation
$u_{tt}+(L_0)^*u=0$. Wave spectra of unitary equivalent operators are
homeomorphic.
In inverse problems, one needs to recover a Riemannian manifold $\Omega$ via
dynamical or spectral boundary data. We show that for a generic class of
manifolds, $\Omega$ is isometric to the wave spectrum $\Omega_{L_0}$ of the
minimal Laplacian $L_0=-\Delta|_{C^\infty_0(\Omega\backslash \partial \Omega)}$
acting in ${\cal H}=L_2(\Omega)$, whereas $L_0$ is determined by the inverse
data up to unitary equivalence. Hence, the manifold can be recovered (up to
isometry) by the scheme `data $\Rightarrow L_0 \Rightarrow \Omega_{L_0}
\overset{\rm isom}= \Omega$'.
The wave spectrum is relevant to a wide class of dynamical systems, which
describe the finite speed wave propagation processes. The paper elucidates the
operator background of the boundary control method (Belishev`1986), which is an
approach to inverse problems based on their relations to control theory.
|
We report the first conformal ultra-wide band (UWB) array on a doubly curved
surface for wide angle electronic scanning. We use a quadrilateral mesh as the
basis for systematically arraying UWB radiators on arbitrary surfaces. A
prototype consisting of a 52 element, dual-polarized Vivaldi array arranged
over a 181 mm diameter hemisphere is developed. The antennas and SMP connectors
are 3D printed out of titanium to allow for simple fabrication and assembly. We
derive the theoretical gain of a hemispherical array based on the antenna size
and number of elements. The measured realized gain of the prototype array is
within 2 dB of the theoretical value from 2-18 GHz and scan angles out to
120{\deg} from the z-axis. This field of view is twice that of a planar array
with the same diameter in agreement with theory. This work provides a baseline
performance for larger conformal arrays that have more uniform meshes.
Furthermore, the basic concept can be extended to other UWB radiating elements.
|
We derive the uniqueness of weak solutions to the Shigesada-Kawasaki-Teramoto
(SKT) systems using the adjoint problem argument. Combining with [PT17] we then
derive the well-posedness for the SKT systems in space dimension $d\le 4$
|
Charge and color breaking minima in SUSY theories might make the standard
vacuum unstable. In this talk a brief review of this issue is performed. When a
complete analysis of all the potentially dangerous directions in the field
space of the theory is carried out, imposing that the standard vacuum should be
the global minimum, the corresponding constraints turn out to be very strong
and, in fact, there are extensive regions in the parameter space of soft
SUSY--breaking terms that become forbidden. For instance, in the context of the
MSSM with universal soft terms, this produces important bounds, not only on the
value of A, but also on the values of B, M and m. In specific SUSY scenarios,
as fixed point models, no-scale supergravity, gauge-mediated SUSY breaking and
superstrings, the charge and color breaking constraints are also very
important. For example, if the dilaton is the source of SUSY breaking in
four-dimensional superstrings, the whole parameter space (m_{3/2},B) is
excluded on these grounds. Cosmological analyses are also briefly reviewed.
|
Piecewise-deterministic Markov processes form a general class of
non-diffusion stochastic models that involve both deterministic trajectories
and random jumps at random times. In this paper, we state a new
characterization of the jump rate of such a process with discrete transitions.
We deduce from this result a nonparametric technique for estimating this
feature of interest. We state the uniform convergence in probability of the
estimator. The methodology is illustrated on a numerical example.
|
A computational paradigm based on neuroscientific concepts is proposed and
shown to be capable of online unsupervised clustering. Because it is an online
method, it is readily amenable to streaming realtime applications and is
capable of dynamically adjusting to macro-level input changes. All operations,
both training and inference, are localized and efficient. The paradigm is
implemented as a cognitive column that incorporates five key elements: 1)
temporal coding, 2) an excitatory neuron model for inference, 3)
winner-take-all inhibition, 4) a column architecture that combines excitation
and inhibition, 5) localized training via spike timing de-pendent plasticity
(STDP). These elements are described and discussed, and a prototype column is
given. The prototype column is simulated with a semi-synthetic benchmark and is
shown to have performance characteristics on par with classic k-means.
Simulations reveal the inner operation and capabilities of the column with
emphasis on excitatory neuron response functions and STDP implementations.
|
Using the general results on the classification of timelike supersymmetric
solutions of all 4-dimensional N >1 supergravity theories, we show how to
construct all the supersymmetric (single- and multi-) black-hole solutions of
N=8 supergravity.
|
Stepwise inference protocols, such as scratchpads and chain-of-thought, help
language models solve complex problems by decomposing them into a sequence of
simpler subproblems. Despite the significant gain in performance achieved via
these protocols, the underlying mechanisms of stepwise inference have remained
elusive. To address this, we propose to study autoregressive Transformer models
on a synthetic task that embodies the multi-step nature of problems where
stepwise inference is generally most useful. Specifically, we define a graph
navigation problem wherein a model is tasked with traversing a path from a
start to a goal node on the graph. Despite is simplicity, we find we can
empirically reproduce and analyze several phenomena observed at scale: (i) the
stepwise inference reasoning gap, the cause of which we find in the structure
of the training data; (ii) a diversity-accuracy tradeoff in model generations
as sampling temperature varies; (iii) a simplicity bias in the model's output;
and (iv) compositional generalization and a primacy bias with in-context
exemplars. Overall, our work introduces a grounded, synthetic framework for
studying stepwise inference and offers mechanistic hypotheses that can lay the
foundation for a deeper understanding of this phenomenon.
|
Different people speak with diverse personalized speaking styles. Although
existing one-shot talking head methods have made significant progress in lip
sync, natural facial expressions, and stable head motions, they still cannot
generate diverse speaking styles in the final talking head videos. To tackle
this problem, we propose a one-shot style-controllable talking face generation
framework. In a nutshell, we aim to attain a speaking style from an arbitrary
reference speaking video and then drive the one-shot portrait to speak with the
reference speaking style and another piece of audio. Specifically, we first
develop a style encoder to extract dynamic facial motion patterns of a style
reference video and then encode them into a style code. Afterward, we introduce
a style-controllable decoder to synthesize stylized facial animations from the
speech content and style code. In order to integrate the reference speaking
style into generated videos, we design a style-aware adaptive transformer,
which enables the encoded style code to adjust the weights of the feed-forward
layers accordingly. Thanks to the style-aware adaptation mechanism, the
reference speaking style can be better embedded into synthesized videos during
decoding. Extensive experiments demonstrate that our method is capable of
generating talking head videos with diverse speaking styles from only one
portrait image and an audio clip while achieving authentic visual effects.
Project Page: https://github.com/FuxiVirtualHuman/styletalk.
|
We explore the scattering amplitudes of fluid quanta described by the
Navier-Stokes equation and its non-Abelian generalization. These amplitudes
exhibit universal infrared structures analogous to the Weinberg soft theorem
and the Adler zero. Furthermore, they satisfy on-shell recursion relations
which together with the three-point scattering amplitude furnish a pure
S-matrix formulation of incompressible fluid mechanics. Remarkably, the
amplitudes of the non-Abelian Navier-Stokes equation also exhibit
color-kinematics duality as an off-shell symmetry, for which the associated
kinematic algebra is literally the algebra of spatial diffeomorphisms. Applying
the double copy prescription, we then arrive at a new theory of a tensor
bi-fluid. Finally, we present monopole solutions of the non-Abelian and tensor
Navier-Stokes equations and observe a classical double copy structure.
|
We examine for representative gaugino-higgsino mixing scenarios
sneutrino-neutralino and sneutrino-chargino production in deep inelastic
ep-scattering at the cm-energy of 1.8 TeV. The cross sections for
sneutrino-chargino production are more than one order of magnitude bigger than
those for sneutrino-squark production. Also for zino-like neutralinos we find
cross sections at least comparable to those for sneutrino-squark production.
|
In this paper, we present a generic and robust multimodal synthesis system
that produces highly natural speech and facial expression simultaneously. The
key component of this system is the Duration Informed Attention Network
(DurIAN), an autoregressive model in which the alignments between the input
text and the output acoustic features are inferred from a duration model. This
is different from the end-to-end attention mechanism used, and accounts for
various unavoidable artifacts, in existing end-to-end speech synthesis systems
such as Tacotron. Furthermore, DurIAN can be used to generate high quality
facial expression which can be synchronized with generated speech with/without
parallel speech and face data. To improve the efficiency of speech generation,
we also propose a multi-band parallel generation strategy on top of the WaveRNN
model. The proposed Multi-band WaveRNN effectively reduces the total
computational complexity from 9.8 to 5.5 GFLOPS, and is able to generate audio
that is 6 times faster than real time on a single CPU core. We show that DurIAN
could generate highly natural speech that is on par with current state of the
art end-to-end systems, while at the same time avoid word skipping/repeating
errors in those systems. Finally, a simple yet effective approach for
fine-grained control of expressiveness of speech and facial expression is
introduced.
|
We study tunneling dynamics of atomic pairs in Bose-Einstein condensates with
Feshbach resonances. It is shown that the tunneling of the atomic pairs depends
on not only the tunneling coupling between the atomic condensate and the
molecular condensate, but also the inter-atomic nonlinear interactions and the
initial number of atoms in these condensates. It is found that in addition to
oscillating tunneling current between the atomic condensate and the molecular
condensate, the nonlinear atomic-pair tunneling dynamics sustains a self-locked
population imbalance: macroscopic quantum self-trapping effect. Influence of
decoherence induced by non-condensate atoms on tunneling dynamics is
investigated. It is shown that decoherence suppresses atomic-pair tunneling.
|
Magnetoacoustic oscillations are nowadays routinely observed in various
regions of the solar corona. This allows them to be used as means of diagnosing
plasma parameters and processes occurring in it. Plasma diagnostics, in turn,
requires a sufficiently reliable MHD model to describe the wave evolution. In
our paper, we focus on obtaining the exact analytical solution to the problem
of the linear evolution of standing slow magnetoacoustic (MA) waves in coronal
loops. Our consideration of the properties of slow waves is conducted using the
infinite magnetic field assumption. The main contribution to the wave dynamics
in this assumption comes from such processes as thermal conduction, unspecified
coronal heating, and optically thin radiation cooling. In our consideration,
the wave periods are assumed to be short enough so that the thermal misbalance
has a weak effect on them. Thus, the main non-adiabatic process affecting the
wave dynamics remains thermal conduction. The exact solution of the
evolutionary equation is obtained using the Fourier method. This means that it
is possible to trace the evolution of any harmonic of the initial perturbation,
regardless of whether it belongs to entropy or slow mode. We show that the
fraction of energy between entropy and slow mode is defined by the thermal
conduction and coronal loop parameters. It is shown for which parameters of
coronal loops it is reasonable to associate the full solution with a slow wave,
and when it is necessary to take into account the entropy wave. Furthermore, we
obtain the relationships for the phase shifts of various plasma parameters
applicable to any values of harmonic number and thermal condition coefficient.
In particular, it is shown that the phase shifts between density and
temperature perturbations for the second harmonic of the slow wave vary between
$\pi/2$ to 0, but are larger than for the fundamental harmonic.
|
We survey lower-bound results in complexity theory that have been obtained
via newfound interconnections between propositional proof complexity, boolean
circuit complexity, and query/communication complexity. We advocate for the
theory of total search problems (TFNP) as a unifying language for these
connections and discuss how this perspective suggests a whole programme for
further research.
|
Recent advancements in integrating large language models (LLMs) with tools
have allowed the models to interact with real-world environments. However,
these tool-augmented LLMs often encounter incomplete scenarios when users
provide partial information or the necessary tools are unavailable. Recognizing
and managing such scenarios is crucial for LLMs to ensure their reliability,
but this exploration remains understudied. This study examines whether LLMs can
identify incomplete conditions and appropriately determine when to refrain from
using tools. To this end, we address a dataset by manipulating instances from
two datasets by removing necessary tools or essential information for tool
invocation. We confirm that most LLMs are challenged to identify the additional
information required to utilize specific tools and the absence of appropriate
tools. Our research can contribute to advancing reliable LLMs by addressing
scenarios that commonly arise during interactions between humans and LLMs.
|
The security of models based on new architectures such as MLP-Mixer and ViTs
needs to be studied urgently. However, most of the current researches are
mainly aimed at the adversarial attack against ViTs, and there is still
relatively little adversarial work on MLP-mixer. We propose an adversarial
attack method against MLP-Mixer called Maxwell's demon Attack (MA). MA breaks
the channel-mixing and token-mixing mechanism of MLP-Mixer by controlling the
part input of MLP-Mixer's each Mixer layer, and disturbs MLP-Mixer to obtain
the main information of images. Our method can mask the part input of the Mixer
layer, avoid overfitting of the adversarial examples to the source model, and
improve the transferability of cross-architecture. Extensive experimental
evaluation demonstrates the effectiveness and superior performance of the
proposed MA. Our method can be easily combined with existing methods and can
improve the transferability by up to 38.0% on MLP-based ResMLP. Adversarial
examples produced by our method on MLP-Mixer are able to exceed the
transferability of adversarial examples produced using DenseNet against CNNs.
To the best of our knowledge, we are the first work to study adversarial
transferability of MLP-Mixer.
|
In many multirobot applications, planning trajectories in a way to guarantee
that the collective behavior of the robots satisfies a certain high-level
specification is crucial. Motivated by this problem, we introduce counting
temporal logics---formal languages that enable concise expression of multirobot
task specifications over possibly infinite horizons. We first introduce a
general logic called counting linear temporal logic plus (cLTL+), and propose
an optimization-based method that generates individual trajectories such that
satisfaction of a given cLTL+ formula is guaranteed when these trajectories are
synchronously executed. We then introduce a fragment of cLTL+, called counting
linear temporal logic (cLTL), and show that a solution to planning problem with
cLTL constraints can be obtained more efficiently if all robots have identical
dynamics. In the second part of the paper, we relax the synchrony assumption
and discuss how to generate trajectories that can be asynchronously executed,
while preserving the satisfaction of the desired cLTL+ specification. In
particular, we show that when the asynchrony between robots is bounded, the
method presented in this paper can be modified to generate robust trajectories.
We demonstrate these ideas with an experiment and provide numerical results
that showcase the scalability of the method.
|
Based on the exact relationship to Random Matrix Theory, we derive the
probability distribution of the k-th smallest Dirac operator eigenvalue in the
microscopic finite-volume scaling regime of QCD and related gauge theories.
|
Structures seen in idealized numerical experiments on compressible
magnetoconvection in an imposed strong vertical magnetic field show important
differences from those detected in observations or realistic numerical
simulations of sunspot umbrae. To elucidate the origin of these discrepancies,
we present a series of idealized 3D compressible magnetoconvection experiments
that differ from previous such experiments in several details, bringing them
closer to realistic solar conditions. An initially vertical magnetic field B 0
is imposed on a time snapshot of fully developed solar-like turbulent
convection in a layer bounded by a stable layer from above. Upon relaxation to
a statistically steady state, the structure of the flow field and magnetic
field is examined. Instead of the vigorous granular convection (GRC) well known
to take place in magnetized or weakly magnetized convection, for high values of
B0 heat is transported by small-scale convection (SSC) in the form of narrow,
persistent convective columns consisting of slender upflows accompanied by
adjacent downflow patches, which are reminiscent of the 'convectons' identified
in earlier semianalytic models. For moderate field strengths, flux separation
(FXS) is observed: isolated field-free inclusions of GRC are embedded in a
strongly magnetized plasma with SSC. Between the SSC and FXS regimes, a
transitional regime (F/S) is identified where convectons dynamically evolve
into multiply segmented granular inclusions and back. Our results agree in some
aspects more closely with observed umbral structures than earlier idealized
models, because they do reproduce the strong localized, patchy downflows
immediately adjacent to the narrow convective columns. Based on recent
observations of umbral dots, we suggest that in some cases the conditions in
sunspot umbrae correspond to the newly identified F/S transitional regime.
|
We consider composition orderings for linear functions of one variable. Given
$n$ linear functions $f_1,\dots,f_n$ and a constant $c$, the objective is to
find a permutation $\sigma$ that minimizes/maximizes
$f_{\sigma(n)}\circ\dots\circ f_{\sigma(1)}(c)$. It was first studied in the
area of time-dependent scheduling, and known to be solvable in $O(n\log n)$
time if all functions are nondecreasing. In this paper, we present a complete
characterization of optimal composition orderings for this case, by regarding
linear functions as two-dimensional vectors. We also show several interesting
properties on optimal composition orderings such as the equivalence between
local and global optimality. Furthermore, by using the characterization above,
we provide a fixed-parameter tractable (FPT) algorithm for the composition
ordering problem for general linear functions, with respect to the number of
decreasing linear functions. We next deal with matrix multiplication orderings
as a generalization of composition of linear functions. Given $n$ matrices
$M_1,\dots,M_n\in\mathbb{R}^{m\times m}$ and two vectors $w,y\in\mathbb{R}^m$,
where $m$ denotes a positive integer, the objective is to find a permutation
$\sigma$ that minimizes/maximizes $w^\top M_{\sigma(n)}\dots M_{\sigma(1)} y$.
The problem is also viewed as a generalization of flow shop scheduling through
a limit. By this extension, we show that the multiplication ordering problem
for $2\times 2$ matrices is solvable in $O(n\log n)$ time if all the matrices
are simultaneously triangularizable and have nonnegative determinants, and FPT
with respect to the number of matrices with negative determinants, if all the
matrices are simultaneously triangularizable. As the negative side, we finally
prove that three possible natural generalizations are NP-hard: 1) when $m=2$,
2) when $m\geq 3$, and 3) the target version of the problem.
|
This paper describes a massively parallel code for a state-of-the art thermal
lattice- Boltzmann method. Our code has been carefully optimized for
performance on one GPU and to have a good scaling behavior extending to a large
number of GPUs. Versions of this code have been already used for large-scale
studies of convective turbulence. GPUs are becoming increasingly popular in HPC
applications, as they are able to deliver higher performance than traditional
processors. Writing efficient programs for large clusters is not an easy task
as codes must adapt to increasingly parallel architectures, and the overheads
of node-to-node communications must be properly handled. We describe the
structure of our code, discussing several key design choices that were guided
by theoretical models of performance and experimental benchmarks. We present an
extensive set of performance measurements and identify the corresponding main
bot- tlenecks; finally we compare the results of our GPU code with those
measured on other currently available high performance processors. Our results
are a production-grade code able to deliver a sustained performance of several
tens of Tflops as well as a design and op- timization methodology that can be
used for the development of other high performance applications for
computational physics.
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We study the variation of the dark matter mass fraction of elliptical
galaxies as a function of their luminosity, stellar mass, and size using a
sample of 29,469 elliptical galaxies culled from the Sloan Digital Sky Survey.
We model ellipticals as a stellar Hernquist profile embedded in an
adiabatically compressed dark matter halo. This model allows us to estimate a
dynamical mass ($M_{dynm}$) at the half-light radius from the velocity
dispersion of the spectra, and to compare these to the stellar mass estimates
($M_{*}$) from Kauffmann et al (2003). We find that $M_{*}/L$ is independent of
luminosity, while $M_{dynm}/L$ increases with luminosity, implying that the
dark matter fraction increases with luminosity. We also observe that at a fixed
luminosity or stellar mass, the dark matter fraction increases with increasing
galaxy size or, equivalently, increases with decreasing surface brightness:
high surface brightness galaxies show almost no evidence for dark matter, while
in low surface brightness galaxies, the dark matter exceeds the stellar mass at
the half light radius. We relate this to the fundamental plane of elliptical
galaxies, suggesting that the tilt of this plane from simple virial predictions
is due to the dark matter in galaxies. We find that a simple model where
galaxies are embedded in dark matter halos and have a star formation efficiency
independent of their surface brightness explains these trends. We estimate the
virial mass of ellipticals as being approximately 7-30 times their stellar
mass, with the lower limit suggesting almost all of the gas within the virial
radius is converted into stars.
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We study the dynamics of a transformation that acts on infinite paths in the
graph associated with Pascal's triangle. For each ergodic invariant measure the
asymptotic law of the return time to cylinders is given by a step function. We
construct a representation of the system by a subshift on a two-symbol alphabet
and then prove that the complexity function of this subshift is asymptotic to a
cubic, the frequencies of occurrence of blocks behave in a regular manner, and
the subshift is topologically weak mixing.
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Based upon the mathematical formulas of Lattice gauge theory and
non-commutative geometry differential calculus, we developed an approach of
generalized gauge theory on a product of the spacetime lattice and the two
discrete points(or a $Z_2$ discrete group). We introduce a differentiation for
non-nearest-neighbour points and find that this differentiation may lead to the
introduction of Wilson term in the free fermion Lagrangian on lattice. The
Wilson-Yukawa chiral model on lattice is constructed by the generalized gauge
theory and a toy model and Smit-Swift model are studied.
|
We consider the dynamics of atomic and field coherent states in the
non-resonant Dicke model. At weak coupling an initial product state evolves
into a superposition of multiple field coherent states that are correlated with
the atomic configuration. This process is accompanied by the buildup and decay
of atom-field entanglement and leads to the periodic collapse and revival of
Rabi oscillations. We provide a perturbative derivation of the underlying
dynamical mechanism that complements the rotating wave approximation at
resonance. The identification of two different time scales explains how the
dynamical signatures depend on the sign of detuning between the atomic and
field frequency, and predicts the generation of either atomic or field cat
states in the two opposite cases. We finally discuss the restrictions that the
buildup of atom-field entanglement during the collapse of Rabi oscillations
imposes on the validity of semi-classical approximations that neglect
entanglement.
|
We define direct sums and a corresponding notion of connectedness for graph
limits. Every graph limit has a unique decomposition as a direct sum of
connected components. As is well-known, graph limits may be represented by
symmetric functions on a probability space; there are natural definitions of
direct sums and connectedness for such functions, and there is a perfect
correspondence with the corresponding properties of the graph limit. Similarly,
every graph limit determines an infinite random graph, which is a.s. connected
if and only if the graph limit is connected. There are also characterizations
in terms of the asymptotic size of the largest component in the corresponding
finite random graphs, and of minimal cuts in sequences of graphs converging to
a given limit.
|
We improve the upper bound for the consistency strength of stationary
reflection at successors of singular cardinals.
|
Recent work has shown that it is sometimes feasible to significantly reduce
the energy usage of some radio-network algorithms by adaptively powering down
the radio receiver when it is not needed. Although past work has focused on
modifying specific network algorithms in this way, we now ask the question of
whether this problem can be solved in a generic way, treating the algorithm as
a kind of black box.
We are able to answer this question in the affirmative, presenting a new
general way to modify arbitrary radio-network algorithms in an attempt to save
energy. At the expense of a small increase in the time complexity, we can
provably reduce the energy usage to an extent that is provably nearly optimal
within a certain class of general-purpose algorithms.
As an application, we show that our algorithm reduces the energy cost of
breadth-first search in radio networks from the previous best bound of
$2^{O(\sqrt{\log n})}$ to $\mathrm{polylog}(n)$, where $n$ is the number of
nodes in the network
A key ingredient in our algorithm is hierarchical clustering based on
additive Voronoi decomposition done at multiple scales. Similar clustering
algorithms have been used in other recent work on energy-aware computation in
radio networks, but we believe the specific approach presented here may be of
independent interest.
|
This paper concerns the $\mathbb{Z}_2$ classification of Fermionic
Time-Reversal (FTR) symmetric partial differential Hamiltonians on the
Euclidean plane. We consider the setting of two insulators separated by an
interface. Hamiltonians that are invariant with respect to spatial translations
along the interface are classified into two categories depending on whether
they may or may not be gapped by continuous deformations. Introducing a related
odd-symmetric Fredholm operator, we show that the classification is stable
against FTR-symmetric perturbations.
The property that non-trivial Hamiltonians cannot be gapped may be
interpreted as a topological obstruction to Anderson localization: no matter
how much (spatially compactly supported) perturbations are present in the
system, a certain amount of transmission in both directions is guaranteed in
the nontrivial phase. We present a scattering theory for such systems and show
numerically that transmission is indeed guaranteed in the presence of
FTR-symmetric perturbations while it no longer is for non-symmetric
fluctuations.
|
The dynamics of inertial particles in Rayleigh-B\'{e}nard convection, where
both particles and fluid exhibit thermal expansion, is studied using direct
numerical simulations (DNS). We consider the effect of particles with a thermal
expansion coefficient larger than that of the fluid, causing particles to
become lighter than the fluid near the hot bottom plate and heavier than the
fluid near the cold top plate. Because of the opposite directions of the net
Archimedes' force on particles and fluid, particles deposited at the plate now
experience a relative force towards the bulk. The characteristic time for this
motion towards the bulk to happen, quantified as the time particles spend
inside the thermal boundary layers (BLs) at the plates, is shown to depend on
the thermal response time, $\tau_T$, and the thermal expansion coefficient of
particles relative to that of the fluid, $K = \alpha_p / \alpha_f$. In
particular, the residence time is constant for small thermal response times,
$\tau_T \lesssim 1$, and increasing with $\tau_T$ for larger thermal response
times, $\tau_T \gtrsim 1$. Also, the thermal BL residence time is increasing
with decreasing $K$. A one-dimensional (1D) model is developed, where particles
experience thermal inertia and their motion is purely dependent on the buoyancy
force. Although the values do not match one-to-one, this highly simplified 1D
model does predict a regime of a constant thermal BL residence time for smaller
thermal response times and a regime of increasing residence time with $\tau_T$
for larger response times, thus explaining the trends in the DNS data well.
|
We study the diffusion of a Brownian probe particle of size $R$ in a dilute
dispersion of active Brownian particles (ABPs) of size $a$, characteristic swim
speed $U_0$, reorientation time $\tau_R$, and mechanical energy $k_s T_s =
\zeta_a U_0^2 \tau_R /6$, where $\zeta_a$ is the Stokes drag coefficient of a
swimmer. The probe has a thermal diffusivity $D_P = k_B T/\zeta_P$, where $k_B
T$ is the thermal energy of the solvent and $\zeta_P$ is the Stokes drag
coefficient for the probe. When the swimmers are inactive, collisions between
the probe and the swimmers sterically hinder the probe's diffusive motion. In
competition with this steric hindrance is an enhancement driven by the activity
of the swimmers. The strength of swimming relative to thermal diffusion is set
by $Pe_s = U_0 a /D_P$. The active contribution to the diffusivity scales as
$Pe_s^2$ for weak swimming and $Pe_s$ for strong swimming, but the transition
between these two regimes is nonmonotonic. When fluctuations in the probe
motion decay on the time scale $\tau_R$, the active diffusivity scales as $k_s
T_s /\zeta_P$: the probe moves as if it were immersed in a solvent with energy
$k_s T_s$ rather than $k_B T$.
|
We consider the parabolic Anderson model $\partial u/\partial t =
\kappa\Delta u + \gamma\xi u$ with $u\colon\, \Z^d\times R^+\to \R^+$, where
$\kappa\in\R^+$ is the diffusion constant, $\Delta$ is the discrete Laplacian,
$\gamma\in\R^+$ is the coupling constant, and $\xi\colon\,\Z^d\times
\R^+\to\{0,1\}$ is the voter model starting from Bernoulli product measure
$\nu_{\rho}$ with density $\rho\in (0,1)$. The solution of this equation
describes the evolution of a "reactant" $u$ under the influence of a "catalyst"
$\xi$. In G\"artner, den Hollander and Maillard 2010 the behavior of the
\emph{annealed} Lyapunov exponents, i.e., the exponential growth rates of the
successive moments of $u$ w.r.t.\ $\xi$, was investigated. It was shown that
these exponents exhibit an interesting dependence on the dimension and on the
diffusion constant. In the present paper we address some questions left open in
G\"artner, den Hollander and Maillard 2010 by considering specifically when the
Lyapunov exponents are the a priori maximal value in terms of strong transience
of the Markov process underlying the voter model.
|
Electro-optic modulators provide a key function in optical transceivers and
increasingly in photonic programmable Application Specific Integrated Circuits
(ASICs) for machine learning and signal processing. However, both foundry ready
silicon based modulators and conventional material based devices utilizing
Lithium niobate fall short in simultaneously providing high chip packaging
density and fast speed. Current driven ITO based modulators have the potential
to achieve both enabled by efficient light matter interactions. Here, we
introduce micrometer compact Mach Zehnder Interferometer (MZI) based modulators
capable of exceeding 100 GHz switching rates. Integrating ITO thin films atop a
photonic waveguide, spectrally broadband, and compact MZI phase shifter.
Remarkably, this allows integrating more than 3500 of these modulators within
the same chip area as only one single silicon MZI modulator. The modulator
design introduced here features a holistic photonic, electronic, and RF-based
optimization and includes an asymmetric MZI tuning step to optimize the
Extinction Ratio (ER) to Insertion Loss (IL) and dielectric thickness sweep to
balance the tradeoffs between ER and speed. Driven by CMOS compatible bias
voltage levels, this device is the first to address next generation modulator
demands for processors of the machine intelligence revolution, in addition to
the edge and cloud computing demands as well as optical transceivers alike.
|
In this paper the soft gluon radiation from partonic interaction of the type:
$2 \to 2$ + gluon has been revisited and a correction term to the widely used
Gunion-Bertsch (GB) formula is obtained.
|
For a general dark-energy equation of state, we estimate the maximum possible
radius of massive structures that are not destabilized by the acceleration of
the cosmological expansion. A comparison with known stable structures
constrains the equation of state. The robustness of the constraint can be
enhanced through the accumulation of additional astrophysical data and a better
understanding of the dynamics of bound cosmic structures.
|
Let $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ be the modified quantum affine
$\frak{sl}_n$ and let ${\bf U}(\widehat{\frak{sl}}_N)^+$ be the positive part
of quantum affine $\frak{sl}_N$. Let $\dot{\mathbf{B}}(n)$ be the canonical
basis of $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ and let
$\mathbf{B}(N)^{\mathrm{ap}}$ be the canonical basis of ${\bf
U}(\widehat{\frak{sl}}_N)^+$. It is proved in \cite{FS} that each structure
constant for the multiplication with respect to $\dot{\mathbf{B}}(n)$ coincide
with a certain structure constant for the multiplication with respect to
$\mathbf{B}(N)^{\mathrm{ap}}$ for $n<N$. In this paper we use the theory of
affine quantum Schur algebras to prove that the structure constants for the
comultiplication with respect to $\dot{\mathbf{B}}(n)$ are determined by the
structure constants for the comultiplication with respect to
$\mathbf{B}(N)^{\mathrm{ap}}$ for $n<N$. In particular, the positivity property
for the comultiplication of $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ follows
from the positivity property for the comultiplication of ${\bf
U}(\widehat{\frak{sl}}_N)^+$.
|
We report on the observation of magnetoresistance oscillations in graphene
p-n junctions. The oscillations have been observed for six samples, consisting
of single-layer and bilayer graphene, and persist up to temperatures of 30 K,
where standard Shubnikov-de Haas oscillations are no longer discernible. The
oscillatory magnetoresistance can be reproduced by tight-binding simulations.
We attribute this phenomenon to the modulated densities of states in the n- and
p- regions.
|
This work numerically investigates the role of viscosity and resistivity on
Rayleigh-Taylor instabilities in magnetized high-energy-density (HED) plasmas
for a high Atwood number and high plasma beta regimes surveying across plasma
beta and magnetic Prandtl numbers. The numerical simulations are performed
using the visco-resistive magnetohydrodynamic (MHD) equations. Results
presented here show that the inclusion of self-consistent viscosity and
resistivity in the system drastically changes the growth of the Rayleigh-Taylor
instability (RTI) as well as modifies its internal structure at smaller scales.
It is seen here that the viscosity has a stabilizing effect on the RTI.
Moreover, the viscosity inhibits the development of small scale structures and
also modifies the morphology of the tip of the RTI spikes. On the other hand,
the resistivity reduces the magnetic field stabilization supporting the
development of small scale structures. The morphology of the RTI spikes is seen
to be unaffected by the presence of resistivity in the system. An additional
novelty of this work is in the disparate viscosity and resistivity profiles
that may exist in HED plasmas and their impact on RTI growth, morphology, and
the resulting turbulence spectra. Furthermore, this work shows that the
dynamics of the magnetic field is independent of viscosity and likewise the
resistivity does not affect the dissipation of enstrophy and kinetic energy. In
addition, power-law scalings of enstrophy, kinetic energy, and magnetic field
energy are provided in both injection range and inertial sub-range which could
be useful for understanding RTI induced turbulent mixing in HED laboratory and
astrophysical plasmas and could aid in the interpretation of observations of
RTI-induced turbulence spectra.
|
There have been several recent efforts towards developing representations for
multivariate time-series in an unsupervised learning framework. Such
representations can prove beneficial in tasks such as activity recognition,
health monitoring, and anomaly detection. In this paper, we consider a setting
where we observe time-series at each node in a dynamic graph. We propose a
framework called GraphTNC for unsupervised learning of joint representations of
the graph and the time-series. Our approach employs a contrastive learning
strategy. Based on an assumption that the time-series and graph evolution
dynamics are piecewise smooth, we identify local windows of time where the
signals exhibit approximate stationarity. We then train an encoding that allows
the distribution of signals within a neighborhood to be distinguished from the
distribution of non-neighboring signals. We first demonstrate the performance
of our proposed framework using synthetic data, and subsequently we show that
it can prove beneficial for the classification task with real-world datasets.
|
The flare activity that is observed in GRBs soon after the prompt emission
with the XRT (0.3-10 KeV) instrument on board of the Swift satellite is leading
to important clues in relation to the physical characteristics of the mechanism
generating the emission of energy in Gamma Ray Bursts. We will briefly refer to
the results obtained with the recent analysis and and discuss the preliminary
results we obtained with a new larger sample of GRBs [limited to early flares]
based on fitting of the flares using the Norris 2005 profile. We find, in
agreement with previous results, that XRT flares follow the main
characteristics observed in Norris 2005 for the prompt emission spikes. The
estimate of the flare energy for the subsample with redshift is rather robust
and an attempt is made, using the redshisft sample, to estimate how the energy
emitted in flares depends on time. We used a $H_0=70 km/s/Mpc$,
$\Omega_\Lambda=0.7$, $\Omega_m=0.3$ cosmology.
|
The finite element method, finite difference method, finite volume method and
spectral method have achieved great success in solving partial differential
equations. However, the high accuracy of traditional numerical methods is at
the cost of high efficiency. Especially in the face of high-dimensional
problems, the traditional numerical methods are often not feasible in the
subdivision of high-dimensional meshes and the differentiability and
integrability of high-order terms. In deep learning, neural network can deal
with high-dimensional problems by adding the number of layers or expanding the
number of neurons. Compared with traditional numerical methods, it has great
advantages. In this article, we consider the Deep Galerkin Method (DGM) for
solving the general Stokes equations by using deep neural network without
generating mesh grid. The DGM can reduce the computational complexity and
achieve the competitive results. Here, depending on the L2 error we construct
the objective function to control the performance of the approximation
solution. Then, we prove the convergence of the objective function and the
convergence of the neural network to the exact solution. Finally, the
effectiveness of the proposed framework is demonstrated through some numerical
experiments.
|
We review five often used quad lens models, each of which has analytical
solutions and can produce four images at most. Each lens model has two
parameters, including one that describes the intensity of non-dimensional mass
density, and the other one that describes the deviation from the circular lens.
In our recent work, we have found that the cusp and the fold summations are not
equal to 0, when a point source infinitely approaches a cusp or a fold from
inner side of the caustic. Based on the magnification invariant theory, which
states that the sum of signed magnifications of the total images of a given
source is a constant, we calculate the cusp summations for the five lens
models. We find that the cusp summations are always larger than 0 for source on
the major cusps, while can be larger or smaller than 0 for source on the minor
cusps. We also find that if these lenses tend to the circular lens, the major
and minor cusp summations will have infinite values, and with positive and
negative signs respectively. The cusp summations do not change significantly if
the sources are slightly deviated from the cusps. In addition, through the
magnification invariants, we also derive the analytical signed cusp relations
on the axes for three lens models. We find that both on the major and the minor
axes the larger the lenses deviated from the circular lens, the larger the
signed cusp relations. The major cusp relations are usually larger than the
absolute minor cusp relations, but for some lens models with very large
deviation from circular lens, the minor cusp relations can be larger than the
major cusp relations.
|
Millions of news articles published online daily can overwhelm readers.
Headlines and entity (topic) tags are essential for guiding readers to decide
if the content is worth their time. While headline generation has been
extensively studied, tag generation remains largely unexplored, yet it offers
readers better access to topics of interest. The need for conciseness in
capturing readers' attention necessitates improved content selection strategies
for identifying salient and relevant segments within lengthy articles, thereby
guiding language models effectively. To address this, we propose to leverage
auxiliary information such as images and captions embedded in the articles to
retrieve relevant sentences and utilize instruction tuning with variations to
generate both headlines and tags for news articles in a multilingual context.
To make use of the auxiliary information, we have compiled a dataset named
XL-HeadTags, which includes 20 languages across 6 diverse language families.
Through extensive evaluation, we demonstrate the effectiveness of our
plug-and-play multimodal-multilingual retrievers for both tasks. Additionally,
we have developed a suite of tools for processing and evaluating multilingual
texts, significantly contributing to the research community by enabling more
accurate and efficient analysis across languages.
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Motivated by some questions in Euclidean Ramsey theory, our aim in this note
is to show that there exists a cyclic quadrilateral that does not embed into
any transitive set (in any dimension). We show that in fact this holds for
almost all cyclic quadrilaterals, and we also give explicit examples of such
cyclic quadrilaterals. These are the first explicit examples of spherical sets
that do not embed into transitive sets.
|
The present paper is a comment regarding the robustness of the chirality in
presence of the space-reflection asymmetry, which leads to pairs of interleaved
positive- and negative-parity bands. The recent results reported in Ref.
\cite{2006.12062} which introduced the $chiture$ and $chiplex$ quantum numbers
to describe an ideal nuclear system with simultaneous chiral and reflection
symmetry breaking, are commented.
|
In many moduli stabilization schemes in string theory, the scale of inflation
appears to be of the same order as the scale of supersymmetry breaking. For
low-scale supersymmetry breaking, therefore, the scale of inflation should also
be low, unless this correlation is avoided in specific models. We explore such
a low-scale inflationary scenario in a racetrack model with a single modulus in
type IIB string theory. Inflation occurs near a point of inflection in the
K\"ahler modulus potential. Obtaining acceptable cosmological density
perturbations leads to the introduction of magnetized D7-branes sourcing
non-perturbative superpotentials. The gravitino mass, m_{3/2}, is chosen to be
around 30 TeV, so that gravitinos that are produced in the inflaton decay do
not affect big-bang nucleosynthesis. Supersymmetry is communicated to the
visible sector by a mixture of anomaly and modulus mediation. We find that the
two sources contribute equally to the gaugino masses, while scalar masses are
decided mainly by anomaly contribution. This happens as a result of the low
scale of inflation and can be probed at the LHC.
|
Upstream reciprocity (also called generalized reciprocity) is a putative
mechanism for cooperation in social dilemma situations with which players help
others when they are helped by somebody else. It is a type of indirect
reciprocity. Although upstream reciprocity is often observed in experiments,
most theories suggest that it is operative only when players form short cycles
such as triangles, implying a small population size, or when it is combined
with other mechanisms that promote cooperation on their own. An expectation is
that real social networks, which are known to be full of triangles and other
short cycles, may accommodate upstream reciprocity. In this study, I extend the
upstream reciprocity game proposed for a directed cycle by Boyd and Richerson
to the case of general networks. The model is not evolutionary and concerns the
conditions under which the unanimity of cooperative players is a Nash
equilibrium. I show that an abundance of triangles or other short cycles in a
network does little to promote upstream reciprocity. Cooperation is less likely
for a larger population size even if triangles are abundant in the network. In
addition, in contrast to the results for evolutionary social dilemma games on
networks, scale-free networks lead to less cooperation than networks with a
homogeneous degree distribution.
|
Polarized Raman spectra of the epitaxial Ba0.5Sr0.5TiO3 film, bi-color
BaTiO3/Ba0.5Sr0.5TiO3 superlattice, and tri-color BaTiO3/Ba0.5Sr0.5TiO3/SrTiO3
superlattice were studied in a broad temperature range of 80-700 K. Based on
the temperature dependence of the polar modes we determined the phase
transitions temperatures in the studied heterostructures. In the sub-THz
frequency range of the Y(XZ)Y spectra, we revealed the coexistence of the
Debye-type central peak and soft mode in bi-color BaTiO3/Ba0.5Sr0.5TiO3
superlattice.
|
The damping of spin waves parametrically excited in the magnetic insulator
Yttrium Iron Garnet (YIG) is controlled by a dc current passed through an
adjacent normal-metal film. The experiment is performed on a macroscopically
sized YIG(100nm)/Pt(10nm) bilayer of 4x2 mm^2 lateral dimensions. The spin-wave
relaxation frequency is determined via the threshold of the parametric
instability measured by Brillouin light scattering (BLS) spectroscopy. The
application of a dc current to the Pt film leads to the formation of a
spin-polarized electron current normal to the film plane due to the spin Hall
effect (SHE). This spin current exerts a spin transfer torque (STT) in the YIG
film and, thus, changes the spin-wave damping. Depending on the polarity of the
applied dc current with respect to the magnetization direction, the damping can
be increased or decreased. The magnitude of its variation is proportional to
the applied current. A variation in the relaxation frequency of +/-7.5% is
achieved for an applied dc current density of 5*10^10 A/m^2.
|
The paper is devoted to the study of two-parametric families of Dirichlet
problems for systems of equations with $p, q$-Laplacians and indefinite
nonlinearities. Continuous and monotone curves $\Gamma_f$ and $\Gamma_e$ on the
parametric plane $\lambda \times \mu$, which are the lower and upper bounds for
a maximal domain of existence of weak positive solutions are introduced. The
curve $\Gamma_f$ is obtained by developing our previous work
\cite{BobkovIlyasov} and it determines a maximal domain of the applicability of
the Nehari manifold and fibering methods. The curve $\Gamma_e$ is derived
explicitly via minimax variational principle of the extended functional method.
|
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