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Continual Learning (CL) aims to learn a sequence of problems (i.e., tasks and
domains) by transferring knowledge acquired on previous problems, whilst
avoiding forgetting of past ones. Different from previous approaches which
focused on CL for one NLP task or domain in a specific use-case, in this paper,
we address a more general CL setting to learn from a sequence of problems in a
unique framework. Our method, HOP, permits to hop across tasks and domains by
addressing the CL problem along three directions: (i) we employ a set of
adapters to generalize a large pre-trained model to unseen problems, (ii) we
compute high-order moments over the distribution of embedded representations to
distinguish independent and correlated statistics across different tasks and
domains, (iii) we process this enriched information with auxiliary heads
specialized for each end problem. Extensive experimental campaign on 4 NLP
applications, 5 benchmarks and 2 CL setups demonstrates the effectiveness of
our HOP.
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This paper is a complement of our recent works on the semilinear Tricomi
equations in [8] and[9].
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We propose a new method to extract the light quark mass ratio $m_u/m_d$ using
the $\Upsilon(4S)\to h_b\pi^0(\eta)$ bottomonia transitions. The decay
amplitudes are dominated by the light quark mass differences, and the
corrections from other effects are rather small, allowing for a precise
extraction. We also discuss how to reduce the theoretical uncertainty with the
help of future experiments. As a by-product, we show that the decay
$\Upsilon(4S)\to h_b\eta$ is expected to be a nice channel for searching for
the $h_b$ state.
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Lectures on Quantum Coulomb gases delivered at the CIME summer school on
Quantum Many Body Systems 2010
|
We present a new conceptual definition of 'productivity' for sustainably
developing research software. Existing definitions are flawed as they are
short-term biased, thus devaluing long-term impact, which we consider to be the
principal goal. Taking a long-term view of productivity helps fix that problem.
We view the outputs of the development process as knowledge and user
satisfaction. User satisfaction is used as a proxy for effective quality. The
explicit emphasis on all knowledge produced, rather than just the
operationalizable knowledge (code) implies that human-reusable knowledge, i.e.
documentation, should also be greatly valued when producing research software.
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A cell method is developed, which takes into account the bubble geometry of
polyhedral foams, and provides for the generalized Rayleigh-Plesset equation
that contains the non-local in time term corresponding to heat relaxation. The
Rayleigh-Plesset equation together with the equations of mass and momentum
balances for an effective single-phase inviscid fluid yield a model for foam
acoustics. The present calculations reconcile observed sound velocity and
attenuation with those predicted using the assumption that thermal dissipation
is the dominant damping mechanism in a range of foam expansions and sound
excitation frequencies.
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We present a second-order monolithic method for solving incompressible
Navier--Stokes equations on irregular domains with quadtree grids. A
semi-collocated grid layout is adopted, where velocity variables are located at
cell vertices, and pressure variables are located at cell centers. Compact
finite difference methods with ghost values are used to discretize the
advection and diffusion terms of the velocity. A pressure gradient and
divergence operator on the quadtree that use compact stencils are developed.
Furthermore, the proposed method is extended to cubical domains with octree
grids. Numerical results demonstrate that the method is second-order convergent
in $L^\infty$ norms and can handle irregular domains for various Reynolds
numbers.
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We introduce the Nuclear Electronic All-Particle Density Matrix
Renormalization Group (NEAP-DMRG) method for solving the time-independent
Schr\"odinger equation simultaneously for electrons and other quantum species.
In contrast to already existing multicomponent approaches, in this work we
construct from the outset a multi-reference trial wave function with
stochastically optimized non-orthogonal Gaussian orbitals. By iterative
refining of the Gaussians' positions and widths, we obtain a compact
multi-reference expansion for the multicomponent wave function. We extend the
DMRG algorithm to multicomponent wave functions to take into account inter- and
intra-species correlation effects. The efficient parametrization of the total
wave function as a matrix product state allows NEAP-DMRG to accurately
approximate full configuration interaction energies of molecular systems with
more than three nuclei and twelve particles in total, which is currently a
major challenge for other multicomponent approaches. We present NEAP-DMRG
results for two few-body systems, i.e., H$_2$ and H$_3^+$, and one larger
system, namely BH$_3$
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In this note, we study asymptotic zero distribution of multivariable full
system of random polynomials with independent Bernoulli coefficients. We prove
that with overwhelming probability their simultaneous zeros sets are discrete
and the associated normalized empirical measure of zeros asymptotic to the Haar
measure on the unit torus.
|
We show that for all positive beta the semigroups of beta-Dyson Brownian
motions of different dimensions are intertwined. The proof relates beta-Dyson
Brownian motions directly to Jack symmetric polynomials and omits an
approximation of the former by discrete space Markov chains, thereby disposing
of the technical assumption beta>1 in [GS]. The corresponding results for
beta-Dyson Ornstein-Uhlenbeck processes are also presented.
|
Nonparametric Bayesian approaches based on Gaussian processes have recently
become popular in the empirical learning community. They encompass many
classical methods of statistics, like Radial Basis Functions or various
splines, and are technically convenient because Gaussian integrals can be
calculated analytically. Restricting to Gaussian processes, however, forbids
for example the implemention of genuine nonconcave priors. Mixtures of Gaussian
process priors, on the other hand, allow the flexible implementation of complex
and situation specific, also nonconcave "a priori" information. This is
essential for tasks with, compared to their complexity, a small number of
available training data. The paper concentrates on the formalism for Gaussian
regression problems where prior mixture models provide a generalisation of
classical quadratic, typically smoothness related, regularisation approaches
being more flexible without having a much larger computational complexity.
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This paper analyses the application of artificial intelligence techniques to
various areas of archaeology and more specifically: a) The use of software
tools as a creative stimulus for the organization of exhibitions; the use of
humanoid robots and holographic displays as guides that interact and involve
museum visitors; b) The analysis of methods for the classification of fragments
found in archaeological excavations and for the reconstruction of ceramics,
with the recomposition of the parts of text missing from historical documents
and epigraphs; c) The cataloguing and study of human remains to understand the
social and historical context of belonging with the demonstration of the
effectiveness of the AI techniques used; d) The detection of particularly
difficult terrestrial archaeological sites with the analysis of the
architectures of the Artificial Neural Networks most suitable for solving the
problems presented by the site; the design of a study for the exploration of
marine archaeological sites, located at depths that cannot be reached by man,
through the construction of a freely explorable 3D version.
|
We study how to generate in minimum time special unitary transformations for
a two-level quantum system under the assumptions that: (i) the system is
subject to a constant drift, (ii) its dynamics can be affected by three
independent, bounded controls, (iii) the bounds on the controls are asymmetric,
that is, the constraint on the control in the direction of the drift is
independent of that on the controls in the orthogonal plane. Using techniques
recently developed for the analysis of SU(2) transformations, we fully
characterize the reachable sets of the system, and the optimal control
strategies for any possible target transformation.
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Recent constraint logic programming (CLP) languages, such as HAL and Mercury,
require type, mode and determinism declarations for predicates. This
information allows the generation of efficient target code and the detection of
many errors at compile-time. Unfortunately, mode checking in such languages is
difficult. One of the main reasons is that, for each predicate mode
declaration, the compiler is required to appropriately re-order literals in the
predicate's definition. The task is further complicated by the need to handle
complex instantiations (which interact with type declarations and higher-order
predicates) and automatic initialization of solver variables. Here we define
mode checking for strongly typed CLP languages which require reordering of
clause body literals. In addition, we show how to handle a simple case of
polymorphic modes by using the corresponding polymorphic types.
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We demonstrate a silicon-chip biphoton source with an unprecedented quantum
cross correlation up to ${\rm g_{si}^{(2)}(0) = (2.58 \pm 0.16) \times 10^4}$.
The emitted biphotons are intrinsically single-mode, with self correlations of
${\rm g_{ss}^{(2)}(0) = 1.90 \pm 0.05}$ and ${\rm g_{ii}^{(2)}(0) = 1.87 \pm
0.06}$ for signal and idler photons, respectively. We observe the waveform
asymmetry of cross correlation between signal and idler photons and reveal the
identical and non-exponential nature of self correlations of individual signal
and idler photon modes, which is a nature of cavity-enhanced nonlinear optical
processes. The high efficiency and high purity of the biphoton source allow us
to herald single photons with a conditional self correlation $\rm
g_{c}^{(2)}(0)$ as low as $\rm 0.0059 \pm 0.0014$ at a pair flux of $\rm 1.95
\times 10^5$ pairs/s, which remains below $\rm 0.026 \pm 0.001$ for a biphoton
flux up to $\rm 2.93 \times 10^6$ pairs/s, with a photon preparation efficiency
in the single-mode fiber up to 51%, among the best values that have ever been
reported. Our work unambiguously demonstrates that silicon photonic chips are
superior material and device platforms for integrated quantum photonics.
|
Population III (Pop III) stars ended the cosmic Dark Ages and began early
cosmological reionization and chemical enrichment. However, in spite of their
importance to the evolution of the early Universe, their properties remain
uncertain because of limitations to previous numerical simulations and the lack
of any observational constraints. Here we investigate Pop III star formation in
five primordial halos with 3D radiation-hydrodynamical cosmological
simulations. We find that multiple stars form in each minihalo and that their
numbers increase over time, with up to 23 stars forming in one of the halos.
Radiative feedback from the stars generates strong outflows, deforms the
surrounding protostellar disk, and delays star formation for a few thousand
years. Star formation rates vary with halo and depend on mass accretion onto
the disk, halo spin number, and the fraction of massive stars in the halo.
Stellar masses in our models range from 0.1-37 $\rm M_{\odot}$, and of the 55
stars that form in our models twelve are $\rm > 10~ M_{\odot}$ and most of the
others are 1-10 $\rm M_{\odot}$. Our simulations thus suggest that Pop III
stars have characteristic masses of 1-10 $\rm M_{\odot}$ and a top-heavy IMF
with dN/dM $\propto M_*^{-1.18}$. Up to 70\% of the stars are ejected from
their disks by three-body interactions which, along with ionizing UV feedback,
limits their final masses.
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Several approaches to testing the hypothesis that two histograms are drawn
from the same distribution are investigated. We note that single-sample
continuous distribution tests may be adapted to this two-sample grouped data
situation. The difficulty of not having a fully-specified null hypothesis is an
important consideration in the general case, and care is required in estimating
probabilities with ``toy'' Monte Carlo simulations. The performance of several
common tests is compared; no single test performs best in all situations.
|
Light field deconvolution allows three-dimensional investigations from a
single snapshot recording of a plenoptic camera. It is based on a linear image
formation model, and iterative volume reconstruction requires to define the
backprojection of individual image pixels into object space. This is
effectively a reversal of the point spread function (PSF), and backprojection
arrays H' can be derived from the shift-variant PSFs H of the optical system,
which is a very time consuming step for high resolution cameras. This paper
illustrates the common structure of backprojection arrays and the significance
of their efficient computation. A new algorithm is presented to determine H'
from H, which is based on the distinct relation of the elements' positions
within the two multi-dimensional arrays. It permits a pure array
re-arrangement, and while results are identical to those from published codes,
computation times are drastically reduced. This is shown by benchmarking the
new method using various sample PSF arrays against existing algorithms. The
paper is complemented by practical hints for the experimental acquisition of
light field PSFs in a photographic setup.
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The paper is concerned with estimating the number of integers smaller than
$x$ whose largest prime divisor is smaller than $y$, denoted $\psi (x,y)$. Much
of the related literature is concerned with approximating $\psi (x,y)$ by
Dickman's function $\rho (u)$, where $u=\ln x/\ln y$. A typical such result is
that $$ \psi (x,y)=x\rho (u)(1+o(1)) \eqno (1) $$ in a certain domain of the
parameters $x$ and $y$.
In this paper a different type of approximation of $\psi (x,y)$, using
iterated logarithms of $x$ and $y$, is presented. We establish that $$ \ln
(\frac {\psi}{x})=-u [\ln ^{(2)}x-\ln ^{(2)}y+\ln ^{(3)}x-\ln ^{(3)}y+\ln
^{(4)}x-a] \eqno (2) $$ where $\underbar{a}<a<\bar{a}$ for some constants
$\underbar{a}$ and $\bar{a}$ (denoting by $\ln ^{(k)}x=\ln ...\ln x$ the
$k$-fold iterated logarithm). The approximation (2) holds in a domain which is
complementary to the one on which the approximation (1) is known to be valid.
One consequence of (2) is an asymptotic expression for Dickman's function,
which is of the form $\ln \rho (u)=-u[\ln u+\ln ^{(2)}u](1+o(1))$, improving
known asymptotic approximations of this type. We employ (2) to establish a
version of Bertrand's Conjecture, and indicate how this method may be used to
sharpen the result.
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We propose an orbifold lattice formulation of QCD suitable for quantum
simulations. We show explicitly how to encode gauge degrees of freedom into
qubits using noncompact variables, and how to write down a simple truncated
Hamiltonian in the coordinate basis. We show that SU(3) gauge group variables
and quarks in the fundamental representation can be implemented
straightforwardly on qubits, for arbitrary truncation of the gauge manifold.
|
In "Quartic Coincidences and the Singular Value Decomposition" by Clifford
and Lachance, Mathematics Magazine, December, 2013, it was shown that if there
is a midpoint ellipse(an ellipse inscribed in a quadrilateral, $Q$, which is
tangent at the midpoints of all four sides of $Q$), then $Q$ must be a
parallelogram. We strengthen this result by showing that if $Q$ is not a
parallelogram, then there is no ellipse inscribed in $Q$ which is tangent at
the midpoint of three sides of $Q$. Second, the only quadrilaterals which have
inscribed ellipses tangent at the midpoint of even two sides of $Q$ are
trapezoids or what we call a midpoint diagonal quadrilateral(the intersection
point of the diagonals of $Q$ coincides with the midpoint of at least one of
the diagonals of $Q$).
|
Oscillations are ubiquitous in sunspots and the associated higher
atmospheres. However, it is still unclear whether these oscillations are driven
by the external acoustic waves (p-modes) or generated by the internal
magnetoconvection. To obtain clues about the driving source of umbral waves in
sunspots, we analyzed the spiral wave patterns (SWPs) in two sunspots
registered by IRIS MgII 2796 {\AA} slit-jaw images. By tracking the motion of
the SWPs, we find for the first time that two one-armed SWPs coexist in the
umbra, and they can rotate either in the same or opposite directions.
Furthermore, by analyzing the spatial distribution of the oscillation centers
of the one-armed SWPs within the umbra (the oscillation center is defined as
the location where the SWP first appears), we find that the chromospheric
umbral waves repeatedly originate from the regions with high oscillation power
and most of the umbral waves occur in the dark nuclei and strong magnetic field
regions of the umbra. Our study results indicate that the chromospheric umbral
waves are likely excited by the p-mode oscillations.
|
Let $X$ be a smooth complex projective algebraic variety. Given a line bundle
$\mathcal{L}$ over $X$ and an integer $r>1$ one defines the stack
$\sqrt[r]{\mathcal{L}/X}$ of $r$-th roots of $\mathcal{L}$. Motivated by
Gromov-Witten theoretic questions, in this paper we analyze the structure of
moduli stacks of genus $0$ twisted stable maps to $\sqrt[r]{\mathcal{L}/X}$.
Our main results are explicit constructions of moduli stacks of genus $0$
twisted stable maps to $\sqrt[r]{\mathcal{L}/X}$ starting from moduli stack of
genus $0$ stable maps to $X$. As a consequence, we prove an exact formula
expressing genus $0$ Gromov-Witten invariants of $\sqrt[r]{\mathcal{L}/X}$ in
terms of those of $X$.
|
We study the optimal control problem of maximizing the spread of an
information epidemic on a social network. Information propagation is modeled as
a Susceptible-Infected (SI) process and the campaign budget is fixed. Direct
recruitment and word-of-mouth incentives are the two strategies to accelerate
information spreading (controls). We allow for multiple controls depending on
the degree of the nodes/individuals. The solution optimally allocates the
scarce resource over the campaign duration and the degree class groups. We
study the impact of the degree distribution of the network on the controls and
present results for Erdos-Renyi and scale free networks. Results show that more
resource is allocated to high degree nodes in the case of scale free networks
but medium degree nodes in the case of Erdos-Renyi networks. We study the
effects of various model parameters on the optimal strategy and quantify the
improvement offered by the optimal strategy over the static and bang-bang
control strategies. The effect of the time varying spreading rate on the
controls is explored as the interest level of the population in the subject of
the campaign may change over time. We show the existence of a solution to the
formulated optimal control problem, which has non-linear isoperimetric
constraints, using novel techniques that is general and can be used in other
similar optimal control problems. This work may be of interest to political,
social awareness, or crowdfunding campaigners and product marketing managers,
and with some modifications may be used for mitigating biological epidemics.
|
With the increase in demand of electrical energy storage devices such as
batteries and supercapacitors, considerable effort is being put to increase the
efficiency and applications of current technology while keeping it sustainable.
Keeping this in mind we have persued the preparation and charatization of waste
biomass derived carbon powders as supercapacitor/battery electrodes.
Additionally, we have evaluated the performance of such carbons in the presence
of an external magnetic field as we expect the graphene like structures to
possess intrinsic magnetic nature. Here, we report the valorization of
bougainvillea flower petals and detritus into graphenic carbon and explore a
novel electrical double layer supercapacitor device that uses Zn+2 ions for
internal charge transport and is able to show increased performance upon
application of an external magnetic field.
|
As deep learning models are becoming larger and data-hungrier, there are
growing ethical, legal and technical concerns over use of data: in practice,
agreements on data use may change over time, rendering previously-used training
data impermissible for training purposes. These issues have driven increased
attention to machine unlearning: removing "the influence of" a subset of
training data from a trained model. In this work, we advocate for a relaxed
definition of unlearning that does not address privacy applications but targets
a scenario where a data owner withdraws permission of use of their data for
training purposes. In this context, we consider the important problem of
\emph{transfer unlearning} where a pretrained model is transferred to a target
dataset that contains some "non-static" data that may need to be unlearned in
the future. We propose a new method that uses a mechanism for selecting
relevant examples from an auxiliary "static" dataset, and finetunes on the
selected data instead of "non-static" target data; addressing all unlearning
requests ahead of time. We also adapt a recent relaxed definition of unlearning
to our problem setting and demonstrate that our approach is an exact transfer
unlearner according to it, while being highly efficient (amortized). We find
that our method outperforms the gold standard "exact unlearning" (finetuning on
only the "static" portion of the target dataset) on several datasets,
especially for small "static" sets, sometimes approaching an upper bound for
test accuracy. We also analyze factors influencing the accuracy boost obtained
by data selection.
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In stochastic low-rank matrix bandit, the expected reward of an arm is equal
to the inner product between its feature matrix and some unknown $d_1$ by $d_2$
low-rank parameter matrix $\Theta^*$ with rank $r \ll d_1\wedge d_2$. While all
prior studies assume the payoffs are mixed with sub-Gaussian noises, in this
work we loosen this strict assumption and consider the new problem of
\underline{low}-rank matrix bandit with \underline{h}eavy-\underline{t}ailed
\underline{r}ewards (LowHTR), where the rewards only have finite $(1+\delta)$
moment for some $\delta \in (0,1]$. By utilizing the truncation on observed
payoffs and the dynamic exploration, we propose a novel algorithm called LOTUS
attaining the regret bound of order $\tilde
O(d^\frac{3}{2}r^\frac{1}{2}T^\frac{1}{1+\delta}/\tilde{D}_{rr})$ without
knowing $T$, which matches the state-of-the-art regret bound under sub-Gaussian
noises~\citep{lu2021low,kang2022efficient} with $\delta = 1$. Moreover, we
establish a lower bound of the order $\Omega(d^\frac{\delta}{1+\delta}
r^\frac{\delta}{1+\delta} T^\frac{1}{1+\delta}) = \Omega(T^\frac{1}{1+\delta})$
for LowHTR, which indicates our LOTUS is nearly optimal in the order of $T$. In
addition, we improve LOTUS so that it does not require knowledge of the rank
$r$ with $\tilde O(dr^\frac{3}{2}T^\frac{1+\delta}{1+2\delta})$ regret bound,
and it is efficient under the high-dimensional scenario. We also conduct
simulations to demonstrate the practical superiority of our algorithm.
|
The spin-split Fermi level crossings of the conduction band in Ni are mapped
out by high-resolution photoemission and compared to the equivalent crossing in
Cu. The area of the quasiparticle peak decreases rapidly below Ef in Ni, but
not in Cu. Majority spins have larger spectral weight at Ef than minority
spins, thereby enhancing the spin-polarization beyond that expected from the
density of states. A large part of the effect can be traced to a rapid
variation of the matrix element with {\bf k} at the point where the s,p-band
begins to hybridize with the $dz^2$ state. However, it is quite possible that
the intensity drop in Ni is reinforced by a transfer of spectral weight from
single-particle to many-electron excitations. The results suggest that the
matrix element should be considered for explaining the enhanced spin
polarization observed for Ni in spin-polarized tunneling.
|
We consider a dynamic scenario for characterizing the late Universe
evolution, aiming to mitigate the Hubble tension. Specifically, we consider a
metric $f(R)$ gravity in the Jordan frame which is implemented to the dynamics
of a flat isotropic Universe. This cosmological model incorporates a matter
creation process, due to the time variation of the cosmological gravitational
field. We model particle creation by representing the isotropic Universe
(specifically, a given fiducial volume) as an open thermodynamic system. The
resulting dynamical model involves four unknowns: the Hubble parameter, the
non-minimally coupled scalar field, its potential, and the energy density of
the matter component. We impose suitable conditions to derive a closed system
for these functions of the redshift. In this model, the vacuum energy density
of the present Universe is determined by the scalar field potential, in line
with the modified gravity scenario. Hence, we construct a viable model,
determining the form of the $f(R)$ theory a posteriori and appropriately
constraining the phenomenological parameters of the matter creation process to
eliminate tachyon modes. Finally, by analyzing the allowed parameter space, we
demonstrate that the Planck evolution of the Hubble parameter can be reconciled
with the late Universe dynamics, thus alleviating the Hubble tension.
|
Motivated by SU(3) structure compactifications, we show explicitly how to
construct half--flat topological mirrors to Calabi--Yau manifolds with NS
fluxes. Units of flux are exchanged with torsion factors in the cohomology of
the mirror; this is the topological complement of previous
differential--geometric mirror rules. The construction modifies explicit SYZ
fibrations for compact Calabi--Yaus. The results are of independent interest
for SU(3) compactifications. For example one can exhibit explicitly which
massive forms should be used for Kaluza--Klein reduction, proving previous
conjectures. Formality shows that these forms carry no topological information;
this is also confirmed by infrared limits and old classification theorems.
|
The BESIII detector on the BEPCII collider collected the world's largest
dataset at the peaks of $J/\psi$, $\psi(3686)$ and $\psi(3770)$. The use of
polarization and entanglement states in multidimensional angular distribution
analysis can provide new probes to the production and decay characteristics of
hyperon anti hyperon pairs. In a recent series of studies, significant
transverse polarization in hyperon decay has been observed in $J/\psi$,
$\psi(3686)$ decaying into the $\Lambda\bar\Lambda$, $\Sigma^+\bar\Sigma^{-}$,
$\Xi^0\bar\Xi^0$ and $\Xi^-\bar\Xi^{+}$ final states. The weak decay parameters
of hyperons and antihyperons are also independently determined for the first
time. The most accurate testing for direct $CP$ violation has been achieved
based on the measured weak decay parameters.
|
Evaporation of a liquid layer on a substrate is examined without the
often-used isothermality assumption -- i.e., temperature variations are
accounted for. Qualitative estimates show that nonisothermality makes the
evaporation rate depend on the conditions the substrate is maintained at. If it
is thermally insulated, evaporative cooling dramatically slows evaporation
down; the evaporation rate tends to zero with time and cannot be determined by
measuring the external parameters only. If, however, the substrate is
maintained at a fixed temperature, the heat flux coming from below sustains
evaporation at a finite rate -- deducible from the fluid's characteristics,
relative humidity, and the layer's depth (whose importance has not been
recognized before). The qualitative predictions are quantified using the
diffuse-interface model applied to a liquid evaporating into its own vapor.
|
The chromatic critical edge theorem of Simonovits states that for a given
color critical graph $H$ with $\chi(H)=k+1$, there exists an $n_0(H)$ such that
the Tur\'an graph $T_{n,k}$ is the only extremal graph with respect to
$ex(n,H)$ provided $n \geq n_0(H)$. Nikiforov's pioneer work on spectral graph
theory implies that the color critical edge theorem also holds if $ex(n,H)$ is
replaced by the maximum spectral radius and $n_0(H)$ is an exponential function
of $|H|$. We want to know which color critical graphs $H$ satisfy that $n_0(H)$
is a linear function of $|H|$. Previous graphs include complete graphs and odd
cycles. In this paper, we find two new classes of graphs: books and theta
graphs. Namely, we prove that every graph on $n$ vertices with
$\rho(G)>\rho(T_{n,2})$ contains a book of size greater than $\frac{n}{6.5}$.
This can be seen as a spectral version of a 1962 conjecture by Erd\H{o}s, which
states that every graph on $n$ vertices with $e(G)>e(T_{n,2})$ contains a book
of size greater than $\frac{n}{6}$. In addition, our result on theta graphs
implies that if $G$ is a graph of order $n$ with $\rho(G)>\rho(T_{n,2})$, then
$G$ contains a cycle of length $t$ for every $t\leq \frac{n}{7}$. This is
related to an open question by Nikiforov which asks to determine the maximum
$c$ such that every graph $G$ of large enough order $n$ with
$\rho(G)>\rho(T_{n,2})$ contains a cycle of length $t$ for every $t\leq cn$.
|
In this paper, we present a characterization of optimal entanglement
witnesses in terms of positive maps and then provide a general method of
checking optimality of entanglement witnesses. Applying it, we obtain new
indecomposable optimal witnesses which have no spanning property. These also
provide new examples which support a recent conjecture saying that the
so-called structural physical approximations to optimal positive maps (optimal
entanglement witnesses) give entanglement breaking maps (separable states).
|
We analyse the spectra of the archival XMM-Newton data of the Seyfert 1 AGN
Zw 229.015 in the energy range $0.3 - 10.0$ keV. When fitted with a simple
power-law, the spectrum shows signatures of weak soft excess below 1.0 keV. We
find that both thermal comptonisation and relativistically blurred reflection
models provide the most acceptable spectral fits with plausible physical
explanations to the origin of the soft excess than do multicolour disc
blackbody and smeared wind absorption models. This motivated us to study the
variability properties of the soft and the hard X-ray emissions from the source
and the relationship between them to put further constraints on the above
models. Our analysis reveals that the variation in the $3.0 - 10.0$ keV band
lags that in the $0.3 - 1.0$ keV by $600^{+290}_{-280}$ s, while the lag
between the $1.0 - 10.0$ keV and $0.3 - 1.0$ keV is $980^{+500}_{-500}$ s. This
implies that the X-ray emissions are possibly emanating from different regions
within the system. From these values, we estimate the X-ray emission region to
be within $20R_g$ of the central supermassive black hole (where $R_g=GM/c^2$,
$M$ is the mass of black hole, $G$ the Newton gravitational constant and $c$
the speed of light). Furthermore, we use XMM-Newton and Kepler photometric
lightcurves of the source to search for possible nonlinear signature in the
flux variability. We find evidence that the variability in the system may be
dominated by stochasticity rather than deterministic chaos which has
implications for the dynamics of the accretion system.
|
The complex zeros of the Riemannn zeta-function are identical to the zeros of
the Riemann xi-function, $\xi(s)$. Thus, if the Riemann Hypothesis is true for
the zeta-function, it is true for $\xi(s)$. Since $\xi(s)$ is entire, the zeros
of $\xi'(s)$, its derivative, would then also satisfy a Riemann Hypothesis. We
investigate the pair correlation function of the zeros of $\xi'(s)$ under the
assumption that the Riemann Hypothesis is true. We then deduce consequences
about the size of gaps between these zeros and the proportion of these zeros
that are simple.
|
The puzzle of computer vision might find new challenging solutions when we
realize that most successful methods are working at image level, which is
remarkably more difficult than processing directly visual streams, just as
happens in nature. In this paper, we claim that their processing naturally
leads to formulate the motion invariance principle, which enables the
construction of a new theory of visual learning based on convolutional
features. The theory addresses a number of intriguing questions that arise in
natural vision, and offers a well-posed computational scheme for the discovery
of convolutional filters over the retina. They are driven by the Euler-Lagrange
differential equations derived from the principle of least cognitive action,
that parallels laws of mechanics. Unlike traditional convolutional networks,
which need massive supervision, the proposed theory offers a truly new scenario
in which feature learning takes place by unsupervised processing of video
signals. An experimental report of the theory is presented where we show that
features extracted under motion invariance yield an improvement that can be
assessed by measuring information-based indexes.
|
Measuring the energy loss and mass of highly ionizing particles predicted by
theories from beyond the Standard Model pose considerable challenges to
conventional detection techniques. Such particles are predicted to experience
energy loss to matter they pass through that exceeds the dynamic range
specified for most readout chips, leading to saturation of the detectors'
electronics. Consequently, achieving precise energy loss and mass measurements
becomes unattainable. We present a new approach to detect such highly ionizing
particles using time projection chambers that overcomes this limitation and
provide a case study for triggering on magnetic monopoles.
|
The asynchrony of the polar SDSS~J085414.02+390537.3 was revealed using the
data of ZTF photometric survey. The light curves show a beat period $P_{beat} =
24.6 \pm 0.1$~days. During this period the system changes its brightness by
$\sim 3^m$. The periodograms show power peaks at the white dwarf's rotation
period $P_{spin} = 113.197 \pm 0.001$~min and orbital period $P_{orb} = 113.560
\pm 0.001$~min with the corresponding polar asynchrony $1-P_{orb}/P_{spin} =
0.3\%$. The photometric behavior of the polar indicates a change of the main
accreting pole during the beat period. Based on the Zeeman splitting of the
H$\beta$ line, an estimate of the mean magnetic field strength of the white
dwarf is found to be $B = 28.5\pm 1.5$~MG. The magnetic field strength $B
\approx 34$~MG near the magnetic pole was found by modeling cyclotron spectra.
Doppler tomograms in the H$\beta$ line demonstrate the distribution of emission
sources typical for polars.
|
The nature of the dark components (dark matter and dark energy) that dominate
the current cosmic evolution is a completely open question at present. In
reality, we do not even know if they really constitute two separated
substances. In this paper we use the recent Cosmic All Sky Survey (CLASS)
lensing sample to test the predictions of one of the candidates for a unified
dark matter/energy scenario, the so-called generalized Chaplygin gas (Cg) which
is parametrized by an equation of state $p = -A/\rho_{Cg}^{\alpha}$ where $A$
and $\alpha$ are arbitrary constants. We show that, although the model is in
good agreement with this radio source gravitational lensing sample, the limits
obtained from CLASS statistics are only marginally compatible with the ones
obtained from other cosmological tests. We also investigate the constraints on
the free parameters of the model from a joint analysis between CLASS and
supernova data.
|
Atomically thin layered two-dimensional materials, including transition-metal
dichacolgenide (TMDC) and black phosphorus (BP), (1) have been receiving much
attention, because of their promising physical properties and potential
applications in flexible and transparent electronic devices . Here, for the
first time we show non-volatile chargetrap memory devices, based on
field-effect transistors with large hysteresis, consisting of a few-layer black
phosphorus channel and a three dimensional (3D) Al2O3 /HfO2 /Al2O3 charge-trap
gate stack. An unprecedented memory window exceeding 12 V is observed, due to
the extraordinary trapping ability of HfO2. The device shows a high endurance
and a stable retention of ?25% charge loss after 10 years, even drastically
lower than reported MoS2 flash memory. The high program/erase current ratio,
large memory window, stable retention and high on/off current ratio, provide a
promising route towards the flexible and transparent memory devices utilising
atomically thin two-dimensional materials. The combination of 2D materials with
traditional high-k charge-trap gate stacks opens up an exciting field of
nonvolatile memory devices.
|
The ordering between Wigner--Yanase--Dyson function and logarithmic mean is
known. Also bounds for logarithmic mean are known. In this paper, we give two
reverse inequalities for Wigner--Yanase--Dyson function and logarithmic mean.
We also compare the obtained results with the known bounds of the logarithmic
mean. Finally, we give operator inequalities based on the obtained results.
|
We have developed a model for pulsar polarization by taking into account of
viewing geometry, rotation and modulation of the emission region. By solving
for the plasma dynamics, we deduced the expressions for curvature radiation
electric field in time as well as frequency domains. We show that both the
'antisymmetric' and 'symmetric' types of circular polarization are possible due
to the combined effect of aberration, viewing geometry and modulation. We argue
that aberration combined with modulation can introduce 'kinky' pattern into the
PPA traverses.
|
The method used by senior geodetic engineer Jean-Georges Affholder to
determine what can be termed as the 'centre of gravity' of physical Europe in
1989 and 2004 relies on mathematical formulae which, in their only published
version, happen to be flawed with typographical errors that do not reflect Mr.
Affholder's actual mathematical exactness. This short epistemological paper
summarizes the major steps of Affholder's method, provides a corrected version
of the general formulae, and briefly recalls some particulars of the specific
determination of the centre of gravity of physical Europe.
|
Systematic analysis of available data for $\omega$-meson photoproduction is
given in frame of Regge theory. At photon energies above 20 GeV the
$\gamma{+}p{\to}\omega{+}p$ reaction is entirely dominated by Pomeron exchange.
However, it was found that Pomeron exchange model can not reproduce the
$\gamma{+}p{\to}\rho{+}p$ and $\gamma{+}p{\to}\omega{+}p$ data at high energies
simultaneously with the same set of parameters. The comparison between $\rho$
and $\omega$ data indicates a large room for meson exchange contribution to
$\omega$-meson photoproduction at low energies. It was found that at low
energies the dominant contribution comes from $\pi$ and $f_2$-meson exchanges.
There is smooth transition between the meson exchange model at low energies and
Regge theory at high energies.
|
We survey recent developments in the Birational Anabelian Geometry program
aimed at the reconstruction of function fields of algebraic varieties over
algebraically closed fields from pieces of their absolute Galois groups.
|
Facial expressions, vital in non-verbal human communication, have found
applications in various computer vision fields like virtual reality, gaming,
and emotional AI assistants. Despite advancements, many facial expression
generation models encounter challenges such as low resolution (e.g., 32x32 or
64x64 pixels), poor quality, and the absence of background details. In this
paper, we introduce FacEnhance, a novel diffusion-based approach addressing
constraints in existing low-resolution facial expression generation models.
FacEnhance enhances low-resolution facial expression videos (64x64 pixels) to
higher resolutions (192x192 pixels), incorporating background details and
improving overall quality. Leveraging conditional denoising within a diffusion
framework, guided by a background-free low-resolution video and a single
neutral expression high-resolution image, FacEnhance generates a video
incorporating the facial expression from the low-resolution video performed by
the individual with background from the neutral image. By complementing
lightweight low-resolution models, FacEnhance strikes a balance between
computational efficiency and desirable image resolution and quality. Extensive
experiments on the MUG facial expression database demonstrate the efficacy of
FacEnhance in enhancing low-resolution model outputs to state-of-the-art
quality while preserving content and identity consistency. FacEnhance
represents significant progress towards resource-efficient, high-fidelity
facial expression generation, Renewing outdated low-resolution methods to
up-to-date standards.
|
The weak tensor product was introduced by Snevily as a way to construct new
graphs that admit $\alpha$-labelings from a pair of known $\alpha$-graphs. In
this article, we show that this product and the application to
$\alpha$-labelings can be generalized by considering as a second factor of the
product, a family $\Gamma$ of bipartite $(p,q)$-graphs, $p$ and $q$ fixed. The
only additional restriction that we should consider is that for every $F\in
\Gamma$, there exists and $\alpha$-labeling $f_F$ with $f_F(V(F))=L\cup H$,
where $L,H \subset [0,q]$ are the stable sets induced by the characteristic of
$f_F$ and they do not depend on $F$. We also obtain analogous applications to
near $\alpha$-labelings and bigraceful labelings.
|
The stability of $q$-Gaussian distributions as particular solutions of the
linear diffusion equation and its generalized nonlinear form,
$\pderiv{P(x,t)}{t} = D \pderiv{^2 [P(x,t)]^{2-q}}{x^2}$, the
\emph{porous-medium equation}, is investigated through both numerical and
analytical approaches. It is shown that an \emph{initial} $q$-Gaussian,
characterized by an index $q_i$, approaches the \emph{final}, asymptotic
solution, characterized by an index $q$, in such a way that the relaxation rule
for the kurtosis evolves in time according to a $q$-exponential, with a
\emph{relaxation} index $q_{\rm rel} \equiv q_{\rm rel}(q)$. In some cases,
particularly when one attempts to transform an infinite-variance distribution
($q_i \ge 5/3$) into a finite-variance one ($q<5/3$), the relaxation towards
the asymptotic solution may occur very slowly in time. This fact might shed
some light on the slow relaxation, for some long-range-interacting many-body
Hamiltonian systems, from long-standing quasi-stationary states to the ultimate
thermal equilibrium state.
|
We answer a 15-year-old open question about the exact upper bound for
bivariate copulas with a given diagonal section by giving an explicit formula
for this bound. As an application, we determine the maximal asymmetry of
bivariate copulas with a given diagonal section and construct a copula that
attains it. We derive a formula for the maximal asymmetry that is simple enough
to be used by practitioners.
|
We introduce a new interacting particles model with blocking and pushing
interactions. Particles evolve on the positive line jumping on their own
volition rightwards or leftwards according to geometric jumps with parameter q.
We show that the model involves a Pieri-type formula for the orthogonal group.
We prove that the two extreme cases - q=0 and q=1 - lead respectively to a
random tiling model studied by Borodin and Kuan and to a random matrix model.
|
An ultrarelativistic electron beam passing through an intense laser pulse
emits radiation around its direction of propagation into a characteristic
angular profile. Here we show that measurement of the variances of this profile
in the planes parallel and perpendicular to the laser polarization, and the
mean initial and final energies of the electron beam, allows the intensity of
the laser pulse to be inferred in way that is independent of the model of the
electron dynamics. The method presented applies whether radiation reaction is
important or not, and whether it is classical or quantum in nature, with
accuracy of a few per cent across three orders of magnitude in intensity. It is
tolerant of electron beams with broad energy spread and finite divergence. In
laser-electron beam collision experiments, where spatiotemporal fluctuations
cause alignment of the beams to vary from shot to shot, this permits inference
of the laser intensity at the collision point, thereby facilitating comparisons
between theoretical calculations and experimental data.
|
Recently, Freyhult, Rej and Staudacher (FRS) proposed an integral equation
determining the leading logarithmic term of the anomalous dimension of sl(2)
twist-operators in N=4 SYM for large Lorentz spin M and twist L at fixed j =
L/log(M). We discuss the large j limit of the FRS equation. This limit can be
matched with the {\em fast long string} limit of AdS_5 X S^5 superstring
perturbation theory at all couplings. In particular, a certain part of the
classical and one-loop string result is known to be protected and can be
computed in the weakly coupled large-j limit of the FRS equation. We present
various analytical and numerical results supporting agreement at one and two
loops in the gauge theory.
|
In this paper we consider the following question: For bounded domains with
smooth boundary, can strong pseudoconvexity be characterized in terms of the
intrinsic complex geometry of the domain? Our approach to answering this
question is based on understanding the dynamical behavior of real geodesics in
the Kobayashi metric and allows us to prove a number of results for domains
with low regularity. For instance, we show that for convex domains with
$C^{2,\epsilon}$ boundary strong pseudoconvexity can be characterized in terms
of the behavior of the squeezing function near the boundary, the behavior of
the holomorphic sectional curvature of the Bergman metric near the boundary, or
any other reasonable measure of the complex geometry near the boundary. The
first characterization gives a partial answer to a question of Forn{\ae}ss and
Wold. As an application of these characterizations, we show that a convex
domain with $C^{2,\epsilon}$ boundary which is biholomorphic to a strongly
pseudoconvex domain is also strongly pseudoconvex.
|
Two-dimensional (2D) palladium ditelluride (PdTe2) and platinum ditelluride
(PtTe2) are two Dirac semimetals which demonstrate fascinating quantum
properties such as superconductivity, magnetism and topological order,
illustrating promising applications in future nanoelectronics and
optoelectronics. However, the synthesis of their monolayers is dramatically
hindered by strong interlayer coupling and orbital hybridization. In this
study, an efficient synthesis method for monolayer PdTe2 and PtTe2 is
demonstrated. Taking advantages of the surface reaction, epitaxial growth of
large-area and high quality monolayers of PdTe2 and patterned PtTe2 is achieved
by direct tellurization of Pd(111) and Pt(111). A well-ordered PtTe2 pattern
with Kagome lattice formed by Te vacancy arrays is successfully grown.
Moreover, multilayer PtTe2 can be also obtained and potential excitation of
Dirac plasmons is observed. The simple and reliable growth procedure of
monolayer PdTe2 and patterned PtTe2 gives unprecedented opportunities for
investigating new quantum phenomena and facilitating practical applications in
optoelectronics.
|
Determining semantic textual similarity is a core research subject in natural
language processing. Since vector-based models for sentence representation
often use shallow information, capturing accurate semantics is difficult. By
contrast, logical semantic representations capture deeper levels of sentence
semantics, but their symbolic nature does not offer graded notions of textual
similarity. We propose a method for determining semantic textual similarity by
combining shallow features with features extracted from natural deduction
proofs of bidirectional entailment relations between sentence pairs. For the
natural deduction proofs, we use ccg2lambda, a higher-order automatic inference
system, which converts Combinatory Categorial Grammar (CCG) derivation trees
into semantic representations and conducts natural deduction proofs.
Experiments show that our system was able to outperform other logic-based
systems and that features derived from the proofs are effective for learning
textual similarity.
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A sunflower is a collection of sets $\{U_1,\ldots, U_n\}$ such that the
pairwise intersection $U_i\cap U_j$ is the same for all choices of distinct $i$
and $j$. We study sunflowers of convex open sets in $\mathbb R^d$, and provide
a Helly-type theorem describing a certain "rigidity" that they possess. In
particular we show that if $\{U_1,\ldots, U_{d+1}\}$ is a sunflower in $\mathbb
R^d$, then any hyperplane that intersects all $U_i$ must also intersect
$\bigcap_{i=1}^{d+1} U_i$. We use our results to describe a combinatorial code
$\mathcal C_n$ for all $n\ge 2$ which is on the one hand minimally non-convex,
and on the other hand has no local obstructions. Along the way we further
develop the theory of morphisms of codes, and establish results on the covering
relation in the poset $\mathbf P_{\mathbf{Code}}$.
|
This paper gives similarity transformations for laminar film condensation on
a vertical flat plate with variable temperature distribution and finds
analytical solutions for arbitrary Prandtl numbers and condensation rates. The
work contrasts with Sparrow and Gregg assertion that wall temperature variation
does not permit similarity solutions. To resolve the long-standing debatable
issue regarding heat transfer in the non-isothermal case, some useful
formulations are obtained, including a significant dependence of varying
Prandtl numbers. Results are compared with the available experimental data.
|
During sudden onset crisis events, the presence of spam, rumors and fake
content on Twitter reduces the value of information contained on its messages
(or "tweets"). A possible solution to this problem is to use machine learning
to automatically evaluate the credibility of a tweet, i.e. whether a person
would deem the tweet believable or trustworthy. This has been often framed and
studied as a supervised classification problem in an off-line (post-hoc)
setting. In this paper, we present a semi-supervised ranking model for scoring
tweets according to their credibility. This model is used in TweetCred, a
real-time system that assigns a credibility score to tweets in a user's
timeline. TweetCred, available as a browser plug-in, was installed and used by
1,127 Twitter users within a span of three months. During this period, the
credibility score for about 5.4 million tweets was computed, allowing us to
evaluate TweetCred in terms of response time, effectiveness and usability. To
the best of our knowledge, this is the first research work to develop a
real-time system for credibility on Twitter, and to evaluate it on a user base
of this size.
|
The study of quantum heat transport in superconducting circuits is
significant for further understanding the connection between quantum mechanics
and thermodynamics, and for possible applications for quantum information. The
first experimental realisations of devices demonstrating photonic heat
transport mediated by a qubit have already been designed and measured.
Motivated by the analysis of such experimental results, and for future
experimental designs, we numerically evaluate the photonic heat transport of
qubit-resonator devices in the linear circuit regime through electromagnetic
simulations using Sonnet software, and compare with microwave circuit theory.
We show that the method is a powerful tool to calculate heat transport and
predict unwanted parasitic resonances and background.
|
I compute exact partition function zeros of the Wako-Saito-Mu\~noz-Eaton
model for various secondary structural elements and for two proteins, 1BBL and
1I6C, using both analytic and numerical methods. Two-state and barrierless
downhill folding transitions can be distinguished by a gap in the distribution
of zeros at the positive real axis.
|
We calculate the fidelity with which an arbitrary state can be encoded into a
[7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator
error environment with the goal of determining whether this encoding can be
used for practical implementations of quantum computation. This determination
is accomplished by applying ideal error correction to the encoded state which
demonstrates the correctability of errors that occurred during the encoding
process. We then apply single-qubit Clifford gates to the encoded state and
determine the accuracy with which these gates can be applied. Finally, fault
tolerant noisy error correction is applied to the encoded states in the
non-equiprobable Pauli operator error environment allowing us to compare noisy
(realistic) and perfect error correction implementations. We note that this
maintains the fidelity of the encoded state for certain error-probability
values. These results have implications for when non-fault tolerant procedures
may be used in practical quantum computation and whether quantum error
correction should be applied at every step in a quantum protocol.
|
Rank-revealing matrix decompositions provide an essential tool in spectral
analysis of matrices, including the Singular Value Decomposition (SVD) and
related low-rank approximation techniques. QR with Column Pivoting (QRCP) is
usually suitable for these purposes, but it can be much slower than the
unpivoted QR algorithm. For large matrices, the difference in performance is
due to increased communication between the processor and slow memory, which
QRCP needs in order to choose pivots during decomposition. Our main algorithm,
Randomized QR with Column Pivoting (RQRCP), uses randomized projection to make
pivot decisions from a much smaller sample matrix, which we can construct to
reside in a faster level of memory than the original matrix. This technique may
be understood as trading vastly reduced communication for a controlled increase
in uncertainty during the decision process. For rank-revealing purposes, the
selection mechanism in RQRCP produces results that are the same quality as the
standard algorithm, but with performance near that of unpivoted QR (often an
order of magnitude faster for large matrices). We also propose two formulas
that facilitate further performance improvements. The first efficiently updates
sample matrices to avoid computing new randomized projections. The second
avoids large trailing updates during the decomposition in truncated low-rank
approximations. Our truncated version of RQRCP also provides a key initial step
in our truncated SVD approximation, TUXV. These advances open up a new
performance domain for large matrix factorizations that will support efficient
problem-solving techniques for challenging applications in science,
engineering, and data analysis.
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In this paper, we consider the wave equation with both a viscous Kelvin-Voigt
and frictional damping as a model of viscoelasticity in which we incorporate an
internal control with a moving support. We prove the null controllability when
the control region, driven by the flow of an ODE, covers all the domain. The
proof is based upon the interpretation of the system as, roughly, the coupling
of a heat equation with an ordinary differential equation (ODE). The presence
of the ODE for which there is no propagation along the space variable makes the
controllability of the system impossible when the control is confined into a
subset in space that does not move. %Accordingly, we consider the control on a
moving support that, along the time interval, covers the whole domain. The null
controllability of the system with a moving control is established in using the
observability of the adjoint system and some Carleman estimates for a coupled
system of a parabolic equation and an ODE with the same singular weight,
adapted to the geometry of the moving support of the control. This extends to
the multi-dimensional case the results by P. Martin et al. on the
one-dimensional case, employing 1-d Fourier analysis techniques.
|
In this paper, we introduce and study the concept of CS-Rickart modules, that
is a module analogue of the concept of ACS rings. A ring $R$ is called a right
weakly semihereditary ring if every its finitly generated right ideal is of the
form $P\oplus S,$ where $P_R$ is a projective module and $S_R$ is a singular
module. We describe the ring $R$ over which $\mathrm{Mat}_n (R)$ is a right ACS
ring for any $n \in \mathbb {N}$. We show that every finitely generated
projective right $R$-module will to be a CS-Rickart module, is precisely when
$R$ is a right weakly semihereditary ring. Also, we prove that if $R$ is a
right weakly semihereditary ring, then every finitely generated submodule of a
projective right $R$-module has the form $P_{1}\oplus \ldots\oplus P_{n}\oplus
S$, where every $P_{1}, \ldots, P_{n}$ is a projective module which is
isomorphic to a submodule of $R_{R}$, and $S_R$ is a singular module. As
corollaries we obtain some well-known properties of Rickart modules and
semihereditary rings.
|
Post-starburst galaxies are believed to be in a rapid transition between
major merger starbursts and quiescent ellipticals, where AGN feedback is
suggested as one of the processes responsible for the quenching. To study the
role of AGN feedback, we constructed a sample of post-starburst candidates with
AGN and indications of ionized outflows. We use MUSE/VLT observations to
resolve the properties of the stars and multi-phased gas in five of them. All
the galaxies show signatures of interaction/merger in their stellar or gas
properties, with some galaxies at an early stage of interaction with companions
at distances $\sim$50 kpc, suggesting that optical post-starburst signatures
may be present well before the final starburst and coalescence. We detect
narrow and broad kinematic components in multiple transitions in all the
galaxies. Our detailed analysis of their kinematics and morphology suggests
that, contrary to our expectation, the properties of the broad kinematic
components are inconsistent with AGN-driven winds in 3 out of 5 galaxies. The
two exceptions are also the only galaxies in which spatially-resolved NaID
P-Cygni profiles are detected. In some cases, the observations are more
consistent with interaction-induced galactic-scale flows, an often overlooked
process. These observations raise the question of how to interpret broad
kinematic components in interacting and perhaps also in active galaxies, in
particular when spatially-resolved observations are not available or cannot
rule out merger-induced galactic-scale motions. We suggest that NaID P-Cygni
profiles are more effective outflow tracers, and use them to estimate the
energy that is carried by the outflow.
|
Despite its simple crystal structure, layered boron nitride features a
surprisingly complex variety of phonon-assisted luminescence peaks. We present
a combined experimental and theoretical study on ultraviolet-light emission in
hexagonal and rhombohedral bulk boron nitride crystals. Emission spectra of
high-quality samples are measured via cathodoluminescence spectroscopy,
displaying characteristic differences between the two polytypes. These
differences are explained using a fully first-principles computational
technique that takes into account radiative emission from ``indirect'',
finite-momentum, excitons via coupling to finite-momentum phonons. We show that
the differences in peak positions, number of peaks and relative intensities can
be qualitatively and quantitatively explained, once a full integration over all
relevant momenta of excitons and phonons is performed.
|
As a result of a non-trivial mixing matrix, neutrinos cannot be
simultaneously in a flavor and mass eigenstate. We formulate and discuss
information entropic relations that quantify the associated quantum
uncertainty. We also formulate a protocol to determine the
Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and
measurements on an entangled lepton-neutrino pair. The entangled state features
neutrino oscillations in a conditional probability involving measurements on
the lepton and the neutrino. They can be switched off by choosing a specific
observable on the lepton side which is determined by the PMNS matrix. The
parameters of the latter, including the CP-violating phase $\delta$, can be
obtained by guessing them and improving the guess by minimizing the remaining
oscillations.
|
The aim of this paper is to study a conjecture predicting a lower bound on
the canonical height on abelian varieties, formulated by S. Lang and
generalized by J. H. Silverman. We give here an asymptotic result on the height
of Heegner points on the modular jacobian $J_{0}(N)$, and we derive non-trivial
remarks about the conjecture.
|
We investigate the star formation main sequence (MS) (SFR-M$_{\star}$) down
to 10$^{8-9}\mathrm{M}_\odot$ using a sample of 34,061 newly-discovered
ultra-faint ($27\lesssim i \lesssim 30$ mag) galaxies at $1<z<3$ detected in
the GOODS-N field. Virtually these galaxies are not contained in previous
public catalogs, effectively doubling the number of known sources in the field.
The sample was constructed by stacking the optical broad-band observations
taken by the HST/GOODS-CANDELS surveys as well as the 25 ultra-deep medium-band
images gathered by the GTC/SHARDS project. Our sources are faint (average
observed magnitudes $<i>\sim28.2$ mag, $<H>\sim27.9$ mag), blue (UV-slope
$<\beta>\sim-1.9$), star-forming (rest-frame colors $<U-V>\sim0.10$ mag,
$<V-J>\sim0.17$ mag) galaxies. These observational characteristics are
identified with young (mass-weighted age $<\mathrm{t_{M-w}}>\sim0.014$ Gyr)
stellar populations subject to low attenuations ($<\mathrm{A(V)}>\sim0.30$
mag). Our sample allows us to probe the MS down to $10^{8.0}\,\mathrm{M}_\odot$
at $z=1$ and $10^{8.5}\,\mathrm{M}_\odot$ at $z=3$, around 0.6 dex deeper than
previous analysis. In the low-mass galaxy regime, we find an average value for
the slope of 0.97 at $1<z<2$ and 1.12 at $2<z<3$. Nearly $\sim$60% of our
sample presents stellar masses in the range $10^{6-8}$ M$_\odot$ between
$1<z<3$. If the slope of the MS remained constant in this regime, the sources
populating the low-mass tail of our sample would qualify as starburst galaxies.
|
Spreadsheet manipulation is widely existing in most daily works and
significantly improves working efficiency. Large language model (LLM) has been
recently attempted for automatic spreadsheet manipulation but has not yet been
investigated in complicated and realistic tasks where reasoning challenges
exist (e.g., long horizon manipulation with multi-step reasoning and ambiguous
requirements). To bridge the gap with the real-world requirements, we introduce
$\textbf{SheetRM}$, a benchmark featuring long-horizon and multi-category tasks
with reasoning-dependent manipulation caused by real-life challenges. To
mitigate the above challenges, we further propose $\textbf{SheetAgent}$, a
novel autonomous agent that utilizes the power of LLMs. SheetAgent consists of
three collaborative modules: $\textit{Planner}$, $\textit{Informer}$, and
$\textit{Retriever}$, achieving both advanced reasoning and accurate
manipulation over spreadsheets without human interaction through iterative task
reasoning and reflection. Extensive experiments demonstrate that SheetAgent
delivers 20-30% pass rate improvements on multiple benchmarks over baselines,
achieving enhanced precision in spreadsheet manipulation and demonstrating
superior table reasoning abilities. More details and visualizations are
available at https://sheetagent.github.io.
|
In monolayers of transition metal dichalcogenides the nonlocal nature of the
effective dielectric screening leads to large binding energies of excitons.
Additional lateral confinement gives rise to exciton localization in quantum
dots. By assuming parabolic confinement for both the electron and the hole, we
derive model wave functions for the relative and the center-of-mass motions of
electron-hole pairs, and investigate theoretically resonant energy transfer
among excitons localized in two neighboring quantum dots. We quantify the
probability of energy transfer for a direct-gap transition by assuming that the
interaction between two quantum dots is described by a Coulomb potential, which
allows us to include all relevant multipole terms of the interaction. We
demonstrate the structural control of the valley-selective energy transfer
between quantum dots.
|
A matroid $N$ is said to be triangle-rounded in a class of matroids
$\mathcal{M}$ if each $3$-connected matroid $M\in \mathcal{M}$ with a triangle
$T$ and an $N$-minor has an $N$-minor with $T$ as triangle. Reid gave a result
useful to identify such matroids as stated next: suppose that $M$ is a binary
$3$-connected matroid with a $3$-connected minor $N$, $T$ is a triangle of $M$
and $e\in T\cap E(N)$; then $M$ has a $3$-connected minor $M'$ with an
$N$-minor such that $T$ is a triangle of $M'$ and $|E(M')|\le |E(N)|+2$. We
strengthen this result by dropping the condition that such element $e$ exists
and proving that there is a $3$-connected minor $M'$ of $M$ with an $N$-minor
$N'$ such that $T$ is a triangle of $M'$ and $E(M')-E(N')\subseteq T$. This
result is extended to the non-binary case and, as an application, we prove that
$M(K_5)$ is triangle-rounded in the class of the regular matroids.
|
As brain-computer interfacing (BCI) systems transition from assistive
technology to more diverse applications, their speed, reliability, and user
experience become increasingly important. Dynamic stopping methods enhance BCI
system speed by deciding at any moment whether to output a result or wait for
more information. Such approach leverages trial variance, allowing good trials
to be detected earlier, thereby speeding up the process without significantly
compromising accuracy. Existing dynamic stopping algorithms typically optimize
measures such as symbols per minute (SPM) and information transfer rate (ITR).
However, these metrics may not accurately reflect system performance for
specific applications or user types. Moreover, many methods depend on arbitrary
thresholds or parameters that require extensive training data. We propose a
model-based approach that takes advantage of the analytical knowledge that we
have about the underlying classification model. By using a risk minimisation
approach, our model allows precise control over the types of errors and the
balance between precision and speed. This adaptability makes it ideal for
customizing BCI systems to meet the diverse needs of various applications. We
validate our proposed method on a publicly available dataset, comparing it with
established static and dynamic stopping methods. Our results demonstrate that
our approach offers a broad range of accuracy-speed trade-offs and achieves
higher precision than baseline stopping methods.
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Tidal disruption event (TDE) can launch an ultrafast outflow. If the black
hole is surrounded by large amounts of clouds, outflow-cloud interaction will
generate bow shocks, accelerate electrons and produce radio emission. Here we
investigate the interaction between a non-relativistic outflow and clouds in
active galaxies, which is manifested as outflow-BLR (broad line region)
interaction, and can be extended to outflow-torus interaction. This process can
generate considerable radio emission, which may account for the radio flares
appearing a few months later after TDE outbursts. Benefitting from efficient
energy conversion from outflow to shocks and the strong magnetic field,
outflow-cloud interaction may play a non-negligible, or even dominating role in
generating radio flares in a cloudy circumnuclear environment if the CNM
density is no more than 100 times the Sgr A*-like one. In this case, the
evolution of radio spectra can be used to directly constrain the properties of
outflows.
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Generalised matrix-matrix multiplication forms the kernel of many
mathematical algorithms. A faster matrix-matrix multiply immediately benefits
these algorithms. In this paper we implement efficient matrix multiplication
for large matrices using the floating point Intel Pentium SIMD (Single
Instruction Multiple Data) architecture. A description of the issues and our
solution is presented, paying attention to all levels of the memory hierarchy.
Our results demonstrate an average performance of 2.09 times faster than the
leading public domain matrix-matrix multiply routines.
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This paper provides an E-theoretic proof of an exact form, due to E.
Troitsky, of the Mischenko-Fomenko Index Theorem for elliptic
pseudodifferential operators over a unital C*-algebra. The main ingredients in
the proof are the use of asymptotic morphisms of Connes and Higson, vector
bundle modification, a Baum-Douglas-type group, and a KK-argument of Kasparov.
|
Exploring abundance and non lacunarity of hyperbolic times for endomorphisms
preserving an ergodic probability with positive Lyapunov exponents, we obtain
that there are periodic points of period growing sublinearly with respect to
the lenght of almost every dynamical ball. In particular, we conclude that any
ergodic measure with positive Lyapunov exponents satisfy the nonuniform
specification property.
As consequences, we (re)-obtain estimates on the recurrence to a ball in
terms of the Lyapunov exponents and we prove that any expanding measure is
limit of Dirac measures on periodic points.
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We study the effect of the MeV-scale asymmetric dark matter annihilation on
the effective number of neutrinos $N_{\rm eff}$ at the epoch of the big bang
nucleosynthesis. If the asymmetric dark matter $\chi$ couples more strongly to
the neutrinos $\nu$ than to the photons $\gamma$ and electrons $e^-$,
$\Gamma_{\chi\gamma, \chi e} \ll \Gamma_{\chi\nu}$, or $\Gamma_{\chi\gamma,
\chi e} \gg \Gamma_{\chi\nu}$, the lower mass limit on the asymmetric dark
matter is about $18$ MeV for $N_{\rm eff}\simeq 3.0$.
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Synchronization over networks depends strongly on the structure of the
coupling between the oscillators. When the coupling presents certain
regularities, the dynamics can be coarse-grained into clusters by means of
External Equitable Partitions of the network graph and their associated
quotient graphs. We exploit this graph-theoretical concept to study the
phenomenon of cluster synchronization, in which different groups of nodes
converge to distinct behaviors. We derive conditions and properties of networks
in which such clustered behavior emerges, and show that the ensuing dynamics is
the result of the localization of the eigenvectors of the associated graph
Laplacians linked to the existence of invariant subspaces. The framework is
applied to both linear and non-linear models, first for the standard case of
networks with positive edges, before being generalized to the case of signed
networks with both positive and negative interactions. We illustrate our
results with examples of both signed and unsigned graphs for consensus dynamics
and for partial synchronization of oscillator networks under the master
stability function as well as Kuramoto oscillators.
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Owing to their periodic and intricate configurations, metamaterials
engineered for acoustic and elastic wave control inevitably suffer from
manufacturing anomalies and deviate from theoretical dispersion predictions.
This work exploits the Polynomial Chaos theory to quantify the magnitude and
extent of these deviations and assess their impact on the desired behavior. It
is shown that uncertainties stemming from surface roughness, tolerances, and
other inconsistencies in a metamaterial's unit cell parameters alter the
targetted band gap width, location and the confidence level with which it is
guaranteed. The effect of uncertainties are projected from a Bloch-wave
dispersion analysis of three distinct phononic and resonant cellular
configurations and are further confirmed in the frequency response the finite
structures. The analysis concludes with a unique algorithm intended to guide
the design of metamaterials in the presence of system uncertainties.
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A knot in a solid torus defines a map on the set of (smooth or topological)
concordance classes of knots in $S^3$. This set admits a group structure, but a
conjecture of Hedden suggests that satellite maps never induce interesting
homomorphisms: we give new evidence for this conjecture in both categories.
First, we use Casson-Gordon signatures to give the first obstruction to a slice
pattern inducing a homomorphism on the topological concordance group,
constructing examples with every winding number besides $\pm 1$. We then
provide subtle examples of satellite maps which map arbitrarily deep into the
$n$-solvable filtration of [COT03], act like homomorphisms on arbitrary finite
sets of knots, and yet which still do not induce homomorphisms. Finally, we
verify Hedden's conjecture in the smooth category for all but one small
crossing number satellite operator.
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In this short note, we come back to the recent proposal put forward by
Kharzeev and Levin [PRL 114 (2015) 24, 242001], in which they
phenomenologically couple the non-perturbative Veneziano ghost to the
perturbative gluon, leading to a modified gluon propagator (the "glost") of the
Gribov type, with complex poles. As such, a possible link was made between the
QCD topological \theta-vacuum (Veneziano ghost) and color confinement (no
physically observable gluons). We discuss some subtleties concerning gauge
(BRST) invariance of this proposal, related to the choice of Feynman gauge. We
furthermore provide an example in the Landau gauge of a similar
phenomenological vertex that also describes the necessary Veneziano ghost but
does not affect the Landau gauge gluon propagator.
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We show that a quantum dot connected via tunnel barriers to superconducting
leads traps a continuously tunable and hence fractional charge. The fractional
charge on the island is due to particle-hole symmetry breaking and can be tuned
via a gate potential acting on the dot or via changes in the phase difference
across the island. We determine the groundstate, equilibrium, and excitation
charges and show how to identify these quantities in an experiment.
|
We present a systematic study of ad blocking - and the associated "arms race"
- as a security problem. We model ad blocking as a state space with four states
and six state transitions, which correspond to techniques that can be deployed
by either publishers or ad blockers. We argue that this is a complete model of
the system. We propose several new ad blocking techniques, including ones that
borrow ideas from rootkits to prevent detection by anti-ad blocking scripts.
Another technique uses the insight that ads must be recognizable by humans to
comply with laws and industry self-regulation. We have built prototype
implementations of three of these techniques, successfully blocking ads and
evading detection. We systematically evaluate our proposed techniques, along
with existing ones, in terms of security, practicality, and legality. We
characterize the order of growth of the development effort required to
create/maintain ad blockers as a function of the growth of the web. Based on
our state-space model, our new techniques, and this systematization, we offer
insights into the likely "end game" of the arms race. We challenge the
widespread assumption that the arms race will escalate indefinitely, and
instead identify a combination of evolving technical and legal factors that
will determine the outcome.
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As machine learning models become more accurate, they typically become more
complex and uninterpretable by humans. The black-box character of these models
holds back its acceptance in practice, especially in high-risk domains where
the consequences of failure could be catastrophic such as health-care or
defense. Providing understandable and useful explanations behind ML models or
predictions can increase the trust of the user. Example-based reasoning, which
entails leveraging previous experience with analogous tasks to make a decision,
is a well known strategy for problem solving and justification. This work
presents a new explanation extraction method called LEAFAGE, for a prediction
made by any black-box ML model. The explanation consists of the visualization
of similar examples from the training set and the importance of each feature.
Moreover, these explanations are contrastive which aims to take the
expectations of the user into account. LEAFAGE is evaluated in terms of
fidelity to the underlying black-box model and usefulness to the user. The
results showed that LEAFAGE performs overall better than the current
state-of-the-art method LIME in terms of fidelity, on ML models with non-linear
decision boundary. A user-study was conducted which focused on revealing the
differences between example-based and feature importance-based explanations. It
showed that example-based explanations performed significantly better than
feature importance-based explanation, in terms of perceived transparency,
information sufficiency, competence and confidence. Counter-intuitively, when
the gained knowledge of the participants was tested, it showed that they
learned less about the black-box model after seeing a feature importance-based
explanation than seeing no explanation at all. The participants found feature
importance-based explanation vague and hard to generalize it to other
instances.
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Possible manipulation of user transactions by miners in a permissionless
blockchain systems is a growing concern. This problem is a pervasive and
systemic issue, known as Miner Extractable Value (MEV), incurs highs costs on
users of decentralised applications. Furthermore, transaction manipulations
create other issues in blockchain systems such as congestion, higher fees, and
system instability. Detecting transaction manipulations is difficult, even
though it is known that they originate from the pre-consensus phase of
transaction selection for a block building, at the base layer of blockchain
protocols. In this paper we summarize known transaction manipulation attacks.
We then present L{\O}, an accountable base layer protocol specifically designed
to detect and mitigate transaction manipulations. L{\O} is built around
accurate detection of transaction manipulations and assignment of blame at the
granularity of a single mining node. L{\O} forces miners to log all the
transactions they receive into a secure mempool data structure and to process
them in a verifiable manner. Overall, L{\O} quickly and efficiently detects
reordering, injection or censorship attempts. Our performance evaluation shows
that L{\O} is also practical and only introduces a marginal performance
overhead.
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The photometric analysis of sample Am stars is carried out to determine the
stellar characteristics and to constrain the stellar dynamics. The
spectroscopic analysis of the studied Am stars confirms their general
characteristics of Am stars. The available data on elemental abundances for HD
113878 and HD 118660 have shown different characteristics during different
epochs of observations. The basic stellar parameters (mass, luminosity, radius,
life time, distance, proper-motion, etc.) are also determined to identify the
stellar habitat zones for earth like exoplanet. Such information is important
to identify suitable planets for human settlement in the near future. In this
connection, the tidal radius and boundaries of the habitable zone of each star
have been computed to support the search of an extra-terrestrial life around
them. Asteroseismic mass scale test shows greater stellar masses comparable to
the solar mass.
|
Using the Coulomb gauge formulation of QED we present a lattice QCD procedure
to calculate the $\pi^+\pi^+$ scattering phase shift including the effects of
the Coulomb potential which appears in this formulation. The approach described
here incorporates the effects of relativity and avoids finite-volume
corrections that vanish as a power of the volume in which the lattice
calculation is performed. This is the first step in developing a complete
lattice QCD calculation of the electromagnetic and isospin-breaking light-quark
mass contributions to $\varepsilon'$, the parameter describing direct CP
violating effects in $K_L\to\pi\pi$ decay.
|
In the framework of wave packet analysis, finite wavelet systems are
particular classes of finite wave packet systems. In this paper, using a
scaling matrix on a permuted version of the discrete Fourier transform (DFT) of
system generator, we derive a locally-scaled version of the DFT of system
genarator and obtain a finite equal-norm Parseval wavelet frame over prime
fields. We also give a characterization of all multiplicative subgroups of the
cyclic multiplicative group, for which the associated wavelet systems form
frames. Finally, we present some concrete examples as applications of our
results.
|
This paper reports the results of a series of field experiments designed to
investigate how peer effects operate in a real work setting. Workers were hired
from an online labor market to perform an image-labeling task and, in some
cases, to evaluate the work product of other workers. These evaluations had
financial consequences for both the evaluating worker and the evaluated worker.
The experiments showed that on average, evaluating high-output work raised an
evaluator's subsequent productivity, with larger effects for evaluators that
are themselves highly productive. The content of the subject evaluations
themselves suggest one mechanism for peer effects: workers readily punished
other workers whose work product exhibited low output/effort. However,
non-compliance with employer expectations did not, by itself, trigger
punishment: workers would not punish non-complying workers so long as the
evaluated worker still exhibited high effort. A worker's willingness to punish
was strongly correlated with their own productivity, yet this relationship was
not the result of innate differences---productivity-reducing manipulations also
resulted in reduced punishment. Peer effects proved hard to stamp out: although
most workers complied with clearly communicated maximum expectations for
output, some workers still raised their production beyond the output ceiling
after evaluating highly productive yet non-complying work products.
|
The puzzling properties of quantum mechanics, wave-particle duality,
entanglement and superposition, were dissected experimentally at past decades.
However, hidden-variable (HV) models, based on three classical assumptions of
wave-particle objectivity, determinism and independence, strive to explain or
even defeat them. The development of quantum technologies enabled us to test
experimentally the predictions of quantum mechanics and HV theories. Here, we
report an experimental demonstration of an entanglement-assisted quantum
delayed-choice scheme using a liquid nuclear magnetic resonance quantum
information processor. This scheme we realized is based on the recently
proposed scheme [Nat. Comms. 5:4997(2014)], which gave different results for
quantum mechanics and HV theories. In our experiments, the intensities and the
visibilities of the interference are in consistent the theoretical prediction
of quantum mechanics. The results imply that a contradiction is appearing when
all three assumptions of HV models are combined, though any two of the above
assumptions are compatible with it.
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We introduce a Kazhdan--Lusztig-dual quantum group for (1,p) Virasoro
logarithmic minimal models as the Lusztig limit of the quantum sl(2) at pth
root of unity and show that this limit is a Hopf algebra. We calculate tensor
products of irreducible and projective representations of the quantum group and
show that these tensor products coincide with the fusion of irreducible and
logarithmic modules in the (1,p) Virasoro logarithmic minimal models.
|
Given a Finsler manifold $(M,F)$, it is proved that the first eigenvalue of
the Finslerian $p$-Laplacian is bounded above by a constant depending on $\ p$,
the dimension of $M$, the Busemann-Hausdorff volume and the reversibility
constant of $(M,F)$.
For a Randers manifold $(M,F:=\sqrt{g}+\beta)$, where $g$ is a Riemannian
metric on $M$ and $\beta$ an appropriate $1$-form on $M$, it is shown that the
first eigenvalue $\lambda_{1,p}(M,F)$ of the Finslerian $p$-Laplacian defined
by the Finsler metric $F$ is controled by the first eigenvalue
$\lambda_{1,p}(M,g)$ of the Riemannian $p$-Laplacian defined on $(M,g)$.
Finally, the Cheeger's inequality for Finsler Laplacian is extended for
$p$-Laplacian, with $p > 1$.
|
We formulate a light-front spectator model for the proton incorporating the
gluonic degree of freedom. In this model, at high energy scattering of the
proton, the active parton is a gluon and the rest is viewed as a
spin-$\frac{1}{2}$ spectator with an effective mass. The light front wave
functions of the proton are constructed using a soft wall AdS/QCD prediction
and parameterized by fitting the unpolarized gluon distribution function to the
NNPDF3.0nlo data set. We investigate the helicity distribution of gluon in this
model. We find that our prediction for the gluon helicity asymmetry agrees well
with existing experimental data and satisfies the perturbative QCD constraints
at small and large longitudinal momentum regions. We also present the
transverse momentum dependent distributions (TMDs) for gluon in this model. We
further show that the model-independent Mulders-Rodrigues inequalities are
obeyed by the TMDs computed in our model.
|
We give an explicit evaluation, in terms of products of Jacobsthal numbers,
of the Hankel determinants of order a power of two for the period-doubling
sequence. We also explicitly give the eigenvalues and eigenvectors of the
corresponding Hankel matrices. Similar considerations give the Hankel
determinants for other orders.
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Laplace's equation appears frequently in physical applications involving
conservable quantities. Among these applications, miniaturized devices have
been of interest, in particular those using interdigitated arrays. Therefore,
we solved the two-dimensional Laplace's equation for a shallow or finite domain
consisting of interdigitated boundaries. We achieved this by using Jacobian
elliptic functions to conformally transform the interdigitated domain into a
parallel plates domain. The obtained expressions for potential distribution,
flux density and flux allow for arbitrary domain height, different band widths
and asymmetric potentials at the interdigitated array, besides considering
fringing effects at both ends of the array. All these expressions depend only
on relative dimensions, instead of absolute ones. With these results we showed
that the behavior in shallow or finite domains approaches that of a
semi-infinite domain, when its height is greater than the separation between
the centers of consecutive bands. We also found that, for any desired but fixed
flux, bands of equal width minimize the total surface of the interdigitated
array. Finally, we present approximate expressions for the flux, based on
elementary functions, which can be applied to ease the calculation of currents
(faradaic or non-faradaic), capacitances and resistances among other possible
applications.
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Using uniform global Carleman estimates for discrete elliptic and
semi-discrete hyperbolic equations, we study Lipschitz and logarithmic
stability for the inverse problem of recovering a potential in a semi-discrete
wave equation, discretized by finite differences in a 2-d uniform mesh, from
boundary or internal measurements. The discrete stability results, when
compared with their continuous counterparts, include new terms depending on the
discretization parameter h. From these stability results, we design a numerical
method to compute convergent approximations of the continuous potential.
|
We investigate the role of Segal's Gamma-spaces in the context of classical
and quantum information, based on categories of finite probabilities with
stochastic maps and density matrices with quantum channels. The information
loss functional extends to the setting of probabilistic Gamma-spaces considered
here. The Segal construction of connective spectra from Gamma-spaces can be
used in this setting to obtain spectra associated to certain categories of
gapped systems.
|
We Microsoft Research Asia made submissions to 11 language directions in the
WMT19 news translation tasks. We won the first place for 8 of the 11 directions
and the second place for the other three. Our basic systems are built on
Transformer, back translation and knowledge distillation. We integrate several
of our rececent techniques to enhance the baseline systems: multi-agent dual
learning (MADL), masked sequence-to-sequence pre-training (MASS), neural
architecture optimization (NAO), and soft contextual data augmentation (SCA).
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Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.