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We consider some conditions under which a smooth projective variety X is
actually the projective space. We also extend to the case of positive
characteristic some results in the theory of vector bundle adjunction. We use
methods and techniques of the so called Mori theory, in particular the study of
rational curves on projective manifolds.
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Non-local correlations are usually understood through the outcomes of
alternative measurements (on two or more parts of a system) that cannot
altogether actually be carried out in an experiment. Indeed, a joint
input/output -- e.g., measurement-setting/outcome -- behavior is non-local if
and only if the outputs for all possible inputs cannot coexist consistently. It
has been argued that this counterfactual view is how Bell's inequalities and
their violations are to be seen. We propose an alternative perspective which
refrains from setting into relation the results of mutually exclusive
measurements, but that is based solely on data actually available. Our approach
uses algorithmic complexity instead of probability, implies non-locality to
have similar consequences as in the probabilistic view, and is conceptually
simpler yet at the same time more general than the latter.
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This paper is devoted to the complexity of the quantified boolean formula
problem. We describe a simple deterministic algorithm that, for a given
quantified boolean formula $F$, stops in time bounded by $O(|F|^4)$ and answers
yes if $F$ is true and no otherwise.
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The equivalence between the Chern-Simons gauge theory on a three-dimensional
manifold with boundary and the WZNW model on the boundary is established in a
simple and general way using the BRST symmetry. Our approach is based on
restoring gauge invariance of the Chern-Simons theory in the presence of a
boundary. This gives a correspondence to the WZNW model that does not require
solving any constraints, fixing the gauge or specifying boundary conditions.
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We investigate the impact between the gas stream from the inner Lagrangian
point and the accretion disk in interacting binaries, using three dimensional
Smooth Particle Hydrodynamics simulations. We find that a significant fraction
of the stream material can ricochet off the disk edge and overflow towards
smaller radii, and that this generates pronounced non-axisymmetric structure in
the absorption column towards the central object. We discuss the implications
of our results for observations and time-dependent models of low-mass X-ray
binaries, cataclysmic variables and supersoft X-ray sources.
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Let $[\, \cdot\,]$ be the floor function. In the present paper we prove that
when $1<c<\frac{12}{11}$ and $\theta>1$ is a fixed, then there exist infinitely
many prime numbers of the form $[n^c \tan^\theta(\log n)]$.
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This paper highlights three known identities, each of which involves sums
over alternating sign matrices. While proofs of all three are known, the only
known derivations are as corollaries of difficult results. The simplicity and
natural combinatorial interpretation of these identities, however, suggest that
there should be direct, bijective proofs.
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The planar graph product structure theorem of Dujmovi\'{c}, Joret, Micek,
Morin, Ueckerdt, and Wood [J. ACM 2020] states that every planar graph is a
subgraph of the strong product of a graph with bounded treewidth and a path.
This result has been the key tool to resolve important open problems regarding
queue layouts, nonrepetitive colourings, centered colourings, and adjacency
labelling schemes. In this paper, we extend this line of research by utilizing
shallow minors to prove analogous product structure theorems for several beyond
planar graph classes. The key observation that drives our work is that many
beyond planar graphs can be described as a shallow minor of the strong product
of a planar graph with a small complete graph. In particular, we show that
powers of planar graphs, $k$-planar, $(k,p)$-cluster planar, fan-planar and
$k$-fan-bundle planar graphs have such a shallow-minor structure. Using a
combination of old and new results, we deduce that these classes have bounded
queue-number, bounded nonrepetitive chromatic number, polynomial $p$-centred
chromatic numbers, linear strong colouring numbers, and cubic weak colouring
numbers. In addition, we show that $k$-gap planar graphs have at least
exponential local treewidth and, as a consequence, cannot be described as a
subgraph of the strong product of a graph with bounded treewidth and a path.
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This study shows the feasibility of an eHealth solution for tackling eating
habits and physical activity in the adolescent population. The participants
were children from 11 to 15 years old. An intervention was carried out on 139
students in the intervention group and 91 students in the control group, in two
schools during 14 weeks. The intervention group had access to the web through a
user account and a password. They were able to create friendship relationships,
post comments, give likes and interact with other users, as well as receive
notifications and information about nutrition and physical activity on a daily
basis and get (virtual) rewards for improving their habits. The control group
did not have access to any of these features. The homogeneity of the samples in
terms of gender, age, body mass index and initial health-related habits was
demonstrated. Pre- and post-measurements were collected through self-reports on
the application website. After applying multivariate analysis of variance, a
significant alteration in the age-adjusted body mass index percentile was
observed in the intervention group versus the control group, as well as in the
PAQ-A score and the KIDMED score. It can be concluded that eHealth
interventions can help to obtain healthy habits. More research is needed to
examine the effectiveness in achieving adherence to these new habits.
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Let $G$ be a group and let $F$ be a field of characteristic different from 2.
Denote by $(FG)^+$ the set of symmetric elements and by $\mathcal{U}^+(FG)$ the
set of symmetric units, under an oriented classical involution of the group
algebra $FG$. We give some lower and upper bounds on the Lie nilpotency index
of $(FG)^+$ and the nilpotency class of $\mathcal{U}^+(FG)$.
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We study spatio-temporal chaos in the complex Ginzburg-Landau equation in
parameter regions of weak amplification and viscosity. Turbulent states
involving many soliton-like pulses appear in the parameter range, because the
complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger
equation. We find that the distributions of amplitude and wavenumber of pulses
depend only on the ratio of the two parameters of the amplification and the
viscosity. This implies that a one-parameter family of soliton turbulence
states characterized by different distributions of the soliton parameters
exists continuously around the completely integrable system.
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The renormalization of singular chiral potentials as applied to NN scattering
and the structure of the deuteron is discussed. It is shown how zero range
theories may be implemented non-perturbatively as constrained from known long
range NN forces.
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The most usual formulation of the Laws of Thermodynamics turns out to be
suitable for local or simple materials, while for non-local systems there are
two different ways: either modify this usual formulation by introducing
suitable extra fluxes or express the Laws of Thermodynamics in terms of
internal powers directly, as we propose in this paper. The first choice is
subject to the criticism that the vector fluxes must be introduced a posteriori
in order to obtain the compatibility with the Laws of Thermodynamics. On the
contrary, the formulation in terms of internal powers is more general, because
it is a priori defined on the basis of the constitutive equations. Besides it
allows to highlight, without ambiguity, the contribution of the internal powers
in the variation of the thermodynamic potentials. Finally, in this paper, we
consider some examples of non-local materials and derive the proper expressions
of their internal powers from the power balance laws.
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This paper provides a technical companion to M. Aguado and E. Seiler,
hep-lat/0406041, in which the fate of perturbation theory in the thermodynamic
limit is discussed for the O(N) model on a 2d lattice and different boundary
conditions. The techniques used to compute perturbative coefficients are
explained, and results for all boundary conditions considered reviewed in
detail.
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Many state-of-the art visualization techniques must be tailored to the
specific type of dataset, its modality (CT, MRI, etc.), the recorded object or
anatomical region (head, spine, abdomen, etc.) and other parameters related to
the data acquisition process. While parts of the information (imaging modality
and acquisition sequence) may be obtained from the meta-data stored with the
volume scan, there is important information which is not stored explicitly
(anatomical region, tracing compound). Also, meta-data might be incomplete,
inappropriate or simply missing.
This paper presents a novel and simple method of determining the type of
dataset from previously defined categories. 2D histograms based on intensity
and gradient magnitude of datasets are used as input to a neural network, which
classifies it into one of several categories it was trained with. The proposed
method is an important building block for visualization systems to be used
autonomously by non-experts. The method has been tested on 80 datasets, divided
into 3 classes and a "rest" class.
A significant result is the ability of the system to classify datasets into a
specific class after being trained with only one dataset of that class. Other
advantages of the method are its easy implementation and its high computational
performance.
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We show that the integers in the HMM LLL HNF algorithm have bit length
O(m.log(m.B)), where m is the number of rows and B is the maximum square length
of a row of the input matrix. This is only a little worse than the estimate
O(m.log(B)) in the LLL algorithm.
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Telehealth helps to facilitate access to medical professionals by enabling
remote medical services for the patients. These services have become gradually
popular over the years with the advent of necessary technological
infrastructure. The benefits of telehealth have been even more apparent since
the beginning of the COVID-19 crisis, as people have become less inclined to
visit doctors in person during the pandemic. In this paper, we focus on
facilitating the chat sessions between a doctor and a patient. We note that the
quality and efficiency of the chat experience can be critical as the demand for
telehealth services increases. Accordingly, we develop a smart auto-response
generation mechanism for medical conversations that helps doctors respond to
consultation requests efficiently, particularly during busy sessions. We
explore over 900,000 anonymous, historical online messages between doctors and
patients collected over nine months. We implement clustering algorithms to
identify the most frequent responses by doctors and manually label the data
accordingly. We then train machine learning algorithms using this preprocessed
data to generate the responses. The considered algorithm has two steps: a
filtering (i.e., triggering) model to filter out infeasible patient messages
and a response generator to suggest the top-3 doctor responses for the ones
that successfully pass the triggering phase. The method provides an accuracy of
83.28\% for precision@3 and shows robustness to its parameters.
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Understanding human mobility is essential for many fields, including
transportation planning. Currently, surveys are the primary source for such
analysis. However, in the recent past, many researchers have focused on Call
Detail Records (CDR) for identifying travel patterns. CDRs have shown
correlation to human mobility behavior. However, one of the main issues in
using CDR data is that it is difficult to identify the precise location of the
user due to the low spacial resolution of the data and other artifacts such as
the load sharing effect. Existing approaches have certain limitations. Previous
studies using CDRs do not consider the transmit power of cell towers when
localizing the users and use an oversimplified approach to identify load
sharing effects. Furthermore, they consider the entire population of users as
one group neglecting the differences in mobility patterns of different segments
of users. This research introduces a novel methodology to user position
localization from CDRs through improved detection of load sharing effects, by
taking the transmit power into account, and segmenting the users into distinct
groups for the purpose of learning any parameters of the model. Moreover, this
research uses several methods to address the existing limitations and validate
the generated results using nearly 4 billion CDR data points with travel survey
data and voluntarily collected mobile data.
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We compute, in the MSSM framework, the total electroweak contributions at one
loop for the process pp -> tW+X, initiated by the parton process bg -> tW. The
supersymmetric effect is analyzed for various choices of the SUSY benchmark
points. Choosing realistic unpolarized and polarized experimental quantities,
we show the size of the various effects and discuss their dependence on the
MSSM parameters.
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The rotation rate in pre-supernova cores is an important ingredient which can
profoundly affect the post-collapse evolution and associated energy release in
supernovae and long gamma ray bursts (LGRBs). Previous work has focused on
whether the specific angular momentum is above or below the critical value
required for the creation of a centrifugally supported disk around a black
hole. Here, we explore the effect of the distribution of angular momentum with
radius in the star, and show that qualitative transitions between high and low
angular momentum flow, corresponding to high and low luminosity accretion
states, can effectively be reflected in the energy output, leading to
variability and the possibility of quiescent times in LGRBs.
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We consider the problem of broadcast with common messages, and focus on the
case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the
message intended for all the receivers in the set $\mathcal{A}$, is the same
for all the set $\mathcal{A}$ of the same cardinality. Instead of attempting to
characterize the capacity region of general broadcast channels, we only
consider the structure of the capacity region that any broadcast channel should
bear. The concept of latent capacity region is useful in capturing these
underlying constraints, and we provide a complete characterization of the
latent capacity region for the symmetric broadcast problem. The converse proof
of this tight characterization relies on a deterministic broadcast channel
model. The achievability proof generalizes the familiar rate transfer argument
to include more involved erasure correction coding among messages, thus
revealing an inherent connection between broadcast with common message and
erasure correction codes.
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It is shown that there is a simple way to get the quantization equation for
the electric and magnetic charges of dyons, $e_ig_j-g_ie_j=m(\hbar c)$, which
also shed light to the origin of such quantization.
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We study a sequence of eruptive events including filament eruption, a GOES
C4.3 flare and a coronal mass ejection. We aim to identify the possible
trigger(s) and precursor(s) of the filament destabilisation; investigate flare
kernel characteristics; flare ribbons/kernels formation and evolution; study
the interrelation of the filament-eruption/flare/coronal-mass-ejection
phenomena as part of the integral active-region magnetic field configuration;
determine H\alpha\ line profile evolution during the eruptive phenomena.
Multi-instrument observations are analysed including H\alpha\ line profiles,
speckle images at H\alpha-0.8 \AA\ and H\alpha+0.8 \AA\ from IBIS at DST/NSO,
EUV images and magnetograms from the SDO, coronagraph images from STEREO and
the X-ray flux observations from FERMI and GOES. We establish that the filament
destabilisation and eruption are the main trigger for the flaring activity. A
surge-like event with a circular ribbon in one of the filament footpoints is
determined as the possible trigger of the filament destabilisation. Plasma
draining in this footpoint is identified as the precursor for the filament
eruption. A magnetic flux emergence prior to the filament destabilisation
followed by a high rate of flux cancelation of 1.34$\times10^{16}$ Mx s$^{-1}$
is found during the flare activity. The flare X-ray lightcurves reveal three
phases that are found to be associated with three different ribbons occurring
consecutively. A kernel from each ribbon is selected and analysed. The kernel
lightcurves and H alpha line profiles reveal that the emission increase in the
line centre is stronger than that in the line wings. A delay of around 5-6 mins
is found between the increase in the line centre and the occurrence of red
asymmetry. Only red asymmetry is observed in the ribbons during the impulsive
phases. Blue asymmetry is only associated with the dynamic filament.
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We revisit the general framework introduced by Fazylab et al. (SIAM J. Optim.
28, 2018) to construct Lyapunov functions for optimization algorithms in
discrete and continuous time. For smooth, strongly convex objective functions,
we relax the requirements necessary for such a construction. As a result we are
able to prove for Polyak's ordinary differential equations and for a
two-parameter family of Nesterov algorithms rates of convergence that improve
on those available in the literature. We analyse the interpretation of Nesterov
algorithms as discretizations of the Polyak equation. We show that the
algorithms are instances of Additive Runge-Kutta integrators and discuss the
reasons why most discretizations of the differential equation do not result in
optimization algorithms with acceleration. We also introduce a modification of
Polyak's equation and study its convergence properties. Finally we extend the
general framework to the stochastic scenario and consider an application to
random algorithms with acceleration for overparameterized models; again we are
able to prove convergence rates that improve on those in the literature.
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The fabrication, characterisation, and superconductivity of MgB2 thick films
grown on stainless steel substrate were studied. XRD, SEM, and magnetic
measurements were carried out. It was found that the MgB2 thick films can be
fast formed by heating samples to 660 oC then immediately cooling down to room
temperature. XRD shows above 90% MgB2 phase and less than 10 % MgO. However,
the samples sintered at 800 oC for 4 h contain both MgB4 and MgO impurities in
addition to MgB2. The fast formed MgB2 films appear to have a good grain
connectivity that gives a Jc of 8 x 10 4 A/cm2at 5 K and 1 T and maintained
this value at 20 K in zero field.
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There would be a perfect correspondence between the laws of classical
thermodynamics and black hole thermodynamics, except for the apparent failure
of black hole thermodynamics to correspond to the Third Law. The classical
Third Law of Thermodynamics entails that as the absolute temperature, T,
approaches zero, the entropy, S, also approaches zero.
This discussion is based upon part of the work published by the author in
1995 that demonstrated that the most general form of the classical Third Law of
Thermodynamics is satisfied by treating the area of the inner-event horizon as
a measure of negative-entropy (negentropy).
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The Praesepe cluster contains a number of Delta Sct and Gamma Dor pulsators.
Asteroseismology of cluster stars is simplified by the common distance, age and
stellar abundances. Since asteroseismology requires a large number of known
frequencies, the small pulsation amplitudes of these stars require space
satellite campaigns. The present study utilizes photometric MOST satellite
measurements in order to determine the pulsation frequencies of two evolved (EP
Cnc, BT Cnc) and two main-sequence (BS Cnc, HD 73872) Delta Sct stars in the
Praesepe cluster. The frequency analysis of the 2008 and 2009 data detected up
to 34 frequencies per star with most amplitudes in the submillimag range. In BS
Cnc, two modes showed strong amplitude variability between 2008 and 2009. The
frequencies ranged from 0.76 to 41.7 c/d. After considering the different
evolutionary states and mean stellar densities of these four stars, the
differences and large ranges in frequency remain.
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This report gives a novel technique of image encryption and authentication by
combining elements of Visual Cryptography and Public Key Cryptography. A
prominent attack involving generation of fake shares to cheat honest users has
been described and a demonstration of the proposed system employing a
centralised server to generate shares and authenticate them on the basis of
requests is made as a counter to the described attack.
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A robust route for the biased production of single-handed chiral structures
has been found in generating non-spherical, multi-component double emulsions
using microfluidics. The specific type of handedness is determined by the final
packing geometry of four different inner drops inside an ultra-thin sheath of
oil. Before three-dimensional chiral structures are formed, the
quasi-one-dimensional chain re-arranges in two dimensions into either
checkerboard or stripe patterns. We derive an analytical model predicting which
pattern is more likely and assembles in the least amount of time. Moreover, our
dimensionless model accurately predicts our experimental results and is based
on local bending dynamics, rather than global surface energy minimization. This
better reflects the underlying self-assembly process which will not, in
general, reach a global energy minimum. In summary, using glass microfluidic
techniques for channeling aqueous fluids through narrow orifices of multi-bore
injection capillaries while encapsulating these fluids as drops inside an
ultra-thin sheath of oil is sufficient to produce single-handed chiral
structures.
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We analyse the global (rigid) symmetries that are realised on the bosonic
fields of the various supergravity actions obtained from eleven-dimensional
supergravity by toroidal compactification followed by the dualisation of some
subset of fields. In particular, we show how the global symmetries of the
action can be affected by the choice of this subset. This phenomenon occurs
even with the global symmetries of the equations of motion. A striking
regularity is exhibited by the series of theories obtained respectively without
any dualisation, with the dualisation of only the Ramond-Ramond fields of the
type IIA theory, with full dualisation to lowest degree forms, and finally for
certain inverse dualisations (increasing the degrees of some forms) to give the
type IIB series. These theories may be called the GL_A, D, E and GL_B series
respectively. It turns out that the scalar Lagrangians of the E series are
sigma models on the symmetric spaces K(E_{11-D})\backslash E_{11-D} (where K(G)
is the maximal compact subgroup of G) and the other three series lead to models
on homogeneous spaces K(G) \backslash G\semi \R^s. These can be understood from
the E series in terms of the deletion of positive roots associated with the
dualised scalars, which implies a group contraction. We also propose a
constrained Lagrangian version of the even dimensional theories exhibiting the
full duality symmetry and begin a systematic analysis of abelian duality
subalgebras.
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Seminal work by Edmonds and Lovasz shows the strong connection between
submodularity and convexity. Submodular functions have tight modular lower
bounds, and subdifferentials in a manner akin to convex functions. They also
admit poly-time algorithms for minimization and satisfy the Fenchel duality
theorem and the Discrete Seperation Theorem, both of which are fundamental
characteristics of convex functions. Submodular functions also show signs
similar to concavity. Submodular maximization, though NP hard, admits constant
factor approximation guarantees. Concave functions composed with modular
functions are submodular, and they also satisfy diminishing returns property.
This manuscript provides a more complete picture on the relationship between
submodularity with convexity and concavity, by extending many of the results
connecting submodularity with convexity to the concave aspects of
submodularity. We first show the existence of superdifferentials, and
efficiently computable tight modular upper bounds of a submodular function.
While we show that it is hard to characterize this polyhedron, we obtain inner
and outer bounds on the superdifferential along with certain specific and
useful supergradients. We then investigate forms of concave extensions of
submodular functions and show interesting relationships to submodular
maximization. We next show connections between optimality conditions over the
superdifferentials and submodular maximization, and show how forms of
approximate optimality conditions translate into approximation factors for
maximization. We end this paper by studying versions of the discrete seperation
theorem and the Fenchel duality theorem when seen from the concave point of
view. In every case, we relate our results to the existing results from the
convex point of view, thereby improving the analysis of the relationship
between submodularity, convexity, and concavity.
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We consider the Bayesian detection statistic for a targeted search for
continuous gravitational waves, known as the $\mathcal{B}$-statistic. This is a
Bayes factor between signal and noise hypotheses, produced by marginalizing
over the four amplitude parameters of the signal. We show that by
Taylor-expanding to first order in certain averaged combinations of antenna
patterns (elements of the parameter space metric), the marginalization integral
can be performed analytically, producing a closed-form approximation in terms
of confluent hypergeometric functions. We demonstrate using Monte Carlo
simulations that this approximation is as powerful as the full
$\mathcal{B}$-statistic, and outperforms the traditional maximum-likelihood
$\mathcal{F}$-statistic, for several observing scenarios which involve an
average over sidereal times. We also show that the approximation does not
perform well for a near-instantaneous observation, so the approximation is
suited to long-time continuous wave observations rather than transient modelled
signals such as compact binary inspiral.
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We report the most precise measurement to date of a parity-violating
asymmetry in elastic electron-proton scattering. The measurement was carried
out with a beam energy of 3.03 GeV and a scattering angle <theta_lab>=6
degrees, with the result A_PV = -1.14 +/- 0.24 (stat) +/- 0.06 (syst) parts per
million. From this we extract, at Q^2 = 0.099 GeV^2, the strange form factor
combination G_E^s + 0.080 G_M^s = 0.030 +/- 0.025 (stat) +/- 0.006 (syst) +/-
0.012 (FF) where the first two errors are experimental and the last error is
due to the uncertainty in the neutron electromagnetic form factor. This result
significantly improves current knowledge of G_E^s and G_M^s at Q^2 ~0.1 GeV^2.
A consistent picture emerges when several measurements at about the same Q^2
value are combined: G_E^s is consistent with zero while G_M^s prefers positive
values though G_E^s=G_M^s=0 is compatible with the data at 95% C.L.
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We give a new fusion procedure for the Brauer algebra by showing that all
primitive idempotents can be found by evaluating a rational function in several
variables which has the form of a product of R-matrix type factors. In
particular, this provides a new fusion procedure for the symmetric group
involving an arbitrary parameter. The R-matrices are solutions of the
Yang--Baxter equation associated with the classical Lie algebras g_N of types
B, C and D. Moreover, we construct an evaluation homomorphism from a reflection
equation algebra B(g_N) to U(g_N) and show that the fusion procedure provides
an equivalence between natural tensor representations of B(g_N) with the
corresponding evaluation modules.
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Let $K$ be a field and $S=K[x_1,\ldots, x_n]$. Let $I$ be a monomial ideal of
$S$ and $u_1,\ldots, u_r$ be monomials in $S$ which form a filter-regular
sequence on $S/I$. We show that $S/I$ is pretty clean if and only if
$S/(I,u_1,\ldots, u_r)$ is pretty clean.
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Quantum algorithms provide an exponential speedup for solving certain classes
of linear systems, including those that model geologic fracture flow. However,
this revolutionary gain in efficiency does not come without difficulty. Quantum
algorithms require that problems satisfy not only algorithm-specific
constraints, but also application-specific ones. Otherwise, the quantum
advantage carefully attained through algorithmic ingenuity can be entirely
negated. Previous work addressing quantum algorithms for geologic fracture flow
has illustrated core algorithmic approaches while incrementally removing
assumptions. This work addresses two further requirements for solving geologic
fracture flow systems with quantum algorithms: efficient system state
preparation and efficient information extraction. Our approach to addressing
each is consistent with an overall exponential speed-up.
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This paper corrects the proof of the Theorem 2 from the Gower's paper
\cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper
\cite{Gower:1986}. The first correction is needed in order to establish the
existence of the kernel function used commonly in the kernel trick e.g. for
$k$-means clustering algorithm, on the grounds of distance matrix. The
correction encompasses the missing if-part proof and dropping unnecessary
conditions. The second correction deals with transformation of the kernel
matrix into a one embeddable in Euclidean space.
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An earlier suggestion that scalar fields in gauge theory may be introduced as
frame vectors or vielbeins in internal symmetry space, and so endowed with
geometric significance, is here sharpened and refined. Applied to a $u(1)
\times su(2)$ theory this gives exactly the Higgs structure of the standard
electroweak theory. Applied to an $su(3)$ theory, it gives a structure having
much in common with a phenomenological model previously constructed to explain
fermion mixing and mass hierarchy. The difference in physical outcome for the
two theories is here traced to the difference in structure between the two
symmetry groups.
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The Biot problem of poroelasticity is extended by Signorini contact
conditions. The resulting Biot contact problem is formulated and analyzed as a
two field variational inequality problem of a perturbed saddle point structure.
We present an a priori error analysis for a general as well as for a $hp$-FE
discretization including convergence and guaranteed convergence rates for the
latter. Moreover, we derive a family of reliable and efficient residual based a
posteriori error estimators, and elaborate how a simple and efficient
primal-dual active set solver can be applied to solve the discrete Galerkin
problem. Numerical results underline our theoretical finding and show that
optimal, in particular exponential, convergence rates can be achieved by
adaptive schemes for two dimensional problems.
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We investigate the sedimentation equilibrium of a charge stabilized colloidal
suspension in the regime of low ionic strength. We analyze the asymptotic
behaviour of the density profiles on the basis of a simple Poisson--Boltzmann
theory and show that the effective mass we can deduce from the barometric law
corresponds to the actual mass of the colloidal particles, contrary to previous
studies.
|
The application of graph theory to model the complex structure and function
of the brain has shed new light on its organization and function, prompting the
emergence of network neuroscience. Despite the tremendous progress that has
been achieved in this field, still relatively few methods exploit the topology
of brain networks to analyze brain activity. Recent attempts in this direction
have leveraged on graph spectral analysis and graph signal processing to
decompose brain activity in connectivity eigenmodes or gradients. If results
are promising in terms of interpretability and functional relevance,
methodologies and terminology are sometimes confusing. The goals of this paper
are twofold. First, we summarize recent contributions related to connectivity
gradients and graph signal processing, and attempt a clarification of the
terminology and methods used in the field, while pointing out current
methodological limitations. Second, we discuss the perspective that the
functional relevance of connectivity gradients could be fruitfully exploited by
considering them as graph Fourier bases of brain activity.
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Embedding rigid inclusions into elastic matrix materials is a procedure of
high practical relevance, for instance for the fabrication of elastic composite
materials. We theoretically analyze the following situation. Rigid spherical
inclusions are enclosed by a homogeneous elastic medium under stick boundary
conditions. Forces and torques are directly imposed from outside onto the
inclusions, or are externally induced between them. The inclusions respond to
these forces and torques by translations and rotations against the surrounding
elastic matrix. This leads to elastic matrix deformations, and in turn results
in mutual long-ranged matrix-mediated interactions between the inclusions.
Adapting a well-known approach from low-Reynolds-number hydrodynamics, we
explicitly calculate the displacements and rotations of the inclusions from the
externally imposed or induced forces and torques. Analytical expressions are
presented as a function of the inclusion configuration in terms of
displaceability and rotateability matrices. The role of the elastic environment
is implicitly included in these relations. That is, the resulting expressions
allow a calculation of the induced displacements and rotations directly from
the inclusion configuration, without having to explicitly determine the
deformations of the elastic environment. In contrast to the hydrodynamic case,
compressibility of the surrounding medium is readily taken into account. We
present the complete derivation based on the underlying equations of linear
elasticity theory. In the future, the method will, for example, be helpful to
characterize the behavior of externally tunable elastic composite materials, to
accelerate numerical approaches, as well as to improve the quantitative
interpretation of microrheological results.
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We explore the connections between automata, groups, limit spaces of
self-similar actions, and tilings. In particular, we show how a group acting
``nicely'' on a tree gives rise to a self-covering of a topological groupoid,
and how the group can be reconstructed from the groupoid and its covering. The
connection is via finite-state automata. These define decomposition rules, or
self-similar tilings, on leaves of the solenoid associated with the covering.
|
The spin- and charge-density-wave order parameters of the itinerant
antiferromagnet chromium are measured directly with non-resonant x-ray
diffraction as the system is driven towards its quantum critical point with
high pressure using a diamond anvil cell. The exponential decrease of the spin
and charge diffraction intensities with pressure confirms the harmonic scaling
of spin and charge, while the evolution of the incommensurate ordering vector
provides important insight into the difference between pressure and chemical
doping as means of driving quantum phase transitions. Measurement of the charge
density wave over more than two orders of magnitude of diffraction intensity
provides the clearest demonstration to date of a weakly-coupled, BCS-like
ground state. Evidence for the coexistence of this weakly-coupled ground state
with high-energy excitations and pseudogap formation above the ordering
temperature in chromium, the charge-ordered perovskite manganites, and the blue
bronzes, among other such systems, raises fundamental questions about the
distinctions between weak and strong coupling.
|
We perform a full nuclear-network numerical calculation of the $r$-process
nuclei in binary neutron-star mergers (NSMs), with the aim of estimating
$\gamma$-ray emissions from the remnants of Galactic NSMs up to $10^6$ years
old. The nucleosynthesis calculation of 4,070 nuclei is adopted to provide the
elemental composition ratios of nuclei with an electron fraction $Y_{\rm e}$
between 0.10 and 0.45 . The decay processes of 3,237 unstable nuclei are
simulated to extract the $\gamma$-ray spectra. As a result, the NSMs have
different spectral color in $\gamma$-ray band from various other astronomical
objects at less than $10^5$ years old. In addition, we propose a new
line-diagnostic method for $Y_{\rm e}$ that uses the line ratios of either
$^{137{\rm m}}$Ba/$^{85}$K or $^{243}$Am/$^{60{\rm m}}$Co, which become larger
than unity for young and old $r$-process sites, respectively, with a low
$Y_{\rm e}$ environment. From an estimation of the distance limit for
$\gamma$-ray observations as a function of the age, the high sensitivity in the
sub-MeV band, at approximately $10^{-9}$ photons s$^{-1}$ cm$^{-2}$ or
$10^{-15}$ erg s$^{-1}$ cm$^{-2}$, is required to cover all the NSM remnants in
our Galaxy if we assume that the population of NSMs by
\citet{2019ApJ...880...23W}. A $\gamma$-ray survey with sensitivities of
$10^{-8}$--$10^{-7}$ photons s$^{-1}$ cm$^{-2}$ or $10^{-14}$--$10^{-13}$ erg
s$^{-1}$ cm$^{-2}$ in the 70--4000 keV band is expected to find emissions from
at least one NSM remnant under the assumption of NSM rate of 30 Myr$^{-1}$. The
feasibility of $\gamma$-ray missions to observe Galactic NSMs are also studied.
|
The aim of this work is to introduce a thermo-electromagnetic model for
calculating the temperature and the power dissipated in cylindrical pieces
whose geometry var\'ies with time and undergoes large deformations; the motion
will be a known data. The work will be a first step towards building a complete
thermoelectromagnetic-mechanical model suitable for simulating electrically
assisted forming processes, which is the main motivation of the work. The
electromagnetic model will be obtained from the time-harmonic eddy current
problem with an inplane current; the source will be given in terms of currents
or voltages defined at sorne parts of the boundary. Finite element methods
based on a Lagrangian weak formulation will be used for the numerical solution.
This approach will avoid the need to compute and remesh the
thermo-electromagnetic domain along the time. The numerical tools will be
implemented in FEniCS and validated by using a suitable test also solved in
Eulerian coordinates.
|
Primordial Black Holes (PBHs) might have formed in the early Universe due to
the collapse of density fluctuations. PBHs may act as the sources for some of
the gravitational waves recently observed. We explored the formation scenarios
of PBHs of stellar mass, taking into account the possible influence of the QCD
phase transition, for which we considered three different models: Crossover
Model (CM), Bag Model (BM), and Lattice Fit Model (LFM). For the fluctuations,
we considered a running-tilt power-law spectrum; when these cross the $\sim
10^{-9}$-$10^{-1}\mathrm{~s}$ Universe horizon they originate
0.05-500~M$_{\odot}$ PBHs which could: i) provide a population of stellar mass
PBHs similar to the ones present on the binaries associated with all known
gravitational wave sources; ii) constitute a broad mass spectrum accounting for
$\sim 76\%$ of all Cold Dark Matter (CDM) in the Universe.
|
Despite many efforts, the behavior of a crowd is not fully understood. The
advent of modern communication media has made it an even more challenging
problem, as crowd dynamics could be driven by both human-to-human and
human-technology interactions. Here, we study the dynamics of a crowd
controlled game (Twitch Plays Pok\'emon), in which nearly a million players
participated during more than two weeks. We dissect the temporal evolution of
the system dynamics along the two distinct phases that characterized the game.
We find that players who do not follow the crowd average behavior are key to
succeed in the game. The latter finding can be well explained by an n-$th$
order Markov model that reproduces the observed behavior. Secondly, we analyze
a phase of the game in which players were able to decide between two different
modes of playing, mimicking a voting system. Our results suggest that under
some conditions, the collective dynamics can be better regarded as a swarm-like
behavior instead of a crowd. Finally, we discuss our findings in the light of
the social identity theory, which appears to describe well the observed
dynamics.
|
We introduce new Langevin-type equations describing the rotational and
translational motion of rigid bodies interacting through conservative and
non-conservative forces, and hydrodynamic coupling. In the absence of
non-conservative forces the Langevin-type equations sample from the canonical
ensemble. The rotational degrees of freedom are described using quaternions,
the lengths of which are exactly preserved by the stochastic dynamics. For the
proposed Langevin-type equations, we construct a weak 2nd order geometric
integrator which preserves the main geometric features of the continuous
dynamics. The integrator uses Verlet-type splitting for the deterministic part
of Langevin equations appropriately combined with an exactly integrated
Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate
both the new Langevin model and the numerical method for it, as well as to
demonstrate how inertia and the coupling of rotational and translational motion
can introduce qualitatively distinct behaviours.
|
We present the results of a detailed spectral analysis of optically faint
hard X-ray sources in the Chandra deep fields selected on the basis of their
high X-ray to optical flux ratio (X/O). The stacked spectra of high X/O sources
in both Chandra deep fields, fitted with a single power-law model, are much
harder than the spectrum of the X-ray background (XRB). The average slope is
also insensitive to the 2-8 keV flux, being approximately constant around
Gamma~1 over more than two decades, strongly indicating that high X/O sources
represent the most obscured component of the XRB. For about half of the sample,
a redshift estimate (in most of the cases a photometric redshift) is available
from the literature. Individual fits of a few of the brightest objects and of
stacked spectra in different redshift bins imply column densities in the range
10^{22-23.5} cm^{-2}. A trend of increasing absorption towards higher redshifts
is suggested.
|
We report the fabrication and characterization of superconducting quantum
interference devices (SQUIDs) based on InAs nanowires and vanadium
superconducting electrodes. These mesoscopic devices are found to be extremely
robust against thermal cycling and to operate up to temperatures of $\sim2.5$~K
with reduced power dissipation. We show that our geometry allows to obtain
nearly-symmetric devices with very large magnetic-field modulation of the
critical current. All these properties make these devices attractive for
on-chip quantum-circuit implementation.
|
We examine theoretically electron paramagnetic resonance (EPR) lineshapes as
functions of resonance frequency, energy level, and temperature for single
crystals of three different kinds of single-molecule nanomagnets (SMMs):
Mn$_{12}$ acetate, Fe$_8$Br, and the $S=9/2$ Mn$_4$ compound. We use a
density-matrix equation and consider distributions in the uniaxial
(second-order) anisotropy parameter $D$ and the $g$ factor, caused by possible
defects in the samples. Additionally, weak intermolecular exchange and
electronic dipole interactions are included in a mean-field approximation. Our
calculated linewidths are in good agreement with experiments. We find that the
distribution in $D$ is common to the three examined single-molecule magnets.
This could provide a basis for a proposed tunneling mechanism due to lattice
defects or imperfections. We also find that weak intermolecular exchange and
dipolar interactions are mainly responsible for the temperature dependence of
the lineshapes for all three SMMs, and that the intermolecular exchange
interaction is more significant for Mn$_4$ than for the other two SMMs. This
finding is consistent with earlier experiments and suggests the role of
spin-spin relaxation processes in the mechanism of magnetization tunneling.
|
A conjecture of Kalai asserts that for $d\geq 4$, the affine type of a prime
simplicial $d$-polytope $P$ can be reconstructed from the space of affine
$2$-stresses of $P$. We prove this conjecture for all $d\geq 5$. We also prove
the following generalization: for all pairs $(i,d)$ with $2\leq i\leq \lceil
\frac d 2\rceil-1$, the affine type of a simplicial $d$-polytope $P$ that has
no missing faces of dimension $\geq d-i+1$ can be reconstructed from the space
of affine $i$-stresses of $P$. A consequence of our proofs is a strengthening
of the Generalized Lower Bound Theorem: it was proved by Nagel that for any
simplicial $(d-1)$-sphere $\Delta$ and $1\leq k\leq \lceil\frac{d}{2}\rceil-1$,
$g_k(\Delta)$ is at least as large as the number of missing $(d-k)$-faces of
$\Delta$; here we show that, for $1\leq k\leq \lfloor\frac{d}{2}\rfloor-1$,
equality holds if and only if $\Delta$ is $k$-stacked. Finally, we show that
for $d\geq 4$, any simplicial $d$-polytope $P$ that has no missing faces of
dimension $\geq d-1$ is redundantly rigid, that is, for each edge $e$ of $P$,
there exists an affine $2$-stress on $P$ with a non-zero value on $e$.
|
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over
a non-Archimedean locally compact infinite field with a non-trivial valuation
are defined and constructed. Measures are considered with values in $\bf R$.
Theorems and criteria are formulated and proved about quasi-invariance and
pseudo-differentiability of measures relative to linear and non-linear
operators on $X$. Characteristic functionals of measures are studied. Moreover,
the non-Archimedean analogs of the Bochner-Kolmogorov and Minlos-Sazonov
theorems are investigated. Infinite products of measures also are considered.
Convergence of quasi-invariant and pseudo-differentiable measures in the
corresponding spaces of measures is investigated.
|
In all applications of gamma-ray spectroscopy, one of the most important and
delicate parts of the data analysis is the fitting of the gamma-ray spectra,
where information as the number of counts, the position of the centroid and the
width, for instance, are associated with each peak of each spectrum. There's a
huge choice of computer programs that perform this type of analysis, and the
most commonly used in routine work are the ones that automatically locate and
fit the peaks; this fit can be made in several different ways -- the most
common ways are to fit a Gaussian function to each peak or simply to integrate
the area under the peak, but some software go far beyond and include several
small corrections to the simple Gaussian peak function, in order to compensate
for secondary effects. In this work several gamma-ray spectroscopy software are
compared in the task of finding and fitting the gamma-ray peaks in spectra
taken with standard sources of $^{137}$Cs, $^{60}$Co, $^{133}$Ba and
$^{152}$Eu. The results show that all of the automatic software can be properly
used in the task of finding and fitting peaks, with the exception of
GammaVision; also, it was possible to verify that the automatic peak-fitting
software did perform as well as -- and sometimes even better than -- a manual
peak-fitting software.
|
The quantum spin Hall (QSH) phase is a time reversal invariant electronic
state with a bulk electronic band gap that supports the transport of charge and
spin in gapless edge states. We show that this phase is associated with a novel
$Z_2$ topological invariant, which distinguishes it from an ordinary insulator.
The $Z_2$ classification, which is defined for time reversal invariant
Hamiltonians, is analogous to the Chern number classification of the quantum
Hall effect. We establish the $Z_2$ order of the QSH phase in the two band
model of graphene and propose a generalization of the formalism applicable to
multi band and interacting systems.
|
We investigate the influence of the helical compactification of spatial
dimension on the local properties of the vacuum state for a charged scalar
field with general curvature coupling parameter. A general background geometry
is considered with rotational symmetry in the subspace with the coordinates
appearing in the helical periodicity condition. It is shown that by a
coordinate transformation the problem is reduced to the problem with standard
quasiperiodicity condition in the same local geometry and with the effective
compactification radius determined by the length of the compact dimension and
the helicity parameter. As an application of the general procedure we have
considered locally de Sitter spacetime with a helical compact dimension. By
using the Hadamard function for the Bunch-Davies vacuum state, the vacuum
expectation values of the field squared, current density, and energy-momentum
tensor are studied. The topological contributions are explicitly separated and
their asymptotics are described at early and late stages of cosmological
expansion. An important difference, compared to the problem with quasiperiodic
conditions, is the appearance of the nonzero off-diagonal component of the
energy-momentum tensor and of the component of the current density along the
uncompact dimension.
|
Video summarization aims at choosing parts of a video that narrate a story as
close as possible to the original one. Most of the existing video summarization
approaches focus on hand-crafted labels. As the number of videos grows
exponentially, there emerges an increasing need for methods that can learn
meaningful summarizations without labeled annotations. In this paper, we aim to
maximally exploit unsupervised video summarization while concentrating the
supervision to a few, personalized labels as an add-on. To do so, we formulate
the key requirements for the informative video summarization. Then, we propose
contrastive learning as the answer to both questions. To further boost
Contrastive video Summarization (CSUM), we propose to contrast top-k features
instead of a mean video feature as employed by the existing method, which we
implement with a differentiable top-k feature selector. Our experiments on
several benchmarks demonstrate, that our approach allows for meaningful and
diverse summaries when no labeled data is provided.
|
Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and
angularly localized wavefunctions for them are found. By combining a few low
angular momentum states, one can construct a quantum state whose spatial
density is close to that of the classical Skyrmion, and has the same
symmetries. For the B=1 case we find the best localized wavefunction among
linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we
find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced
localization compared to the classical solution. For B=4, where the classical
Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by
combining the $j=0$ ground state with the lowest rotationally excited $j=4$
state. We use the rational map approximation to compare the classical and
quantum baryon densities in the B=2 and B=4 cases.
|
The CDF collaboration recently reported a measurement of the $W$-bosos mass,
$M_W$, showing a large positive deviation from the Standard Model (SM)
prediction. The question arises whether extensions of the SM exist that can
accommodate such large values, and what further phenomenological consequences
arise from this. We give a brief review of the implications of the new CDF
measurement on the SM, as well as on Higgs-sector extensions. In particular, we
review the compatibility of the $M_W$ measurement of CDF with excesses observed
in the light Higgs-boson searches at $\sim 95$ GeV, as well as with the Minimal
Supersymmetric Standard Model in conjunction with the anomalous magnetic moment
of the muon, $(g-2)_\mu$.
|
Even with the recent advances in convolutional neural networks (CNN) in
various visual recognition tasks, the state-of-the-art action recognition
system still relies on hand crafted motion feature such as optical flow to
achieve the best performance. We propose a multitask learning model
ActionFlowNet to train a single stream network directly from raw pixels to
jointly estimate optical flow while recognizing actions with convolutional
neural networks, capturing both appearance and motion in a single model. We
additionally provide insights to how the quality of the learned optical flow
affects the action recognition. Our model significantly improves action
recognition accuracy by a large margin 31% compared to state-of-the-art
CNN-based action recognition models trained without external large scale data
and additional optical flow input. Without pretraining on large external
labeled datasets, our model, by well exploiting the motion information,
achieves competitive recognition accuracy to the models trained with large
labeled datasets such as ImageNet and Sport-1M.
|
We present a new two-parameter family of solutions of Einstein gravity with
negative cosmological constant in 2+1 dimensions. These solutions are obtained
by squashing the anti-de Sitter geometry along one direction and posses four
Killing vectors. Global properties as well as the four dimensional
generalization are discussed, followed by the investigation of the geodesic
motion. A simple global embedding of these spaces as the intersection of four
quadratic surfaces in a seven dimensional space is obtained. We argue also that
these geometries describe the boundary of a four dimensional nutty-bubble
solution and are relevant in the context of AdS/CFT correspondence.
|
Starting from a factorization theorem in effective field theory, we present
resummed results for two non-global observables: the invariant-mass
distribution of jets and the energy distribution outside jets. Our results
include the full next-to-leading-order corrections to the hard, jet and soft
functions and are implemented in a parton-shower framework which generates the
renormalization-group running in the effective theory. The inclusion of these
matching corrections leads to an improved description of the data and reduced
theoretical uncertainties. They will have to be combined with two-loop running
in the future, but our results are an important first step towards the
higher-logarithmic resummation of non-global observables.
|
Based on the principle of the Lorentz covariance the transition matrix
elements from an off-shell photon state to the vacuum are decomposed into the
light-cone photon DAs, in which only two transversal DAs survive in the
on-shell limit. The eight off-shell light-cone photon distribution amplitudes
(DAs) corresponding to chiral-odd and chiral-even up to twist-four and the
corresponding coupling constants are studied systematically in the instanton
vacuum model of quantum chromodynamics (QCD). The various individual photon DA
multiplied by its corresponding coupling constant is expressed in terms of the
correlation functions, which are connected with the spectral densities of an
effective quark propagator, and then evaluated in the low-energy effective
theory derived from the instanton vacuum model of QCD. The explicit analytical
expressions and the numerical results for the photon DAs and their coupling
constants are given.
|
The Narrow-line Seyfert I galaxy, 1H0707-495, has been well observed in the
0.3-10 keV band, revealing a dramatic drop in flux in the iron K alpha band, a
strong soft excess, and short timescale reverberation lags associated with
these spectral features. In this paper, we present the first results of a deep
250 ks NuSTAR observation of 1H0707-495, which includes the first sensitive
observations above 10 keV. Even though the NuSTAR observations caught the
source in an extreme low-flux state, the Compton hump is still significantly
detected. NuSTAR, with its high effective area above 7 keV, clearly detects the
drop in flux in the iron K alpha band, and by comparing these observations with
archival XMM-Newton observations, we find that the energy of this drop
increases with increasing flux. We discuss possible explanations for this, the
most likely of which is that the drop in flux is the blue wing of the
relativistically broadened iron K alpha emission line. When the flux is low,
the coronal source height is low, thus enhancing the most gravitationally
redshifted emission.
|
We derive a formalism to describe the scattering of polarized radiation over
the full spectral range encompassed by atomic transitions belonging to the same
spectral series (e.g., the H I Lyman and Balmer series, the UV multiplets of Fe
I and Fe II). This allows us to study the role of radiation-induced coherence
among the upper terms of the spectral series, and its contribution to Rayleigh
scattering and the polarization of the solar continuum. We rely on previous
theoretical results for the emissivity of a three-term atom of the
$\Lambda$-type taking into account partially coherent scattering, and
generalize its expression in order to describe a "multiple $\Lambda$" atomic
system underlying the formation of a spectral series. Our study shows that
important polarization effects must be expected because of the combined action
of partial frequency redistribution and radiation-induced coherence among the
terms of the series. In particular, our model predicts the correct asymptotic
limit of 100% polarization in the far wings of a \emph{complete} (i.e., $\Delta
L=0,\pm 1$) group of transitions, which must be expected on the basis of the
principle of spectroscopic stability.
|
Modeling groundwater levels continuously across California's Central Valley
(CV) hydrological system is challenging due to low-quality well data which is
sparsely and noisily sampled across time and space. The lack of consistent well
data makes it difficult to evaluate the impact of 2017 and 2019 wet years on CV
groundwater following a severe drought during 2012-2015. A novel machine
learning method is formulated for modeling groundwater levels by learning from
a 3D lithological texture model of the CV aquifer. The proposed formulation
performs multivariate regression by combining Gaussian processes (GP) and deep
neural networks (DNN). The hierarchical modeling approach constitutes training
the DNN to learn a lithologically informed latent space where non-parametric
regression with GP is performed. We demonstrate the efficacy of GP-DNN
regression for modeling non-stationary features in the well data with fast and
reliable uncertainty quantification, as validated to be statistically
consistent with the empirical data distribution from 90 blind wells across CV.
We show how the model predictions may be used to supplement hydrological
understanding of aquifer responses in basins with irregular well data. Our
results indicate that on average the 2017 and 2019 wet years in California were
largely ineffective in replenishing the groundwater loss caused during previous
drought years.
|
For every positive integer $n$, an infinite family of positive integral
solutions of the diophantine equation $x^n - y^n = z^{n+1}$ is constructed.
|
We propose a unified model combining the first-order liquid-liquid and the
second-order ferroelectric phase transitions models and explaining various
features of the $\lambda$-point of liquid water within a single theoretical
framework. It becomes clear within the proposed model that not only does the
long-range dipole-dipole interaction of water molecules yield a large value of
dielectric constant $\epsilon$ at room temperatures, our analysis shows that
the large dipole moment of the water molecules also leads to a ferroelectric
phase transition at a temperature close to the lambda-point. Our more refined
model suggests that the phase transition occurs only in the low density
component of the liquid and is the origin of the singularity of the dielectric
constant recently observed in experiments with supercooled liquid water at
temperature T~233K. This combined model agrees well with nearly every available
set of experiments and explains most of the well-known and even recently
obtained results of MD simulations.
|
We consider the statics and dynamics of distinguishable spin-1/2 systems on
an arbitrary graph G with N vertices. In particular, we consider systems of
quantum spins evolving according to one of two hamiltonians: (i) the XY
hamiltonian H_XY, which contains an XY interaction for every pair of spins
connected by an edge in G; and (ii) the Heisenberg hamiltonian H_Heis, which
contains a Heisenberg interaction term for every pair of spins connected by an
edge in G. We find that the action of the XY (respectively, Heisenberg)
hamiltonian on state space is equivalent to the action of the adjacency matrix
(respectively, combinatorial laplacian) of a sequence G_k, k=0,..., N of graphs
derived from G (with G_1=G). This equivalence of actions demonstrates that the
dynamics of these two models is the same as the evolution of a free particle
hopping on the graphs G_k. Thus we show how to replace the complicated dynamics
of the original spin model with simpler dynamics on a more complicated
geometry. A simple corollary of our approach allows us to write an explicit
spectral decomposition of the XY model in a magnetic field on the path
consisting of N vertices. We also use our approach to utilise results from
spectral graph theory to solve new spin models: the XY model and heisenberg
model in a magnetic field on the complete graph.
|
Kinetics of silicon dry oxidation are investigated theoretically and
experimentally at low temperature in the nanometer range where the limits of
the Deal and Grove model becomes critical. Based on a fine control of the
oxidation process conditions, experiments allow the investigation of the growth
kinetics of nanometric oxide layer. The theoretical model is formulated using a
reaction rate approach. In this framework, the oxide thickness is estimated
with the evolution of the various species during the reaction. Standard
oxidation models and the reaction rate approach are confronted with these
experiments. The interest of the reaction rate approach to improve silicon
oxidation modeling in the nanometer range is clearly demonstrated.
|
The Atlantic Meridional Overturning Circulation (AMOC) distributes heat and
salt into the Northern Hemisphere via a warm surface current toward the
subpolar North Atlantic, where water sinks and returns southwards as a deep
cold current. There is substantial evidence that the AMOC has slowed down over
the last century. We introduce a conceptual box model for the evolution of
salinity and temperature on the surface of the North Atlantic Ocean, subject to
the influx of meltwater from the Greenland ice sheets. Our model, which extends
a model due to Welander, describes the interaction between a surface box and a
deep-water box of constant temperature and salinity, which may be convective or
non-convective, depending on the density difference. Its two main parameters
$\mu$ and $\eta$ describe the influx of freshwater and the threshold density
between the two boxes, respectively.
We use bifurcation theory to analyse two cases of the model: instantaneous
switching between convective or non-convective interaction, where the system is
piecewise-smooth (PWS), and the full smooth model with more gradual switching.
For the PWS model we derive analytical expressions for all bifurcations. The
resulting bifurcation diagram in the $(\mu,\eta)$-plane identifies all regions
of possible dynamics, which we show as phase portraits - both at typical
parameter points, as well as at the different transitions between them. We also
present the bifurcation diagram for the case of smooth switching and show how
it arises from that of the PWS case. In this way, we determine exactly where
one finds bistability and self-sustained oscillations of the AMOC in both
versions of the model. In particular, our results show that oscillations
between temperature and salinity on the surface North Atlantic Ocean disappear
completely when the transition between the convective and non-convective
regimes is too slow.
|
We present a new scheme of compact Rubidium cold-atom clock which performs
the diffuse light cooling, the microwave interrogation and the detection of the
clock signal in a cylindrical microwave cavity. The diffuse light is produced
by the reflection of the laser light at the inner surface of the microwave
cavity. The pattern of injected laser beams is specially designed to make most
of the cold atoms accumulate in the center of the microwave cavity. The
microwave interrogation of cold atoms in the cavity leads to Ramsey fringes
whose line-width is 24.5 Hz and the contrast of 95.6% when the free evolution
time is 20 ms. The frequency stability of $7.3\times10^{-13}\tau^{-1/2}$ has
been achieved recently. The scheme of this physical package can largely reduce
the complexity of the cold atom clock, and increase the performance of the
clock.
|
We introduce Bayesian Estimation Applied to Multiple Species (BEAMS), an
algorithm designed to deal with parameter estimation when using contaminated
data. We present the algorithm and demonstrate how it works with the help of a
Gaussian simulation. We then apply it to supernova data from the Sloan Digital
Sky Survey (SDSS), showing how the resulting confidence contours of the
cosmological parameters shrink significantly.
|
We perform an analysis of the $b\to c\tau\nu$ data, including $R(D^{(*)})$,
$R(J/\psi)$, $P_\tau(D^{*})$ and $F_L^{D^*}$, within and beyond the Standard
Model (SM). We fit the $B\to D^{(*)}$ hadronic form factors in the HQET
parametrization to the lattice and the light-cone sum rule (LCSR) results,
applying the general strong unitarity bounds corresponding to $J^P=1^-$, $1^+$,
$0^-$ and $0^+$. Using the obtained HQET relations between helicity amplitudes,
we give the strong unitarity bounds on individual helicity amplitudes, which
can be used in the BGL fits. Using the fitted form factors and taking into
account the most recent Belle measurement of $R(D^{(*)})$ we investigate the
model-independent and the leptoquark model explanations of the $b\to c\tau\nu$
anomalies. Specifically, we consider the one-operator, the two-operator new
physics (NP) scenarios and the NP models with a single $R_2$, $S_1$ or $U_1$
leptoquark which is supposed to be able to address the $b\to c\tau\nu$
anomalies, and our results show that the $R_2$ leptoquark model is in tension
with the limit $\mathcal B(B_c\to \tau\nu)<10\%$. Furthermore, we give
predictions for the various observables in the SM and the NP
scenarios/leptoquark models based on the present form factor study and the
analysis of NP.
|
The Wronski map is a finite, PGL_2(C)-equivariant morphism from the
Grassmannian Gr(d,n) to a projective space (the projectivization of a vector
space of polynomials). We consider the following problem. If C_r < PGL_2(C) is
a cyclic subgroup of order r, how may C_r-fixed points are in the in a fibre of
the Wronski map over a C_r-fixed point in the base?
In this paper, we compute a general answer in terms of r-ribbon tableaux.
When r=2, this computation gives the number of real points in the fibre of the
Wronski map over a real polynomial with purely imaginary roots. More generally,
we can compute the number of real points in certain intersections of Schubert
varieties.
When r divides d(n-d) our main result says that the generic number of
C_r-fixed points in the fibre is the number of standard r-ribbon tableaux
rectangular shape (n-d)^d. Computing by a different method, we show that the
answer in this case is also given by the number of of standard Young tableaux
of shape (n-d)^d that are invariant under N/r iterations of jeu de taquin
promotion. Together, these two results give a new proof of Rhoades' cyclic
sieving theorem for promotion on rectangular tableaux.
We prove analogous results for dihedral group actions.
|
We use a tunable laser ARPES to study the electronic properties of the
prototypical multiband BCS superconductor MgB2. Our data reveal a strong
renormalization of the dispersion (kink) at ~65 meV, which is caused by
coupling of electrons to the E2g phonon mode. In contrast to cuprates, the 65
meV kink in MgB2 does not change significantly across Tc. More interestingly,
we observe strong coupling to a second, lower energy collective mode at binding
energy of 10 meV. This excitation vanishes above Tc and is likely a signature
of the elusive Leggett mode.
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The Gerda experiment designed to search for the neutrinoless double beta
decay in 76Ge has successfully completed the first data collection. No signal
excess is found, and a lower limit on the half life of the process is set, with
T1/2 > 2.1x10^25 yr (90% CL). After a review of the experimental setup and of
the main Phase I results, the hardware upgrade for Gerda Phase II is described,
and the physics reach of the new data collection is reported.
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We introduce SODA, a self-supervised diffusion model, designed for
representation learning. The model incorporates an image encoder, which
distills a source view into a compact representation, that, in turn, guides the
generation of related novel views. We show that by imposing a tight bottleneck
between the encoder and a denoising decoder, and leveraging novel view
synthesis as a self-supervised objective, we can turn diffusion models into
strong representation learners, capable of capturing visual semantics in an
unsupervised manner. To the best of our knowledge, SODA is the first diffusion
model to succeed at ImageNet linear-probe classification, and, at the same
time, it accomplishes reconstruction, editing and synthesis tasks across a wide
range of datasets. Further investigation reveals the disentangled nature of its
emergent latent space, that serves as an effective interface to control and
manipulate the model's produced images. All in all, we aim to shed light on the
exciting and promising potential of diffusion models, not only for image
generation, but also for learning rich and robust representations.
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We review some recent results obtained in studying superspace formulations of
2D N=(4,4) matter-coupled supergravity. For a superspace geometry described by
the minimal supergravity multiplet, we first describe how to reduce to
components the chiral integral by using ``ectoplasm'' superform techniques as
in arXiv:0907.5264 and then we review the bi-projective superspace formalism
introduced in arXiv:0911.2546. After that, we elaborate on the curved
bi-projective formalism providing a new result: the solution of the covariant
type-I twisted multiplet constraints in terms of a weight-(-1,-1) bi-projective
superfield.
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Magnetic skyrmions are nanoscale spin textures touted as next-generation
computing elements. When subjected to lateral currents, skyrmions move at
considerable speeds. Their topological charge results in an additional
transverse deflection known as the skyrmion Hall effect (SkHE). While
promising, their dynamic phenomenology with current, skyrmion size, geometric
effects and disorder remain to be established. Here we report on the ensemble
dynamics of individual skyrmions forming dense arrays in Pt/Co/MgO wires by
examining over 20,000 instances of motion across currents and fields. The
skyrmion speed reaches 24 m/s in the plastic flow regime and is surprisingly
robust to positional and size variations. Meanwhile, the SkHE saturates at
$\sim 22^\circ$, is substantially reshaped by the wire edge, and crucially
increases weakly with skyrmion size. Particle model simulations suggest that
the SkHE size dependence - contrary to analytical predictions - arises from the
interplay of intrinsic and pinning-driven effects. These results establish a
robust framework to harness SkHE and achieve high-throughput skyrmion motion in
wire devices.
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This short note considers the effects of quantum theory on the linear
evolution of the magnetic fields during and after inflation. The analysis
appears to show that the magnetic fields decay exponentially in the
high-temperature radiation era due to a combination of ohmic dissipation and
vacuum polarisation.
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Sensitivity analysis (SA) is a procedure for studying how sensitive are the
output results of large-scale mathematical models to some uncertainties of the
input data. The models are described as a system of partial differential
equations. Often such systems contain a large number of input parameters.
Obviously, it is important to know how sensitive is the solution to some
uncontrolled variations or uncertainties in the input parameters of the model.
Algorithms based on analysis of variances technique (ANOVA) for calculating
numerical indicators of sensitivity and computationally efficient Monte Carlo
integration techniques have recently been developed by the authors. They have
been successfully applied to sensitivity studies of air pollution levels
calculated by the Unified Danish Eulerian Model (UNI-DEM) with respect to
several important input parameters. In this paper a comprehensive theoretical
and experimental study of the Monte Carlo algorithm based on
\textit{symmetrised shaking} of Sobol sequences has been done. It has been
proven that this algorithm has an optimal rate of convergence for functions
with continuous and bounded second derivatives in terms of probability and mean
square error. Extensive numerical experiments with Monte Carlo, quasi-Monte
Carlo (QMC) and scrambled quasi-Monte Carlo algorithms based on Sobol sequences
are performed to support the theoretical studies and to analyze applicability
of the algorithms to various classes of problems. The numerical tests show that
the Monte Carlo algorithm based on \textit{symmetrised shaking} of Sobol
sequences gives reliable results for multidimensional integration problems
under consideration.
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The amount of screening of a proton in a metal, migrating under the influence
of an applied electric field, is calculated using different theoretical
formulations. First the lowest order screening expression derived by Sham
(1975) is evaluated. In addition 'exact' expressions are evaluated which were
derived according to different approaches. For a proton in a metal modeled as a
jellium the screening appears to be 15 +/- 10 %, which is neither negligible
not reconcilable with the controversial full-screening point of view of
Bosvieux and Friedel (1962). In reconsidering the theory of electromigration, a
new simplified linear-response expression for the driving force is shown to
lead to essentially the same result as found by Sorbello (1985), who has used a
rather complicated technique. The expressions allow for a reduction such that
only the scattering phase shifts of the migrating impurity are required.
Finally it is shown that the starting formula for the driving force of Bosvieux
and Friedel leads exactly to the zero-temperature limit of well-established
linear response descriptions, by which the sting of the controversy has been
removed.
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We use a recently constructed linearized soliton sector perturbation theory
to calculate the form factors relevant to the elastic scattering of
ultrarelativistic mesons off of nonrelativistic kinks. Both localized kink wave
packets and also delocalized momentum eigenstate kinks are considered. In the
delocalized case, the leading term is just the classical kink solution, as was
found by Goldstone and Jackiw. The leading delocalized quantum correction
agrees with that found by Gervais, Jevicki and Sakita in the $\phi^4$ model and
Weisz in the Sine-Gordon model. In the case of localized kink wave packets,
some corrections are found which scale with the wave packet width, and so will
be relevant for the coherent scattering of mesons off of kink wave packets.
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Nuclear Star Clusters (NSCs) are often present in spiral galaxies as well as
resolved Stellar Nuclei (SNi) in elliptical galaxies centres. Ever growing
observational data indicate the existence of correlations between the
properties of these very dense central star aggregates and those of host
galaxies, which constitute a significant constraint for the validity of
theoretical models of their origin and formation. In the framework of the well
known 'migratory and merger' model for NSC and SN formation, in this paper we
obtain, first, by a simple argument the expected scaling of the NSC/SN mass
with both time and parent galaxy velocity dispersion in the case of dynamical
friction as dominant effect on the globular cluster system evolution. This
generalizes previous results by \cite{TrOsSp} and is in good agreement with
available observational data showing a shallow correlation between NSC/SN mass
and galactic bulge velocity dispersion. Moreover, we give statistical relevance
to predictions of this formation model, obtaining a set of parameters to
correlate with the galactic host parameters. We find that the correlations
between the masses of NSCs in the migratory model and the global properties of
the hosts reproduce quite well the observed correlations, supporting the
validity of the migratory-merger model. In particular, one important result is
the flattening or even decrease of the value of the NSC/SN mass obtained by the
merger model as function of the galaxy mass for high values of the galactic
mass, i.e. $\gtrsim 3\times 10^{11}$M$_\odot$, in agreement with some growing
observational evidence.
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Consider a quadratic rational self-map of the Riemann sphere such that one
critical point is periodic of period 2, and the other critical point lies on
the boundary of its immediate basin of attraction. We will give explicit
topological models for all such maps. We also discuss the corresponding
parameter picture.
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Application size and complexity are the underlying cause of numerous security
vulnerabilities in code. In order to mitigate the risks arising from such
vulnerabilities, various techniques have been proposed to isolate the execution
of sensitive code from the rest of the application and from other software on
the platform (e.g. the operating system). However, even with these partitioning
techniques, it is not immediately clear exactly how they can and should be used
to partition applications. What overall partitioning scheme should be followed;
what granularity of the partitions should be. To some extent, this is dependent
on the capabilities and performance of the partitioning technology in use. For
this work, we focus on the upcoming Intel Software Guard Extensions (SGX)
technology as the state-of-the-art in this field. SGX provides a trusted
execution environment, called an enclave, that protects the integrity of the
code and the confidentiality of the data inside it from other software,
including the operating system. We present a novel framework consisting of four
possible schemes under which an application can be partitioned. These schemes
range from coarse-grained partitioning, in which the full application is
included in a single enclave, through ultra-fine partitioning, in which each
application secret is protected in an individual enclave. We explain the
specific security benefits provided by each of the partitioning schemes and
discuss how the performance of the application would be affected. To compare
the different partitioning schemes, we have partitioned OpenSSL using four
different schemes. We discuss SGX properties together with the implications of
our design choices in this paper.
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The performance of lithium and sodium ion batteries relies notably on the
accessibility to carbon electrodes of controllable porous structure and
chemical composition. This work reports a facile synthesis of well-defined
porous N-doped carbons (NPCs) using a poly(ionic liquid) (PIL) as precursor,
and graphene oxide (GO)-stabilized poly(methyl methacrylate) (PMMA)
nanoparticles as sacrificial template. The GO-stabilized PMMA nanoparticles
were first prepared and then decorated by a thin PIL coating before
carbonization. The resulting NPCs reached a satisfactory specific surface area
of up to 561 m2/g and a hierarchically meso- and macroporous structure while
keeping a nitrogen content of 2.6 wt %. Such NPCs delivered a high reversible
charge/discharge capacity of 1013 mA h/g over 200 cycles at 0.4 A/g for lithium
ion batteries (LIBs), and showed a good capacity of 204 mA h/g over 100 cycles
at 0.1 A/g for sodium ion batteries (SIBs).
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Radar simulation is a promising way to provide data-cube with effectiveness
and accuracy for AI-based approaches to radar applications. This paper develops
a channel simulator to generate frequency-modulated continuous-wave (FMCW)
waveform multiple inputs multiple outputs (MIMO) radar signals. In the proposed
simulation framework, an open-source animation tool called Blender is utilized
to model the scenarios and render animations. The ray tracing (RT) engine
embedded can trace the radar propagation paths, i.e., the distance and signal
strength of each path. The beat signal models of time division multiplexing
(TDM)-MIMO are adapted to RT outputs. Finally, the environment-based models are
simulated to show the validation.
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The structure and elastic properties of (5,5) and (10,10) nanotubes, as well
as barriers for relative rotation of the walls and their relative sliding along
the axis in a double-walled (5,5)@(10,10) carbon nanotube, are calculated using
the density functional method. The results of these calculations are the basis
for estimating the following physical quantities: shear strengths and diffusion
coefficients for relative sliding along the axis and rotation of the walls, as
well as frequencies of relative rotational and translational oscillations of
the walls. The commensurability-incommensurability phase transition is
analyzed. The length of the incommensurability defect is estimated on the basis
of ab initio calculations. It is proposed that (5,5)@(10,10) double-walled
carbon nanotube be used as a plain bearing. The possibility of experimental
verification of the results is discussed.
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A nilspace system is a generalization of a nilsystem, consisting of a compact
nilspace X equipped with a group of nilspace translations acting on X. Nilspace
systems appear in different guises in several recent works, and this motivates
the study of these systems per se as well as their relation to more classical
types of systems. In this paper we study morphisms of nilspace systems, i.e.,
nilspace morphisms with the additional property of being consistent with the
actions of the given translations. A nilspace morphism does not necessarily
have this property, but one of our main results shows that it factors through
some other morphism which does have the property. As an application we obtain a
strengthening of the inverse limit theorem for compact nilspaces, valid for
nilspace systems. This is used in work of the first and third named authors to
generalize the celebrated structure theorem of Host and Kra on characteristic
factors.
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We investigate the spectral and timing signatures of the internal-shock model
for blazars. For this purpose, we develop a semi-analytical model for the
time-dependent radiative output from internal shocks arising from colliding
relativistic shells in a blazar jet. The emission through synchrotron and
synchrotron-self Compton (SSC) radiation as well as Comptonization of an
isotropic external radiation field are taken into account. We evaluate the
discrete correlation function (DCF) of the model light curves in order to
evaluate features of photon-energy dependent time lags and the quality of the
correlation, represented by the peak value of the DCF. The almost completely
analytic nature of our approach allows us to study in detail the influence of
various model parameters on the resulting spectral and timing features. This
paper focuses on a range of parameters in which the gamma-ray production is
dominated by Comptonization of external radiation, most likely appropriate for
gamma-ray bright flat-spectrum radio quasars (FSRQs) or low-frequency peaked BL
Lac objects (LBLs). In most cases relevant for FSRQs and LBLs, the variability
of the optical emission is highly correlated with the X-ray and high-energy
(HE: > 100 MeV) gamma-ray emission. Our baseline model predicts a lead of the
optical variability with respect to the higher-energy bands by 1 - 2 hours and
of the HE gamma-rays before the X-rays by about 1 hour. We show that variations
of certain parameters may lead to changing signs of inter-band time lags,
potentially explaining the lack of persistent trends of time lags in most
blazars.
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Many business applications involve adversarial relationships in which both
sides adapt their strategies to optimize their opposing benefits. One of the
key characteristics of these applications is the wide range of strategies that
an adversary may choose as they adapt their strategy dynamically to sustain
benefits and evade authorities. In this paper, we present a novel way of
approaching these types of applications, in particular in the context of
Anti-Money Laundering. We provide a mechanism through which diverse, realistic
and new unobserved behavior may be generated to discover potential unobserved
adversarial actions to enable organizations to preemptively mitigate these
risks. In this regard, we make three main contributions. (a) Propose a novel
behavior-based model as opposed to individual transactions-based models
currently used by financial institutions. We introduce behavior traces as
enriched relational representation to represent observed human behavior. (b) A
modelling approach that observes these traces and is able to accurately infer
the goals of actors by classifying the behavior into money laundering or
standard behavior despite significant unobserved activity. And (c) a synthetic
behavior simulator that can generate new previously unseen traces. The
simulator incorporates a high level of flexibility in the behavioral parameters
so that we can challenge the detection algorithm. Finally, we provide
experimental results that show that the learning module (automated
investigator) that has only partial observability can still successfully infer
the type of behavior, and thus the simulated goals, followed by customers based
on traces - a key aspiration for many applications today.
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Kirigami-inspired metamaterials are attracting increasing interest because of
their ability to achieve extremely large strains and shape changes via
out-of-plane buckling. While in flat kirigami sheets the ligaments buckle
simultaneously as Euler columns leading to a continuous phase transition, here
we demonstrate that kirigami shells can also support discontinuous phase
transitions. Specifically, we show via a combination of experiments, numerical
simulations and theoretical analysis that in cylindrical kirigami shells the
snapping-induced curvature inversion of the initially bent ligaments results in
a pop-up process that first localizes near an imperfection and then, as the
deformation is increased, progressively spreads through the structure. Notably,
we find that the width of the transition zone as well as the stress at which
propagation of the instability is triggered can be controlled by carefully
selecting the geometry of the cuts and the curvature of the shell. Our study
significantly expands the ability of existing kirigami metamaterials and opens
avenues for the design of the next generation of responsive surfaces, as
demonstrated by the design of a smart skin that significantly enhance the
crawling efficiency of a simple linear actuator.
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In this paper, we extend a spherical variant of the Kowalski-S\{l}odkowski
theorem due to Li, Peralta, Wang and Wang. As a corollary, we prove that every
2-local map in the set of all surjective isometries (without assuming
linearity) on a certain function space is in fact a surjective isometry. This
gives an affirmative answer to the problem on 2-local isometries posed by
Moln\'ar.
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This paper presents Generative Adversarial Talking Head (GATH), a novel deep
generative neural network that enables fully automatic facial expression
synthesis of an arbitrary portrait with continuous action unit (AU)
coefficients. Specifically, our model directly manipulates image pixels to make
the unseen subject in the still photo express various emotions controlled by
values of facial AU coefficients, while maintaining her personal
characteristics, such as facial geometry, skin color and hair style, as well as
the original surrounding background. In contrast to prior work, GATH is purely
data-driven and it requires neither a statistical face model nor image
processing tricks to enact facial deformations. Additionally, our model is
trained from unpaired data, where the input image, with its auxiliary identity
label taken from abundance of still photos in the wild, and the target frame
are from different persons. In order to effectively learn such model, we
propose a novel weakly supervised adversarial learning framework that consists
of a generator, a discriminator, a classifier and an action unit estimator. Our
work gives rise to template-and-target-free expression editing, where still
faces can be effortlessly animated with arbitrary AU coefficients provided by
the user.
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It is shown that the generation linewidth of an auto-oscillator with a
nonlinear frequency shift (i.e. an auto-oscillator in which frequency depends
on the oscillation amplitude) is substantially larger than the linewidth of a
conventional quasi-linear auto-oscillator due to the renormalization of the
phase noise caused by the nonlinearity of the oscillation frequency. The
developed theory, when applied to a spin-torque nano-contact auto-oscillator,
predicts a minimum of the generation linewidth when the nano-contact is
magnetized at a critical angle to its plane, corresponding to the minimum
nonlinear frequency shift, in good agreement with recent experiments.
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Non-autoregressive translation (NAT) achieves faster inference speed but at
the cost of worse accuracy compared with autoregressive translation (AT). Since
AT and NAT can share model structure and AT is an easier task than NAT due to
the explicit dependency on previous target-side tokens, a natural idea is to
gradually shift the model training from the easier AT task to the harder NAT
task. To smooth the shift from AT training to NAT training, in this paper, we
introduce semi-autoregressive translation (SAT) as intermediate tasks. SAT
contains a hyperparameter k, and each k value defines a SAT task with different
degrees of parallelism. Specially, SAT covers AT and NAT as its special cases:
it reduces to AT when k = 1 and to NAT when k = N (N is the length of target
sentence). We design curriculum schedules to gradually shift k from 1 to N,
with different pacing functions and number of tasks trained at the same time.
We called our method as task-level curriculum learning for NAT (TCL-NAT).
Experiments on IWSLT14 De-En, IWSLT16 En-De, WMT14 En-De and De-En datasets
show that TCL-NAT achieves significant accuracy improvements over previous NAT
baselines and reduces the performance gap between NAT and AT models to 1-2 BLEU
points, demonstrating the effectiveness of our proposed method.
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We obtain many results and solve some problems about feebly compact
paratopological groups.
We obtain necessary and sufficient conditions for such a group to be
topological. One of them is the quasiregularity. We prove that each
$2$-pseudocompact paratopological group is feebly compact and that each
Hausdorff $\sigma$-compact feebly compact paratopological group is a compact
topological group. Our particular attention concerns periodic and topologically
periodic groups.
We construct examples of various compact-like paratopological groups which
are not topological groups, among them a $T_0$ sequentially compact group, a
$T_1$ $2$-pseudocompact group, a functionally Hausdorff countably compact group
(under the axiomatic assumption that there is an infinite torsion-free abelian
countably compact topological group without non-trivial convergent sequences),
and a functionally Hausdorff second countable group sequentially pracompact
group.
We investigate cone topologies of paratopological groups which provide a
general tool to construct pathological examples, especially examples of
compact-like paratopological groups with discontinuous inversion. We find a
simple interplay between the algebraic properties of a basic cone subsemigroup
$S$ of a group $G$ and compact-like properties of two basic semigroup
topologies generated by $S$ on the group $G$.
We prove that the product of a family of feebly compact paratopological
groups is feebly compact, and that a paratopological group $G$ is feebly
compact provided it has a feebly compact normal subgroup $H$ such that a
quotient group $G/H$ is feebly compact.
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