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Hydrodynamic simulations are used to calculate the identical pion HBT radii,
as a function of the pair momentum $k_{\rm T}$. This dependence is sensitive to
the magnitude of the collective radial flow in the transverse plane, and thus
comparison to ALICE data enables us to derive its magnitude. By using hydro
solutions with variable initial parameters we conclude that in this case
fireball explosions start with a very small initial size, well below 1 ${\rm
fm}$.
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The passive approach to quantum key distribution (QKD) consists of
eliminating all optical modulators and random number generators from QKD
systems, in so reaching an enhanced simplicity, immunity to modulator side
channels, and potentially higher repetition rates. In this work, we provide
finite-key security bounds for a fully passive decoy-state BB84 protocol,
considering a passive QKD source recently presented. With our analysis, the
attainable secret key rate is comparable to that of the perfect parameter
estimation limit, in fact differing from the key rate of the active approach by
less than one order of magnitude. This demonstrates the practicality of fully
passive QKD solutions.
|
In dynamic Windows malware detection, deep learning models are extensively
deployed to analyze API sequences. Methods based on API sequences play a
crucial role in malware prevention. However, due to the continuous updates of
APIs and the changes in API sequence calls leading to the constant evolution of
malware variants, the detection capability of API sequence-based malware
detection models significantly diminishes over time. We observe that the API
sequences of malware samples before and after evolution usually have similar
malicious semantics. Specifically, compared to the original samples, evolved
malware samples often use the API sequences of the pre-evolution samples to
achieve similar malicious behaviors. For instance, they access similar
sensitive system resources and extend new malicious functions based on the
original functionalities. In this paper, we propose a frame(MME), a framework
that can enhance existing API sequence-based malware detectors and mitigate the
adverse effects of malware evolution. To help detection models capture the
similar semantics of these post-evolution API sequences, our framework
represents API sequences using API knowledge graphs and system resource
encodings and applies contrastive learning to enhance the model's encoder.
Results indicate that, compared to Regular Text-CNN, our framework can
significantly reduce the false positive rate by 13.10% and improve the F1-Score
by 8.47% on five years of data, achieving the best experimental results.
Additionally, evaluations show that our framework can save on the human costs
required for model maintenance. We only need 1% of the budget per month to
reduce the false positive rate by 11.16% and improve the F1-Score by 6.44%.
|
We obtain some equations for Hamiltonian-minimal Lagrangian surfaces in CP^2
and give their particular solutions in the case of tori.
|
We investigate a nonperturbative formulation of quantum gravity defined via
Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the
path integral. We are motivated to revisit this older formulation of dynamical
triangulations by hints from renormalization group approaches that gravity may
be asymptotically safe and by the emergence of a semiclassical phase in causal
dynamical triangulations (CDT). We study the phase diagram of this model and
identify the two phases that are well known from previous work: the branched
polymer phase and the collapsed phase. We verify that the order of the phase
transition dividing the branched polymer phase from the collapsed phase is
almost certainly first-order. The nontrivial measure term enlarges the phase
diagram, allowing us to explore a region of the phase diagram that has been
dubbed the crinkled region. Although the collapsed and branched polymer phases
have been studied extensively in the literature, the crinkled region has not
received the same scrutiny. We find that the crinkled region is likely a part
of the collapsed phase with particularly large finite-size effects.
Intriguingly, the behavior of the spectral dimension in the crinkled region at
small volumes is similar to that of CDT, as first reported in arXiv:1104.5505,
but for sufficiently large volumes the crinkled region does not appear to have
4-dimensional semiclassical features. Thus, we find that the crinkled region of
the EDT formulation does not share the good features of the extended phase of
CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent
results of arXiv:1307.2270, in which the authors used a somewhat different
discretization of EDT from the one presented here.
|
Accurate tooth identification and segmentation in Cone Beam Computed
Tomography (CBCT) dental images can significantly enhance the efficiency and
precision of manual diagnoses performed by dentists. However, existing
segmentation methods are mainly developed based on large data volumes training,
on which their annotations are extremely time-consuming. Meanwhile, the teeth
of each class in CBCT dental images being closely positioned, coupled with
subtle inter-class differences, gives rise to the challenge of indistinct
boundaries when training model with limited data. To address these challenges,
this study aims to propose a tasked-oriented Masked Auto-Encoder paradigm to
effectively utilize large amounts of unlabeled data to achieve accurate tooth
segmentation with limited labeled data. Specifically, we first construct a
self-supervised pre-training framework of masked auto encoder to efficiently
utilize unlabeled data to enhance the network performance. Subsequently, we
introduce a sparse masked prompt mechanism based on graph attention to
incorporate boundary information of the teeth, aiding the network in learning
the anatomical structural features of teeth. To the best of our knowledge, we
are pioneering the integration of the mask pre-training paradigm into the CBCT
tooth segmentation task. Extensive experiments demonstrate both the feasibility
of our proposed method and the potential of the boundary prompt mechanism.
|
For a smooth scheme $X$ over a perfect field $k$ of positive characteristic,
we define (for each $m\in\mathbb{Z}$) a sheaf of rings
$\mathcal{\widehat{D}}_{W(X)}^{(m)}$ of differential operators (of level $m$)
over the Witt vectors of $X$. If $\mathfrak{X}$ is a lift of $X$ to a smooth
formal scheme over $W(k)$, then for $m\geq0$ modules over
$\mathcal{\widehat{D}}_{W(X)}^{(m)}$ are closely related to modules over
Berthelot's ring $\widehat{\mathcal{D}}_{\mathfrak{X}}^{(m)}$ of differential
operators of level $m$ on $\mathfrak{X}$. Our construction therefore gives an
description of suitable categories of modules over these algebras, which
depends only on the special fibre $X$. There is an embedding of the category of
crystals on $X$ (over $W_{r}(k)$) into modules over
$\mathcal{\widehat{D}}_{W(X)}^{(0)}/p^{r}$; and so we obtain an alternate
description of this category as well. For a map $\varphi:X\to Y$ we develop the
formalism of pullback and pushforward of
$\mathcal{\widehat{D}}_{W(X)}^{(m)}$-modules and show all of the expected
properties. When working mod $p^{r}$, this includes compatibility with the
corresponding formalism for crystals, assuming $\varphi$ is smooth. In this
case we also show that there is a ``relative de Rham Witt resolution''
(analogous to the usual relative de Rham resolution in $\mathcal{D}$-module
theory) and therefore that the pushforward of (a quite general subcategory of)
modules over $\mathcal{\widehat{D}}_{W(X)}^{(0)}/p^{r}$ can be computed via the
reduction mod $p^{r}$ of Langer-Zink's relative de Rham Witt complex. Finally
we explain a generalization of Bloch's theorem relating integrable de Rham-Witt
connections to crystals.
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By exploiting the contact Hamiltonian dynamics $(T^*M\times\mathbb R,\Phi_t)$
around the Aubry set of contact Hamiltonian systems, we provide a relation
among the Mather set, the $\Phi_t$-recurrent set, the strongly static set, the
Aubry set, the Ma\~{n}\'{e} set and the $\Phi_t$-non-wandering set. Moreover,
we consider the strongly static set, as a new flow-invariant set between the
Mather set and the Aubry set, in the strictly increasing case. We show that
this set plays an essential role in the representation of certain minimal
forward weak KAM solution and the existence of transitive orbits around the
Aubry set.
|
The fourth industrial revolution leads to an increased use of embedded
computation and intercommunication in an industrial environment. While reducing
cost and effort for set up, operation and maintenance, and increasing the time
to operation or market respectively as well as the efficiency, this also
increases the attack surface of enterprises. Industrial enterprises have become
targets of cyber criminals in the last decade, reasons being espionage but also
politically motivated. Infamous attack campaigns as well as easily available
malware that hits industry in an unprepared state create a large threat
landscape. As industrial systems often operate for many decades and are
difficult or impossible to upgrade in terms of security, legacy-compatible
industrial security solutions are necessary in order to create a security
parameter. One plausible approach in industry is the implementation and
employment of side-channel sensors. Combining readily available sensor data
from different sources via different channels can provide an enhanced insight
about the security state. In this work, a data set of an experimental
industrial set up containing side channel sensors is discussed conceptually and
insights are derived.
|
This paper presents a design technique for obtaining regular time-invariant
low-density parity-check convolutional (RTI-LDPCC) codes with low complexity
and good performance. We start from previous approaches which unwrap a
low-density parity-check (LDPC) block code into an RTI-LDPCC code, and we
obtain a new method to design RTI-LDPCC codes with better performance and
shorter constraint length. Differently from previous techniques, we start the
design from an array LDPC block code. We show that, for codes with high rate, a
performance gain and a reduction in the constraint length are achieved with
respect to previous proposals. Additionally, an increase in the minimum
distance is observed.
|
Modularity Q is an important function for identifying community structure in
complex networks. In this paper, we prove that the modularity maximization
problem is equivalent to a nonconvex quadratic programming problem. This result
provide us a simple way to improve the efficiency of heuristic algorithms for
maximizing modularity Q. Many numerical results demonstrate that it is very
effective.
|
Let $E_\alpha \colon \mathcal{W} \to \mathbb{R}$ denote the expectation value
of the Hamiltonian of point interaction in $\mathbb{R}^3$ with inverse
scattering length $\alpha \in ]0, \infty[$ and consider an energy functional
$I_\alpha \colon \mathcal{W} \to \mathbb{R}$ of the form $$ I_\alpha (u) =
\frac{1}{2} E_\alpha (u) + T (u), $$ where $T \colon \mathcal{W} \to
\mathbb{R}$ is a given nonlinear functional. We propose a set of conditions on
$\rho$, $I_\alpha$ and $T$ under which the problem $$ I_\alpha (u) = \inf
\left\{I_\alpha (v) : \|v\|_{L^2}^2 = \rho^2\right\}; \quad \|u\|_{L^2}^2 =
\rho^2 $$ has a solution. As an application, we prove the existence of ground
states with sufficiently small mass $\rho$ for the following nonlinear problems
with a point interaction: (i) a Kirchhoff-type equation, (ii) the
Schr\"odinger--Poisson system and (iii) the Schr\"odinger--Bopp--Podolsky
system.
|
Photometric follow-ups of transiting exoplanets may lead to discoveries of
additional, less massive bodies in extrasolar systems. This is possible by
detecting and then analysing variations in transit timing of transiting
exoplanets. We present photometric observations gathered in 2009 and 2010 for
exoplanet WASP-3b during the dedicated transit-timing-variation campaign. The
observed transit timing cannot be explained by a constant period but by a
periodic variation in the observations minus calculations diagram. Simplified
models assuming the existence of a perturbing planet in the system and
reproducing the observed variations of timing residuals were identified by
three-body simulations. We found that the configuration with the hypothetical
second planet of the mass of about 15 Earth masses, located close to the outer
2:1 mean motion resonance is the most likely scenario reproducing observed
transit timing. We emphasize, however, that more observations are required to
constrain better the parameters of the hypothetical second planet in WASP-3
system. For final interpretation not only transit timing but also photometric
observations of the transit of the predicted second planet and the high
precision radial-velocity data are needed.
|
A recent HyperCP observation of three events in the decay Sigma^+ -> p mu^+
mu^- is suggestive of a new particle with mass 214.3 MeV. In order to confront
models that contain a light Higgs boson with this observation, it is necessary
to know the Higgs production rate in hyperon decay. The contribution to this
rate from penguin-like two-quark operators has been considered before and found
to be too large. We point out that there are additional four-quark
contributions to this rate that could be comparable in size with the two-quark
contributions, and that could bring the total rate to the observed level in
some models. To this effect we implement the low-energy theorems that dictate
the couplings of light Higgs bosons to hyperons at leading order in chiral
perturbation theory. We consider the cases of scalar and pseudoscalar Higgs
bosons in the standard model and in its two-Higgs-doublet extensions to
illustrate the challenges posed by existing experimental constraints and
suggest possible avenues for models to satisfy them.
|
Out-of-town recommendation is designed for those users who leave their
home-town areas and visit the areas they have never been to before. It is
challenging to recommend Point-of-Interests (POIs) for out-of-town users since
the out-of-town check-in behavior is determined by not only the user's
home-town preference but also the user's travel intention. Besides, the user's
travel intentions are complex and dynamic, which leads to big difficulties in
understanding such intentions precisely. In this paper, we propose a
TRAvel-INtention-aware Out-of-town Recommendation framework, named TRAINOR. The
proposed TRAINOR framework distinguishes itself from existing out-of-town
recommenders in three aspects. First, graph neural networks are explored to
represent users' home-town check-in preference and geographical constraints in
out-of-town check-in behaviors. Second, a user-specific travel intention is
formulated as an aggregation combining home-town preference and generic travel
intention together, where the generic travel intention is regarded as a mixture
of inherent intentions that can be learned by Neural Topic Model (NTM). Third,
a non-linear mapping function, as well as a matrix factorization method, are
employed to transfer users' home-town preference and estimate out-of-town POI's
representation, respectively. Extensive experiments on real-world data sets
validate the effectiveness of the TRAINOR framework. Moreover, the learned
travel intention can deliver meaningful explanations for understanding a user's
travel purposes.
|
Statistical tasks such as density estimation and approximate Bayesian
inference often involve densities with unknown normalising constants.
Score-based methods, including score matching, are popular techniques as they
are free of normalising constants. Although these methods enjoy theoretical
guarantees, a little-known fact is that they exhibit practical failure modes
when the unnormalised distribution of interest has isolated components -- they
cannot discover isolated components or identify the correct mixing proportions
between components. We demonstrate these findings using simple distributions
and present heuristic attempts to address these issues. We hope to bring the
attention of theoreticians and practitioners to these issues when developing
new algorithms and applications.
|
In this paper, we investigate the energy function, formation rate and
environment of fast radio bursts (FRBs) using Parkes sample and Australian
Square Kilometer Array Pathfinder (ASKAP) sample. For the first time, the
metallicity effect on the formation rate is considered. If FRBs are produced by
the mergers of compact binaries, the formation rate of FRBs should have a time
delay relative to cosmic star formation rate (CSFR). We get the time delay is
about 3-5 Gyr and the index of differential energy function $\gamma$
($dN/dE\propto E^{-\gamma}$) is between 1.6 and 2.0 from redshift cumulative
distribution. The value of $\gamma$ is similar to that of FRB 121102, which
indicates single bursts may share the same physical mechanism with the
repeaters. In another case, if the formation rate of FRB is proportional to the
SFR without time delay, the index $\gamma$ is about 2.3. In both cases, we find
that FRBs may prefer to occur in low-metallicity environment with $ 12
+\log(\rm{O/H}) \simeq 8.40$, which is similar to those of long gamma-ray
bursts (GRBs) and hydrogen-poor superluminous supernovae (SLSNe-I).
|
Coherent diffraction imaging (CDI) is high-resolution lensless microscopy
that has been applied to image a wide range of specimens using synchrotron
radiation, X-ray free electron lasers, high harmonic generation, soft X-ray
laser and electrons. Despite these rapid advances, it remains a challenge to
reconstruct fine features in weakly scattering objects such as biological
specimens from noisy data. Here we present an effective iterative algorithm,
termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction
intensities. OSS exploits the correlation information among the pixels or
voxels in the region outside of a support in real space. By properly applying
spatial frequency filters to the pixels or voxels outside the support at
different stage of the iterative process (i.e. a smoothness constraint), OSS
finds a balance between the hybrid input-output (HIO) and error reduction (ER)
algorithms to search for a global minimum in solution space, while reducing the
oscillations in the reconstruction. Both our numerical simulations with Poisson
noise and experimental data from a biological cell indicate that OSS
consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms
at all noise levels in terms of accuracy and consistency of the
reconstructions. We expect OSS to find application in the rapidly growing CDI
field as well as other disciplines where phase retrieval from noisy Fourier
magnitudes is needed.
|
In this article, we study nonlinear Vlasov equations with a smooth
interaction kernel on a compact manifold without boundary where the geodesic
flow exhibits strong chaotic behavior, known as the Anosov property. We show
that, for small initial data with finite regularity and supported away from the
null section, there exist global solutions to the nonlinear Vlasov equations
which weakly converge to an equilibrium of the free transport equation, and
whose potential strongly converges to zero, both with exponential speed.
Central to our approach are microlocal anisotropic Sobolev spaces, originally
developed for studying Pollicott-Ruelle resonances, that we further refine to
deal with the geometry of the full cotangent bundle, which paves the way to the
analysis of nonlinear Vlasov equations.
|
In this paper we study the extension of structure group of principal bundles
with a reductive algebraic group as structure group on smooth projective
varieties defined over algebraically closed field of positive characteristic.
Our main result is to show that given a representation {\rho} of a reductive
algebraic group G, there exists an integer t such that any semistable G-bundle
whose first t frobenius pullbacks are semistable induces a semistable vector
bundle on extension of structure group via {\rho}. Moreover we quantify the
number of such frobenius pullbacks required.
|
We present an analytical model of the relation between the surface density of
gas and star formation rate in galaxies and clouds, as a function of the
presence of supersonic turbulence and the associated structure of the
interstellar medium. The model predicts a power-law relation of index 3/2,
flattened under the effects of stellar feedback at high densities or in very
turbulent media, and a break at low surface densities when ISM turbulence
becomes too weak to induce strong compression. This model explains the
diversity of star formation laws and thresholds observed in nearby spirals and
their resolved regions, the Small Magellanic Cloud, high-redshift disks and
starbursting mergers, as well as Galactic molecular clouds. While other models
have proposed interstellar dust content and molecule formation to be key
ingredients to the observed variations of the star formation efficiency, we
demonstrate instead that these variations can be explained by interstellar
medium turbulence and structure in various types of galaxies.
|
Negative piezoelectrics contract in the direction of applied electric field,
which are opposite to normal piezoelectrics and rare in dielectric materials.
The raising of low dimensional ferroelectrics, with unconventional mechanisms
of polarity, opens a fertile branch for candidates with prominent negative
piezoelectricity. Here, the distorted $\alpha$-Bi monolayer, a newly-identified
elementary ferroelectric with puckered black phosphorous-like structure [J.
Guo, {\it et al}. Nature \textbf{617}, 67 (2023)], is computationally studied,
which manifests a large negative in-plane piezoelectricity (with
$d_{33}\sim-26$ pC/N). Its negative piezoelectricity originates from its unique
buckling ferroelectric mechanism, namely the inter-column sliding.
Consequently, a moderate tensile strain can significantly reduce its
ferroelectric switching energy barrier, while the compressive strain can
significantly enhance its prominent nonlinear optical response. The physical
mechanism of in-plane negative piezoelectricity also applies to other
elementary ferroeletric monolayers.
|
We introduce a method based on matrix product states (MPS) for computing
spectral functions of (quasi) one-dimensional spin chains, working directly in
momentum space in the thermodynamic limit. We simulate the time evolution after
applying a momentum operator to an MPS ground state by working with the
momentum superposition of a window MPS. We show explicitly for the spin-1
Heisenberg chain that the growth of entanglement is smaller in momentum space,
even inside a two-particle continuum, such that we can attain very accurate
spectral functions with relatively small bond dimension. We apply our method to
compute spectral lineshapes of the gapless XXZ chain and the square-lattice
J1-J2 Heisenberg model on a six-leg cylinder.
|
We present an update to the NNLL RG-improved QCD prediction of top-antitop
production in electron-positron annihilation at threshold. It includes for the
first time a complete NNLL resummation of ultrasoft logarithms, which are
dominant at this order and give a sizable correction. The renormalization scale
dependence of the total resonance cross section decreases substantially
compared to earlier predictions, where the ultrasoft logarithms were included
only partially.
|
Signal transmission at the molecular level in many biological complexes
occurs through allosteric transitions. They describe the response a complex to
binding of ligands at sites that are spatially well separated from the binding
region. We describe the Structural Perturbation Method (SPM), based on phonon
propagation in solids, that can be used to determine the signal transmitting
allostery wiring diagram (AWD) in large but finite-sized biological complexes.
Applications to the bacterial chaperonin GroEL-GroES complex shows that the AWD
determined from structures also drive the allosteric transitions dynamically.
Both from a structural and dynamical perspective these transitions are largely
determined by formation and rupture of salt-bridges. The molecular description
of allostery in GroEL provides insights into its function, which is
quantitatively described by the Iterative Annealing Mechanism. Remarkably, in
this complex molecular machine, a deep connection is established between the
structures, reaction cycle during which GroEL undergoes a sequence of
allosteric transitions, and function in a self-consistent manner.
|
The type-I intermittency route to (or out of) chaos is investigated within
the Horizontal Visibility graph theory. For that purpose, we address the
trajectories generated by unimodal maps close to an inverse tangent bifurcation
and construct, according to the Horizontal Visibility algorithm, their
associated graphs. We show how the alternation of laminar episodes and chaotic
bursts has a fingerprint in the resulting graph structure. Accordingly, we
derive a phenomenological theory that predicts quantitative values of several
network parameters. In particular, we predict that the characteristic power law
scaling of the mean length of laminar trend sizes is fully inherited in the
variance of the graph degree distribution, in good agreement with the numerics.
We also report numerical evidence on how the characteristic power-law scaling
of the Lyapunov exponent as a function of the distance to the tangent
bifurcation is inherited in the graph by an analogous scaling of the block
entropy over the degree distribution. Furthermore, we are able to recast the
full set of HV graphs generated by intermittent dynamics into a renormalization
group framework, where the fixed points of its graph-theoretical RG flow
account for the different types of dynamics. We also establish that the
nontrivial fixed point of this flow coincides with the tangency condition and
that the corresponding invariant graph exhibit extremal entropic properties.
|
The aim of this paper is to examine the effects of the horizontal turbulence
in differentially rotating stars on the GSF instability and apply our results
to pre-supernova models. For this purpose we derive the expression for the GSF
instability with account of the thermal transport and smoothing of the
mu-gradient by the horizontal turbulence. We apply the new expressions in
numerical models of a 20 solar mass star. We show that if N^2_{Omega} < 0 the
Rayleigh-Taylor instability cannot be killed by the stabilizing thermal and
mu-gradients, so that the GSF instability is always there and we derive the
corresponding diffusion coefficient. The GSF instability grows towards the very
latest stages of stellar evolution. Close to the deep convective zones in
pre-supernova stages, the transport coefficient of elements and angular
momentum by the GSF instability can very locally be larger than the shear
instability and even as large as the thermal diffusivity. However the zones
over which the GSF instability is acting are extremely narrow and there is not
enough time left before the supernova explosion for a significant mixing to
occur. Thus, even when the inhibiting effects of the mu-gradient are reduced by
the horizontal turbulence, the GSF instability remains insignificant for the
evolution. We conclude that the GSF instability in pre-supernova stages cannot
be held responsible for the relatively low rotation rate of pulsars compared to
the predictions of rotating star models.
|
In this paper, we study the parameterized complexity of a generalized
domination problem called the [${\sigma}, {\rho}$] Dominating Set problem. This
problem generalizes a large number of problems including the Minimum Dominating
Set problem and its many variants. The parameterized complexity of the
[${\sigma}, {\rho}$] Dominating Set problem parameterized by treewidth is well
studied. Here the properties of the sets ${\sigma}$ and ${\rho}$ that make the
problem tractable are identified [1]. We consider a larger parameter and
investigate the existence of polynomial sized kernels. When ${\sigma}$ and
${\rho}$ are finite, we identify the exact condition when the [${\sigma},
{\rho}$] Dominating Set problem parameterized by vertex cover admits polynomial
kernels. Our lower and upper bound results can also be extended to more general
conditions and provably smaller parameters as well.
|
In this paper we treat Grothendieck Duality for noetherian rings via rigid
dualizing complexes. In particular, we prove that every ring, essentially
finite type over a regular base ring, has a unique rigid dualizing complex. The
rigid dualizing complexes have strong functorial properties, allowing us to
construct the twisted induction pseudofunctor, which is our ring-theoretic
version of the twisted inverse pseudofunctor $f^{!}$. This is the first article
of a bigger project, whose final goal is establishing Grothendieck Duality,
including global duality for proper maps, for Deligne-Mumford stacks.
|
The understanding of the Physics underlying the performances of organic
spin-valve devices is still incomplete. According to some recent models, spin
transport takes place in an impurity band inside the fundamental gap of organic
semiconductors. This seems to be confirmed by recent experiments performed with
La$_{0.7}$Sr$_{0.3}$MnO$_3$/Alq$_3$/AlO$_x$/Co devices. The reported results
suggest a possible correlation between the magnetoresistance and the variable
oxygen doping in the Alq$_3$ spacer. In this paper we investigate by means of
first-principles calculations the electronic and magnetic properties of O$_2$
molecules and ions in Alq$_3$ films to establish whether oxygen plays any
important role for spin transport in
La$_{0.7}$Sr$_{0.3}$MnO$_3$/Alq$_3$/AlO$_x$/Co devices. The conclusion is that
it does not. In fact, we show that O$_2$ molecules do not form an impurity band
and there is no magnetic interaction between them. In contrast, we suggest that
spin-transport may be enabled by the direct exchange coupling between Alq$_3^-$
ions.
|
Nikolai Durov introduced the theory of generalized rings and schemes to study
Arakelov geometry in an alternative algebraic framework, and introduced the
residue field at the infinite place. We show an elementary algebraic approach
to modules and algebras over this object, define prime congruences, show that
the polynomial ring of n variables is of Krull dimension n, and derive a prime
decomposition theorem for these primes.
|
Annihilating dark matter (DM) models offer promising avenues for future DM
detection, in particular via modification of astrophysical signals. However
when modelling such potential signals at high redshift the emergence of both
dark matter and baryonic structure, as well as the complexities of the energy
transfer process, need to be taken into account. In the following paper we
present a detailed energy deposition code and use this to examine the energy
transfer efficiency of annihilating dark matter at high redshift, including the
effects on baryonic structure. We employ the PYTHIA code to model
neutralino-like DM candidates and their subsequent annihilation products for a
range of masses and annihilation channels. We also compare different density
profiles and mass-concentration relations for 10^5-10^7 M_sun haloes at
redshifts 20 and 40. For these DM halo and particle models, we show radially
dependent ionisation and heating curves and compare the deposited energy to the
haloes' gravitational binding energy. We use the "filtered" annihilation
spectra escaping the halo to calculate the heating of the circumgalactic medium
and show that the mass of the minimal star forming object is increased by a
factor of 2-3 at redshift 20 and 4-5 at redshift 40 for some DM models.
|
We consider the effects of particle transport in the topological
defect-mediated electroweak baryogenesis scenarios of Ref. 1. We analyze the
cases of both thin and thick defects and demonstrate an enhancement of the
original mechanism in both cases due to an increased effective volume in which
baryogenesis occurs. This phenomenon is a result of imperfect cancellation
between the baryons and antibaryons produced on opposite faces of the defect.
|
We argue that the effective pion mass in nuclear matter obtained from chiral
effective lagrangians is unique and does not depend on off-mass-shell
extensions of the pion fields as e.g. the PCAC choice. The effective pion mass
in isospin symmetric nuclear matter is predicted to increase slightly with
increasing nuclear density, whereas the effective time-like pion decay constant
and the magnitude of the density-dependent quark condensate decrease
appreciably. The in-medium Gell-Mann-Oakes-Renner relation as well as other
in-medium identities are studied in addition. Finally, several constraints on
effective lagrangians for the description of the pion propagation in isospin
symmetric, isotropic and homogenous nuclear matter are discussed. (Talk
presented at the workshop ``Hirschegg '95: Hadrons in Nuclear Matter'',
Hirschegg, Kleinwalsertal, Austria, January 16-21, 1995)
|
We establish an interesting upper bound for the moments of truncated
Dirichlet convolution of M\"obius function, a function noted $M(n,z)$. Our
result implies that $M(n,j)$ is usually quite small for $j \in \{1,\dots,n\}$.
Also, we establish an estimate for the multiplicative energy of the set of
divisors of an integer $n$.
|
Let $M$ denote a finitely generated module over a Noetherian ring $R$. For an
ideal $I \subset R$ there is a study of the endomorphisms of the local
cohomology module $H^g_I(M), g = \operatorname{grade} (I,M),$ and related
results. Another subject is the study of left derived functors of the $I$-adic
completion $\Lambda^I_i(H^g_I(M))$, motivated by a characterization of
Gorenstein rings given in the book by Simon and the author. This provides
another Cohen-Macaulay criterion. The results are illustrated by several
examples. There is also an extension to the case of homomorphisms of two
different local cohomology modules.
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We have obtained improved spectra of key fundamental band lines of H3+,
R(1,1)l, R(3,3)l, and R(2,2)l, and ro-vibrational transitions of CO on
sightlines toward the luminous infrared sources GCIRS 3 and GCIRS 1W, each
located in the Central Cluster of the Galactic center within several arcseconds
of Sgr A*. The spectra reveal absorption occurring in three kinds of gaseous
environments: (1) cold dense and diffuse gas associated with foreground
spiral/lateral arms; (2) warm and diffuse gas absorbing over a wide and mostly
negative velocity range, which appears to fill a significant fraction of the
Galaxy's Central Molecular Zone (CMZ); and (3) warm, dense and compact clouds
with velocities near +50 km s^-1 probably within 1-2 pc of the center. The
absorptions by the first two cloud types are nearly identical for all the
sources in the Central Cluster, and are similar to those previously observed on
sightlines from Sgr A* to 30 pc east of it. Cloud type (3), which has only been
observed toward the Central Cluster, shows distinct differences between the
sightlines to GCIRS 3 and GCIRS 1W, which are separated on the sky by only 0.33
pc in projection. We identify this material as part of an inward extension of
the Circumnuclear Disk previously known from HCN mapping. Lower limits on the
products of the hydrogen ionization rate zeta and the path length L are 2.3 x
10^5 cm s^-1 and 1.5 x 10^3 cm s^-1 for the warm and diffuse CMZ gas and for
the warm and dense clouds in the core, respectively. The limits indicate that
the ionization rates in these regions are well above 10^-15 s^-1.
|
This tutorial aims to introduce the fundamentals of adversarial robustness of
deep learning, presenting a well-structured review of up-to-date techniques to
assess the vulnerability of various types of deep learning models to
adversarial examples. This tutorial will particularly highlight
state-of-the-art techniques in adversarial attacks and robustness verification
of deep neural networks (DNNs). We will also introduce some effective
countermeasures to improve the robustness of deep learning models, with a
particular focus on adversarial training. We aim to provide a comprehensive
overall picture about this emerging direction and enable the community to be
aware of the urgency and importance of designing robust deep learning models in
safety-critical data analytical applications, ultimately enabling the end-users
to trust deep learning classifiers. We will also summarize potential research
directions concerning the adversarial robustness of deep learning, and its
potential benefits to enable accountable and trustworthy deep learning-based
data analytical systems and applications.
|
We study a fundamental measure for wireless interference in the SINR model
known as (weighted) inductive independence. This measure characterizes the
effectiveness of using oblivious power --- when the power used by a transmitter
only depends on the distance to the receiver --- as a mechanism for improving
wireless capacity.
We prove optimal bounds for inductive independence, implying a number of
algorithmic applications. An algorithm is provided that achieves --- due to
existing lower bounds --- capacity that is asymptotically best possible using
oblivious power assignments. Improved approximation algorithms are provided for
a number of problems for oblivious power and for power control, including
distributed scheduling, connectivity, secondary spectrum auctions, and dynamic
packet scheduling.
|
A dataset of fully quantum flux-flux correlation functions and reaction rate
constants was constructed for organic heterogeneous catalytic surface
reactions. Gaussian process regressors were successfully fitted to training
data to predict previously unseen test set reaction rate constant products and
Cauchy fits of the flux-flux correlation function. The optimal regressor
prediction mean absolute percent errors were on the order of 0.5% for test set
reaction rate constant products and 1.0% for test set flux-flux correlation
functions. The Gaussian process regressors were accurate both when looking at
kinetics at new temperatures and reactivity of previously unseen reactions and
provide a significant speedup respect to the computationally demanding time
propagation of the flux-flux correlation function.
|
We propose a technique to improve the probability of single-photon emission
with an electrically pumped quantum dot in an optical microcavity, by
continuously monitoring the energy state of the dot and using feedback to
control when to stop pumping. The goal is to boost the probability of
single-photon emission while bounding the probability of two or more photons.
We model the system by a stochastic master equation that includes
post-measurement operations. Ideally, feedback should be based on the entire
continuous measurement record, but in practice, it may be difficult to do such
processing in real-time. We show that even a simple threshold-based feedback
scheme using measurements at a single time can improve performance over
deterministic (open-loop) pumping. This technique is particularly useful for
strong dot-cavity coupling with lower rates of pumping, as can be the case for
electrical pumping. It is also numerically tractable since we can perform
ensemble averaging with a single master equation rather than averaging over a
large number of quantum trajectories.
|
Over the years, Machine Learning models have been successfully employed on
neuroimaging data for accurately predicting brain age. Deviations from the
healthy brain aging pattern are associated to the accelerated brain aging and
brain abnormalities. Hence, efficient and accurate diagnosis techniques are
required for eliciting accurate brain age estimations. Several contributions
have been reported in the past for this purpose, resorting to different
data-driven modeling methods. Recently, deep neural networks (also referred to
as deep learning) have become prevalent in manifold neuroimaging studies,
including brain age estimation. In this review, we offer a comprehensive
analysis of the literature related to the adoption of deep learning for brain
age estimation with neuroimaging data. We detail and analyze different deep
learning architectures used for this application, pausing at research works
published to date quantitatively exploring their application. We also examine
different brain age estimation frameworks, comparatively exposing their
advantages and weaknesses. Finally, the review concludes with an outlook
towards future directions that should be followed by prospective studies. The
ultimate goal of this paper is to establish a common and informed reference for
newcomers and experienced researchers willing to approach brain age estimation
by using deep learning models
|
The rapid transmission of the highly contagious novel coronavirus has been
represented through several data-guided approaches across targeted geographies,
in an attempt to understand when the pandemic will be under control and imposed
lockdown measures can be relaxed. However, these epidemiological models
predominantly based on training data employing number of cases and fatalities
are limited in that they do not account for the spatiotemporal population
dynamics that principally contributes to the disease spread. Here, a stochastic
cellular automata enabled predictive model is presented that is able to
accurate describe the effect of demography-dependent population dynamics on
disease transmission. Using the spread of coronavirus in the state of New York
as a case study, results from the computational framework remarkably agree with
the actual count for infected cases and deaths as reported across
organizations. The predictions suggest that an extended lockdown in some form,
for up to 180 days, can significantly reduce the risk of a second wave of the
outbreak. In addition, increased availability of medical testing is able to
reduce the number of infected patients, even when less stringent social
distancing guidelines and imposed. Equipping this stochastic approach with
demographic factors such as age ratio, pre-existing health conditions,
robustifies the model to predict the transmittivity of future outbreaks before
they transform into an epidemic.
|
We present the results from an extensive atomistic molecular dynamics
simulation study of poly(ethylene oxide) (PEO) doped with various amounts of
lithium-bis(trifluoromethane)sulfonimide (LiTFSI) salt under the influence of
external electric field strengths up to $1\,$V/nm. The motivation stems from
recent experimental reports on the nonlinear response of mobilities to the
application of an electric field in such electrolyte systems and arising
speculations on field-induced alignment of the polymer chains, creating
channel-like structures that facilitate ion passage. Hence, we systematically
examine the electric field impact on the lithium coordination environment,
polymer structure as well as ionic transport properties and further present a
procedure to quantify the susceptibility of both structural and dynamical
observables to the external field. Our investigation reveals indeed a
coiled-to-stretched transformation of the PEO strands along with a concurrent
nonlinear behavior of the dynamic properties. However, from studying the
temporal response of the unperturbed electrolyte system to field application we
are able to exclude a structurally conditioned enhancement of ion transport and
surprisingly observe a slowing down. A microscopic understanding is supplied.
|
The virial theorem is related to the dilatation properties of bound states.
This is realized, in particular, by the Landau-Lifshitz formulation of the
relativistic virial theorem, in terms of the trace of the energy-momentum
tensor. We construct a Hamiltonian formulation of dilatations in which the
relativistic virial theorem naturally arises as the condition of stability
against dilatations. A bound state becomes scale invariant in the
ultrarelativistic limit, in which its energy vanishes. However, for very
relativistic bound states, scale invariance is broken by quantum effects and
the virial theorem must include the energy-momentum tensor trace anomaly. This
quantum field theory virial theorem is directly related to the Callan-Symanzik
equations. The virial theorem is applied to QED and then to QCD, focusing on
the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4
of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.
|
The use of correlation matrices to evaluate the number of uncorrelated
stirrer positions of reverberation chamber has widespread applications in
electromagnetic compatibility. We present a comparative study of recent
techniques based on multivariate correlation functions aimed at relating
space-frequency inhomogeneities/anisotropies to the reduction of uncorrelated
positions. Full wave finite-difference time domain simulations of an actual
reverberation chamber are performed through an in-house parallel code. The
efficiency of this code enables for capturing extensive
inhomogeneous/anisotropic spatial volumes (frequency ranges). The concept of
threshold crossing is revised under the light of random field sampling, which
is important to the performance of arbitrary reverberation chambers.
|
The performance of existing approaches to the recovery of frequency-sparse
signals from compressed measurements is limited by the coherence of required
sparsity dictionaries and the discretization of frequency parameter space. In
this paper, we adopt a parametric joint recovery-estimation method based on
model selection in spectral compressive sensing. Numerical experiments show
that our approach outperforms most state-of-the-art spectral CS recovery
approaches in fidelity, tolerance to noise and computation efficiency.
|
The gravitationally lensed star WHL0137-LS, nicknamed Earendel, was
identified with a photometric redshift $z_{phot} = 6.2 \pm 0.1$ based on images
taken with the Hubble Space Telescope. Here we present James Webb Space
Telescope (JWST) Near Infrared Camera (NIRCam) images of Earendel in 8 filters
spanning 0.8--5.0$\mu$m. In these higher resolution images, Earendel remains a
single unresolved point source on the lensing critical curve, increasing the
lower limit on the lensing magnification to $\mu > 4000$ and restricting the
source plane radius further to $r < 0.02$ pc, or $\sim 4000$ AU. These new
observations strengthen the conclusion that Earendel is best explained by an
individual star or multiple star system, and support the previous photometric
redshift estimate. Fitting grids of stellar spectra to our photometry yields a
stellar temperature of $T_{\mathrm{eff}} \simeq 13000$--16000 K assuming the
light is dominated by a single star. The delensed bolometric luminosity in this
case ranges from $\log(L) = 5.8$--6.6 $L_{\odot}$, which is in the range where
one expects luminous blue variable stars. Follow-up observations, including
JWST NIRSpec scheduled for late 2022, are needed to further unravel the nature
of this object, which presents a unique opportunity to study massive stars in
the first billion years of the universe.
|
The subsequent series of responses to big events may exhibit a synchronicity
of event number, frequency and energy release in different fault zones. This
synchronicity is a reliable source for probing non-intuitive geological
structures, assessing regional seismicity hazard map and even predicting the
next big events. The synchronicity of main faults in the eastern margin of the
Qinghai-Tibetan Plateau is still unknown to us. We propose to examine the
correlation of earthquake occurrence among different fault zones to indicate
this synchronicity, and to obtain a preliminary understanding of geodynamics
processes and the unrecognized characteristics of deep evolution in the eastern
margin of the Qinghai-Tibetan Plateau. We estimate temporal changes of
completeness level, frequency seismicity, and intensity seismicity, referring
respectively to Mc, Z, and E values, of 21 main fault zones, using a seismic
catalogue from 1970 to 2015. Our results reveal that six fault zone pairs of
fault zones exhibit relative high correlation (>0.6) by all three indicators,
while four fault zone pairs are non-adjacent with close internal affinity
offsetting the limit of spatial distance, such as the pair of Rongjing-mabian
fault and Minjiang-huya fault. Most strikingly, some fault zone pairs showing
typical high correlation (>0.8) of seismicity frequency or seismicity
intensity, the faults surprisingly belong to neither the same seismic belt nor
the same geological block, exhibiting a regional scale remote triggering
pattern of earthquakes or structures. An embryonic pattern to predict the next
possible events will also be presented. This correlation analysis discovers a
previously unrecognized strong coupling relationship among main faults with
high earthquake risk in the eastern margin of the Qinghai-Tibetan Plateau.
|
Recent interest in Arctic exploration has brought new challenges concerning
the mechanical behavior of lightweight materials for offshore structures.
Exposure to seawater and cold temperatures are known to degrade the mechanical
properties of several materials, thus, compromising the safety of personnel and
structures. This study aims to investigate the low-velocity impact behavior of
woven carbon/vinyl ester sandwich composites with PVC foam core at low
temperatures for marine applications. The tests were performed in a drop tower
impact system with an in-built environmental chamber. Impact responses, such as
the contact force, displacement and absorbed energy, at four impact energies of
7.5 J, 15 J, 30 J, and 60 J were determined at four in-situ temperatures of 25
C, 0 C, -25 C and -50 C. Results showed that temperature has a significant
influence on the dynamic impact behavior of sandwich composites. The sandwich
composites were rendered stiff and brittle as the temperature decreased, which
has a detrimental effect on their residual strength and durability. For
example, at 60 J for all temperatures, the samples experienced perforation of
the top facing and core, and the back facing exhibited varying extent of
damage. At -25 C and -50 C, the sandwich composite samples were almost
completely perforated. At all impact energies, the sandwich composites were
rendered stiff and brittle as the temperature decreased, which has a
detrimental effect on their residual strength and durability.
|
Wireless networks at millimeter wavelengths have significant implementation
difficulties. The path loss at these frequencies naturally leads us to consider
antenna arrays with many elements. In these arrays, local oscillator (LO)
generation is particularly challenging since the LO specifications affect the
system architecture, signal processing design, and circuit implementation. We
thoroughly analyze the effect of LO architecture design choices on the
performance of a mm-wave massive MIMO uplink. This investigation focuses on the
tradeoffs involved in centralized and distributed LO generation, correlated and
uncorrelated phase noise sources, and the bandwidths of PLLs and carrier
recovery loops. We show that, from both a performance and implementation
complexity standpoint, the optimal LO architecture uses several distributed
subarrays locked to a single intermediate-frequency reference in the low GHz
range. Additionally, we show that the choice of PLL and carrier recovery loop
bandwidths strongly affects the performance; for typical system parameters,
loop bandwidths on the order of tens of MHz achieve SINRs suitable for
high-order constellations. Finally, we present system simulations incorporating
a complete model of the LO generation system and consider the case of a
128-element array with 16x-spatial multiplexing and a 2 GHz channel bandwidth
at 75 GHz carrier. Using our optimization procedure we show that the system can
support 16-way spatial multiplexing with 64-QAM modulation.
|
Due to dispersion, light with different wavelengths, or colors, is refracted
at different angles. Our purpose is to determine when is it possible to design
a lens made of a single homogeneous material so that it refracts light
superposition of two colors into a desired fixed final direction. Two problems
are considered: one is when light emanates in a parallel beam and the other is
when light emanates from a point source. For the first problem, and when the
direction of the parallel beam is different from the final desired direction,
we show that such a lens does not exist; otherwise we prove the solution is
trivial, i.e., the lens is confined between two parallel planes. For the second
problem we prove that is impossible to design such a lens when the desired
final direction is not among the set of incident directions. Otherwise, solving
an appropriate system of functional equations we show that a local solution
exists.
|
The introduction of saliency map algorithms as an approach for assessing the
interoperability of images has allowed for a deeper understanding of current
black-box models with Artificial Intelligence. Their rise in popularity has led
to these algorithms being applied in multiple fields, including medical
imaging. With a classification task as important as those in the medical
domain, a need for rigorous testing of their capabilities arises. Current works
examine capabilities through assessing the localization of saliency maps upon
medical abnormalities within an image, through comparisons with human
annotations. We propose utilizing Segment Anything Model (SAM) to both further
the accuracy of such existing metrics, while also generalizing beyond the need
for human annotations. Our results show both high degrees of similarity to
existing metrics while also highlighting the capabilities of this methodology
to beyond human-annotation. Furthermore, we explore the applications (and
challenges) of SAM within the medical domain, including image pre-processing
before segmenting, natural language proposals to SAM in the form of CLIP-SAM,
and SAM accuracy across multiple medical imaging datasets.
|
We report the results of experimental investigations on structural, magnetic,
resistivity, caloric properties of Fe$_2$RhZ (Z=Si,Ge) along with
\textit{ab-initio} band structure calculations using first principle
simulations. Both these alloys are found to crystallize in inverse Heusler
structure but with disorder in tetrahedral sites between Fe and Rh. Fe$_2$RhSi
has saturation moment of 5.00 $\mu_B$ and while its counterpart has 5.19
$\mu_B$. Resistivity measurement reveals metallic nature in both of them.
Theoretical simulations using generalized gradient approximation(GGA) predict
inverse Heusler structure with ferromagnetic ordering as ground state for both
the alloys. However it underestimates the experimentally observed moments.
GGA+$U$ approach, with Hubbard $U$ values estimated from density functional
perturbation theory helps to improve the comparison of the experimental
results. Fe$_2$RhSi is found to be half metallic ferromagnet while Fe$_2$RhGe
is not. Varying $U$ values on Fe and Rh sites does not change the net moment
much in Fe$_2$RhSi, unlike in Fe$_2$RhGe. Relatively small exchange splitting
of orbitals in Fe$_2$RhGe compared to that of Fe$_2$RhSi is the reason for not
opening the band gap in the minority spin channel in the former. High ordering
temperature and moment make Fe$_2$RhSi useful for spintronics applications.
|
We consider typical finite dimensional complex irreducible representations of
a basic classical simple Lie superalgebra, and give a sufficient condition on
when unique factorization of finite tensor products of such representations
hold. We also prove unique factorization of tensor products of singly atypical
finite dimensional irreducible modules for $\mathfrak{sl}(m+1,n+1)$,
$\mathfrak{osp}(2,2n)$, $G(3)$ and $F(4)$ under an additional assumption. This
result is a Lie superalgebra analogue of Rajan's fundamental result
\cite{MR2123935} on unique factorization of tensor products for finite
dimensional complex simple Lie algebras.
|
In [GT], Goldin and the second author extend some ideas from Schubert
calculus to the more general setting of Hamiltonian torus actions on compact
symplectic manifolds with isolated fixed points. (See also [Kn99] and [Kn08].)
The main goal of this paper is to build on this work by finding more effective
formulas. More explicitly, given a generic component of the moment map, they
define a canonical class $\alpha_p$ in the equivariant cohomology of the
manifold $M$ for each fixed point $p \in M$. When they exist, canonical classes
form a natural basis of the equivariant cohomology of $M$. In particular, when
$M$ is a flag variety, these classes are the equivariant Schubert classes. It
is a long standing problem in combinatorics to find positive integral formulas
for the equivariant structure constants associated to this basis. Since
computing the restriction of the canonical classes to the fixed points
determines these structure constants, it is important to find effective
formulas for these restrictions. In this paper, we introduce new techniques for
calculating the restrictions of a canonical class $\alpha_p$ to a fixed point
$q$. Our formulas are nearly always simpler, in the sense that they count the
contributions over fewer paths. Moreover, our formula is manifestly positive
and integral in certain important special cases.
|
Hierarchical modeling is wonderful and here to stay, but hyperparameter
priors are often chosen in a casual fashion. Unfortunately, as the number of
hyperparameters grows, the effects of casual choices can multiply, leading to
considerably inferior performance. As an extreme, but not uncommon, example use
of the wrong hyperparameter priors can even lead to impropriety of the
posterior. For exchangeable hierarchical multivariate normal models, we first
determine when a standard class of hierarchical priors results in proper or
improper posteriors. We next determine which elements of this class lead to
admissible estimators of the mean under quadratic loss; such considerations
provide one useful guideline for choice among hierarchical priors. Finally,
computational issues with the resulting posterior distributions are addressed.
|
The effects of uniaxial strain on the structural, orbital, optical, and
magnetic properties of LaMnO_3 are calculated using a general elastic energy
expression, along with a tight-binding parameterization of the band theory.
Tensile uniaxial strain of the order of 2 % (i.e., of the order of magnitude of
those induced in thin films by lattice mismatch with substrates) is found to
lead to changes in the magnetic ground state, leading to dramatic changes in
the band structure and optical conductivity spectrum. The magnetostriction
effect associated with the Neel transition of bulk(unstrained) LaMnO_3 is also
determined. Due to the Jahn-Teller coupling, the uniform tetragonal distortion
mode is softer in LaMnO_3 than in doped cubic manganates. Reasons why the
observed (\pi \pi 0) orbital ordering is favored over a (\pi \pi \pi)
periodicity are discussed.
|
Vastly different time and length scales are a common problem in numerical
simulations of astrophysical phenomena. Here, we present an approach to
numerical modeling of such objects on the example of Type Ia supernova
simulations. The evolution towards the explosion proceeds on much longer time
scales than the explosion process itself. The physical length scales relevant
in the explosion process cover 11 orders of magnitude and turbulent effects
dominate the physical mechanism. Despite these challenges, three-dimensional
simulations of Type Ia supernova explosions have recently become possible and
pave the way to a better understanding of these important astrophysical
objects.
|
The mass and isotope dependence of limiting temperatures for hot nuclei are
investigated. The predicted mass dependence of limiting temperatures is in good
agreement with data derived from the caloric curve data. The predicted isotope
distribution of limiting temperatures appears to be a parabolic shape and its
centroid is not located at the isotope on the $\beta$-stability line(T=0) but
at neutron-rich side. Our study shows that the mass and isotope dependence of
limiting temperatures depend on the interaction and the form of surface tension
and its isopin dependence sensitively.
|
The most general phenomenological model involving a lepton triplet with
hypercharge $\pm 1$ is constructed. A distinctive feature of this model is the
prediction of a doubly charged lepton, and a new heavy Dirac neutrino. We study
the phenomenology of these exotic leptons in both low-energy experiments and at
the LHC. The model predicts FCNC processes such as rare muon decays, which are
studied in detail in order to constrain the model parameters. All the decay
channels of the exotic leptons are described for a wide range of parameters. It
is found that, if the mixing parameters between the exotic and light leptons
are not too small ($>10^{-6}$), then they can be observable to a $3-5\sigma$
statistical significance at the 7 TeV LHC with 10-50 fb$^{-1}$ luminosity for a
400 GeV mass, and 14 TeV with 100-300 fb$^{-1}$ luminosity for a 800 GeV mass.
|
Intelligent reflecting surfaces (IRSs) improve both the bandwidth and energy
efficiency of wideband communication systems by using low-cost passive elements
for reflecting the impinging signals with adjustable phase shifts. To realize
the full potential of IRS-aided systems, having accurate channel state
information (CSI) is indispensable, but it is challenging to acquire, since
these passive devices cannot carry out transmit/receive signal processing. The
existing channel estimation methods conceived for wideband IRS-aided
communication systems only consider the channel's frequency selectivity, but
ignore the effect of beam squint, despite its severe performance degradation.
Hence we fill this gap and conceive wideband channel estimation for IRS-aided
communication systems by explicitly taking the effect of beam squint into
consideration. We demonstrate that the mutual correlation function between the
spatial steering vectors and the cascaded two-hop channel reflected by the IRS
has two peaks, which leads to a pair of estimated angles for a single
propagation path, due to the effect of beam squint. One of these two estimated
angles is the frequency-independent `actual angle', while the other one is the
frequency-dependent `false angle'. To reduce the influence of false angles on
channel estimation, we propose a twin-stage orthogonal matching pursuit
(TS-OMP) algorithm.
|
Detailed numerical analyses of the orbital motion of a test particle around a
spinning primary are performed. They aim to investigate the possibility of
using the post-Keplerian (pK) corrections to the orbiter's periods (draconitic,
anomalistic and sidereal) as a further opportunity to perform new tests of
post-Newtonian (pN) gravity. As a specific scenario, the S-stars orbiting the
Massive Black Hole (MBH) supposedly lurking in Sgr A$^\ast$ at the center of
the Galaxy is adopted. We, first, study the effects of the pK Schwarzchild,
Lense-Thirring and quadrupole moment accelerations experienced by a target star
for various possible initial orbital configurations. It turns out that the
results of the numerical simulations are consistent with the analytical ones in
the small eccentricity approximation for which almost all the latter ones were
derived. For highly elliptical orbits, the size of all the three pK corrections
considered turn out to increase remarkably. The periods of the observed S2 and
S0-102 stars as functions of the MBH's spin axis orientation are considered as
well. The pK accelerations considered lead to corrections of the orbital
periods of the order of 1-100d (Schwarzschild), 0.1-10h (Lense-Thirring) and
1-10^3s (quadrupole) for a target star with a=300-800~AU and e ~ 0.8, which
could be possibly measurable by the future facilities.
|
The exponential mechanism is a fundamental tool of Differential Privacy (DP)
due to its strong privacy guarantees and flexibility. We study its extension to
settings with summaries based on infinite dimensional outputs such as with
functional data analysis, shape analysis, and nonparametric statistics. We show
that one can design the mechanism with respect to a specific base measure over
the output space, such as a Guassian process. We provide a positive result that
establishes a Central Limit Theorem for the exponential mechanism quite
broadly. We also provide an apparent negative result, showing that the
magnitude of the noise introduced for privacy is asymptotically non-negligible
relative to the statistical estimation error. We develop an \ep-DP mechanism
for functional principal component analysis, applicable in separable Hilbert
spaces. We demonstrate its performance via simulations and applications to two
datasets.
|
The goal of this paper is to construct a category of motivic "sheaves" on an
algebraic variety defined over a subfield of C, using Nori's method. This
categoryis abelian and it possesses faithful exact realization functors to the
categoriesof constructible sheaves for the classical and etale topologies.
Moreover, there is a tannakian subcategory of motivic local systems with a
realization functor into the category of variations of mixed Hodge structures.
Conversely, all basic geometric examples of the latter come from this motivic
category.
|
The aim of the present paper is to obtain a classification of all the
irreducible modular representations of the symmetric group on $n$ letters of
dimension at most $n^3$, including dimension formulae. This is achieved by
improving an idea, originally due to G. James, to get hands on dimension
bounds, by building on the current knowledge about decomposition numbers of
symmetric groups and their associated Iwahori-Hecke algebras, and by employing
a mixture of theory and computation.
|
In this paper we construct an injection from the linear space of
trigonometric polynomials defined on $\mathbb{T}^d$ with bounded degrees with
respect to each variable to a suitable linear subspace $L^1_E\subset
L^1(\mathbb{T})$. We give such a quantitative condition on $L^1_E$ that this
injection is a isomorphism of a Banach spaces equipped with $L^1$ norm and the
norm of the isomorphism is independent on the dimension $d$.
|
We investigate opinion dynamics based on an agent-based model, and are
interested in predicting the evolution of the percentages of the entire agent
population that share an opinion. Since these opinion percentages can be seen
as an aggregated observation of the full system state, the individual opinions
of each agent, we view this in the framework of the Mori-Zwanzig projection
formalism. More specifically, we show how to estimate a nonlinear
autoregressive model (NAR) with memory from data given by a time series of
opinion percentages, and discuss its prediction capacities for various specific
topologies of the agent interaction network. We demonstrate that the inclusion
of memory terms significantly improves the prediction quality on examples with
different network topologies.
|
We present a measurement of electron neutrino interactions from the Fermilab
Booster Neutrino Beam using the MicroBooNE liquid argon time projection chamber
to address the nature of the excess of low energy interactions observed by the
MiniBooNE collaboration. Three independent electron neutrino searches are
performed across multiple single electron final states, including an exclusive
search for two-body scattering events with a single proton, a semi-inclusive
search for pion-less events, and a fully inclusive search for events containing
all hadronic final states. With differing signal topologies, statistics,
backgrounds, reconstruction algorithms, and analysis approaches, the results
are found to be consistent with the nominal electron neutrino rate expectations
from the Booster Neutrino Beam and no excess of electron neutrino events is
observed.
|
The contact model for the spread of disease may be viewed as a directed
percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented
in the direction of increasing time. Techniques from percolation have enabled a
fairly complete analysis of the contact model at and near its critical point.
The corresponding process when the time-axis is unoriented is an undirected
percolation model to which now standard techniques may be applied. One may
construct in similar vein a random-cluster model on $\ZZ \times \RR$, with
associated continuum Ising and Potts models. These models are of independent
interest, in addition to providing a path-integral representation of the
quantum Ising model with transverse field. This representation may be used to
obtain a bound on the entanglement of a finite set of spins in the quantum
Ising model on $\ZZ$, where this entanglement is measured via the entropy of
the reduced density matrix. The mean-field version of the quantum Ising model
gives rise to a random-cluster model on $K_n \times \RR$, thereby extending the
Erdos-Renyi random graph on the complete graph $K_n$.
|
The constraints of electric dipole moments (EDMs) of electron and neutron on
the parameter space in supergravity (SUGRA) models with nonuniversal gaugino
masses are analyzed. It is shown that with a light sparticle spectrum, the
sufficient cancellations in the calculation of EDMs can happen for all phases
being order of one in the small tan$\beta$ case and all phases but $\phi_{\mu}$
($|\phi_{\mu}| <\sim \pi/6$) order of one in the large tan$\beta$ case. This is
in contrast to the case of mSUGRA in which in the parameter space where
cancellations among various SUSY contributions to EDMs happen $|\phi_{\mu}|$
must be less than $\pi/10$ for small $tan\beta$ and ${\cal{O}}(10^{-2})$ for
large $tan\beta$. Direct CP asymmetries and the T-odd polarization of lepton in
$B\to X_s l^+l^-$ are investigated in the models. In the large tan$\beta$ case,
$A_{CP}^2$ and $P_N$ for l=$\mu$ ($\tau$) can be enhanced by about a factor of
ten (ten) and ten (three) respectively compared to those of mSUGRA.
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With the recent success of deep neural networks, remarkable progress has been
achieved on face recognition. However, collecting large-scale real-world
training data for face recognition has turned out to be challenging, especially
due to the label noise and privacy issues. Meanwhile, existing face recognition
datasets are usually collected from web images, lacking detailed annotations on
attributes (e.g., pose and expression), so the influences of different
attributes on face recognition have been poorly investigated. In this paper, we
address the above-mentioned issues in face recognition using synthetic face
images, i.e., SynFace. Specifically, we first explore the performance gap
between recent state-of-the-art face recognition models trained with synthetic
and real face images. We then analyze the underlying causes behind the
performance gap, e.g., the poor intra-class variations and the domain gap
between synthetic and real face images. Inspired by this, we devise the SynFace
with identity mixup (IM) and domain mixup (DM) to mitigate the above
performance gap, demonstrating the great potentials of synthetic data for face
recognition. Furthermore, with the controllable face synthesis model, we can
easily manage different factors of synthetic face generation, including pose,
expression, illumination, the number of identities, and samples per identity.
Therefore, we also perform a systematically empirical analysis on synthetic
face images to provide some insights on how to effectively utilize synthetic
data for face recognition.
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We discuss the propagation of gravity in five-dimensional Minkowski space in
the presence of a four-dimensional brane. We show that there exists a solution
to the wave equation that leads to a propagator exhibiting four-dimensional
behavior at low energies (long distances) with five-dimensional effects showing
up as corrections at high energies (short distances). We compare our results
with propagators derived in previous analyses exhibiting five-dimensional
behavior at low energies. We show that different solutions correspond to
different physical systems.
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We define a notion of strong shift equivalence for $C^*$-correspondences and
show that strong shift equivalent $C^*$-correspondences have strongly Morita
equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong
shift equivalent square matrices with non-negative integer entries give stably
isomorphic Cuntz-Krieger algebras.
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We study a generalized discrete-time multi-type Wright-Fisher population
process. The mean-field dynamics of the stochastic process is induced by a
general replicator difference equation. We prove several results regarding the
asymptotic behavior of the model, focusing on the impact of the mean-field
dynamics on it. One of the results is a limit theorem that describes sufficient
conditions for an almost certain path to extinction, first eliminating the type
which is the least fit at the mean-field equilibrium. The effect is explained
by the metastability of the stochastic system, which under the conditions of
the theorem spends almost all time before the extinction event in a
neighborhood of the equilibrium. In addition, to limit theorems, we propose a
variation of Fisher's maximization principle, fundamental theorem of natural
selection, for a completely general deterministic replicator dynamics and study
implications of the deterministic maximization principle for the stochastic
model.
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We present a probabilistic modeling framework and adaptive sampling algorithm
wherein unsupervised generative models are combined with black box predictive
models to tackle the problem of input design. In input design, one is given one
or more stochastic "oracle" predictive functions, each of which maps from the
input design space (e.g. DNA sequences or images) to a distribution over a
property of interest (e.g. protein fluorescence or image content). Given such
stochastic oracles, the problem is to find an input that is expected to
maximize one or more properties, or to achieve a specified value of one or more
properties, or any combination thereof. We demonstrate experimentally that our
approach substantially outperforms other recently presented methods for
tackling a specific version of this problem, namely, maximization when the
oracle is assumed to be deterministic and unbiased. We also demonstrate that
our method can tackle more general versions of the problem.
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When training samples are scarce, the semantic embedding technique, ie,
describing class labels with attributes, provides a condition to generate
visual features for unseen objects by transferring the knowledge from seen
objects. However, semantic descriptions are usually obtained in an external
paradigm, such as manual annotation, resulting in weak consistency between
descriptions and visual features. In this paper, we refine the coarse-grained
semantic description for any-shot learning tasks, ie, zero-shot learning (ZSL),
generalized zero-shot learning (GZSL), and few-shot learning (FSL). A new
model, namely, the semantic refinement Wasserstein generative adversarial
network (SRWGAN) model, is designed with the proposed multihead representation
and hierarchical alignment techniques. Unlike conventional methods, semantic
refinement is performed with the aim of identifying a bias-eliminated condition
for disjoint-class feature generation and is applicable in both inductive and
transductive settings. We extensively evaluate model performance on six
benchmark datasets and observe state-of-the-art results for any-shot learning;
eg, we obtain 70.2% harmonic accuracy for the Caltech UCSD Birds (CUB) dataset
and 82.2% harmonic accuracy for the Oxford Flowers (FLO) dataset in the
standard GZSL setting. Various visualizations are also provided to show the
bias-eliminated generation of SRWGAN. Our code is available.
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Recent Planck measurements show some CMB anomalies on large angular scales,
which confirms the early observations by WMAP. We show that an inflationary
model, in which before the slow-roll inflation the Universe is in a
superinflationary phase, can generate a large-scale cutoff in the primordial
power spectrum, which may account for not only the power suppression on large
angular scales, but also a large dipole power asymmetry in the CMB. We discuss
an implementation of our model in string theory.
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Most of industrial robots are still programmed using the typical teaching
process, through the use of the robot teach pendant. In this paper is proposed
an accelerometer-based system to control an industrial robot using two low-cost
and small 3-axis wireless accelerometers. These accelerometers are attached to
the human arms, capturing its behavior (gestures and postures). An Artificial
Neural Network (ANN) trained with a back-propagation algorithm was used to
recognize arm gestures and postures, which then will be used as input in the
control of the robot. The aim is that the robot starts the movement almost at
the same time as the user starts to perform a gesture or posture (low response
time). The results show that the system allows the control of an industrial
robot in an intuitive way. However, the achieved recognition rate of gestures
and postures (92%) should be improved in future, keeping the compromise with
the system response time (160 milliseconds). Finally, the results of some tests
performed with an industrial robot are presented and discussed.
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In this paper, we consider complete non-catenoidal minimal surfaces of finite
total curvature with two ends. A family of such minimal surfaces with least
total absolute curvature is given. Moreover, we obtain a uniqueness theorem for
this family from its symmetries.
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Surrogate-based optimization, nature-inspired metaheuristics, and hybrid
combinations have become state of the art in algorithm design for solving
real-world optimization problems. Still, it is difficult for practitioners to
get an overview that explains their advantages in comparison to a large number
of available methods in the scope of optimization. Available taxonomies lack
the embedding of current approaches in the larger context of this broad field.
This article presents a taxonomy of the field, which explores and matches
algorithm strategies by extracting similarities and differences in their search
strategies. A particular focus lies on algorithms using surrogates,
nature-inspired designs, and those created by design optimization. The
extracted features of components or operators allow us to create a set of
classification indicators to distinguish between a small number of classes. The
features allow a deeper understanding of components of the search strategies
and further indicate the close connections between the different algorithm
designs. We present intuitive analogies to explain the basic principles of the
search algorithms, particularly useful for novices in this research field.
Furthermore, this taxonomy allows recommendations for the applicability of the
corresponding algorithms.
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Soft behaviour of closed string amplitudes involving dilatons, gravitons and
anti-symmetric tensors, is studied in the framework of bosonic string theory.
The leading double soft limit of gluons is analysed as well, starting from
scattering amplitudes computed in the open bosonic string. Field theory
expressions are then obtained by sending the string tension to infinity. The
presented results have been derived in the papers of Ref.[1].
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In this paper we provide an asymptotic analysis of generalised bipower
measures of the variation of price processes in financial economics. These
measures encompass the usual quadratic variation, power variation and bipower
variations which have been highlighted in recent years in financial
econometrics. The analysis is carried out under some rather general Brownian
semimartingale assumptions, which allow for standard leverage effects.
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Using an event-driven molecular dynamics simulation, we show that simple
monodisperse granular beads confined in coupled columns may oscillate as a new
type of granular clock. To trigger this oscillation, the system needs to be
driven against gravity into a density-inverted state, with a high-density
clustering phase supported from below by a gas-like low-density phase
(Leidenfrost effect) in each column. Our analysis reveals that the
density-inverted structure and the relaxation dynamics between the phases can
amplify any small asymmetry between the columns, and lead to a giant
oscillation. The oscillation occurs only for an intermediate range of the
coupling strength, and the corresponding phase diagram can be universally
described with a characteristic height of the density-inverted structure. A
minimal two-phase model is proposed and linear stability analysis shows that
the triggering mechanism of the oscillation can be explained as a switchable
two-parameter Hopf bifurcation. Numerical solutions of the model also reproduce
similar oscillatory dynamics to the simulation results.
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A general Bayesian framework for model selection on random network models
regarding their features is considered. The goal is to develop a principle
Bayesian model selection approach to compare different fittable, not
necessarily nested, models for inference on those network realisations. The
criterion for random network models regarding the comparison is formulated via
Bayes factors and penalizing using the mostwidely used loss functions.
Parametrizations are different in different spaces. To overcome this problem we
incorporate and encode different aspects of complexities in terms of observable
spaces. Thus, given a range of values for a feature, network realisationsare
extracted. The proposed principle approach is based on finding random network
models, such that a reasonable trade off between the interested feature and the
complexity of the model is preserved, avoiding overfitting problems.
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We consider the phenomenon of spectral pollution arising in calculation of
spectra of self-adjoint operators by projection methods. We suggest a strategy
of dealing with spectral pollution by using the so-called second order relative
spectra. The effectiveness of the method is illustrated by a detailed analysis
of two model examples.
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Among the various generative adversarial network (GAN)-based image inpainting
methods, a coarse-to-fine network with a contextual attention module (CAM) has
shown remarkable performance. However, owing to two stacked generative
networks, the coarse-to-fine network needs numerous computational resources
such as convolution operations and network parameters, which result in low
speed. To address this problem, we propose a novel network architecture called
PEPSI: parallel extended-decoder path for semantic inpainting network, which
aims at reducing the hardware costs and improving the inpainting performance.
PEPSI consists of a single shared encoding network and parallel decoding
networks called coarse and inpainting paths. The coarse path produces a
preliminary inpainting result to train the encoding network for the prediction
of features for the CAM. Simultaneously, the inpainting path generates higher
inpainting quality using the refined features reconstructed via the CAM. In
addition, we propose Diet-PEPSI that significantly reduces the network
parameters while maintaining the performance. In Diet-PEPSI, to capture the
global contextual information with low hardware costs, we propose novel
rate-adaptive dilated convolutional layers, which employ the common weights but
produce dynamic features depending on the given dilation rates. Extensive
experiments comparing the performance with state-of-the-art image inpainting
methods demonstrate that both PEPSI and Diet-PEPSI improve the qualitative
scores, i.e. the peak signal-to-noise ratio (PSNR) and structural similarity
(SSIM), as well as significantly reduce hardware costs such as computational
time and the number of network parameters.
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The Kalman-Bucy filter is the optimal state estimator for an
Ornstein-Uhlenbeck diffusion given that the system is partially observed via a
linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a
finite-dimensional exact implementation of the optimal Bayes filter. It is
generally the only such finite-dimensional exact instance of the Bayes filter
for continuous state-space models. Consequently, this filter has been studied
extensively in the literature since the seminal 1961 paper of Kalman and Bucy.
The purpose of this work is to review, re-prove and refine existing results
concerning the dynamical properties of the Kalman-Bucy filter so far as they
pertain to filter stability and convergence. The associated differential matrix
Riccati equation is a focal point of this study with a number of bounds,
convergence, and eigenvalue inequalities rigorously proven. New results are
also given in the form of exponential and comparison inequalities for both the
filter and the Riccati flow.
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We generalize Wheeler-Feynman electrodynamics with a variational
boundary-value problem with past and future boundary segments that can include
velocity discontinuity points. Critical-point trajectories must satisfy the
Euler-Lagrange equations of the action functional, which are
neutral-differential delay equations of motion (the Wheeler-Feynman equations
of motion). At velocity discontinuity points, critical-point orbits must
satisfy the Weierstrass-Erdmann conditions of continuity of partial momenta and
partial energies. We study a special class of boundary data having the shortest
time-separation between boundary segments, for which case the Wheeler-Feynman
equations reduce to a two-point boundary problem for an ordinary differential
equation. For this simple case we prove that the extended variational problem
has solutions with discontinuous velocities. We construct a numerical method to
solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann
conditions and calculate some numerical orbits with discontinuous velocities.
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We derive asymptotic expansions up to order $n^{-1/2}$ for the nonnull
distribution functions of the likelihood ratio, Wald, score and gradient test
statistics in the class of dispersion models, under a sequence of Pitman
alternatives. The asymptotic distributions of these statistics are obtained for
testing a subset of regression parameters and for testing the precision
parameter. Based on these nonnull asymptotic expansions it is shown that there
is no uniform superiority of one test with respect to the others for testing a
subset of regression parameters. Furthermore, in order to compare the
finite-sample performance of these tests in this class of models, Monte Carlo
simulations are presented. An empirical application to a real data set is
considered for illustrative purposes.
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We study two possible explanations for short baseline neutrino oscillation
anomalies, such as the LSND and MiniBooNE anti-neutrino data, and for the
reactor anomaly. The first scenario is the mini-seesaw mechanism with two
eV-scale sterile neutrinos. We present both analytic formulas and numerical
results showing that this scenario could account for the short baseline and
reactor anomalies and is consistent with the observed masses and mixings of the
three active neutrinos. We also show that this scenario could arise naturally
from an effective theory containing a TeV-scale VEV, which could be related to
other TeV-scale physics. The minimal version of the mini-seesaw relates the
active-sterile mixings to five real parameters and favors an inverted
hierarchy. It has the interesting property that the effective Majorana mass for
neutrinoless double beta decay vanishes, while the effective masses relevant to
tritium beta decay and to cosmology are respectively around 0.2 and 2.4 eV. The
second scenario contains only one eV-scale sterile neutrino but with an
effective non-unitary mixing matrix between the light sterile and active
neutrinos. We find that though this may explain the anomalies, if the
non-unitarity originates from a heavy sterile neutrino with a large
(fine-tuned) mixing angle, this scenario is highly constrained by cosmological
and laboratory observations.
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We make an extensive study of evolution of gravitational perturbations of
D-dimensional black holes in Gauss-Bonnet theory. There is an instability at
higher multi-poles $\ell$ and large Gauss-Bonnet coupling $\alpha$ for $D= 5,
6$, which is stabilized at higher $D$. Although small negative gap of the
effective potential for scalar type of gravitational perturbations, exists for
higher $D$ and whatever $\alpha$, it does not lead to any instability.
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Using data from the Wide-field Infrared Survey Explorer (WISE) we show that
the mid infrared (MIR) colors of low-luminosity AGNs (LLAGNs) are significanlty
different from those of post-asymptotic giant branch stars (PAGBs). This is due
to a difference in spectral energy distribution (SEDs), the LLAGNs showing a
flat component due to an AGN. Consistent with this interpretation we show that
in a MIR color-color diagram the LINERs and the Seyfert~2s follow a power law
with specific colors that allow to distinguish them from each other, and from
star forming galaxies, according to their present level of star formation.
Based on this result we present a new diagnostic diagram in the MIR that
confirms the classification obtained in the optical using standard diagnostic
diagrams, clearly identifying LINERs and LLAGNs as genuine AGNs.
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The current status of the phenomenology of short-baseline neutrino
oscillations induced by light sterile neutrinos in the framework of 3+1 mixing
is reviewed.
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Supermassive black holes in the centers of active galactic nuclei (AGN) are
surrounded by broad-line regions (BLRs). The broad emission lines seen in the
AGN spectra are emitted in this spatially unresolved region. We intend to
obtain information on the structure and geometry of this BLR based on observed
line profiles. We modeled the rotational and turbulent velocities in the
line-emitting region on the basis of the line-width FWHM and line dispersion
sigma_line of the variable broad emission lines in NGC5548. Based on these
velocities we estimated the height of the line-emitting regions above the
midplane in the context of their distances from the center. The broad emission
lines originate at distances of 2 to 27 light days from the center. Higher
ionized lines originate in the inner region (lesser equal 13 light days) in
specific filamentary structures 1 to 14 light days above the midplane. In
contrast, the Hbeta line is emitted in an outer (6 - 26 light days), more
flattened configuration at heights of 0.7 to 4 light days only above the
midplane. The derived geometry of the line-emitting region in NGC5548 is
consistent with an outflowing wind launched from an accretion disk.
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For flexibility of an octahedron we find necessary metric conditions in terms
of edge lengths. These conditions yield a new description of Bricard's
octahedra, suitable for solving some problems in metric geometry of octahedra,
in particular, for searching the proof of I.\,Hh~Sabitov hypothesis that all
non-leading coefficients of the volume polynomial for an octahedron of third
type are zero.
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Toric quasifolds are highly singular spaces that were first introduced in
order to address, from the symplectic viewpoint, the longstanding open problem
of extending the classical constructions of toric geometry to those simple
convex polytopes that are not rational. We illustrate toric quasifolds, and
their atlases, by describing some notable examples. We conclude with a number
of considerations.
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Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation
which sits between entanglement and Bell nonlocality. While a number of
qualitative steering criteria exist, very little has been achieved for what
concerns quantifying steerability. We introduce a computable measure of
steering for arbitrary bipartite Gaussian states of continuous variable
systems. For two-mode Gaussian states, the measure reduces to a form of
coherent information, which is proven never to exceed entanglement, and to
reduce to it on pure states. We provide an operational connection between our
measure and the key rate in one-sided device-independent quantum key
distribution. We further prove that Peres' conjecture holds in its stronger
form within the fully Gaussian regime: namely, steering bound entangled
Gaussian states by Gaussian measurements is impossible.
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Here I propose an approximate way of simulating the outcomes of a
single-experiment density measurement that is performed on a state of N bosons.
The approximation is accurate if occupation of single-particle modes is
macroscopic.
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The symmetric Macdonald polynomials are able to be constructed out of the
non-symmetric Macdonald polynomials. This allows us to develop the theory of
the symmetric Macdonald polynomials by first developing the theory of their
non-symmetric counterparts. In taking this approach we are able to obtain new
results as well as simpler and more accessible derivations of a number of the
known fundamental properties of both kinds of polynomials.
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