  The polyhedral product constructed from a collection of pairs of cones and
their bases and a simplicial complex $K$ is studied by investigating its
filtration called the fat wedge filtration. We give a sufficient condition for
decomposing the polyhedral product in terms of the fat wedge filtration of the
real moment-angle complex for $K$, which is a desuspension of the decomposition
of the suspension of the polyhedral product due to Bahri, Bendersky, Cohen, and
Gitler. We show that the condition also implies a strong connection with the
Golodness of $K$, and is satisfied when $K$ is dual sequentially Cohen-Macaulay
over $\mathbb{Z}$ or $\lceil\frac{\dim K}{2}\rceil$-neighborly so that the
polyhedral product decomposes. Specializing to moment-angle complexes, we also
give a necessary and sufficient condition for their decomposition and
co-H-structures in terms of their fat wedge filtration.


  Gaia will obtain astrometry and spectrophotometry for essentially all sources
in the sky down to a broad band magnitude limit of G=20, an expected yield of
10^9 stars. Its main scientific objective is to reveal the formation and
evolution of our Galaxy through chemo-dynamical analysis. In addition to
inferring positions, parallaxes and proper motions from the astrometry, we must
also infer the astrophysical parameters of the stars from the
spectrophotometry, the BP/RP spectrum. Here we investigate the performance of
three different algorithms (SVM, ILIUM, Aeneas) for estimating the effective
temperature, line-of-sight interstellar extinction, metallicity and surface
gravity of A-M stars over a wide range of these parameters and over the full
magnitude range Gaia will observe (G=6-20mag). One of the algorithms, Aeneas,
infers the posterior probability density function over all parameters, and can
optionally take into account the parallax and the Hertzsprung-Russell diagram
to improve the estimates. For all algorithms the accuracy of estimation depends
on G and on the value of the parameters themselves, so a broad summary of
performance is only approximate. For stars at G=15 with less than two
magnitudes extinction, we expect to be able to estimate Teff to within 1%, logg
to 0.1-0.2dex, and [Fe/H] (for FGKM stars) to 0.1-0.2dex, just using the BP/RP
spectrum (mean absolute error statistics are quoted). Performance degrades at
larger extinctions, but not always by a large amount. Extinction can be
estimated to an accuracy of 0.05-0.2mag for stars across the full parameter
range with a priori unknown extinction between 0 and 10mag. Performance
degrades at fainter magnitudes, but even at G=19 we can estimate logg to better
than 0.2dex for all spectral types, and [Fe/H] to within 0.35dex for FGKM
stars, for extinctions below 1mag.


  Linear stability of solitary waves near transcritical bifurcations is
analyzed for the generalized nonlinear Schroedinger equations with arbitrary
forms of nonlinearity and external potentials in arbitrary spatial dimensions.
Bifurcation of linear-stability eigenvalues associated with this transcritical
bifurcation is analytically calculated. Based on this eigenvalue bifurcation,
it is shown that both solution branches undergo stability switching at the
transcritical bifurcation point. In addition, the two solution branches have
opposite linear stability. These stability properties closely resemble those
for transcritical bifurcations in finite-dimensional dynamical systems. This
resemblance for transcritical bifurcations contrasts those for saddle-node and
pitchfork bifurcations, where stability properties in the generalized nonlinear
Schroedinger equations differ significantly from those in finite-dimensional
dynamical systems. The analytical results are also compared with numerical
results, and good agreement is obtained.


  For any Kac-Moody group $G$ with Borel $B$, we give a monoidal equivalence
between the derived category of $B$-equivariant mixed complexes on the flag
variety $G/B$ and (a certain completion of) the derived category of
$B^\vee$-monodromic mixed complexes on the enhanced flag variety
$G^\vee/U^\vee$, here $G^\vee$ is the Langlands dual of $G$. We also prove
variants of this equivalence, one of which is the equivalence between the
derived category of $U$-equivariant mixed complexes on the partial flag variety
$G/P$ and certain "Whittaker model" category of mixed complexes on
$G^\vee/B^\vee$. In all these equivalences, intersection cohomology sheaves
correspond to (free-monodromic) tilting sheaves. Our results generalize the
Koszul duality patterns for reductive groups in the work of Beilinson, Ginzburg
and Soergel .


  This paper theoretically analyzes the optical transmission characteristics of
an optical waveguide when coupling to a micro cavity array. The results showed
that not only were there sharp peaks on the transmission and reflection
spectra, but also that a certain system configuration can produce a backward
wave to obtain a phase shift in the small detuning range between the incident
wave and the micro cavities. Based on a discussion of the relationship between
the transmission and the number and the dissipation coefficients of each
coupled micro cavity, the paper proposes a high efficiency all-optical switch
model.


  We propose a simple uniform lower bound on the spacings between the
successive zeros of the Laguerre polynomials $L_n^{(\alpha)}$ for all
$\alpha>-1$. Our bound is sharp regarding the order of dependency on $n$ and
$\alpha$ in various ranges. In particular, we recover the orders given in
\cite{ahmed} for $\alpha \in (-1,1]$.


  Thermal dark matter at the MeV scale faces stringent bounds from a variety of
cosmological probes. Here we perform a detailed evaluation of BBN bounds on the
annihilation cross section of dark matter with a mass $1\,\text{MeV} \lesssim
m_\chi \lesssim 1\,\text{GeV}$. For $p-wave suppressed annihilations,
constraints from BBN turn out to be significantly stronger than the ones from
CMB observations, and are competitive with the strongest bounds from other
indirect searches. We furthermore update the lower bound from BBN on the mass
of thermal dark matter using improved determinations of primordial abundances.
While being of similar strength as the corresponding bound from CMB, it is
significantly more robust to changes in the particle physics model.


  We discuss a preliminary design for a high luminosity 4 TeV center of mass
$\mu^+\,\mu^-$ collider ring.


  We study the effects of bond disorder on triangular and honeycomb lattices
where each spring has a probability p to be odd elastic. Using an effective
medium theory and numerical simulations, we uncover the behavior of odd moduli
in the presence of disorder, which we interpret as a crossover between the
affine response of the passive elastic backbone, and a rigidity percolation
transition in the odd elastic components. Though oddness is generally robust
against disorder even at low p, we find that fine-tuned features of an odd
elastic honeycomb lattice are not robust against disorder.


  We introduce a supersymmetric lattice fermion model that contains both
fermion pairing and the interacting Nicolai model. This model possesses a
single control parameter, $g$, introduced through the anticommutator of the
supersymmetry generators (supercharge), and it is shown that supersymmetry is
broken in both finite and infinite systems as long as $g$ is finite.
Additionally, the single-mode approximation is employed to establish an upper
bound on the dispersion relation of Nambu-Goldstone (NG) fermions,
demonstrating their gaplessness. Finally, it is shown, through numerical and
analytic calculations, that the anticipated extensive ground-state degeneracy
and a zero-energy flat band does not occur for generic values of the parameter
$g$.


  Variational quantum eigensolver (VQE) solves the ground state problem of a
given Hamiltonian by finding the parameters of a quantum circuit ansatz that
minimizes the Hamiltonian expectation value. Among possible quantum circuit
ans\"{a}tze, the Hamiltonian variational ansatz (HVA) is widely studied for
quantum many-body problems as the ansatz with sufficiently large depth is
theoretically guaranteed to express the ground state. However, since the HVA
shares the same symmetry with the Hamiltonian, it is not necessarily good at
finding the symmetry-broken ground states that prevail in nature. In this
paper, we systematically explore the limitations of the HVA for solving
symmetry-broken systems and propose an alternative quantum circuit ansatz with
symmetry-breaking layers. With extensive numerical simulations, we show that
the proposed ansatz finds the ground state in depth significantly shorter than
the bare HVA when the target Hamiltonian has symmetry-broken ground states.


  Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful
framework for recovering stochastic dynamics via their marginal observations at
different time points. Despite numerous successful applications, existing
algorithms for solving DSBs have so far failed to utilize the structure of
aligned data, which naturally arises in many biological phenomena. In this
paper, we propose a novel algorithmic framework that, for the first time,
solves DSBs while respecting the data alignment. Our approach hinges on a
combination of two decades-old ideas: The classical Schr\"odinger bridge theory
and Doob's $h$-transform. Compared to prior methods, our approach leads to a
simpler training procedure with lower variance, which we further augment with
principled regularization schemes. This ultimately leads to sizeable
improvements across experiments on synthetic and real data, including the tasks
of predicting conformational changes in proteins and temporal evolution of
cellular differentiation processes.


  This commentary dedicates to envision what role THz is going to play in the
coming human-centric 6G era. Three distinct THz network types including
outdoor, indoor, and body area networks are discussed, with an emphasis on
their capabilities in human body detection. Synthesizing these networks will
unlock a bunch of fascinating applications across industrial, biomedical and
entertainment fields, significantly enhancing the quality of human life.


  Quasi-static speckles are a current limitation to faint companion imaging of
bright stars. Here we show through simulation and theory that an adaptive pupil
mask can be used to reduce these speckles and increase the visibility of faint
companions. This is achieved by placing an adaptive mask in the conjugate pupil
plane of the telescope. The mask consists of a number of independently
controllable elements which can either allow the light in the subaperture to
pass or block it. This actively changes the shape of the telescope pupil and
hence the diffraction pattern in the focal plane. By randomly blocking
subapertures we force the quasi-static speckles to become dynamic. The long
exposure PSF is then smooth, absent of quasi-static speckles. However, as the
PSF will now contain a larger halo due to the blocking, the signal to noise
ratio (SNR) is reduced requiring longer exposure times to detect the companion.
For example, in the specific case of a faint companion at 5xlambda/D the
exposure time to achieve the same SNR will be increased by a factor of 1.35. In
addition, we show that the visibility of companions can be greatly enhanced in
comparison to long-exposures, when the dark speckle method is applied to short
exposure images taken with the adaptive pupil mask. We show that the contrast
ratio between PSF peak and the halo is then increased by a factor of
approximately 100 (5 magnitudes), and we detect companions 11 magnitudes
fainter than the star at 5xlambda/D and up to 18 magnitudes fainter at
22.5xlambda/D.


  User online behavior and interests will play a central role in future mobile
networks. We introduce a systematic method for large-scale multi-dimensional
analysis of online activity for thousands of mobile users across 79 buildings
over a variety of web domains. We propose a modeling approach based on
self-organizing maps (SOM) for discovering, organizing and visualizing
different mobile users' trends from billions of WLAN records. We find
surprisingly that users' trends based on domains and locations can be
accurately modeled using a self-organizing map with clearly distinct
characteristics. We also find many non-trivial correlations between different
types of web domains and locations. Based on our analysis, we introduce a
mixture model as an initial step towards realistic simulation of wireless
network usage.


  In quantum chromodynamics (QCD), gluons acquire a mass scale through the
action of the Schwinger mechanism. This mass emerges as a result of the
dynamical formation of massless bound-states of gluons which manifest as
longitudinally coupled poles in the vertices. In this contribution, we show how
the presence of these poles can be determined from lattice QCD results for the
propagators and vertices. The crucial observation that allows this
determination is that the Schwinger mechanism poles induce modifications,
called ``displacements'', to the Ward identities (WIs) relating two- and
three-point functions. Importantly, the displacement functions correspond
precisely to the Bethe-Salpeter amplitudes of the massless bound-states. We
apply this idea to the case of the three-gluon vertex in pure Yang-Mills SU(3).
Using lattice results in the corresponding WI, we find an unequivocal
displacement and show that it is consistent with the prediction based on the
Bethe-Salpeter equation.


  The gravitational waves (GW) from core-collapse supernovae (CCSN) have been
proposed as a probe to investigate physical properties inside of the supernova.
However, how to search and extract the GW signals from core-collapse supernovae
remains an open question due to its complicated time-frequency structure. In
this paper, we apply the Ensemble Empirical Mode Decomposition (EEMD) method to
decompose and reconstruct simulated GW data generated by magnetorotational
mechanism and neutrino-driven mechanism within the advanced LIGO, using the
match score as the criterion for assessing the quality of the reconstruction.
The results indicate that by decomposing the data, the sum of the first six
intrinsic mode functions (IMFs) can be used as the reconstructed waveform. To
determine the probability that our reconstructed waveform corresponds to a real
GW waveform, we calculate the false alarm probability of reconstruction (FAPR).
By setting the threshold of the match score to be 0.75, we obtain FAPR of GW
sources at a distance of 5 kpc and 10 kpc to be $6\times10^{-3}$ and
$1\times10^{-2}$ respectively. If we normalize the maximum amplitude of the GW
signal to $5\times10^{-21}$, the FAPR at this threshold is $4\times10^{-3}$.
Furthermore, in our study, the reconstruction distance is not equivalent to the
detection distance. When the strain of GW reaches $7 \times 10^{-21}$, and the
match score threshold is set at 0.75, we can reconstruct GW waveform up to
approximately 36 kpc.


  Many researchers from a variety of fields including computer science, network
science and mathematics have focused on how to contain the outbreaks of
Internet misinformation that threaten social systems and undermine societal
health. Most research on this topic treats the connections among individuals as
static, but these connections change in time, and thus social networks are also
temporal networks. Currently there is no theoretical approach to the problem of
containing misinformation outbreaks in temporal networks. We thus propose a
misinformation spreading model for temporal networks and describe it using a
new theoretical approach. We propose a heuristic-containing (HC) strategy based
on optimizing final outbreak size that outperforms simplified strategies such
as those that are random-containing (RC) and targeted-containing (TC). We
verify the effectiveness of our HC strategy on both artificial and real-world
networks by performing extensive numerical simulations and theoretical
analyses. We find that the HC strategy greatly increases the outbreak threshold
and decreases the final outbreak threshold.


  Instrumenting programs for performing run-time checking of properties, such
as regular shapes, is a common and useful technique that helps programmers
detect incorrect program behaviors. This is specially true in dynamic languages
such as Prolog. However, such run-time checks inevitably introduce run-time
overhead (in execution time, memory, energy, etc.). Several approaches have
been proposed for reducing such overhead, such as eliminating the checks that
can statically be proved to always succeed, and/or optimizing the way in which
the (remaining) checks are performed. However, there are cases in which it is
not possible to remove all checks statically (e.g., open libraries which must
check their interfaces, complex properties, unknown code, etc.) and in which,
even after optimizations, these remaining checks still may introduce an
unacceptable level of overhead. It is thus important for programmers to be able
to determine the additional cost due to the run-time checks and compare it to
some notion of admissible cost. The common practice used for estimating
run-time checking overhead is profiling, which is not exhaustive by nature.
Instead, we propose a method that uses static analysis to estimate such
overhead, with the advantage that the estimations are functions parameterized
by input data sizes. Unlike profiling, this approach can provide guarantees for
all possible execution traces, and allows assessing how the overhead grows as
the size of the input grows. Our method also extends an existing assertion
verification framework to express "admissible" overheads, and statically and
automatically checks whether the instrumented program conforms with such
specifications. Finally, we present an experimental evaluation of our approach
that suggests that our method is feasible and promising.


  This paper deals with positivity properties for a pseudodifferential
calculus, generalizing Weyl's classical quantization, and set on an infinite
dimensional phase space, the Wiener space. In this frame, we show that a
positive symbol does not, in general, give a positive operator. In order to
measure the nonpositivity, we establish a G\r{a}rding's inequality, which holds
for the symbol classes at hand. Nevertheless, for symbols with radial aspects,
additional assumptions ensure the positivity of the associated operator.


  ACO2163 is one of the hottest (mean $kT=12-15.5$ keV) and extremely X-ray
overluminous merging galaxy clusters which is located at $z=0.203$. The cluster
hosts one of the largest giant radio halos which are observed in most of the
merging clusters, and a candidate radio relic. Recently, three merger shock
fronts were detected in this cluster, explaining its extreme temperature and
complex structure. Furthermore, previous XMM-Newton and Chandra observations
hinted at the presence of a shock front that is associated with the gas
`bullet' crossing the main cluster in the west-ward direction, and which heated
the intra-cluster medium, leading to adiabatic compression of the gas behind
the 'bullet'. The goal of this paper is to report on the detection of this
shock front as revealed by the temperature discontinuity in the X-ray
XMM-Newton image, and the edge in the Very Large Array (VLA) radio image. We
also report on the detection of a relic source in the north-eastern region of
the radio halo in the KAT-7 data, confirming the presence of an extended relic
in this cluster. The brightness edge in the X-rays corresponds to a shock front
with a Mach number $M= 2.2\pm0.3$, at a distance of 0.2 Mpc from the cluster
centre. An estimate from the luminosity jump gives $M=1.9\pm0.4$. We consider a
simple explanation for the electrons at the shock front, and for the observed
discrepancy between the average spectral index of the radio halo emission and
that predicted by the $M=2.2$ shock which precedes the 'bullet'.


  Attitude is one of the crucial parameters for space objects and plays a vital
role in collision prediction and debris removal. Analyzing light curves to
determine attitude is the most commonly used method. In photometric
observations, outliers may exist in the obtained light curves due to various
reasons. Therefore, preprocessing is required to remove these outliers to
obtain high quality light curves. Through statistical analysis, the reasons
leading to outliers can be categorized into two main types: first, the
brightness of the object significantly increases due to the passage of a star
nearby, referred to as "stellar contamination," and second, the brightness
markedly decreases due to cloudy cover, referred to as "cloudy contamination."
Traditional approach of manually inspecting images for contamination is
time-consuming and labor-intensive. However, We propose the utilization of
machine learning methods as a substitute. Convolutional Neural Networks (CNN)
and Support Vector Machines (SVM) are employed to identify cases of stellar
contamination and cloudy contamination, achieving F1 scores of 1.00 and 0.98 on
test set, respectively. We also explored other machine learning methods such as
Residual Network-18 (ResNet-18) and Light Gradient Boosting Machine (lightGBM),
then conducted comparative analyses of the results.


  As the number of recorded meetings increases, it becomes increasingly
important to utilize summarization technology to create useful summaries of
these recordings. However, there is a crucial lack of annotated meeting corpora
for developing this technology, as it can be hard to collect meetings,
especially when the topics discussed are confidential. Furthermore, meeting
summaries written by experienced writers are scarce, making it hard for
abstractive summarizers to produce sensible output without a reliable
reference. This lack of annotated corpora has hindered the development of
meeting summarization technology. In this paper, we present MeetingBank, a new
benchmark dataset of city council meetings over the past decade. MeetingBank is
unique among other meeting corpora due to its divide-and-conquer approach,
which involves dividing professionally written meeting minutes into shorter
passages and aligning them with specific segments of the meeting. This breaks
down the process of summarizing a lengthy meeting into smaller, more manageable
tasks. The dataset provides a new testbed of various meeting summarization
systems and also allows the public to gain insight into how council decisions
are made. We make the collection, including meeting video links, transcripts,
reference summaries, agenda, and other metadata, publicly available to
facilitate the development of better meeting summarization techniques. Our
dataset can be accessed at: https://meetingbank.github.io


  At present, the cloud storage used in searchable symmetric encryption schemes
(SSE) is provided in a private way, which cannot be seen as a true cloud.
Moreover, the cloud server is thought to be credible, because it always returns
the search result to the user, even they are not correct. In order to really
resist this malicious adversary and accelerate the usage of the data, it is
necessary to store the data on a public chain, which can be seen as a
decentralized system. As the increasing amount of the data, the search problem
becomes more and more intractable, because there does not exist any effective
solution at present.
  In this paper, we begin by pointing out the importance of storing the data in
a public chain. We then innovatively construct a model of SSE using
blockchain(SSE-using-BC) and give its security definition to ensure the privacy
of the data and improve the search efficiency. According to the size of data,
we consider two different cases and propose two corresponding schemes. Lastly,
the security and performance analyses show that our scheme is feasible and
secure.


  The leading term for the energy of a bound state of k-quarks and k-antiquarks
is proportional to its separation L. These k-string configurations have a
Luscher term associated with their quantum fluctuations which is typically a
1/L correction to the energy. We review the status of tensions and Luscher
terms in the context of lattice gauge theory, Hamiltonian methods, and
gauge/gravity correspondence. Furthermore we explore how different
representations of the k-string manifest themselves in the gauge/gravity
duality. We calculate the Luscher term for a strongly coupled SU(N) gauge
theory in (2+1) dimensions using the gauge/gravity correspondence. Namely, we
compute one-loop corrections to a probe D4-brane embedded in the Cvetic,
Gibbons, Lu, and Pope supergravity background. We investigate quantum
fluctuations of both the bosonic and the fermionic sectors.


  I report on the discovery of quantum compatible local variables that are
shared between subsystems of quantum-conventionally entangled physical systems
such that they determine the correlations of spatially separated systems while
preserving strict Einstein locality. This puts an end to the mystery of spooky
action at a distance and alleged collapse at a distance, answering vital
questions, first raised in the EPR paper, on the behaviour of spatially
separated entangled systems. The solution helps to understand quantitative
measures of entanglement in a transparent way. It also provides new insight,
consistent with strict locality, of the physics of quantum teleportation and
related phenomena.


  We have studied analytically the longitudinally boost-invariant motion of a
relativistic dissipative fluid with spin. We have derived the analytic
solutions of spin density and spin chemical potential as a function of proper
time $\tau$ in the presence of viscous tensor and the second order relaxation
time corrections for spin. Interestingly, analogous to the ordinary particle
number density and chemical potential, we find that the spin density and spin
chemical potential decay as $\sim\tau^{-1}$ and $\sim\tau^{-1/3}$,
respectively. It implies that the initial spin density may not survive at the
freezeout hyper-surface. These solutions can serve both to gain insight on the
dynamics of spin polarization in relativistic heavy-ion collisions and as
testbeds for further numerical codes.


  We present charged-particle distributions sensitive to the underlying event,
measured by the ATLAS detector in proton-proton collisions at a centre-of-mass
energy of 13 TeV, in low-luminosity Large Hadron Collider fills corresponding
to an integrated luminosity of 1.6 nb$^{-1}$. The distributions were
constructed using charged particles with absolute pseudorapidity less than 2.5
and with transverse momentum greater than 500 MeV, in events with at least one
such charged particle with transverse momentum above 1 GeV. These distributions
characterise the angular distribution of energy and particle flows with respect
to the charged particle with highest transverse momentum, as a function of both
that momentum and of charged-particle multiplicity. The results have been
corrected for detector effects and are compared to the predictions of various
Monte Carlo event generators, experimentally establishing the level of
underlying-event activity at LHC Run 2 energies and providing inputs for the
development of event generator modelling. The current models in use for UE
modelling typically describe this data to 5% accuracy, compared with data
uncertainties of less than 1%.


  This note discusses properties of parametric discrete-time Mixed-Integer
Optimal Control Problems (MIOCPs) as they often arise in mixed-integer NMPC. We
argue that in want for a handle on similarity properties of parametric MIOCPs
the classical turnpike notion from optimal control is helpful. We provide
sufficient turnpike conditions based on a dissipativity notion of MIOCPs, and
we show that the turnpike property allows specific and accurate guesses for the
integer-valued controls. Moreover, we show how the turnpike property can be
used to derive efficient node-weighted branch-and-bound schemes tailored to
parametric MIOCPs. We draw upon numerical examples to illustrate our findings.


  By exploiting the relation between Fredholm modules and the
Segal-Shale-Stinespring version of canonical quantization, and taking as
starting point the first-quantized fields described by Connes' axioms for
noncommutative spin geometries, a Hamiltonian framework for fermion quantum
fields over noncommutative manifolds is introduced. We analyze the ultraviolet
behaviour of second-quantized fields over noncommutative 3-tori, and discuss
what behaviour should be expected on other noncommutative spin manifolds.


  This manuscript introduces a regression-type formulation for approximating
the Perron-Frobenius Operator by relying on distributional snapshots of data.
These snapshots may represent densities of particles. The Wasserstein metric is
leveraged to define a suitable functional optimization in the space of
distributions. The formulation allows seeking suitable dynamics so as to
interpolate the distributional flow in function space. A first-order necessary
condition for optimality is derived and utilized to construct a gradient flow
approximating algorithm. The framework is exemplied with numerical simulations.


  This study suggests a new data-driven model for the prediction of geomagnetic
storm. The model which is an instance of Brain Emotional Learning Inspired
Models (BELIMs), is known as the Brain Emotional Learning-based Prediction
Model (BELPM). BELPM consists of four main subsystems; the connection between
these subsystems has been mimicked by the corresponding regions of the
emotional system. The functions of these subsystems are explained using
adaptive networks. The learning algorithm of BELPM is defined using the
steepest descent (SD) and the least square estimator (LSE). BELPM is employed
to predict geomagnetic storms using two geomagnetic indices, Auroral Electrojet
(AE) Index and Disturbance Time (Dst) Index. To evaluate the performance of
BELPM, the obtained results have been compared with ANFIS, WKNN and other
instances of BELIMs. The results verify that BELPM has the capability to
achieve a reasonable accuracy for both the short-term and the long-term
geomagnetic storms prediction.


  We consider the attenuated geodesic ray transform defined on pairs of
symmetric $2$-tensors and $1$-forms on a simple Riemannian manifold. We prove
injectivity and stability results for a class of generic simple metrics and
attenuations containing real analytic ones. In fact, methods used in this paper
can be modified to generalize our results for a class of non-simple manifolds
similar to Stefanov-Uhlmann [American Journal of Mathematics, {\bf 130}
(1):239--268 (2008)].


  Protected database search systems cryptographically isolate the roles of
reading from, writing to, and administering the database. This separation
limits unnecessary administrator access and protects data in the case of system
breaches. Since protected search was introduced in 2000, the area has grown
rapidly; systems are offered by academia, start-ups, and established companies.
  However, there is no best protected search system or set of techniques.
Design of such systems is a balancing act between security, functionality,
performance, and usability. This challenge is made more difficult by ongoing
database specialization, as some users will want the functionality of SQL,
NoSQL, or NewSQL databases. This database evolution will continue, and the
protected search community should be able to quickly provide functionality
consistent with newly invented databases.
  At the same time, the community must accurately and clearly characterize the
tradeoffs between different approaches. To address these challenges, we provide
the following contributions:
  1) An identification of the important primitive operations across database
paradigms. We find there are a small number of base operations that can be used
and combined to support a large number of database paradigms.
  2) An evaluation of the current state of protected search systems in
implementing these base operations. This evaluation describes the main
approaches and tradeoffs for each base operation. Furthermore, it puts
protected search in the context of unprotected search, identifying key gaps in
functionality.
  3) An analysis of attacks against protected search for different base
queries.
  4) A roadmap and tools for transforming a protected search system into a
protected database, including an open-source performance evaluation platform
and initial user opinions of protected search.


  SPARC collaboration at FAIR pursues the worldwide unique research program by
utilizing storage ring and trapping facilities for highly-charged heavy ions.
The main focus is laid on the exploration of the physics at strong, ultra-short
electromagnetic fields including the fundamental interactions between electrons
and heavy nuclei as well as on the experiments at the border between nuclear
and atomic physics. Very recently SPARC worked out a realization scheme for
experiments with highly-charged heavy-ions at relativistic energies in the
High-Energy Storage Ring HESR and at very low-energies at the CRYRING coupled
to the present ESR. Both facilities provide unprecedented physics opportunities
already at the very early stage of FAIR operation. The installation of CRYRING,
dedicated Low-energy Storage Ring (LSR) for FLAIR, may even enable a much
earlier realisation of the physics program of FLAIR with slow anti-protons.


  We focus on online second price auctions, where bids are made sequentially,
and the winning bidder pays the maximum of the second-highest bid and a seller
specified reserve price. For many such auctions, the seller does not see all
the bids or the total number of bidders accessing the auction, and only
observes the current selling prices throughout the course of the auction. We
develop a novel non-parametric approach to estimate the underlying consumer
valuation distribution based on this data. Previous non-parametric approaches
in the literature only use the final selling price and assume knowledge of the
total number of bidders. The resulting estimate, in particular, can be used by
the seller to compute the optimal profit-maximizing price for the product. Our
approach is free of tuning parameters, and we demonstrate its computational and
statistical efficiency in a variety of simulation settings, and also on an Xbox
7-day auction dataset on eBay.


  Efficiently querying Description Logic (DL) ontologies is becoming a vital
task in various data-intensive DL applications. Considered as a basic service
for answering object queries over DL ontologies, instance checking can be
realized by using the most specific concept (MSC) method, which converts
instance checking into subsumption problems. This method, however, loses its
simplicity and efficiency when applied to large and complex ontologies, as it
tends to generate very large MSC's that could lead to intractable reasoning. In
this paper, we propose a revision to this MSC method for DL SHI, allowing it to
generate much simpler and smaller concepts that are specific-enough to answer a
given query. With independence between computed MSC's, scalability for query
answering can also be achieved by distributing and parallelizing the
computations. An empirical evaluation shows the efficacy of our revised MSC
method and the significant efficiency achieved when using it for answering
object queries.


  With appropriate boundary conditions the anisotropic $XY$ chain in a magnetic
field is known to be invariant under quantum group transformations. We
generalize this model defining a class of integrable chains with several
fermionic degrees of freedom per site. In order to maintain the quantum group
symmetry a general condition on the parameters of these systems is derived. It
is shown that the corresponding quantum algebra is a multi-parameter
deformation of the Clifford algebra. Discussing a special physical example we
observe a new type of zero modes.


  Continuous graph neural networks (CGNNs) have garnered significant attention
due to their ability to generalize existing discrete graph neural networks
(GNNs) by introducing continuous dynamics. They typically draw inspiration from
diffusion-based methods to introduce a novel propagation scheme, which is
analyzed using ordinary differential equations (ODE). However, the
implementation of CGNNs requires significant computational power, making them
challenging to deploy on battery-powered devices. Inspired by recent spiking
neural networks (SNNs), which emulate a biological inference process and
provide an energy-efficient neural architecture, we incorporate the SNNs with
CGNNs in a unified framework, named Continuous Spiking Graph Neural Networks
(COS-GNN). We employ SNNs for graph node representation at each time step,
which are further integrated into the ODE process along with time. To enhance
information preservation and mitigate information loss in SNNs, we introduce
the high-order structure of COS-GNN, which utilizes the second-order ODE for
spiking representation and continuous propagation. Moreover, we provide the
theoretical proof that COS-GNN effectively mitigates the issues of exploding
and vanishing gradients, enabling us to capture long-range dependencies between
nodes. Experimental results on graph-based learning tasks demonstrate the
effectiveness of the proposed COS-GNN over competitive baselines.


  Bing doubling is an operation which produces a 2-component boundary link B(K)
from a knot K. If K is slice, then B(K) is easily seen to be boundary slice. In
this paper, we investigate whether the converse holds. Our main result is that
if B(K) is boundary slice, then K is algebraically slice. We also show that the
Rasmussen invariant can tell that certain Bing doubles are not smoothly slice.


  The chemical enrichment of the Universe; the mass spectrum of planetary
nebulae, white dwarfs and gravitational wave progenitors; the frequency
distribution of Type I and II supernovae; the fate of exoplanets ... a
multitude of phenomena which is highly regulated by the amounts of mass that
stars expel through a powerful wind. For more than half a century, these winds
of cool ageing stars have been interpreted within the common interpretive
framework of 1-dimensional (1D) models. I here discuss how that framework now
appears to be highly problematic.
  * Current 1D mass-loss rate formulae differ by orders of magnitude, rendering
contemporary stellar evolution predictions highly uncertain.
  These stellar winds harbour 3D complexities which bridge 23 orders of
magnitude in scale, ranging from the nanometer up to thousands of astronomical
units. We need to embrace and understand these 3D spatial realities if we aim
to quantify mass loss and assess its effect on stellar evolution. We therefore
need to gauge
  * the 3D life of molecules and solid-state aggregates: the gas-phase clusters
that form the first dust seeds are not yet identified. This limits our ability
to predict mass-loss rates using a self-consistent approach.
  * the emergence of 3D clumps: they contribute in a non-negligible way to the
mass loss, although they seem of limited importance for the wind-driving
mechanism.
  * the 3D lasting impact of a (hidden) companion: unrecognised binary
interaction has biased previous mass-loss rate estimates towards values that
are too large.
  Only then will it be possible to drastically improve our predictive power of
the evolutionary path in 4D (classical) spacetime of any star.


  We study the instability of a doubly quantized vortex topologically imprinted
on $^{23}$Na condensate, as reported in recent experiment [Phys. Rev. Lett.
\textbf{93}, 160406 (2004)]. We have performed numerical simulations using
three-dimensional Gross-Pitaevskii equation with classical thermal noise.
Splitting of a doubly quantized vortex turns out to be a process that is very
sensitive to the presence of thermal atoms. We observe that even ve ry small
thermal fluctuations, corresponding to 10 to 15% of thermal atoms, ca use the
decay of doubly quantized vortex into two singly quantized vortices in tens of
milliseconds. As in the experiment, the lifetime of doubly quantized vortex i s
a monotonic function of the interaction strength.


  We demonstrate an exceptionally bright photon source based on a single
nitrogen- vacancy center (NV-center) in a nanodiamond (ND), placed in the
nanoscale gap between two monocrystalline silver cubes in a dimer
configuration. The system is operated near saturation at a stable photon rate
of 850 kcps, while we further achieve strongly polarized emission and high
single photon purity, evident by the measured auto-correlation with a
g(2)(0)-value of 0.08. These photon source features are key parameters for
quantum technological applications, such as secure communication based on
quantum key distribution. The cube antenna is assembled with an atomic force
microscope, which allows us to predetermine the dipole orientation of the
NV-center and optimize cube positioning accordingly, while also tracking the
evolution of emission parameters from isolated ND to the 1 and 2 cube
configuration. The experiment is well described by finite element modelling,
assuming an instrinsic quantum efficiency of 0.35. We attribute the large
photon rate of the assembled photon source, to increased quantum efficiency of
the NV-center and high antenna efficiency.


  The nature of fast magnetoacoustic and Alfv\'en waves is investigated in a
zero $\beta$ plasma. This gives an indication of wave propagation in the low
$\beta$ solar corona. It is found that for a two-dimensional null point, the
fast wave is attracted to that point and the front of the wave slows down as it
approaches the null point, causing the current density to accumulate there and
rise rapidly. Ohmic dissipation will extract the energy in the wave at this
point. This illustrates that null points play an important role in the rapid
dissipation of fast magnetoacoustic waves and suggests the location where wave
heating will occur in the corona. The Alfv\'en wave behaves in a different
manner in that the wave energy is dissipated along the separatrices. For
Alfv\'en waves that are decoupled from fast waves, the value of the plasma
$\beta$ is unimportant. However, the phenomenon of dissipating the majority of
the wave energy at a specific place is a feature of both wave types.


  We prove that Kahler-Einstein Fano manifolds with finite automorphism groups
form Hausdorff moduli algebraic space with only quotient singularities. We also
discuss the limits as Q-Fano varieties which should be put on the boundary of
its canonical compactification.


  We define and investigate, via numerical analysis, a one dimensional
toy-model of a cloud chamber. An energetic quantum particle, whose initial
state is a superposition of two identical wave packets with opposite average
momentum, interacts during its evolution and exchanges (small amounts of)
energy with an array of localized spins. Triggered by the interaction with the
environment, the initial superposition state turns into an incoherent sum of
two states describing the following situation: or the particle is going to the
left and a large number of spins on the left side changed their states, or the
same is happening on the right side. This evolution is reminiscent of what
happens in a cloud chamber where a quantum particle, emitted as a spherical
wave by a radioactive source, marks its passage inside a supersaturated
vapour-chamber in the form of a sequence of small liquid bubbles arranging
themselves around a possible classical trajectory of the particle.


  We report the transition to an active state of the nucleus in the Seyfert 1.9
galaxy NGC 2992, discovered by means of new hard X-ray data. While the 2-10 keV
flux declined by a factor of ~ 20 from 1978 to 1994, two recent BeppoSAX
observations in 1997 and in 1998 caught the nuclear emission raising back to
the same level of activity observed in 1978.
  In both BeppoSAX observations the X-ray spectrum of the source is well
represented by a power law with spectral index Gamma ~ 1.7, absorbed by a
column density of N_H ~ 10^{22} cm^{-2} and characterized by a prominent iron
K\alpha line. While in the second BeppoSAX data set the line properties appear
to be consistent with those expected from accretion disc models, in the first
BeppoSAX data set the iron feature is rather peculiar. The broadening is not
significant and the line energy is E_{K\alpha}=6.62 +/- 0.07 keV, indicating
emission from highly ionized iron. The line has too high equivalent width (~
700 eV) to be produced by a hot scattering medium. By comparing these data with
data previously in the literature, we interpret the spectral and flux changes
in terms of different phases of rebuilding an accretion disc. The timescale for
the disc rebuilding is estimated to range between 1 and 5 years.
  The X-ray data are complemented with optical and near-infrared followup
spectra taken 1.5 months after the discovery of the X-ray burst. The spectra
are characterized by prominent broad emission lines. There is also evidence for
hot dust emission in the H and K bands that, however, is probably still in the
process of increasing.


  We report first-principles GW-Bethe Salpeter Equation and Quantum Monte Carlo
calculations of the optical and electronic properties of molecular and
crystalline rubrene (C$_{42}$H$_{28}$). Many-body effects dominate the optical
spectrum and quasi-particle gap of molecular crystals. We interpret the
observed yellow-green photoluminescence in rubrene microcrystals as a result of
the formation of intermolecular, charge-transfer spin-singlet excitons. In
contrast, spin-triplet excitons are localized and intramolecular with a
predicted phosphorescence at the red end of the optical spectrum. We find that
the exchange energy plays a fundamental role in raising the energy of
intramolecular spin-singlet excitons above the intermolecular ones. Exciton
binding energies are predicted to be around 0.5 eV (spin singlet) to 1 eV (spin
triplet). The calculated electronic gap is 2.8 eV. The theoretical absorption
spectrum agrees very well with recent ellipsometry data.


  An implicit Euler finite-volume scheme for general cross-diffusion systems
with volume-filling constraints is proposed and analyzed. The diffusion matrix
may be nonsymmetric and not positive semidefinite, but the diffusion system is
assumed to possess a formal gradient-flow structure that yields $L^\infty$
bounds on the continuous level. Examples include the Maxwell-Stefan systems for
gas mixtures, tumor-growth models, and systems for the fabrication of thin-film
solar cells. The proposed numerical scheme preserves the structure of the
continuous equations, namely the entropy dissipation inequality as well as the
nonnegativity of the concentrations and the volume-filling constraints. The
discrete entropy structure is a consequence of a new vector-valued discrete
chain rule. The existence of discrete solutions, their positivity, and the
convergence of the scheme is proved. The numerical scheme is implemented for a
one-dimensional Maxwell-Stefan model and a two-dimensional thin-film solar cell
system. It is illustrated that the convergence rate in space is of order two
and the discrete relative entropy decays exponentially.


  In this note we prove that in a metric measure space $(X, d, m)$ verifying
the measure contraction property with parameters $K \in \mathbb{R}$ and $1< N<
\infty$, any optimal transference plan between two marginal measures is induced
by an optimal map, provided the first marginal is absolutely continuous with
respect to $m$ and the space itself is essentially non-branching. In particular
this shows that there exists a unique transport plan and it is induced by a
map.


  A distributed binary hypothesis testing problem, in which multiple observers
transmit their observations to a detector over noisy channels, is studied.
Given its own side information, the goal of the detector is to decide between
two hypotheses for the joint distribution of the data. Single-letter upper and
lower bounds on the optimal type 2 error exponent (T2-EE), when the type 1
error probability vanishes with the block-length are obtained. These bounds
coincide and characterize the optimal T2-EE when only a single helper is
involved. Our result shows that the optimal T2-EE depends on the marginal
distributions of the data and the channels rather than their joint
distribution. However, an operational separation between HT and channel coding
does not hold, and the optimal T2-EE is achieved by generating channel inputs
correlated with observed data.


  Graph transformers typically lack third-order interactions, limiting their
geometric understanding which is crucial for tasks like molecular geometry
prediction. We propose the Triplet Graph Transformer (TGT) that enables direct
communication between pairs within a 3-tuple of nodes via novel triplet
attention and aggregation mechanisms. TGT is applied to molecular property
prediction by first predicting interatomic distances from 2D graphs and then
using these distances for downstream tasks. A novel three-stage training
procedure and stochastic inference further improve training efficiency and
model performance. Our model achieves new state-of-the-art (SOTA) results on
open challenge benchmarks PCQM4Mv2 and OC20 IS2RE. We also obtain SOTA results
on QM9, MOLPCBA, and LIT-PCBA molecular property prediction benchmarks via
transfer learning. We also demonstrate the generality of TGT with SOTA results
on the traveling salesman problem (TSP).


  We give a simple and direct treatment of the strong convergence of quantum
random walks to quantum stochastic operator cocycles, via the semigroup
decomposition of such cocycles. Our approach also delivers convergence of the
pointwise product of quantum random walks to the quantum stochastic Trotter
product of the respective limit cocycles, thereby revealing the algebraic
structure of the limiting procedure. The repeated quantum interactions model is
shown to fit nicely into the convergence scheme described.


  The goal of this PhD thesis was to characterize the properties of friction in
nanotubes and from a more general point of view the understanding of the
microscopic origin of friction. Indeed, the relative simplicity of the system
allows us to interpret more easily the physical phenomenon observed than in
larger systems. In order to achieve this goal, non-equilibrium statistical
mechanics permitted first to develop models based on Langevin equations
describing the dynamics of rotation and translation in double walled nanotubes.
The molecular dynamics simulations then permitted to validate these analytical
models, and thus to study general properties of friction such as the dependence
on area of contact, temperature and the geometry of the nanotubes. The results
obtained shows that friction increases linearly with the sliding velocity or
the angular velocity until very high values beyond which non-linearities appear
enhancing dissipation. In the linear regime, it is shown that the
proportionality factor between the dynamic friction force and the velocity is
given by the time integral of the autocorrelation function of the restoring
force for the sliding friction and of the torque for the rotational friction.
Furthermore, a novel resonant friction phenomenon increasing significantly
dissipation was observed for the sliding motion in certain types of nanotubes.
The effect arises at sliding velocities corresponding to certain vibrational
modes of the nanotubes. When the dynamics is described by the linear friction
in velocity, the empirical law stating that friction is proportional to the
area of contact is very well verified thanks to the molecular dynamics
simulations. On the other hand, friction increases with temperature.


  We report the results of an extensive FUSE study of high velocity OVI
absorption along 102 complete sight lines through the Galactic halo. The high
velocity OVI traces a variety of phenomena, including tidal interactions with
the Magellanic Clouds, accretion of gas, outflow from the Galactic disk,
warm/hot gas interactions in a highly extended Galactic corona, and
intergalactic gas in the Local Group. We identify 85 high velocity OVI features
at velocities of -500 < v(LSR) < +500 km/s along 59 of the 102 sight lines.
Approximately 60% of the sky (and perhaps as much as 85%) is covered by high
velocity H+ associated with the high velocity OVI. Some of the OVI is
associated with known high velocity HI structures (e.g., the Magellanic Stream,
Complexes A and C), while some OVI features have no counterpart in HI 21cm
emission. The smaller dispersion in the OVI velocities in the GSR and LGSR
reference frames compared to the LSR is necessary (but not conclusive) evidence
that some of the clouds are extragalactic. Most of the OVI cannot be produced
by photoionization, even if the gas is irradiated by extragalactic background
radiation. Collisions in hot gas are the primary OVI ionization mechanism. We
favor production of some of the OVI at the boundaries between warm clouds and a
highly extended [R > 70 kpc], hot [T > 10^6 K], low-density [n < 10^-4 cm^-3]
Galactic corona or Local Group medium. A hot Galactic corona or Local Group
medium and the prevalence of high velocity OVI are consistent with predictions
of galaxy formation scenarios. Distinguishing between the various phenomena
producing high velocity OVI will require continuing studies of the distances,
kinematics, elemental abundances, and physical states of the different types of
high velocity OVI features found in this study. (abbreviated)


  We build explicit supersymmetric unification models where grand unified gauge
symmetry breaking and supersymmetry (SUSY) breaking are caused by the same
sector. Besides, the SM-charged particles are also predicted by the symmetry
breaking sector, and they give the soft SUSY breaking terms through the
so-called gauge mediation. We investigate the mass spectrums in an explicit
model with SU(5) and additional gauge groups, and discuss its phenomenological
aspects. Especially, nonzero A-term and B-term are generated at one-loop level
according to the mediation via the vector superfields, so that the electro-weak
symmetry breaking and 125 GeV Higgs mass may be achieved by the large B-term
and A-term even if the stop mass is around 1 TeV.


  For a given integer $k$, an identity of the following shape is defined as:
finite sum of \begin{align*} \sum_{(i_1,\cdots,1_k)\in
S}\frac{(-1)^{t(i_1,\cdots,i_k)}q^{Q(i_1,\cdots,i_k)}}{(q^{n_1};q^{n_1})_{i_1}\cdots(q^{n_k};q^{n_k})_{i_k}}=\prod_{(a,n)\in
P}(q^a;q^n)_{\infty}^{r(a,n)} \end{align*} as a Rogers-Ramanujan type
identities of $index(n_1,n_2,\cdots,n_k)$, where $t(i_1,\cdots,i_k)$ is an
integer-valued function, $Q(i_1,\cdots,i_k)$ is a rational polynomials in
variables $i_1,\cdots,i_k,n_1,\cdots,n_k$ are positive integers with
$gcd(n_1,n_2,\cdots,n_k)=1$, $S$ is a subset of $\mathbb{Z}^k$, $P$ is a finite
subset of $\mathbb{Q}^2$ and $r(a,n)$ are integer-valued functions. We
construct some Rogers-Ramanujan type identities by using the constant term
method.


  Topological insulators display unusual light-matter interactions due to the
helical nature of surface electronic states. We study the near-field
interaction of light propagating in an optical fiber with crystals of Sb2Te3, a
3D topological insulator (TI), and observe a large apparent Faraday rotation.
The origin of this unexpected polarization rotation in the optical fiber is
attributed to a magneto-optical Kerr effect at the TI-fiber interface. We show
that the combined effects of time-reversal symmetry breaking, which arises from
Zeeman coupling of the electromagnetic field with the surface electrons of the
TI, and inversion symmetry breaking of optical excitations, which arises from
the exponential decay of the evanescent light across the TI crystal, are
central to realizing this giant polarization rotation. Our work demonstrates a
facile approach for realizing large magneto-optical effects without any
magnetic fields by exploiting the unique physics of light-matter interactions
at TI surfaces.


  A necessary and sufficient compactness criterion in Schauder Spaces is
proved.


  These are seven corrigenda to equations in the Lehmer article in American
Mathematical Monthly 92 (1985), pp 449--457, partially reproduced in the
Apelblat tables of integrals and series.


  The formal study of completely prime modules was initiated by N. J.
Groenewald and the current author in the paper; Completely prime submodules,
{\it Int. Elect. J. Algebra}, {\bf 13}, (2013), 1--14. In this paper, the study
of completely prime modules is continued. Firstly, the advantage completely
prime modules have over prime modules is highlited and different situations
that lead to completely prime modules given. Later, emphasis is put on fully
completely prime modules, (i.e., modules whose all submodules are completely
prime). For a fully completely prime left $R$-module $M$, if $a, b\in R$ and
$m\in M$, then $abm=bam$, $am=a^km$ for all positive integers $k$, and either
$am=abm$ or
  $bm=abm$. In the last section, two different torsion theories induced by the
completely prime radical are given.


  In its simplest form, the traffic flow prediction problem is restricted to
predicting a single time-step into the future. Multi-step traffic flow
prediction extends this set-up to the case where predicting multiple time-steps
into the future based on some finite history is of interest. This problem is
significantly more difficult than its single-step variant and is known to
suffer from degradation in predictions as the time step increases. In this
paper, two approaches to improve multi-step traffic flow prediction performance
in recursive and multi-output settings are introduced. In particular, a model
that allows recursive prediction approaches to take into account the temporal
context in term of time-step index when making predictions is introduced. In
addition, a conditional generative adversarial network-based data augmentation
method is proposed to improve prediction performance in the multi-output
setting. The experiments on a real-world traffic flow dataset show that the two
methods improve on multi-step traffic flow prediction in recursive and
multi-output settings, respectively.


  The famous open Vizing conjecture claims that the domination number of the
Cartesian product graph of two graphs $G$ and $H$ is at least the product of
the domination numbers of $G$ and $H$. Recently Gaar, Krenn, Margulies and
Wiegele used the graph class $\mathcal{G}$ of all graphs with $n_\mathcal{G}$
vertices and domination number $k_\mathcal{G}$ and reformulated Vizing's
conjecture as the problem that for all graph classes $\mathcal{G}$ and
$\mathcal{H}$ the Vizing polynomial is sum-of-squares (SOS) modulo the Vizing
ideal. By solving semidefinite programs (SDPs) and clever guessing they derived
SOS-certificates for some values of $k_\mathcal{G}$, $n_\mathcal{G}$,
$k_\mathcal{H}$, and $n_\mathcal{H}$.
  In this paper, we consider their approach for $k_\mathcal{G} = k_\mathcal{H}
= 1$. For this case we are able to derive the unique reduced Gr\"obner basis of
the Vizing ideal. Based on this, we deduce the minimum degree $(n_\mathcal{G} +
n_\mathcal{H} - 1)/2$ of an SOS-certificate for Vizing's conjecture, which is
the first result of this kind. Furthermore, we present a method to find
certificates for graph classes $\mathcal{G}$ and $\mathcal{H}$ with
$n_\mathcal{G} + n_\mathcal{H} -1 = d$ for general $d$, which is again based on
solving SDPs, but does not depend on guessing and depends on much smaller SDPs.
We implement our new method in SageMath and give new SOS-certificates for all
graph classes $\mathcal{G}$ and $\mathcal{H}$ with
$k_\mathcal{G}=k_\mathcal{H}=1$ and $n_\mathcal{G} + n_\mathcal{H} \leq 15$.


  Fix n>2. Let s be a principally embedded sl(2)-subalgebra in sl(n). A special
case of results of the second author and Gregg Zuckerman implies that there
exists a positive integer b(n) such that for any finite dimensional
sl(n)-representation, V, there exists an irreducible s-representation embedding
in V with dimension at most b(n). We prove that b(n)=n is the sharpest possible
bound. We also address embeddings other than the principal one.
  The exposition involves an application of the Cartan--Helgason theorem, Pieri
rules, Hermite reciprocity, and a calculation in the "branching algebra"
introduced by Roger Howe, Eng-Chye Tan, and the second author.


  We quantitatively scrutinize the effects of the radiation drag arising from
the radiation fields in a galactic bulge in order to examine the possibility
that the radiation drag could be an effective mechanism to extract angular
momentum in a spheroidal system like a bulge and allow plenty of gas to accrete
onto the galactic center. For this purpose, we numerically solve the
relativistic radiation hydrodynamical equation coupled with the accurate
radiative transfer and quantitatively assess the radiation drag efficiency. As
a result, we find that in an optically thick regime the radiation drag
efficiency is sensitively dependent on the density distributions of
interstellar medium (ISM). The efficiency drops according to $\tau_{\rm
T}^{-2}$ in an optically thick {\it uniform} ISM, where $\tau_{\rm T}$ is the
total optical depth of the dusty ISM, whereas the efficiency remains almost
constant at a high level if the ISM is {\it clumpy}. Hence, if the bulge
formation begins with a star formation event in a clumpy ISM, the radiation
drag will effectively work to remove the angular momentum and the accreted gas
may form a supermassive black hole. As a natural consequence, this mechanism
reproduces a putative linear relation between the mass of a supermassive black
hole and the mass of a galactic bulge, although further detailed modeling for
stellar evolution is required for the more precise prediction.


  We here study Finite Impulse Response (FIR) rectangular, not necessarily
causal, systems which are (para)-unitary on the unit circle (=the class
$\mathcal{U}$). First, we offer three characterizations of these systems. Then,
introduce a %easy-to-use description of all FIRs in $\mathcal{U}$, as copies of
a real polytope, parametrized by the dimensions and the McMillan degree of the
FIRs.
  Finally, we present six simple ways (along with their combinations) to
construct, from any FIR, a large family of FIRs, of various dimensions and
McMillan degrees, so that whenever the original system is in $\mathcal{U}$, so
is the whole family.
  A key role is played by Hankel matrices.


  Albeit the scalable performance of vision transformers (ViTs), the dense
computational costs (training & inference) undermine their position in
industrial applications. Post-training quantization (PTQ), tuning ViTs with a
tiny dataset and running in a low-bit format, well addresses the cost issue but
unluckily bears more performance drops in lower-bit cases. In this paper, we
introduce I&S-ViT, a novel method that regulates the PTQ of ViTs in an
inclusive and stable fashion. I&S-ViT first identifies two issues in the PTQ of
ViTs: (1) Quantization inefficiency in the prevalent log2 quantizer for
post-Softmax activations; (2) Rugged and magnified loss landscape in
coarse-grained quantization granularity for post-LayerNorm activations. Then,
I&S-ViT addresses these issues by introducing: (1) A novel shift-uniform-log2
quantizer (SULQ) that incorporates a shift mechanism followed by uniform
quantization to achieve both an inclusive domain representation and accurate
distribution approximation; (2) A three-stage smooth optimization strategy
(SOS) that amalgamates the strengths of channel-wise and layer-wise
quantization to enable stable learning. Comprehensive evaluations across
diverse vision tasks validate I&S-ViT' superiority over existing PTQ of ViTs
methods, particularly in low-bit scenarios. For instance, I&S-ViT elevates the
performance of 3-bit ViT-B by an impressive 50.68%.


  While image forensics is concerned with whether an image has been tampered
with, image anti-forensics attempts to prevent image forensics methods from
detecting tampered images. The competition between these two fields started
long before the advancement of deep learning. JPEG compression, blurring and
noising, which are simple methods by today's standards, have long been used for
anti-forensics and have been the subject of much research in both forensics and
anti-forensics. Although these traditional methods are old, they make it
difficult to detect fake images and are used for data augmentation in training
deep image forgery detection models. In addition to making the image difficult
to detect, these methods leave traces on the image and consequently degrade the
image quality. Separate image forensics methods have also been developed to
detect these traces. In this study, we go one step further and improve the
image quality after these methods with deep image restoration models and make
it harder to detect the forged image. We evaluate the impact of these methods
on image quality. We then test both our proposed methods with deep learning and
methods without deep learning on the two best existing image manipulation
detection models. In the obtained results, we show how existing image forgery
detection models fail against the proposed methods. Code implementation will be
publicly available at https://github.com/99eren99/DIRFIAF .


  Preparing problems for execution on quantum computers can require many
compilation steps. Automated compilation software is useful not only for easier
and faster problem execution, but also for facilitating the comparison between
different algorithmic choices. Here we describe mat2qubit, a Python package for
encoding several classes of classical and quantum problems into qubit
representations. It is intended for use especially on Hamiltonians and
functions defined over variables (e.g. particles) with cardinality larger than
2. More specifically, mat2qubit may be used to compile bosonic,
phononic/vibrational, and spin-$s$ problems, as well as classical problems such
as graph coloring, routing, scheduling, and classical linear algebra more
generally. In order to facilitate numerical analyses and ease of
programmability, a built-in computer algebra system (CAS) allows for fully
symbolic preparation and manipulation of problems (with symbolic operators,
symbolic coefficients, and symbolic particle labels) before the final
compilation into qubits is performed. We expect this code to be useful in the
preparation and analysis of various classes of physics, chemistry, materials,
and optimization problems for execution on digital quantum computers.


  The new interpolation model of state of binary mixture is investigated. This
model use only two parameters and produce many type of phase diagrams.


  We classify, up to homeomorphisms, the closed simply-connected 4-manifolds
that admit a Riemannian metric for which averages of pairs of sectional
curvatures of orthogonal planes are positive.


  The rapidly developing field of ferromagnetism in diluted magnetic
semiconductors, where a semiconductor host is magnetically doped by transition
metal impurities to produce a ferromagnetic semiconductor (e.g. Ga_{1-x}Mn_xAs
with x ~ 1-10 %), is discussed with the emphasis on elucidating the physical
mechanisms underlying the magnetic properties. Recent key developments are
summarized with critical discussions of the roles of disorder, localization,
band structure, defects, and the choice of materials in producing good magnetic
quality and high Curie temperature. The correlation between magnetic and
transport properties is argued to be a crucial ingredient in developing a full
understanding of the properties of ferromagnetic semiconductors.


  A detailed study of charge collection efficiency has been performed on the
Silicon Drift Detectors (SDD) of the ALICE experiment. Three different methods
to study the collected charge as a function of the drift time have been
implemented. The first approach consists in measuring the charge at different
injection distances moving an infrared laser by means of micrometric step
motors. The second method is based on the measurement of the charge injected by
the laser at fixed drift distance and varying the drift field, thus changing
the drift time. In the last method, the measurement of the charge deposited by
atmospheric muons is used to study the charge collection efficiency as a
function of the drift time. The three methods gave consistent results and
indicated that no charge loss during the drift is observed for the sensor types
used in 99% of the SDD modules mounted on the ALICE Inner Tracking System. The
atmospheric muons have also been used to test the effect of the
zero-suppression applied to reduce the data size by erasing the counts in cells
not passing the thresholds for noise removal. As expected, the zero suppression
introduces a dependence of the reconstructed charge as a function of drift time
because it cuts the signal in the tails of the electron clouds enlarged by
diffusion effects. These measurements allowed also to validate the correction
for this effect extracted from detailed Monte Carlo simulations of the detector
response and applied in the offline data reconstruction.


  The extrusion of polymer melts is known to be susceptible to `melt fracture'
instabilities, which can deform the extrudate, or cause it to break entirely.
Motivated by this, we consider the impact that the recently discovered polymer
diffusive instability (PDI) can have on polymer melts and other concentrated
polymeric fluids using the Oldroyd-B model with the effects of polymer stress
diffusion included. Analytic progress can be made in the concentrated limit
(when the solvent-to-total-viscosity ratio $\beta \rightarrow 0$), illustrating
the boundary layer structure of PDI, and allowing the prediction of its
eigenvalues for both plane Couette and channel flow. We draw connections
between PDI and the polymer melt `sharkskin' instability, both of which are
short wavelength instabilities localised to the extrudate surface. Inertia is
shown to have a destabilising effect, reducing the smallest Weissenberg number
($W$) where PDI exists in a concentrated fluid from $W\sim 8$ in inertialess
flows, to $W \sim 2$ when inertia is significant.


  In many years ago, Isgur and Llewellyn Smith addressed that PQCD is
inapplicable to exclusive processes, such as the pion form factor.The main
problem is that the asymptotic of PQCD is only about one fourth of the
experimental value. We reexamine this PQCD deep problem. By including NLO power
corrections to the pion form factor, we may arrive at a perturbative
explanation for the data. The key realization is that we need to interprete
that the strong interaction coupling constant involved in the PQCD result
should be taken as an effective coupling constant under nonperturbative QCD
vaccum. This implies that one can equally identify the relevant scale for the
effective coupling constant as the factorization scale about 1 GeV. We also
find that the average momentum fraction variable locates about 0.5, which is in
favor of the asymptotic pion wave function. By employing photon-pion form
factor with NLO power corrections to factorize out the nonperturbative effects
involved in the effective coupling constant, we can extract an effective
running coupling constant, which represents an effective coupling involving in
the hard scattering subprocesses. The difference between the effective running
coupling constant and the usual perturbative running coupling constant
($\Lambda_{QCD}=0.3$ GeV) is very small for $Q^2> 1 GeV^2$. The effective
running coupling constant $\alpha_s/\pi$ is smaller than 0.2 for $Q^2>1 GeV^2$.
  This directly showes that PQCD is applicable to exclusive processes at energy
$Q^2> 1 GeV^2$. In summary, with NLO power corrections, PQCD can completely
explain the $Q^2$ spectrum of pion form factor.


  The Large Hadron Collider (LHC) uses a multi-stage collimator system to
absorb the growing halo of circulating beams to protect and ensure reliable
operation of superconducting magnets. A similar system is planned for the
Future Circular Collider (FCC). In anticipation of the LHC operation with high
luminosity, research is being conducted to improve the collimation system.
Studies have shown that one of the solutions to improve beam collimation is to
use channeling in a short curved crystal, which acts as a primary collimator,
throwing particles deep into the secondary collimator by channeling. This
system is very sensitive to the angular position of the crystal and possible
vibrations of different nature. In this paper, we propose a different approach
to crystal collimation based on the volume reflection of particles from curved
crystallographic planes in a sequence of crystals. The positive qualities of
this scheme are substantiated and a multi-strip crystal device capable of
implementing it is proposed.


  We present estimates of the direct (in decay amplitudes) and indirect
(mixing- induced) CP-violating asymmetries in the non-leptonic charmless
two-body decay rates for $B \to PP$, $B \to PV$ and $B \to VV$ decays and their
charged conjugates, where P(V) is a light pseudoscalar (vector) meson. These
estimates are based on a generalized factorization approach making use of
next-to-leading order perturbative QCD contributions which generate the
required strong phases. No soft final state interactions are included. We study
the dependence of the asymmetries on a number of input parameters and show that
there are at least two (possibly three) classes of decays in which the
asymmetries are parametrically stable in this approach. The decay modes of
particular interest are: $\optbar{B^0} \to \pi^+ \pi^-$, $\optbar{B^0} \to
K_S^0 \pi^0$, $\optbar{B^0} \to K_S^0 \eta^\prime$, $\optbar{B^0} \to K_S^0
\eta$ and $\optbar{B^0} \to \rho^+ \rho^-$. Likewise, the CP-violating
asymmetry in the decays $\optbar{B^0} \to K_S^0 h^0$ with $h^0=\pi^0,K_S^0,
\eta,\eta^\prime$ is found to be parametrically stable and large. Measurements
of these asymmetries will lead to a determination of the phases $\sin 2\alpha$
and $\sin 2 \beta$ and we work out the relationships in these modes in the
present theoretical framework. We also show the extent of the so-called
"penguin pollution" in the rate asymmetry $A_{CP}(\pi^+ \pi^-)$ and of the
"tree shadow" in the asymmetry $A_{CP}(K_S^0\eta^\prime)$ which will effect the
determination of $\sin 2 \alpha$ and $\sin 2 \beta$ from the respective
measurements. CP-violating asymmetries in $B^\pm \to \pi^\pm \eta^\prime$,
$B^\pm \to K^{*\pm} \eta$, $B^\pm \to K^{*\pm} \eta^\prime$ and $B^\pm \to
K^{*\pm}\rho^0$ are potentially interesting and are studied here.


  In the coming decades, the United States aims to undergo an energy transition
away from fossil fuels and toward a fully decarbonized power grid. There are
many pathways that the US could pursue toward this objective, each of which
relies on different types of generating technologies to provide clean and
reliable electricity. One potential contributor to these pathways is advanced
nuclear fission, which encompasses various innovative nuclear reactor designs.
However, little is known about how cost-competitive these reactors would be
compared to other technologies, or about which aspects of their designs offer
the most value to a decarbonized power grid. We employ an electricity system
optimization model and a case study of a decarbonized U.S. Eastern
Interconnection circa 2050 to generate initial indicators of future economic
value for advanced reactors and the sensitivity of future value to various
design parameters, the availability of competing technologies, and the
underlying policy environment. These results can inform long-term cost targets
and guide near-term innovation priorities, investments, and reactor design
decisions. We find that advanced reactors should cost \$5.1-\$6.6/W to gain an
initial market share (assuming 30 year asset life and 3.5-6.5% real WACC),
while those that include thermal storage in their designs can cost up to
\$5.5-\$7.0/W (not including cost of storage). Since the marginal value of
advanced fission reactors declines as market penetration increases, break-even
costs fall around 19% at 100 GW of cumulative capacity and around 40% at 300
GW. Additionally, policies that provide investment tax credits for nuclear
energy create the most favorable environment for advanced nuclear fission.
Stakeholders and investors should consider these findings when deciding which
technologies to consider for decarbonizing the US power grid.


  A model of a particle in finite space is developed and the properties that
the particle may possess under this model are studied. The possibility that
particles attract each other due to their own wave nature is discussed. The
assumption that the particles are spatially confined oscillations (SCO) in the
medium is used. The relation between the SCO and the refractive index of the
medium in the idealized universe is derived. Due to the plane wave constituents
of SCOs, the presence of a refractive index field with a nonzero gradient
causes the SCO to accelerate. The SCO locally changes the refractive index such
that another SCO is accelerated towards it, and vice versa. It is concluded
that the particles can attract each other due to their wave nature and an
inverse-square-type acceleration emerges. The constant parameter in the
inverse-square-type acceleration is used to compare with the gravitational
constant $G_N$, and the possibility of non inverse-square-type behavior is
preliminary discussed.


  In this letter, Parikh-Wilczek tunnelling framework, which treats Hawking
radiation as a tunnelling process, is extended, and the emission rate of a
charged particle tunnelling from the Kerr-Newman black hole is calculated. The
emission spectrum takes the same functional form as that of uncharged particles
and consists with an underlying unitary theory but deviates from the pure
thermal spectrum. Moreover, our calculation indicates that the emission process
is treated as a reversible process in the Parikh-Wilczek tunnelling framework,
and the information conservation is a natural result of the first law of black
hole thermodynamics.


  Monitoring of cardiovascular activity is highly desired and can enable novel
applications in diagnosing potential cardiovascular diseases and maintaining an
individual's well-being. Currently, such vital signs are measured using
intrusive contact devices such as an electrocardiogram (ECG), chest straps, and
pulse oximeters that require the patient or the health provider to manually
implement. Non-contact, device-free human sensing methods can eliminate the
need for specialized heart and blood pressure monitoring equipment. Non-contact
methods can have additional advantages since they are scalable with any
environment where video can be captured, can be used for continuous
measurements, and can be used on patients with varying levels of dexterity and
independence, from people with physical impairments to infants (e.g., baby
camera). In this paper, we used a non-contact method that only requires face
videos recorded using commercially-available webcams. These videos were
exploited to predict the health attributes like pulse rate and variance in
pulse rate. The proposed approach used facial recognition to detect the face in
each frame of the video using facial landmarks, followed by supervised learning
using deep neural networks to train the machine learning model. The videos
captured subjects performing different physical activities that result in
varying cardiovascular responses. The proposed method did not require training
data from every individual and thus the prediction can be obtained for the new
individuals for which there is no prior data; critical in approach
generalization. The approach was also evaluated on a dataset of people with
different ethnicity. The proposed approach had less than a 4.6\% error in
predicting the pulse rate.


  Earth's inner core exhibits an unusually high Poisson's ratio and noticeable
elastic anisotropy. The mechanisms responsible for these features are critical
for understanding the evolution of the Earth but remain unclear. This study
indicates that once the correct formula for the shear modulus is used, shear
softening can simultaneously explain the high Poisson's ratio and strong
anisotropy of the inner core. Body-centred-cubic (bcc) iron shows shear
instability at the pressures found in the inner-core and can be dynamically
stabilized by temperature and light elements. It is very likely that some
combinations of light elements stabilize the bcc iron alloy under inner-core
conditions. Such a bcc phase would exhibit significant shear softening and
match the geophysical constraints of the inner core. Identifying which light
elements and what concentrations of these elements stabilize the bcc phase will
provide critical information on the light elements of the inner core.


  In traditional conversational intelligence from speech, a cascaded pipeline
is used, involving tasks such as voice activity detection, diarization,
transcription, and subsequent processing with different NLP models for tasks
like semantic endpointing and named entity recognition (NER). Our paper
introduces TokenVerse, a single Transducer-based model designed to handle
multiple tasks. This is achieved by integrating task-specific tokens into the
reference text during ASR model training, streamlining the inference and
eliminating the need for separate NLP models. In addition to ASR, we conduct
experiments on 3 different tasks: speaker change detection, endpointing, and
NER. Our experiments on a public and a private dataset show that the proposed
method improves ASR by up to 7.7% in relative WER while outperforming the
cascaded pipeline approach in individual task performance. Additionally, we
present task transfer learning to a new task within an existing TokenVerse.


  M. Khovanov and L. Rozansky gave a categorification of the HOMFLY-PT
polynomial. This study is a generalization of the Khovanov-Rozansky homology.
We define a homology associated to the quantum $(sl_n,\land V_n)$ link
invariant, where $\land V_n$ is the set of the fundamental representations of
the quantum group of $sl_n$. In the case of a [1,k]-colored link diagram, we
prove that its homology is a link invariant. In the case of an [i,j]-colored
link diagram, we define a normalized Poincare polynomial of its homology and
prove the polynomial is a link invariant.


  A major problem in motor control is understanding how the brain plans and
executes proper movements in the face of delayed and noisy stimuli. A prominent
framework for addressing such control problems is Optimal Feedback Control
(OFC). OFC generates control actions that optimize behaviorally relevant
criteria by integrating noisy sensory stimuli and the predictions of an
internal model using the Kalman filter or its extensions. However, a
satisfactory neural model of Kalman filtering and control is lacking because
existing proposals have the following limitations: not considering the delay of
sensory feedback, training in alternating phases, and requiring knowledge of
the noise covariance matrices, as well as that of systems dynamics. Moreover,
the majority of these studies considered Kalman filtering in isolation, and not
jointly with control. To address these shortcomings, we introduce a novel
online algorithm which combines adaptive Kalman filtering with a model free
control approach (i.e., policy gradient algorithm). We implement this algorithm
in a biologically plausible neural network with local synaptic plasticity
rules. This network performs system identification and Kalman filtering,
without the need for multiple phases with distinct update rules or the
knowledge of the noise covariances. It can perform state estimation with
delayed sensory feedback, with the help of an internal model. It learns the
control policy without requiring any knowledge of the dynamics, thus avoiding
the need for weight transport. In this way, our implementation of OFC solves
the credit assignment problem needed to produce the appropriate sensory-motor
control in the presence of stimulus delay.


  In the absence of a randomized experiment, a key assumption for drawing
causal inference about treatment effects is the ignorable treatment assignment.
Violations of the ignorability assumption may lead to biased treatment effect
estimates. Sensitivity analysis helps gauge how causal conclusions will be
altered in response to the potential magnitude of departure from the
ignorability assumption. However, sensitivity analysis approaches for
unmeasured confounding in the context of multiple treatments and binary
outcomes are scarce. We propose a flexible Monte Carlo sensitivity analysis
approach for causal inference in such settings. We first derive the general
form of the bias introduced by unmeasured confounding, with emphasis on
theoretical properties uniquely relevant to multiple treatments. We then
propose methods to encode the impact of unmeasured confounding on potential
outcomes and adjust the estimates of causal effects in which the presumed
unmeasured confounding is removed. Our proposed methods embed nested multiple
imputation within the Bayesian framework, which allow for seamless integration
of the uncertainty about the values of the sensitivity parameters and the
sampling variability, as well as use of the Bayesian Additive Regression Trees
for modeling flexibility. Expansive simulations validate our methods and gain
insight into sensitivity analysis with multiple treatments. We use the
SEER-Medicare data to demonstrate sensitivity analysis using three treatments
for early stage non-small cell lung cancer. The methods developed in this work
are readily available in the R package SAMTx.


  We study two-stage adjustable robust linear programming in which the
right-hand sides are uncertain and belong to a convex, compact uncertainty set.
This problem is NP-hard, and the affine policy is a popular, tractable
approximation. We prove that under standard and simple conditions, the
two-stage problem can be reformulated as a copositive optimization problem,
which in turn leads to a class of tractable, semidefinite-based approximations
that are at least as strong as the affine policy. We investigate several
examples from the literature demonstrating that our tractable approximations
significantly improve the affine policy. In particular, our approach solves
exactly in polynomial time a class of instances of increasing size for which
the affine policy admits an arbitrarily large gap.


  Cold, dense gas clouds have been proposed as a major component of the
Galactic dark matter; such clouds can be revealed by the gamma-ray emission
which arises from cosmic-rays interacting with the gas. If this dark matter
component is clustered then highly luminous GeV sources result, preferentially
at low to mid Galactic latitudes where they lie within the cosmic-ray disk. The
predicted emission for such clusters is steady, continuum emission with peak
power emerging at several hundred MeV. These sources would not have obvious
counterparts at other wavelengths and are thus of interest in connection with
the UnIDentified (UID) EGRET sources. Here we present a Monte Carlo simulation
of the gamma-ray source population due to cold gas clouds, assuming a
Cold-Dark-Matter-like mass spectrum for the clustering. We find that ~280 EGRET
sources are predicted by this model, with a median Galactic latitude of 12
degrees for the population, and a median angular size of 2.2 degrees. The
latitude and size distributions are consistent with the UID EGRET source data,
but the source counts are clearly overpredicted. On the basis of these results
we propose that clusters of cold gas clouds comprise the majority population of
the observed UID EGRET sources. Our interpretation implies that there should be
microwave counterparts to most of the UID sources, and will thus be strongly
constrained by data from the present generation of microwave anisotropy
experiments.


  The advent of modern, high-speed electron detectors has made the collection
of multidimensional hyperspectral transmission electron microscopy datasets,
such as 4D-STEM, a routine. However, many microscopists find such experiments
daunting since such datasets' analysis, collection, long-term storage, and
networking remain challenging. Some common issues are the large and unwieldy
size of the said datasets, often running into several gigabytes,
non-standardized data analysis routines, and a lack of clarity about the
computing and network resources needed to utilize the electron microscope
fully. However, the existing computing and networking bottlenecks introduce
significant penalties in each step of these experiments, and thus, real-time
analysis-driven automated experimentation for multidimensional TEM is
exceptionally challenging. One solution is integrating microscopy with edge
computing, where moderately powerful computational hardware performs the
preliminary analysis before handing off the heavier computation to HPC systems.
In this perspective, we trace the roots of computation in modern electron
microscopy, demonstrate deep learning experiments running on an edge system,
and discuss the networking requirements for tying together microscopes, edge
computers, and HPC systems.


  We give local upper and lower bounds for the eigenvalues of the modular
operator associated to an ergodic action of a compact quantum group on a unital
C*-algebra. They involve the modular theory of the quantum group and the growth
rate of quantum dimensions of its representations and they become sharp if
other integral invariants grow subexponentially. For compact groups, this
reduces to the finiteness theorem of Hoegh-Krohn, Landstad and Stormer.
Consequently, compact quantum groups of Kac type admitting an ergodic action
with a non-tracial invariant state must have representations whose dimensions
grow exponentially. In particular, S_{-1}U(d) acts ergodically only on tracial
C*-algebras. For quantum groups with non-involutive coinverse, we derive a
lower bound for the parameters 0<\lambda<1 of factors of type III_\lambda that
can possibly arise from the GNS representation of the invariant state of an
ergodic action with a factorial centralizer.


  Exploiting synthetic data to learn deep models has attracted increasing
attention in recent years. However, the intrinsic domain difference between
synthetic and real images usually causes a significant performance drop when
applying the learned model to real world scenarios. This is mainly due to two
reasons: 1) the model overfits to synthetic images, making the convolutional
filters incompetent to extract informative representation for real images; 2)
there is a distribution difference between synthetic and real data, which is
also known as the domain adaptation problem. To this end, we propose a new
reality oriented adaptation approach for urban scene semantic segmentation by
learning from synthetic data. First, we propose a target guided distillation
approach to learn the real image style, which is achieved by training the
segmentation model to imitate a pretrained real style model using real images.
Second, we further take advantage of the intrinsic spatial structure presented
in urban scene images, and propose a spatial-aware adaptation scheme to
effectively align the distribution of two domains. These two modules can be
readily integrated with existing state-of-the-art semantic segmentation
networks to improve their generalizability when adapting from synthetic to real
urban scenes. We evaluate the proposed method on Cityscapes dataset by adapting
from GTAV and SYNTHIA datasets, where the results demonstrate the effectiveness
of our method.


  Applying proper orthogonal decomposition to a usual finite element (FE)
formulation for space fractional partial differential equation, we get a
reduced FE model, which greatly reduces the complexity of computation. Then,
the stability analysis and error estimate for the reduced model are presented.
Finally, we verify the effectiveness of the algorithm by numerical experiments.


  A parity is a rule to assign labels to the crossings of knot diagrams in a
way compatible with Reidemeister moves. Parity functors can be viewed as
parities which provide to each knot diagram its own coefficient group that
contains parities of the crossings. In the article we describe the universal
oriented parity functors for free knots and for knots in a fixed surface.


  Collisions of particles near a rotating black hole can lead to unbound
energies $E_{c.m.}$ in their centre of mass frame. There are indications that
the Killing energy of debris at infinity can also be unbound for some scenarios
of collisions near the extremal black hole horizon (so-called super-Penrose
process). They include participation of a particle that (i) has generic (not
fine-tuned) parameters and (ii) moves away from a black hole before collision.
We show that for any finite particle's mass, such a particle cannot be obtained
as a result of the preceding collision. However, this can be done if one of
initial infalling particles has the mass of the order $N^{-2}$ that generalizes
previous observations made in literature for radial infall in the Kerr
background.


  We propose a series of simple models for the microstructure of a double
auction market without intermediaries. We specialize to those markets, such
interdealer broker markets, which are dominated by professional traders, who
trade mainly through limit orders, watch markets closely, and move their limit
order prices frequently. We model these markets as a set of buyers and a set of
sellers diffusing in price space and interacting through an annihilation
interaction. We seek to compute the purely statistical effects of the presence
of large numbers of traders, as scaling laws on various measures of liquidity,
and to this end we allow our model very few parameters. We find that the
bid-offer spread scales as $\sqrt{1/{\rm Deal Rate}}$.In addition we
investigate the scaling of other intuitive relationships, such as the relation
between fluctuations of the best bid/offer and the density of buyers/sellers.
We then study this model and its scaling laws under the influence of random
disturbances to trader drift, trader volatility, and entrance rate. We also
study possible extensions to the model, such as the addition of market order
traders, and an interaction that models momentum-type trading. Finally, we
discuss how detailed simulations may be carried out to study scaling in all of
these settings, and how the models may be tested inactual markets.


  We give a detailed proof to Gromov's statement that precompact sets of metric
measure spaces are bounded with respect to the box distance and the Lipschitz
order.


  Importance sampling (IS) is a Monte Carlo technique that relies on weighted
samples, simulated from a proposal distribution, to estimate intractable
integrals. The quality of the estimators improves with the number of samples.
However, for achieving a desired quality of estimation, the required number of
samples is unknown and depends on the quantity of interest, the estimator, and
the chosen proposal. We present a sequential stopping rule that terminates
simulation when the overall variability in estimation is relatively small. The
proposed methodology closely connects to the idea of an effective sample size
in IS and overcomes crucial shortcomings of existing metrics, e.g., it
acknowledges multivariate estimation problems. Our stopping rule retains
asymptotic guarantees and provides users a clear guideline on when to stop the
simulation in IS.


  It is widely known that Paul Ehrenfest formulated and applied his adiabatic
hypothesis in the early 1910s. Niels Bohr, in his first attempt to construct a
quantum theory in 1916, used it for fundamental purposes in a paper which
eventually did not reach the press. He decided not to publish it after having
received the new results by Sommerfeld in Munich. Two years later, Bohr
published "On the quantum theory of line-spectra." There, the adiabatic
hypothesis played an important role, although it appeared with another name:
the principle of mechanical transformability. In the subsequent variations of
his theory, Bohr never suppressed this principle completely. We discuss the
role of Ehrenfest's principle in the works of Bohr, paying special attention to
its relation to the correspondence principle. We will also consider how
Ehrenfest faced Bohr's uses of his more celebrated contribution to quantum
theory, as well as his own participation in the spreading of Bohr's ideas.


  We propose a new mechanism of lepton (L) number asymmetry generation, hence
offer an explanation of matter-antimatter imbalance when a significant amount
of baryon number is later transformed from this L-number by known electroweak
sphaleron mediated process. The basic theoretical framework is a recently
proposed multiple scalar-tensor gravity that dynamically solves the
cosmological constant problem. The L-asymmetry generation in one of two
proposed scenarios is triggered by dynamical relaxation of scalar inflaton
field towards the zero cosmological constant. CPT violation (C= charge
conjugation, P = parity operation, T= time reversal) in the presence of a
chemical potential gives the necessary time arrow, and lepton number violating
scattering in cosmic thermal medium generates a net cosmological L-number via
resonance formation. Another scenario is L-asymmetry generation from
evaporating primordial black holes. These proposed mechanisms do not require CP
violating phases in physics beyond the standard model: the new required physics
is existence of heavy Majorana leptons of masses $ 10^{15} \sim 10^{17}$ GeV
that realizes the seesaw mechanism. We identify the cosmological epoch of
lepto-genesis in two scenarios, which may give the right amount of observed
baryon to entropy ratio. It might even be possible to experimentally determine
microscopic physics parameter, masses of three heavy Majorana leptons by
observing astrophysical footprints of primordial black hole evaporation at
specified hole masses.


  The production cross sections of $e^+e^- $ to a heavy quarkonium with
$C$-parity even $S-$wave and $P-$wave associated with a photon are analyzed in
the framework of non-relativistic Quantum Chromodynamics(NRQCD) factorization
formalism. The short-distance coefficients are determined up to the
next-to-leading order(NLO) QCD radiative corrections for $S-$ and $P-$wave and
NLO relativistic corrections for $S-$wave in analytical forms. Applying the
results to estimate the cross sections we find that both the radiative and
relativistic corrections are considerable.