  This paper studies the active flux (AF) methods for two-dimensional
hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for
the point value update and bound-preserving (BP) limitings, which is an
extension of our previous work [J.M. Duan, W. Barsukow, C. Klingenberg,
arXiv:2405.02447]. The FVS-based point value update is shown to address the
mesh alignment issue that appeared in a quasi-2D Riemann problem along one axis
direction on Cartesian meshes. Consequently, the AF methods based on the FVS
outperform those using Jacobian splitting, which are prone to transonic and
mesh alignment issues. A shock sensor-based limiting is proposed to enhance the
convex limiting for the cell average, which can reduce oscillations well. Some
benchmark problems are tested to verify the accuracy, BP property, and
shock-capturing ability of our BP AF method. Moreover, for the double Mach
reflection and forward-facing step problems, the present AF method can capture
comparable or better small-scale features compared to the third-order
discontinuous Galerkin method with the TVB limiter on the same mesh resolution,
while using fewer degrees of freedom, demonstrating the efficiency and
potential of our BP AF method for high Mach number flows.


  Extreme ultraviolet (EUV) waves are impressive coronal propagating
disturbances. They are closely associated with various eruptions, and can used
for the global coronal seismology and the acceleration of solar energetic
particles. Hence, the study of EUV waves plays an important role in solar
eruptions and Space Weather. Here we present an EUV wave associated with a
filament activation that did not evolve into any eruption. Due to the
continuous magnetic flux emergence and cancellation around its one end, the
filament rose with untwisting motion, and the filament mass flowed towards
another end along the rising fields. Intriguingly, following the filament
activation, an EUV wave formed with a fast constant speed ($\sim$500 km
s$^{-1}$) ahead of the mass flow, and the overlying coronal loops expanded both
in lateral and radial directions. Excluding the possibility of a remote flare
and an absent coronal mass ejection, we suggest that the EUV wave was only
closely associated with the filament activation. Furthermore, their intimate
spacial and temporal relationship indicates that the EUV wave was likely
directly triggered by the lateral expansion of overlying loops. We propose that
the EUV wave can be interpreted as linear fast-mode wave, and the most vital
key for the successful generation of the EUV wave is the impulsive early-phase
lateral expansion of overlying loops that was driven by the activated filament
mass flow without any eruption.


  Here, we propose a new tool to estimate the complexity of a time series: the
entropy of difference (ED). The method is based solely on the sign of the
difference between neighboring values in a time series. This makes it possible
to describe the signal as efficiently as prior proposed parameters such as
permutation entropy (PE) or modified permutation entropy (mPE), but (1) reduces
the size of the sample that is necessary to estimate the parameter value, and
(2) enables the use of the Kullback-Leibler divergence to estimate the distance
between the time series data and random signals.


  We describe a novel effect of the generation of direct current which may
arise in semiconductors or semiconductor microstructures due to a mixing of
coherent electromagnetic radiations of commensurate frequencies. The effect is,
in essence, due to a nonparabolicity of the electron energy bands and is
stronger in systems where this nonparabolicity is greater. We have made exact
calculations in the framework of the Kane model, applicable to narrow gap
semiconductors and the tight-binding model which we employ for a description of
a semiconductor superlattice.


  The well-known formula $det(A\cdot B)=\det A \cdot \det B$ can be easily
proved for finite dimensional matrices but it may be incorrect for the
functional determinants of differential operators, including the ones which are
relevant for Quantum Field Theory applications. Considerable work has been done
to prove that this equality can be violated, but in all previously known cases
the difference could be reduced to renormalization ambiguity. We present the
first example, where the difference between the two functional determinants is
a nonlocal expression and therefore can not be explained by the renormalization
ambiguity. Moreover, through the use of other even dimensions we explain the
origin of this difference at qualitative level.


  The photoelectric effect established by Einstein is well known, which
indicates that electrons on lower energy levels can jump up to higher levels by
absorbing photons, or jump down from higher levels to lower levels and give out
photons1-3. However, how do photons act on electrons and further on atoms have
kept unknown up to now. Here we show the results that photons collide on
electrons with energy-transmission in semiconductors and pass their momenta to
electrons, which make the electrons jump up from lower energy levels to higher
levels. We found that (i) photons have rest mass of 7.287exp(-38) kg and
2.886exp(-35) kg, in vacuum and silicon respectively; (ii) excited by photons
with energy of 1.12eV, electrons in silicon may jump up from the top of valance
band to the bottom of conduction band with initial speed of 2.543exp(3) m/s and
taking time of 4.977exp(-17) s; (iii) acted by photons with energy of 4.6eV,
the atoms who lose electrons may be catapulted out of the semiconductors by the
extruded neighbor atoms, and taking time of 2.224exp(-15) s. These results make
reasonable explanation to rapid thermal annealing, laser ablation and laser
cutting.


  We rigorously prove that the Heisenberg chain with next-nearest-neighbor
interaction, which is anticipated to be non-integrable, is indeed
non-integrable in the sense that this system has no nontrivial local conserved
quantity. Our result covers two important models, the Majundhar-Ghosh model and
the Shastry-Sutherland model, as special cases. These models are shown to be
non-integrable while have some solvable energy eigenstates.


  In this work, we theoretically investigate the superluminal and subluminal
reflected group delay from an air-Weyl semimetal film-Weyl semimetal substrate
layered structure by using 4*4 magneto-optical matrix. We show a tunable
transition between positive and negative group delays of reflection pulse in
such a layered structure controlled by the properties of the Weyl Semimetal
layer and reveal its mechanism to control the propagation properties of the
light pulse reflected from such structure. It is demonstrated that the
reflected group delays are tunable from positive to negative values and vice
versa, which are adjusted by tuning the incident angle, thickness of Weyl
semimetal film, tilt parameter, and Fermi energy. The control of the magnitude
and the sign of the reflected group delay of light propagation represent a key
point in slow and fast light technologies. Our results are helpful to control
the pulse propagations and are useful for design of Weyl semimetal-based delay
devices.


  Topological chaos relies on the periodic motion of obstacles in a
two-dimensional flow in order to form nontrivial braids. This motion generates
exponential stretching of material lines, and hence efficient mixing. Boyland
et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277
(2000)] have studied a specific periodic motion of rods that exhibits
topological chaos in a viscous fluid. We show that it is possible to extend
their work to cases where the motion of the stirring rods is topologically
trivial by considering the dynamics of special periodic points that we call
ghost rods, because they play a similar role to stirring rods. The ghost rods
framework provides a new technique for quantifying chaos and gives insight into
the mechanisms that produce chaos and mixing. Numerical simulations for Stokes
flow support our results.


  Several studies on the transition voltage ($V_t$) are based on calculations
of the tunneling current within the Simmons model. In this paper devoted to
vacuum nano-junctions, we compare the Simmons results for $V_t$ with those
obtained from the exact Schrodinger equation by exactly including the classical
image effects. The comparison reveals that the Simmons estimates for $V_t$ are
completely unacceptable for nanogap sizes ($d$) at which image effects are
important. The Simmons treatment drastically overestimates these effects,
because it misses the famous 1/2 factor related to the fact that the image
interaction energy is a self energy. The maximum of the Simmons curve $V_t$ vs.
$d$ turns out to be merely an artefact of an inappropriate approximation.
Unlike the Simmons approach, the "exact" WKB method yields results, which
qualitatively agree with the exact ones; quantitative differences are
important, demonstrating that the transmission prefactor has a significant
impact on $V_t$. Further, we show that a difference between the work functions
of the left and right electrodes, which gives rise to a Volta field, may be
important for the ubiquitous asymmetry of the measured $I$-$V$-characteristics
in general, and for the different $V_t$-values at positive and negative biases
reported in vacuum nanojunctions in particular. The weak dependence $V_t =
V_t(d)$ found experimentally in vacuum nanojunctions contrasts to the
pronounced dependence obtained by including the exact electrostatic image
contribution into the Schrodinger equation. This demonstrates that not only the
molecular transport, but also the transport through a vacuum nanogap represents
a nontrivial problem, which requires further refinements, e.g., a realistic
description of contacts' geometry, retardation effects due to the finite
tunneling time, local phonons, surface plasmons or electron image states.


  The use of imitation learning to learn a single policy for a complex task
that has multiple modes or hierarchical structure can be challenging. In fact,
previous work has shown that when the modes are known, learning separate
policies for each mode or sub-task can greatly improve the performance of
imitation learning. In this work, we discover the interaction between sub-tasks
from their resulting state-action trajectory sequences using a directed
graphical model. We propose a new algorithm based on the generative adversarial
imitation learning framework which automatically learns sub-task policies from
unsegmented demonstrations. Our approach maximizes the directed information
flow in the graphical model between sub-task latent variables and their
generated trajectories. We also show how our approach connects with the
existing Options framework, which is commonly used to learn hierarchical
policies.


  Temporal graphs are graphs with time-stamped edges. We study the problem of
finding a small vertex set (the separator) with respect to two designated
terminal vertices such that the removal of the set eliminates all temporal
paths connecting one terminal to the other. Herein, we consider two models of
temporal paths: paths that pass through arbitrarily many edges per time step
(non-strict) and paths that pass through at most one edge per time step
(strict). Regarding the number of time steps of a temporal graph, we show a
complexity dichotomy (NP-hardness versus polynomial-time solvability) for both
problem variants. Moreover we prove both problem variants to be NP-complete
even on temporal graphs whose underlying graph is planar. We further show that,
on temporal graphs with planar underlying graph, if additionally the number of
time steps is constant, then the problem variant for strict paths is solvable
in quasi-linear time. Finally, we introduce and motivate the notion of a
temporal core (vertices whose incident edges change over time). We prove that
the non-strict variant is fixed-parameter tractable when parameterized by the
size of the temporal core, while the strict variant remains NP-complete, even
for constant-size temporal cores.


  There are numerous applications where we have to deal with temporal
uncertainty associated with events. The Temporal Probabilistic (TP) Logic
Programs should provide support for valid-time indeterminacy of events, by
proposing the concept of an indeterminate instant, that is, an interval of
time-points (event's time-window) with an associated, lower and upper,
probability distribution. In particular, we propose the new semantics, for the
TP Logic Programs of Dekhtyar and Subrahmanian. Our semantics, based on the
possible world semantics is a generalization of the possible world semantics
for (non temporal) Probabilistic Logic Programming, and we define the new
syntax for PT-programs, with time variable explicitly represented in all atoms,
and show how the standard role of Herbrand interpretations used as possible
worlds for probability distributions is coherently extended to Temporal
Probabilistic Logic Programming.


  In this paper we provide necessary and sufficient conditions in order to
guarantee the energy-dissipation balance of a Mode III crack, growing on a
prescribed smooth path. Moreover, we characterize the singularity of the
displacement near the crack tip, generalizing the result in [S.Nicaise,
A.M.Sandig - \textit{J. Math. Anal. Appl.} 2007] valid for straight fractures.


  We show that a realization of a closed connected PL-manifold of dimension n-1
in n-dimensional Euclidean space (n>2) is the boundary of a convex polyhedron
(finite or infinite) if and only if the interior of each (n-3)-face has a
point, which has a neighborhood lying on the boundary of an n-dimensional
convex body. No initial assumptions about the topology or orientability of the
input surface are made. The theorem is derived from a refinement and
generalization of Van Heijenoort's theorem on locally convex manifolds to
spherical spaces. Our convexity criterion for PL-manifolds implies an easy
polynomial-time algorithm for checking convexity of a given PL-surface in
n-dimensional Euclidean or spherical space, n>2. The algorithm is worst case
optimal with respect to both the number of operations and the algebraic degree.
The algorithm works under significantly weaker assumptions and is easier to
implement than convexity verification algorithms suggested by Mehlhorn et al
(1996-1999), and Devillers et al.(1998). A paradigm of approximate convexity is
suggested and a simplified algorithm of smaller degree and complexity is
suggested for approximate floating point convexity verification.


  This paper investigates options to complement a diesel engine airpath
feedback controller with a feedforward. The control objective is to track the
intake manifold pressure and exhaust gas recirculation (EGR) rate targets by
manipulating the EGR valve and variable geometry turbine (VGT) while satisfying
state and input constraints. The feedback controller is based on rate-based
Model Predictive Control (MPC) that provides integral action for tracking. Two
options for the feedforward are considered one based on a look-up table that
specifies the feedforward as a function of engine speed and fuel injection
rate, and another one based on a (non-rate-based) MPC that generates dynamic
feedforward trajectories. The controllers are designed and verified using a
high-fidelity engine model in GT-Power and exploit a low-order rate-based
linear parameter-varying (LPV) model for prediction which is identified from
transient response data generated by the GT-Power model. It is shown that the
combination of feedforward and feedback MPC has the potential to improve the
performance and robustness of the control design. In particular, the feedback
MPC without feedforward can lose stability at low engine speeds, while
MPC-based feedforward results in the best transient response. Mechanisms by
which feedforward is able to assist in stabilization and improve performance
are discussed.


  Hawking's topology theorem in general relativity restricts the cross-section
of the event horizon of a black hole in $3+1$ dimension to be either spherical
or toroidal. The toroidal case is ruled out by the topology censorship
theorems. In this article, we discuss the generalization of this result to
black holes in $f(R)$ gravity in $3+1$ and higher dimensions. We obtain a
sufficient differential condition on the function $f'(R)$, which restricts the
topology of the horizon cross-section of a black hole in $f(R)$ gravity in
$3+1$ dimension to be either $S^2$ or $S^1 \times S^1$. We also extend the
result to higher dimensional black holes and show that the same sufficient
condition also restricts the sign of the Yamabe invariant of the horizon
cross-section.


  In the setting of sequential prediction of individual $\{0, 1\}$-sequences
with expert advice, we show that by allowing the learner to abstain from the
prediction by paying a cost marginally smaller than $\frac 12$ (say, $0.49$),
it is possible to achieve expected regret bounds that are independent of the
time horizon $T$. We exactly characterize the dependence on the abstention cost
$c$ and the number of experts $N$ by providing matching upper and lower bounds
of order $\frac{\log N}{1-2c}$, which is to be contrasted with the best
possible rate of $\sqrt{T\log N}$ that is available without the option to
abstain. We also discuss various extensions of our model, including a setting
where the sequence of abstention costs can change arbitrarily over time, where
we show regret bounds interpolating between the slow and the fast rates
mentioned above, under some natural assumptions on the sequence of abstention
costs.


  Based on the ideas in [CKP], we introduce the weighted analogue of the
branching rule for the classical hook length formula, and give two proofs of
this result. The first proof is completely bijective, and in a special case
gives a new short combinatorial proof of the hook length formula. Our second
proof is probabilistic, generalizing the (usual) hook walk proof of
Green-Nijenhuis-Wilf, as well as the q-walk of Kerov. Further applications are
also presented.


  It was recently shown \cite{STV} that satisfiability is polynomially solvable
when the incidence graph is an interval bipartite graph (an interval graph
turned into a bipartite graph by omitting all edges within each partite set).
Here we relax this condition in several directions: First, we show that it
holds for $k$-interval bigraphs, bipartite graphs which can be converted to
interval bipartite graphs by adding to each node of one side at most $k$ edges;
the same result holds for the counting and the weighted maximization version of
satisfiability. Second, given two linear orders, one for the variables and one
for the clauses, we show how to find, in polynomial time, the smallest $k$ such
that there is a $k$-interval bigraph compatible with these two orders. On the
negative side we prove that, barring complexity collapses, no such extensions
are possible for CSPs more general than satisfiability. We also show
NP-hardness of recognizing 1-interval bigraphs.


  We report an investigation of current transport in Nb/Au/CaSrCuO/YBaCuO
heterostructures including an antiferromagnetic interlayer (CaSrCuO). Epitaxial
thin films of YBaCuO and CaSrCuO were grown by laser ablation on NdGaO
substrates; the thicknesses of CaSrCuO films were 20 and 50 nm, and x=0.15 or
0.5. Our experimental results show that the superconducting current transport
is increased in the Nb/Au/CaSrCuO/YBaCuO heterostructures in comparison with
the ones observed in previously studied Nb/Au/YBaCuO heterostructures. It was
found that the critical current of the structure is very sensitive to the
absolute value and direction of the external magnetic field.


  We recall the emergence of a generalized gauge theory from a noncommutative
Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This
includes a gauge group determined by the unitaries in the $*$-algebra $A$ and
gauge fields arising from a so-called perturbation semigroup which is
associated to $A$. Our main new result is the interpretation of this
generalized gauge theory in terms of an upper semi-continuous $C^*$-bundle on a
(Hausdorff) base space $X$. The gauge group acts by vertical automorphisms on
this $C^*$-bundle and can (under some mild conditions) be identified with the
space of continuous sections of a group bundle on $X$. This then allows for a
geometrical description of the group of inner automorphisms of $A$.
  We exemplify our construction by Yang-Mills theory and toric noncommutative
manifolds and show that they actually give rise to continuous $C^*$-bundles.
Moreover, in these examples the corresponding inner automorphism groups can be
realized as spaces of sections of group bundles that we explicitly determine.


  In a qualitative study, Gregory, Gibson and Robinson proposed a framework of
items grouped in seven dimensions reflecting oral health related perceptions,
attitudes and behavior to encompass what is relevant when patients assess their
own oral health related quality of life (OHRQOL). The aim of this study is to
quantify the dimensions of Gregory relevance framework and confirm, or
otherwise, the influence on the change in the OHIP-14, an instrument widely
used to measure OHRQOL. The study was observational and longitudinal with the
OHIP-14 measured before a tooth extraction, and two and four weeks thereafter.
Statistical methods of analysis consisted of generalised estimating equations.
Responsiveness (or sensitivity to change) of the OHIP-14 was established in our
patient population. The dimensions of Gregory relevance framework featured
significantly in the models. Patients trust in dental products, perception of
own oral health as normal in relation to the average person, preference for
natural teeth, character bias in judgement and control by adherence to dentists
instructions, were all found to be significant factors in the longitudinal
change of the OHIP-14. Borderline significance was found in terms of dental
anxiety and symptoms. Perceptions, behaviour and attitudes, rather than
socio-demographic characteristics or oral health related knowledge, influence
change in OHRQOL. Trusting that the dentist values the patient as a person and
the importance the patient gives to having good oral health, are not found
significant, yet adhering to dentists advice has a beneficial effect on OHRQOL.


  On geometrically finite negatively curved surfaces, we give necessary and
sufficient conditions for a one-sided horocycle $(h^s u)_{s\ge 0}$ to be dense
in the nonwandering set of the geodesic flow. We prove that all dense one-sided
orbits $(h^su)_{s\ge 0}$ are equidistributed, extending results of [Bu] and
[Scha2] where symmetric horocycles $(h^su)_{s\in\R}$ were considered.


  We propose a framework that unifies the description of light transport in
three-dimensional amorphous dielectric materials that exhibit both localization
and a photonic bandgap. To this end, we argue that coherent reflection near and
in the bandgap attenuates the generation of diffuse or localized photons. Using
the self-consistent theory of localization and considering the density of
states of photons, we can quantitatively describe all transport regimes:
Transparency, light diffusion, localization, and bandgap. Comparing the model
with numerical data on optical transport in hyperuniform dielectric networks
confirms our findings.


  We examine the conditions under which a signed graph contains an edge or a
vertex that is contained in a unique negative circle or a unique positive
circle. For an edge in a unique signed circle, the positive and negative case
require the same structure on the underlying graph, but the requirements on the
signature are different. We characterize the structure of the underlying graph
necessary to support such an edge in terms of bridges of a circle. We then use
the results from the edge version of the problem to help solve the vertex
version.


  The decay of the string perturbative vacuum into our present cosmological
state is associated to the transition from a phase of growing curvature and
growing dilaton, to a phase of decreasing curvature and frozen dilaton. The
possible approaches to a classical and quantum description of such a transition
are introduced and briefly discussed.


  This work presents the magnetic field geometry in a complex of three cometary
(with head-tail morphology) globules, namely LDN 323, LDN 328, and LDN 331,
using R-band polarization measurements of background stars. These observations
were combined with a Planck sky survey to study the large-scale morphology of
the magnetic fields in the region. The distances of the target stars were
adopted from the Gaia catalog. The variation of degree of polarization and
polarization position angle with distances of stars is analyzed. The field
geometry is mostly found to follow the cometary shape of the cloud, with some
randomness at certain locations. For studying the correlation between cloud
morphology and magnetic field orientations, a modified version of the Histogram
of Relative Orientation analysis was employed.


  The Blanco DECam Bulge Survey (BDBS) provides near-ultraviolet to
near-infrared photometry for ~250 million unique stars. By combining BDBS
photometry with the latest Gaia astrometry, we characterize the chemo-dynamics
of red clump stars across the BDBS footprint, using an unprecedented sample
size and sky coverage. We construct a sample of ~2.3 million red clump giants
in the bulge with photometric metallicities, BDBS photometric distances, and
proper motions. We study the kinematics of the red clump stars as a function of
sky position and metallicity, by investigating proper motion rotation curves,
velocity dispersions, and proper motion correlations across the southern
Galactic bulge. We find that metal-poor red clump stars exhibit lower rotation
amplitudes, at ~29 km s$^{-1}$ kpc^{-1}. The peak of the angular velocity is
~39 km s^{-1} kpc^{-1} for [Fe/H] ~ -0.2 dex, exhibiting declining rotation at
higher [Fe/H]. The velocity dispersion is higher for metal-poor stars, while
metal-rich stars show a steeper gradient with Galactic latitude, with a maximum
dispersion at low latitudes along the bulge minor axis. Only metal-rich stars
([Fe/H] >~ -0.5 dex) show clear signatures of the bar in their kinematics,
while the metal-poor population exhibits isotropic motions with an axisymmetric
pattern around Galactic longitude l = 0. This work reports the largest sample
of bulge stars with distance, metallicity, and astrometry and shows clear
kinematic differences with metallicity. The global kinematics over the bulge
agrees with earlier studies. However, we see striking changes with increasing
metallicity and for the first time, see kinematic differences for stars with
[Fe/H]>-0.5, suggesting that the bar itself may have kinematics that depends on
metallicity.


  We perform a parton level study of angular correlations, in higher
dimensional black hole events scenarios at the LHC. We start by discussing some
features of the angular spectrum in the high energy limit using the geometrical
optics approximation. This allows us to recover the high energy limit of the
Hawking fluxes. Then we use the full Hawking angular fluxes on the brane, for a
singly rotating Myers-Perry black hole, to motivate the construction of various
angular observables as to maximise the angular asymmetries due to rotation.
This is finally adapted to a parton level simulation using the CHARYBDIS2
generator. We explore two types of variables based on: axis reconstruction and
two-particle angular correlators. We find energy cuts which have the potential
to help identify the effects of rotation in semi-classical rotating black hole
events at the LHC during the 14 TeV run, especially for spin-1 particles.


  We studied the acceleration mechanisms of chromospheric jets associated with
emerging flux using a two dimensional magnetohydrodynamic (MHD) simulation. We
found that slow mode shock waves generated by magnetic reconnection in the
chromosphere and the photosphere play key roles in the acceleration mechanisms
of chromospheric jets. An important parameter is the height of magnetic
reconnection. When magnetic reconnection takes place near the photosphere, the
reconnection out- flow collides with the region where the plasma beta is much
larger than unity. Then the plasma moves along a magnetic field. This motion
generates a slow mode wave. The slow mode wave develops to a strong slow shock
as it propagates upward. When the slow shock crosses the transition region, the
transition region is lifted up. As a result, we obtain a chromospheric jet as
the lifted transition region. When magnetic reconnection takes place in the
upper chromosphere, the chromospheric plasma is accelerated due to the
combination of the Lorentz force and the whip-like motion of magnetic field. We
found that the chromospheric plasma is further accelerated through the
interaction between the transition region (steep density gradient) and a slow
shock emanating from the reconnection point. This is an MHD effect which has
not been discussed before.


  We investigate and clarify the mutual compatibility of the higher order
corrections arising in supergravity and string theory effective actions and the
non-linear duality symmetries of these theories. Starting from a conventional
tree level action leading to duality invariant equations of motion, we show how
to accommodate duality invariant counterterms given as functionals of both
electric and magnetic fields in a perturbative expansion, and to deduce from
them a non-polynomial bona fide action satisfying the Gaillard-Zumino
constraint. There exists a corresponding consistency constraint in the
non-covariant Henneaux-Teitelboim formalism which ensures that one can always
restore diffeomorphism invariance by perturbatively solving this functional
identity. We illustrate how this procedure works for the R^2 \nabla F \nabla F
and F^4 counterterms in Maxwell theory.


  We have recently identified a protected topological semimetal in graphene
which presents a zero-energy edge mode robust to disorder and interactions.
Here, we address the characteristics of this semimetal and show that the
$\mathbb{Z}$ topological invariant of the Hall conductivity associated to the
lowest energy band can be equivalently measured from the resonant response to
circularly polarized light resolved at the Dirac points. The (non-quantized)
conductivity responses of the intermediate energy bands, including the Fermi
surface, also give rise to a $\mathbb{Z}_2$ invariant. We emphasize on the
bulk-edge correspondence as a half-topological protected semimetal, i.e. one
spin-population polarized in the plane is in the insulating phase related to
the robust edge mode while the other is in the metallic regime. The quantized
transport at the edges is also equivalent to a $\frac{1}{2}-\frac{1}{2}$
conductance for spin polarizations along $z$ direction. We also build a
parallel between the topological Hall response through the quantized light
response at the Dirac points and a pair of half numbers (half Skyrmions).


  We study an ultracold Bose gas in an optical dipole trap consisting of one
single focused laser beam. An analytical expression for the corresponding
density of states beyond the usual harmonic approximation is obtained. We are
thus able to discuss the existence of a critical temperature for Bose-Einstein
condensation and find that the phase transition must be enabled by a cutoff
near the threshold. Moreover, we study the dynamics of evaporative cooling and
observe significant deviations from the findings for the well-established
harmonic approximation. Furthermore, we investigate Bose-Einstein condensates
in such a trap in Thomas-Fermi approximation and determine analytical
expressions for chemical potential, internal energy and Thomas-Fermi radii
beyond the usual harmonic approximation.


  We study Noether's problem from the perspective of torsors under linear
algebraic groups and descent.


  Online algorithms are usually analyzed using the notion of competitive ratio
which compares the solution obtained by the algorithm to that obtained by an
online adversary for the worst possible input sequence. Often this measure
turns out to be too pessimistic, and one popular approach especially for
scheduling problems has been that of "resource augmentation" which was first
proposed by Kalyanasundaram and Pruhs. Although resource augmentation has been
very successful in dealing with a variety of objective functions, there are
problems for which even a (arbitrary) constant speedup cannot lead to a
constant competitive algorithm. In this paper we propose a "rejection model"
which requires no resource augmentation but which permits the online algorithm
to not serve an epsilon-fraction of the requests.
  The problems considered in this paper are in the restricted assignment
setting where each job can be assigned only to a subset of machines. For the
load balancing problem where the objective is to minimize the maximum load on
any machine, we give $O(\log^2 1/\eps)$-competitive algorithm which rejects at
most an $\eps$-fraction of the jobs. For the problem of minimizing the maximum
weighted flow-time, we give an $O(1/\eps^4)$-competitive algorithm which can
reject at most an $\eps$-fraction of the jobs by weight. We also extend this
result to a more general setting where the weights of a job for measuring its
weighted flow-time and its contribution towards total allowed rejection weight
are different. This is useful, for instance, when we consider the objective of
minimizing the maximum stretch. We obtain an $O(1/\eps^6)$-competitive
algorithm in this case.
  Our algorithms are immediate dispatch, though they may not be immediate
reject. All these problems have very strong lower bounds in the speed
augmentation model.


  We study simple branched coverings of degree d of the 2- and 3- dimensional
sphere branched over oriented links. We demonstrate how to use braid charts to
develop embeddings of these into $S^k \times D^2$ for $k=2,3 when $d=2,3$. This
is an initial part of our study and represents the manuscript submitted to the
RIMS workshop at Intelligence of Low Dimensional Topology.


  The thermoelectric properties in one- and two-dimensional silicon and
germanium structures have been investigated using first-principle density
functional techniques and linear response for the thermal and electrical
transport. We have considered here the two-dimensional silicene and germanene,
together with nano-ribbons of different widths. For the nano-ribbons, we have
also investigated the possibility of nano-structuring these systems by mixing
silicon and germanium. We found that the figure of merit at room temperature of
these systems is remarkably high, up to 2.5.


  We show that some results from the theory of group automata and monoid
automata still hold for more general classes of monoids and models. Extending
previous work for finite automata over commutative groups, we demonstrate a
context-free language that can not be recognized by any rational monoid
automaton over a finitely generated permutable monoid. We show that the class
of languages recognized by rational monoid automata over finitely generated
completely simple or completely 0-simple permutable monoids is a semi-linear
full trio. Furthermore, we investigate valence pushdown automata, and prove
that they are only as powerful as (finite) valence automata. We observe that
certain results proven for monoid automata can be easily lifted to the case of
context-free valence grammars.


  Hospital discharge documentation is among the most essential, yet
time-consuming documents written by medical practitioners. The objective of
this study was to automatically generate hospital discharge summaries using
neural network summarization models. We studied various data preparation and
neural network training techniques that generate discharge summaries. Using
nursing notes and discharge summaries from the MIMIC-III dataset, we studied
the viability of the automatic generation of various sections of a discharge
summary using four state-of-the-art neural network summarization models (BART,
T5, Longformer and FLAN-T5). Our experiments indicated that training
environments including nursing notes as the source, and discrete sections of
the discharge summary as the target output (e.g. "History of Present Illness")
improve language model efficiency and text quality. According to our findings,
the fine-tuned BART model improved its ROUGE F1 score by 43.6% against its
standard off-the-shelf version. We also found that fine-tuning the baseline
BART model with other setups caused different degrees of improvement (up to 80%
relative improvement). We also observed that a fine-tuned T5 generally achieves
higher ROUGE F1 scores than other fine-tuned models and a fine-tuned FLAN-T5
achieves the highest ROUGE score overall, i.e., 45.6. For majority of the
fine-tuned language models, summarizing discharge summary report sections
separately outperformed the summarization the entire report quantitatively. On
the other hand, fine-tuning language models that were previously instruction
fine-tuned showed better performance in summarizing entire reports. This study
concludes that a focused dataset designed for the automatic generation of
discharge summaries by a language model can produce coherent Discharge Summary
sections.


  In open-domain dialogues, predictive uncertainties are mainly evaluated in a
domain shift setting to cope with out-of-distribution inputs. However, in
real-world conversations, there could be more extensive distributional shifted
inputs than the out-of-distribution. To evaluate this, we first propose two
methods, Unknown Word (UW) and Insufficient Context (IC), enabling gradual
distributional shifts by corruption on the dialogue dataset. We then
investigate the effect of distributional shifts on accuracy and calibration.
Our experiments show that the performance of existing uncertainty estimation
methods consistently degrades with intensifying the shift. The results suggest
that the proposed methods could be useful for evaluating the calibration of
dialogue systems under distributional shifts.


  We briefly describe the three existing scenarios for forming massive stars
and emphasize that the arguments often used to reject the accretion scenario
for massive stars are misleading. It is usually not accounted for the fact that
the turbulent pressure associated to large turbulent velocities in clouds
necessarily imply relatively high accretion rates for massive stars. We show
the basic difference between the formation of low and high mass stars based on
the values of the free fall time and of the Kelvin-Helmoltz timescale, and
define the concept of birthline for massive stars.
  Due to D-burning, the radius and location of the birthline in the HR diagram,
as well as the lifetimes are very sensitive to the accretion rate \dot M_accr.
If a form \dot M_accr=A (M/M_sun)^phi is adopted, the observations in the HR
diagram and the lifetimes support a value of A=10^{-5} M_sun/yr and a value of
phi>1. Remarkably, such a law is consistent with the relation found by
Churchwell (1998) and Henning et al. (2000) between the outflow rates and the
luminosities of ultra--compact HII regions, if we assume that a fraction 0.15
to 0.3 of the global inflow is accreted. The above relation implies high \dot
M_accr=10^{-3} M_sun/yr for the most massive stars. The physical possibility of
such high \dot M_accr is supported by current numerical models.
  Finally, we give simple analytical arguments in favour of the growth of \dot
M_accr with the already accreted mass. We also suggest that due to Bondi-Hoyle
accretion, the formation of binary stars is largely favoured among massive
stars in the accretion scenario.


  Due to the strong correlation between adjacent pixels, most image encryption
schemes perform multiple rounds of confusion and diffusion to protect the image
against attacks. Such operations, however, are time-consuming, cannot meet the
real-time requirements of video encryption. Existing works, therefore, realize
video encryption by simplifying the encryption process or encrypting specific
parts of video frames, which results in lower security compared to image
encryption. To solve the problem, this paper proposes a real-time chaotic video
encryption strategy based on multithreaded parallel confusion and diffusion. It
takes a video as the input, splits the frame into subframes, creates a set of
threads to simultaneously perform five rounds of confusion and diffusion
operations on corresponding subframes, and efficiently outputs the encrypted
frames. The encryption speed evaluation shows that our method significantly
improves the confusion and diffusion speed, realizes real-time 480x480,
576x576, and 768x768 24FPS video encryption using Intel Core i5-1135G7, Intel
Core i7-8700, and Intel Xeon Gold 6226R, respectively. The statistical and
security analysis prove that the deployed cryptosystems have outstanding
statistical properties, can resist attacks, channel noise, and data loss.
Compared with existing works, to the best of our knowledge, the proposed
strategy achieves the fastest encryption speed, and realizes the first
real-time chaotic video encryption that reaches the security level of image
encryption. In addition, it is suitable for many confusion, diffusion
algorithms and can be easily deployed with both hardware and software.


  We prove sharp embedding inequalities for certain reduced Sobolev spaces that
arise naturally in the context of Dirichlet problems with $L^1$ data. We also
find the optimal target spaces for such embeddings, which in dimension 2 could
be considered as limiting cases of the Hansson-Brezis-Wainger spaces, for the
optimal embeddings of borderline Sobolev spaces $W_0^{k,n/k}$.


  This report represents the response of the Intensity Frontier Quark Flavor
Physics Working Group to the Snowmass charge. We summarize the current status
of quark flavor physics and identify many exciting future opportunities for
studying the properties of strange, charm, and bottom quarks. The ability of
these studies to reveal the effects of new physics at high mass scales make
them an essential ingredient in a well-balanced experimental particle physics
program.


  We compare two advanced designs for gravitational-wave antennas in terms of
their ability to detect two possible gravitational wave sources. Spherical,
resonant mass antennas and interferometers incorporating resonant sideband
extraction (RSE) were modeled using experimentally measurable parameters. The
signal-to-noise ratio of each detector for a binary neutron star system and a
rapidly rotating stellar core were calculated. For a range of plausible
parameters we found that the advanced LIGO interferometer incorporating RSE
gave higher signal-to-noise ratios than a spherical detector resonant at the
same frequency for both sources. Spheres were found to be sensitive to these
sources at distances beyond our galaxy. Interferometers were sensitive to these
sources at far enough distances that several events per year would be expected.


  In quantum gravity, it is expected that the Big Bang singularity is resolved
and the universe undergoes a bounce. We find that for generic initial data,
matter-gravity entanglement entropy rises rapidly during the bounce, declines,
and then approaches a steady-state value following the bounce. These
observations suggest that matter-gravity entanglement is a feature of the
macroscopic universe and that there is no Second Law of entanglement entropy.


  Coexpression of genes or, more generally, similarity in the expression
profiles poses an unsurmountable obstacle to inferring the gene regulatory
network (GRN) based solely on data from DNA microarray time series. Clustering
of genes with similar expression profiles allows for a course-grained view of
the GRN and a probabilistic determination of the connectivity among the
clusters. We present a model for the temporal evolution of a gene cluster
network which takes into account interactions of gene products with genes and,
through a non-constant degradation rate, with other gene products. The number
of model parameters is reduced by using polynomial functions to interpolate
temporal data points. In this manner, the task of parameter estimation is
reduced to a system of linear algebraic equations, thus making the computation
time shorter by orders of magnitude. To eliminate irrelevant networks, we test
each GRN for stability with respect to parameter variations, and impose
restrictions on its behavior near the steady state. We apply our model and
methods to DNA microarray time series' data collected on Escherichia coli
during glucose-lactose diauxie and infer the most probable cluster network for
different phases of the experiment.


  There is a intriguing relation between quantum information theory and super
gravity, discovered by M.J. Duff and S. Ferrara. It relates entanglement
measures for qubits to black hole entropy, which in a certain case involves the
quartic invariant on the 56-dimensional representation of the Lie group E7. In
this paper we recall the relatively straightforward manner in which
three-qubits lead to E7, or at least to the Weyl group of E7. We also show how
the Fano plane emerges in this context.


  We establish a sprinkled decoupling inequality for increasing events of
Gaussian vectors with an error that depends only on the maximum pairwise
correlation. As an application we prove the non-triviality of the percolation
phase transition for Gaussian fields on $\mathbb{Z}^d$ or $\mathbb{R}^d$ with
(i) uniformly bounded local suprema, and (ii) correlations which decay at least
polylogarithmically in the distance with exponent $\gamma > 3$; this expands
the scope of existing results on non-triviality of the phase transition,
covering new examples such as non-stationary fields and monochromatic random
waves.


  Cover song generation stands out as a popular way of music making in the
music-creative community. In this study, we introduce Piano Cover Generation
(PiCoGen), a two-stage approach for automatic cover song generation that
transcribes the melody line and chord progression of a song given its audio
recording, and then uses the resulting lead sheet as the condition to generate
a piano cover in the symbolic domain. This approach is advantageous in that it
does not required paired data of covers and their original songs for training.
Compared to an existing approach that demands such paired data, our evaluation
shows that PiCoGen demonstrates competitive or even superior performance across
songs of different musical genres.


  We show that the set of all formulas in n variables valid in a finite class A
of finite algebras is always a regular tree language, and compute a finite
axiom set for A. We give a rational reconstruction of Barzdins' liquid flow
algorithm (Barzdin+Barzdin, 1991). We show a sufficient condition for the
existence of a class A of prototype algebras for a given theory T. Such a set
allows us to prove T |= p simply by testing whether p holds in A.


  Finite time blow up vs global regularity question for 3D Euler equation of
fluid mechanics is a major open problem. Several years ago, Luo and Hou
\cite{HouLuo14} proposed a new finite time blow up scenario based on extensive
numerical simulations. The scenario is axi-symmetric and features fast growth
of vorticity near a ring of hyperbolic points of the flow located at the
boundary of a cylinder containing the fluid. An important role is played by a
small boundary layer where intense growth is observed. Several simplified
models of the scenario have been considered, all leading to finite time blow up
\cite{CKY15,CHKLVY17,HORY,KT1,HL15,KY1}. In this paper, we propose two models
that are designed specifically to gain insight in the evolution of fluid near
the hyperbolic stagnation point of the flow located at the boundary. One model
focuses on analysis of the depletion of nonlinearity effect present in the
problem. Solutions to this model are shown to be globally regular. The second
model can be seen as an attempt to capture the velocity field near the boundary
to the next order of accuracy compared with the one-dimensional models such as
\cite{CKY15,CHKLVY17}. Solutions to this model blow up in finite time.


  A commuting triple of Hilbert space operators $(A,B,P)$, for which the closed
tetrablock $\bar{\mathbb E}$ is a spectral set, is called a
\textit{tetrablock-contraction} or simply an $\mathbb E$-\textit{contraction},
where \[ \mathbb E=\{(a_{11},a_{22}, \det A):\, A=[a_{ij}]\in \mathcal
M_2(\mathbb C), \; \|A\| <1 \} \subset \mathbb C^3 \] is a polynomially convex
domain which is naturally associated with the $\mu$-synthesis problem. We
introduce triangular $\mathbb E$-contractions and prove that every pure
triangular $\mathbb E$-contraction dilates to a pure triangular $\mathbb
E$-isometry. We construct a functional model for a pure triangular $\mathbb
E$-isometry and apply that model to find a new proof for the famous
Berger-Coburn-Lebow Model Theorem for commuting isometries. Next we give an
alternative proof to the more generalized version of Berger-Coburn-Lebow Model,
namely the factorization of a pure contraction due to Das, Sarkar and Sarkar
(\textit{Adv. Math.} 322 (2017), 186 -- 200). We find a necessary and
sufficient condition for the existence of $\mathbb E$-unitary dilation of an
$\mathbb E$-contraction $(A,B,P)$ on the smallest dilation space and show that
it is equivalent to the existence of a distinguished variety in $\mathbb E$
when the defect space $D_{P^*}$ is finite dimensional.


  Neural Architecture Search (NAS), aiming at automatically designing neural
architectures by machines, has been considered a key step toward automatic
machine learning. One notable NAS branch is the weight-sharing NAS, which
significantly improves search efficiency and allows NAS algorithms to run on
ordinary computers. Despite receiving high expectations, this category of
methods suffers from low search effectiveness. By employing a generalization
boundedness tool, we demonstrate that the devil behind this drawback is the
untrustworthy architecture rating with the oversized search space of the
possible architectures. Addressing this problem, we modularize a large search
space into blocks with small search spaces and develop a family of models with
the distilling neural architecture (DNA) techniques. These proposed models,
namely a DNA family, are capable of resolving multiple dilemmas of the
weight-sharing NAS, such as scalability, efficiency, and multi-modal
compatibility. Our proposed DNA models can rate all architecture candidates, as
opposed to previous works that can only access a subsearch space using
heuristic algorithms. Moreover, under a certain computational complexity
constraint, our method can seek architectures with different depths and widths.
Extensive experimental evaluations show that our models achieve
state-of-the-art top-1 accuracy of 78.9% and 83.6% on ImageNet for a mobile
convolutional network and a small vision transformer, respectively.
Additionally, we provide in-depth empirical analysis and insights into neural
architecture ratings. Codes available: \url{https://github.com/changlin31/DNA}.


  We present a new census of the Orion Nebula Cluster (ONC) over a large field
of view (>30'x30'), significantly increasing the known population of stellar
and substellar cluster members with precisely determined properties. We develop
and exploit a technique to determine stellar effective temperatures from
optical colors, nearly doubling the previously available number of objects with
effective temperature determinations in this benchmark cluster. Our technique
utilizes colors from deep photometry in the I-band and in two medium-band
filters at lambda~753 and 770nm, which accurately measure the depth of a
molecular feature present in the spectra of cool stars. From these colors we
can derive effective temperatures with a precision corresponding to better than
one-half spectral subtype, and importantly this precision is independent of the
extinction to the individual stars. Also, because this technique utilizes only
photometry redward of 750nm, the results are only mildly sensitive to optical
veiling produced by accretion. Completing our census with previously available
data, we place some 1750 sources in the Hertzsprung-Russel diagram and assign
masses and ages down to 0.02 solar masses. At faint luminosities, we detect a
large population of background sources which is easily separated in our
photometry from the bona fide cluster members. The resulting initial mass
function of the cluster has good completeness well into the substellar mass
range, and we find that it declines steeply with decreasing mass. This suggests
a deficiency of newly formed brown dwarfs in the cluster compared to the
Galactic disk population.


  Entanglement witness is an effective method to detect entanglement in unknown
states without doing full tomography. One of the most widespread schemes of
witnessing entanglement is measuring its fidelity with respect to a pure
entangled state. Recently, a large class of states whose entanglement can not
be detected with the fidelity witness has been discovered in Phys.Rev.Lett
\textbf{124},200502(2020). They are called unfaithful states. In this paper we
propose a new way to detect entanglement by calculating the lower bound of
entanglement using measurement results. Numerical simulation shows our method
can detect entanglement in unfaithful states with a small number of
measurements. Moreover, we generalize our scheme to multipartite states and
show that it can tolerate higher noise than previous entanglement witness
operators with same number of measurement settings.


  Directed acyclic graphs (DAGs) and associated probability models are widely
used to model neural connectivity and communication channels. In many
experiments, data are collected from multiple subjects whose connectivities may
differ but are likely to share many features. In such circumstances it is
natural to leverage similarity between subjects to improve statistical
efficiency. The first exact algorithm for estimation of multiple related DAGs
was recently proposed by Oates et al. 2014; in this letter we present examples
and discuss implications of the methodology as applied to the analysis of fMRI
data from a multi-subject experiment. Elicitation of tuning parameters requires
care and we illustrate how this may proceed retrospectively based on technical
replicate data. In addition to joint learning of subject-specific connectivity,
we allow for heterogeneous collections of subjects and simultaneously estimate
relationships between the subjects themselves. This letter aims to highlight
the potential for exact estimation in the multi-subject setting.


  Two-photon processes have so far been considered only as resulting from
frequency-matched second-order expansions of light-matter interaction, with
consequently small coupling strengths. However, a variety of novel physical
phenomena arises when such coupling values become comparable with the system
characteristic frequencies. Here, we propose a realistic implementation of
two-photon quantum Rabi and Dicke models in trapped-ion technologies. In this
case, effective two-phonon processes can be explored in all relevant parameter
regimes. In particular, we show that an ion chain under bichromatic laser
drivings exhibits a rich dynamics and highly counterintuitive spectral
features, such as interaction-induced spectral collapse.


  It is shown that the DFT exchange and correlation functionals satisfy an
expression that couples exchange and correlation functionals and functional
derivatives evaluated at three different densities and for two particle
numbers. This equation can be used as a stringent test to check the internal
self-consistency of approximations to the exchange and correlation functionals.


  Locality-sensitive hashing (LSH) is a well-known solution for approximate
nearest neighbor (ANN) search in high-dimensional spaces due to its robust
theoretical guarantee on query accuracy. Traditional LSH-based methods mainly
focus on improving the efficiency and accuracy of the query phase by designing
different query strategies, but pay little attention to improving the
efficiency of the indexing phase. They typically fine-tune existing
data-oriented partitioning trees to index data points and support their query
strategies. However, their strategy to directly partition the multi-dimensional
space is time-consuming, and performance degrades as the space dimensionality
increases. In this paper, we design an encoding-based tree called Dynamic
Encoding Tree (DE-Tree) to improve the indexing efficiency and support
efficient range queries based on Euclidean distance. Based on DE-Tree, we
propose a novel LSH scheme called DET-LSH. DET-LSH adopts a novel query
strategy, which performs range queries in multiple independent index DE-Trees
to reduce the probability of missing exact NN points, thereby improving the
query accuracy. Our theoretical studies show that DET-LSH enjoys probabilistic
guarantees on query accuracy. Extensive experiments on real-world datasets
demonstrate the superiority of DET-LSH over the state-of-the-art LSH-based
methods on both efficiency and accuracy. While achieving better query accuracy
than competitors, DET-LSH achieves up to 6x speedup in indexing time and 2x
speedup in query time over the state-of-the-art LSH-based methods. This paper
was published in PVLDB 2024.


  This study aims to develop a framework for multicriteria analysis to evaluate
alternatives for sustainable corn agricultural area planning, considering the
integration of ecological, economic, and social aspects as pillars of
sustainability. The research method uses qualitative and quantitative
approaches to integrate ecological, economic, and social aspects in the
multicriteria analysis. The analysis involves land evaluation, subcriteria
identification, and data integration using Multidimensional Scaling and
Analytical Hierarchy Process methods to prioritize developing sustainable corn
agricultural areas. Based on the results of the RAP-Corn analysis, it indicates
that the ecological dimension depicts less sustainability. The AHP results
yield weight distribution and highly relevant scores that describe tangible
preferences. Priority directions are grouped as strategic steps toward
achieving the goals of sustainable corn agricultural area planning.


  Automated f ault detection and monitoring in engineering are critical but
frequently difficult owing to the necessity for collecting and labeling large
amounts of defective samples . We present an unsupervised method that uses the
high end Segment Anything Model (SAM) and a moving window approach. SAM has
gained recognition in AI image segmentation communities for its accuracy and
versatility. However, its performance can be inconsistent when dealing with
certain unexpected shapes , such as shadows and subtle surface irregularities.
This limitation raise s concerns about its applicability for fault detection in
real world scenarios We aim to overcome these challenges without requiring fine
tun ing or labeled data. Our technique divides pictures into smaller windows,
which are subsequently processed using SAM. This increases the accuracy of
fault identification by focusing on localized details. We compute the sizes of
the segmented sections and then us e a clustering technique to discover
consistent fault areas while filtering out noise. To further improve the
method's robustness , we propose adding the Exponentially Weighted Moving
Average (EWMA) technique for continuous monitoring in industrial settings,
which would improve the method's capacity to trace faults over time. We compare
our method to various well established methods u sing a real case study where
our model achieve s 0.96 accuracy compared to 0. 8 5 for the second best
method. W e also compare our method us ing two open source datasets where our
model attains a consistent 0. 86 accuracy across the datasets compared to 0.53
and 0.54 for second best model s.


  We consider the method of entanglement witness operator to verify genuine
multipartite entanglement for single-particle W states involving N parties. In
particular, linear optical schemes using photo detectors and beam splitters are
proposed to implement two different types of witness operator in experiment.
The first scheme that requires only a single measurement setting is shown to
detect genuine multipartite entanglement for the overall efficiency beyond
1-1/N. On the other hand, the second scheme with N+1 measurement settings
achieves success at a significantly lowered efficiency than 1-1/N.


  We study a class of McKean-Vlasov type stochastic differential equations
(SDEs) which arise from the random vortex dynamics and other physics models. By
introducing a new approach we resolve the existence and uniqueness of both the
weak and strong solutions for the McKean-Vlasov stochastic differential
equations whose coefficients are defined in terms of singular integral kernels
such as the Biot-Savart kernel. These SDEs which involve the distributions of
solutions are in general not Lipschitz continuous with respect to the usual
distances on the space of distributions such as the Wasserstein distance.
Therefore there is an obstacle in adapting the ordinary SDE method for the
study of this class of SDEs, and the conventional methods seem not appropriate
for dealing with such distributional SDEs which appear in applications such as
fluid mechanics.


  By looking at cooled configurations on the lattice, we study the presence of
peaks in the action density, or its electric and magnetic components, in the
SU(2) gauge vacuum. The peaks are seen to be of instanton-like nature and their
number variation takes care of the drop in the string tension observed when
cooling. Possible explanations of this finding are analysed.


  Quantum entanglement is an essential resource for quantum networks. However,
the generation of entanglement between physical devices at remote network nodes
is a challenging task towards practical implementation of quantum networks. In
this work, we use the open-source Simulator of QUantum Network Communication
(SeQUeNCe), developed by our team, to simulate entanglement generation between
two atomic frequency comb (AFC) absorptive quantum memories to be deployed on
the Argonne-Chicago quantum network. We realize the representation of photonic
quantum states within truncated Fock spaces in SeQUeNCe and build models for a
spontaneous parametric down-conversion (SPDC) source, AFC absorptive quantum
memories, and measurement devices with non-number-resolving photon detectors.
Based on these developments, we observe varying fidelity with SPDC source mean
photon number, and varying entanglement generation rate with both mean photon
number and memory mode number. We also simulate tomographic reconstruction of
the effective density matrix for the bipartite photonic states retrieved from
quantum memories. Our work extends the usability of the SeQUeNCe simulator with
new hardware modules and Fock state representation that will improve the
simulation of near term quantum network hardware and protocols.


  We consider the general physical situation of a quantum system $\H_0$
interacting with a chain of exterior systems $\bigotimes_\N \H$, one after the
other, during a small interval of time $h$ and following some Hamiltonian $H$
on $\H_0 \otimes \H$. We discuss the passage to the limit to continuous
interactions ($h \to 0$) in a setup which allows to compute the limit of this
Hamiltonian evolution in a single state space: a continuous field of exterior
systems $\otimes_{\R} \H$. Surprisingly, the passage to the limit shows the
necessity for 3 different time scales in $H$. The limit evolution equation is
shown to spontaneously produce quantum noises terms: we obtain a quantum
Langevin equation as limit of the Hamiltonian evolution. For the very first
time, these quantum Langevin equations are obtained as the effective limit from
repeated to continuous interactions and not only as a model. These results
justify the usual quantum Langevin equations considered in continual quantum
measurement or in quantum optics. We show that the three time scales correspond
to the normal regime, the weak coupling limit and the low density limit. Our
approach allows to consider these two physical limits altogether for the first
time. Their combination produces an effective Hamiltonian on the small system,
which had never been described before. We apply these results to give an
Hamiltonian description of the von Neumann measurement. We also consider the
approximation of continuous time quantum master equations by discrete time
ones. In particular we show how any Lindblad generator is obtained as the limit
of completely positive maps.


  Segmenting brain tumors is complex due to their diverse appearances and
scales. Brain metastases, the most common type of brain tumor, are a frequent
complication of cancer. Therefore, an effective segmentation model for brain
metastases must adeptly capture local intricacies to delineate small tumor
regions while also integrating global context to understand broader scan
features. The TransUNet model, which combines Transformer self-attention with
U-Net's localized information, emerges as a promising solution for this task.
In this report, we address brain metastases segmentation by training the
3D-TransUNet model on the Brain Tumor Segmentation (BraTS-METS) 2023 challenge
dataset. Specifically, we explored two architectural configurations: the
Encoder-only 3D-TransUNet, employing Transformers solely in the encoder, and
the Decoder-only 3D-TransUNet, utilizing Transformers exclusively in the
decoder. For Encoder-only 3D-TransUNet, we note that Masked-Autoencoder
pre-training is required for a better initialization of the Transformer Encoder
and thus accelerates the training process. We identify that the Decoder-only
3D-TransUNet model should offer enhanced efficacy in the segmentation of brain
metastases, as indicated by our 5-fold cross-validation on the training set.
However, our use of the Encoder-only 3D-TransUNet model already yield notable
results, with an average lesion-wise Dice score of 59.8\% on the test set,
securing second place in the BraTS-METS 2023 challenge.


  We study a Batalin-Vilkovisky algebra structure on the Hochschild cohomology
of the group ring of finitely generated abelian groups. The Batalin-Vilkovisky
algebra structure for finite abelian groups comes from the fact that the group
ring of finite groups is a symmetric algebra, and the Batalin-Vilkovisky
algebra structure for free abelian groups of finite rank comes from the fact
that its group ring is a Calabi-Yau algebra.


  The present paper is a review of the current state of Graph-Link Theory
(graph-links are also closely related to homotopy classes of looped
interlacement graphs), dealing with a generalisation of knots obtained by
translating the Reidemeister moves for links into the language of intersection
graphs of chord diagrams. In this paper we show how some methods of classical
and virtual knot theory can be translated into the language of abstract graphs,
and some theorems can be reproved and generalised to this graphical setting. We
construct various invariants, prove certain minimality theorems and construct
functorial mappings for graph-knots and graph-links. In this paper, we first
show non-equivalence of some graph-links to virtual links.


  We generalise the geometric analysis of square fishnet integrals in two
dimensions to the case of hexagonal fishnets with three-point vertices. Our
results support the conjecture that fishnet Feynman integrals in two
dimensions, together with their associated geometry, are completely fixed by
their Yangian and permutation symmetries. As a new feature for the hexagonal
fishnets, the star-triangle identity introduces an ambiguity in the graph
representation of a given Feynman integral. This translates into a map between
different geometric interpretations attached to a graph. We demonstrate
explicitly how these fishnet integrals can be understood as Calabi-Yau
varieties, whose Picard-Fuchs ideals are generated by the Yangian over the
conformal algebra. In analogy to elliptic curves, which represent the simplest
examples of fishnet integrals with four-point vertices, we find that the
simplest examples of three-point fishnets correspond to Picard curves with
natural generalisations at higher loop orders.


  Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems.


  It is well known that when the fused silica is irradiated with focused
femtosecond laser beams, space selective chemical etching can be achieved. The
etching rate depends sensitively on the polarization of the laser.
Surprisingly, we observe that by chirping the Fourier-transform-limited
femtosecond laser pulses to picosecond pulses, the polarization dependence of
the etching rate disappears, whereas an efficient etching rate can still be
maintained. Observation with a scanning electron microscope reveals that the
chirped pulses can induce interconnected nanocracks in the irradiated areas
which facilitates efficient introduction of the etchant into the microchannel.
The reported technology is of great use for fabrication of three-dimensional
(3D) microfluidic systems and glass-based 3D printing.


  We describe a generic theoretical framework, denoted as the
Boltzmann-Ginzburg-Landau approach, to derive continuous equations for the
polar and/or nematic order parameters describing the large scale behavior of
assemblies of point-like active particles interacting through polar or nematic
alignment rules. Our study encompasses three main classes of dry active
systems, namely polar particles with 'ferromagnetic' alignment (like the
original Vicsek model), nematic particles with nematic alignment ("active
nematics"), and polar particles with nematic alignment ("self-propelled rods").
The Boltzmann-Ginzburg-Landau approach combines a low-density description in
the form of a Boltzmann equation, with a Ginzburg-Landau-type expansion close
to the instability threshold of the disordered state. We provide the generic
form of the continuous equations obtained for each class, and comment on the
relationships and differences with other approaches.


  Let $(X, \omega, J)$ be a toric variety of dimension $2n$ determined by a
Delzant polytope. In this paper, we first construct the polarizations
$\shP_{k}$ by the Hamiltonian $T^{k}$-action on $X$ (see Theorem 3.11). We will
show that $\shP_{k}$ is a singular mixed polarization for $1\le k < n$, and
$\shP_{n}$ is a singular real polarization which coincides with the real
polarization studied in \cite{BFMN} on the open dense subset of $X$. Then for
each $1\le k \le n$, we will find a one-parameter family of K\"ahler
polarizations $\shP_{k,t}$ on $X$ that converges to $\shP_{k}$ (see Theorem
3.12). Finally, we will show that $\shH_{k,t}^{T}$ the space of
$T^{k}$-invariant $J_{k,t}$-holomorphic sections converges to $\shH_{k}^{0}$
(see Theorem 3.18).


  A search is made for the highly-suppressed B meson decays $B^{+}\rightarrow
K^{+}K^{+}\pi^{-}$ and $B^{+}\rightarrow \pi^{+}\pi^{+}K^{-}$ using a data
sample corresponding to an integrated luminosity of 3.0 $fb^{-1}$ collected by
the LHCb experiment in proton-proton collisions at centre-of-mass energies of 7
and 8 TeV. No evidence is found for the decays, and upper limits at 90\%
confidence level are determined to be $\mathcal{B}(B^{+}\rightarrow
K^{+}K^{+}\pi^{-}) < 1.1\times 10^{-8}$ and $\mathcal{B}(B^{+}\rightarrow
\pi^{+}\pi^{+}K^{-}) < 4.6\times 10^{-8}$.


  We calculate the decay amplitude of a harmonically trapped Bose-Einstein
condensate with attractive interaction via the Feynman path integral. We find
that when the number of particles is less than a critical number, the
condensate decays relatively slowly through quantum tunneling. When the number
exceeds the critical one, a "black hole" opens up at the center of the trap, in
which density fluctuations become large due to a negative pressure, and
collisional loss will drain the particles from the trap. As the black hole is
fed by tunneling particles, we have a novel system in which quantum tunneling
serves as a hydrodynamic source.


  Controlling the topological properties of quantum matter is a major goal of
condensed matter physics. A major effort in this direction has been devoted to
using classical light in the form of Floquet drives to manipulate and induce
states with non-trivial topology. A different route can be achieved with cavity
photons. Here we consider a prototypical model for topological phase
transition, the one-dimensional Su-Schrieffer-Heeger (SSH) model, coupled to a
single mode cavity. We show that quantum light can affect the topological
properties of the system, including the finite-length energy spectrum hosting
edge modes and the topological phase diagram. In particular we show that
depending on the lattice geometry and the strength of light-matter coupling one
can either turn a trivial phase into a topological one or viceversa using
quantum cavity fields. Furthermore, we compute the polariton spectrum of the
coupled electron-photon system, and we note that the lower polariton branch
disappears at the topological transition point. This phenomenon can be used to
probe the phase transition in the SSH model.


  Cilia and flagella are hairlike organelles that propel cells through fluid.
The active motion of the axoneme, the motile structure inside cilia and
flagella, is powered by molecular motors of the dynein family. These motors
generate forces and torques that slide and bend the microtubule doublets within
the axoneme. To create regular waveforms the activities of the dyneins must be
coordinated. It is thought that coordination is mediated by stresses due to
radial, transverse, or sliding deformations, that build up within the moving
axoneme. However, which particular component of the stress regulates the motors
to produce the observed flagellar waveforms remains an open question. To
address this question, we describe the axoneme as a three-dimensional bundle of
filaments and characterize its mechanics. We show that regulation of the motors
by radial and transverse stresses can lead to a coordinated flagellar motion
only in the presence of twist. By comparison, regulation by shear stress is
possible without twist. We calculate emergent beating patterns in twisted
axonemes resulting from regulation by transverse stresses. The waveforms are
similar to those observed in flagella of Chlamydomonas and sperm. Due to the
twist, the waveform has non-planar components, which result in swimming
trajectories such as twisted ribbons and helices that agree with observations.


  This paper develops a simple method to construct confidence bands, centered
at a principal component analysis (PCA) based estimator, for the slope function
in a functional linear regression model with a scalar response variable and a
functional predictor variable. The PCA-based estimator is a series estimator
with estimated basis functions, and so construction of valid confidence bands
for it is a non-trivial challenge. We propose a confidence band that aims at
covering the slope function at "most" of points with a prespecified probability
(level), and prove its asymptotic validity under suitable regularity
conditions. Importantly, this is the first paper that derives confidence bands
having theoretical justifications for the PCA-based estimator. We also propose
a practical method to choose the cut-off level used in PCA-based estimation,
and conduct numerical studies to verify the finite sample performance of the
proposed confidence band. Finally, we apply our methodology to spectrometric
data, and discuss extensions of our methodology to cases where additional
vector-valued regressors are present.


  We study the transresistivity $\tensor\rho_{21}$ (or equivalently, the drag
rate) of two Coulomb-coupled quantum wells in the presence of a perpendicular
magnetic field, using semi-classical transport theory. Elementary arguments
seem to preclude any possibility of observation of ``Hall drag'' (i.e., a
non-zero off-diagonal component in $\tensor\rho_{21}$). We show that these
arguments are specious, and in fact Hall drag can be observed at sufficiently
high temperatures when the {\sl intra}layer transport time $\tau$ has
significant energy-dependence around the Fermi energy $\varepsilon_F$. The
ratio of the Hall to longitudinal transresistivities goes as $T^2 B s$, where
$T$ is the temperature, $B$ is the magnetic field, and $s = [\partial\tau/
\partial\varepsilon] (\varepsilon_F)$.


  In the supervised high dimensional settings with a large number of variables
and a low number of individuals, one objective is to select the relevant
variables and thus to reduce the dimension. That subspace selection is often
managed with supervised tools. However, some data can be missing, compromising
the validity of the sub-space selection. We propose a Partial Least Square
(PLS) based method, called Multi-block Data-Driven sparse PLS mdd-sPLS,
allowing jointly variable selection and subspace estimation while training and
testing missing data imputation through a new algorithm called Koh-Lanta. This
method was challenged through simulations against existing methods such as mean
imputation, nipals, softImpute and imputeMFA. In the context of supervised
analysis of high dimensional data, the proposed method shows the lowest
prediction error of the response variables. So far this is the only method
combining data imputation and response variable prediction. The superiority of
the supervised multi-block mdd-sPLS method increases with the intra-block and
inter-block correlations. The application to a real data-set from a rVSV-ZEBOV
Ebola vaccine trial revealed interesting and biologically relevant results. The
method is implemented in a R-package available on the CRAN and a Python-package
available on pypi.


  Next-generation, atomically thin devices require in-plane, one-dimensional
heterojunctions to electrically connect different two-dimensional (2D)
materials. However, the lattice mismatch between most 2D materials leads to
unavoidable strain, dislocations, or ripples, which can strongly affect their
mechanical, optical, and electronic properties. We have developed an approach
to map 2D heterojunction lattice and strain profiles with sub-picometer
precision and to identify dislocations and out-of-plane ripples. We collected
diffraction patterns from a focused electron beam for each real-space scan
position with a high-speed, high dynamic range, momentum-resolved detector -
the electron microscope pixel array detector (EMPAD). The resulting
four-dimensional (4D) phase space datasets contain the full spatially resolved
lattice information of the sample. By using this technique on tungsten
disulfide (WS2) and tungsten diselenide (WSe2) lateral heterostructures, we
have mapped lattice distortions with 0.3 pm precision across multi-micron
fields of view and simultaneously observed the dislocations and ripples
responsible for strain relaxation in 2D laterally-epitaxial structures.


  We determine the orbit types of the action of the group of local gauge
transformations on the space of connections in a principal bundle with
structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold
of dimension 4. Complemented with earlier results on U(n) and SU(n) this
completes the classification of the orbit types for all classical compact gauge
groups over such space-time manifolds. On the way we derive the classification
of principal bundles with structure group SO(n) over these manifolds and the
Howe subgroups of SO(n).


  Traffic violations like illegal parking, illegal turning, and speeding have
become one of the greatest challenges in urban transportation systems, bringing
potential risks of traffic congestions, vehicle accidents, and parking
difficulties. To maximize the utility and effectiveness of the traffic
enforcement strategies aiming at reducing traffic violations, it is essential
for urban authorities to infer the traffic violation-prone locations in the
city. Therefore, we propose a low-cost, comprehensive, and dynamic framework to
infer traffic violation-prone locations in cities based on the large-scale
vehicle trajectory data and road environment data. Firstly, we normalize the
trajectory data by map matching algorithms and extract key driving behaviors,
i.e., turning behaviors, parking behaviors, and speeds of vehicles. Secondly,
we restore spatiotemporal contexts of driving behaviors to get corresponding
traffic restrictions such as no parking, no turning, and speed restrictions.
After matching the traffic restrictions with driving behaviors, we get the
traffic violation distribution. Finally, we extract the spatiotemporal patterns
of traffic violations, and build a visualization system to showcase the
inferred traffic violation-prone locations. To evaluate the effectiveness of
the proposed method, we conduct extensive studies on large-scale, real-world
vehicle GPS trajectories collected from two Chinese cities, respectively.
Evaluation results confirm that the proposed framework infers traffic
violation-prone locations effectively and efficiently, providing comprehensive
decision supports for traffic enforcement strategies.


  In accessibility tests for digital preservation, over time we experience
drifts of localized and labelled content in statistical models of evolving
semantics represented as a vector field. This articulates the need to detect,
measure, interpret and model outcomes of knowledge dynamics. To this end we
employ a high-performance machine learning algorithm for the training of
extremely large emergent self-organizing maps for exploratory data analysis.
The working hypothesis we present here is that the dynamics of semantic drifts
can be modeled on a relaxed version of Newtonian mechanics called social
mechanics. By using term distances as a measure of semantic relatedness vs.
their PageRank values indicating social importance and applied as variable
`term mass', gravitation as a metaphor to express changes in the semantic
content of a vector field lends a new perspective for experimentation. From
`term gravitation' over time, one can compute its generating potential whose
fluctuations manifest modifications in pairwise term similarity vs. social
importance, thereby updating Osgood's semantic differential. The dataset
examined is the public catalog metadata of Tate Galleries, London.


  Flow-based generative models, conceptually attractive due to tractability of
both the exact log-likelihood computation and latent-variable inference, and
efficiency of both training and sampling, has led to a number of impressive
empirical successes and spawned many advanced variants and theoretical
investigations. Despite their computational efficiency, the density estimation
performance of flow-based generative models significantly falls behind those of
state-of-the-art autoregressive models. In this work, we introduce masked
convolutional generative flow (MaCow), a simple yet effective architecture of
generative flow using masked convolution. By restricting the local connectivity
in a small kernel, MaCow enjoys the properties of fast and stable training, and
efficient sampling, while achieving significant improvements over Glow for
density estimation on standard image benchmarks, considerably narrowing the gap
to autoregressive models.


  Aside from graph neural networks (GNNs) attracting significant attention as a
powerful framework revolutionizing graph representation learning, there has
been an increasing demand for explaining GNN models. Although various
explanation methods for GNNs have been developed, most studies have focused on
instance-level explanations, which produce explanations tailored to a given
graph instance. In our study, we propose Prototype-bAsed GNN-Explainer (PAGE),
a novel model-level GNN explanation method that explains what the underlying
GNN model has learned for graph classification by discovering
human-interpretable prototype graphs. Our method produces explanations for a
given class, thus being capable of offering more concise and comprehensive
explanations than those of instance-level explanations. First, PAGE selects
embeddings of class-discriminative input graphs on the graph-level embedding
space after clustering them. Then, PAGE discovers a common subgraph pattern by
iteratively searching for high matching node tuples using node-level embeddings
via a prototype scoring function, thereby yielding a prototype graph as our
explanation. Using six graph classification datasets, we demonstrate that PAGE
qualitatively and quantitatively outperforms the state-of-the-art model-level
explanation method. We also carry out systematic experimental studies by
demonstrating the relationship between PAGE and instance-level explanation
methods, the robustness of PAGE to input data scarce environments, and the
computational efficiency of the proposed prototype scoring function in PAGE.


  Let $\pi$ be an irreducible, complex, smooth representation of $GL_n$ over a
local non-archimedean (skew) field. Assuming $\pi$ has regular Zelevinsky
parameters, we give a geometric necessary and sufficient criterion for the
irreducibility of the parabolic induction of $\pi\otimes\pi$ to $GL_{2n}$. The
latter irreducibility property is the $p$-adic analogue of a special case of
the notion of "real representations" introduced by Leclerc and studied recently
by Kang-Kashiwara-Kim-Oh (in the context of KLR or quantum affine algebras).
Our criterion is in terms of singularities of Schubert varieties of type $A$
and admits a simple combinatorial description. It is also equivalent to a
condition studied by Geiss-Leclerc-Schr\"oer.


  To segment a sequence of independent random variables at an unknown number of
change-points, we introduce new procedures that are based on thresholding the
likelihood ratio statistic. We also study confidence regions based on the
likelihood ratio statistic for the change-points and joint confidence regions
for the change-points and the parameter values. Applications to segment array
CGH data are discussed.


  The magnetic and quadrupole moments of the light-vector and axial-vector
mesons are calculated in the light cone QCD sum rules. Our results for the
static properties of these mesons are compared with the predictions of lattice
QCD as well as other approaches existing in the literature.


  Inspired by the recent work of Chen-Sti\'enon-Xu on Atiyah classes associated
to inclusions of Lie algebroids, we give a very simple criterium (in terms of
those classes) for relative Poincar\'e-Birkhoff-Witt type results to hold. The
tools we use (e.g. the first infinitesimal neighbourhood Lie algebroid) are
straightforward generalizations of the ones previously developped by Caldararu,
Tu and the author for Lie algebra inclusions.


  We compare the entanglement of formation with a measure defined as the
modulus of the negative eigenvalue of the partial transpose. In particular, we
investigate whether both measures give the same ordering of density operators
with respect to the amount of entanglement.


  Let $n$ be a nonnegative integer. For each composition $\alpha$ of $n$, Berg
$\textit{et al.}$ introduced a cyclic indecomposable $H_n(0)$-module
$\mathcal{V}_\alpha$ with a dual immaculate quasisymmetric function as the
image of the quasisymmetric characteristic. In this paper, we study
$\mathcal{V}_\alpha$'s from the homological viewpoint. To be precise, we
construct a minimal projective presentation of $\mathcal{V}_\alpha$ and a
minimal injective presentation of $\mathcal{V}_\alpha$ as well. Using them, we
compute ${\rm Ext}^1_{H_n(0)}(\mathcal{V}_\alpha, {\bf F}_\beta)$ and ${\rm
Ext}^1_{H_n(0)}( {\bf F}_\beta, \mathcal{V}_\alpha)$, where ${\bf F}_\beta$ is
the simple $H_n(0)$-module attached to a composition $\beta$ of $n$. We also
compute ${\rm Ext}_{H_n(0)}^i(\mathcal{V}_\alpha,\mathcal{V}_{\beta})$ when
$i=0,1$ and $\beta \le_l \alpha$, where $\le_l$ represents the lexicographic
order on compositions.


  Global VLBI imaging at millimeter and sub-millimeter wavelength overcomes the
opacity barrier of synchrotron self-absorption in AGN and opens the direct view
into sub-pc scale regions not accessible before. Since AGN variability is more
pronounced at short millimeter wavelength, mm-VLBI can reveal structural
changes in very early stages after outbursts. When combined with observations
at longer wavelength, global 3mm and 1mm VLBI adds very detailed information.
This helps to determine fundamental physical properties at the jet base, and in
the vicinity of super-massive black holes at the center of AGN. Here we present
new results from multi-frequency mm-VLBI imaging of OJ287 during a major
outburst. We also report on a successful 1.3mm VLBI experiment with the APEX
telescope in Chile. This observation sets a new record in angular resolution.
It also opens the path towards future mm-VLBI with ALMA, which aims at the
mapping of the black hole event horizon in nearby galaxies, and the study of
the roots of jets in AGN.


  We address the two main questions relevant to microscopic nuclear structure
calculations starting from a free NN potential. These concern the accuracy of
these kinds of calculations and the extent to which they depend on the
potential used as input. Regarding the first question, we present some results
obtained for nuclei around doubly magic 132Sn and 208Pb by making use of an
effective interaction derived from the Bonn A potential. Comparison shows that
our results are in very good agreement with the experimental data. As for the
second question, we present the results obtained for the nucleus 134Te by
making use of four different NN potentials. They indicate that nuclear
structure calculations may help in understanding the off-shell nature of the NN
potential.


  We show that a recently introduced stochastic thermostat [J. Chem. Phys. 126
(2007) 014101] can be considered as a global version of the Langevin
thermostat. We compare the global scheme and the local one (Langevin) from a
formal point of view and through practical calculations on a model
Lennard-Jones liquid. At variance with the local scheme, the global thermostat
preserves the dynamical properties for a wide range of coupling parameters, and
allows for a faster sampling of the phase-space.


  In this paper, we study the problem of testing the mean vectors of high
dimensional data in both one-sample and two-sample cases. The proposed testing
procedures employ maximum-type statistics and the parametric bootstrap
techniques to compute the critical values. Different from the existing tests
that heavily rely on the structural conditions on the unknown covariance
matrices, the proposed tests allow general covariance structures of the data
and therefore enjoy wide scope of applicability in practice. To enhance powers
of the tests against sparse alternatives, we further propose two-step
procedures with a preliminary feature screening step. Theoretical properties of
the proposed tests are investigated. Through extensive numerical experiments on
synthetic datasets and an human acute lymphoblastic leukemia gene expression
dataset, we illustrate the performance of the new tests and how they may
provide assistance on detecting disease-associated gene-sets. The proposed
methods have been implemented in an R-package HDtest and are available on CRAN.


  We present Hybrid Infused Reranking for Passages Retrieval (HYRR), a
framework for training rerankers based on a hybrid of BM25 and neural retrieval
models. Retrievers based on hybrid models have been shown to outperform both
BM25 and neural models alone. Our approach exploits this improved performance
when training a reranker, leading to a robust reranking model. The reranker, a
cross-attention neural model, is shown to be robust to different first-stage
retrieval systems, achieving better performance than rerankers simply trained
upon the first-stage retrievers in the multi-stage systems. We present
evaluations on a supervised passage retrieval task using MS MARCO and zero-shot
retrieval tasks using BEIR. The empirical results show strong performance on
both evaluations.


  We investigate whether young neutron stars with fall-back disks can produce
Anomalous X-Ray Pulsars (AXPs) within timescales indicated by the ages of
associated supernova remnants. The system passes through a propeller stage
before emerging as an AXP or a radio pulsar. The evolution of the disk is
described by a diffusion equation which has self-similar solutions with either
angular momentum or total mass of the disk conserved. We associate these two
types of solutions with accretor and propeller regimes, respectively. Our
numerical calculations of thin disk models with changing inner radius take into
account the super-critical accretion at the early stages, and electron
scattering and bound-free opacities with rich metal content. Our results show
that, assuming a fraction of the mass inflow is accreted onto the neutron star,
the fall-back disk scenario can produce AXPs for acceptable parameters.


  We show, theoretically, that the phase of the interlayer exchange coupling
(IEC) undergoes a topological change of approximately $2\pi$ as the chemical
potential of the ferromagnetic (FM) lead moves across a hybridization gap (HG).
The effect is largely independent of the detailed parameters of the system, in
particular the width of the gap. The implication is that for a narrow gap, a
small perturbation in the chemical potential of the lead can give a sign
reversal of the exchange coupling. This offers the possibility of controlling
magnetization switching in spintronic devices such as MRAM, with little power
consumption. Furthermore we believe that this effect has already been
indirectly observed, in existing measurements of the IEC as a function of
temperature and of doping of the leads.


  In this paper we first consider a linear time invariant systems with almost
periodic forcing term. We propose a new deterministic quadratic control
problem, motivated by Da-Prato. With the help of associated degenerate Riccati
equation we study the existence and uniqueness of an almost automorphic
solutions.


  Separating the mixture of the $ K_{1}(1270)$ and $K_{1}(1400) $ states, the
$B\to K_{1}(1270, 1400)\nu\bar{\nu}$ transition form factors are calculated in
the three-point QCD sum rules approach. The longitudinal, transverse and total
decay widths as well as the asymmetry parameter, characterizing the
polarization of the axial $K_{1}(1270, 1400)$ and the branching ratio for these
decays are evaluated.


  We report the discovery of an extremely broad H-alpha emission line in the
LINER nucleus of NGC 4579. From ground-based observations, the galaxy was
previously known to contain a Type 1 nucleus with a broad H-alpha line of FWHM
= 2300 km/s and FWZI ~ 5000 km/s. New spectra obtained with the Hubble Space
Telescope and a 0.2 arcsec-wide slit reveal an H-alpha component with FWZI ~
18,000 km/s. The line is not obviously double-peaked, but it does possess
shoulders on the red and blue sides which resemble the H-alpha profiles of
double-peaked emitters such as NGC 4203 and NGC 4450. This similarity suggests
that the very broad H-alpha profile in NGC 4579 may represent emission from an
accretion disk. Three such objects have been found recently in two HST programs
which have targeted a total of 30 galaxies, demonstrating that double-peaked or
extremely broad-line emission in LINERs must be much more common than would be
inferred from ground-based surveys. The ratio of the narrow [S II] 6716, 6731
lines shows a pronounced gradient indicating a steep rise in density toward the
nucleus. The direct detection of a density gradient within the inner arcsecond
of the narrow-line region confirms expectations from previous observations of
linewidth-critical density correlations in several LINERs.


  This article contributes to a global history of relativity, by exploring how
Einstein's theory was appropriated in Belgium. This may sound as a
contradiction in terms, yet the early-twentieth-century Belgian context,
because of its cultural diversity and reflectiveness of global conditions (the
principal example being the First World War), proves well-suited to expose
transnational flows and patterns in the global history of relativity. The
attempts of Belgian physicist Th\'eophile de Donder to contribute to relativity
physics during the 1910s and 1920s illustrate the role of the war in shaping
the transnational networks through which relativity circulated. The local
attitudes of conservative Belgian Catholic scientists and philosophers, who
denied that relativity was philosophically significant, exemplify a global
pattern: while critics of relativity feared to become marginalized by the
scientific, political, and cultural revolutions that Einstein and his theory
were taken to represent, supporters sympathized with these revolutions.