  We study transport properties and also local density of states in a clean
superconductor-normal metal-superconductor Josephson junction with triplet
f-wave superconductors based on the Eilenberger equation. Effects of thickness
of normal metal and misorientation between gap vector of superconductors on the
spin and charge currents are investigated. Spin current, which stems from the
misalignment of d-vectors, in the absence of charge current for some values of
phase difference between superconductors is found. We also find unconventional
behavior of the spin current associated with 0-pitransition. The misalignment
of d-vectors also gives rise to a zero energy peak in the density of states in
the normal metal.


  Single-particle cryo-electron microscopy (cryo-EM) has become one of the
mainstream structural biology techniques because of its ability to determine
high-resolution structures of dynamic bio-molecules. However, cryo-EM data
acquisition remains expensive and labor-intensive, requiring substantial
expertise. Structural biologists need a more efficient and objective method to
collect the best data in a limited time frame. We formulate the cryo-EM data
collection task as an optimization problem in this work. The goal is to
maximize the total number of good images taken within a specified period. We
show that reinforcement learning offers an effective way to plan cryo-EM data
collection, successfully navigating heterogenous cryo-EM grids. The approach we
developed, cryoRL, demonstrates better performance than average users for data
collection under similar settings.


  Plants are a paradigm for active shape control in response to stimuli. For
instance, it is well-known that a tilted plant will eventually straighten
vertically, demonstrating the influence of both an external stimulus, gravity,
and an internal stimulus, proprioception. These effects can be modulated when a
potted plant is additionally rotated along the plant's axis, as in a rotating
clinostat, leading to intricate shapes. We use a morphoelastic model for the
response of growing plants to study the joint effect of both stimuli at all
rotation speeds. In the absence of rotation, we identify a universal planar
shape towards which all shoots eventually converge. With rotation, we
demonstrate the existence of a stable family of three-dimensional dynamic
equilibria where the plant axis is fixed in space. Further, the effect of axial
growth is to induce steady behaviors, such as solitary waves. Overall, this
study offers new insight into the complex out-of-equilibrium dynamics of a
plant in three dimensions and further establishes that internal stimuli in
active materials are key for robust shape control.


  Let $A$ be a unital separable simple amenable $C^*$-algebra with finite
tracial rank which satisfies the Universal Coefficient Theorem (UCT). Suppose
$\af$ and $\bt$ are two automorphisms with the Rokhlin property that {induce
the same action on the $K$-theoretical data of $A$.} We show that $\af$ and
$\bt$ are strongly cocycle conjugate and uniformly approximately conjugate,
that is, there exists a sequence of unitaries $\{u_n\}\subset A$ and a sequence
of strongly asymptotically inner automorphisms $\sigma_n$ such that $$ \af={\rm
Ad}\, u_n\circ \sigma_n\circ \bt\circ \sigma_n^{-1}\andeqn
\lim_{n\to\infty}\|u_n-1\|=0, $$ and that the converse holds. {We then give a
$K$-theoretic description as to exactly when $\af$ and $\bt$ are cocycle
conjugate, at least under a mild restriction. Moreover, we show that given any
$K$-theoretical data, there exists an automorphism $\af$ with the Rokhlin
property which has the same $K$-theoretical data.


  We show that the correlator of three large charge operators with minimal
scaling dimension can be computed semiclassically in CFTs with a $U(1)$
symmetry for arbitrary fixed values of the ratios of their charges. We obtain
explicitly the OPE coefficient from the numerical solution of a nonlinear
boundary value problem in the conformal superfluid EFT in $3d$. The result
applies in all three-dimensional CFTs with a $U(1)$ symmetry whose large charge
sector is a superfluid.


  We investigate the possibility of spontaneous loop currents in the two-leg
ladder cuprate Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ by applying cluster dynamical
mean field theory (CDMFT) to a seven-band Hubbard model for that compound, with
an exact diagonalization solver. We sample several values of the local
interaction $U_d$ and of the Cu-O energy difference $E_{pd}$, by applying an
external field that induces loop currents. We find no instance of spontaneous
loop currents once the external field is brought to zero.


  The main contribution of this paper is to analyze a long networked flying
platform (NFP)-based millimeter wave (mmWave) backhaul link that is offered as
a cost effective and easy to deploy solution to connect a disaster or remote
area to the nearest core network. For this aim, we characterize the backhaul
channel as a function of realistic physical parameters such as heights and
distances of obstacles along the route, flight altitude and the intensity of
NFPs' vibrations, the real 3D antenna pattern provided by 3GPP, etc. For the
characterized channel, we derive an analytical closed-form expression for the
outage probability. Finally, using the obtained results, we provide a fast
algorithm for the optimal parameter design of the considered system that
minimizes the cost.


  Hadron properties are modified when the hadron is embedded in a nuclear
medium. Here we discuss the Gerasimov-Drell-Hearn, GDH, sum rule for polarised
photoproduction from a polarised nucleon within a polarised nuclear target.
Strong enhancement is expected with the suppression of the proton and nucleon
resonance masses and enhancement of the proton's anomalous magnetic moment in
medium. This could be tested in polarised photoproduction experiments with
interesting targets being polarised deuterons, $^3$He, $^6$Li and $^7$Li. The
largest contribution to the GDH sum rule comes from the $\Delta$ resonance
excitation. In existing data with polarised deuterons and $^3$He the $\Delta$
excitation is shifted to slightly lower energy when compared to model
predictions where the $\Delta$ is treated with its free mass.


  We derive the polarizability of an electron system in (i) the superconducting
phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor
pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a
d-wave hidden order parameter, but no pairing. Such a calculation is motivated
by the recent proposals that imaging the effects of an isolated impurity may
distinguish between precursor pairing and dDW order in the pseudogap regime of
the high-Tc superconductors. In all three cases, the wave-vector dependence of
the polarizability is characterized by an azymuthal modulation, consistent with
the d-wave symmetry of the underlying state. However, only the dDW result shows
the fingerprints of nesting, with nesting wave-vector Q=(pi,pi), albeit
imperfect, due to a nonzero value of the hopping ratio t'/t in the band
dispersion relation. As a consequence of nesting, the presence of hole pockets
is also exhibited by the (q,omega) dependence of the retarded polarizability.


  We report the discovery of 14 low-mass binary systems containing mid-M to
mid-L dwarf companions with separations larger than 250 AU. We also report the
independent discovery of 9 other systems with similar characteristics that were
recently discovered in other studies. We have identified these systems by
searching for common proper motion sources in the vicinity of known high proper
motion stars, based on a cross-correlation of wide area near-infrared surveys
(2MASS, SDSS, and SIMP). An astrometric follow-up, for common proper motion
confirmation, was made with SIMON and/or CPAPIR at the OMM 1.6 m and CTIO 1.5 m
telescopes for all the candidates identified. A spectroscopic follow-up was
also made with GMOS or GNIRS at Gemini to determine the spectral types of 11 of
our newly identified companions and 10 of our primaries. Statistical arguments
are provided to show that all of the systems we report here are very likely to
be physical binaries. One of the new systems reported features a brown dwarf
companion: LSPM J1259+1001 (M5) has an L4.5 (2M1259+1001) companion at about
340 AU. This brown dwarf was previously unknown. Seven other systems have a
companion of spectral type L0-L1 at a separation in the 250-7500 AU range. Our
sample includes 14 systems with a mass ratio below 0.3.


  We present numerical results on spontaneous symmetry breaking strain
localization in axisymmetric triaxial shear tests of granular materials. We
simulated shear band formation using three-dimensional Distinct Element Method
with spherical particles. We demonstrate that the local shear intensity, the
angular velocity of the grains, the coordination number, and the local void
ratio are correlated and any of them can be used to identify shear bands,
however the latter two are less sensitive. The calculated shear band
morphologies are in good agreement with those found experimentally. We show
that boundary conditions play an important role. We discuss the formation
mechanism of shear bands in the light of our observations and compare the
results with experiments. At large strains, with enforced symmetry, we found
strain hardening.


  We consider the problem of designing a low-complexity decoder for antipodal
uniquely decodable (UD) /errorless code sets for overloaded synchronous
code-division multiple access (CDMA) systems, where the number of signals Kamax
is the largest known for the given code length L. In our complexity analysis,
we illustrate that compared to maximum-likelihood (ML) decoder, which has an
exponential computational complexity for even moderate code lengths, the
proposed decoder has a quasi-quadratic computational complexity. Simulation
results in terms of bit-error-rate (BER) demonstrate that the performance of
the proposed decoder has only a 1-2 dB degradation in signal-to-noise ratio
(SNR) at a BER of 10^-3 when compared to ML. Moreover, we derive the proof of
the minimum Manhattan distance of such UD codes and we provide the proofs for
the propositions; these proofs constitute the foundation of the formal proof
for the maximum number users Kamax for L=8 .


  Wearable devices are a fast-growing technology with impact on personal
healthcare for both society and economy. Due to the widespread of sensors in
pervasive and distributed networks, power consumption, processing speed, and
system adaptation are vital in future smart wearable devices. The visioning and
forecasting of how to bring computation to the edge in smart sensors have
already begun, with an aspiration to provide adaptive extreme edge computing.
Here, we provide a holistic view of hardware and theoretical solutions towards
smart wearable devices that can provide guidance to research in this pervasive
computing era. We propose various solutions for biologically plausible models
for continual learning in neuromorphic computing technologies for wearable
sensors. To envision this concept, we provide a systematic outline in which
prospective low power and low latency scenarios of wearable sensors in
neuromorphic platforms are expected. We successively describe vital potential
landscapes of neuromorphic processors exploiting complementary metal-oxide
semiconductors (CMOS) and emerging memory technologies (e.g. memristive
devices). Furthermore, we evaluate the requirements for edge computing within
wearable devices in terms of footprint, power consumption, latency, and data
size. We additionally investigate the challenges beyond neuromorphic computing
hardware, algorithms and devices that could impede enhancement of adaptive edge
computing in smart wearable devices.


  Recent advances in high-throughput cDNA sequencing (RNA-Seq) technology have
revolutionized transcriptome studies. A major motivation for RNA-Seq is to map
the structure of expressed transcripts at nucleotide resolution. With accurate
computational tools for transcript reconstruction, this technology may also
become useful for genome (re-)annotation, which has mostly relied on de novo
gene finding where gene structures are primarily inferred from the genome
sequence. We developed a machine-learning method, called mTim (margin-based
transcript inference method) for transcript reconstruction from RNA-Seq read
alignments that is based on discriminatively trained hidden Markov support
vector machines. In addition to features derived from read alignments, it
utilizes characteristic genomic sequences, e.g. around splice sites, to improve
transcript predictions. mTim inferred transcripts that were highly accurate and
relatively robust to alignment errors in comparison to those from Cufflinks, a
widely used transcript assembly method.


  In this paper, we study a polynomial decomposition model that arises in
problems of system identification, signal processing and machine learning. We
show that this decomposition is a special case of the X-rank decomposition ---
a powerful novel concept in algebraic geometry that generalizes the tensor CP
decomposition. We prove new results on generic/maximal rank and on
identifiability of a particular polynomial decomposition model. In the paper,
we try to make results and basic tools accessible for general audience
(assuming no knowledge of algebraic geometry or its prerequisites).


  Modern big data workflows are characterized by computationally intensive
kernels. The simulated results are often combined with knowledge extracted from
AI models to ultimately support decision-making. These energy-hungry workflows
are increasingly executed in data centers with energy-efficient hardware
accelerators since FPGAs are well-suited for this task due to their inherent
parallelism. We present the H2020 project EVEREST, which has developed a system
development kit (SDK) to simplify the creation of FPGA-accelerated kernels and
manage the execution at runtime through a virtualization environment. This
paper describes the main components of the EVEREST SDK and the benefits that
can be achieved in our use cases.


  We explore residually finite and profinite quandles. We prove that the
endomorphism monoid and the automorphism group of finitely generated residually
finite quandles are residually finite. In fact, we establish the similar result
for a broad class of residually finite quandles. We provide a topological
characterization of profinite quandles. We establish necessary and sufficient
conditions for profinite quandles ensuring that their endomorphism monoids and
automorphism groups are profinite.


  Motivated by the interest in searches for violation of CPT invariance, we
study its possible effects in the flavour ratios of high-energy neutrinos
coming from cosmic accelerators. In particular, we focus on the effect of an
energy independent new physics contribution to the neutrino flavour oscillation
phase and explore whether it is observable in future detectors. Such a
contribution could be related not only to CPT violation but also to a
nonuniversal coupling of neutrinos to a torsion field. We conclude that this
extra phase contribution only becomes observable, in the best case, at energies
greater than 10^{16.5} GeV, which is about five orders of magnitude higher than
the most energetic cosmological neutrinos to be detected in the near future.
Therefore, if these effects are present only in the oscillation phase, they are
going to be unobservable, unless a new mechanism or source capable to produce
neutrinos of such energy were detected.


  In this article we construct a new motivic measure called the ${\it Jacques}$
${\it Tits}$ ${\it motivic}$ ${\it measure}$. As a first main application of
the Jacques Tits motivic measure, we prove that two Severi-Brauer varieties
(or, more generally, two twisted Grassmannian varieties), associated to
$2$-torsion central simple algebras, have the same class in the Grothendieck
ring of varieties if and only if they are isomorphic. In addition, we prove
that if two Severi-Brauer varieties, associated to central simple algebras of
period $\{3, 4, 5, 6\}$, have the same class in the Grothendieck ring of
varieties, then they are necessarily birational to each other. As a second main
application of the Jacques Tits motivic measure, we prove that two quadric
hypersurfaces (or, more generally, two involution varieties), associated to
quadratic forms of dimension $6$ or to quadratic forms of arbitrary dimension
defined over a base field $k$ with $I^3(k)=0$, have the same class in the
Grothendieck ring of varieties if and only if they are isomorphic. In addition,
we prove that the latter main application also holds for products of quadric
hypersurfaces.


  The reaction 13C(alpha,n) is considered to be the main source of neutrons for
the s-process in AGB stars. At low energies the cross section is dominated by
the 1/2+ 6.356 MeV sub-threshold resonance in 17O whose contribution is
determined with a very large uncertainty of ~1000% at stellar temperatures. In
this work we performed the most precise determination of the low-energy
astrophysical S factor using the indirect asymptotic normalization (ANC)
technique. The alpha-particle ANC for the sub-threshold state has been measured
using the sub-Coulomb alpha-transfer reaction (6Li,d). Using the determined ANC
we calculated S(0), which turns out to be an order of magnitude smaller than in
the NACRE compilation.


  We show that a modification of the first layer of a Graph Convolutional
Network (GCN) can be used to effectively propagate label information across
neighbor nodes, for binary and multi-class classification problems. This is
done by selectively eliminating self-loops for the label features during the
training phase of a GCN. The GCN architecture is otherwise unchanged, without
any extra hyper-parameters, and can be used in both a transductive and
inductive setting. We show through several experiments that, depending on how
many labels are available during the inference phase, this strategy can lead to
a substantial improvement in the model performance compared to a standard GCN
approach, including with imbalanced datasets.


  We present an implementation of the rotationally invariant slave boson
technique as an impurity solver for density functional theory plus dynamical
mean field theory (DFT+DMFT). Our approach provides explicit relations between
quantities in the local correlated subspace treated with DMFT and the Bloch
basis used to solve the DFT equations. In particular, we present an expression
for the mass enhancement of the quasiparticle states in reciprocal space. We
apply the method to the study of the electronic correlations in Sr$_2$RuO$_4$
under anisotropic strain. We find that the spin-orbit coupling plays a crucial
role in the mass enhancement differentiation between the quasi-one-dimensional
$\alpha$ and $\beta$ bands, and on its momentum dependence over the Fermi
surface. The mass enhancement, however, is only weakly affected by either
uniaxial or biaxial strain, even across the Lifshitz transition induced by the
strain.


  We prove a quantitative distortion theorem for iterated function systems that
generate sets of continued fractions. As a consequence, we obtain upper and
lower bounds on the Hausdorff dimension of any set of real or complex continued
fractions. These bounds are solutions to Moran-type equations in the
convergents that can be easily implemented in a computer algebra system.


  Direct3{\gamma}PET is a novel, comprehensive pipelinefor direct estimation of
emission points in three-gamma (3-{\gamma})positron emission tomography (PET)
imaging using \b{eta}+ and {\gamma}emitters. This approach addresses
limitations in existing directreconstruction methods for 3-{\gamma} PET, which
often struggle withdetector imperfections and uncertainties in estimated
intersectionpoints. The pipeline begins by processing raw data, managingprompt
photon order in detectors, and propagating energy andspatial uncertainties on
the line of response (LOR). It thenconstructs histo-images backprojecting
non-symmetric Gaussianprobability density functions (PDFs) in the histo-image,
withattenuation correction applied when such data is available.
Athree-dimensional (3-D) convolutional neural network (CNN)performs image
translation, mapping the histo-image to radioac-tivity image. This architecture
is trained using both supervisedand adversarial approaches. Our evaluation
demonstrates thesuperior performance of this method in balancing event
inclu-sion and accuracy. For image reconstruction, we compare bothsupervised
and adversarial neural network (NN) approaches.The adversarial approach shows
better structural preservation,while the supervised approach provides slightly
improved noisereduction.


  Generalising a result of classical mechanics an infinite set of conserved
quantities can be found for the bare equations of motion describing the
evolution of a scalar field in out of equilibrium quantum field theory, in the
large N approximation, with initial conditions corresponding to a thermal
system of the free Hamiltonian. Using these new conserved quantities, sum-rules
relating integrals over the mode-functions (momenta) can be derived. More, the
corresponding renormalised quantities can also be computed out thus giving
information about the evolution of the already known renormalised equations;
finally it is also possible to write a renormalised version of the sum-rules.


  A refinement of the Hardy inequality has been presented by use of
superquadratic function.


  The self-expressive property of data points, i.e., each data point can be
linearly represented by the other data points in the same subspace, has proven
effective in leading subspace clustering methods. Most self-expressive methods
usually construct a feasible affinity matrix from a coefficient matrix,
obtained by solving an optimization problem. However, the negative entries in
the coefficient matrix are forced to be positive when constructing the affinity
matrix via exponentiation, absolute symmetrization, or squaring operations.
This consequently damages the inherent correlations among the data. Besides,
the affine constraint used in these methods is not flexible enough for
practical applications. To overcome these problems, in this paper, we introduce
a scaled simplex representation (SSR) for subspace clustering problem.
Specifically, the non-negative constraint is used to make the coefficient
matrix physically meaningful, and the coefficient vector is constrained to be
summed up to a scalar s<1 to make it more discriminative. The proposed SSR
based subspace clustering (SSRSC) model is reformulated as a linear
equality-constrained problem, which is solved efficiently under the alternating
direction method of multipliers framework. Experiments on benchmark datasets
demonstrate that the proposed SSRSC algorithm is very efficient and outperforms
state-of-the-art subspace clustering methods on accuracy. The code can be found
at https://github.com/csjunxu/SSRSC.


  This paper is a fusion of a survey and a research article. We focus on
certain rigidity phenomena in function spaces associated to a symplectic
manifold. Our starting point is a lower bound obtained in an earlier paper with
Zapolsky for the uniform norm of the Poisson bracket of a pair of functions in
terms of symplectic quasi-states. After a short review of the theory of
symplectic quasi-states, we extend this bound to the case of iterated Poisson
brackets. A new technical ingredient is the use of symplectic integrators. In
addition, we discuss some applications to symplectic approximation theory and
present a number of open problems.


  We consider a two-phase flow of two incompressible, viscous and immiscible
fluids which are separated by a sharp interface in the case of a simple phase
transition. In this model the interface is no longer material and its evolution
is governed by a convective mean curvature flow equation, which is coupled to a
two-phase Navier-Stokes equation with Young-Laplace law. The problem arises as
a sharp interface limit of a diffuse interface model, which consists of a
Navier-Stokes system coupled with an Allen-Cahn equation. We prove existence of
strong solutions for sufficiently small times and regular initial data.


  Requirement traceability is the process of identifying the inter-dependencies
between requirements. It poses a significant challenge when conducted manually,
especially when dealing with requirements at various levels of abstraction. In
this work, we propose a novel approach to automate the task of linking
high-level business requirements with more technical system requirements. The
proposed approach begins by representing each requirement using a Bag of-Words
(BOW) model combined with the Term Frequency-Inverse Document Frequency
(TF-IDF) scoring function. Then, we suggested an enhanced cosine similarity
that uses recent advances in word embedding representation to correct
traditional cosine similarity function limitations. To evaluate the
effectiveness of our approach, we conducted experiments on three well-known
datasets: COEST, WARC(NFR), and WARC(FRS). The results demonstrate that our
approach significantly improves efficiency compared to existing methods. We
achieved better results with an increase of approximately 18.4% in one of the
datasets, as measured by the F2 score.


  We construct a new Yang-Mills 3D-solution on the space of negative scalar
curvarure. We discuss a problem of non-abelian gauge symmetry is broken with
the assumption that a scalar curvature of the domain is a negative small
parameter. In this case we use the following fact: a geometrical scale related
with Vassiliev's discriminant of magnetic lines coincids with a physical
Kolmogorov scale. This gives an estimation of $\alpha$-effect by the dispersion
of the asymptotic ergodic Hopf invariant in the limite with a negative scalar
curvature parameter.


  The capacity region of a two-transmitter Gaussian multiple access channel
(MAC) under average input power constraints is studied, when the receiver
employs a zero-threshold one-bit analog-to-digital converter (ADC). It is
proved that the input distributions of the two transmitters that achieve the
boundary points of the capacity region are discrete. Based on the position of a
boundary point, upper bounds on the number of the mass points of the
corresponding distributions are derived.


  We propose a modified BCS wavefunction as the ground state of a correlated
superconductor with the correlation specified between $k$ and $-k$ electrons in
the reciprocal space. Owing to this correlation, low-energy excitations are not
conventional BCS Bogoliubov quasiparticles. They display at least four poles in
the Green's function and their particle-hole weights in the tunneling and
photon-emission spectrum become asymmetric. The superfluid density or
superfluid stiffness also deviates from the BCS predictions with finite
paramagnetic terms inside the total diamagnetic response. Moreover, a $d$-wave
correlated pairing state becomes robust against weak disorders. Hence, this
state can explain many mysterious features observed in unconventional
superconductors like cuprates.


  The development of long, tunable structures is critical to increasing energy
gain in laser-driven dielectric accelerators (DLAs). Here we combine
pulse-front-tilt illumination with slab-geometry structures assembled by
precisely aligning off-the-shelf 4~mm long transmission gratings to achieve up
to 200 keV energy modulation for 6 MeV injected electrons. The effective
interaction length is longer than 1~mm, limited by dephasing of the accelerated
particles in the structure. The piezo-based independent mounting system for the
gratings allows tuning of the gap and field distribution inside the structure.


  It is known that in order for a supersymmetric gauge theory to be dynamically
broken a necessary but not sufficient condition is that the Witten index
$(-1)^F=n_b^0-n_f^0$ is zero. In the case the Witten index is zero it is in
general hard to distinguish between theories with or without dynamical
supersymmetry breaking. In this work we show that for a large class of theories
the cancellation of the Witten index by itself signals the formation of a quark
condensate and therefore produces dynamical supersymmetry breaking.


  This letter provides a review of fundamental distributed systems and economic
Cloud computing principles. These principles are frequently deployed in their
respective fields, but their inter-dependencies are often neglected. Given that
Cloud Computing first and foremost is a new business model, a new model to sell
computational resources, the understanding of these concepts is facilitated by
treating them in unison. Here, we review some of the most important concepts
and how they relate to each other.


  Transcranial ultrasound is more and more used for therapy and imaging of the
brain. However, the skull is a highly attenuating and aberrating medium, with
different structures and acoustic properties between samples and even within a
sample. Thus, case-specific simulations are needed to perform transcranial
focused ultrasound interventions safely. In this article, we provide a review
of the different methods used to model the skull and to simulate ultrasound
propagation through it.


  For the Kowalevski gyrostat change of variables similar to that of the
Kowalevski top is done. We establish one to one correspondence between the
Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski
variables for the gyrostat practically coincide with elliptic coordinates on
sphere for the Clebsch case. Equivalence of considered integrable systems
allows to construct two Lax matrices for the gyrostat using known rational and
elliptic Lax matrices for the Clebsch model. Associated with these matrices
solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat
problem are discussed. The Kotter solution of the Clebsch system in modern
notation is presented in detail.


  Schaeffer's regularity theorem for scalar conservation laws can be loosely
speaking formulated as follows. Assume that the flux is uniformly convex, then
for a generic smooth initial datum the admissible solution is smooth outside a
locally finite number of curves in the (t,x) plane. Here the term `generic' is
to be interpreted in a suitable sense, related to the Baire Category Theorem.
Whereas other regularity results valid for scalar conservation laws with convex
fluxes have been extended to systems of conservation laws with genuinely
nonlinear characteristic fields, in this work we exhibit an explicit
counterexample which rules out the possibility of extending Schaeffer's
Theorem. The analysis relies on careful interaction estimates and uses fine
properties of the wave front-tracking approximation.


  We have investigated the impact of dissipationless minor galaxy mergers on
the angular momentum of the remnant. Our simulations cover a range of initial
orbital characteristics and the system consists of a massive galaxy with a
bulge and disk merging with a much less massive (one-tenth or one-twentieth)
gasless companion which has a variety of morphologies (disk- or
elliptical-like) and central baryonic mass concentrations. During the process
of merging, the orbital angular momentum is redistributed into the internal
angular momentum of the final system; the internal angular momentum of the
primary galaxy can increase or decrease depending on the relative orientation
of the orbital spin vectors (direct or retrograde), while the initially
non-rotating dark matter halo always gains angular momentum. The specific
angular momentum of the stellar component always decreases independent of the
orbital parameters or morphology of the satellite, the decrease in the rotation
velocity of the primary galaxy is accompanied by a change in the anisotropy of
the orbits, and the ratio of rotation speed to velocity dispersion of the
merger remnant is lower than the initial value, not only due to an increase in
the dispersion but also to the slowing -down of the disk rotation. We briefly
discuss several astrophysical implications of these results, suggesting that
minor mergers do not cause a "random walk" process of the angular momentum of
the stellar disk component of galaxies, but rather a steady decrease. Minor
mergers may play a role in producing the large scatter observed in the
Tully-Fisher relation for S0 galaxies, as well as in the increase of the
velocity dispersion and the decrease in $v/\sigma$ at large radii as observed
in S0 galaxies.


  In this thesis, we focus on higher-curvature extensions of Einstein gravity
as toy models to probe universal properties of conformal field theory (CFT)
using the gauge/gravity duality. In this context, we are particularly
interested in generalized quasi-topological gravities, i.e., theories whose
equations of motion for statically spherically symmetric solutions are of
second order at most. Here, we characterize the number of these theories
existing at a given curvature order and dimensions. Moreover, we show that any
effective higher-curvature theory is connected, via field redefinitions to some
generalized quasi-topological gravity. The situation is special for three
spacetime dimensions, as theories of this type have trivial equations of
motion. However, when matter fields are added into the picture, the equations
of motion become non-trivial, describing, among other solutions,
multiparametric generalizations of the Ba\~nados-Teitelboim-Zanelli black hole.
  From the CFT side, entanglement entropy arises as a prominent quantity that
encodes important information about the field theory, such as the type A and
type B trace anomalies in even dimensions and the sphere free energy of the
theory in odd dimensions when considering spherical entangling regions. As
entanglement entropy also includes divergences, we employ the Kounterterms
scheme to extract the physically relevant quantities. In the case of
three-dimensional CFTs dual to Einstein gravity, we show that the finite part
is isolated and can be written in terms of the Willmore energy, providing an
upper bound based on its properties. We extend this remarkable result to
arbitrary CFTs under consideration. Besides, we show the validity of the
Kounterterms scheme for general quadratic curvature gravity, extracting the
type A, type B anomalies of the theory in even dimensions and the sphere free
energy in odd ones.


  We give a review of the works devoted to the treatment of the Kerr super
black hole solution as a spinning particle. The real, complex and stringy
structures of the Kerr and super-Kerr geometries are discussed, as well as the
recent results on the regular matter source for the Kerr spinning particle. It
is shown that the source has to represent a rotating bag-like bubble having
(A)dS interior and a smooth domain wall boundary. The given by Morris
supersymmetric generalization of the U(I) x U'(I) field model (which was used
by Witten to describe cosmic superconducting strings) is considered, and it is
shown that this model can be adapted for description of superconducting bags
having a long range external electromagnetic field and another gauge field
confined inside the bag.


  The catastrophic senescence of the Pacific salmon is among the initial tests
used to validate the Penna aging model. Based on the mutation accumulation
theory, the sudden decrease in fitness following reproduction may be solely
attributed to the semelparity of the species. In this work, we report other
consequences of mutation accumulation. Contrary to earlier findings, such
dramatic manifestation of aging depends not only on the choice of breeding
strategy but also on the value of the reproduction age, R, and the mutation
threshold, T. Senescence is catastrophic when $T \leq R$. As the organism's
tolerance for harmful genetic mutations increases, the aging process becomes
more gradual. We observe senescence that is threshold dependent whenever T>R.
That is, the sudden drop in survival rate occurs at age equal to the mutation
threshold value.


  A number of deeply virtual exclusive experiments will allow us to access the
Generalized Parton Distributions which are embedded in the complex amplitudes
for such processes. The extraction from experiment is particularly challenging
both because of the large number of kinematical variables and observables to be
pinned down in each experimental analysis and because, at variance with
inclusive experiments, the variables representing the quark momentum fraction
appear integrated over in the physical amplitudes and cannot be accessed
directly. We present a strategy for the extraction from experiment that makes
use of constraints from both elastic and inclusive scattering as well as
information from lattice QCD results.


  We prove the semi-Riemannian bumpy metric theorem using equivariant
variational genericity. The theorem states that, on a given compact manifold
$M$, the set of semi-Riemannian metrics that admit only nondegenerate closed
geodesics is generic relatively to the $C^k$-topology, $k=2,...,\infty$, in the
set of metrics of a given index on $M$. A higher order genericity Riemannian
result of Klingenberg and Takens is extended to semi-Riemannian geometry.


  Asymmetric variability in ultraviolet images of the Homunculus obtained with
the Advanced Camera for Surveys/High Resolution Camera on the Hubble Space
Telescope suggests that Eta Carinae is indeed a binary system. Images obtained
before, during, and after the recent ``spectroscopic event'' in 2003.5 show
alternating patterns of bright spots and shadows on opposite sides of the star
before and after the event, providing a strong geometric argument for an
azimuthally-evolving, asymmetric UV radiation field as one might predict in
some binary models. The simplest interpretation of these UV images, where
excess UV escapes from the secondary star in the direction away from the
primary, places the major axis of the eccentric orbit roughly perpendicular to
our line of sight, sharing the same equatorial plane as the Homunculus, and
with apastron for the hot secondary star oriented toward the southwest of the
primary. However, other orbital orientations may be allowed with more
complicated geometries. Selective UV illumination of the wind and ejecta may be
partly responsible for line profile variations seen in spectra. The brightness
asymmetries cannot be explained plausibly with delays due to light travel time
alone, so a single-star model would require a seriously asymmetric shell
ejection.


  Crowd feedback systems have the potential to support creative workers with
feedback from the crowd. In this position paper for the Workshop on Designing
Crowd-powered Creativity Support Systems (DC2S2) at CHI '19, we present three
creativity support tools in which we explore how creative workers can be
assisted with crowdsourced formative and summative feedback. For each of the
three crowd feedback systems, we provide one idea for future research.


  The structure of a Bayesian network includes a great deal of information
about the probability distribution of the data, which is uniquely identified
given some general distributional assumptions. Therefore it's important to
study its variability, which can be used to compare the performance of
different learning algorithms and to measure the strength of any arbitrary
subset of arcs.
  In this paper we will introduce some descriptive statistics and the
corresponding parametric and Monte Carlo tests on the undirected graph
underlying the structure of a Bayesian network, modeled as a multivariate
Bernoulli random variable. A simple numeric example and the comparison of the
performance of some structure learning algorithm on small samples will then
illustrate their use.


  In this work we are going to establish H\"older continuity of harmonic maps
from an open set $\Omega$ in an ${\rm RCD}(K,N)$ space valued into a ${\rm
CAT}(\kappa)$ space, with the constraint that the image of $\Omega$ via the map
is contained in a sufficiently small ball in the target. Building on top of
this regularity and assuming a local Lipschitz regularity of the map, we
establish a weak version of the Bochner-Eells-Sampson inequality in such a
non-smooth setting. Finally we study the boundary regularity of such maps.


  A recent proposal to "redefine statistical significance" (Benjamin, et al.
Nature Human Behaviour, 2017) claims that false positive rates "would
immediately improve" by factors greater than two and replication rates would
double simply by changing the conventional cutoff for 'statistical
significance' from P<0.05 to P<0.005. I analyze the veracity of these claims,
focusing especially on how Benjamin, et al neglect the effects of P-hacking in
assessing the impact of their proposal. My analysis shows that once P-hacking
is accounted for the perceived benefits of the lower threshold all but
disappear, prompting two main conclusions: (i) The claimed improvements to
false positive rate and replication rate in Benjamin, et al (2017) are
exaggerated and misleading. (ii) There are plausible scenarios under which the
lower cutoff will make the replication crisis worse.


  The present article highlights an approach to generate contrasting patterns
from drying droplets in a liquid bridge configuration, different from
well-known coffee rings. Reduction of the confinement distance (the gap between
the solid surfaces) leads to systematized nano-particle agglomeration yielding
to spokes-like patterns similar to those found on scallop shells instead of
circumferential edge deposition. Alteration of the confinement length modulates
the curvature that entails variations in the evaporation flux across the
liquid-vapor interface. Consequently, flow inside different liquid bridges
(LBs) varies significantly for different confinement lengths. Small confinement
lengths result in the stick-slip motion of squeezed liquid bridges. On the
contrary, the stretched LBs exhibit pinned contact lines. We decipher a
proposition that a drying liquid thin film present during dewetting near the
three-phase contact line is responsible for the aligned deposition of
particles. The confinement distance determines the height of this thin film,
and its theoretical estimations are validated against the experimental
observations using reflection interferometry, further exhibiting good agreement
(in order of magnitude). Modulating the particle size does not significantly
influence the precipitate patterns; however, particle concentration can
substantially affect the deposition patterns. The differences in deposition
patterns are attributed to the complex interplay of the gradient of evaporation
flux induced motion of contact line in combination with the drying of thin
liquid film during dewetting.


  We consider the dynamics of an electrostatically actuated thin elastic plate
being clamped at its boundary above a rigid plate. The model includes the
harmonic electrostatic potential in the three-dimensional time-varying region
between the plates along with a fourth-order semilinear parabolic equation for
the elastic plate deflection which is coupled to the square of the gradient
trace of the electrostatic potential on this plate. The strength of the
coupling is tuned by a parameter $\lambda$ proportional to the square of the
applied voltage. We prove that this free boundary problem is locally well-posed
in time and that for small values of $\lambda$ solutions exist globally in
time. We also derive the existence of a branch of asymptotically stable
stationary solutions for small values of $\lambda$ and non-existence of
stationary solutions for large values thereof, the latter being restricted to a
disc-shaped plate.


  In the first part of this article we present some known results about
isospectral potentials on compact manifolds and on finite intervals. Then we
look at a weaker notion called quasi-isospectrality and deduce some properties
of quasi-isospectral potentials.


  We extend the Hopf algebra description of a simple quantum system given
previously, to a more elaborate Hopf algebra, which is rich enough to encompass
that related to a description of perturbative quantum field theory (pQFT). This
provides a {\em mathematical} route from an algebraic description of
non-relativistic, non-field theoretic quantum statistical mechanics to one of
relativistic quantum field theory. Such a description necessarily involves
treating the algebra of polyzeta functions, extensions of the Riemann Zeta
function, since these occur naturally in pQFT. This provides a link between
physics, algebra and number theory. As a by-product of this approach, we are
led to indicate {\it inter alia} a basis for concluding that the Euler gamma
constant $\gamma$ may be rational.


  Expert interpretation of anatomical images of the human brain is the central
part of neuro-radiology. Several machine learning-based techniques have been
proposed to assist in the analysis process. However, the ML models typically
need to be trained to perform a specific task, e.g., brain tumour segmentation
or classification. Not only do the corresponding training data require
laborious manual annotations, but a wide variety of abnormalities can be
present in a human brain MRI - even more than one simultaneously, which renders
representation of all possible anomalies very challenging. Hence, a possible
solution is an unsupervised anomaly detection (UAD) system that can learn a
data distribution from an unlabelled dataset of healthy subjects and then be
applied to detect out of distribution samples. Such a technique can then be
used to detect anomalies - lesions or abnormalities, for example, brain
tumours, without explicitly training the model for that specific pathology.
Several Variational Autoencoder (VAE) based techniques have been proposed in
the past for this task. Even though they perform very well on controlled
artificially simulated anomalies, many of them perform poorly while detecting
anomalies in clinical data. This research proposes a compact version of the
"context-encoding" VAE (ceVAE) model, combined with pre and post-processing
steps, creating a UAD pipeline (StRegA), which is more robust on clinical data,
and shows its applicability in detecting anomalies such as tumours in brain
MRIs. The proposed pipeline achieved a Dice score of 0.642$\pm$0.101 while
detecting tumours in T2w images of the BraTS dataset and 0.859$\pm$0.112 while
detecting artificially induced anomalies, while the best performing baseline
achieved 0.522$\pm$0.135 and 0.783$\pm$0.111, respectively.


  The mixed metric dimension ${\rm mdim}(G)$ of a graph $G$ is the cardinality
of a smallest set of vertices that (metrically) resolves each pair of elements
from $V(G)\cup E(G)$. We say that $G$ is a max-mdim graph if ${\rm mdim}(G) =
n(G)$. It is proved that a max-mdim graph $G$ with $n(G)\ge 7$ contains a
vertex of degree at least $5$. Using the strong product of graphs and
amalgamations large families of max-mdim graphs are constructed. The mixed
metric dimension of graphs with at least one universal vertex is determined.
The mixed metric dimension of graphs $G$ with cut vertices is bounded from the
above and the mixed metric dimension of block graphs computed.


  Since the advent of the web, the amount of data on wen has been increased
several million folds. In recent years web data generated is more than data
stored for years. One important data format is text. To answer user queries
over the internet, and to overcome the problem of information overload one
possible solution is text document summarization. This not only reduces query
access time, but also optimize the document results according to specific users
requirements. Summarization of text document can be categorized as abstractive
and extractive. Most of the work has been done in the direction of Extractive
summarization. Extractive summarized result is a subset of original documents
with the objective of more content coverage and lea redundancy. Our work is
based on Extractive approaches. In the first approach, we are using some
statistical features and semantic-based features. To include sentiment as a
feature is an idea cached from a view that emotion plays an important role. It
effectively conveys a message. So, it may play a vital role in text document
summarization.


  A number of stellar sources have been advocated as the origin of the enriched
material required to explain the abundance anomalies seen in ancient globular
clusters (GCs). Most studies to date have compared the yields from potential
sources (asymptotic giant branch stars (AGBs), fast rotating massive stars
(FRMS), high mass interacting binaries (IBs), and very massive stars (VMS))
with observations of specific elements that are observed to vary from
star-to-star in GCs, focussing on extreme GCs such as NGC 2808, which display
large He variations. However, a consistency check between the results of
fitting extreme cases with the requirements of more typical clusters, has
rarely been done. Such a check is particularly timely given the constraints on
He abundances in GCs now available. Here we show that all of the popular
enrichment sources fail to reproduce the observed trends in GCs, focussing
primarily on Na, O and He. In particular, we show that any model that can fit
clusters like NGC 2808, will necessarily fail (by construction) to fit more
typical clusters like 47 Tuc or NGC 288. All sources severely over-produce He
for most clusters. Additionally, given the large differences in He spreads
between clusters, but similar spreads observed in Na--O, only sources with
large degrees of stochasticity in the resulting yields will be able to fit the
observations. We conclude that no enrichment source put forward so far (AGBs,
FRMS, IBs, VMS - or combinations thereof) is consistent with the observations
of GCs. Finally, the observed trends of increasing [N/Fe] and He spread with
increasing cluster mass cannot be resolved within a self-enrichment framework,
without further exacerbating the mass budget problem.


  The Weil algebra of a semisimple Lie group and an exterior algebra of a
symplectic manifold possess antibrackets. They are applied to formulate the
models of non--abelian equivariant cohomologies.


  Cognitive Language Processing (CLP), situated at the intersection of Natural
Language Processing (NLP) and cognitive science, plays a progressively pivotal
role in the domains of artificial intelligence, cognitive intelligence, and
brain science. Among the essential areas of investigation in CLP, Cognitive
Signal Decoding (CSD) has made remarkable achievements, yet there still exist
challenges related to insufficient global dynamic representation capability and
deficiencies in multi-domain feature integration. In this paper, we introduce a
novel paradigm for CLP referred to as Disentangled Frequency-Spatial-Temporal
Attention(D-FaST). Specifically, we present an novel cognitive signal decoder
that operates on disentangled frequency-space-time domain attention. This
decoder encompasses three key components: frequency domain feature extraction
employing multi-view attention, spatial domain feature extraction utilizing
dynamic brain connection graph attention, and temporal feature extraction
relying on local time sliding window attention. These components are integrated
within a novel disentangled framework. Additionally, to encourage advancements
in this field, we have created a new CLP dataset, MNRED. Subsequently, we
conducted an extensive series of experiments, evaluating D-FaST's performance
on MNRED, as well as on publicly available datasets including ZuCo, BCIC IV-2A,
and BCIC IV-2B. Our experimental results demonstrate that D-FaST outperforms
existing methods significantly on both our datasets and traditional CSD
datasets including establishing a state-of-the-art accuracy score 78.72% on
MNRED, pushing the accuracy score on ZuCo to 78.35%, accuracy score on BCIC
IV-2A to 74.85% and accuracy score on BCIC IV-2B to 76.81%.


  We study azimuthal variations in the mean stellar metallicity, <[Fe/H]>, in a
self-consistent, isolated simulation in which all stars form out of gas. We
find <[Fe/H]> variations comparable to those observed in the Milky Way and
which are coincident with the spiral density waves. The azimuthal variations
are present in young and old stars and therefore are not a result of recently
formed stars. Similar variations are present in the mean age and
alpha-abundance. We measure the pattern speeds of the <[Fe/H]>-variations and
find that they match those of the spirals, indicating that they are at the
origin of the metallicity patterns. Because younger stellar populations are not
just more [Fe/H]-rich and alpha-poor but also dynamically cooler, we expect
them to more strongly support spirals, which is indeed the case in the
simulation. However, if we measure the radial action, J_R, using the Stackel
axisymmetric approximation, we find that the spiral ridges are traced by
regions of high J_R, contrary to expectations. Assuming that the passage of
stars through the spirals leads to unphysical variations in the measured J_R,
we obtain an improved estimate of J_R by averaging over a 1 Gyr time interval.
This time-averaged J_R is a much better tracer of the spiral structure, with
minima at the spiral ridges. We conclude that the errors incurred by the
axisymmetric approximation introduce correlated deviations large enough to
render the instantaneous radial action inadequate for tracing spirals.


  In this paper different optimization of Ad-hoc routing algorithm is surveyed
and a new method using training based optimization algorithm for reducing the
complexity of routing algorithms is suggested. A binary matrix is assigned to
each node in the network and gets updated after each data transfer using the
protocols. The use of optimization algorithm in routing algorithm can reduce
the complexity of routing to the least amount possible.


  As astronomy enters the petascale data era, astronomers are faced with new
challenges relating to storage, access and management of data. A shift from the
traditional approach of combining data and analysis at the desktop to the use
of remote services, pushing the computation to the data, is now underway. In
the field of cosmological gravitational microlensing, future synoptic all--sky
surveys are expected to bring the number of multiply imaged quasars from the
few tens that are currently known to a few thousands. This inflow of
observational data, together with computationally demanding theoretical
modelling via the production of microlensing magnification maps, requires a new
approach. We present our technical solutions to supporting the GPU-Enabled,
High Resolution cosmological MicroLensing parameter survey (GERLUMPH). This
extensive dataset for cosmological microlensing modelling comprises over 70,000
individual magnification maps and ${\sim}10^6$ related results. We describe our
approaches to hosting, organizing, and serving ${\sim}$30 Terabytes of data and
metadata products. We present a set of online analysis tools developed with
PHP, JavaScript and WebGL to support access and analysis of GELRUMPH data in a
Web browser. We discuss our use of graphics processing units (GPUs) to
accelerate data production, and we release the core of the GPU-D direct inverse
ray--shooting code (Thompson et al., 2010; Astrophysics Source Code Library,
record ascl:1403.001) used to generate the magnification maps. All of the
GERLUMPH data and tools are available online from http://gerlumph.swin.edu.au .
This project made use of gSTAR, the GPU Supercomputer for Theoretical
Astrophysical Research.


  Nonnegative matrix factorization (NMF), a dimensionality reduction and factor
analysis method, is a special case in which factor matrices have low-rank
nonnegative constraints. Considering the stochastic learning in NMF, we
specifically address the multiplicative update (MU) rule, which is the most
popular, but which has slow convergence property. This present paper introduces
on the stochastic MU rule a variance-reduced technique of stochastic gradient.
Numerical comparisons suggest that our proposed algorithms robustly outperform
state-of-the-art algorithms across different synthetic and real-world datasets.


  Protein motifs are conserved fragments occurred frequently in protein
sequences. They have significant functions, such as active site of an enzyme.
Search and clustering protein sequence motifs are computational intensive. Most
existing methods are not fast enough to analyze large data sets for motif
finding or achieve low accuracy for motif clustering. We present a new protein
sequence motif finding and clustering algorithm, called HSEARCH. It converts
fixed length protein sequences to data points in high dimensional space, and
applies locality-sensitive hashing to fast search homologous protein sequences
for a motif. HSEARCH is significantly faster than the brute force algorithm for
protein motif finding and achieves high accuracy for protein motif clustering.


  Based on extensions of the grand-canonical Quantum Monte-Carlo algorithm to
incorporate magnetic fields, we provide numerical data confirming the existence
of a Kosterlitz-Thouless transition in the attractive Hubbard model. Here, we
calculate the temperature derivative of the superfluid density, to pin down the
transition. Away from half-band filling, the above quantity, shows a response
which increases with lattice size at the transition temperature. In contrast,
such a signal is not observed for the case of a half-band filling.


  In this paper, we propose three approaches for the estimation of the Tucker
decomposition of multi-way arrays (tensors) from partial observations. All
approaches are formulated as convex minimization problems. Therefore, the
minimum is guaranteed to be unique. The proposed approaches can automatically
estimate the number of factors (rank) through the optimization. Thus, there is
no need to specify the rank beforehand. The key technique we employ is the
trace norm regularization, which is a popular approach for the estimation of
low-rank matrices. In addition, we propose a simple heuristic to improve the
interpretability of the obtained factorization. The advantages and
disadvantages of three proposed approaches are demonstrated through numerical
experiments on both synthetic and real world datasets. We show that the
proposed convex optimization based approaches are more accurate in predictive
performance, faster, and more reliable in recovering a known multilinear
structure than conventional approaches.


  Deep learning based methods have become a paradigm for cover song
identification (CSI) in recent years, where the ByteCover systems have achieved
state-of-the-art results on all the mainstream datasets of CSI. However, with
the burgeon of short videos, many real-world applications require matching
short music excerpts to full-length music tracks in the database, which is
still under-explored and waiting for an industrial-level solution. In this
paper, we upgrade the previous ByteCover systems to ByteCover3 that utilizes
local features to further improve the identification performance of short music
queries. ByteCover3 is designed with a local alignment loss (LAL) module and a
two-stage feature retrieval pipeline, allowing the system to perform CSI in a
more precise and efficient way. We evaluated ByteCover3 on multiple datasets
with different benchmark settings, where ByteCover3 beat all the compared
methods including its previous versions.


  We provide power series approximations for a structured batch arrival single
server retrial system with two infinite capacity weighted fair orbit queues,
i.e., the re-transmission rate of an orbit depends on the state of the other
orbit queue. We consider both exponential and arbitrary distributed service
times. In both cases we obtain power series expansions of the generating
functions of the stationary joint orbit queue-length distributions, and provide
a recursive approach to calculate their coefficients. We also show how to
obtain the generating function of the stationary joint orbit queue-length
distribution with the aid of a Riemann boundary value problem. Power series
approximations are also provided for the model with two independent Poisson
streams of jobs with single arrivals. Numerical illustrations are performed and
show the accuracy of our approach.


  M subdwarfs are metal poor and cool stars. They are important probes of the
old galactic populations. However, they remain elusive due to their low
luminosity. Observational and modeling efforts are required to fully understand
the physics and to investigate the effect of metallicity in their cool atmo-
spheres. We perform a detail study of a sample of subdwarfs to determine their
stellar parameters and constrain the atmosphere models. We present UVES/VLT
high resolution spectra of 21 M subdwarfs. Our atlas covers the optical region
from 6400{\deg}A up to the near infrared at 10000{\deg}A. We show spectral
details of cool atmospheres at very high resolution (R = 40 000) and compare
with synthetic spectra computed from the recent BT-Settl atmosphere models. Our
comparison shows that molecular features (TiO, VO, CaH), and atomic features
(Fe, Ti, Na, K) are well fitted by current models. We produce an effective
temperature versus spectral type relation all over the subdwarf spectral
sequence.


  This lecture discusses the mathematical relationship between network
structure and network utilization of transportation network. Network structure
means the graph itself. Network utilization represent the aggregation of
trajectories of agents in using the network graph. I show the similarity and
relationship between the structural pattern of the network and network
utilization.


  Generating ligand molecules for specific protein targets, known as
structure-based drug design, is a fundamental problem in therapeutics
development and biological discovery. Recently, target-aware generative models,
especially diffusion models, have shown great promise in modeling
protein-ligand interactions and generating candidate drugs. However, existing
models primarily focus on learning the chemical distribution of all drug
candidates, which lacks effective steerability on the chemical quality of model
generations. In this paper, we propose a novel and general alignment framework
to align pretrained target diffusion models with preferred functional
properties, named AliDiff. AliDiff shifts the target-conditioned chemical
distribution towards regions with higher binding affinity and structural
rationality, specified by user-defined reward functions, via the preference
optimization approach. To avoid the overfitting problem in common preference
optimization objectives, we further develop an improved Exact Energy Preference
Optimization method to yield an exact and efficient alignment of the diffusion
models, and provide the closed-form expression for the converged distribution.
Empirical studies on the CrossDocked2020 benchmark show that AliDiff can
generate molecules with state-of-the-art binding energies with up to -7.07 Avg.
Vina Score, while maintaining strong molecular properties.


  It is expected that the interplay between non-trivial band topology and
strong electron correlation will lead to very rich physics. Thus a controlled
study of the competition between topology and correlation is of great interest.
Here, employing large-scale quantum Monte Carlo (QMC) simulations, we provide a
concrete example of the Kane-Mele-Hubbard (KMH) model on an AA stacking bilayer
honeycomb lattice with inter-layer antiferromagnetic interaction. Our
simulation identified several different phases: a quantum spin-Hall insulator
(QSH), a $xy$-plane antiferromagnetic Mott insulator ($xy$-AFM) and an
inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona
fide topological phase transition between the QSH and the dimer-singlet
insulators, purely driven by the inter-layer antiferromagnetic interaction is
found. At the transition, the spin and charge gap of the system close while the
single-particle excitations remain gapped, which means that this transition has
no mean field analogue and it can be viewed as a transition between bosonic SPT
states. At one special point, this transition is described by a $(2+1)d$ $O(4)$
nonlinear sigma model (NLSM) with {\it exact} $SO(4)$ symmetry, and a
topological term at {\it exactly} $\Theta = \pi$. Relevance of this work
towards more general interacting SPT states is discussed.


  We consider bivariate piecewise polynomial finite element spaces for curved
domains bounded by piecewise conics satisfying homogeneous boundary conditions,
construct stable local bases for them using Bernstein-B\'ezier techniques,
prove error bounds and develop optimal assembly algorithms for the finite
element system matrices. Numerical experiments confirm the effectiveness of the
method.


  The following theorem is proved.
  {\bf Theorem.} {\it Let $P(x) = \sum_{k=0}^{2n} a_k x^k$ be a polynomial with
positive coefficients. If the inequalities $\frac{a_{2k+1}^2}{a_{2k}a_{2k+ 2}}
< \frac{1}{cos^2(\frac{\pi}{n+2})} $ hold for all $ k=0, 1, ..., n-1, $ then
$P(x)>0$ for every $x\in\mathbb{R} $ .}
  We show that the constant $\frac{1}{cos^2(\frac{\pi}{n+2})}$ in this theorem
could not be increased. We also present some corollaries of this theorem.


  Data-based mathematical modeling of biochemical reaction networks, e.g. by
nonlinear ordinary differential equation (ODE) models, has been successfully
applied. In this context, parameter estimation and uncertainty analysis is a
major task in order to assess the quality of the description of the system by
the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of
the objective function covering orders of magnitudes was observed and has been
termed as sloppiness. In this work, we investigate the origin of sloppiness
from structures in the sensitivity matrix arising from the properties of the
model topology and the experimental design. Furthermore, we present strategies
using optimal experimental design methods in order to circumvent the sloppiness
issue and present non-sloppy designs for a benchmark model.


  We consider the problem of recovering items matching a partially specified
pattern in multidimensional trees (quadtrees and $k$-d trees). We assume the
traditional model where the data consist of independent and uniform points in
the unit square. For this model, in a structure on $n$ points, it is known that
the number of nodes $C_n(\xi )$ to visit in order to report the items matching
a random query $\xi$, independent and uniformly distributed on $[0,1]$,
satisfies $\mathbf {E}[{C_n(\xi )}]\sim\kappa n^{\beta}$, where $\kappa$ and
$\beta$ are explicit constants. We develop an approach based on the analysis of
the cost $C_n(s)$ of any fixed query $s\in[0,1]$, and give precise estimates
for the variance and limit distribution of the cost $C_n(x)$. Our results
permit us to describe a limit process for the costs $C_n(x)$ as $x$ varies in
$[0,1]$; one of the consequences is that $\mathbf
{E}[{\max_{x\in[0,1]}C_n(x)}]\sim \gamma n^{\beta}$; this settles a question of
Devroye [Pers. Comm., 2000].


  In this paper, we propose to learn temporal embeddings of video frames for
complex video analysis. Large quantities of unlabeled video data can be easily
obtained from the Internet. These videos possess the implicit weak label that
they are sequences of temporally and semantically coherent images. We leverage
this information to learn temporal embeddings for video frames by associating
frames with the temporal context that they appear in. To do this, we propose a
scheme for incorporating temporal context based on past and future frames in
videos, and compare this to other contextual representations. In addition, we
show how data augmentation using multi-resolution samples and hard negatives
helps to significantly improve the quality of the learned embeddings. We
evaluate various design decisions for learning temporal embeddings, and show
that our embeddings can improve performance for multiple video tasks such as
retrieval, classification, and temporal order recovery in unconstrained
Internet video.


  The LIGO-Virgo collaboration reported in their third run the coalescence
event GW190814 involving a 2.6 $M_{\odot}$ object with a 23 $M_{\odot}$ black
hole. In this letter we study the conditions under which
Thorne-$\dot{\textrm{Z}}$ytkow objects (T$\dot{\textrm{Z}}$Os) can be connected
to that type of events. We evaluate first the rate of appearance of
T$\dot{\textrm{Z}}$Os in the local Universe. Under the assumption that
T$\dot{\textrm{Z}}$Os eventually become low mass gap black holes we evaluate
how those black holes end up in binaries with other stellar mass black holes
and compare to the reported rate for GW190814-type of events (1-23
$\textrm{Gpc}^{-3} \textrm{yr}^{-1}$). We find that T$\dot{\textrm{Z}}$Os in
dense stellar clusters can not explain the LIGO-Virgo rate without a
T$\dot{\textrm{Z}}$Os population in the field providing a dominant
contribution. We also find that T$\dot{\textrm{Z}}$Os formed within
hierarchical triple systems in the field with the third more distant star being
the progenitor of a stellar mass black hole, may be able to give a rate
comparable to that of GW190814-type events. In that case, future observations
should discover mergers between stellar mass and low mass gap black holes, with
the lower mass spanning the entire low mass gap range.


  We propose a class of incompatibility measures for quantum observables based
on quantifying the effect of a measurement of one observable on the statistics
of the outcomes of another. Specifically, for a pair of observables $A$ and $B$
with purely discrete spectra, we compare the following two probability
distributions: one resulting from a measurement of $A$ followed by a
measurement of $B$ on a given state, and the other obtained from a measurement
of $B$ alone on the same state. We show that maximizing the distance between
these two distributions over all states yields a valid measure of the
incompatibility of observables $A$ and $B$, which is zero if and only if they
commute and is strictly greater than zero (and less than or equal to one)
otherwise.
  For finite dimensional systems, we obtain a tight upper bound on the
incompatibility of any pair of observables and show that the bound is attained
when the observables are totally non-degenerate and associated with mutually
unbiased bases. In the process, we also establish an important connection
between the incompatibility of a pair of observables and the maximal
disturbances due to their measurements. Finally, we indicate how these measures
of incompatibility and disturbance can be extended to the more general class of
non-projective measurements. In particular, we obtain a non-trivial upper bound
on the incompatibility of one L\"uders instrument with another.


  In the Bayesian analysis of contingency table data, the selection of a prior
distribution for either the log-linear parameters or the cell probabilities
parameter is a major challenge. Though the conjugate prior on cell
probabilities has been defined by Dawid and Lauritzen (1993) for decomposable
graphical models, it has not been identified for the larger class of graphical
models Markov with respect to an arbitrary undirected graph or for the even
wider class of hierarchical log-linear models. In this paper, working with the
log-linear parameters used by GLIM, we first define the conjugate prior for
these parameters and then derive the induced prior for the cell probabilities:
this is done for the general class of hierarchical log-linear models. We show
that the conjugate prior has all the properties that one expects from a prior:
notational simplicity, ability to reflect either no prior knowledge or a priori
expert knowledge, a moderate number of hyperparameters and mathematical
convenience. It also has the strong hyper Markov property which allows for
local updates within prime components for graphical models.


  The celebrated theorem of Berger, Coburn and Lebow on pairs of commuting
isometries can be formulated as follows: a pure isometry $V$ on a Hilbert space
$\mathcal{H}$ is a product of two commuting isometries $V_1$ and $V_2$ in
$\mathcal{B}(\mathcal{H})$ if and only if there exists a Hilbert space
$\mathcal{E}$, a unitary $U$ in $\mathcal{B}(\mathcal{E})$ and an orthogonal
projection $P$ in $\mathcal{B}(\mathcal{E})$ such that $(V, V_1, V_2)$ and
$(M_z, M_{\Phi}, M_{\Psi})$ on $H^2_{\mathcal{E}}(\mathbb{D})$ are unitarily
equivalent, where \[ \Phi(z)=(P+zP^{\perp})U^*\;\text{and}\;
\Psi(z)=U(P^{\perp}+zP) \;;(z \in \mathbb{D}). \] Here we prove a similar
factorization result for pure contractions. More particularly, let $T$ be a
pure contraction on a Hilbert space $\mathcal{H}$ and let $P_{\mathcal{Q}}
M_z|_{\mathcal{Q}}$ be the Sz.-Nagy and Foias representation of $T$ for some
canonical $\mathcal{Q} \subseteq H^2_{\mathcal{D}}(\mathbb{D})$. Then $T = T_1
T_2$, for some commuting contractions $T_1$ and $T_2$ on $\mathcal{H}$, if and
only if there exists $\mathcal{B}(\mathcal{D})$-valued polynomials $\varphi$
and $\psi$ of degree $ \leq 1$ such that $\mathcal{Q}$ is a joint
$(M_{\varphi}^*, M_{\psi}^*)$-invariant subspace, \[P_{\mathcal{Q}}
M_z|_{\mathcal{Q}} = P_{\mathcal{Q}} M_{\varphi \psi}|_{\mathcal{Q}} =
P_{\mathcal{Q}} M_{\psi \varphi}|_{\mathcal{Q}} \; \mbox{and} \;(T_1, T_2)
\cong (P_{\mathcal{Q}} M_{\varphi}|_{\mathcal{Q}}, P_{\mathcal{Q}}
M_{\psi}|_{\mathcal{Q}}).\]


  The continuous-time analysis of existing iterative algorithms for
optimization has a long history. This work proposes a novel continuous-time
control-theoretic framework for equality-constrained optimization. The key idea
is to design a feedback control system where the Lagrange multipliers are the
control input, and the output represents the constraints. The system converges
to a stationary point of the constrained optimization problem through suitable
regulation. Regarding the Lagrange multipliers, we consider two control laws:
proportional-integral control and feedback linearization. These choices give
rise to a family of different methods. We rigorously develop the related
algorithms, theoretically analyze their convergence and present several
numerical experiments to support their effectiveness concerning the
state-of-the-art approaches.


  Let $G$ be a compact connected Lie group. The question of when a weighted
Fourier algebra on $G$ is completely isomorphic to an operator algebra will be
investigated in this paper. We will demonstrate that the dimension of the group
plays an important role in the question. More precisely, we will get a positive
answer to the question when we consider a polynomial type weight coming from a
length function on $G$ with the order of growth strictly bigger than the half
of the dimension of the group. The case of SU(n) will be examined, focusing
more on the details including negative results. The proof for the positive
directions depends on a non-commutative version of Littlewood multiplier
theory, which we will develop in this paper, and the negative directions will
be taken care of by restricting to a maximal torus.


  We study higher dimensional counterparts to the well-known theorem of
Pavlovic \cite{pa3}, that every harmonic quasiconformal mapping of the disk is
bi-Lipschitz.


  Finding an object of a specific class in an unseen environment remains an
unsolved navigation problem. Hence, we propose a hierarchical learning-based
method for object navigation. The top-level is capable of high-level planning,
and building a memory on a floorplan-level (e.g., which room makes the most
sense for the agent to visit next, where has the agent already been?). While
the lower-level is tasked with efficiently navigating between rooms and looking
for objects in them. Instructions can be provided to the agent using a simple
synthetic language. The top-level intelligently enhances the instructions in
order to make the overall task more tractable. Language grounding, mapping
instructions to visual observations, is performed by utilizing an additional
separate supervised trained goal assessment module. We demonstrate the
effectiveness of our method on a dynamic configurable domestic environment.


  Recent theoretical investigations of the two-times measurement entropy
production (2TMEP) in quantum statistical mechanics have shed a new light on
the mathematics and physics of the quantum-mechanical probabilistic rules.
Among notable developments are the extensions of entropic fluctuation relations
to quantum domain and discovery of a deep link between 2TMEP and modular theory
of operator algebras. All these developments concerned the setting where the
state of the system at the instant of the first measurement is the same as the
state whose entropy production is measured. In this work we consider the case
where these two states are different and link this more general 2TEMP to
modular theory. The established connection allows us to show that under general
ergodicity assumptions the 2TEMP is essentially independent of the choice of
the system state at the instant of the first measurement due to a decoherence
effect induced by the first measurement. This stability sheds a new light on
the concept of quantum entropy production, and, in particular, on possible
quantum formulations of the celebrated classical Gallavotti--Cohen Fluctuation
Theorem which will be studied in the continuation of this work.


  We report on the first spatially resolved observation of mesoscopic flux
jumps in superconducting films. Magneto-optical imaging was used to visualize
the flux penetration in MgB2 films subjected to a slowly varying perpendicular
field. Below 10 K, flux jumps with typical size 10-20 microns and regular shape
are found to occur at random locations along the flux front. The total number
of vortices participating in one jump is varying between 50 and 10000.
Simultaneously, big dendritic jumps with dimensions comparable to the sample
size (10^6-10^8 vortices) are also found in this temperature range. We believe
that both types of jumps result from thermo-magnetic instability.


  We develop a theoretical study of non-terminating hypergeometric summations
with one free parameter. Composing various methods in complex and asymptotic
analysis, geometry and arithmetic of certain transcendental curves and rational
approximations of irrational numbers, we are able to obtain some necessary
conditions of arithmetic flavor for a given hypergeometric sum to admit a gamma
product formula. This kind of research seems to be new even in the most
classical case of the Gauss hypergeometric series.


  We consider the problem of sums of dilates in groups of prime order. We show
that given $A\subset \Z{p}$ of sufficiently small density then $$\big|
\lambda_{1}A+\lambda_{2}A+...+ \lambda_{k}A \big|
\,\ge\,\bigg(\sum_{i}|\lambda_{i}|\bigg)|A|- o(|A|),$$ whereas on the other
hand, for any $\epsilon>0$, we construct subsets of density $1/2-\epsilon$ such
that $|A+\lambda A|\leq (1-\delta)p$, showing that there is a very different
behaviour for subsets of large density.


  Given any $K>0$, we construct two equivalent $C^2$ flows, one of which has
positive topological entropy larger than $K$ and admits zero as the exponential
growth of periodic orbits, in contrast, the other has zero topological entropy
and super-exponential growth of periodic orbits. Moreover we establish a
$C^{\infty}$ flow on $\mathbb{S}^2$ with super-exponential growth of periodic
orbits, which is also equivalent to another flow with zero exponential growth
of periodic orbits. On the other hand, any two dimensional flow has only zero
topological entropy.


  Stochastic sampling strategies such as top-k and top-p have been widely used
in dialogue generation task. However, as an open-domain chatting system, there
will be two different conversation scenarios, i.e. chit-chat and
knowledge-based question answering. In the former situation, responses
diversity is essential due to the one-to-many nature in dialogue. The latter,
on the other hand, requires less randomness given that stochastic decoding
strategy entails the risk of generating incorrect information. As a result, an
adaptive and flexible decoding strategy is needed to cope with these two
scenarios simultaneously. To this end, we propose the dynamic decoding strategy
(DDS), which can adjust the decoding space w.r.t. different contexts. In DDS,
both sequence-level and token-level adaptive search can be achieved to adjust
the decoding process in a unified framework. Besides, our adaptive algorithm
can not only be used during model inference, but it can also be applied during
the model training stage to further enhance the performance. Comprehensive
experiments indicate that the proposed decoding strategy can consistently
improve the performance of pre-trained dialogue models when coupled with four
well-used stochastic decoding algorithms.


  Considering Langevin dynamics we derive the general form of the stochastic
differential that satisfies the Gallavotti-Cohen symmetry. This extends the
work previously done by Kurchan, and Lebowitz and Spohn on such systems, and we
treat systems with and without inertia in a unified manner. We further shown
that for systems with a time-reversal invariant steady state there exists a
stochastic differential for which then the Gallavotti-Cohen symmetry, and all
its consequences, are valid for finite times. For these systems the
differential can be seen as the direct analogy of the Gibbs-entropy creation
along paths in deterministic systems. It differs from previously studied
differentials in that it identically zero for equilibrium systems while on
average strictly positive for non-equilibrium system. When the steady state is
not time-reversal invariant the Gallavotti-Cohen symmetry is asymptotically
valid in the usual long time limit.


  This paper investigates tradeoffs among optimization errors, statistical
rates of convergence and the effect of heavy-tailed errors for high-dimensional
robust regression with nonconvex regularization. When the additive errors in
linear models have only bounded second moment, we show that iteratively
reweighted $\ell_1$-penalized adaptive Huber regression estimator satisfies
exponential deviation bounds and oracle properties, including the oracle
convergence rate and variable selection consistency, under a weak beta-min
condition. Computationally, we need as many as $O(\log s + \log\log d)$
iterations to reach such an oracle estimator, where $s$ and $d$ denote the
sparsity and ambient dimension, respectively. Extension to a general class of
robust loss functions is also considered. Numerical studies lend strong support
to our methodology and theory.


  The detrimental effect of tail states on the radiative and non-radiative
voltage loss has been demonstrated to be a limiting factor for the open circuit
voltage in Cu(In,Ga)Se2 solar cells. A strategy that has proven effective in
reducing tail states is the addition of alkali metals, the effect of which has
been associated with the passivation of charged defects at grain boundaries.
Herein, tail states in Cu(In,Ga)Se2 are revisited by studying the effect of
compositional variations and alkali incorporation into single crystals. The
results demonstrate that alkalis decrease the density of tail states despite
the absence of grain boundaries, suggesting that there is more to alkalis than
just grain boundary effects. Moreover, an increase in doping as a result of
alkali incorporation is shown to contribute to the reduced tail states, which
are demonstrated to arise largely from electrostatic potential fluctuations and
to be determined by grain interior properties. By analyzing the voltage loss in
high-efficiency polycrystalline and single crystalline devices, this work
presents a model that explains the entirety of the voltage loss in Cu(In,Ga)Se2
based on the combined effect of doping on tail states and VOC.


  Declarative styles such as functional programming (FP) are rapidly gaining
ground on their imperative cousins, including procedural and object-oriented
programming. The shift is subtle because it is happening within the context of
multiparadigm programming languages such as JavaScript. FP is better suited to
modern processes like test-driven development (TDD), and architectures like
massively parallel, cloud-based computing. This article describes the technical
details that characterize the shift from imperative to FP and implications for
software quality management, particularly reuse and testability.


  We put forward a new CNOT gate scheme with atoms and ions based on quantum
interrogation and a bosonic particle extension of the models of linear optics
quantum computation. We show how the possibility of particle collision can
provide the strong interaction that is needed for universal quantum gates. Two
atom optics proposals are provided. Unlike previous schemes, these gates are at
the same time nondestructive, valid for arbitrary inputs and can work with a
probability as close to unity as desired in the lossless case. Data is encoded
into position modes and the gates only require basic atom optics elements,
which gives potentially simpler quantum computer implementations.


  The tensor glueball is searched for in BESIII data on radiative $J/\psi$
decays into $\pi^0\pi^0$ and $K_sK_s$. The $\pi\pi$ invariant mass distribution
exhibits an enhancement that can be described by a pole at $(2210\pm 60)
-i(180\pm 60)$\,MeV. We speculate if the tensor glueball could be distributed
among high-mass tensor mesons.


  Pulsars are known to emit non-thermal radio emission that is generally a
power-law function of frequency. In some cases, a turnover is seen at
frequencies around 100~MHz. Kijak et al. have reported the presence of a new
class of ''Gigahertz Peaked Spectrum'' (GPS) pulsars that show spectral
turnovers at frequencies around 1 GHz. We apply a model based on free-free
thermal absorption to explain these turnovers in terms of surrounding material
such as the dense environments found in HII regions, Pulsar Wind Nebulae
(PWNe), or in cold, partially ionized molecular clouds. We show that the
turnover frequency depends on the electron temperature of the environment close
to the pulsar, as well as the emission measure along the line of sight. We
fitted this model to the radio fluxes of known GPS pulsars and show that it can
replicate the GHz turnover. From the thermal absorption model, we demonstrate
that normal pulsars would exhibit a GPS-like behaviour if they were in a dense
environment. We discuss the application of this model in the context of
determining the population of neutron stars within the central parsec of the
Galaxy. We show that a non-negligible fraction of this population might exhibit
high-frequency spectral turnovers, which has implications on the detectability
of these sources in the Galactic centre.


  We consider the problem of zeroing an error output of a nonlinear
discrete-time system in the presence of constant exogenous disturbances,
subject to hard convex constraints on the input signal. The design
specification is formulated as a variational inequality, and we adapt a
forward-backward splitting algorithm to act as an integral controller which
ensures that the input constraints are met at each time step. We establish a
low-gain stability result for the closed-loop system when the plant is
exponentially stable, generalizing previously known results for integral
control of discrete-time systems. Specifically, it is shown that if the
composition of the plant equilibrium input-output map and the integral feedback
gain is strongly monotone, then the closed-loop system is exponentially stable
for all sufficiently small integral gains. The method is illustrated via
application to a four-tank process.


  Exploiting the fact that Kaluza-Klein monopoles and the associated
generalized orbifold planes are sources for geometrical fluxes, omega, we show
that the standard constraint omega.omega=0, valid for superstring
compactifications on twisted tori, can be consistently relaxed. This leads to
novel possibilities for constructing superstring models with fluxes and
localized sources, as well as for stabilizing moduli. This also explains the
ten-dimensional origin of a family of N=4 gauged supergravities, whose
interpretation in type-IIA orientifold compactifications was lacking.


  We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic
PDE under the characteristic $3:2:1$ scaling of time, space and fluctuations.
We study the correlation of fluctuations at two different times. We show that
when the times are close to each other, the correlation approaches one at a
power-law rate with exponent $2/3$, while when the two times are remote from
each other, the correlation tends to zero at a power-law rate with exponent
$-1/3$. We also prove exponential-type tail bounds for differences of the
solution at two space-time points.
  Three main tools are pivotal to proving these results: 1) a representation
for the two-time distribution in terms of two independent narrow wedge
solutions; 2) the Brownian Gibbs property of the KPZ line ensemble; and 3)
recently proved one-point tail bounds on the narrow wedge solution.


  We study the dg-algebra $\Omega ^\bullet_{A|\mathbb{R}}$ of algebraic de Rham
forms of a real soft function algebra $A$, i.e., the algebra of global sections
of a soft subsheaf of $C_X$, the sheaf of continuous functions on a space $X$.
We obtain a canonical splitting $\mathrm H ^n (\Omega ^\bullet_{A|\mathbb{R}})
\cong \mathrm H ^n (X,\mathbb{R})\oplus V$, where $V$ is some vector space. In
particular, we consider the cases $A=C(X)$ for $X$ a compact Hausdorff space
and $A = C^\infty (X)$ for $X$ a compact smooth manifold. For the algebra
$\mathrm{PPol}_K (|K|)$ of piecewise polynomial functions on a polyhedron $K$
the above splitting reduces to a canonical isomorphism $\mathrm H ^* (\Omega
^\bullet_{\mathrm{PPol}_K (|K|)|\mathbb{R}}) \cong \mathrm H ^*
(|K|,\mathbb{R})$. We also prove that the algebraic de Rham cohomology $\mathrm
H ^n (\Omega ^\bullet_{C(X)|\mathbb{R}})$ is nontrivial for each $n\geq 1$ if
$X$ is an infinite compact Hausdorff space.


  The high-pressure melting curves of metals provide simple and useful tests
for theories of melting, as well as important constraints for the modeling of
planetary interiors. Here, we present an experimental technique that reveals
the latent heat of fusion of a metal sample compressed inside a diamond anvil
cell. The technique combines microsecond-timescale pulsed electrical heating
with an internally-heated diamond anvil cell for the first time. Further, we
use the technique to measure the melting curve of platinum to the highest
pressure measured to date. Melting temperature increases from $\sim 3000$ K at
34 GPa to $\sim 4500$ K at 107 GPa, thermodynamic conditions that are between
the steep and shallow experimental melting curves reported previously. The
melting curve is a linear function of compression over the 0 to 20% range of
compression studied here, allowing a good fit to the Kraut-Kennedy empirical
model with fit parameter $C=6.0$.


  The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation
$$u_t + u_{xxx} + \partial_x^{-1}u_{yy}= (u^l)_x, \quad l \ge 3,$$ is shown to
be locally well-posed in almost critical anisotropic Sobolev spaces. The proof
combines local smoothing and maximal function estimates as well as bilinear
refinements of Strichartz type inequalities via multilinear interpolation in
$X_{s,b}$-spaces.


  Young solar-type stars frequently produce superflares, serving as a unique
window into the young Sun-Earth environments. Large solar flares are closely
linked to coronal mass ejections (CMEs) associated with filament/prominence
eruptions, but its observational evidence for stellar superflares remains
scarce. Here, we present a 12-day multi-wavelength campaign observation of
young solar-type star EK Draconis (G1.5V, 50-120 Myr age) utilizing TESS,
NICER, and Seimei telescope. The star has previously exhibited blueshifted
H$\alpha$ absorptions as evidence for a filament eruption associated with a
superflare. Our simultaneous optical and X-ray observations identified three
superflares of $1.5\times10^{33}$ -- $1.2\times10^{34}$ erg. We report the
first discovery of two prominence eruptions on a solar-type star, observed as
blueshifted H$\alpha$ emissions at speed of 690 and 430 km s$^{-1}$ and masses
of $1.1\times10^{19}$ and $3.2\times10^{17}$ g, respectively. The faster,
massive event shows a candidate of post-flare X-ray dimming with the amplitude
of up to $\sim$10 \%. Several observational aspects consistently point to the
occurrence of a fast CME associated with this event. The comparative analysis
of the estimated length scales of flare loops, prominences, possible dimming
region, and starspots provides the overall picture of the eruptive phenomena.
Furthermore, the energy partition of the observed superflares in the optical
and X-ray bands is consistent with flares from the Sun, M-dwarfs, and close
binaries, yielding the unified empirical relations. These discoveries provide
profound implications of impact of these eruptive events on the early Venus,
Earth and Mars and young exoplanets.


  Data makes science possible. Sharing data improves visibility, and makes the
research process transparent. This increases trust in the work, and allows for
independent reproduction of results. However, a large proportion of data from
published research is often only available to the original authors. Despite the
obvious benefits of sharing data, and scientists' advocating for the importance
of sharing data, most advice on sharing data discusses its broader benefits,
rather than the practical considerations of sharing. This paper provides
practical, actionable advice on how to actually share data alongside research.
The key message is sharing data falls on a continuum, and entering it should
come with minimal barriers.


  Halo artifacts significantly impact display quality. We propose a method to
reduce halos in Local Histogram Equalization (LHE) algorithms by separately
addressing dark and light variants. This approach results in visually natural
images by exploring the relationship between lateral inhibition and halo
artifacts in the human visual system.


  In this paper, we propose a generalized natural inflation (GNI) model to
study axion-like particle (ALP) inflation and dark matter (DM). GNI contains
two additional parameters $(n_1, n_2)$ in comparison with the natural
inflation, that make GNI more general. The $n_1$ build the connection between
GNI and other ALP inflation model, $n_2$ controls the inflaton mass. After
considering the cosmic microwave background and other cosmological observation
limits, the model can realize small-field inflation with a wide mass range, and
the ALP inflaton considering here can serve as the DM candidate for certain
parameter spaces.


  Let $a(1) >0$, $a(n) \ge 0$ for $n \ge 2$ and $a(n) = O(n^\varepsilon)$ for
any $\varepsilon >0$, and put $Z(\sigma + it):= \sum_{n=1}^\infty a(n)
n^{-\sigma - it}$ where $\sigma , t \in {\mathbb{R}}$. In the present paper, we
show that any zeta distribution whose characteristic function is defined by
${\mathcal{Z}}_\sigma (t) :=Z(\sigma + it)/Z(\sigma)$ is pretended infinitely
divisible if $\sigma >1$ is sufficiently large. Moreover, we prove that if
${\mathcal{Z}}_\sigma (t)$ is an infinitely divisible characteristic function
for some $\sigma_{id} >1$, then ${\mathcal{Z}}_\sigma (t)$ is infinitely
divisible for all $\sigma >1$. Note that the corresponding L\'evy or
quasi-L\'evy measure can be given explicitly. A key of the proof is a corrected
version of Theorem 11.14 in Apostol's famous textbook.


  Continuous detection of human activities and presence is essential for
developing a pervasive interactive smart space. Existing literature lacks
robust wireless sensing mechanisms capable of continuously monitoring multiple
users' activities without prior knowledge of the environment. Developing such a
mechanism requires simultaneous localization and tracking of multiple subjects.
In addition, it requires identifying their activities at various scales, some
being macro-scale activities like walking, squats, etc., while others are
micro-scale activities like typing or sitting, etc. In this paper, we develop a
holistic system called MARS using a single Commercial off the-shelf (COTS)
Millimeter Wave (mmWave) radar, which employs an intelligent model to sense
both macro and micro activities. In addition, it uses a dynamic spatial time
sharing approach to sense different subjects simultaneously. A thorough
evaluation of MARS shows that it can infer activities continuously with a
weighted F1-Score of > 94% and an average response time of approx 2 sec, with 5
subjects and 19 different activities.


  Accurately predicting the likelihood of interaction between two objects
(compound-protein sequence, user-item, author-paper, etc.) is a fundamental
problem in Computer Science. Current deep-learning models rely on learning
accurate representations of the interacting objects. Importantly, relationships
between the interacting objects, or features of the interaction, offer an
opportunity to partition the data to create multi-views of the interacting
objects. The resulting congruent and non-congruent views can then be exploited
via contrastive learning techniques to learn enhanced representations of the
objects.


  The singular value and spectral distribution of Toeplitz matrix sequences
with Lebesgue integrable generating functions is well studied. Early results
were provided in the classical Szeg{\H{o}} theorem and the Avram-Parter
theorem, in which the singular value symbol coincides with the generating
function. More general versions of the theorem were later proved by Zamarashkin
and Tyrtyshnikov, and Tilli. Considering (real) nonsymmetric Toeplitz matrix
sequences, we first symmetrize them via a simple permutation matrix and then we
show that the singular value and spectral distribution of the symmetrized
matrix sequence can be obtained analytically, by using the notion of
approximating class of sequences. In particular, under the assumption that the
symbol is sparsely vanishing, we show that roughly half of the eigenvalues of
the symmetrized Toeplitz matrix (i.e. a Hankel matrix) are negative/positive
for sufficiently large dimension, i.e. the matrix sequence is symmetric
(asymptotically) indefinite.