  Observations show that there is a proton spectral "break" with E$_{break}$ at
1-10MeV in some large CME-driven shocks. Theoretical model usually attribute
this phenomenon to a diffusive shock acceleration. However, the underlying
physics of the shock acceleration still remains uncertain. Although previous
numerical models can hardly predict this "break" due to either high
computational expense or shortcomings of current models, the present paper
focuses on simulating this energy spectrum in converged two shocks by Monte
Carlo numerical method. Considering the Dec 13 2006 CME-driven shock
interaction with an Earth bow shock, we examine whether the energy spectral
"break" could occur on an interaction between two shocks. As result, we indeed
obtain the maximum proton energy up to 10MeV, which is the premise to
investigate the existence of the energy spectral "break". Unexpectedly, we
further find a proton spectral "break" appears distinctly at the energy
$\sim$5MeV.


  Recent supernovae (SNe) observations have motivated renewed interest in SN
shock breakouts from stars surrounded by thick winds. In such events the
interaction with the wind powers the observed luminosity, and predictions
include observable hard X-rays. Wind breakouts on timescales of a day or longer
are currently the most probable for detection. Here we study the signal that
follows such events. We start from the breakout of the radiation mediated
shock, finding that the breakout temperature can vary significantly from one
event to another ($10^4 - 5 \times 10^6$ K) due to possible deviation from
thermal equilibrium. In general, events with longer breakout pulse duration,
$t_{bo}$, are softer. We follow the observed radiation through the evolution of
the collisionless shock which forms after the breakout of the radiation
mediated shock. We restrict the study of the collisionless shock evolution to
cases where the breakout itself is in thermal equilibrium, peaking in
optical/UV. In these cases the post-breakout emission contains two spectral
components - soft (optical/UV) and hard (X-rays and possibly soft
$\gamma$-rays). Right after the breakout pulse X-rays are strongly suppressed,
and they carry only a small fraction of the total luminosity. The hard
component becomes harder and its luminosity rises quickly afterwards, gaining
dominance at $\sim 10-50 \,t_{bo}$. The ratio of the peak optical/UV to the
peak X-ray luminosity depends mostly on the breakout time. In terms of
prospects for X-ray and soft gamma-ray detections, it is best to observe
100-500 days after explosions with breakout timescales between a week and a
month.


  We examine the possibility of the inclusion of objects having lifetimes lower
than the disk age in the database of recent determinations of the G dwarf
metallicity distribution for the solar neighbourhood. As a preliminary step,
stars with lifetimes potentially lower than the disk age are identified by
means of a relation between (b-y), or mass, and [Fe/H], from evolutionary
models of stars at the zero-age main sequence. We apply these results to the G
dwarf samples of Rocha-Pinto and Maciel (1996) and Wyse and Gilmore (1995). We
show that the majority of G dwarfs in these samples can be regarded as
long-lived objects for chemical evolution purposes, provided the disk age is
greater than 12 Gyr. We also find that the G dwarf problem is not an effect of
the metallicity dependence of the stellar lifetimes.


  We present background concepts of the nuclear density functional theory (DFT)
and applications of the time-dependent DFT with the Skyrme energy functional
for nuclear response functions. Practical methods for numerical applications of
the time-dependent Hartree-Fock-Bogoliubov theory (TDHFB) are proposed; finite
amplitude method and canonical-basis TDHFB. These approaches are briefly
reviewed and some numerical applications are shown to demonstrate their
feasibility.


  We introduce a measure of quantum correlations in the $N$-qubit quantum
system which is invariant with respect to the $SU(2^N)$ group of
transformations of this system. This measure is a modification of the quantum
discord introduced earlier and is referred to as the unitary or
$SU(2^N)$-invariant discord. Since the evolution of a quantum system is
equivalent to the proper unitary transformation, the introduced measure is an
integral of motion and is completely defined by eigenvalues of the density
matrix. As far as the calculation of the unitary invariant discord is rather
complicated computational problem, we propose its modification which may be
found in a simpler way. The case N=2 is considered in details. In particular,
it is shown that the modified SU(4)-invariant discord reaches the maximum value
for a pure state.
  {A geometric measure of the unitary invariant discord of an $N$-qubit state
is introduced and a simple formula for this measure is derived, which allows
one to consider this measure as a witness of quantum correlations.} The
relation of the unitary invariant discord with the quantum state transfer along
the spin chain is considered. We also compare the modified SU(4)-invariant
discord with the geometric measure of SU(4)-invariant discord of the two-qubit
systems in the thermal equilibrium states governed by the different
Hamiltonians.


  The huge demand for computation in artificial intelligence (AI) is driving
unparalleled investments in hardware and software systems for AI. This leads to
an explosion in the number of specialized hardware devices, which are now
offered by major cloud vendors. By hiding the low-level complexity through a
tensor-based interface, tensor computation runtimes (TCRs) such as PyTorch
allow data scientists to efficiently exploit the exciting capabilities offered
by the new hardware. In this paper, we explore how database management systems
can ride the wave of innovation happening in the AI space.
  We design, build, and evaluate Tensor Query Processor (TQP): TQP transforms
SQL queries into tensor programs and executes them on TCRs. TQP is able to run
the full TPC-H benchmark by implementing novel algorithms for relational
operators on the tensor routines. At the same time, TQP can support various
hardware while only requiring a fraction of the usual development effort.
Experiments show that TQP can improve query execution time by up to 10$\times$
over specialized CPU- and GPU-only systems. Finally, TQP can accelerate queries
mixing ML predictions and SQL end-to-end, and deliver up to 9$\times$ speedup
over CPU baselines.


  We show the surprising result that the cutpoint isolation problem is
decidable for Probabilistic Finite Automata (PFA) where input words are taken
from a letter-bounded context-free language. A context-free language
$\mathcal{L}$ is letter-bounded when $\mathcal{L} \subseteq a_1^*a_2^* \cdots
a_\ell^*$ for some finite $\ell > 0$ where each letter is distinct. A cutpoint
is isolated when it cannot be approached arbitrarily closely. The decidability
of this problem is in marked contrast to the situation for the (strict)
emptiness problem for PFA which is undecidable under the even more severe
restrictions of PFA with polynomial ambiguity, commutative matrices and input
over a letter-bounded language as well as to the injectivity problem which is
undecidable for PFA over letter-bounded languages. We provide a constructive
nondeterministic algorithm to solve the cutpoint isolation problem, which holds
even when the PFA is exponentially ambiguous. We also show that the problem is
at least NP-hard and use our decision procedure to solve several related
problems.


  High-contrast adaptive optics imaging is a powerful technique to probe the
architectures of planetary systems from the outside-in and survey the
atmospheres of self-luminous giant planets. Direct imaging has rapidly matured
over the past decade and especially the last few years with the advent of
high-order adaptive optics systems, dedicated planet-finding instruments with
specialized coronagraphs, and innovative observing and post-processing
strategies to suppress speckle noise. This review summarizes recent progress in
high-contrast imaging with particular emphasis on observational results,
discoveries near and below the deuterium-burning limit, and a practical
overview of large-scale surveys and dedicated instruments. I conclude with a
statistical meta-analysis of deep imaging surveys in the literature. Based on
observations of 384 unique and single young ($\approx$5--300~Myr) stars
spanning stellar masses between 0.1--3.0~\Msun, the overall occurrence rate of
5--13~\Mjup \ companions at orbital distances of 30--300~AU is
0.6$^{+0.7}_{-0.5}$\% assuming hot-start evolutionary models. The most massive
giant planets regularly accessible to direct imaging are about as rare as hot
Jupiters are around Sun-like stars. Dividing this sample into individual
stellar mass bins does not reveal any statistically-significant trend in planet
frequency with host mass: giant planets are found around 2.8$^{+3.7}_{-2.3}$\%
of BA stars, $<$4.1\% of FGK stars, and $<$3.9\% of M dwarfs. Looking forward,
extreme adaptive optics systems and the next generation of ground- and
space-based telescopes with smaller inner working angles and deeper detection
limits will increase the pace of discovery to ultimately map the demographics,
composition, evolution, and origin of planets spanning a broad range of masses
and ages.


  First this report presents a restricted set of finite transducers used to
synthesise structural time-series constraints described by means of a
multi-layered function composition scheme. Second it provides the corresponding
synthesised catalogue of structural time-series constraints where each
constraint is explicitly described in terms of automata with registers.


  Given a maximal $\mathbb{Q}$-torus in $SL(N,\mathbb{Q})$, its orbit from
identity coset in $SL(N,\mathbb{R})/SL(N,\mathbb{Z})$ naturally carries a
possibly infinite Haar measure. We classify all possible limit measures of it
when translated by a sequence of elements from $SL(N,\mathbb{R})$. This is a
natural extension of Shapira and Zheng's work where only $\mathbb{Q}$-split
tori are considered.


  We present a brief pedagogical introduction to the Effective Electroweak
Chiral Lagrangians, which provide a model independent description of the WW
interactions in the strong regime. When it is complemented with some
unitarization or a dispersive approach, this formalism allows the study of the
general strong scenario expected at the LHC, including resonances.


  Decaying superheavy particles can be produced by Topological Defects or, in
case they are quasi-stable, as relics from the early Universe. The decays of
these particles can be the sources of observed Ultra High Energy Cosmic Rays
($E \sim 10^{10} - 10^{12} GeV$). The Topological Defects as the UHE CR sources
are critically reviewed and cosmic necklaces and monopole-antiminopole pairs
are identified as most plausible sources. The relic superheavy particles are
shown to be clustering in the halo and their decays produce UHE CR without GZK
cutoff. The Lightest Supersymmetric Particles with Ultra High Energies are
naturally produced in the cascades accompanying the decays of superheavy
particles. These particles are discussed as UHE carriers in the Universe.


  Prepare and measure quantum key distribution protocols can be decomposed into
two basic steps: delivery of the signals over a quantum channel and
distillation of a secret key from the signal and measurement records by
classical processing and public communication. Here we formalize the
distillation process for a general protocol in a purely quantum-mechanical
framework and demonstrate that it can be viewed as creating an ``effective''
quantum channel between the legitimate users Alice and Bob. The process of
secret key generation can then be viewed as entanglement distribution using
this channel, which enables application of entanglement-based security proofs
to essentially any prepare and measure protocol. To ensure secrecy of the key,
Alice and Bob must be able to estimate the channel noise from errors in the
key, and we further show how symmetries of the distillation process simplify
this task. Applying this method, we prove the security of several key
distribution protocols based on equiangular spherical codes.


  To check the impact of the multiple population scenario for globular clusters
on their HB, we present an analysis of the composition of 110 red HB (RHB)
stars in 47 Tucanae and of 61 blue HB (BHB) and 30 RHB stars in M5. In 47 Tuc
we found tight relations between the colours of the stars and their abundances
of p-capture elements. This strongly supports the idea that the He content -
which is expected to be closely correlated with the abundances of p-capture
elements - is the third parameter (after overall metallicity and age) that
determines the colour of HB stars. However, the range in He abundance must be
small (Delta Y<0.03) in 47 Tuc to reproduce our observations; this agrees with
previous analyses. There is possibly a correlation between the abundances of p-
and n-capture elements in 47 Tuc. If confirmed, this might suggest that AGB
stars of moderate mass contributed to the gas from which second-generation
stars formed. Considering the selection effects in our sample (which does not
include stars warmer than 11000 K and RR Lyrae variables) is important to
understand our results for M5. In this case, we find that, as expected, RHB
stars are Na-poor and O-rich, and likely belong to the primordial population.
There is a clear correlation of the [Na/O] ratio and N abundance with colour
along the BHB. A derivation of the He abundance for these stars yields a low
value of Y=0.22\pm 0.03. This is expected because HB stars of a putative
He-rich population in this cluster should be warmer than 11000 K, and would
accordingly not have been sampled by our analysis. However, we need some
additional source of scatter in the total mass loss of stars climbing up the
RGB to reproduce our results for M5. Finally, we found a C-star on the HB of 47
Tuc and a Ba-rich, fast-rotating, likely binary star on the HB of M5. These
stars are among the brightest and coolest HB stars.


  In space applications, hardware (HW) implementation is made more expensive
not only by the levels of performance required, but also by complex and
rigorous HW qualification tests. Reducing qualification cost and time is thus a
key design requirement. In this paper, a new versatile transmitter is proposed
for space telemetry, capable of soft-switching across different linear and
continuous phase modulation schemes while maintaining the same hardware
structure. This permits a single HW qualification to ``cover'' diverse uses of
the same hardware, and thus avoid re-qualification in case of configuration
changes. The envisaged solution foresees the use of a single filter, suitable
not only for linear modulations such as M-QAM, but also for continuous phase
modulation methods. At this stage, we focus on pulse code modulation/frequency
modulation (PCM/FM), for which we propose a minimum mean square error (MMSE)
algorithm. The proposed algorithm, which adds to the system flexibility and
effectiveness, may use a single first filter based on Laurent decomposition for
initialization, if needed. Performances are assessed using the mean square
error (MSE) measure between the proposed MMSE-modulated signal and the
completely modulated signal. Simulation results confirm that the proposed
algorithm leads to MSE values that are lower than the case of Laurent
decomposition using the first component only.


  We consider the task of recovering a Sobolev function on a connected compact
Riemannian manifold $M$ when given a sample on a finite point set. We prove
that the quality of the sample is given by the $L_\gamma(M)$-average of the
geodesic distance to the point set and determine the value of $\gamma\in
(0,\infty]$. This extends our findings on bounded convex domains [IMA J. Numer.
Anal., 44:1346--1371, 2024]. As a byproduct, we prove the optimal rate of
convergence of the $n$-th minimal worst case error for $L_q(M)$-approximation
for all $1\le q \le \infty$.
  Further, a limit theorem for moments of the average distance to a set
consisting of i.i.d.\ uniform points is proven. This yields that a random
sample is asymptotically as good as an optimal sample in precisely those cases
with $\gamma<\infty$. In particular, we obtain that cubature formulas with
random nodes are asymptotically as good as optimal cubature formulas if the
weights are chosen correctly. This closes a logarithmic gap left open by Ehler,
Gr\"af and Oates [Stat. Comput., 29:1203-1214, 2019].


  The discovery of correlated insulating states in moir\'e heterostructures has
renewed the interest in strongly-coupled electron systems where spin and valley
(or layer) degrees of freedom are intertwined. In the strong-coupling limit,
such systems can be effectively described by SU(4) spin-valley models akin to
Kugel-Khomskii models long studied in the context of spin-orbit coupled
materials. However, typical moir\'e heterostructures also exhibit interactions
that break the SU(4) symmetry down to
SU(2)${}_{\mathrm{spin}}\otimes$U(1)${}_{\mathrm{valley}}$. Here we investigate
the impact of such symmetry-breaking couplings on the magnetic phase diagram
for triangular superlattices considering a filling of two electrons (or holes)
per moir\'e unit cell. We explore a broad regime of couplings -- including XXZ
anisotropies, Dzyaloshinskii-Moriya exchange and on-site Hund's couplings --
using semi-classical Monte Carlo simulations. We find a multitude of
classically ordered phases, including (anti-)ferromagnetic, incommensurate, and
stripe order, manifesting in different sectors of the spin-valley model's
parameter space. Zooming in on the regimes where quantum fluctuations are
likely to have an effect, we employ pseudo-fermion functional renormalization
group (pf-FRG) calculations to resolve quantum disordered ground states such as
spin-valley liquids, which we indeed find for certain parameter regimes. As a
concrete example, we discuss the case of trilayer graphene aligned with
hexagonal boron nitride using material-specific parameters.


  The line shape of resonances in the overlapping regime is studied by using
the eigenvalues and eigenfunctions of the effective Hamiltonian of an open
quantum system. A generalized expression $\tilde q_k(E)$ for the Fano parameter
of the resonance state $k$ is derived that contains the interaction of the
state $k$ with neighboured states $l\ne k$ via the continuum. It is energy
dependent since the coupling coefficients between the state $k$ and the
continuum show a resonance-like behaviour at the energies of the neighboured
states $l\ne k$. Under certain conditions, the energy dependent $\tilde q_k(E)$
are equivalent to the generalized complex energy independent Fano parameters
that are introduced by Kobayashi et al. in analyzing experimental data.
Long-lived states appear mostly isolated from one another in the cross section,
also when they are overlapped by short-lived resonance states. The $\tilde
q_k(E)$ of narrow resonances allow therefore to study the complicated interplay
between different time scales in the regime of overlapping resonance states by
controlling them as a function of an external parameter.


  We answer the question of Vidaux and Videla about the distribution of the
Northcott numbers for the Weil height. We solve the same problem for the
weighted Weil heights. These heights generalize both the absolute and relative
Weil height. Our results also refine those of Pazuki, Technau, and Widmer.


  In this paper we study networks of nodes characterised by binary traits that
change both endogenously and through nearest-neighbour interaction. Our
analytical results show that those traits can be ranked according to the
noisiness of their transmission using only measures of order in the stationary
state. Crucially, this ranking is independent of network topology. As an
example, we explain why, in line with a long-standing hypothesis, the relative
stability of the structural traits of languages can be estimated from their
geospatial distribution. We conjecture that similar inferences may be possible
in a more general class of Markovian systems. Consequently, in many empirical
domains where longitudinal information is not easily available the propensities
of traits to change could be estimated from spatial data alone.


  We discuss the origin, an improved definition and the key reciprocity
property of the trilinear symbol introduced by R\'edei in the study of 8-ranks
of narrow class groups of quadratic number fields. It can be used to show that
such 8-ranks are governed by Frobenius conditions on the primes dividing the
discriminant, a fact used the recent work of A. Smith. In addition, we explain
its impact in the progress towards proving my conjectural density for
solvability of the negative Pell equation.


  We present results of searches for B-meson decays to charmless final states
that include a K*, rho, omega, or phi meson accompanied by a second meson.
Using the entire data sample of 9.7 million BBbar pairs collected with the CLEO
II and CLEO II.V detectors, we observe a signal for the decay B+ -> omega pi+,
and measure a branching fraction of B(B+ -> omega pi+) = (11.3^{+3.3}_{-2.9}
\pm 1.5) \times 10^{-6}. We also see evidence for the decay B0 -> omega K0, and
set limits for the decays B0 -> rho0 pi0 and B0 -> K*0 pi0. In addition to
these new results, we also summarize previous CLEO results on related channels.
All quoted results are preliminary.


  Any one-field inflation is actually realized in a multifield configuration
because the inflaton must have couplings with other fields to reheat the
universe and is coupled to all other fields at least gravitationally. In all
single inflaton models, it is explicitly or implicitly assumed that the heavier
fields are stuck to their potential minima during inflation, which are
time-dependent in general. We present a formalism to calculate curvature
perturbations in such a time-dependent background and show that the proper
expression can be obtained using a single-field analysis with a reduced
potential in which all these heavy fields are situated at their respective,
time-dependent minima. Our results provide a firm ground on the conventional
calculation.


  We show how spectral submanifold theory can be used to provide analytic
predictions for the response of periodically forced multi-degree-of-freedom
mechanical systems. These predictions include an explicit criterion for the
existence of isolated forced responses that will generally be missed by
numerical continuation techniques. Our analytic predictions can be refined to
arbitrary precision via an algorithm that does not require the numerical
solutions of the mechanical system. We illustrate all these results on low- and
high-dimensional nonlinear vibration problems. We find that our SSM-based
forced-response predictions remain accurate in high-dimensional systems, in
which numerical continuation of the periodic response is no longer feasible.


  In recent years, lepton flavour violating (LFV) decays are one of the most
trending topics to probe new physics (NP). The latest results of LHCb have
motivated us to study the LFV decays through b to s transition. The branching
ratios, forward backward asymmetries and longitudinal polarization fractions of
B(B_s) to K^* ({phi})l_1 l_2 decays are studied in non-universal Z^' model.
Here, we have structured the four-fold angular distribution of the decays in
terms of transversity amplitudes. The variation of the observables in whole
kinematic region shows the sensitivity of NP. The observables estimated in this
work are very intriguing and might lead a new track towards NP in near future.


  We introduce pseudocubical objects with pseudoconnections in an arbitrary
category, obtained from the Brown-Higgins structure of a cubical object with
connections by suitably relaxing their identities, and construct a cubical
analog of the Tierney-Vogel theory of simplicial derived functors. The crucial
point in the construction is that projective precubical resolutions which are
naturally used to define our cubical derived functors possess
pseudodegeneracies and pseudoconnections. The same fact is essentially used for
proving that in the case of an additive functor between abelian categories, our
theory coincides with the classical relative theory of derived functors by
Eilenberg-Moore.


  One of the key problems related to the Bak-Sneppen evolution model on the
circle is to compute the limit distribution of the fitness at a fixed
observation vertex in the stationary regime, as the size of the system tends to
infinity. Simulations in \cite{J} and \cite{B} suggest that this limit
distribution is uniform on $(f,1)$, for some $f\sim2/3$. In this paper we prove
that the mean of the fitness in the stationary regime is bounded away from 1,
uniformly in the size of the system, thereby establishing the non-triviality of
the limit behaviour.
  The Bak-Sneppen dynamics can easily be defined on any finite connected graph.
We also present a generalisation of the phase-transition result in the context
of an increasing sequence of such graphs. This generalisation covers the
multi-dimentional Bak-Sneppen model as well as the Bak-Sneppen model on a tree.
  Our proofs are based on a `self-similar' graphical representation of the
avalanches.


  We present a new analysis of stellar mass functions (MF) in the COSMOS field
to fainter limits than has been previously probed to z~1. Neither the total nor
the passive or star-forming MF can be well fit with a single Schechter function
once one probes below 3e9 Msun. We observe a dip or plateau at masses ~1e10
Msun, and an upturn towards a steep faint-end slope of -1.7 at lower mass at
any z<1. This bimodal nature of the MF is not solely a result of the blue/red
dichotomy. The blue MF is by itself bimodal at z~1. This suggests a new
dichotomy in galaxy formation that predates the appearance of the red sequence.
We propose two interpretations for this bimodality. If the gas fraction
increases towards lower mass, galaxies with M_baryon~1e10 Msun would shift to
lower stellar masses, creating the observed dip. This would indicate a change
in star formation efficiency, perhaps linked to supernovae feedback becoming
much more efficient. Therefore, we investigate whether the dip is present in
the baryonic (stars+gas) MF. Alternatively, the dip could be created by an
enhancement of the galaxy assembly rate at ~1e11 Msun, a phenomenon that
naturally arises if the baryon fraction peaks at M_halo ~1e12 Msun. In this
scenario, galaxies occupying the bump around M* would be identified with
central galaxies and the second fainter component having a steep faint-end
slope with satellites. While the dip is apparent in the total MF at any z, it
appears to shift from the blue to red population, likely as a result of
transforming high-mass blue galaxies into red ones. At the same time, we detect
a drastic upturn in the number of low-mass red galaxies. Their increase with
time reflects a decrease in the number of blue systems and so we tentatively
associate them with satellite dwarf galaxies that have undergone quenching.


  We define geometric matrix midranges for positive definite Hermitian matrices
and study the midrange problem from a number of perspectives. Special attention
is given to the midrange of two positive definite matrices before considering
the extension of the problem to $N > 2$ matrices. We compare matrix midrange
statistics with the scalar and vector midrange problem and note the special
significance of the matrix problem from a computational standpoint. We also
study various aspects of geometric matrix midrange statistics from the
viewpoint of linear algebra, differential geometry and convex optimization.


  This works handles the inverse reinforcement learning problem in
high-dimensional state spaces, which relies on an efficient solution of
model-based high-dimensional reinforcement learning problems. To solve the
computationally expensive reinforcement learning problems, we propose a
function approximation method to ensure that the Bellman Optimality Equation
always holds, and then estimate a function based on the observed human actions
for inverse reinforcement learning problems. The time complexity of the
proposed method is linearly proportional to the cardinality of the action set,
thus it can handle high-dimensional even continuous state spaces efficiently.
We test the proposed method in a simulated environment to show its accuracy,
and three clinical tasks to show how it can be used to evaluate a doctor's
proficiency.


  We examine the string cosmology equations with a dilaton potential in the
context of the Pre-Big Bang Scenario with the desired scale factor duality, and
give a generic algorithm for obtaining solutions with appropriate evolutionary
properties. This enables us to find pre-big bang type solutions with suitable
dilaton behaviour that are regular at $t=0$, thereby solving the graceful exit
problem. However to avoid fine tuning of initial data, an `exotic' equation of
state is needed that relates the fluid properties to the dilaton field. We
discuss why such an equation of state should be required for reliable dilaton
behaviour at late times.


  Consider a space object in an orbit about the earth. An uncertain initial
state can be represented as a point cloud which can be propagated to later
times by the laws of Newtonian motion. If the state of the object is
represented in Cartesian earth centered inertial (Cartesian-ECI) coordinates,
then even if initial uncertainty is Gaussian in this coordinate system, the
distribution quickly becomes non-Gaussian as the propagation time increases.
Similar problems arise in other standard fixed coordinate systems in
astrodynamics, e.g. Keplerian and to some extent equinoctial. To address these
problems, a local "Adapted STructural (AST)'' coordinate system has been
developed in which uncertainty is represented in terms of deviations from a
"central state".
  Given a sequence of angles-only measurements, the iterated nonlinear extended
(IEKF) and unscented (IUKF) Kalman filters are often the most appropriate
variants to use. In particular, they can be much more accurate than the more
commonly used non-iterated versions, the extended (EKF) and unscented (UKF)
Kalman filters, especially under high eccentricity. In addition, iterated
Kalman filters can often be well-approximated by two new closed form filters,
the observation-centered extended (OCEKF) and unscented (OCUKF) Kalman filters.


  We discuss a possibility to control a heat conductivity in simple
one-dimensional models of dielectrics by means of external mechanical loads. To
illustrate such possibilities we consider first a well-studied chain with
degenerate double-well potential of the interparticle interaction. Contrary to
previous studies, we consider varying length of the chain with fixed number of
particles. Number of possible energetically degenerate ground states strongly
depends on the overall length of the chain, or, in other terms, on average
length of the link between neighboring particles. These degenerate states
correspond to mechanical equilibrium, therefore one can say that the transition
between them mimics to some extent a process of plastic deformation. We
demonstrate that such modification of the chain length can lead to quite
profound (almost five-fold) reduction of the heat conduction coefficient. Even
more profound effect is revealed for a model with single-well non-convex
potential. It is demonstrated that in certain range of constant external
forcing this model becomes "effectively"\ double-well, and has a multitude of
possible states of equilibrium for the same value of the external load. Thus,
the heat conduction coefficient can be reduced by two orders of magnitude. We
suggest a mechanical model of a chain with periodic double-well potential,
which allows control over the heat conduction. The models considered may be
useful for description of heat transport in biological macromolecules and for
control of the heat transport in microsystems.


  Software for mixed-integer linear programming can return incorrect results
for a number of reasons, one being the use of inexact floating-point
arithmetic. Even solvers that employ exact arithmetic may suffer from
programming or algorithmic errors, motivating the desire for a way to produce
independently verifiable certificates of claimed results. Due to the complex
nature of state-of-the-art MILP solution algorithms, the ideal form of such a
certificate is not entirely clear. This paper proposes such a certificate
format, illustrating its capabilities and structure through examples. The
certificate format is designed with simplicity in mind and is composed of a
list of statements that can be sequentially verified using a limited number of
simple yet powerful inference rules. We present a supplementary verification
tool for compressing and checking these certificates independently of how they
were created. We report computational results on a selection of mixed-integer
linear programming instances from the literature. To this end, we have extended
the exact rational version of the MIP solver SCIP to produce such certificates.


  We study the effects of the finite size of baryons on the equation of state
of homogeneous hadronic matter. The finite extension of hadrons is introduced
in order to improve the performance of field theoretical models at very high
densities. We simulate the in-medium averaged baryon-baryon strong repulsion at
very short distances by introducing a Van der Waals like normalization of the
fields. This is done in the framework of the Quark Meson Coupling model, that
allows to take care of the quark structure of baryons. Since within this model
the confinement volume evolves with the fields configuration, the treatment is
not equivalent to a simple hard-core potential. We investigate the phase
transition to quark matter and the structure of neutron stars. We have found
significant corrections at high densities.


  Metal-organic frameworks (MOFs) have been widely investigated for challenging
catalytic transformations due to their well-defined structures and high degree
of synthetic tunability. These features, at least in principle, make MOFs
ideally suited for a computational approach towards catalyst design and
discovery. Nonetheless, the widespread use of data science and machine learning
to accelerate the discovery of MOF catalysts has yet to be substantially
realized. In this review, we provide an overview of recent work that sets the
stage for future high-throughput computational screening and machine learning
studies involving MOF catalysts. This is followed by a discussion of several
challenges currently facing the broad adoption of data-centric approaches in
MOF computational catalysis, and we share possible solutions that can help
propel the field forward.


  This paper given at the Strasbourg NATO school on the CMB and cosmology
reports the contents of four hours of lectures on the CMB spectrum, potential
distortions, and implications. It was followed by 6 hours of lectures on CMB
anisotropy. This paper reviews the observations and theoretical implications
for the CMB frequency spectrum - both for the monopole (essentially total
power) and the dipole and higher order anisotropies including the
Sunyaev-Zeldovich effect.


  With the advent of foundation models, prompt tuning has positioned itself as
an important technique for directing model behaviors and eliciting desired
responses. Prompt tuning regards selecting appropriate keywords included into
the input, thereby adapting to the downstream task without adjusting or
fine-tuning the model parameters. There is a wide range of work in prompt
tuning, from approaches that directly harness the backpropagated gradient
signals from the model, to those employing black-box optimization such as
reinforcement learning (RL) methods. Our primary focus is on RLPrompt, which
aims to find optimal prompt tokens leveraging soft Q-learning. While the
results show promise, we have observed that the prompts frequently appear
unnatural, which impedes their interpretability. We address this limitation by
using sparse Tsallis entropy regularization, a principled approach to filtering
out unlikely tokens from consideration. We extensively evaluate our approach
across various tasks, including few-shot text classification, unsupervised text
style transfer, and textual inversion from images. The results indicate a
notable improvement over baselines, highlighting the efficacy of our approach
in addressing the challenges of prompt tuning. Moreover, we show that the
prompts discovered using our method are more natural and interpretable compared
to those from other baselines.


  We investigate the entanglement entropy in gravity duals of confining large
$N_c$ gauge theories using the proposal of arXiv:hep-th/0603001,
arXiv:hep-th/0605073. Dividing one of the directions of space into a line
segment of length $l$ and its complement, the entanglement entropy between the
two subspaces is given by the classical action of the minimal bulk hypersurface
which approaches the endpoints of the line segment at the boundary. We find
that in confining backgrounds there are generally two such surfaces. One
consists of two disconnected components localized at the endpoints of the line
segment. The other contains a tube connecting the two components. The
disconnected surface dominates the entropy for $l$ above a certain critical
value $l_{\rm crit}$ while the connected one dominates below that value. The
change of behavior at $l=l_{\rm crit}$ is reminiscent of the finite temperature
deconfinement transition: for $l < l_{\rm crit}$ the entropy scales as $N_c^2$,
while for $l > l_{\rm crit}$ as $N_c^0$. We argue that a similar transition
should occur in any field theory with a Hagedorn spectrum of non-interacting
bound states. The requirement that the entanglement entropy has a phase
transition may be useful in constraining gravity duals of confining theories.


  This paper is the first in a series. The main goal of the series is to
present a geometric construction of certain remarkable tensor categories
arising from quantum groups coresponding to the value of deformation parameter
$q$ equal to a root of unity.
  In the present paper we study perverse sheaves over a complex affine space
which are smooth along the stratification determined by a finite arrangement of
complex affine hyperplanes defined by real equations. In particular, we
construct explicitely (in terms of combinatorial data) complexes computing
cohomology of Goresky-MacPherson extensions of one-dimensional local systems
over the complement of hyperplanes.


  Within the framework of McLaughlin-Scott perturbation theory the
equation-of-motion of the dislocation kink in the pinning potential is
linearized, assuming the simultaneous influence of ac and dc forces. Based on
the equations derived, the probability of kink depinning was studied. The
dependencies of the depinning probability on dc and ac forces are analyzed in
details.


  This paper presents a modal analysis based on the reciprocity theorem to
calculate the coupled/penetrated fields into an open-ended waveguide mounted on
a finite flange. Although there is no limitation on the geometry and type of
the external source, an infinitesimal dipole is chosen to produce a plane wave
incident to the waveguide aperture. The proposed method relates the amplitude
of each penetrated mode into the waveguide to the far-field radiation
components of that mode from the waveguide aperture. The accuracy of the final
result depends on the accuracy of the calculated radiated fields. The radiated
field components are calculated considering the reflected fields due to the
aperture and the diffracted fields due to the flange edges. For the first time,
the impact of a finite flange on the penetrated fields into a waveguide is
discussed comprehensively. The geometry of a rectangular waveguide mounted on a
thick square flange is selected to be evaluated. The effects of changing the
main parameters of the geometry on the penetrated fields are discussed
rigorously in various examples. Our results are compared with 3D full-wave
simulations, and an excellent agreement was found between the results while our
analytical approach showing a 60 times faster performance. In addition, we
compared our results with the measurement reported in a previous study.


  We consider an m-dimensional analytic cocycle with underlying dynamics given
by an irrational translation on the circle. Assuming that the d-dimensional
upper left corner of the cocycle is typically large enough, we prove that the d
largest Lyapunov exponents associated with this cocycle are bounded away from
zero. The result is uniform relative to certain measurements on the matrix
blocks forming the cocycle. As an application of this result, we obtain
nonperturbative (in the spirit of Sorets-Spencer theorem) positive lower bounds
of the nonnegative Lyapunov exponents for various models of band lattice
Schroedinger operators.


  Light sterile neutrinos might mix with the active ones and be copiously
produced in the early Universe. In the present paper, a detailed multi-flavor
analysis of sterile neutrino production is performed. Making some justified
approximations allows us to consider not only neutrino interactions with the
primeval medium and neutrino coherence breaking effects, but also oscillation
effects arising from the presence of three light (mostly-active) neutrino
states mixed with two heavier (mostly-sterile) states. First, we emphasize the
underlying physics via an analytical description of sterile neutrino abundances
that is valid for cases with small mixing between active and sterile neutrinos.
Then, we study in detail the phenomenology of (3+2) sterile neutrino models in
light of short-baseline oscillation data, including the LSND and MiniBooNE
results. Finally, by using the information provided by this analysis, we obtain
the expected sterile neutrino cosmological abundances and then contrast them
with the most recent available data from Cosmic Microwave Background and Large
Scale Structure observations. We conclude that (3+2) models are significantly
more disfavored by the internal inconsistencies between sterile neutrino
interpretations of appearance and disappearance short-baseline data themselves,
rather than by the used cosmological data.


  We examine rare evolutionary routes of binary systems where the initially
more massive primary star of ~5.5-8.5Mo, forms a white dwarf (WD), while the
secondary star of 4Mo < M_2,0 < M_1,0 accretes mass from the evolved primary
and later terminates as a core collapse supernova (CCSN). In such a WD-NS
reverse evolution a neutron star (NS) or a potential NS-progenitor massive core
is formed after the WD. These SN explosions are likely to be preceded by strong
interaction of the WD with the giant secondary's core, leading to an
Intermediate-Luminosity Optical Transient (ILOT; Red Transient; Red Nova)
event, weeks to years before the explosion. The common envelope phase of the WD
and the giant ends with a merger that forms an ILOT, or an envelope ejection
that leads, after a CCSN of the giant's core, to a NS-NS or WD-NS surviving
binary. The WD could suffer a thermonuclear explosion, that might be observed
as a Type Ia SN. Most of these CCSN and thermonuclear explosions will be
peculiar. We calculate the stellar evolution of representative cases using
Modules for Experiments in Stellar Astrophysics (MESA). The occurrence rate of
these systems is ~3-5 percent of that of CCSNe.


  Let $ G $ be a Lie group with Lie algebra $ \mathfrak{g} $. An element $ X
\in \mathfrak{g} $ is called $\mathrm{Ad}_G$-real if $ -X=gXg^{-1} $ for some $
g \in G $. Moreover, if $ -X=gXg^{-1} $ holds for some involution $ g\in G $,
then $ X $ is called strongly $\mathrm{Ad}_G$-real. We have classified the
$\mathrm{Ad}_G$-real and the strongly $\mathrm{Ad}_G$-real orbits in the
special linear Lie algebra $\mathfrak{sl}(n,\mathbb{F}) $ for $
\mathbb{F}=\mathbb{C}$ or $\mathbb{H} $.


  In 2001, Leo Breiman wrote of a divide between "data modeling" and
"algorithmic modeling" cultures. Twenty years later this division feels far
more ephemeral, both in terms of assigning individuals to camps, and in terms
of intellectual boundaries. We argue that this is largely due to the "data
modelers" incorporating algorithmic methods into their toolbox, particularly
driven by recent developments in the statistical understanding of Breiman's own
Random Forest methods. While this can be simplistically described as "Breiman
won", these same developments also expose the limitations of the
prediction-first philosophy that he espoused, making careful statistical
analysis all the more important. This paper outlines these exciting recent
developments in the random forest literature which, in our view, occurred as a
result of a necessary blending of the two ways of thinking Breiman originally
described. We also ask what areas statistics and statisticians might currently
overlook.


  V(I) characteristics have been performed in a monocrystalline microbridge of
$Bi[Pb]-2212$. The vortex phase diagram has been greatly investigated. Linear
but non-ohmic Voltage(Current) (V(I)) curves with well defined critical current
have been observed. A departure from this behavior is observed near the peak
effect where an out of equilibrium high threshold current can be stabilized. At
high temperature, the critical current persists in the "liquid" state despite
the dissipation at the lowest bias. Some implications of these results are
discussed. In particular, it is proposed that the surface disorder, rather than
the bulk disorder, is responsible for the vortex pinning in this sample.


  We study the evolution of solidification microstructures using a phase-field
model computed on an adaptive, finite element grid. We discuss the details of
our algorithm and show that it greatly reduces the computational cost of
solving the phase-field model at low undercooling. In particular we show that
the computational complexity of solving any phase-boundary problem scales with
the interface arclength when using an adapting mesh. Moreover, the use of
dynamic data structures allows us to simulate system sizes corresponding to
experimental conditions, which would otherwise require lattices greater that
$2^{17}\times 2^{17}$ elements. We examine the convergence properties of our
algorithm. We also present two dimensional, time-dependent calculations of
dendritic evolution, with and without surface tension anisotropy. We benchmark
our results for dendritic growth with microscopic solvability theory, finding
them to be in good agreement with theory for high undercoolings. At low
undercooling, however, we obtain higher values of velocity than solvability
theory at low undercooling, where transients dominate, in accord with a
heuristic criterion which we derive.


  Nuclear magnetic resonance (NMR) measurements of an iron (Fe)-based
superconductor LaFeAsO_{1-x}F_x (x = 0.08 and 0.14) were performed at ambient
pressure and under pressure. The relaxation rate 1/T_1 for the overdoped
samples (x = 0.14) shows T-linear behavior just above T_c, and pressure
application enhances 1/T_1T similar to the behavior of T_c. This implies that
1/T_1T = constant originates from the Korringa relation, and an increase in the
density of states at the Fermi energy D(E_F) leads to the enhancement of T_c.
In the underdoped samples (x = 0.08), 1/T_1T measured at ambient pressure also
shows T-independent behavior in a wide temperature range above T_c. However, it
shows Curie-Weiss-like T dependence at 3.0 GPa accompanied by a small increase
in T_c, suggesting that predominant antiferromagnetic fluctuation suppresses
development of superconductivity or remarkable enhancement of T_c. The
qualitatively different features between underdoped and overdoped samples are
systematically explained by a band calculation with hole and electron pockets.


  In this paper we focus on preprocessing for persistent homology computations.
We adapt some techniques which were successfully used for standard homology
computations. The main idea is to reduce the complex prior to generating its
boundary matrix, which is costly to store and process. We discuss the following
reduction methods: elementary collapses, coreductions (as defined by Mrozek and
Batko) and acyclic subspace method (introduced by Mrozek, Pilarczyk and
\.Zelazna).


  This paper is concerned with the holonomy of a class of spaces which includes
Landsberg spaces of Finsler geometry. The methods used are those of Lie
groupoids and algebroids as developed by Mackenzie. We prove a version of the
Ambrose-Singer Theorem for such spaces. The paper ends with a discussion of how
the results may be extended to Finsler spaces and homogeneous nonlinear
connections in general.


  The problems of stripper target behavior in the nonstationary intense
particle beams are considered. The historical sketch of studying of radiation
damage failure of carbon targets under ion bombardment is presented. The simple
model of evaporation of a target by an intensive pulsing beam is supposed.
Stripper foils lifetimes in the nonstationary intense particle can be described
by two failure mechanisms: radiation damage accumulation and evaporation of
target. At the maximal temperatures less than 2500K the radiation damage are
dominated; at temperatures above 2500K the mechanism of evaporation of a foil
prevails. The proposed approach has been applied to the discription of
behaviour of stripper foils in the BNL linac and SNS conditions.


  Random intersection graphs have received much attention for nearly two
decades, and currently have a wide range of applications ranging from key
predistribution in wireless sensor networks to modeling social networks. In
this paper, we investigate the strengths of connectivity and robustness in a
general random intersection graph model. Specifically, we establish sharp
asymptotic zero-one laws for $k$-connectivity and $k$-robustness, as well as
the asymptotically exact probability of $k$-connectivity, for any positive
integer $k$. The $k$-connectivity property quantifies how resilient is the
connectivity of a graph against node or edge failures. On the other hand,
$k$-robustness measures the effectiveness of local diffusion strategies (that
do not use global graph topology information) in spreading information over the
graph in the presence of misbehaving nodes. In addition to presenting the
results under the general random intersection graph model, we consider two
special cases of the general model, a binomial random intersection graph and a
uniform random intersection graph, which both have numerous applications as
well. For these two specialized graphs, our results on asymptotically exact
probabilities of $k$-connectivity and asymptotic zero-one laws for
$k$-robustness are also novel in the literature.


  The symmetry requirement and the origin of magnetic orders coexisting with
superconductivity have been strongly debated issues of iron-based
superconductors (FeSCs). Observation of C$_4$-symmetric antiferromagnetism in
violation of the inter-band nesting condition of spin-density waves in
superconducting ground state will require significant change in our
understanding of the mechanism of FeSC. The superconducting material
Sr$_2$VO$_3$FeAs, a bulk version of monolayer FeSC in contact with a perovskite
layer with its magnetism (T$_N$ ~ 50 K) and superconductivity (T$_c$ ~ 37 K)
coexisting at parent state, has no reported structural orthorhombic distortion
and thus makes a perfect system to look for theoretically expected C$_4$
magnetisms. Based on variable temperature spin-polarized scanning tunneling
microscopy (SPSTM) with newly discovered imaging mechanism that removes the
static surface reconstruction (SR) pattern by fluctuating it rapidly with
spin-polarized tunneling current, we could visualize underlying C$_4$ symmetric
(2$\times$2) magnetic domains and its phase domain walls. We find that this
magnetic order is perfectly consistent with the plaquette antiferromagnetic
order in tetragonal Fe spin lattice expected from theories based on the
Heisenberg exchange interaction of local Fe moments and the quantum order by
disorder. The inconsistency of its modulation Q vectors from the nesting
condition also implies that the nesting-based C$_2$ symmetric magnetism is not
a unique prerequisite of high-T$_c$ FeSC. Furthermore, the plaquette
antiferromagnetic domain wall dynamics under the influence of small spin torque
effect of spin-polarized tunneling current are shown to be consistent with
theoretical simulation based on the extended Landau-Lifshitz-Gilbert equation.


  In recent years, we have witnessed an increased interest in temporal modeling
of patient records from large scale Electronic Health Records (EHR). While
simpler RNN models have been used for such problems, memory networks, which in
other domains were found to generalize well, are underutilized. Traditional
memory networks involve diffused and non-linear operations where influence of
past events on outputs are not readily quantifiable. We posit that this lack of
interpretability makes such networks not applicable for EHR analysis. While
networks with explicit memory have been proposed recently, the discontinuities
imposed by the discrete operations make such networks harder to train and
require more supervision. The problem is further exacerbated in the limited
data setting of EHR studies. In this paper, we propose a novel memory
architecture that is more interpretable than traditional memory networks while
being easier to train than explicit memory banks. Inspired by well-known models
of human cognition, we propose partitioning the external memory space into (a)
a primary explicit memory block to store exact replicas of recent events to
support interpretations, followed by (b) a secondary blurred memory block that
accumulates salient aspects of past events dropped from the explicit block as
higher level abstractions and allow training with less supervision by stabilize
the gradients. We apply the model for 3 learning problems on ICU records from
the MIMIC III database spanning millions of data points. Our model performs
comparably to the state-of the art while also, crucially, enabling ready
interpretation of the results.


  This manuscript puts forward and verifies an analytical approach to design
phononic crystals that feature a bandgap at the lowest possible frequencies.
This new approach is verified against numerical optimization. It rests on the
exact form of the trace of the cumulative transfer matrix. This matrix arises
from the product of N elementary transfer matrices, where N represents the
number of layers in the unit cell of the crystal. The paper presents first a
new proof of the harmonic decomposition of the trace (which, unlike the
original derivation, does not resort to group-theoretical concepts), and then
goes to demonstrate that the long-wavelength asymptotics of the function that
governs the dispersion relation can be described in closed form for any
layering, plus that it possesses a simple and explicit form that facilitates
its study. Using this asymptotic result for low frequencies, we then propose an
analytical curvature-minimization approach to devise layerings that yield an
opening of the first frequency bandgap at the lowest possible frequency value.
Finally, we also show that minimizing the frequency at which the first gap
opens can be at odds with obtaining broadband attenuation, i.e., maximizing the
width of the first frequency bandgap.


  We discuss why there are no negative gravitational sources in General
Relativity and show that it is possible to extend the classical theory such
that repulsive gravitational interaction occurs.


  In this article we study the role of the Green function for the Laplacian in
a compact Riemannian manifold as a tool for obtaining well-distributed points.
In particular, we prove that a sequence of minimizers for the Green energy is
asymptotically uniformly distributed. We pay special attention to the case of
locally harmonic manifolds.


  We have measured the radial profiles of isophotal ellipticity ($\varepsilon$)
and disky/boxy parameter A$_4$ out to radii of about three times the semi-major
axes for $\sim4,600$ star-forming galaxies (SFGs) at intermediate redshifts
$0.5<z<1.8$ in the CANDELS/GOODS-S and UDS fields. Based on the average size
versus stellar-mass relation in each redshift bin, we divide our galaxies into
Small SFGs (SSFGs), i.e., smaller than average for its mass, and Large SFGs
(LSFGs), i.e., larger than average. We find that, at low masses ($M_{\ast} <
10^{10}M_{\odot}$), the SSFGs generally have nearly flat $\varepsilon$ and
A$_4$ profiles for both edge-on and face-on views, especially at redshifts
$z>1$. Moreover, the median A$_4$ values at all radii are almost zero. In
contrast, the highly-inclined, low-mass LSFGs in the same mass-redshift bins
generally have monotonically increasing $\varepsilon$ with radius and are
dominated by disky values at intermediate radii. These findings at intermediate
redshifts imply that low-mass SSFGs are not disk-like, while low-mass LSFGs
appear to harbour disk-like components flattened by significant rotation. At
high masses ($M_{\ast} > 10^{10}M_{\odot}$), highly-inclined SSFGs and LSFGs
both exhibit a general, distinct trend for both $\varepsilon$ and A$_4$
profiles: increasing values with radius at lower radii, reaching maxima at
intermediate radii, and then decreasing values at larger radii. Such a trend is
more prevalent for more massive ($M_{\ast} > 10^{10.5}M_{\odot}$) galaxies or
those at lower redshifts ($z<1.4$). The distinct trend in $\varepsilon$ and
A$_4$ can be simply explained if galaxies possess all three components: central
bulges, disks in the intermediate regions, and halo-like stellar components in
the outskirts.


  Our understanding of how exoplanets form and evolve relies on analyses of
both the mineralogy of protoplanetary disks and their detailed structures;
however, these key complementary aspects of disks are usually studied
separately. We present initial results from a hybrid model that combines the
empirical characterization of the mineralogy of a disk, as determined from its
mid-infrared spectral features, with the MCFOST radiative transfer disk model,
a combination we call the EaRTH Disk Model. With the results of the mineralogy
detection serving as input to the radiative transfer model, we generate
mid-infrared spectral energy distributions (SEDs) that reflect both the
mineralogical and structural parameters of the corresponding disk. Initial fits
of the SED output by the resulting integrated model to Spitzer Space T elescope
mid-infrared (IRS) spectra of the protoplanetary disk orbiting the nearby T
Tauri star MP Mus demonstrate the potential advantages of this approach by
revealing details like the dominance of micron-sized olivine and micron-sized
forsterite in this dusty disk. The simultaneous insight into disk composition
and structure provided by the EaRTH Disk methodology should be directly
applicable to the interpretation of mid-infrared spectra of protoplanetary
disks that will be produced by the James Webb Space Telescope.


  In this chapter, we review the Ra\~{n}ada field line solutions of Maxwell's
equations in the vacuum, which describe a topologically non-trivial
electromagnetic field, as well as their relation with the knot theory. Also, we
present a generalization of these solutions to the non-linear electrodynamics
recently published in the literature.


  The goal of this thesis is to calculate properties of D-Mesons with
QCD-Sum-Rules in order to understand the nature of D-Mesons with positive
parity. The result is that such D-Mesons most probably are Mesons with a four
quark rather than a two quark structure. In this thesis a spectral function
which contains two resonances is used to calculate the decay constants of the
first and the second resonance in the spectral function. Moreover, a
Breit-Wigner curve instead of a delta-function is used to approximate the peaks
of the resonances in the spectral function. The decay constants of the
resonaces corresponding to the second peak in the spectral functions have never
been calculated before.Also very practical problems are attacked, see the
paragraph about the misscalculation of D-Meson Sum-Rules. Another topic of this
thesis was the establishment of basical knowledge about QCD-Sum-Rules, the
Operator-Product-Expansion and Dispersion-Integrals. A discussion of these
topics and many explicite calculations are included.


  Transfer learning (TL) is an increasingly popular approach to training deep
learning (DL) models that leverages the knowledge gained by training a
foundation model on diverse, large-scale datasets for use on downstream tasks
where less domain- or task-specific data is available. The literature is rich
with TL techniques and applications; however, the bulk of the research makes
use of deterministic DL models which are often uncalibrated and lack the
ability to communicate a measure of epistemic (model) uncertainty in
prediction. Unlike their deterministic counterparts, Bayesian DL (BDL) models
are often well-calibrated, provide access to epistemic uncertainty for a
prediction, and are capable of achieving competitive predictive performance. In
this study, we propose variational inference pre-trained audio neural networks
(VI-PANNs). VI-PANNs are a variational inference variant of the popular
ResNet-54 architecture which are pre-trained on AudioSet, a large-scale audio
event detection dataset. We evaluate the quality of the resulting uncertainty
when transferring knowledge from VI-PANNs to other downstream acoustic
classification tasks using the ESC-50, UrbanSound8K, and DCASE2013 datasets. We
demonstrate, for the first time, that it is possible to transfer calibrated
uncertainty information along with knowledge from upstream tasks to enhance a
model's capability to perform downstream tasks.


  The development of medical imaging techniques has made a significant
contribution to clinical decision-making. However, the existence of suboptimal
imaging quality, as indicated by irregular illumination or imbalanced
intensity, presents significant obstacles in automating disease screening,
analysis, and diagnosis. Existing approaches for natural image enhancement are
mostly trained with numerous paired images, presenting challenges in data
collection and training costs, all while lacking the ability to generalize
effectively. Here, we introduce a pioneering training-free Diffusion Model for
Universal Medical Image Enhancement, named UniMIE. UniMIE demonstrates its
unsupervised enhancement capabilities across various medical image modalities
without the need for any fine-tuning. It accomplishes this by relying solely on
a single pre-trained model from ImageNet. We conduct a comprehensive evaluation
on 13 imaging modalities and over 15 medical types, demonstrating better
qualities, robustness, and accuracy than other modality-specific and
data-inefficient models. By delivering high-quality enhancement and
corresponding accuracy downstream tasks across a wide range of tasks, UniMIE
exhibits considerable potential to accelerate the advancement of diagnostic
tools and customized treatment plans.


  Shock wave reaction results in various characteristic regimes in porous
material. The geometrical and topological properties of these regimes are
highly concerned in practical applications. Via the morphological analysis to
characteristic regimes with high temperature, we investigate the thermodynamics
of shocked porous materials whose mechanical properties cover a wide range from
hyperplasticity to elasticity. It is found that, under fixed shock strength,
the total fractional area $A$ of the high-temperature regimes with $T \geq
T_{th}$ and its saturation value first increase, then decrease with the
increasing of the initial yield $\sigma_{Y0}$, where $T_{th}$ is a given
threshold value of temperature $T$. In the shock-loading procedure, the
fractional area $A(t)$ may show the same behavior if $T_{th}$ and $\sigma_{Y0}$
are chosen appropriately. Under the same $A(t)$ behavior, $T_{th}$ first
increases then decreases with $\sigma_{Y0}$. At the maximum point
$\sigma_{Y0M}$, the shock wave contributes the maximum plastic work. Around
$\sigma_{Y0M}$, two materials with different mechanical properties may share
the same $A(t)$ behavior even for the same $T_{th}$. The characteristic regimes
in the material with the larger $\sigma_{Y0}$ are more dispersed.


  We study the behavior of a quantum gyroscope, that is, a quantum system which
singles out a direction in space in order to measure certain properties of
incoming particles such as the orientation of their spins. We show that
repeated Heisenberg interactions of the gyroscope with several incoming
spin-1/2 particles provides a simple model of decoherence which exhibits both
relaxation and dephasing. Focusing on the semiclassical limit, we derive
equations of motion for the evolution of a coherent state and investigate the
evolution of a superposition of such states. While a coherent state evolves on
a timescale given by the classical ratio of the angular momentum of the
gyroscope to that of the incoming particles, dephasing acts on a much shorter
timescale that depends only on the angular difference of the states in the
superposition.


  Threefold Hopf semimetals are a novel type of topological semimetals that
possess an internal anisotropy characterized by a dipolar structure of the
Berry curvature and an isotropic energy band structure consisting of a Dirac
cone and a flat band. In this study, we theoretically investigate the impact of
internal anisotropy on plasmons in threefold Hopf semimetals using random-phase
approximation. In contrast to the classical intuition that isotropy of the
energy band dispersion leads to isotropic plasmons in the classical regime
(i.e., in the wavelength limit), we find that plasmons in threefold Hopf
semimetals exhibit notable anisotropy even in the long-wavelength limit. We
derive an explicit analytical form of the long-wavelength plasmon frequency,
and numerically demonstrate the validity of our results in a wide range of
situations. Our work reveals that the anisotropy of long-wavelength plasmons
can reach 25%, making it experimentally observable.


  We measure the temperature dependence of the Raman spectra of metallic and
semiconducting nanotubes. We show that the different trend in metallic tubes is
due to phonon re-normalization induced by the variation in electronic
temperature, which is modeled including non-adiabatic contributions to account
for the dynamic, time dependent nature


  The QCD hadronic string is supplemented with the reparameterization-invariant
boundary interaction to background chiral fields associated with pions in a way
compatible with the conformal symmetry. It allows the full reconstruction of
the P-even part of the Chiral Lagrangian in a good agreement with the
phenomenology of P-even meson interactions. The modification of boundary
interaction necessary to induce the parity-odd Chiral Dynamics (WZW action) is
outlined.


  Development of reliable methods for optimised energy storage and generation
is one of the most imminent challenges in moder power systems. In this paper an
adaptive approach to load leveling problem using novel dynamic models based on
the Volterra integral equations of the first kind with piecewise continuous
kernels. These integral equations efficiently solve such inverse problem taking
into account both the time dependent efficiencies and the availability of
generation/storage of each energy storage technology. In this analysis a direct
numerical method is employed to find the least-cost dispatch of available
storages. The proposed collocation type numerical method has second order
accuracy and enjoys self-regularization properties, which is associated with
confidence levels of system demand. This adaptive approach is suitable for
energy storage optimisation in real time. The efficiency of the proposed
methodology is demonstrated on the Single Electricity Market of Republic of
Ireland and Sakhalin island in the Russian Far East.


  This paper deals with the distributed processing in the search for an optimum
classification model using evolutionary product unit neural networks. For this
distributed search we used a cluster of computers. Our objective is to obtain a
more efficient design than those net architectures which do not use a
distributed process and which thus result in simpler designs. In order to get
the best classification models we use evolutionary algorithms to train and
design neural networks, which require a very time consuming computation. The
reasons behind the need for this distribution are various. It is complicated to
train this type of nets because of the difficulty entailed in determining their
architecture due to the complex error surface. On the other hand, the use of
evolutionary algorithms involves running a great number of tests with different
seeds and parameters, thus resulting in a high computational cost


  The nanoflare paradigm of coronal heating has proven extremely promising for
explaining the presence of hot, multi-million degree loops in the solar corona.
In this paradigm, localized heating events supply enough energy to heat the
solar atmosphere to its observed temperatures. Rigorously modeling this
process, however, has proven difficult, since it requires an accurate treatment
of both the magnetic field dynamics and reconnection as well as the plasma's
response to magnetic perturbations. In this paper, we combine fully 3D
magnetohydrodynamic (MHD) simulations of coronal active region plasma driven by
photospheric motions with spatially-averaged, time-dependent hydrodynamic (HD)
modeling of coronal loops to obtain physically motivated observables that can
be quantitatively compared with observational measurements of active region
cores. We take the behavior of reconnected field lines from the MHD simulation
and use them to populate the HD model to obtain the thermodynamic evolution of
the plasma and subsequently the emission measure distribution. We find the that
the photospheric driving of the MHD model produces only very low-frequency
nanoflare heating which cannot account for the full range of active region core
observations as measured by the low-temperature emission measure slope.
Additionally, we calculate the spatial and temporal distributions of field
lines exhibiting collective behavior, and argue that loops occur due to random
energization occurring on clusters of adjacent field lines.


  An algebraic cohomological characterization of a class of linearly broken
Ward identities is provided. The examples of the topological vector
supersymmetry and of the Landau ghost equation are discussed in detail. The
existence of such a linearly broken Ward identities turns out to be related to
BRST exact antifield dependent cocycles with negative ghost number.


  Let $S$ be a set of $n$ points in $\mathbb{R}^3$, no three collinear and not
all coplanar. If at most $n-k$ are coplanar and $n$ is sufficiently large, the
total number of planes determined is at least $1 + k
\binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2})$. For similar conditions and
sufficiently large $n$, (inspired by the work of P. D. T. A. Elliott in
\cite{Ell67}) we also show that the number of spheres determined by $n$ points
is at least $1+\binom{n-1}{3}-t_3^{orchard}(n-1)$, and this bound is best
possible under its hypothesis. (By $t_3^{orchard}(n)$, we are denoting the
maximum number of three-point lines attainable by a configuration of $n$
points, no four collinear, in the plane, i.e., the classic Orchard Problem.)
New lower bounds are also given for both lines and circles.


  We have observed the clump G34.43+00.24 MM3 associated with an infrared dark
cloud in DNC $J$=3--2, HN$^{13}$C $J$=3--2, and N$_2$H$^+$ $J$=3--2 with the
Atacama Large Millimeter/submillimeter Array (ALMA). The N$_2$H$^+$ emission is
found to be relatively weak near the hot core and the outflows, and its
distribution is clearly anti-correlated with the CS emission. This result
indicates that a young outflow is interacting with cold ambient gas. The
HN$^{13}$C emission is compact and mostly emanates from the hot core, whereas
the DNC emission is extended around the hot core. Thus, the DNC and HN$^{13}$C
emission traces warm regions near the protostar differently. The DNC emission
is stronger than the HN$^{13}$C emission toward most parts of this clump. The
DNC/HNC abundance ratio averaged within a $15^{\prime\prime} \times
15^{\prime\prime}$ area around the phase center is higher than 0.06. This ratio
is much higher than the value obtained by the previous single-dish observations
of DNC and HN$^{13}$C $J$=1--0 ($\sim$0.003). It seems likely that the DNC and
HNC emission observed with the single-dish telescope traces lower density
envelopes, while that observed with ALMA traces higher density and highly
deuterated regions. We have compared the observational results with
chemical-model results in order to investigate the behavior of DNC and HNC in
the dense cores. Taking these results into account, we suggest that the low
DNC/HNC ratio in the high-mass sources obtained by the single-dish observations
are at least partly due to the low filling factor of the high density regions.


  The dynamic reflection probability and the spectral reflection probability
for a one-dimensional Schroedinger operator $H = - \Delta + V$ are
characterized in terms of the scattering theory of the pair $(H, H_\infty)$
where $H_\infty$ is the operator obtained by decoupling the left and right
half-lines $\mathbb{R}_{\leq 0}$ and $\mathbb{R}_{\geq 0}$. An immediate
consequence is that these reflection probabilities are in fact the same, thus
providing a short and transparent proof of the main result of Breuer, J., E.
Ryckman, and B. Simon (2010) . This approach is inspired by recent developments
in non-equilibrium statistical mechanics of the electronic black box model and
follows a strategy parallel to the Jacobi case.


  Two non-identical quantum emitters, when placed within a cavity and
coherently excited at the two-photon resonance, can reach stationary states of
nearly maximal entanglement. In Vivas-Via\~na et al., we introduce a
frequency-resolved Purcell effect stabilizing entangled $W$ states among
strongly interacting quantum emitters embedded in a cavity. Here, we delve
deeper into a specific configuration with a particularly rich phenomenology:
two interacting quantum emitters under coherent excitation at the two-photon
resonance. This scenario yields two resonant cavity frequencies where the
combination of two-photon driving and Purcell-enhanced decay stabilizes the
system into the sub- and superradiant states, respectively. By considering the
case of non-degenerate emitters and exploring the parameter space of the
system, we show that this mechanism is merely one among a complex family of
phenomena that can generate both stationary and metastable entanglement when
driving the emitters at the two-photon resonance. We provide a global
perspective of this landscape of mechanisms and contribute analytical
characterizations and insights into these phenomena, establishing connections
with previous reports in the literature and discussing how some of these
effects can be optically detected.


  We provide a differential structure on arbitrary cleft extensions
$B:=A^{\mathrm{co}H}\subseteq A$ for an $H$-comodule algebra $A$. This is
achieved by constructing a covariant calculus on the corresponding crossed
product algebra $B\#_\sigma H$ from the data of a bicovariant calculus on the
structure Hopf algebra $H$ and a calculus on the base algebra $B$, which is
compatible with the $2$-cocycle and measure of the crossed product. The result
is a quantum principal bundle with canonical strong connection and we describe
the induced bimodule covariant derivatives on associated bundles of the crossed
product. It is proven that connections of the quantum principal bundle are in
bijection with connection $1$-forms. All results specialize to trivial
extensions and smash product algebras $B\#H$ and we give a characterization of
the smash product calculus in terms of the differentials of the cleaving map
$j\colon H\to A$ and the inclusion $B\hookrightarrow A$. The construction is
exemplified for pointed Hopf algebras. In particular, the case of Radford Hopf
algebras $H_{(r,n,q)}$ is spelled out in detail.


  We present the first analysis of the p19MSSM with neutralino dark matter, in
light of 13 TeV LHC data with an integrated luminosity of ~14/fb. We recast
twelve experimental analyses performed by the ATLAS collaboration and derive
exclusion bounds on the parameter space of the model. We find that 25% of the
model points can be excluded at 95% C.L. by a combination of the implemented
searches. The spectrum allowed after the 13 TeV results are taken into account
presents stops heavier than at least 400 GeV, gluinos heavier than at least 790
GeV, and squarks of the first and second generation heavier than at least 440
GeV.


  Session-based recommendation which has been witnessed a booming interest
recently, focuses on predicting a user's next interested item(s) based on an
anonymous session. Most existing studies adopt complex deep learning techniques
(e.g., graph neural networks) for effective session-based recommendation.
However, they merely address co-occurrence between items, but fail to well
distinguish causality and correlation relationship. Considering the varied
interpretations and characteristics of causality and correlation relationship
between items, in this study, we propose a novel method denoted as CGSR by
jointly modeling causality and correlation relationship between items. In
particular, we construct cause, effect and correlation graphs from sessions by
simultaneously considering the false causality problem. We further design a
graph neural network-based method for session-based recommendation. To
conclude, we strive to explore the relationship between items from specific
``causality" (directed) and ``correlation" (undirected) perspectives. Extensive
experiments on three datasets show that our model outperforms other
state-of-the-art methods in terms of recommendation accuracy. Moreover, we
further propose an explainable framework on CGSR, and demonstrate the
explainability of our model via case studies on Amazon dataset.


  The ages of globular clusters in our own Milky Way are known with precision
of about \pm 1 Gyr, hence their formation at redshifts z>~3 and their role in
hierarchical cosmology and the reionization of the intergalactic medium remain
relatively undetermined. Here we analyze the effect of globular cluster
formation on the observed rest-frame UV luminosity functions (LFs) and UV
continuum slopes of high redshift galaxies in the Hubble Ultra Deep Fields. We
find that the majority of present day globular clusters have formed during two
distinct epochs: at redshifts z ~ 2-3 and at redshifts z>~6. The birth of
proto-GC systems produce the steep, faint-end slopes of the galaxy LFs, and
because the brightness of proto-GCs fades 5 Myrs after their formation, their
blue colors are in excellent agreement with observations.
  Our results suggest that: i) the bulk of the old globular cluster population
with estimated ages >~12 Gyr (about 50% of the total population), formed in the
relatively massive dwarf galaxies at redshifts z>~6; ii) proto-GC formation was
an important mode of star formation in those dwarf galaxies, and likely
dominated the reionization process. Another consequence of this scenario is
that some of the most massive Milky Way satellites may be faint and yet
undiscovered because tidal stripping of a dominant GC population precedes
significant stripping of the dark matter halos of these satellites. This
scenario may alleviate some remaining tensions between CDM simulations and
observations.


  The statistical properties of level spacings provide valuable insights into
the dynamical properties of a many-body quantum systems. We investigate the
level statistics of the Fermi-Hubbard model with dimerized hopping amplitude
and find that after taking into account translation, reflection, spin and
{\eta} pairing symmetries to isolate irreducible blocks of the Hamiltonian, the
level spacings in the limit of large system sizes follow the distribution
expected for hermitian random matrices from the Gaussian orthogonal ensemble.
We show this by analyzing the distribution of the ratios of consecutive level
spacings in this system, its cumulative distribution and quantify the
deviations of the distributions using their mean, standard deviation and
skewness.


  The context information such as product category plays a critical role in
sequential recommendation. Recent years have witnessed a growing interest in
context-aware sequential recommender systems. Existing studies often treat the
contexts as auxiliary feature vectors without considering the sequential
dependency in contexts. However, such a dependency provides valuable clues to
predict the user's future behavior. For example, a user might buy electronic
accessories after he/she buy an electronic product.
  In this paper, we propose a novel seq2seq translation architecture to
highlight the importance of sequential dependency in contexts for sequential
recommendation. Specifically, we first construct a collateral context sequence
in addition to the main interaction sequence. We then generalize recent
advancements in translation model from sequences of words in two languages to
sequences of items and contexts in recommender systems. Taking the category
information as an item's context, we develop a basic coupled and an extended
tripled seq2seq translation models to encode the category-item and
item-category-item relations between the item and context sequences. We conduct
extensive experiments on three real world datasets. The results demonstrate the
superior performance of the proposed model compared with the state-of-the-art
baselines.


  Long duration gamma-ray bursts are powerful sources that can accelerate
particles to ultra-high energies. Acceleration of protons in the forward shock
of the highly relativistic GRB blastwave allows PeV--EeV neutrino production by
photopion interactions of ultra-high energy protons with X-ray to optical
photons of the GRB afterglow emission. Four different blastwave evolution
scenarios are considered: adiabatic and fully radiative blastwaves in a
constant density circumburst medium and in a wind environment with the particle
density in the wind decreasing inversley proportional to the square of the
radius from the center of the burst. The duration of the neutrino flux depends
on the evolution of the blastwave, and can last up to a day in the case of an
adibatic blastwave in a constant density medium. Neutrino fluxes from the three
other blastwave evolution scenarios are also calculated. Diffuse neutrino
fluxes calculated using the observed rate of long-duration GRBs are consistent
with the recent IceCube upper limit on the prompt GRB neutrino flux below PeV.
The diffuse neutrino flux needed to explain the two neutrino events at PeV
energies recently detected by IceCube can partially come from the presented GRB
blastwave diffuse fluxes. Future observations by IceCube and upcoming huge
radio Askaryan experiments will be able to probe the flux models presented here
or constrain the GRB blastwave properties.


  We derive generic predictions at hadron colliders from the large
forward-backward asymmetry observed at the Tevatron, assuming the latter arises
from heavy new physics beyond the Standard Model. We use an effective field
theory approach to characterize the associated unknown dynamics. By fitting the
Tevatron t \bar t data we derive constraints on the form of the new physics.
Furthermore, we show that heavy new physics explaining the Tevatron data
generically enhances at high invariant masses both the top pair production
cross section and the charge asymmetry at the LHC. This enhancement can be
within the sensitivity of the 8 TeV run, such that the 2012 LHC data should be
able to exclude a large class of models of heavy new physics or provide hints
for its presence. The same new physics implies a contribution to the
forward-backward asymmetry in bottom pair production at low invariant masses of
order a permil at most.


  In recent years, various methods and benchmarks have been proposed to
empirically evaluate the alignment of artificial neural networks to human
neural and behavioral data. But how aligned are different alignment metrics? To
answer this question, we analyze visual data from Brain-Score (Schrimpf et al.,
2018), including metrics from the model-vs-human toolbox (Geirhos et al.,
2021), together with human feature alignment (Linsley et al., 2018; Fel et al.,
2022) and human similarity judgements (Muttenthaler et al., 2022). We find that
pairwise correlations between neural scores and behavioral scores are quite low
and sometimes even negative. For instance, the average correlation between
those 80 models on Brain-Score that were fully evaluated on all 69 alignment
metrics we considered is only 0.198. Assuming that all of the employed metrics
are sound, this implies that alignment with human perception may best be
thought of as a multidimensional concept, with different methods measuring
fundamentally different aspects. Our results underline the importance of
integrative benchmarking, but also raise questions about how to correctly
combine and aggregate individual metrics. Aggregating by taking the arithmetic
average, as done in Brain-Score, leads to the overall performance currently
being dominated by behavior (95.25% explained variance) while the neural
predictivity plays a less important role (only 33.33% explained variance). As a
first step towards making sure that different alignment metrics all contribute
fairly towards an integrative benchmark score, we therefore conclude by
comparing three different aggregation options.


  Let $L$ be a special Lagrangian submanifold of a compact, Calabi-Yau manifold
$M$ with boundary lying on the symplectic, codimension 2 submanifold $W$. It is
shown how deformations of $L$ which keep the boundary of $L$ confined to $W$
can be described by an elliptic boundary value problem, and two results about
minimal Lagrangian submanifolds with boundary are derived using this fact. The
first is that the space of minimal Lagrangian submanifolds near $L$ with
boundary on $W$ is found to be finite dimensional and is parametrised over the
space of harmonic 1-forms of $L$ satisfying Neumann boundary conditions. The
second is that if $W'$ is a symplectic, codimension 2 submanifold sufficiently
near $W$, then under suitable conditions, there exists a minimal Lagrangian
submanifold $L'$ near $L$ with boundary on $W'$.


  A classifier is developed that defines a joint distribution of global
character features, number of sub-units and local sub-unit features to model
Hindi online handwritten characters. The classifier uses latent variables to
model the structure of sub-units. The classifier uses histograms of points,
orientations, and dynamics of orientations (HPOD) features to represent
characters at global character level and local sub-unit level and is
independent of character stroke order and stroke direction variations. The
parameters of the classifier is estimated using maximum likelihood method.
Different classifiers and features used in other studies are considered in this
study for classification performance comparison with the developed classifier.
The classifiers considered are Second Order Statistics (SOS), Sub-space (SS),
Fisher Discriminant (FD), Feedforward Neural Network (FFN) and Support Vector
Machines (SVM) and the features considered are Spatio Temporal (ST), Discrete
Fourier Transform (DFT), Discrete Cosine Transform (SCT), Discrete Wavelet
Transform (DWT), Spatial (SP) and Histograms of Oriented Gradients (HOG). Hindi
character datasets used for training and testing the developed classifier
consist of samples of handwritten characters from 96 different character
classes. There are 12832 samples with an average of 133 samples per character
class in the training set and 2821 samples with an average of 29 samples per
character class in the testing set. The developed classifier has the highest
accuracy of 93.5\% on the testing set compared to that of the classifiers
trained on different features extracted from the same training set and
evaluated on the same testing set considered in this study.


  In the context of search and rescue, we consider the problem of mission
planning for heterogeneous teams that can include human, robotic, and animal
agents. The problem is tackled using a mixed integer mathematical programming
formulation that jointly determines the path and the activity scheduling of
each agent in the team. Based on the mathematical formulation, we propose the
use of soft constraints and penalties that allow the flexible strategic control
of spatio-temporal relations among the search trajectories of the agents. In
this way, we can enable the mission planner to obtain solutions that maximize
the area coverage and, at the same time, control the spatial proximity among
the agents (e.g., to minimize mutual task interference, or to promote local
cooperation and data sharing). Through simulation experiments, we show the
application of the strategic framework considering a number of scenarios of
interest for real-world search and rescue missions.


  Most distortion correction methods focus on simple forms of distortion, such
as radial or linear distortions. These works undistort images either based on
measurements in the presence of a calibration grid, or use multiple views to
find point correspondences and predict distortion parameters. When possible
distortions are more complex, e.g. in the case of a camera being placed behind
a refractive surface such as glass, the standard method is to use a calibration
grid. Considering a high variety of distortions, it is nonviable to conduct
these measurements. In this work, we present a single view distortion
correction method which is capable of undistorting images containing
arbitrarily complex distortions by exploiting recent advancements in
differentiable image sampling and in the usage of semantic information to
augment various tasks. The results of this work show that our model is able to
estimate and correct highly complex distortions, and that incorporating
semantic information mitigates the process of image undistortion.


  This work proposes a new method for computing acceptance regions of exact
multinomial tests. From this an algorithm is derived, which finds exact
p-values for tests of simple multinomial hypotheses. Using concepts from
discrete convex analysis, the method is proven to be exact for various popular
test statistics, including Pearson's chi-square and the log-likelihood ratio.
The proposed algorithm improves greatly on the naive approach using full
enumeration of the sample space. However, its use is limited to multinomial
distributions with a small number of categories, as the runtime grows
exponentially in the number of possible outcomes.
  The method is applied in a simulation study and uses of multinomial tests in
forecast evaluation are outlined. Additionally, properties of a test statistic
using probability ordering, referred to as the "exact multinomial test" by some
authors, are investigated and discussed. The algorithm is implemented in the
accompanying R package ExactMultinom.


  In this work, we present a new way to compute the Taylor polynomial of the
matrix exponential which reduces the number of matrix multiplications in
comparison with the de-facto standard Patterson-Stockmeyer method. This
reduction is sufficient to make the method superior in performance to Pad\'e
approximants by 10-30% over a range of values for the matrix norms and thus we
propose its replacement in standard software kits. Numerical experiments show
the performance of the method and illustrate its stability.


  Personalized federated learning (PFL) has been widely investigated to address
the challenge of data heterogeneity, especially when a single generic model is
inadequate in satisfying the diverse performance requirements of local clients
simultaneously. Existing PFL methods are inherently based on the idea that the
relations between the generic global and personalized local models are captured
by the similarity of model weights. Such a similarity is primarily based on
either partitioning the model architecture into generic versus personalized
components, or modeling client relationships via model weights. To better
capture similar (yet distinct) generic versus personalized model
representations, we propose \textit{spectral distillation}, a novel
distillation method based on model spectrum information. Building upon spectral
distillation, we also introduce a co-distillation framework that establishes a
two-way bridge between generic and personalized model training. Moreover, to
utilize the local idle time in conventional PFL, we propose a wait-free local
training protocol. Through extensive experiments on multiple datasets over
diverse heterogeneous data settings, we demonstrate the outperformance and
efficacy of our proposed spectral co-distillation method, as well as our
wait-free training protocol.


  We present an efficient physics-informed neural networks (PINNs) framework,
termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of
interface problems with discontinuous coefficients and/or interfacial jumps.
This framework is an enhanced version of its predecessor, Interface PINNs or
I-PINNs (Sarma et al.; https://dx.doi.org/10.2139/ssrn.4766623), which involves
domain decomposition and assignment of different predefined activation
functions to the neural networks in each subdomain across a sharp interface,
while keeping all other parameters of the neural networks identical. In
AdaI-PINNs, the activation functions vary solely in their slopes, which are
trained along with the other parameters of the neural networks. This makes the
AdaI-PINNs framework fully automated without requiring preset activation
functions. Comparative studies on one-dimensional, two-dimensional, and
three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs
outperform I-PINNs, reducing computational costs by 2-6 times while producing
similar or better accuracy.


  We propose a precision measurement of time variations of the proton-electron
mass ratio using ultracold molecules in an optical lattice. Vibrational energy
intervals are sensitive to changes of the mass ratio. In contrast to
measurements that use hyperfine-interval-based atomic clocks, the scheme
discussed here is model-independent and does not require separation of time
variations of different physical constants. The possibility of applying the
zero-differential-Stark-shift optical lattice technique is explored to measure
vibrational transitions at high accuracy.


  In this paper, we study phase diagram of a system of two-component hard-core
bosons with nearest-neighbor (NN) pseudo-spin antiferromagnetic (AF)
interactions in a stacked triangular lattice. Hamiltonian of the system
contains three parameters one of which is the hopping amplitude $t$ between NN
sites, and the other two are the NN pseudo-spin exchange interaction $J$ and
the one that measures anisotropy of pseudo-spin interactions. We investigate
the system by means of the Monte-Carlo simulations and clarify the
low-temperature phase diagram. In particular, we are interested in how the
competing orders, i.e., AF order and superfluidity, are realized, and also
whether supersolid forms as a result of hole doping into the state of the
$\sqrt{3}\times \sqrt{3}$ pseudo-spin pattern with the $120^o$ structure.


  Bell (1988) introduced the one-switch property for preferences over sequences
of dated outcomes. This property concerns the effect of adding a common delay
to two such sequences: it says that the preference ranking of the delayed
sequences is either independent of the delay, or else there is a unique delay
such that one strict ranking prevails for shorter delays and the opposite
strict ranking for longer delays. For preferences that have a discounted
utility (DU) representation, Bell (1988) argues that the only discount
functions consistent with the one-switch property are sums of exponentials.
This paper proves that discount functions of the linear times exponential form
also satisfy the one-switch property. We further demonstrate that preferences
which have a DU representation with a linear times exponential discount
function exhibit increasing impatience (Takeuchi (2011)). We also clarify an
ambiguity in the original Bell (1988) definition of the one-switch property by
distinguishing a weak one-switch property from the (strong) one-switch
property. We show that the one-switch property and the weak one-switch property
definitions are equivalent in a continuous-time version of the Anscombe and
Aumann (1963) setting.


  In this paper, we study a sextic del Pezzo fibration over a curve
comprehensively. We obtain certain formulae of several basic invariants of such
a fibration. We also establish the embedding theorem of such a fibration which
asserts that every such a fibration is a relative linear section of a Mori
fiber space with the general fiber $(\mathbb{P}^{1})^{3}$ and that with the
general fiber $(\mathbb{P}^{2})^{2}$. As an application of this embedding
theorem, we classify singular fibers of such a fibrations and answer a question
of T. Fujita about existence of non-normal fibers.


  In this paper, we propose a novel adaptive stochastic extended iterative
method, which can be viewed as an improved extension of the randomized extended
Kaczmarz (REK) method, for finding the unique minimum Euclidean norm
least-squares solution of a given linear system. In particular, we introduce
three equivalent stochastic reformulations of the linear least-squares problem:
stochastic unconstrained and constrained optimization problems, and the
stochastic multiobjective optimization problem. We then alternately employ the
adaptive variants of the stochastic heavy ball momentum (SHBM) method, which
utilize iterative information to update the parameters, to solve the stochastic
reformulations. We prove that our method converges linearly in expectation,
addressing an open problem in the literature related to designing theoretically
supported adaptive SHBM methods. Numerical experiments show that our adaptive
stochastic extended iterative method has strong advantages over the
non-adaptive one.