  The treatment of mixing processes is still one of the major uncertainties in
1D stellar evolution models. This is mostly due to the need to parametrize and
approximate aspects of hydrodynamics in hydrostatic codes. In particular, the
effect of hydrodynamic instabilities in rotating stars, for example, dynamical
shear instability, evades consistent description. We intend to study the
accuracy of the diffusion approximation to dynamical shear in hydrostatic
stellar evolution models by comparing 1D models to a first-principle
hydrodynamics simulation starting from the same initial conditions. We chose an
initial model calculated with the stellar evolution code GENEC that is just at
the onset of a dynamical shear instability but does not show any other
instabilities (e.g., convection). This was mapped to the hydrodynamics code SLH
to perform a 2D simulation in the equatorial plane. We compare the resulting
profiles in the two codes and compute an effective diffusion coefficient for
the hydro simulation. Shear instabilities develop in the 2D simulation in the
regions predicted by linear theory to become unstable in the 1D model. Angular
velocity and chemical composition is redistributed in the unstable region,
thereby creating new unstable regions. Eventually the 2D simulation settles in
a symmetric, steady state, which is Richardson stable everywhere, whereas the
instability remains for longer in the 1D model due to current limitations in
the 1D code. A spatially resolved diffusion coefficient is extracted by
comparing the initial and final profiles of mean atomic mass. The presented
simulation gives a first insight on hydrodynamics of shear instabilities in a
real stellar environment and even allows us to directly extract an effective
diffusion coefficient. We see evidence for a critical Richardson number of 0.25
as regions above this value remain stable for the course of the simulation.


  The photometric time series of solar-like stars can exhibit rotational
modulation due to active regions co-rotating with the stellar surface, allowing
us to constrain stellar rotation and magnetic activity. In this work we
investigate the behavior, particularly the variability, of the photometric
magnetic activity of Kepler solar-like stars and compare it with that of the
Sun. We adopted the photometric magnetic activity proxy Sph, which was computed
with a cadence of 5 x the rotation period, Prot. The average Sph was taken as
the mean activity level, and the standard deviation was taken as a measure of
the temporal variation of the magnetic activity over the observations. We also
analyzed Sun-as-a-star photometric data from VIRGO. Sun-like stars were
selected from a very narrow parameter space around the solar properties. We
also looked into KIC 8006161 (HD 173701), an active metal-rich G dwarf, and we
compared its magnetic activity to that of stars with similar stellar
parameters. We find that the amplitude of Sph variability is strongly
correlated with its mean value, independent of spectral type. An equivalent
relationship has been found for ground-based observations of chromospheric
activity emission and magnetic field strength, but in this work we show that
photometric Kepler data also present the same behavior. While, depending on the
cycle phase, the Sun is among the less active stars, we find that the solar Sph
properties are consistent with those observed in Kepler Sun-like stars. KIC
8006161 is, however, among the most active of its peers, which tend to be
metal-rich. This results from an underlying relationship between Prot and
metallicity and supports the following interpretation of the magnetic activity
of KIC 8006161: its strong activity is a consequence of its high metallicity,
which affects the depth of the convection zone and, consequently, the
efficiency of the dynamo.


  The maximum gap $g(f)$ of a polynomial $f$ is the maximum of the differences
(gaps) between two consecutive exponents that appear in $f$. Let $\Phi_{n}$ and
$\Psi_{n}$ denote the $n$-th cyclotomic and $n$-th inverse cyclotomic
polynomial, respectively. In this paper, we give several lower bounds for
$g(\Phi_{n})$ and $g(\Psi_{n})$, where $n$ is the product of odd primes. We
observe that they are very often exact. We also give an exact expression for
$g(\Psi_{n})$ under a certain condition. Finally we conjecture an exact
expression for $g(\Phi_{n})$ under a certain condition.


  The formation of singularity and breakdown of strong solutions to the
two-dimensional (2D) Cauchy problem of the full compressible Navier-Stokes
equations with zero heat conduction are considered. It is shown that for the
initial density allowing vacuum, the strong solution exists globally if the
density $\rho$ and the pressure $P$ satisfy
$\|\rho\|_{L^{\infty}(0,T;L^\infty)}+\|P\|_{L^{\infty}(0,T;L^\infty)}<\infty$.
In addition, the initial density can even have compact support. The
logarithm-type estimate for the Lam{\'e} system and some weighted estimates
play a crucial role in the proof.


  The accurate determination of transport coefficients in numerical simulations
is becoming increasingly important in a wide range of applications. Here we
consider the linear response in systems driven away from thermal equilibrium
into a non-equilibrium steady state with non-vanishing entropy production rate.
A simple derivation of a general response formula is presented. For Markov
processes we explicitly construct the conjugate quantities and discuss their
relation with known response formulas. Emphasis is put on the formal analogy
with thermodynamic potentials and some consequences are discussed.


  Describing particle transport at the macroscopic or mesoscopic level in
non-ideal environments poses fundamental theoretical challenges in domains
ranging from inter and intra-cellular transport in biology to diffusion in
porous media. Yet, often the nature of the constraints coming from many-body
interactions or reflecting a complex and confining environment are better
understood and modeled at the microscopic level.
  In this paper we investigate the subtle link between microscopic exclusion
processes and the mean-field equations that ensue from them in the continuum
limit. We derive a generalized nonlinear advection diffusion equation suitable
for describing transport in a inhomogeneous medium in the presence of an
external field. Furthermore, taking inspiration from a recently introduced
exclusion process involving agents with non-zero size, we introduce a modified
diffusion equation appropriate for describing transport in a non-ideal fluid of
$d$-dimensional hard spheres.
  We consider applications of our equations to the problem of diffusion to an
absorbing sphere in a non-ideal self-crowded fluid and to the problem of
gravitational sedimentation. We show that our formalism allows one to recover
known results. Moreover, we introduce the notions of point-like and extended
crowding, which specify distinct routes for obtaining macroscopic transport
equations from microscopic exclusion processes.


  Designing controllers to achieve natural motor capabilities for multi-joint
robots is a significant challenge. However, animals in nature are naturally
with basic motor abilities and can master various complex motor skills through
acquired learning. On the basis of analyzing the mechanism of the central motor
system in mammals, we propose a novel pre-training reinforcement learning
algorithm that enables robots to learn rich motor skills and apply them to
complex task environments without relying on external data. We first design a
skill based network similar to the cerebellum by utilizing the selection
mechanism of voluntary movements in the basal ganglia and the basic motor
regulation ability of the cerebellum. Subsequently, by imitating the structure
of advanced centers in the central motor system, we propose a high-level policy
to generate different skill combinations, thereby enabling the robot to acquire
natural motor abilities. We conduct experiments on 4 types of robots and 22
task environments, and the results show that the proposed method can enable
different types of robots to achieve flexible motor skills. Overall, our
research provides a promising framework for the design of neural network motor
controllers.


  In this paper, we show that if $(X,g)$ is an oriented four dimensional
Einstein manifold which is self-dual or anti-self-dual then superminimal
surfaces in $X$ of appropriate spin enjoy the Calabi-Yau property, meaning that
every immersed surface of this type from a bordered Riemann surface can be
uniformly approximated by complete superminimal surfaces with Jordan
boundaries. The proof uses the theory of twistor spaces and the Calabi-Yau
property of holomorphic Legendrian curves in complex contact manifolds.


  We introduce Directional Stimulus Prompting, a novel framework for guiding
black-box large language models (LLMs) toward specific desired outputs. Instead
of directly adjusting LLMs, our method employs a small tunable policy model
(e.g., T5) to generate an auxiliary directional stimulus prompt for each input
instance. These directional stimulus prompts act as nuanced, instance-specific
hints and clues to guide LLMs in generating desired outcomes, such as including
specific keywords in the generated summary. Our approach sidesteps the
challenges of direct LLM tuning by optimizing the policy model to explore
directional stimulus prompts that align LLMs with desired behaviors. The policy
model can be optimized through 1) supervised fine-tuning using labeled data and
2) reinforcement learning from offline or online rewards based on the LLM's
output. We assess our method across summarization, dialogue response
generation, and chain-of-thought reasoning tasks. Our experiments demonstrate
that the framework consistently improves LLMs' (e.g., ChatGPT, Codex,
InstructGPT) performance on these supervised tasks using minimal labeled data.
Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances
ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully
supervised start-of-the-art models. Additionally, the instance-specific
chain-of-thought prompt generated by our approach improves InstructGPT's
reasoning accuracy compared to human-crafted or automatically generated
prompts. The code and data are publicly available at
\url{https://github.com/Leezekun/Directional-Stimulus-Prompting}.


  We propose a chemical potential dependent effective gluon propagator and
study the chiral quark condensate in strongly interacting matter in the
framework of Dyson-Schwinger equation approach. The obtained results manifest
that, as the effect of the chemical potential on the effective gluon propagator
is taken into account, the chiral quark condensate decreases gradually with the
increasing of the chemical potential if it is less than the critical value, and
the condensate vanishes suddenly at the critical chemical potential. The
inclusion of the chemical potential in the effective gluon propagator enhances
the decreasing rate and decreases the critical chemical potential. It indicates
that the chiral symmetry can be restored completely at a critical chemical
potential and restored partially as the chemical potential is less than the
critical value. If the effective gluon propagator is independent of the
chemical potential, the chiral symmetry can only be restored suddenly but no
gradual restoration.


  The properties of a locally frozen (in a region of diameter 0.5 mm) magnetic
field in a YBa2Cu3O7-x slab 0.5 mm thick are investigated as a function of the
value of the excitation field, the regime of freezing, and the transport
current through the sample. The first regime is cooling of the ceramic to 77 K
in the excitation field with a subsequent turning off of the excitation field,
and the second regime is cooling in the Earth's magnetic field with a
subsequent turning on and off of the excitation field. At an excitation field
up to 2000 A/m in these regimes two different types of macroscopic current
vortex structures, which generate the frozen field, are formed. The local
critical field of excitation when the vortex structure is formed in the second
regime exceeds the uniform perpendicular critical field of the slab by a factor
of 10 and equals 1700 A/m. On the other hand, the vortex structure of the first
type can be formed by practically any weak excitation field, including fields
smaller than the critical field of the vortex structure of the second type. In
a representation of the ceramic as a Josephson medium, physical models of the
two types of vortex structures are proposed which correspond most fully to the
results of experiments. The displacement of the vortex structure of the first
type upon the passage of transport current through the slab, as a result of the
action of the Lorentz force on that structure, is registered. This makes it
possible to calculate the pinning force Fp and to estimate the value of the
viscosity n for the motion of such a vortex structure in the ceramic: Fp=6x10-8
N, n =6x10-5 kg/s.


  The situational analysis lies in the basis of space and ground-based
experiment planning. It is connected with the use of complex computation models
of environment and with verification of the restricting conditions, due to the
character of the conducted experiments and the solved scientific tasks. The
present work proposes a formulation of the situational analysis on the basis of
the finite abstract automata theory. On this basis, optimization of the
situational analysis is suggested by formal schemes for adaptation to the
conditions of the model environment. The efficiency enhancement is illustrated
by results from the application of the proposed real-time optimization for
photometric system control.


  Holographic dark energy theories present a fascinating interface to probe
late-time cosmology, as guided by contemporary ideas about quantum gravity. In
this work, we present a new holographic dark energy scenario designated
Fractional Holographic Dark Energy (FHDE). This model extends the conventional
framework of HDEs by incorporating specific features from fractional calculus
recently applied, e.g., in cosmological settings. In this manner, we retrieve a
novel form of HDE energy density. We then show how FHDE can provide a
consistent picture of the evolution of the late-time universe even with the
simple choice of the Hubble horizon as the IR (infrared) cutoff. We provide
detailed descriptions of the cosmological evolution, showing how the fractional
calculus ingredients can alleviate quite a few issues associated with the
conventional HDE scenario. Concretely, we compute and plot diagrams using the
Hubble horizon cutoff for HDE. The density parameters for DE and dark matter
(DM), the deceleration parameter, and the DE EoS parameter indicate how the
universe may evolve within our FHDE model, fitting within an appropriate
scenario of late-time cosmology.


  The elastodynamic Peach-Koehler force is computed for a fully-regularized
straight dislocation with isotropic core in continuum isotropic elastic
elasticity, in compact forms involving partial mass or impulsion functions
relative to shear and compressional waves. The force accounts for both dynamic
radiation damping and inertia. The expressions are valid indifferently for
subsonic or supersonic velocities. Results are compared with the case of a
flat-core dislocation of the Peierls-Eshelby type, for a motion of jump from
rest to constant velocity. In the steady-state limit, the Lagrangian function
relevant to expressing the force in the flat-core case must be replaced by a
related but different function for the regularized dislocation. However, by
suitably defining the regularizing dislocation width, the steady-state limits
of the force for the fully-regularized and flat-core dislocations can be
matched exactly.


  Silicon nanocrystals (SiNCs) have been under active investigation in the last
decades and have been considered as a promising candidate for many
optoelectronic applications including highly-efficient solar cells. Some of the
fundamental properties of interest in these nanostructures is the temperature
dependence of their optical absorption onset, and how this is controlled by
different passivation regimes. In the present work we employ first-principles
calculations in conjunction with the special displacement method to study the
temperature dependence of the band gap renormalization of free-standing
hydrogen-terminated, and oxidized SiNCs, as well as matrix-embedded SiNCs in
amorphous silica, and we obtain good agreement with experimental
photoluminescence data. We also provide strong evidence that the
electron-phonon interplay at the surface of the nanocrystal is suppressed by
oxidation and the surrounding amorphous matrix. For the matrix-embedded SiNCs,
we show a high correlation between the temperature dependence of the band gap
and the Si-Si strained bonds. This result emphasizes the immanent relationship
of electron-phonon coupling and thermal structural distortions. We also
demonstrate that, apart from quantum confinement, Si- Si strained bonds are the
major cause of zero-phonon quasidirect transitions in matrix-embedded SiNCs. As
a final point, we clarify that, unlike optical absorption in bulk Si,
phonon-assisted electronic transitions play a secondary role in SiNCs.


  Neutral pions have been measured in $^3$He+Au collisions at
$\sqrt{s_{_{NN}}}$=200 GeV up to 20 GeV/$c$ in the RHIC Year-2014 run. The
nuclear modification factor $R_{\rm AA}$ was measured and compared with that
from $d$+Au collisions. The integrated $R_{\rm AA}$ as a function of $N_{\rm
part}$ was calculated for $d$+Au, $^3$He+Au and Au+Au collisions at
$\sqrt{s_{_{NN}}}$=200 GeV, and found to converge for $N_{\rm part}>$12, while
a clear system ordering $R_{\rm dAu}$$>$$R_{\rm HeAu}$$>$$R_{\rm AuAu}$ was
observed for $N_{\rm part}<$12. The fractional momentum loss for the most
central $^3$He+Au collisions was also estimated.


  We present here an analysis of the light curves of 5.3 million stars in the
Small Magellanic Cloud observed by EROS (Exp\'erience de Recherche d'Objets
Sombres). One star exhibits a variation that is best interpreted as due to
gravitational microlensing by an unseen object. This candidate was also
reported by the MACHO collaboration. Once corrected for blending, the Einstein
radius crossing time is 123 days, corresponding to lensing by a Halo object of
$2.6^{+8.2}_{-2.3} M_{\odot}$. The maximum magnification is a factor of 2.6.
The light curve also displays a periodic modulation with a 2.5% amplitude and a
period of 5.1 days. Parallax analysis of the candidate indicates that a Halo
lens would need to have a mass of at least $0.3 M_{\odot}$, although a lens in
the SMC could have a mass as low as $0.07 M_{\odot}}$. We estimate the optical
depth for microlensing towards the SMC due to this event to be $\sim 3.3 \times
10^{-7}$, with an uncertainty dominated by Poisson statistics. We show that
this optical depth corresponds to about half that expected for a spherical
isothermal Galactic Halo comprised solely of such objects, and that it is
consistent with SMC self-lensing if the SMC is elongated along the
line-of-sight by at least 5 kpc.


  Many applications of imitation learning require the agent to generate the
full distribution of behaviour observed in the training data. For example, to
evaluate the safety of autonomous vehicles in simulation, accurate and diverse
behaviour models of other road users are paramount. Existing methods that
improve this distributional realism typically rely on hierarchical policies.
These condition the policy on types such as goals or personas that give rise to
multi-modal behaviour. However, such methods are often inappropriate for
stochastic environments where the agent must also react to external factors:
because agent types are inferred from the observed future trajectory during
training, these environments require that the contributions of internal and
external factors to the agent behaviour are disentangled and only internal
factors, i.e., those under the agent's control, are encoded in the type.
Encoding future information about external factors leads to inappropriate agent
reactions during testing, when the future is unknown and types must be drawn
independently from the actual future. We formalize this challenge as
distribution shift in the conditional distribution of agent types under
environmental stochasticity. We propose Robust Type Conditioning (RTC), which
eliminates this shift with adversarial training under randomly sampled types.
Experiments on two domains, including the large-scale Waymo Open Motion
Dataset, show improved distributional realism while maintaining or improving
task performance compared to state-of-the-art baselines.


  We perform an $\textit{ab initio}$ calculation of the $N_c$ scaling of the
low-energy couplings of the chiral Lagrangian of low-energy strong
interactions, extracted from the mass dependence of meson masses and decay
constants. We compute these observables on the lattice with four degenerate
fermions, $N_f=4$, and varying number of colours, $N_c=3-6$, at a lattice
spacing of $a\simeq 0.075$ fm. We find good agreement with the expected $N_c$
scaling and measure the coefficients of the leading and subleading terms in the
large $N_c$ expansion. From the subleading $N_c$ corrections, we can also infer
the $N_f$ dependence, that we use to extract the value of the low-energy
couplings for different values of $N_f$. We find agreement with previous
determinations at $N_c=3$ and $N_f=2, 3$ and also, our results support a strong
paramagnetic suppression of the chiral condensate in moving from $N_f=2$ to
$N_f=3$.


  We present the first results from an all-sky all-frequency (ASAF) search for
an anisotropic stochastic gravitational-wave background using the data from the
first three observing runs of the Advanced LIGO and Advanced Virgo detectors.
Upper limit maps on broadband anisotropies of a persistent stochastic
background were published for all observing runs of the LIGO-Virgo detectors.
However, a broadband analysis is likely to miss narrowband signals as the
signal-to-noise ratio of a narrowband signal can be significantly reduced when
combined with detector output from other frequencies. Data folding and the
computationally efficient analysis pipeline, {\tt PyStoch}, enable us to
perform the radiometer map-making at every frequency bin. We perform the search
at 3072 {\tt{HEALPix}} equal area pixels uniformly tiling the sky and in every
frequency bin of width $1/32$~Hz in the range $20-1726$~Hz, except for bins
that are likely to contain instrumental artefacts and hence are notched. We do
not find any statistically significant evidence for the existence of narrowband
gravitational-wave signals in the analyzed frequency bins. Therefore, we place
$95\%$ confidence upper limits on the gravitational-wave strain for each
pixel-frequency pair, the limits are in the range $(0.030 - 9.6)
\times10^{-24}$. In addition, we outline a method to identify candidate
pixel-frequency pairs that could be followed up by a more sensitive (and
potentially computationally expensive) search, e.g., a matched-filtering-based
analysis, to look for fainter nearly monochromatic coherent signals. The ASAF
analysis is inherently independent of models describing any spectral or spatial
distribution of power. We demonstrate that the ASAF results can be
appropriately combined over frequencies and sky directions to successfully
recover the broadband directional and isotropic results.


  This paper addresses the pursuit-evasion problem involving three agents -- a
purser, an evader, and a defender. We develop cooperative guidance laws for the
evader-defender team that guarantee that the defender intercepts the pursuer
before it reaches the vicinity of the evader. Unlike heuristic methods, optimal
control, differential game formulation, and recently proposed time-constrained
guidance techniques, we propose a geometric solution to safeguard the evader
from the pursuer's incoming threat. The proposed strategy is computationally
efficient and expected to be scalable as the number of agents increases.
Another alluring feature of the proposed strategy is that the evader-defender
team does not require the knowledge of the pursuer's strategy and that the
pursuer's interception is guaranteed from arbitrary initial engagement
geometries. We further show that the necessary error variables for the
evader-defender team vanish within a time that can be exactly prescribed prior
to the three-body engagement. Finally, we demonstrate the efficacy of the
proposed cooperative defense strategy via simulation in diverse engagement
scenarios.


  We construct a class of renormalizable models for lepton mixing that generate
predictions given in terms of the charged-lepton mass ratios. We show that one
of those models leads, when one takes into account the known experimental
values, to almost maximal CP-breaking phases and to almost maximal neutrinoless
double-beta decay. We study in detail the scalar potential of the models,
especially the bounds imposed by unitarity on the values of the quartic
couplings.


  Making use of the gauge/string duality, it is possible to study some aspects
of the string breaking phenomenon in the three quark system. Our results point
out that the string breaking distance is not universal and depends on quark
geometry. The estimates of the ratio of the string breaking distance in the
three quark system to that in the quark-antiquark system would range
approximately from $\frac{2}{3}$ to $1$. In addition, it is shown that there
are special geometries which allow more than one breaking distance.


  In this paper, we consider the Cauchy problem of the incompressible liquid
crystal equations in $n$ dimensions. We prove the local well-posedness of mild
solutions to the liquid crystal equations with $L^\infty$ initial data, in
particular, the initial energy may be infinite. We prove that the solutions are
smooth with respect to the space variables away from the initial time. Based on
this regularity estimate, we employ the blow up argument and Liouville type
theorems to establish vorticity direction type blow up criterions for the type
I mild solutions established in the present paper.


  Reverberation can severely degrade the quality of speech signals recorded
using microphones in an enclosure. In acoustic sensor networks with spatially
distributed microphones, a similar dereverberation performance may be achieved
using only a subset of all available microphones. Using the popular convex
relaxation method, in this paper we propose to perform microphone subset
selection for the weighted prediction error (WPE) multi-channel dereverberation
algorithm by introducing a group sparsity penalty on the prediction filter
coefficients. The resulting problem is shown to be solved efficiently using the
accelerated proximal gradient algorithm. Experimental evaluation using measured
impulse responses shows that the performance of the proposed method is close to
the optimal performance obtained by exhaustive search, both for
frequency-dependent as well as frequency-independent microphone subset
selection. Furthermore, the performance using only a few microphones for
frequency-independent microphone subset selection is only marginally worse than
using all available microphones.


  Coarse grained molecular dynamics simulations are presented in which the
sensitivity of the ice nucleation rate to the hydrophilicity of a graphene
nanoflake is investigated. We find that an optimal interaction strength for
promoting ice nucleation exists, which coincides with that found previously for
a face centered cubic (111) surface. We further investigate the role that the
layering of interfacial water plays in heterogeneous ice nucleation and
demonstrate that the extent of layering is not a good indicator of ice
nucleating ability for all surfaces. Our results suggest that to be an
efficient ice nucleating agent, a surface should not bind water too strongly if
it is able to accommodate high coverages of water.


  The previous smart contract code comment (SCC) generation approaches can be
divided into two categories: fine-tuning paradigm-based approaches and
information retrieval-based approaches. However, for the fine-tuning
paradigm-based approaches, the performance may be limited by the quality of the
gathered dataset for the downstream task and they may have knowledge-forgetting
issues. While for the information retrieval-based approaches, it is difficult
for them to generate high-quality comments if similar code does not exist in
the historical repository. Therefore we want to utilize the domain knowledge
related to SCC generation in large language models (LLMs) to alleviate the
disadvantages of these two types of approaches. In this study, we propose an
approach SCCLLM based on LLMs and in-context learning. Specifically, in the
demonstration selection phase, SCCLLM retrieves the top-k code snippets from
the historical corpus by considering syntax, semantics, and lexical
information. In the in-context learning phase, SCCLLM utilizes the retrieved
code snippets as demonstrations, which can help to utilize the related
knowledge for this task. We select a large corpus from a smart contract
community Etherscan.io as our experimental subject. Extensive experimental
results show the effectiveness of SCCLLM when compared with baselines in
automatic evaluation and human evaluation.


  We give criteria for products of Toeplitz and Hankel operators on the Fock
(Segal-Bargmann) space to belong to the Dixmier class, and compute their
Dixmier trace. At the same time, analogous results for the Weyl
pseudodifferential operators are also obtained.


  We study online multidimensional variants of the generalized assignment
problem which are used to model prominent real-world applications, such as the
assignment of virtual machines with multiple resource requirements to physical
infrastructure in cloud computing. These problems can be seen as an extension
of the well known secretary problem and thus the standard online worst-case
model cannot provide any performance guarantee. The prevailing model in this
case is the random-order model, which provides a useful realistic and robust
alternative. Using this model, we study the $d$-dimensional generalized
assignment problem, where we introduce a novel technique that achieves an
$O(d)$-competitive algorithms and prove a matching lower bound of $\Omega(d)$.
Furthermore, our algorithm improves upon the best-known competitive-ratio for
the online (one-dimensional) generalized assignment problem and the online
knapsack problem.


  For most black holes in string theory, the Schwarzschild radius in string
units decreases as the string coupling is reduced. We formulate a
correspondence principle, which states that (i) when the size of the horizon
drops below the size of a string, the typical black hole state becomes a
typical state of strings and D-branes with the same charges, and (ii) the mass
does not change abruptly during the transition. This provides a statistical
interpretation of black hole entropy. This approach does not yield the
numerical coefficient, but gives the correct dependence on mass and charge in a
wide range of cases, including neutral black holes.


  The Ethereum block-building process has changed significantly since the
emergence of Proposer-Builder Separation. Validators access blocks through a
marketplace, where block builders bid for the right to construct the block and
earn MEV (Maximal Extractable Value) rewards in an on-chain competition, known
as the MEV-boost auction. While more than 90% of blocks are currently built via
MEV-Boost, trade-offs between builders' strategic behaviors and auction design
remain poorly understood. In this paper we address this gap. We introduce a
game-theoretic model for MEV-Boost auctions and use simulations to study
different builders' bidding strategies observed in practice. We study various
strategic interactions and auction setups and evaluate how the interplay
between critical elements such as access to MEV opportunities and improved
connectivity to relays impact bidding performance. Our results demonstrate the
importance of latency on the effectiveness of builders' strategies and the
overall auction outcome from the proposer's perspective.


  We show that a single exciton state in an individual ordered conjugated
polymer chain exhibits macroscopic quantum spatial coherence reaching tens of
microns, limited by the chain length. The spatial coherence of the k=0 exciton
state is demonstrated by selecting two spatially separated emitting regions of
the chain and observing their interference.


  In this paper, we obtain order estimates for the Kolmogorov widths of
periodic Sobolev classes with restictions on derivatives of order $r_j$ with
respect to $j$th variable in metrics $L_{p_j}$ ($1\le j\le d$).


  The scalar field associated with fluctuations in the positions of the two
branes, the ``radion'', plays an important role determining the cosmology and
collider phenomenology of the Randall-Sundrum solution to the hierarchy
problem. It is now well known that the radion mass is of order the weak scale,
and that its couplings to standard model fields are order 1/TeV to the trace of
the energy momentum tensor. We calculate longitudinal vector boson scattering
amplitudes to explore the constraints on the radion mass and its coupling from
perturbative unitarity. The scattering cross section can indeed become
non-perturbative at energies prior to reaching the TeV brane cutoff scale, but
only when some curvature-Higgs mixing on the TeV brane is present. We show that
the coefficient of the curvature-Higgs mixing operator must be less than about
3 for the 4-d effective theory to respect perturbative unitarity up to the TeV
brane cutoff scale. Mass bounds on the Higgs boson and the radion are also
discussed.


  The onset of structural arrest and glass formation in a concentrated
suspension of silica nanoparticles in a water-lutidine binary mixture near its
consolute point is studied by exploiting the near-critical fluid degrees of
freedom to control the strength of an attraction between particles and
multispeckle x-ray photon correlation spectroscopy to determine the particles'
collective dynamics. This model system undergoes a glass transition both on
cooling and on heating, and the intermediate liquid realizes unusual
logarithmic relaxations. How vitrification occurs for the two different glass
transitions is characterized in detail and comparisons are drawn to recent
theoretical predictions for glass formation in systems with attractive
interactions.


  We use the Lie group analysis method to investigate the invariance properties
and the solutions of \begin{align*} x_{n+1} =\frac{x_{n-5}x_{n-3}}{x_{n-1}(a_n
+b_nx_{n-5}x_{n-3})}. \end{align*} We show that this equation has a
two-dimensional Lie algebra and that its solutions can be presented in a
unified manner. Besides presenting solutions of the recursive sequence above
where $(a_n)$ and $(b_n)$ are sequences of real numbers, some specific cases
are emphasized.


  In this paper, we present a novel state of the art system for automatic
downbeat tracking from music signals. The audio signal is first segmented in
frames which are synchronized at the tatum level of the music. We then extract
different kind of features based on harmony, melody, rhythm and bass content to
feed convolutional neural networks that are adapted to take advantage of each
feature characteristics. This ensemble of neural networks is combined to obtain
one downbeat likelihood per tatum. The downbeat sequence is finally decoded
with a flexible and efficient temporal model which takes advantage of the
metrical continuity of a song. We then perform an evaluation of our system on a
large base of 9 datasets, compare its performance to 4 other published
algorithms and obtain a significant increase of 16.8 percent points compared to
the second best system, for altogether a moderate cost in test and training.
The influence of each step of the method is studied to show its strengths and
shortcomings.


  The Kobayashi-Maskawa (KM) hypothesis about the existence of a third
generation of quarks represents a cornerstone of the Standard Model (SM). Fifty
years after this seminal paper, flavor physics continues to represent a
privileged observatory on physics occurring at high energy scales. In this
paper I first review this statement using general effective-theory arguments,
highlighting some interesting modern lessons from the KM paper. I then discuss
some novel extensions of the SM based on the concept of flavor deconstruction:
the hypothesis that gauge interactions are manifestly flavor non universal in
the ultraviolet. The phenomenological consequences of this class of models are
also briefly illustrated.


  Production of supersymmetric particles in TeV scale polarized photon-proton
collisions is discussed. Polarizations of both photon and proton beams are
considered. Associated productions of squark-chargino and squark-gluino, and
production of squark pairs have been examined. Although the cross sections for
different initial beam polarizations do not differ much, the polarization
asymmetry is sensitive to the sparticle mass. We conclude that the capacity of
future linac-ring type TeV scale photon-proton colliders is quite promising in
the search for SUSY particles.


  The link recommendation problem consists in suggesting a set of links to the
users of a social network in order to increase their social circles and the
connectivity of the network. Link recommendation is extensively studied in the
context of social networks and of general complex networks due to its wide
range of applications. Most of the existing link recommendation methods
estimate the likelihood that a link is adopted by users and recommend links
that are likely to be established. However, most of such methods overlook the
impact that the suggested links have on the capability of the network to spread
information. Indeed, such capability is directly correlated with both the
engagement of a single user and the revenue of online social networks. In this
paper, we study link recommendation systems from the point of view of
information diffusion. In detail, we consider the problem in which we are
allowed to spend a given budget to create new links so to suggest a bounded
number of possible persons to whom become friend in order to maximize the
influence of a given set of nodes. We model the influence diffusion in a
network with the popular Independent Cascade model.


  With the full Tevatron data set collected and being analyzed, many new
results have been recently released. This includes heavy flavor physics studies
such as CP violation parameter measurements with B^{+/-} -> J/\psi K^{+/-} and
B^{+/-} -> J/\psi pi^{+/-} and $D^0-D^0bar mixing. Of the QCD and electroweak
results, photon plus heavy flavor measurements and a search for anomalous
quartic gauge couplings will be reviewed. These various studies help to clarify
the agreement between data and physics models and to search for new physics.


  The neutron star X-ray binary (NSXRB) Cygnus X-2 was observed by the Swift
satellite 51 times over a 4 month period in 2008 with the XRT, UVOT, and BAT
instruments. During this campaign, we observed Cyg X-2 in all three branches of
the Z track (horizontal, normal, and flaring branches). We find that the NUV
emission is uncorrelated with the soft X-ray flux detected with the XRT, and is
anticorrelated with the BAT X-ray flux and the hard X-ray color. The observed
anticorrelation is inconsistent with simple models of reprocessing as the
source of the NUV emission. The anticorrelation may be a consequence of the
high inclination angle of Cyg X-2, where NUV emission is preferentially
scattered by a corona that expands as the disk is radiatively heated.
Alternatively, if the accretion disk thickens as Cyg X-2 goes down the normal
branch toward the flaring branch, this may be able to explain the observed
anticorrelation. In these models the NUV emission may not be a good proxy for
$\dot m$ in the system. We also discuss the implications of using Swift/XRT to
perform spectral modeling of the continuum emission of NSXRBs.


  By combining temperature-dependent resistivity and Hall effect measurements,
we investigate donor state energy in Si-doped \b{eta}-Ga2O3 films grown using
metal-organic vapor phase epitaxy (MOVPE). High magnetic field Hall effect
measurements (H = +/-90 kOe) showed non-linear Hall resistance for T < 150 K
revealing two-band conduction. Further analyses revealed carrier freeze-out
characteristics in both bands yielding donor state energies of ~ 33.7 and ~
45.6 meV. The former is consistent with the donor energy of Si in \b{eta}-Ga2O3
whereas the latter suggests a residual donor state, likely associated with a DX
center. This study provides a critical insight into the impurity band
conduction and the defect energy states in \b{eta}-Ga2O3 using high-field
magnetotransport measurements.


  We study the structure of neutron stars in scalar-tensor theories for the
nonminimal coupling of the form $(1+\kappa \xi \phi^{2})\cal R$. We solve the
hydrostatic equilibrium equations for two different types of scalar field
potentials and three different equations of state representative of different
degrees of stiffness. We obtain the mass-radius relations of the configurations
and determine the allowed ranges for the term $\xi\phi^2$ at the center of the
star and spatial infinity based on the measured maximum value of the mass for
neutron stars and the recent constraints on the radius coming from
gravitational wave observations. Thus we manage to limit the deviation of the
model from general relativity. We examine the possible constraints on the
parameters of the model and compare the obtained restrictions with the ones
inferred from other cosmological probes that give the allowed ranges for the
coupling constant only. In the case of the Higgs-like potential, we also find
that the central value for the scalar field cannot be chosen arbitrarily but it
depends on the vacuum expectation value of the field. Finally, we discuss the
effect of the scalar field potential on the mass and the radius of the star by
comparing the results obtained for the cases considered here.


  Embedded system software is highly constrained from performance, memory
footprint, energy consumption and implementing cost view point. It is always
desirable to obtain better Instructions per Cycle. Instruction cache has major
contribution in improving IPC. Cache memories are realized on the same chip
where the processor is running. This considerably increases the system cost as
well. Hence, it is required to maintain a trade off between cache sizes and
performance improvement offered. Determining the number of cache lines and size
of cache line are important parameters for cache designing. The design space
for cache is quite large. It is time taking to execute the given application
with different cache sizes on an instruction set simulator to figure out the
optimal cache size. In this paper, a technique is proposed to identify a number
of cache lines and cache line size for the L1 instruction cache that will offer
best or nearly best IPC. Cache size is derived, at a higher abstraction level,
from basic block analysis in the Low Level Virtual Machine environment. The
cache size estimated is cross validated by simulating the set of benchmark
applications with different cache sizes in simple scalar simulator. The
proposed method seems to be superior in terms of estimation accuracy and
estimation time as compared to the existing methods for estimation of optimal
cache size parameters like cache line size, number of cache lines.


  Exactly solvable $N$-dimensional model of the quantum isotropic singular
oscillator in the relativistic configurational $\vec r_N$-space is proposed. It
is shown that through the simple substitutions the finite-difference equation
for the $N$-dimensional singular oscillator can be reduced to the similar
finite-difference equation for the relativistic isotropic three-dimensional
singular oscillator. We have found the radial wavefunctions and energy spectrum
of the problem and constructed a dynamical symmetry algebra.


  This paper describes a new method of bond portfolio optimization based on
stochastic string models of correlation structure in bond returns. The paper
shows how to approximate correlation function of bond returns, compute the
optimal portfolio allocation using Wiener-Hopf factorization, and check whether
a collection of bonds presents arbitrage opportunities.


  The competition between reptation and Rouse Dynamics is incorporated in the
Rubinstein-Duke model for polymer motion by extending it with sideways motions,
which cross barriers and create or annihilate hernias. Using the Density-Matrix
Renormalization-Group Method as solver of the Master Equation, the renewal time
and the diffusion coefficient are calculated as function of the length of the
chain and the strength of the sideways motion. These new types of moves have a
strong and delicate influence on the asymptotic behavior of long polymers. The
effects are analyzed as function of the chain length in terms of effective
exponents and crossover scaling functions.


  The nilpotence order of the mod 2 Hecke operators.
  Let $\Delta=\sum_{m=0}^\infty q^{(2m+1)^2} \in F_2[[q]]$ be the reduction mod
2 of the $\Delta$ series. A modular form f modulo 2 of level 1 is a polynomial
in $\Delta$. If p is an odd prime, then the Hecke operator Tp transforms f in a
modular form Tp(f) which is a polynomial in $\Delta$ whose degree is smaller
than the degree of f, so that Tp is nilpotent. The order of nilpotence of f is
defined as the smallest integer g = g(f) such that, for every family of g odd
primes p1, p2, ..., pg, the relation Tp1Tp2... Tpg (f) = 0 holds. We show how
one can compute explicitly g(f); if f is a polynomial of degree d in $\Delta$,
one finds that g(f) << d^(1/2).


  The Douglas-Rachford algorithm is a classical and powerful splitting method
for minimizing the sum of two convex functions and, more generally, finding a
zero of the sum of two maximally monotone operators. Although this algorithm is
well understood when the involved operators are monotone or strongly monotone,
the convergence theory for weakly monotone settings is far from being complete.
In this paper, we propose an adaptive Douglas-Rachford splitting algorithm for
the sum of two operators, one of which is strongly monotone while the other one
is weakly monotone. With appropriately chosen parameters, the algorithm
converges globally to a fixed point from which we derive a solution of the
problem. When one operator is Lipschitz continuous, we prove global linear
convergence, which sharpens recent known results.


  We are currently facing a highly critical case of a world-wide pandemic. The
novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely
contagious and the original outbreak from Asia has now spread to all
continents. This situation will fruitfully profit from the study in regards of
the spread of the virus, assessing effective countermeasures to weight the
impact of the adopted strategies. The standard Susceptible-Infectious-Recovered
(SIR) model is a very successful and widely used mathematical model for
predicting the spread of an epidemic. We adopt the SIR model on a random
network and extend the model to include control strategies {\em lockdown} and
{\em testing} -- two often employed mitigation strategies. The ability of these
strategies in controlling the pandemic spread is investigated by varying the
effectiveness with which they are implemented. The possibility of a second
outbreak is evaluated in detail after the mitigation strategies are withdrawn.
We notice that, in any case, a sudden interruption of such mitigation
strategies will likely induce a resurgence of a second outbreak, whose peak
will be correlated to the number of susceptible individuals. In fact, we find
that a population will remain vulnerable to the infection until the herd
immunity is achieved. We also test our model with real statistics and
information on the epidemic spread in South Korea, Germany, and New York and
find a remarkable agreement with the simulation data.


  Knowledge of the mechanism of neutrino mass generation would help understand
a lot more about Lepton Number Violation (LNV), the cosmological evolution of
the Universe, or the evolu tion of astronomical objects. Here we propose a
verifiable and viable extension of the Standard model for neutrino mass
generation, with a low-scale seesaw mechanism via LNV condensation in the
sector of sterile neutrinos. To prove the concept, we analyze a simplified
model of just one single family of elementary particles and check it against a
set of phenomenological constraints coming from electroweak symmetry breaking,
neutrino masses, leptogenesis and dark matter. The model predicts (i) TeV scale
quasi-degenerate heavy sterile neutrinos, suitable for leptogenesis with
resonant enhancement of the CP asymmetry, (ii) a set of additional heavy Higgs
bosons whose existence can be challenged at the LHC, (iii) an additional light
and sterile Higgs scalar which is a candidate for decaying warm dark matter,
and (iv) a majoron. Since the model is based on simple and robust principles of
dynamical mass generation, its parameters are very restricted, but remarkably
it is still within current phenomenological limits.


  New images from the Hubble Space Telescope of the FRII radio galaxy Pictor A
reveal a number of jet knot candidates which coincide with previously detected
radio and x-ray knots. Previous observations in x-ray and radio bands show the
entire jet to be 1.9' long, with interesting variability, but an optical
component was previously unknown. The discovered optical component is faint,
and knot candidates must be teased out from a bright host galaxy. Using three
broadband filters, we extract knot fluxes and upper-bounds on the flux for
multiple knot candidates at wavelengths of 1600nm, 814nm and 475nm. We find
that the data suggest that localized particle re-accleration events followed by
synchrotron emission could explain the observed knot candidates, but those
electrons could not supply enough x-ray flux to match prior observations. Our
data provide key evidence suggesting a second, higher energy electron
population which was previously hypothesized, but could not be confirmed.


  We consider a cognitive radio-based Internet-of-Things (CR-IoT) network
consisting of one primary IoT (PIoT) system and one secondary IoT (SIoT)
system. The IoT devices of both the PIoT and the SIoT respectively monitor one
physical process and send randomly generated status updates to their associated
access points (APs). The timeliness of the status updates is important as the
systems are interested in the latest condition (e.g., temperature, speed and
position) of the IoT device. In this context, two natural questions arise: (1)
How to characterize the timeliness of the status updates in CR-IoT systems? (2)
Which scheme, overlay or underlay, is better in terms of the timeliness of the
status updates. To answer these two questions, we adopt a new performance
metric, named the age of information (AoI). We analyze the average peak AoI of
the PIoT and the SIoT for overlay and underlay schemes, respectively. Simple
asymptotic expressions of the average peak AoI are also derived when the PIoT
operates at high signal-to-noise ratio (SNR). Based on the asymptotic
expressions, we characterize a critical generation rate of the PIoT system,
which can determine the superiority of overlay and underlay schemes in terms of
the average peak AoI of the SIoT. Numerical results validate the theoretical
analysis and uncover that the overlay and underlay schemes can outperform each
other in terms of the average peak AoI of the SIoT for different system setups.


  We construct a metric on a vector bundle $E \rightarrow Z$ restricted to a
conic neighbourhood of a relatively compact $1$-convex section of a submersion
$Z \rightarrow X$ with at most polynomial poles at the boundary and positive
Nakano curvature tensor in bidegree $(p,q).$


  The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem
on non-atomic measure spaces. Here we prove a finite version with a completely
constructive proof.


  We present a formal quantum mechanical analysis of the communication protocol
of Prevedel {\it et al.}\ [Phys. Rev. Lett. \textbf{106}, 110505 (2011)], in
which entanglement shared by sender and receiver is used to enhance, beyond
that achievable via the optimal classical strategy, the probability of
successful transmission of a bit through a particular noisy classical channel
${\cal N}$. We provide a full analysis of this protocol when the shared
entanglement resides in a two-qubit system. Our analysis shows the measurement
choices specified by the protocol yield the maximum possible enhancement of the
probability of successful communication of the bit with one use of the channel
${\cal N}$. We determine that shared entanglement residing in a two-qudit
system with $d > 2$ cannot provide enhancement beyond that produced by
entangled qubits. Finally, we show how the protocol should be extended when
probability parameters for the channel ${\cal N}$ are allowed to vary.


  An elementary proof is given for the existence of infinite dimensional
abelian subalgebras in quantum W-algebras. In suitable realizations these
subalgebras define the conserved charges of various quantum integrable systems.
We consider all principle W-algebras associated with the simple Lie algebras.
The proof is based on the more general result that for a class of vertex
operators the quantum operators are related to their classical counterparts by
an equivalence transformation.


  We study finite-dimensional integrals in a way that elucidates the
mathematical meaning behind the formal manipulations of path integrals
occurring in quantum field theory. This involves a proper understanding of how
Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a
series expansion in a formal parameter irrespective of convergence properties.
We establish invariance properties of such a Wick expansion under coordinate
changes and the action of a Lie group of symmetries, and we use this to study
essential features of path integral manipulations, including coordinate
changes, Ward identities, Schwinger-Dyson equations, Faddeev-Popov
gauge-fixing, and eliminating fields by their equation of motion. We also
discuss the asymptotic nature of the Wick expansion and the implications this
has for defining path integrals perturbatively and nonperturbatively.


  The electrophysical properties of quasi-one-dimensional conductors with a
charge-density wave change qualitatively upon a decrease in their transverse
sizes. A brief review of various finite-size effects and the present-day
knowledge of their origin is presented.


  We discuss how to experimentally study the electroweak symmetry breaking
(EWSB) sector by observing $WW \to WW$ interactions in the TeV region. We
discuss some general features of the event structure in the signal and the
background events. Various techniques to enhance the signal-to-background ratio
are also presented. We show how to detect longitudinal W-bosons either in the
central rapidity region of the detector or in the beam pipe direction. Finally,
we globally classify the sensitivities of the Large Hadron Collider and the
Linear Colliders to probing the next-to-leading order bosonic operators of the
electroweak chiral lagrangian used to parametrize models of strongly coupled
EWSB sector.


  A recently presented method for the study of evolving self-gravitating
relativistic spheres is applied to the description of the evolution of
relativistic polytropes. Two different definitions of relativistic polytrope,
yielding the same Newtonian limit, are considered. Some examples are explicitly
worked out, describing collapsing polytropes and bringing out the differences
between both types of polytropes.


  Measurement-device-independent quantum key distribution (MDI-QKD) with
decoy-state method is believed to be securely applied to defeat various hacking
attacks in practical quantum key distribution systems. Recently, the
coherent-state superpositions (CSS) have emerged as an alternative to
single-photon qubits for quantum information processing and metrology. Here, in
this Letter, CSS are exploited as the source in MDI-QKD. We present an
analytical method which gives two tight formulas to estimate the lower bound of
yield and the upper bound of bit error rate. We exploit the standard
statistical analysis and Chernoff bound to perform the parameter estimation.
Chernoff bound can provide good bounds in the long distance MDI-QKD. Our
results show that with CSS, both the security transmission distance and secure
key rate are significantly improved compared with those of the weak coherent
states in the finite-data case.


  We investigate the target space geometry of supersymmetric sigma models in
two dimensions with Euclidean signature, and the conditions for N=2
supersymmetry. For a real action, the geometry for the N=2 model is not the
generalized Kahler geometry that arises for Lorentzian signature, but is an
interesting modification of this which is not a complex geometry.


  This work has the goal of briefly surveying some key stabilization techniques
for general nonlinear systems, for which, as it is well known, a smooth control
Lyapunov function may fail to exist. A general overview of the situation with
smooth and nonsmooth stabilization is provided, followed by a concise summary
of basic tools and techniques, including general stabilization, sliding-mode
control and nonsmooth backstepping. Their presentation is accompanied with
examples. The survey is concluded with some remarks on computational aspects
related to determination of sampling times and control actions.


  Depression is a major debilitating disorder which can affect people from all
ages. With a continuous increase in the number of annual cases of depression,
there is a need to develop automatic techniques for the detection of the
presence and extent of depression. In this AVEC challenge we explore different
modalities (speech, language and visual features extracted from face) to design
and develop automatic methods for the detection of depression. In psychology
literature, the PHQ-8 questionnaire is well established as a tool for measuring
the severity of depression. In this paper we aim to automatically predict the
PHQ-8 scores from features extracted from the different modalities. We show
that visual features extracted from facial landmarks obtain the best
performance in terms of estimating the PHQ-8 results with a mean absolute error
(MAE) of 4.66 on the development set. Behavioral characteristics from speech
provide an MAE of 4.73. Language features yield a slightly higher MAE of 5.17.
When switching to the test set, our Turn Features derived from audio
transcriptions achieve the best performance, scoring an MAE of 4.11
(corresponding to an RMSE of 4.94), which makes our system the winner of the
AVEC 2017 depression sub-challenge.


  This paper describes an issue that arises when inverting elements of the
homotopy groups of an equivariant commutative ring. Equivariant commutative
rings possess an enhanced multiplicative structure arising from the presence of
"indexed products" (products indexed by a set with a non-trivial action of the
group). The formation of the "multiplicative closure" of a set must be altered
in order to accomodate this structure, and the result of localizing an
equivariant commutative ring can have an unexpected homotopy type.


  We propose an effective framework for computing the prepotential of the
topological B-model on a class of local Calabi--Yau geometries related to the
circle compactification of five-dimensional $\mathcal{N}=1$ super Yang--Mills
theory with simple gauge group. In the simply-laced case, we construct
Picard--Fuchs operators from the Dubrovin connection on the Frobenius manifolds
associated to the extended affine Weyl groups of type $\mathrm{ADE}$. In
general, we propose a purely algebraic construction of Picard--Fuchs ideals
from a canonical subring of the space of regular functions on the ramification
locus of the Seiberg--Witten curve, encompassing non-simply-laced cases as
well.
  We offer several precision tests of our proposal. Whenever a candidate
spectral curve is known from string theory/brane engineering, we perform
non-perturbative comparisons with the gauge theory prepotentials obtained from
the K-theoretic blow-up equations, finding perfect agreement. We also employ
our formalism to rule out some proposals from the theory of integrable systems
of Seiberg--Witten geometries for non-simply laced gauge groups.


  Visual cues, like lip motion, have been shown to improve the performance of
Automatic Speech Recognition (ASR) systems in noisy environments. We propose
LipGER (Lip Motion aided Generative Error Correction), a novel framework for
leveraging visual cues for noise-robust ASR. Instead of learning the
cross-modal correlation between the audio and visual modalities, we make an LLM
learn the task of visually-conditioned (generative) ASR error correction.
Specifically, we instruct an LLM to predict the transcription from the N-best
hypotheses generated using ASR beam-search. This is further conditioned on lip
motions. This approach addresses key challenges in traditional AVSR learning,
such as the lack of large-scale paired datasets and difficulties in adapting to
new domains. We experiment on 4 datasets in various settings and show that
LipGER improves the Word Error Rate in the range of 1.1%-49.2%. We also release
LipHyp, a large-scale dataset with hypothesis-transcription pairs that is
additionally equipped with lip motion cues to promote further research in this
space


  J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing
homology group of the simplicial complex of graphs of degree at most two on
seven vertices. We use this result to demonstrate that there is 5-torsion also
in the bottom nonvanishing homology group of the matching complex $M_{14}$ on
14 vertices. Combining our observation with results due to Bouc and to
Shareshian and Wachs, we conclude that the case $n=14$ is exceptional; for all
other $n$, the torsion subgroup of the bottom nonvanishing homology group has
exponent three or is zero. The possibility remains that there is other torsion
than 3-torsion in higher-degree homology groups of $M_n$ when $n \ge 13$ and $n
\neq 14$.


  We performed high-pressure transport studies on the flat-band Kagome
compounds, Pd$_3$P$_2$(S$_{1-x}$Se$_x$)$_8$ ($x$ = 0, 0.25), with a diamond
anvil cell. For both compounds, the resistivity exhibits an insulating behavior
with pressure up to 17 GPa. With pressure above 20 GPa, a metallic behavior is
observed at high temperatures in Pd$_3$P$_2$S$_8$, and superconductivity
emerges at low temperatures. The onset temperature of superconducting
transition $T_{\rm C}$ rises monotonically from 2 K to 4.8 K and does not
saturate with pressure up to 43 GPa. For the Se-doped compound
Pd$_3$P$_2$(S$_{0.75}$Se$_{0.25}$)$_8$, the $T_{\rm C}$ is about 1.5 K higher
than that of the undoped one over the whole pressure range, and reaches 6.4 K
at 43 GPa. The upper critical field with field applied along the $c$ axis at
typical pressures is about 50$\%$ of the Pauli limit, suggesting a 3D
superconductivity. The Hall coefficient in the metallic phase is low and
exhibits a peaked behavior at about 30 K, which suggests either a multi-band
electronic structure or an electron correlation effect in the system.


  Deep learning is also known as hierarchical learning, where the learner
_learns_ to represent a complicated target function by decomposing it into a
sequence of simpler functions to reduce sample and time complexity. This paper
formally analyzes how multi-layer neural networks can perform such hierarchical
learning _efficiently_ and _automatically_ by SGD on the training objective.
  On the conceptual side, we present a theoretical characterizations of how
certain types of deep (i.e. super-constant layer) neural networks can still be
sample and time efficiently trained on some hierarchical tasks, when no
existing algorithm (including layerwise training, kernel method, etc) is known
to be efficient. We establish a new principle called "backward feature
correction", where the errors in the lower-level features can be automatically
corrected when training together with the higher-level layers. We believe this
is a key behind how deep learning is performing deep (hierarchical) learning,
as opposed to layerwise learning or simulating some non-hierarchical method.
  On the technical side, we show for every input dimension $d > 0$, there is a
concept class of degree $\omega(1)$ multi-variate polynomials so that, using
$\omega(1)$-layer neural networks as learners, SGD can learn any function from
this class in $\mathsf{poly}(d)$ time to any $\frac{1}{\mathsf{poly}(d)}$
error, through learning to represent it as a composition of $\omega(1)$ layers
of quadratic functions using "backward feature correction." In contrast, we do
not know any other simpler algorithm (including layerwise training, applying
kernel method sequentially, training a two-layer network, etc) that can learn
this concept class in $\mathsf{poly}(d)$ time even to any $d^{-0.01}$ error. As
a side result, we prove $d^{\omega(1)}$ lower bounds for several
non-hierarchical learners, including any kernel methods.


  Recently, a novel bio-inspired spike camera has been proposed, which
continuously accumulates luminance intensity and fires spikes while the
dispatch threshold is reached. Compared to the conventional frame-based cameras
and the emerging dynamic vision sensors, the spike camera has shown great
advantages in capturing fast-moving scene in a frame-free manner with full
texture reconstruction capabilities. However, it is difficult to transmit or
store the large amount of spike data. To address this problem, we first
investigate the spatiotemporal distribution of inter-spike intervals and
propose an intensity-based measurement of spike train distance. Then, we design
an efficient spike coding method, which integrates the techniques of adaptive
temporal partitioning, intra-/inter-pixel prediction, quantization and entropy
coding into a unified lossy coding framework. Finally, we construct a PKU-Spike
dataset captured by the spike camera to evaluate the compression performance.
The experimental results on the dataset demonstrate that the proposed approach
is effective in compressing such spike data while maintaining the fidelity.


  In the limit of small values of the aspect ratio parameter (or wave
steepness) which measures the amplitude of a surface wave in units of its
wave-length, a model equation is derived from the Euler system in infinite
depth (deep water) without potential flow assumption. The resulting equation is
shown to sustain periodic waves which on the one side tend to the proper linear
limit at small amplitudes, on the other side possess a threshold amplitude
where wave crest peaking is achieved. An explicit expression of the crest angle
at wave breaking is found in terms of the wave velocity. By numerical
simulations, stable soliton-like solutions (experiencing elastic interactions)
propagate in a given velocities range on the edge of which they tend to the
peakon solution.


  (Gd,La)$_2$Si$_2$O$_7$:Ce (La-GPS:Ce) is a new scintillator material with
high light output, high energy resolution, and fast decay time. Moreover, the
scintillator has a good light output even at high temperature (up to
150$^\circ$C) and is non-hygroscopic in nature; thus, it is especially suitable
for underground resource exploration. Particle identification greatly expands
the possible applications of scintillator. For resource exploration, the
particle identification should be completed in a single pulse only. The
pulse-shape discrimination of the scintillator was confirmed. We compared two
methods; a double gate method and a digital filter method. Using digital filter
method (shape indicator), F-measure to evaluate a separation between $\alpha$
and $\gamma$ particles was obtained to be 0.92 at 0.66 MeVee.


  The kinematic region covered by the LHC experiments probes low values of
Bjorken-$x$. At the scale relevant for $W$ and $Z$ production the central
rapidity region covers $10^{-3} < x < 10^{-1}$. This means that it is the HERA
data which give the most insight into the behaviour of parton distribution
functions (PDFs) for the early phase of running at the LHC. The H1 and ZEUS
experiments are combining their data so as to provide a legacy of HERA results.
The present status of the data combinations and the impact of these data on our
knowledge of parton distribution functions is explored.


  Forecasting the formation and development of clouds is a central element of
modern weather forecasting systems. Incorrect clouds forecasts can lead to
major uncertainty in the overall accuracy of weather forecasts due to their
intrinsic role in the Earth's climate system. Few studies have tackled this
challenging problem from a machine learning point-of-view due to a shortage of
high-resolution datasets with many historical observations globally. In this
paper, we present a novel satellite-based dataset called ``CloudCast''. It
consists of 70,080 images with 10 different cloud types for multiple layers of
the atmosphere annotated on a pixel level. The spatial resolution of the
dataset is 928 x 1530 pixels (3x3 km per pixel) with 15-min intervals between
frames for the period 2017-01-01 to 2018-12-31. All frames are centered and
projected over Europe. To supplement the dataset, we conduct an evaluation
study with current state-of-the-art video prediction methods such as
convolutional long short-term memory networks, generative adversarial networks,
and optical flow-based extrapolation methods. As the evaluation of video
prediction is difficult in practice, we aim for a thorough evaluation in the
spatial and temporal domain. Our benchmark models show promising results but
with ample room for improvement. This is the first publicly available
global-scale dataset with high-resolution cloud types on a high temporal
granularity to the authors' best knowledge.


  We analytically derive a decomposition of the lattice fermion determinant for
Wilson's Dirac operator with chemical potential into winding sectors, i.e.,
factors with a fixed number of quarks. Dividing the lattice into four domains,
the determinant is factorized into terms which can be classified with respect
to the winding number of the closed loops they consist of. The individual
factors are expressed in terms of subdeterminants and propagators on the
domains of the lattice. We numerically analyze properties of the factorization
formula and discuss two applications for the determination of canonical
partition functions with a fixed quark number: A speedup for the Fourier
transformation technique through a dimensional reduction, and a power series
expansion.


  Parabolic partial differential equations with state-dependent delays (SDDs)
are investigated. The delay term presented by Stieltjes integral simultaneously
includes discrete and distributed SDDs. The singular Lebesgue-Stieltjes measure
is also admissible. The conditions for the corresponding initial value problem
to be well-posed are presented. The existence of a compact global attractor is
proved.


  Generalised unitarity techniques are used to calculate the coefficients of
box and triangle integral functions of one-loop gluon scattering amplitudes in
gauge theories with $N < 4$ supersymmetries. We show that the box coefficients
in N=1 and N=0 theories inherit the same coplanar and collinear constraints as
the corresponding N=4 coefficients. We use triple cuts to determine the
coefficients of the triangle integral functions and present, as an example, the
full expression for the one-loop amplitude $A^{N=1}(1^-,2^-,3^-,4^+,..,n^+)$.


  The 21-cm forest is a promising probe of the Epoch of Reionization. The local
state of the intergalactic medium (IGM) is encoded in the spectrum of a
background source (radio-loud quasars or gamma ray burst afterglow) by
absorption at the local 21-cm wavelength, resulting in a continuous and
fluctuating absorption level. Small-scale structures (filaments and minihaloes)
in the IGM are responsible for the strongest absorption features. The
absorption can also be modulated on large scales by inhomogeneous heating and
Wouthuysen-Field coupling.
  We present the results from a simulation that attempts to preserve the
cosmological environment while resolving some of the small-scale structures (a
few kpc resolution in a 50 Mpc/h box). The simulation couples the dynamics and
the ionizing radiative transfer and includes X-ray and Lyman lines radiative
transfer for a detailed physical modelling. As a result we find that soft X-ray
self-shielding, Lyman-alpha self-shielding and shock heating all have an impact
on the predicted values of the 21-cm optical depth of moderately overdense
structures like filaments. An correct treatment of the peculiar velocities is
also critical. Modelling these processes seems necessary for accurate
predictions and can be done only at high enough resolution. As a result, based
on our fiducial model, we estimate that LOFAR should be able to detect a few
(strong) absorptions features in a frequency range of a few tens of MHz for a
20 mJy source located at z=10, while the SKA would extract a large fraction of
the absorption information for the same source.


  Cl\'ery and van der Geer determined generators for some modules of vector
valued Picard modular forms on the two dimensional ball. In this paper we
consider the case of a three dimensional ball with the action of the Picard
modular group $\Gamma_3[\sqrt{-3}]$.
  The corresponding modular variety of dimension 3 is a copy of the Segre
cubic.


  We show how to measure the structural witnesses proposed in [P. Krammer et
al., Phys. Rev. Lett. 103, 100502 (2009)] for detecting entanglement in a spin
chain using photon scattering. The procedure, moreover, allows one to measure
the two-point correlation function of the spin array. This proposal could be
performed in existing experimental platforms realizing ion chains in Paul traps
or atomic arrays in optical lattices.


  In 1998, the detector H1 at HERA has been equipped with a small backward
spectrometer, the Very Low Q^2 (VLQ) spectrometer comprising a silicon tracker,
a tungsten - scintillator sandwich calorimeter, and a Time-of-Flight system.
The spectrometer was designed to measure electrons scattered under very low
angles, equivalent to very low squared four - momentum transfers Q^2, and high
energy photons with good energy and spatial resolution. The VLQ was in
operation during the 1999 and 2000 run periods. This paper describes the design
and construction of the VLQ calorimeter, a compact device with a fourfold
projective energy read-out, and its performance during test runs and in the
experiment.


  We take the classic facility location problem and consider a variation, in
which each agent's individual cost function is equal to their distance from the
facility multiplied by a scaling factor which is determined by the facility
placement. In addition to the general class of continuous scaling functions, we
also provide results for piecewise linear scaling functions which can
effectively approximate or model the scaling of many real world scenarios. We
focus on the objectives of total and maximum cost, describing the computation
of the optimal solution. We then move to the approximate mechanism design
setting, observing that the agents' preferences may no longer be single-peaked.
Consequently, we characterize the conditions on scaling functions which ensure
that agents have single-peaked preferences. Under these conditions, we find
results on the total and maximum cost approximation ratios achievable by
strategyproof and anonymous mechanisms.


  As a basic requirement of the renormalization group invariance, any physical
observable must be independent of the choice of both the renormalization scheme
and the initial renormalization scale. In this paper, we show that by using the
newly suggested $C$-scheme coupling, one can obtain a demonstration that the
{\it Principle of Maximum Conformality} prediction is scheme-independent to
all-orders for any renormalization schemes, thus satisfying all of the
conditions of the renormalization group invariance. We illustrate these
features for the non-singlet Adler function and for $\tau $ decay to $\nu +$
hadrons at the four-loop level.


  A cluster update (the ``operator-loop'') is developed within the framework of
a numerically exact quantum Monte Carlo method based on the power series
expansion of exp(-BH) (stochastic series expansion). The method is generally
applicable to a wide class of lattice Hamiltonians for which the expansion is
positive definite. For some important models the operator-loop algorithm is
more efficient than loop updates previously developed for ``worldline''
simulations. The method is here tested on a two-dimensional anisotropic
Heisenberg antiferromagnet in a magnetic field.


  We study the problem of cross-lingual voice conversion in non-parallel speech
corpora and one-shot learning setting. Most prior work require either parallel
speech corpora or enough amount of training data from a target speaker.
However, we convert an arbitrary sentences of an arbitrary source speaker to
target speaker's given only one target speaker training utterance. To achieve
this, we formulate the problem as learning disentangled speaker-specific and
context-specific representations and follow the idea of [1] which uses
Factorized Hierarchical Variational Autoencoder (FHVAE). After training FHVAE
on multi-speaker training data, given arbitrary source and target speakers'
utterance, we estimate those latent representations and then reconstruct the
desired utterance of converted voice to that of target speaker. We investigate
the effectiveness of the approach by conducting voice conversion experiments
with varying size of training utterances and it was able to achieve reasonable
performance with even just one training utterance. We also examine the speech
representation and show that World vocoder outperforms Short-time Fourier
Transform (STFT) used in [1]. Finally, in the subjective tests, for one
language and cross-lingual voice conversion, our approach achieved
significantly better or comparable results compared to VAE-STFT and GMM
baselines in speech quality and similarity.


  We construct an exact solution describing the collision of two Kaluza-Klein
"bubbles of nothing" in 3+1 dimensions. When the bubbles collide, a curvature
singularity forms which is hidden inside an event horizon. However, unlike the
formation of ordinary black holes, in this case the spacetime resembles the
entire maximally extended Schwarzschild solution. We also point out that there
are inequivalent bubbles that can be constructed from Kerr black holes.


  Interstellar communications are achievable with gram-scale spacecraft using
swarm techniques introduced herein if an adequate energy source, clocks and a
suitable communications protocol exist. The essence of our approach to the
Breakthrough Starshot challenge is to launch a long string of 100s of
gram-scale interstellar probes at 0.2c in a firing campaign up to a year long,
maintain continuous contact with them (directly amongst each other and via
Earth utilizing the launch laser), and gradually, during the 20-year cruise,
dynamically coalesce the long string into a lens-shaped mesh network
$\sim$100,000 km across centered on the target planet Proxima b at the time of
fly-by.
  In-flight formation would be accomplished using the "time on target"
technique of grossly modulating the initial launch velocity between the head
and the tail of the string, and combined with continual fine control or
"velocity on target" by adjusting the attitude of selected probes, exploiting
the drag imparted by the ISM.
  Such a swarm could tolerate significant attrition, e.g., by collisions
enroute with interstellar dust grains, thus mitigating the risk that comes with
"putting all your eggs in one basket". It would also enable the observation of
Proxima b at close range from a multiplicity of viewpoints. Swarm
synchronization with state-of-the-art space-rated clocks would enable
operational coherence if not actual phase coherence in the swarm optical
communications. Betavoltaic technology, which should be commercialized and
space-rated in the next decade, can provide an adequate primary energy storage
for these swarms. The combination would thus enable data return rates orders of
magnitude greater than possible from a single probe.


  The lace expansion has been a powerful tool for investigating mean-field
behavior for various stochastic-geometrical models, such as self-avoiding walk
and percolation, above their respective upper-critical dimension. In this
paper, we prove the lace expansion for the Ising model that is valid for any
spin-spin coupling. For the ferromagnetic case, we also prove that the
expansion coefficients obey certain diagrammatic bounds that are similar to the
diagrammatic bounds on the lace-expansion coefficients for self-avoiding walk.
As a result, we obtain Gaussian asymptotics of the critical two-point function
for the nearest-neighbor model with d>>4 and for the spread-out model with d>4
and L>>1, without assuming reflection positivity.


  We address the question of the time needed by $N$ particles, initially
located on the first sites of a finite 1D lattice of size $L$, to exit that
lattice when they move according to a TASEP transport model. Using analytical
calculations and numerical simulations, we show that when $N \ll L$, the mean
exit time of the particles is asymptotically given by $T_N(L) \sim L+\beta_N
\sqrt{L}$ for large lattices. Building upon exact results obtained for 2
particles, we devise an approximate continuous space and time description of
the random motion of the particles that provides an analytical recursive
relation for the coefficients $\beta_N$. The results are shown to be in very
good agreement with numerical results. This approach sheds some light on the
exit dynamics of $N$ particles in the regime where $N$ is finite while the
lattice size $L\rightarrow \infty$. This complements previous asymptotic
results obtained by Johansson in \cite{Johansson2000} in the limit where both
$N$ and $L$ tend to infinity while keeping the particle density $N/L$ finite.


  This is a largely expository paper in which we discuss various sets having a
Catalan number of objects and some well-known bijections between these sets
presented in a new and hopefully interesting way. We call these concepts
"bookshelf" and "baseball" constructions. No knowledge of these topics is
assumed. These are the final student papers for a course at Brandeis
University.


  We consider the process of changing reference frames in the case where the
reference frames are quantum systems. We find that, as part of this process,
decoherence is necessarily induced on any quantum system described relative to
these frames. We explore this process with examples involving reference frames
for phase and orientation. Quantifying the effect of changing quantum reference
frames serves as a first step in developing a relativity principle for theories
in which all objects including reference frames are necessarily quantum.


  Artificial neural networks are powerful pattern classifiers; however, they
have been surpassed in accuracy by methods such as support vector machines and
random forests that are also easier to use and faster to train.
Backpropagation, which is used to train artificial neural networks, suffers
from the herd effect problem which leads to long training times and limit
classification accuracy. We use the disjunctive normal form and approximate the
boolean conjunction operations with products to construct a novel network
architecture. The proposed model can be trained by minimizing an error function
and it allows an effective and intuitive initialization which solves the
herd-effect problem associated with backpropagation. This leads to state-of-the
art classification accuracy and fast training times. In addition, our model can
be jointly optimized with convolutional features in an unified structure
leading to state-of-the-art results on computer vision problems with fast
convergence rates. A GPU implementation of LDNN with optional convolutional
features is also available


  We study spin oscillations of neutrinos gravitationally scattered off a
nonrotating black hole (BH). We derive the transition and survival
probabilities of spin oscillations in quadratures when neutrinos interacts with
BH only. The dependence of the probabilities on the impact parameter is
analyzed. Then, we obtain the effective Schr\"{o}dinger equation for neutrino
spin oscillations in neutrino scattering off BH surrounded by background
matter. This equation is solved numerically in the case of a supermassive BH
with a realistic accretion disk. We find that the observed neutrino fluxes can
be reduced almost 20% because of spin oscillations when neutrinos experience
gravitational scattering. The neutrino interaction with an accretion disk
results in the additional asymmetry in the intensities of outgoing fluxes
depending on the neutrino trajectory.


  We use the NIRSPEC near-IR spectrometer on Keck II to obtain moderate
resolution (R = 1540) spectroscopy that shows conclusively that the C IV
emission line in the z = 5.74 quasar SDSSp J104433.04-012502.2 is accompanied
by broad, blueshifted C IV absorption. The line has a "balnicity index" of 900
km/s and a rest-frame equivalent width of 13.1 +/- 1.3 relative to the
continuum. This confirms its membership in the class of objects called
"broad-absorption line" (BAL) QSOs. SDSSP J1044-0125 was previously suggested
to be a BAL QSO based on its larger UV-to-X-ray flux ratio than most non-BAL
QSOs. The C IV emission is of normal strength, implying a metallicity similar
to that found in other, lower-redshift QSOs.


  Current research on soft-biometrics showed that privacy-sensitive information
can be deduced from biometric templates of an individual. Since for many
applications, these templates are expected to be used for recognition purposes
only, this raises major privacy issues. Previous works focused on supervised
privacy-enhancing solutions that require privacy-sensitive information about
individuals and limit their application to the suppression of single and
pre-defined attributes. Consequently, they do not take into account attributes
that are not considered in the training. In this work, we present Negative Face
Recognition (NFR), a novel face recognition approach that enhances the
soft-biometric privacy on the template-level by representing face templates in
a complementary (negative) domain. While ordinary templates characterize facial
properties of an individual, negative templates describe facial properties that
does not exist for this individual. This suppresses privacy-sensitive
information from stored templates. Experiments are conducted on two publicly
available datasets captured under controlled and uncontrolled scenarios on
three privacy-sensitive attributes. The experiments demonstrate that our
proposed approach reaches higher suppression rates than previous work, while
maintaining higher recognition performances as well. Unlike previous works, our
approach does not require privacy-sensitive labels and offers a more
comprehensive privacy-protection not limited to pre-defined attributes.


  In the General Theory, Keynes remarked that the economy's state depends on
expectations, and that these expectations can be subject to sudden swings. In
this work, we develop a multiple equilibria behavioural business cycle model
that can account for demand or supply collapses due to abrupt drops in consumer
confidence, which affect both consumption propensity and investment. We show
that, depending on the model parameters, four qualitatively different outcomes
can emerge, characterised by the frequency of capital scarcity and/or demand
crises. In the absence of policy measures, the duration of such crises can
increase by orders of magnitude when parameters are varied, as a result of the
"paradox of thrift". Our model suggests policy recommendations that prevent the
economy from getting trapped in extended stretches of low output, low
investment and high unemployment.


  Encoder-decoder architectures are widely adopted for medical image
segmentation tasks. With the lateral skip connection, the models can obtain and
fuse both semantic and resolution information in deep layers to achieve more
accurate segmentation performance. However, in many applications (e.g., blurry
boundary images), these models often cannot precisely locate complex boundaries
and segment tiny isolated parts. To solve this challenging problem, we firstly
analyze why simple skip connections are not enough to help accurately locate
indistinct boundaries and argue that it is due to the fuzzy information in the
skip connection provided in the encoder layers. Then we propose a
semantic-guided encoder feature learning strategy to learn both high resolution
and rich semantic encoder features so that we can more accurately locate the
blurry boundaries, which can also enhance the network by selectively learning
discriminative features. Besides, we further propose a soft contour constraint
mechanism to model the blurry boundary detection. Experimental results on real
clinical datasets show that our proposed method can achieve state-of-the-art
segmentation accuracy, especially for the blurry regions. Further analysis also
indicates that our proposed network components indeed contribute to the
improvement of performance. Experiments on additional datasets validate the
generalization ability of our proposed method.


  In theories like SM or MSSM with a complex gauge group structure the complete
set of Feynman diagrams contributed to a particular physics process can be
splited to exact gauge invariant subsets. Arguments and examples given in the
review demonstrate that in many cases computations and analysis of the gauge
invariant subsets are important.


  The one-dimensional lattice Schwinger model has recently been realized by
using bosons in optical lattices. This model contains both confinement and
deconfinement phases, whose phase diagram is controlled by the mass of the
matter field and the topological angle. Since varying the mass of matter field
is straightforward experimentally, we propose how to tune the topological
angle, allowing accessing the entire phase diagram. We propose that direct
experimental evidence of confinement and deconfinement can be obtained by
measuring whether a physical charge is localized around a fixed gauge charge to
screen it. We also discuss the PXP model realized in the Rydberg atoms array,
which is equivalent to the lattice Schwinger model when all local gauge charges
are fixed as zero. Although the gauge charges are fixed, we can alternatively
probe the confinement and the deconfinement in the PXP model by studying the
relative motion of a pair of a physical charge and an anti-charge. Our scheme
can be directly implemented in these two relevant experimental platforms of
ultracold atom quantum simulators.


  We study the neutrino-induced production of nuclides in explosive supernova
nucleosynthesis for progenitor stars with solar metallicity including neutrino
nucleus reactions for all nuclei with charge numbers $Z < 76$ with average
neutrino energies in agreement with modern Supernova simulations. Considering
progenitors with initial main sequence masses between 13~M$_\odot$ and
30~M$_\odot$, we find a significant production of $^{11}$B, $^{138}$La, and
$^{180}$Ta by neutrino nucleosynthesis, despite the significantly reduced
neutrino energies. The production of $^{19}$F turns out to be more sensitive to
the progenitor mass and structure than to the $\nu$ process. With our complete
set of cross sections we have identified effects of the $\nu$~process on
several stable nuclei including $^{33}$S, $^{40}$Ar, $^{41}$K, $^{59}$Co, and
$^{113}$In at the 10\% level. Neutrino-induced reactions contribute to a
similar extent to the production of radioactive ${}^{26}$Al and increase the
yield of $^{22}$Na by 50\%. Future $\gamma$~ray astronomy missions may reach
the precision at which the contribution from the $\nu$~process becomes
relevant. We find that the production of $^{22}$Na by the $\nu$~process could
explain the Ne-E(L) component of meteoritic graphite grains. The $\nu$~process
enhances the yield of $^{36}$Cl and we point out that the resulting
$^{36}$Cl/$^{35}$Cl ratio is in agreement with the values infrerred for the
early solar system. Our extended set of neutrino-nucleus interactions also
allows us to exclude any further effects of the $\nu$ process on stable nuclei
and to quantify the effects on numerous, hitherto unconsidered radioactive
nuclei, e.g., $^{36}$Cl, $^{72}$As, $^{84}$Rb, and $^{88}$Y.


  A variational principle is introduced to provide a new formulation and
resolution for several boundary value problems with a variational structure.
This principle allows one to deal with problems well beyond the weakly compact
structure. As a result, we study several super-critical semilinear Elliptic
problems.


  The algebraic properties of drift-flux two-phase fluids models without
gravitational and wall friction forces are studied. More precisely, for the two
fluids we consider equation of states of polytropic gases. We perform a
classification scheme of the unknown parameters of the model such that to
determine all the possible admitted Lie symmetries. We find that in the most
general case the dynamical system of hyperbolic equations is invariant under
the action of a four dimensional Lie algebra, while the larger number of
admitted Lie symmetries is six. For each admitted Lie algebra the
one-dimensional optimal system is derived which is applied for the
determination of all the unique similarity transformations which lead to
similarity solutions. Our results are compared with that of previous studies
from where we see that most of the solutions presented in this study have not
found before in the literature.


  We investigate the secure communications over correlated wiretap Rayleigh
fading channels assuming the full channel state information (CSI) available.
Based on the information theoretic formulation, we derive closed-form
expressions for the average secrecy capacity and the outage probability.
Simulation results confirm our analytical expressions.


  In the present paper, it is shown that the existence of the Casimir
electromotive force (EMF) is possible in nanosized configurations with
nonclosed nonparallel metal plates. The nature of such EMF is associated with
the drag current generation at the noncompensated Casimir action of virtual
photons on the electrons in the nano-configurations. In the case of a classical
configuration withstrictly parallel plates, EMF is not generated. However, EMF
can be generated when even an insignificant angle between the plates appears.
Angles between the plates and their effective lengths have been found, at which
maximally possible EMF is generated in a configuration.


  Let $A$ be a finite-dimensional $\mathbb{C}$-algebra of finite global
dimension and $\mathcal{A}$ be the category of finitely generated right
$A$-modules. By using of the category of two-periodic projective complexes
$\mathcal{C}_2(\mathcal{P})$, we construct the motivic Bridgeland's Hall
algebra for $\mathcal{A}$, where structure constants are given by Poincar\'{e}
polynomials in $t$, then construct a $\mathbb{C}$-Lie subalgebra
$\mathfrak{g}=\mathfrak{n}\oplus \mathfrak{h}$ at $t=-1$, where $\mathfrak{n}$
is constructed by stack functions about indecomposable radical complexes, and
$\mathfrak{h}$ is by contractible complexes. For the stable category
$\mathcal{K}_2(\mathcal{P})$ of $\mathcal{C}_2(\mathcal{P})$, we construct its
moduli spaces and a $\mathbb{C}$-Lie algebra
$\tilde{\mathfrak{g}}=\tilde{\mathfrak{n}}\oplus \tilde{\mathfrak{h}}$, where
$\tilde{\mathfrak{n}}$ is constructed by support-indecomposable constructible
functions, and $\tilde{\mathfrak{h}}$ is by the Grothendieck group of
$\mathcal{K}_2(\mathcal{P})$. We prove that the natural functor
$\mathcal{C}_2(\mathcal{P})\rightarrow \mathcal{K}_2(\mathcal{P})$ together
with the natural isomorphism between Grothendieck groups of $\mathcal{A}$ and
$\mathcal{K}_2(\mathcal{P})$ induces a Lie algebra isomorphism
$\mathfrak{g}\cong\tilde{\mathfrak{g}}$. This makes clear that the structure
constants at $t=-1$ provided by Bridgeland in [5] in terms of exact structure
of $\mathcal{C}_2(\mathcal{P})$ precisely equal to that given in [30] in terms
of triangulated category structure of $\mathcal{K}_2(\mathcal{P})$.


  In many combinatorial games, one can prove that the first player wins under
best play using a simple but non-constructive argument called
strategy-stealing. This work is about the complexity behind these proofs: how
hard is it to actually find a winning move in a game, when you know by
strategy-stealing that one exists? We prove that this problem is PSPACE-hard
already for Minimum Poset Games and Symmetric Maker-Maker Games, which are
simple classes of games that capture two of the main types of strategy-stealing
arguments in the current literature.