  Our understanding of emission from a collection of emitters strongly
interacting among them and also with other polarizable matter in proximity has
been approximated by independent emission from the emitters. This is primarily
due to our inability to evaluate the self-energy matrices and the collective
eigenstates of emitters in heterogeneous ensembles. A method to evaluate the
self-energy matrices that is not limited by the geometry and the material
composition is presented here to understand and exploit such collective
excitations. Numerical evaluations using this method are used to highlight the
significant differences between independent and the collective modes of
emission in heterostructures. A set of n emitters driving each other and m
other polarizable entities, where N=m+n, is used to represent the coupled
system of a generalized geometry in a volume integral approach. Closed form
relations between the Green tensors of entity pairs in free space and their
correspondents in a heterostructure are derived concisely. This is made
possible for general geometries because the global matrices consisting of all
free-space Green dyads are subject to conservation laws. The self-energy matrix
of the emitters can then be assembled using the evaluated Green tensors of the
heterostructure, but a decomposition of its components into their radiative and
non-radiative decay contributions is non-trivial. This is accomplished using
matrix decomposition identities applied to the global matrices containing all
free-space dyads. The relations to compute the observables of the eigenstates
(such as quantum efficiency, power/energy of emission, radiative and
non-radiative decay rates) are presented. We conclude with a note on extension
of this method to collective excitations that also include strong interactions
with a surface in the near-field.


  Many inspiraling and merging stellar remnants emit both gravitational and
electromagnetic radiation as they orbit or collide. These gravitational wave
events together with their associated electromagnetic counterparts provide
insight about the nature of the merger, allowing us to further constrain
properties of the binary. With the future launch of the Laser Interferometer
Space Antenna (LISA), follow up observations and models are needed of
ultracompact binary (UCB) systems. Current and upcoming long baseline time
domain surveys will observe many of these UCBs. We present a new fast periodic
object search tool capable of searching for generic periodic signals based on
the Conditional Entropy algorithm. This new implementation allows for a grid
search over both the period ($P$) and the time derivative of the period
($\dot{P}$). To demonstrate the usage of this tool, we use a small, hand-picked
subset of a UCB population generated from the population synthesis code
\cosmic, as well as a custom catalog for varying periods at fixed intrinsic
parameters. We simulate light curves as likely to be observed by future time
domain surveys by using an existing eclipsing binary light curve model
accounting for the change in orbital period due to gravitational radiation. We
find that a search with $\dot{P}$ values is necessary for detecting binaries at
orbital periods less than $\sim$10 min. We also show it is useful in finding
and characterizing binaries with longer periods, but at a higher computational
cost. Our code is called gce (GPU-Accelerated Conditional Entropy). It is
available at https://github.com/mikekatz04/gce.


  Automatic Speech Recognition (ASR) technology has made significant progress
in recent years, providing accurate transcription across various domains.
However, some challenges remain, especially in noisy environments and
specialized jargon. In this paper, we propose a novel approach for improved
jargon word recognition by contextual biasing Whisper-based models. We employ a
keyword spotting model that leverages the Whisper encoder representation to
dynamically generate prompts for guiding the decoder during the transcription
process. We introduce two approaches to effectively steer the decoder towards
these prompts: KG-Whisper, which is aimed at fine-tuning the Whisper decoder,
and KG-Whisper-PT, which learns a prompt prefix. Our results show a significant
improvement in the recognition accuracy of specified keywords and in reducing
the overall word error rates. Specifically, in unseen language generalization,
we demonstrate an average WER improvement of 5.1% over Whisper.


  The formation and evolution of clusters of galaxies are sensitive to the
underlying cosmological model. Constraints on cosmological parameters of cold
dark matter models have been derived from mass, temperature and luminosity
functions of clusters. We study the importance of including cluster formation
history and a correction for collapsed fraction of objects in determining the
cluster X-ray temperature function. We find that both effects are important. We
compare temperature functions obtained by using a power law approximation for
the mass variance normalized to X-ray clusters to those obtained by using a
COBE normalized full CDM treatment. We conclude that the temperature function
could be a powerful test on the average density of the Universe if we could
find the correct way of interpreting the data.


  Since 2016, sharding has become an auspicious solution to tackle the
scalability issue in legacy blockchain systems. Despite its potential to
strongly boost the blockchain throughput, sharding comes with its own security
issues. To ease the process of deciding which shard to place transactions,
existing sharding protocols use a hash-based transaction sharding in which the
hash value of a transaction determines its output shard. Unfortunately, we show
that this mechanism opens up a loophole that could be exploited to conduct a
single-shard flooding attack, a type of Denial-of-Service (DoS) attack, to
overwhelm a single shard that ends up reducing the performance of the system as
a whole.
  To counter the single-shard flooding attack, we propose a countermeasure that
essentially eliminates the loophole by rejecting the use of hash-based
transaction sharding. The countermeasure leverages the Trusted Execution
Environment (TEE) to let blockchain's validators securely execute a transaction
sharding algorithm with a negligible overhead. We provide a formal
specification for the countermeasure and analyze its security properties in the
Universal Composability (UC) framework. Finally, a proof-of-concept is
developed to demonstrate the feasibility and practicality of our solution.


  A semi-microscopic self-consistent quantum approach developed recently to
describe the inner crust structure of neutron stars within the Wigner-Seitz
(WS) method with the explicit inclusion of neutron and proton pairing
correlations is further developed. In this approach, the generalized energy
functional is used which contains the anomalous term describing the pairing. It
is constructed by matching the realistic phenomenological functional by Fayans
et al. for describing the nuclear-type cluster in the center of the WS cell
with the one calculated microscopically for neutron matter. Previously the
anomalous part of the latter was calculated within the BCS approximation. In
this work corrections to the BCS theory which are known from the many-body
theory of pairing in neutron matter are included into the energy functional in
an approximate way. These modifications have a sizable influence on the
equilibrium configuration of the inner crust, i.e. on the proton charge Z and
the radius R_c of the WS cell. The effects are quite significant in the region
where the neutron pairing gap is larger.


  We present an analog of O'Neill's Theorem (Theorem 5.2 in [17]) for finite
games, which reveals a picture of the structure of equilibria under payoff
perturbations in finite games.


  We discuss the late-time property of universe and phantom field in the
SO(1,1) dark energy model for the potential $V=V_0e^{-\beta\Phi^\alpha}$ with
$\alpha$ and $\beta$ two positive constants. We assume in advance some
conditions satisfied by the late-time field to simplify equations, which are
confirmed to be correct from the eventual results. For $\alpha<2$, the filed
falls exponentially off and the phantom equation of state rapidly approaches
-1. When $\alpha=2$, the kinetic energy $\rho_k$ and the coupling energy
$\rho_c$ become comparable but there is always $\rho_k<-\rho_c$ so that the
phantom property of field proceeds to hold. The analysis on the perturbation to
the late-time field $\Phi$ illustrates the square effective mass of the
perturbation field is always positive and thus the phantom is stable. The
universe considered currently may evade the future sudden singularity and will
evolve to de Sitter expansion phase.


  Many real world networks consist of multiple types of nodes with edges that
are heterogeneous in nature. However, most of the existing work for community
detection only focused on homogeneous network consisting of a single layer. In
this paper, we propose a modified Degree-Corrected Stochastic Model (DCBM) for
modeling multilayer heterogeneous network. We develop a spectral clustering
method that can unify the information contained in each sub-network, and
demonstrate its efficiency to detect communities on simulated data and on
Authorship/Citation network data. As a by-product, we present a novel algorithm
called BiScore for clustering bipartite network under DCBM, and show that under
mild conditions BiScore is guaranteed to yield consistent results.


  Much of what EuSpRIG discusses is concerned with the integrity of individual
spreadsheets. In businesses, interlocking spreadsheets are regularly used to
fill functional gaps in core administrative systems. The growth and deployment
of such integrated spreadsheet SYSTEMS raises the scale of issues to a whole
new level. The correct management of spreadsheet systems is necessary to ensure
that the business achieves its goals of improved performance and good corporate
governance, within the constraints of legislative compliance - poor management
will deliver the opposite. This paper is an anatomy of the real-life issues of
the commercial use of spreadsheets in business, and demonstrates how
Qtier-Rapor has been used to instil best practice in the use of integrated
commercial spreadsheet systems.


  To formulate gravity in spacetimes bounded by a null boundary, an arbitrary
hypothetical null surface, boundary degrees of freedom (d.o.f) should be added
to account for the d.o.f and dynamics in the spacetime regions excised behind
the null boundary. In the D dimensional example, boundary d.o.f are labelled by
D charges defined at D-2 dimensional spacelike slices at the null boundary.
While boundary modes can have their own boundary dynamics, their interaction
with the bulk modes is governed by flux-balance equations which may be
interpreted as a diffusion equation describing "dissolution" of bulk gravitons
into the boundary. From boundary viewpoint, boundary d.o.f obey local
thermodynamical equations at the boundary. Our description suggests a new
"semiclassical" quantization of the system in which boundary d.o.f are
quantized while bulk is classical. This semiclassical treatment may be relevant
to questions in black hole physics.


  We present results from four new broadband X-ray observations of the extreme
ultraluminous X-ray source Holmberg IX X-1 ($L_{\rm{X}} > 10^{40}$ erg/s),
performed by $Suzaku$ and $NuSTAR$ in coordination. Combined with the archival
data, we now have broadband observations of this remarkable source from six
separate epochs. Two of these new observations probe lower fluxes than seen
previously, allowing us to extend our knowledge of the broadband spectral
variability exhibited. The spectra are well fit by two thermal blackbody
components, which dominate the emission below 10 keV, as well as a steep
($\Gamma \sim 3.5$) powerlaw tail which dominates above $\sim$15 keV.
Remarkably, while the 0.3-10.0 keV flux varies by a factor of $\sim$3 between
all these epochs, the 15-40 keV flux varies by only $\sim$20%. Although the
spectral variability is strongest in the $\sim$1-10 keV band, both of the
thermal components are required to vary when all epochs are considered. We also
re-visit the search for iron absorption features, leveraging the high-energy
$NuSTAR$ data to improve our sensitivity to extreme velocity outflows in light
of the ultra-fast outflow recently detected in NGC 1313 X-1. Iron absorption
from a similar outflow along our line of sight can be ruled out in this case.
We discuss these results in the context of super-Eddington accretion models
that invoke a funnel-like geometry for the inner flow, and propose a scenario
in which we have an almost face-on view of a funnel that expands to larger
radii with increasing flux, resulting in an increasing degree of geometrical
collimation for the emission from intermediate temperature regions.


  We report the results of a study of multiphase flow in porous media. A
Darcy's law for steady multiphase flow was investigated for both binary and
ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager
reciprocity were shown to be a good approximation of the simulation data. The
dependence of the relative permeability coefficients on water saturation was
investigated and showed good qualitative agreement with experimental data.
Non-steady state invasion flows were investigated, with particular interest in
the asymptotic residual oil saturation. The addition of surfactant to the
invasive fluid was shown to significantly reduce the residual oil saturation.


  This study proposes an approach for establishing an optimal multihop ad-hoc
network using multiple unmanned aerial vehicles (UAVs) to provide emergency
communication in disaster areas. The approach includes two stages, one uses
particle swarm optimization (PSO) to find optimal positions to deploy UAVs, and
the other uses a behavior-based controller to navigate the UAVs to their
assigned positions without colliding with obstacles in an unknown environment.
Several constraints related to the UAVs' sensing and communication ranges have
been imposed to ensure the applicability of the proposed approach in real-world
scenarios. A number of simulation experiments with data loaded from real
environments have been conducted. The results show that our proposed approach
is not only successful in establishing multihop ad-hoc routes but also meets
the requirements for real-time deployment of UAVs.


  We report the detection of a gas-giant planet in orbit around both stars of
an eclipsing binary star system that also contains the smaller, inner
transiting planet TOI-1338b. The new planet, called TOI-1338/BEBOP-1c, was
discovered using radial-velocity data collected with the HARPS and ESPRESSO
spectrographs. Our analysis reveals it is a $65.2~\rm{M_{\oplus}}$ circumbinary
planet with a period of $215.5~$days. This is the first detection of a
circumbinary planet using radial-velocity observations alone, and makes
TOI-1338/BEBOP-1 only the second confirmed multiplanet circumbinary system to
date. We do not detect the smaller inner transiting planet with radial-velocity
data, and can place an upper limit on the inner planet's mass at
$21.8~\mathrm{M}_\oplus$ with $99\%$ confidence. The inner planet is the first
circumbinary planet amenable for atmospheric characterisation, using the James
Webb Space Telescope.


  This paper presents a new joint radar and communication technique based on
the classical stepped frequency radar waveform. The randomization in the
waveform, which is achieved by using permutations of the sequence of frequency
tones, is utilized for data transmission. A new signaling scheme is proposed in
which the mapping between incoming data and waveforms is performed based on an
efficient combinatorial transform called the Lehmer code. Considering the
optimum maximum likelihood (ML) detection, the union bound and the nearest
neighbour approximation on the communication block error probability is derived
for communication in an additive white Gaussian noise (AWGN) channel. The
results are further extended to incorporate the Rician fading channel model, of
which the Rayleigh fading channel model is presented as a special case.
Furthermore, an efficient communication receiver implementation is discussed
based on the Hungarian algorithm which achieves optimum performance with much
less operational complexity when compared to an exhaustive search. From the
radar perspective, two key analytical tools, namely, the ambiguity function
(AF) and the Fisher information matrix are derived. Furthermore, accurate
approximations to the Cramer-Rao lower bounds (CRLBs) on the delay and Doppler
estimation errors are derived based on which the range and velocity estimation
accuracy of the waveform is analysed. Numerical examples are used to highlight
the accuracy of the analysis and to illustrate the performance of the proposed
waveform.


  We will show the rationality of the function field of two variables under
certain Cremona transformation.


  Nanomechanical resonators can now be realized that achieve fundamental
resonance frequencies exceeding 1 GHz, with quality factors (Q) in the range
1,000 - 100,000. The minuscule active masses of these devices, in conjunction
with their high Qs, translate into unprecedented inertial mass sensitivities.
This makes them natural candidates for a variety of mass sensing applications.
Here we evaluate the ultimate mass sensitivity limits for nanomechanical
resonators operating in vacuo, which are imposed by a number of fundamental
physical noise processes. Our analyses indicate that nanomechanical resonators
offer immense potential for mass sensing - ultimately with resolution at the
level of individual molecules.


  This work presents new surface photometry and two-dimensional modeling of the
light distribution of the Polar Ring Galaxy NGC 4650A, based on near-infrared
(NIR) observations and high resolution optical imaging acquired during the
Hubble Heritage program. The NIR and optical integrated colors of the S0 and
the polar ring, and their scale parameters, are compared with those for
standard galaxy morphological types. The polar structure appears to be a disk
of a very young age, while the colors and light distribution of the host galaxy
do not resemble that of a typical early-type system. We compare these
observational results with the predictions from different formation scenarios
for polar ring galaxies. The peculiarities of the central S0 galaxy, the polar
disk structure and stellar population ages suggest that the polar ring galaxy
NGC 4650A may be the result of a dissipative merger event, rather than of an
accretion process.


  We experimentally realize the dual-wavelength active optical clock for the
first time. As the Cs cell temperature is kept between 118 $^{\circ }C$ and 144
$^{\circ }C$, both the 1359 nm and the 1470 nm stimulated emission output of Cs
four-level active optical clock are detected. The 1470 nm output linewidth of
each experimental setup of Cs four-level active optical clock is measured to be
590 Hz with the main cavity length unstabilized. To stabilize the cavity length
of active optical clock, the experimental scheme of 633 nm and 1359 nm good-bad
cavity dual-wavelength active optical clock is proposed, where 633 nm and 1359
nm stimulated emission is working at good-cavity and bad-cavity regime
respectively. The cavity length is stabilized by locking the 633 nm output
frequency to a super-cavity with the Pound-Drever-Hall (PDH) technique. The
frequency stability of 1359 nm bad-cavity stimulated emission output is then
expected to be further improved by at least 1 order of magnitude than the 633
nm PDH system due to the suppressed cavity pulling effect of active optical
clock, and the quantum limited linewidth of 1359 nm output is estimated to be
77.6 mHz.


  The kinetics of the process of defect accumulation in rare-gas solids as a
result of exciton self-trapping was studied using the selective vacuum
ultraviolet photoluminescence method for monitoring of the crystal structure of
the samples. The simple kinetic model of defect accumulation in rare-gas
samples was applied to the fitting of the dose dependences of luminescence from
solid Xe and Ne. The characteristic kinetic parameters were obtained by linear
transformation of the time dependence of luminescence intensity of "defect"
subbands.


  We present a test of General Relativity, the measurement of the Earth's
dragging of inertial frames. Our result is obtained using about 3.5 years of
laser-ranged observations of the LARES, LAGEOS and LAGEOS 2 laser-ranged
satellites together with the Earth's gravity field model GGM05S produced by the
space geodesy mission GRACE. We measure $\mu = (0.994 \pm 0.002) \pm 0.05$,
where $\mu$ is the Earth's dragging of inertial frames normalized to its
General Relativity value, 0.002 is the 1-sigma formal error and 0.05 is the
estimated systematic error mainly due to the uncertainties in the Earth's
gravity model GGM05S. Our result is in agreement with the prediction of General
Relativity.


  We introduce GROOT, an imitation learning method for learning robust policies
with object-centric and 3D priors. GROOT builds policies that generalize beyond
their initial training conditions for vision-based manipulation. It constructs
object-centric 3D representations that are robust toward background changes and
camera views and reason over these representations using a transformer-based
policy. Furthermore, we introduce a segmentation correspondence model that
allows policies to generalize to new objects at test time. Through
comprehensive experiments, we validate the robustness of GROOT policies against
perceptual variations in simulated and real-world environments. GROOT's
performance excels in generalization over background changes, camera viewpoint
shifts, and the presence of new object instances, whereas both state-of-the-art
end-to-end learning methods and object proposal-based approaches fall short. We
also extensively evaluate GROOT policies on real robots, where we demonstrate
the efficacy under very wild changes in setup. More videos and model details
can be found in the appendix and the project website:
https://ut-austin-rpl.github.io/GROOT .


  This study aims to comprehensively investigate the deep ensemble approach, an
approximate Bayesian inference, in the multi-output regression task for
predicting the aerodynamic performance of a missile configuration. To this end,
the effect of the number of neural networks used in the ensemble, which has
been blindly adopted in previous studies, is scrutinized. As a result, an
obvious trend towards underestimation of uncertainty as it increases is
observed for the first time, and in this context, we propose the deep ensemble
framework that applies the post-hoc calibration method to improve its
uncertainty quantification performance. It is compared with Gaussian process
regression and is shown to have superior performance in terms of regression
accuracy ($\uparrow55\sim56\%$), reliability of estimated uncertainty
($\uparrow38\sim77\%$), and training efficiency ($\uparrow78\%$). Finally, the
potential impact of the suggested framework on the Bayesian optimization is
briefly examined, indicating that deep ensemble without calibration may lead to
unintended exploratory behavior. This UQ framework can be seamlessly applied
and extended to any regression task, as no special assumptions have been made
for the specific problem used in this study.


  We report on a detailed study of the water maser kinematics and radio
continuum emission toward the most massive and young object in the star-forming
region AFGL 2591. Our analysis shows at least two spatial scales of multiple
star formation, one projected across 0.1 pc on the sky and another one at about
2000 AU from a ZAMS star of about 38 Solar masses. This young stellar object
drives a powerful jet- and wind-driven outflow system with the water masers
associated to the outflow walls, previously detected as a limb-brightened
cavity in the NIR band. At about 1300 AU to the north of this object a younger
protostar drives two bow shocks, outlined by arc-like water maser emission, at
200 AU either side of the source. We have traced the velocity profile of the
gas that expands along these arc-like maser structures and compared it with the
jet-driven outflow model. This analysis suggests that the ambient medium around
the northern protostar is swept up by a jet-driven shock (>66 km/s) and perhaps
a lower-velocity (~10 km/s) wind with an opening angle of about 20 degrees from
the jet axis.


  We consider linear elliptic equations in divergence form with stationary
random coefficients of integrable correlations. We characterize the
fluctuations of a macroscopic observable of a solution to relative order
$\frac{d}{2}$, where $d$ is the spatial dimension; the fluctuations turn out to
be Gaussian. As for previous work on the leading order, this higher-order
characterization relies on a pathwise proximity of the macroscopic fluctuations
of a general solution to those of the (higher-order) correctors, via a
(higher-order) two-scale expansion injected into the homogenization commutator,
thus confirming the scope of this notion. This higher-order generalization
sheds a clearer light on the algebraic structure of the higher-order versions
of correctors, flux correctors, two-scale expansions, and homogenization
commutators. It reveals that in the same way as this algebra provides a
higher-order theory for microscopic spatial oscillations, it also provides a
higher-order theory for macroscopic random fluctuations, although both
phenomena are not directly related. We focus on the model framework of an
underlying Gaussian ensemble, which allows for an efficient use of
(second-order) Malliavin calculus for stochastic estimates. On the technical
side, we introduce annealed Calder\'on-Zygmund estimates for the elliptic
operator with random coefficients, which conveniently upgrade the known
quenched large-scale estimates.


  Traffic management in a city has become a major problem due to the increasing
number of vehicles on roads. Intelligent Transportation System (ITS) can help
the city traffic managers to tackle the problem by providing accurate traffic
forecasts. For this, ITS requires a reliable traffic prediction algorithm that
can provide accurate traffic prediction at multiple time steps based on past
and current traffic data. In recent years, a number of different methods for
traffic prediction have been proposed which have proved their effectiveness in
terms of accuracy. However, most of these methods have either considered
spatial information or temporal information only and overlooked the effect of
other. In this paper, to address the above problem a deep learning based
approach has been developed using both the spatial and temporal dependencies.
To consider spatio-temporal dependencies, nearby road sensors at a particular
instant are selected based on the attributes like traffic similarity and
distance. Two pre-trained deep auto-encoders were cross-connected using the
concept of latent space mapping and the resultant model was trained using the
traffic data from the selected nearby sensors as input. The proposed deep
learning based approach was trained using the real-world traffic data collected
from loop detector sensors installed on different highways of Los Angeles and
Bay Area. The traffic data is freely available from the web portal of the
California Department of Transportation Performance Measurement System (PeMS).
The effectiveness of the proposed approach was verified by comparing it with a
number of machine/deep learning approaches. It has been found that the proposed
approach provides accurate traffic prediction results even for 60-min ahead
prediction with least error than other techniques.


  In this paper, we will study the large scale structure formation using the
gravitational partition function. We will assertively argue that the system of
gravitating galaxies can be analyzed using the Tsallis statistical mechanics.
The divergences in the Tsallis gravitational partition function can be removed
using the mathematical riches of the generalization of the dimensional
regularization (GDR). The finite gravitational partition function thus obtained
will be used to evaluate the thermodynamics of the system of galaxies and thus,
to understand the clustering of galaxies in the universe. The correlation
function which is believed to contain the information of clustering of galaxies
will also be discussed in this formalism.


  Let $S$ and $T$ be hyperbolic endomorphisms of $\mathbb{T}^d$ with the
property that the span of the subspace contracted by $S$ along with the
subspace contracted by $T$ is $\mathbb{R}^d$. We show that the Hausdorff
dimension of the intersection of the set of points with equidistributing orbits
under $S$ with the set of points with nondense orbit under $T$ is full. In the
case that $S$ and $T$ are quasihyperbolic automorphisms, we prove that the
Hausdorff dimension of the intersection is again full when we assume that
$\mathbb{R}^d$ is spanned by the subspaces contracted by $S$ and $T$ along with
the central eigenspaces of $S$ and $T$.


  We study the accumulation of an elliptic fixed point of a real analytic
Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with
Diophantine frequency vector $\o_0$ is always accumulated by invariant complex
analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff
normal form of the Hamiltonian at the invariant point satisfies a R\"ussmann
transversality condition, the fixed point is accumulated by real analytic
KAM-tori which cover positive Lebesgue measure in the phase space (in this part
it suffices to assume that $\o_0$ has rationally independent coordinates). If
the Birkhoff normal form is degenerate, there exists an analytic subvariety of
complex dimension at least $d+1$ passing through 0 that is foliated by complex
analytic KAM-tori with frequency $\omega_0$. This is an extension of previous
results obtained in \cite{EFK} to the case of an elliptic fixed point.


  We consider the problem of counting the number of varieties in a family over
a number field which contain a rational point. In particular, for products of
Brauer-Severi varieties and closely related counting functions associated to
Brauer group elements. Using harmonic analysis on toric varieties, we provide a
positive answer to a question of Serre on such counting functions in some
cases. We also formulate some conjectures on generalisations of Serre's
problem.


  As shown by Overhauser and others, accurate pair densities for the uniform
electron gas may be found by solving a two-electron scattering problem with an
effective screened electron-electron repulsion. In this work we explore the
extension of this approach to nonuniform systems, and we discuss its potential
for density functional theory. For the spherically- and system-averaged pair
density of two-electron atoms we obtain very accurate short-range properties,
including, for nuclear charge $Z\ge 2$, ``on-top'' values (zero
electron-electron distance) essentially indistinguishable from those coming
from precise variational wavefunctions. By means of a nonlinear adiabatic
connection that separates long- and short-range effects, we also obtain
Kohn-Sham correlation energies whose error is less than 4 mHartree, again for
$Z\ge 2$, and short-range-only correlation energies whose accuracy is one order
of magnitude better.


  A comparative stochastic and deterministic study of a family of SEIRS
epidemic dynamic models for malaria is presented. The family type is determined
by the qualitative behavior of the nonlinear incidence rates of the disease.
Furthermore, the malaria models exhibit three random delays:- two of the delays
represent the incubation periods of the disease inside the vector and human
hosts, whereas the third delay is the period of effective natural immunity
against the disease. The stochastic malaria models are improved by including
the random environmental fluctuations in the disease transmission and natural
death rates of humans. Insights about the effects of the delays and the noises
on the malaria dynamics are gained via comparative analyses of the family of
stochastic and deterministic models, and further critical examination of the
significance of the intensities of the white noises in the system on (1) the
existence and stability of the equilibria, and also on (2) the eradication and
persistence of malaria in the human population. The basic reproduction numbers
and other threshold values for malaria in the stochastic and deterministic
settings are determined and compared for the cases of constant or random delays
in the system. Numerical simulation results are presented.


  Farkas' Lemma is a foundational result in linear programming, with
implications in duality, optimality conditions, and stochastic and bilevel
programming. Its generalizations are known as theorems of the alternative.
There exist theorems of the alternative for integer programming and conic
programming. We present theorems of the alternative for conic integer
programming. We provide a nested procedure to construct a function that
characterizes feasibility over right-hand sides and can determine which
statement in a theorem of the alternative holds.


  In a previous paper we have proven that any multi-resolution analysis of
$L^2(\R)$ produces, for even values of the inverse filling factor and for a
square lattice, a single-electron wave function of the lowest Landau level
(LLL) which, together with its (magnetic) translated, gives rise to an
orthonormal set in the LLL. We have also discussed the inverse construction.
  In this paper we simplify the procedure, clarifying the role of the
kq-representation. Moreover, we extend our previous results to the more
physically relevant case of a triangular lattice and to odd values of the
inverse filling factor. We also comment on other possible shapes of the lattice
as well as on the extension to other Landau levels.
  Finally, just as a first application of our technique, we compute (an
approximation of) the Coulomb energy for the Haar wavefunction, for a filling
$\nu={1/3}$.


  Distributed consensus algorithms such as Paxos have been studied extensively.
They all use the same definition of safety. Liveness is especially important in
practice despite well-known theoretical impossibility results. However, many
different liveness properties and assumptions have been stated, and there are
no systematic comparisons for better understanding of these properties.
  This paper systematically studies and compares different liveness properties
stated for over 30 prominent consensus algorithms and variants. We introduce a
precise high-level language and formally specify these properties in the
language. We then create a hierarchy of liveness properties combining two
hierarchies of the assumptions used and a hierarchy of the assertions made, and
compare the strengths and weaknesses of algorithms that ensure these
properties. Our formal specifications and systematic comparisons led to the
discovery of a range of problems in various stated liveness properties, from
too weak assumptions for which no liveness assertions can hold, to too strong
assumptions making it trivial to achieve the assertions. We also developed TLA+
specifications of these liveness properties, and we use model checking of
execution steps to illustrate liveness patterns for Paxos.


  We present a novel method to combine QCD calculations at
next-to-next-to-leading order (NNLO) with parton shower (PS) simulations, that
can be applied to the production of heavy systems in hadronic collisions, such
as colour singlets or a $t\bar{t}$ pair. The NNLO corrections are included by
connecting the MiNLO$^\prime$ method with transverse-momentum resummation, and
they are calculated at generation time without any additional reweighting,
making the algorithm considerably efficient. Moreover, the combination of
different jet multiplicities does not require any unphysical merging scale, and
the matching preserves the structure of the leading logarithmic corrections of
the Monte Carlo simulation for parton showers ordered in transverse momentum.
We present proof-of-concept applications to hadronic Higgs production and the
Drell-Yan process at the LHC.


  A crucial and problematical feature of quantum mechanics (QM) is
nonobjectivity of properties. The ESR model restores objectivity reinterpreting
quantum probabilities as conditional on detection and embodying the
mathematical formalism of QM into a broader noncontextual (hence local)
framework. We propose here an improved presentation of the ESR model containing
a more complete mathematical representation of the basic entities of the model.
We also extend the model to mixtures showing that the mathematical
representations of proper mixtures does not coincide with the mathematical
representation of mixtures provided by QM, while the representation of improper
mixtures does. This feature of the ESR model entails that some interpretative
problems raising in QM when dealing with mixtures are avoided. From an
empirical point of view the predictions of the ESR model depend on some
parameters which may be such that they are very close to the predictions of QM
in most cases. But the nonstandard representation of proper mixtures allows us
to propose the scheme of an experiment that could check whether the predictions
of QM or the predictions of the ESR model are correct.


  We consider strictly ergodic and strictly weak mixing $C^*$-dynamical
systems. We prove that the system is strictly weak mixing if and only if its
tensor product is strictly ergodic, moreover strictly weak mixing too. We also
investigate some other mixing properties of the system.


  (abridged) Protostellar outflows exhibit large variations in their structure
depending on the observed gas emission. This study analyzes the atomic jet and
molecular outflow in the Class I protostar, TMC1A to characterize morphology
and identify previously undetected spatial features with JWST's NIRSpec IFU. In
addition to identifying a large number of Fe II and H2 lines, we have detected
the bipolar Fe jet by revealing, for the first time, the presence of a
red-shifted atomic jet. Similarly, the red-shifted component of the H2 slower
wide-angle outflow is observed. Both Fe II and H2 red-shifted emission exhibit
significantly lower flux densities compared to their blue-shifted counterparts.
Additionally, we report the detection of a collimated high-velocity (100 km
s-1), blue-shifted H2 outflow, suggesting the presence of a molecular jet in
addition to the well-known wider angle low-velocity structure. The Fe II and H2
jets show multiple intensity peaks along the jet axis, which may be associated
with ongoing or recent outburst events. In addition to the variation in their
intensities, the H2 wide-angle outflow exhibits a "ring"-like structure. The
blue-shifted H2 outflow also shows a left-right brightness asymmetry likely due
to interactions with the surrounding ambient medium and molecular outflows.
Using the Fe II line ratios, the extinction along the atomic jet is estimated
to be between Av = 10-30 on the blue-shifted side, with a trend of decreasing
extinction with distance from the protostar. A similar Av is found for the
red-shifted side, supporting the argument for an intrinsic red-blue outflow
lobe asymmetry rather than environmental effects such as extinction. This
intrinsic difference revealed by the unprecedented sensitivity of JWST,
suggests that younger outflows already exhibit the red-blue side asymmetry more
commonly observed towards jets associated with Class II disks.


  We investigate the potential of the sparse data produced by the Catalina Sky
Survey astrometric project (CSS for short) in asteroid shape and rotational
state determination by the lightcurve inversion method. We show that although
the photometric quality of the CSS data, compared to the dense data, is
significantly worse, it is in principle possible that these data are for some
asteroids with high lightcurve amplitudes sufficient for a unique shape
determination. CSS data are available for $\sim$180 asteroids for which shape
models were previously derived from different photometric data sets. For 13
asteroids from this sample, we derive their unique shape models based only on
CSS data, compare the two independent shape models together and discuss the
reliability of models derived from only CSS data. We also use CSS data to
determine shape models for asteroids with already known rotational period
values, derive 12 unique models and compare previously published periods with
periods determined from the full 3D modeling by the lightcurve inversion
method. Finally, we test different shape resolutions used in the lightcurve
inversion method in order to find reliable asteroid models.


  A deformation of the algebra of diffeomorphisms is constructed for
canonically deformed spaces with constant deformation parameter theta. The
algebraic relations remain the same, whereas the comultiplication rule (Leibniz
rule) is different from the undeformed one. Based on this deformed algebra a
covariant tensor calculus is constructed and all the concepts like metric,
covariant derivatives, curvature and torsion can be defined on the deformed
space as well. The construction of these geometric quantities is presented in
detail. This leads to an action invariant under the deformed diffeomorphism
algebra and can be interpreted as a theta-deformed Einstein-Hilbert action. The
metric or the vierbein field will be the dynamical variable as they are in the
undeformed theory. The action and all relevant quantities are expanded up to
second order in theta.


  We investigate a Kac-type many particle model that allows a reference-free
description of plastic deformation.
  In the framework of the model a solid body is described by a set of particle
positions. A lattice is fitted to the particle configuration around each point
on a mesoscopic scale. The lattice parameters are used as an argument of a
non-linear elasticity energy functional. There are two main results in this
paper. First, we prove an estimate for the difference between the fitted
lattice parameters of points of low energy density that are sufficiently close
to each other. Sequences of these points can be used for homotopy type
arguments. In particular it is possible to identify dislocations as topological
defects in this framework. Furthermore, we use the fitted lattice parameters as
local Lagrangian coordinates and bound the energy from below with a functional
of these coordinates.


  Data from HERA, LEP and the Tevatron, as well as from low energy experiments
are used to constrain the scale of possible electron-quark contact
interactions. Some models are found to describe the existing experimental data
much better than the Standard Model. The possibility of scalar or vector
leptoquark contribution is studied using the Buchmuller-Ruckl-Wyler effective
model. Increase in the global probability observed for scenarios including S_1
or ~V_o leptoquark production/exchange corresponds to more than a 3 sigma
effect. Assuming that a real leptoquark signal is observed, calculated is an
allowed region in the coupling-mass plane.


  Most virtual try-on research is motivated to serve the fashion business by
generating images to demonstrate garments on studio models at a lower cost.
However, virtual try-on should be a broader application that also allows
customers to visualize garments on themselves using their own casual photos,
known as in-the-wild try-on. Unfortunately, the existing methods, which achieve
plausible results for studio try-on settings, perform poorly in the in-the-wild
context. This is because these methods often require paired images (garment
images paired with images of people wearing the same garment) for training.
While such paired data is easy to collect from shopping websites for studio
settings, it is difficult to obtain for in-the-wild scenes.
  In this work, we fill the gap by (1) introducing a StreetTryOn benchmark to
support in-the-wild virtual try-on applications and (2) proposing a novel
method to learn virtual try-on from a set of in-the-wild person images directly
without requiring paired data. We tackle the unique challenges, including
warping garments to more diverse human poses and rendering more complex
backgrounds faithfully, by a novel DensePose warping correction method combined
with diffusion-based conditional inpainting. Our experiments show competitive
performance for standard studio try-on tasks and SOTA performance for street
try-on and cross-domain try-on tasks.


  We provide further analytical and first numerical results on the solvable
$\lambda\phi^4_4$-NCQFT model. We prove that for $\lambda<0$ the singular
integral equation has a unique solution, whereas for $\lambda>0$ there is
considerable freedom. Furthermore we provide integral formulae for partial
derivatives of the matrix 2-point function, which are the key to investigate
reflection positivity.
  The numerical implementation of these equations gives evidence for phase
transitions. The derivative of the finite wavefunction renormalisation with
respect to $\lambda$ is discontinuous at $\lambda_c \approx -0.39$. This leads
to singularities in higher correlation functions for $\lambda<\lambda_c$. The
phase $\lambda >0$ is not yet under control because of the freedom in the
singular integral equation.
  Reflection positivity requires that the two-point function is Stieltjes.
Implementing Widder's criteria for Stieltjes functions we exclude reflection
positivity outside the phase $[\lambda_c,0]$. For the phase $\lambda_c<\lambda
\leq 0$ we show that refining the discrete approximation we satisfy Widder to
higher and higher order. This is clear evidence, albeit no proof, of reflection
positivity in that phase.


  Higgs boson productions at the LHC will serve as a sensitive probe of various
little Higgs models. In this work we comparatively study two littlest Higgs
models with different T-parity constructions through examining their effects in
three production processes of the Higgs boson at the LHC, namely the
productions of a single Higgs, a Higgs-pair, as well as a Higgs boson
associated with a pair of top and anti-top quarks. The two models are
characterized by predicting a top partner canceling the Higgs mass quadratic
divergence contributed by the top quark with even and odd T-parity,
respectively. We find that both models can alter the SM cross sections sizably
and their corrections also differ significantly. Therefore, the Higgs boson
productions at the LHC may shed some light on these two models or even
distinguish them.


  We demonstrate experimentally and theoretically that two-dimensional (2D)
heavy hole systems in single heterostructures exhibit a \emph{decrease} in
spin-orbit interaction-induced spin splitting with an increase in perpendicular
electric field. Using front and back gates, we measure the spin splitting as a
function of applied electric field while keeping the density constant. Our
results are in contrast to the more familiar case of 2D electrons where spin
splitting increases with electric field.


  In the present paper we construct novel non-topological, spontaneously
scalarized neutron stars in multi-scalar Gauss-Bonnet gravity with maximally
symmetric target space, and nontrivial map $\varphi:spacetime \rightarrow
target\ space$. The theory is characterized by the fact that for some classes
of coupling functions the field equations allow solutions with trivial scalar
field, which coincide with the general relativistic ones. For a certain range
of parameters those solutions lose stability and new branches of solutions with
nontrivial scalar field bifurcate from the trivial branch. For a given set of
parameters, those branches are characterized by the number of zeros of the
scalar field, and they are energetically more favorable than the general
relativistic ones.


  We construct dynamical black ring solutions in the five dimensional
Einstein-Maxwell system with a positive cosmological constant and investigate
the geometrical structure. The solutions describe the physical process such
that a thin black ring at early time shrinks and changes into a single black
hole as time increase. We also discuss the multi-black rings and the
coalescence of them.


  Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) have
a long history together in the standard cosmology. The general concordance
between the predicted and observed light element abundances provides a direct
probe of the universal baryon density. Recent CMB anisotropy measurements,
particularly the observations performed by the WMAP satellite, examine this
concordance by independently measuring the cosmic baryon density. Key to this
test of concordance is a quantitative understanding of the uncertainties in the
BBN light element abundance predictions. These uncertainties are dominated by
systematic errors in nuclear cross sections. We critically analyze the cross
section data, producing representations that describe this data and its
uncertainties, taking into account the correlations among data, and explicitly
treating the systematic errors between data sets. Using these updated nuclear
inputs, we compute the new BBN abundance predictions, and quantitatively
examine their concordance with observations. Depending on what deuterium
observations are adopted, one gets the following constraints on the baryon
density: OmegaBh^2=0.0229\pm0.0013 or OmegaBh^2 = 0.0216^{+0.0020}_{-0.0021} at
68% confidence, fixing N_{\nu,eff}=3.0. Concerns over systematics in helium and
lithium observations limit the confidence constraints based on this data
provide. With new nuclear cross section data, light element abundance
observations and the ever increasing resolution of the CMB anisotropy, tighter
constraints can be placed on nuclear and particle astrophysics. ABRIDGED


  Topologically stable magnetic skyrmion has a much lower depinning current
density that may be useful for memory as well as neuromorphic computing.
However, skyrmion-based devices suffer from the Magnus force originating from
the skyrmion Hall effect, which may result in unwanted skyrmion annihilation if
the magnitude of the driving current gets too large. A design of an artificial
neuron and a synapse using a synthetic antiferromagnetically coupled bilayer
device, which nullifies the Magnus force, is demonstrated in this work. The
leak term in the artificial leaky integrate-and-fire neuron is achieved by
engineering the uniaxial anisotropy profile of the neuronal device. The
synaptic device has a similar structure as the neuronal device but has a
constant uniaxial anisotropy. The synaptic device also has a linear and
symmetric weight update, which is a highly desirable trait of an artificial
synapse. Neuronal and synaptic devices based on magnetic domain-wall (DW)
motion are also studied and compared to skyrmionic devices. Our simulation
results show the energy required to perform such operation in DW or
skyrmion-based devices is on the order of a few fJ.


  In a model where constituent quarks and diquarks interact through quark
exchange the Bethe-Salpeter equation in ladder approximation for the nucleon is
solved. Quark and diquark confinement is effectively parametrized by choosing
appropriately modified propagators. The coupling to external currents is
implemented via nontrivial vertex functions for quarks and diquarks to ensure
gauge invariance at the constituent level. Nucleon matrix elements are
evaluated in a generalised impulse approximation, and electromagnetic, pionic
and axial form factors are calculated.


  Particle beams provided by accelerators occupy a finite volume of the four
dimensional transverse phase space. The latter is spanned by the four degrees
of freedom, i.e., horizontal/vertical position and momentum. This volume is
referred to as emittance. Horizontal and vertical emittances are obtained
through projections onto the two transverse sub-phase spaces. Eigen-emittances
are obtained from the latter by removing all horizontal-vertical correlations
through an appropriate beam optics section. Canonical vorticity flux is used
for instance for modelling dynamics of tubes formed by magnetic field lines and
particle currents embedded into plasmas. This report is on the relation of
eigen-emittances and canonical vorticity flux. Change of beam eigen-emittances
is equivalent to change of beam canonical vorticity flux.


  We use quasimap Floer cohomology for varying symplectic quotients to resolve
several puzzles regarding displaceability of toric moment fibers. For example,
we (i) present a compact Hamiltonian torus action containing an {\em open}
subset of non-displaceable orbits and a codimension four singular set, partly
answering a question of McDuff, and (ii) determine displaceability for most of
the moment fibers of a symplectic ellipsoid.


  The surging demand for cloud computing resources, driven by the rapid growth
of sophisticated large-scale models and data centers, underscores the critical
importance of efficient and adaptive resource allocation. As major tech
enterprises deploy massive infrastructures with thousands of GPUs, existing
cloud platforms still struggle with low resource utilization due to key
challenges: capturing hierarchical indicator structures, modeling non-Gaussian
distributions, and decision-making under uncertainty. To address these
challenges, we propose HRAMONY, an adaptive Hierarchical Attention-based
Resource Modeling and Decision-Making System. HARMONY combines hierarchical
multi-indicator distribution forecasting and uncertainty-aware Bayesian
decision-making. It introduces a novel hierarchical attention mechanism that
comprehensively models complex inter-indicator dependencies, enabling accurate
predictions that can adapt to evolving environment states. By transforming
Gaussian projections into adaptive non-Gaussian distributions via Normalizing
Flows. Crucially, HARMONY leverages the full predictive distributions in an
adaptive Bayesian process, proactively incorporating uncertainties to optimize
resource allocation while robustly meeting SLA constraints under varying
conditions. Extensive evaluations across four large-scale cloud datasets
demonstrate HARMONY's state-of-the-art performance, significantly outperforming
nine established methods. A month-long real-world deployment validated
HARMONY's substantial practical impact, realizing over 35,000 GPU hours in
savings and translating to $100K+ in cost reduction, showcasing its remarkable
economic value through adaptive, uncertainty-aware scaling. Our code is
available at https://github.com/Floating-LY/HARMONY1.


  Concept lattice drawings are an important tool to visualize complex relations
in data in a simple manner to human readers. Many attempts were made to
transfer classical graph drawing approaches to order diagrams. Although those
methods are satisfying for some lattices they unfortunately perform poorly in
general. In this work we present a novel tool to draw concept lattices that is
purely motivated by the order structure.


  Electron beam ion traps (EBIT) are ideal tools for both production and study
of highly charged ions (HCI). In order to reduce their construction,
maintenance, and operation costs we have developed a novel, compact,
room-temperature design, the Heidelberg Compact EBIT (HC-EBIT). Four already
commissioned devices operate at the strongest fields (up to 0.86 T) reported
for such EBITs using permanent magnets, run electron beam currents up to 80 mA
and energies up to 10 keV. They demonstrate HCI production, trapping, and
extraction of pulsed Ar$^{16+}$ bunches and continuous 100 pA ion beams of
highly charged Xe up to charge state 29+, already with a 4 mA, 2 keV electron
beam. Moreover, HC-EBITs offer large solid-angle ports and thus high photon
count rates, e. g., in x-ray spectroscopy of dielectronic recombination in HCIs
up to Fe$^{24+}$, achieving an electron-energy resolving power of $E/\Delta E >
1500$ at 5 keV. Besides traditional on-axis electron guns, we have also
implemented a novel off-axis gun for laser, synchrotron, and free-electron
laser applications, offering clear optical access along the trap axis. We
report on its first operation at a synchrotron radiation facility demonstrating
resonant photoexcitation of highly charged oxygen.


  The Newlander-Nirenberg theorem says that a formally integrable complex
structure is locally equivalent to the complex structure in the complex
Euclidean space. We will show two results about the Newlander-Nirenberg theorem
with parameter. The first extends the Newlander-Nirenberg theorem to a
parametric version, and its proof yields a sharp regularity result as Webster's
proof for the Newlander-Nirenberg theorem. The second concerns a version of
Nirenberg's complex Frobenius theorem and its proof yields a result with a mild
loss of regularity.


  Differential Privacy (DP) mechanisms usually {force} reduction in data
utility by producing "out-of-bound" noisy results for a tight privacy budget.
We introduce the Budget Recycling Differential Privacy (BR-DP) framework,
designed to provide soft-bounded noisy outputs for a broad range of existing DP
mechanisms. By "soft-bounded," we refer to the mechanism's ability to release
most outputs within a predefined error boundary, thereby improving utility and
maintaining privacy simultaneously. The core of BR-DP consists of two
components: a DP kernel responsible for generating a noisy answer per
iteration, and a recycler that probabilistically recycles/regenerates or
releases the noisy answer. We delve into the privacy accounting of BR-DP,
culminating in the development of a budgeting principle that optimally
sub-allocates the available budget between the DP kernel and the recycler.
Furthermore, we introduce algorithms for tight BR-DP accounting in composition
scenarios, and our findings indicate that BR-DP achieves reduced privacy
leakage post-composition compared to DP. Additionally, we explore the concept
of privacy amplification via subsampling within the BR-DP framework and propose
optimal sampling rates for BR-DP across various queries. We experiment with
real data, and the results demonstrate BR-DP's effectiveness in lifting the
utility-privacy tradeoff provided by DP mechanisms.


  Profiles of radially symmetric thin plate spline surfaces minimizing the
Beppo Levi energy over a compact annulus $R_{1}\leq r\leq R_{2}$ have been
studied by Rabut via reproducing kernel methods. Motivated by our recent
construction of Beppo Levi polyspline surfaces, we focus here on minimizing the
radial energy over the full semi-axis $0<r<\infty$. Using a $L$-spline
approach, we find two types of minimizing profiles: one is the limit of Rabut's
solution as $R_{1}\rightarrow0$ and $R_{2}\rightarrow\infty$ (identified as a
`non-singular' $L$-spline), the other has a second-derivative singularity and
matches an extra data value at $0$. For both profiles and $p\in\left[
2,\infty\right] $, we establish the $L^{p}$-approximation order $3/2+1/p$ in
the radial energy space. We also include numerical examples and obtain a novel
representation of the minimizers in terms of dilates of a basis function.


  Crystalline sheets (e.g., graphene and transition metal dichalcogenides)
liberated from a substrate are a paradigm for materials at criticality because
flexural phonons can fluctuate into the third dimension. Although studies of
static critical behaviors (e.g., the scale-dependent elastic constants) are
plentiful, investigations of dynamics remain limited. Here, we use molecular
dynamics to study the time dependence of the midpoint (the height
center-of-mass) of doubly clamped nanoribbons, as prototypical graphene
resonators, under a wide range of temperature and strain conditions. By
treating the ribbon midpoint as a Brownian particle confined to a nonlinear
potential (which assumes a double-well shape beyond the buckling transition),
we formulate an effective theory describing the ribbon's tunneling rate across
the two wells and its oscillations inside a given well. We find that, for
nanoribbbons compressed above the Euler buckling point and thermalized above a
temperature at which the non-linear effects due to thermal fluctuations become
significant, the exponential term (the ratio between energy barrier and
temperature) depends only on the geometry, but not the temperature, unlike the
usual Arrhenius behavior. Moreover, we find that the natural oscillation time
for small strain shows a non-trivial scaling $\tau_{\rm o}\sim
L_0^{\,z}T^{-\eta/4}$, with $L_0$ being the ribbon length, $z=2-\eta/2$ being
the dynamic critical exponent, $\eta=0.8$ being the scaling exponent describing
scale-dependent elastic constants, and $T$ being the temperature. These unusual
scale- and temperature-dependent dynamics thus exhibit dynamic criticality and
could be exploited in the development of graphene-based nanoactuators.


  Upon the absence of signals of new physics at the LHC, a reasonable strategy
is to assume that new particles are very heavy and the other model parameters
are unknown yet. In the aligned two Higgs doublet model, however, heavy Higgs
boson masses above 500 GeV enhance some couplings in the scalar potential,
which causes a breakdown of the perturbative unitariry in general. Some tuning
among model parameters is required. We find that one information on the heavy
Higgs boson mass, say $M_H$, has significant theoretical implications: (i) the
other heavy Higgs bosons should have similar masses to $M_H$ within $\pm
\mathcal{O}(10)\%$; (ii) the inequalities from the theoretical constraints are
practically reduced to an equation such that $m_{12}^2 \tan\beta$ is constant,
where $m_{12}^2$ is the soft $Z_2$ breaking parameter and $\tan\beta$ is the
ratio of two vacuum expectation values; (iii) the triple Higgs coupling
$\lambda_{HHh}$ is constant over $\tan\beta$ while $\lambda_{HHH}$ and
$\lambda_{AAH}$ are linearly proportional to $\tan\beta$. The double
Higgs-strahlung process of $e^+ e^- \to ZHH$ is also studied, of which the
total cross section is almost constant with the given $M_H$.


  Generative Adversarial Networks (GANs) have achieved a great success in
unsupervised learning. Despite its remarkable empirical performance, there are
limited theoretical studies on the statistical properties of GANs. This paper
provides approximation and statistical guarantees of GANs for the estimation of
data distributions that have densities in a H\"{o}lder space. Our main result
shows that, if the generator and discriminator network architectures are
properly chosen, GANs are consistent estimators of data distributions under
strong discrepancy metrics, such as the Wasserstein-1 distance. Furthermore,
when the data distribution exhibits low-dimensional structures, we show that
GANs are capable of capturing the unknown low-dimensional structures in data
and enjoy a fast statistical convergence, which is free of curse of the ambient
dimensionality. Our analysis for low-dimensional data builds upon a universal
approximation theory of neural networks with Lipschitz continuity guarantees,
which may be of independent interest.


  We show the equivalence of several constructions of the category of condensed
sets by using free resolutions of compact Hausdorff spaces. We also give an
elementary construction of the condensed set associated to any presheaf on
compact Hausdorff spaces.


  The results of VLBI total intensity (I) and linear polarization (P)
observations at 6cm are presented for ten radio bright BL Lacertae objects.
These images complete first-epoch polarization observations for the 1-Jy sample
of northern BL Lacertae objects defined by Kuhr and Schmidt. Estimates of
superluminal speeds are presented for several sources, bringing the total
number of sources in the sample for which such estimates are available to 16.
Second epoch observations currently being reduced should yield speed estimates
for VLBI features in essentially all the sources in the sample. The jet
magnetic fields of these BL Lacertae objects are usually transverse to the
local jet direction, but a sizeable minority (about 30%) have VLBI jet
components with longitudinal magnetic fields. This may suggest that the
conditions in the VLBI jets of BL Lacertae objects are favorable for the
formation of relativistic shocks; alternatively, it may be that the toroidal
component of the intrinsic jet magnetic field is characteristically dominant in
these sources.


  We propose a detector of adversarial samples that is based on the view of
neural networks as discrete dynamic systems. The detector tells clean inputs
from abnormal ones by comparing the discrete vector fields they follow through
the layers. We also show that regularizing this vector field during training
makes the network more regular on the data distribution's support, thus making
the activations of clean inputs more distinguishable from those of abnormal
ones. Experimentally, we compare our detector favorably to other detectors on
seen and unseen attacks, and show that the regularization of the network's
dynamics improves the performance of adversarial detectors that use the
internal embeddings as inputs, while also improving test accuracy.


  Given a connected graph $G$ whose vertices are perfectly reliable and whose
edges each fail independently with probability $q\in[0,1],$ the
\textit{(all-terminal) reliability} of $G$ is the probability that the
resulting subgraph of operational edges contains a spanning tree (this
probability is always a polynomial in $q$). The location of the roots of
reliability polynomials has been well studied, with particular interest in
finding those with the largest moduli. In this paper, we will discuss a related
problem -- among all reliability polynomials of graphs on $n$ vertices, which
has a root of smallest modulus? We prove that, provided $n \geq 3$, the roots
of smallest moduli occur precisely for the cycle graph $C_n$, and the root is
unique.


  In this paper, we address the problem of autonomous multi-robot mapping,
exploration and navigation in unknown, GPS-denied indoor or urban environments
using a swarm of robots equipped with directional sensors with limited sensing
capabilities and limited computational resources. The robots have no a priori
knowledge of the environment and need to rapidly explore and construct a map in
a distributed manner using existing landmarks, the presence of which can be
detected using onboard senors, although little to no metric information
(distance or bearing to the landmarks) is available. In order to correctly and
effectively achieve this, the presence of a necessary density/distribution of
landmarks is ensured by design of the urban/indoor environment. We thus address
this problem in two phases: 1) During the design/construction of the
urban/indoor environment we can ensure that sufficient landmarks are placed
within the environment. To that end we develop a filtration-based approach for
designing strategic placement of landmarks in an environment. 2) We develop a
distributed algorithm using which a team of robots, with no a priori knowledge
of the environment, can explore such an environment, construct a topological
map requiring no metric/distance information, and use that map to navigate
within the environment. This is achieved using a topological representation of
the environment (called a Landmark Complex), instead of constructing a complete
metric/pixel map. The representation is built by the robot as well as used by
them for navigation through a balance between exploration and exploitation. We
use tools from homology theory for identifying "holes" in the
coverage/exploration of the unknown environment and hence guiding the robots
towards achieving a complete exploration and mapping of the environment.


  The 7Li(p,n) reaction in combination with a 3.7 MV Van de Graaff accelerator
was routinely used at FZK to perform activation as well as time-of-flight
measurements with neutrons in the keV-region. Planned new setups with much
higher proton currents like SARAF and FRANZ and the availability of
liquid-lithium target technology will trigger a renaissance of this method. A
detailed understanding of the neutron spectrum is not only important during the
planning phase of an experiment, but also during for the analysis of activation
experiments. Therefore, the Monte-Carlo based program PINO (Protons In Neutrons
Out) was developed, which allows the simulation of neutron spectra considering
the geometry of the setup and the proton-energy distribution.


  We obtain some nonlocal characterizations for a class of variable exponent
Sobolev spaces arising in nonlinear elasticity, in the theory of
electrorheological fluids as well as in image processing for the regions where
the variable exponent $p(x)$ reaches the value $1$.


  Describing the comprehensive evolutionary scenario for asteroids is key to
explaining the various physical processes of the solar system. Bulk-scale
carbonaceous chondrites (CCs) possibly record the primordial information
associated with the formation processes of their parent bodies. In this study,
we tried to estimate the relative formation region of volatile-rich asteroids
by utilizing the nucleosynthetic Cr isotopic variation (54Cr/52Cr) in
bulk-scale CCs. Numerical calculations were conducted to track the temporal
evolution of isotopically different (solar and presolar) dust and 54Cr/52Cr
values for mixed materials with disk radius. First, we found that isotopic
heterogeneities in CC formation regions would be preserved with a weak
turbulence setting that would increase the timescales of the advection and
diffusion in the disk. Second, we assessed the effects of gaps formed by giant
planets. Finally, the distance from the injected supernovae and Cr isotopic
compositions of the presolar grains were investigated in terms of the estimated
formation region of CCs. In our results, a plausible formation region of four
types of CCs can be obtained with the supernova from approximately 2 pc and
typical Cr isotopic compositions of presolar grains. Among the parent bodies of
CCs (i.e., volatile-rich asteroids), B-type asteroids formed in the outermost
region, which is inconsistent with the present population, showing that D-type
asteroids are generally located beyond most of the C-complex asteroids. Both
the initial and present orbits of asteroids might be explained by the scatter
attributed to the inward-outward migration of Jupiter and Saturn.


  The impact of the solar activity on the heliosphere has a strong influence on
the modulation of the flux of low energy galactic cosmic rays arriving at
Earth. Different instruments, such as neutron monitors or muon detectors, have
been recording the variability of the cosmic ray flux at ground level for
several decades. Although the Pierre Auger Observatory was designed to observe
cosmic rays at the highest energies, it also records the count rates of low
energy secondary particles (the scaler mode) for the self-calibration of its
surface detector array. From observations using the scaler mode at the Pierre
Auger Observatory, modulation of galactic cosmic rays due to solar transient
activity has been observed (e.g., Forbush decreases). Due to the high total
count rate coming from the combined area of its detectors, the Pierre Auger
Observatory (its detectors have a total area greater than $16\,000$\,m$^2$)
detects a flux of secondary particles of the order of $\sim 10^8$\,counts per
minute. Time variations of the cosmic ray flux related to the activity of the
heliosphere can be determined with high accuracy. In this paper we briefly
describe the scaler mode and analyze a Forbush decrease together with the
interplanetary coronal mass ejection that originated it. The Auger scaler data
are now publicly available.


  Working over a pseudo-Riemannian manifold, for each vector bundle with
connection we construct a sequence of three differential operators which is a
complex (termed a Yang-Mills detour complex) if and only if the connection
satisfies the full Yang-Mills equations. A special case is a complex
controlling the deformation theory of Yang-Mills connections. In the case of
Riemannian signature the complex is elliptic. If the bundle connection respects
a metric on the vector bundle then the complex is formally self-adjoint. In
dimension 4 the complex is conformally invariant and generalises, to the full
Yang-Mills setting, the composition of (two operator) Yang-Mills complexes for
(anti-)self-dual Yang-Mills connections. Via a prolonged system and tractor
connection a diagram of differential operators is constructed which, when
commutative, generates differential complexes of natural operators from the
Yang-Mills detour complex. In dimension 4 this construction is conformally
invariant and is used to yield two new sequences of conformal operators which
are complexes if and only if the Bach tensor vanishes everywhere. In Riemannian
signature these complexes are elliptic. In one case the first operator is the
twistor operator and in the other sequence it is the operator for Einstein
scales. The sequences are detour sequences associated to certain
Bernstein-Gelfand-Gelfand sequences.


  For a family of random walks $\{S^{(a)}\}$ satisfying
$\mathbf{E}S_1^{(a)}=-a<0$ we consider ladder epochs $\tau^{(a)}=\min\{k\geq1:
S_k^{(a)}<0\}$. We study the asymptotic, as $a\to0$, behaviour of
$\mathbf{P}(\tau^{(a)}>n)$ in the case when $n=n(a)\to\infty$. As a consequence
we obtain also the growth rates of the moments of $\tau^{(a)}$.


  We introduce two lattice growth models: aggregation of $l$-dimensional boxes
and aggregation of partitions with $l$ parts. We describe properties of the
models: the parameter set of aggregations, the moments of the random variable
of the number of growth directions, asymptotical behavior of proportions of the
most frequent transitions of two- and three-dimensional self-aggregations.


  We have grown untwinned YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) films on (110) MgO
substrates that were pre-annealed at high temperature in oxygen atmosphere. The
annealing results in surface reconstruction with shallow facets, which induce
the suppression of the YBCO twinning domains, and the preferential alignment of
the CuO chains along one of the in-plane directions of the substrate. Because
of the large mismatch between the in-plane lattice parameters of film and
substrate, the strain induced by the MgO into the YBCO layer is strong and very
peculiar. The YBCO film is compressed, with respect to the bulk, and presents a
unidirectional buckling of the atomic planes, along the chains' direction, due
to a deformation of the copper-oxygen octahedra. The YBCO films, which can be
grown with thicknesses down to few unit cells and oxygen doping levels spanning
most of the superconducting dome, are patterned into nanowires with dimensions
down to 50 nm. The anisotropies due to the untwinning state are preserved in
these structures; moreover, additional anisotropies appear, in ultrathin
structures where strain effects become more pronounced. Such untwinned and
compressively strained films can therefore be used as a platform to study the
interplay between strain and the various local orders in the normal state of
YBCO.


  Using general arguments of an optimization taking place between the pair wave
function and the repulsive part of the electron-electron interaction, we
analyze the superconducting gap in materials with multiple Fermi-surface (FS)
pockets, with exemplary application to two proto-type ferropnictide setups. On
the basis of functional renormalization group (FRG) calculations for a wide
parameter span of the bare interactions, we show that the symmetry of the gap
and the nodal versus nodeless behavior is driven by this optimization
requirement.


  The simulation of the elastodynamics equations at high-frequency suffers from
the well known pollution effect. We present a Petrov--Galerkin multiscale
sub-grid correction method that remains pollution free in natural resolution
and oversampling regimes. This is accomplished by generating corrections to
coarse-grid spaces with supports determined by oversampling lengths related to
the $\log(k)$, $k$ being the wavenumber. Key to this method are
polynomial-in-$k$ bounds for stability constants and related inf-sup constants.
To this end, we establish polynomial-in-$k$ bounds for the elastodynamics
stability constants in general Lipschitz domains with radiation boundary
conditions in $\mathbb{R}^3$. Previous methods relied on variational
techniques, Rellich identities, and geometric constraints. In the context of
elastodynamics, these suffer from the need to hypothesize a Korn's inequality
on the boundary. The methods in this work are based on boundary integral
operators and estimation of Green's function's derivatives dependence on $k$
and do not require this extra hypothesis. We also implemented numerical
examples in two and three dimensions to show the method eliminates pollution in
the natural resolution and oversampling regimes, as well as performs well when
compared to standard Lagrange finite elements.


  In this paper, we optimize a Wireless Powered Communication (WPC) system
including multiple pair of users, where transmitters employ single-antenna to
transmit their information and power to their receivers with the help of one
multiple-antennas Amplify-and-Forward (AF) relay or an active Intelligent
Reflecting Surface (IRS). We propose a joint Time Switching (TS) scheme in
which transmitters, receivers, and the relay/IRS are either in their energy or
information transmission/reception modes. The transmitted multi-carrier
unmodulated and modulated waveforms are used for Energy Harvesting (EH) and
Information Decoding (ID) modes, respectively. In order to design an optimal
fair system, we maximize the minimum rate of all pairs for both relay and IRS
systems through a unified framework. This framework allows us to simultaneously
design energy waveforms, find optimal relay/IRS amplification/reflection
matrices, allocate powers for information waveforms, and allocate time
durations for various phases. In addition, we take into account the
non-linearity of the EH circuits in our problem. This problem turns out to be
non-convex. Thus, we propose an iterative algorithm by using the
Minorization-Maximization (MM) technique, which quickly converges to the
optimal solution. Numerical examples show that the proposed method improves the
performance of the multi-pair WPC relay/IRS system under various setups.


  To contain the Coronavirus disease (COVID-19) pandemic, one of the
non-pharmacological epidemic control measures in response to the COVID-19
outbreak is reducing the transmission rate of SARS-COV-2 in the population
through (physical) social distancing. An interactive web-based mapping platform
that provides timely quantitative information on how people in different
counties and states reacted to the social distancing guidelines was developed
with the support of the National Science Foundation (NSF). It integrates
geographic information systems (GIS) and daily updated human mobility
statistical patterns derived from large-scale anonymized and aggregated
smartphone location big data at the county-level in the United States, and aims
to increase risk awareness of the public, support governmental decision-making,
and help enhance community responses to the COVID-19 outbreak.


  In order to be effective partners for humans, robots must become increasingly
comfortable with making contact with their environment. Unfortunately, it is
hard for robots to distinguish between ``just enough'' and ``too much'' force:
some force is required to accomplish the task but too much might damage
equipment or injure humans. Traditional approaches to designing compliant
force-feedback controllers, such as stiffness control, require difficult
hand-tuning of control parameters and make it difficult to build safe,
effective robot collaborators. In this paper, we propose a novel yet
easy-to-implement force feedback controller that uses control barrier functions
(CBFs) to derive a compliant controller directly from users' specifications of
the maximum allowable forces and torques. We compare our approach to
traditional stiffness control to demonstrate potential advantages of our
control architecture, and we demonstrate the effectiveness of our controller on
an example human-robot collaboration task: cooperative manipulation of a bulky
object.


  The complexity of linear mixed-effects (LME) models means that traditional
diagnostics are rendered less effective. This is due to a breakdown of
asymptotic results, boundary issues, and visible patterns in residual plots
that are introduced by the model fitting process. Some of these issues are well
known and adjustments have been proposed. Working with LME models typically
requires that the analyst keeps track of all the special circumstances that may
arise. In this paper we illustrate a simpler but generally applicable approach
to diagnosing LME models. We explain how to use new visual inference methods
for these purposes. The approach provides a unified framework for diagnosing
LME fits and for model selection. We illustrate the use of this approach on
several commonly available data sets. A large-scale Amazon Turk study was used
to validate the methods. R code is provided for the analyses.


  Let $\mathcal C$ be a category with finite colimits, and let $(\mathcal
E,\mathcal M)$ be a factorisation system on $\mathcal C$ with $\mathcal M$
stable under pushouts. Writing $\mathcal C;\mathcal M^{\mathrm{op}}$ for the
symmetric monoidal category with morphisms cospans of the form $\stackrel{c}\to
\stackrel{m}\leftarrow$, where $c \in \mathcal C$ and $m \in \mathcal M$, we
give method for constructing a category from a symmetric lax monoidal functor
$F\colon (\mathcal C; \mathcal M^{\mathrm{op}},+) \to (\mathrm{Set},\times)$. A
morphism in this category, termed a \emph{decorated corelation}, comprises (i)
a cospan $X \to N \leftarrow Y$ in $\mathcal C$ such that the canonical
copairing $X+Y \to N$ lies in $\mathcal E$, together with (ii) an element of
$FN$. Functors between decorated corelation categories can be constructed from
natural transformations between the decorating functors $F$. This provides a
general method for constructing hypergraph categories---symmetric monoidal
categories in which each object is a special commutative Frobenius monoid in a
coherent way---and their functors. Such categories are useful for modelling
network languages, for example circuit diagrams, and such functors their
semantics.


  Let $F$ be a non-archimedean local field of characteristic not equal to 2. In
this paper, we prove the local converse theorem for quasi-split $\O_{2n}(F)$
and $\SO_{2n}(F)$, via the description of the local theta correspondence
between $\O_{2n}(F)$ and $\Sp_{2n}(F)$. More precisely, as a main step, we
explicitly describe the precise behavior of the $\gamma$-factors under the
correspondence. Furthermore, we apply our results to prove the weak rigidity
theorems for irreducible generic cuspidal automorphic representations of
$\O_{2n}(\A)$ and $\SO_{2n}(\mathbb{A})$, respectively, where $\A$ is a ring of
adele of a global number field $L$.


  We study soliton gauge states in the spectrum of bosonic string compatified
on torus. The enhenced Kac-Moody gauge symmetry, and thus T-duality, is shown
to be related to the existence of these soliton gauge states in some moduli
points.


  For a general class of percolation models with long-range correlations on
$\mathbb Z^d$, $d\geq 2$, introduced in arXiv:1212.2885, we establish
regularity conditions of Barlow arXiv:math/0302004 that mesoscopic subballs of
all large enough balls in the unique infinite percolation cluster have regular
volume growth and satisfy a weak Poincar\'e inequality. As immediate
corollaries, we deduce quenched heat kernel bounds, parabolic Harnack
inequality, and finiteness of the dimension of harmonic functions with at most
polynomial growth. Heat kernel bounds and the quenched invariance principle of
arXiv:1310.4764 allow to extend various other known results about Bernoulli
percolation by mimicking their proofs, for instance, the local central limit
theorem of arXiv:0810.2467 or the result of arXiv:1111.4853 that the dimension
of at most linear harmonic functions on the infinite cluster is $d+1$.
  In terms of specific models, all these results are new for random
interlacements at every level in any dimension $d\geq 3$, as well as for the
vacant set of random interlacements arXiv:0704.2560, arXiv:0808.3344 and the
level sets of the Gaussian free field arXiv:1202.5172 in the regime of the
so-called local uniqueness (which is believed to coincide with the whole
supercritical regime for these models).


  Amid the expanding use of pre-training data, the phenomenon of benchmark
dataset leakage has become increasingly prominent, exacerbated by opaque
training processes and the often undisclosed inclusion of supervised data in
contemporary Large Language Models (LLMs). This issue skews benchmark
effectiveness and fosters potentially unfair comparisons, impeding the field's
healthy development. To address this, we introduce a detection pipeline
utilizing Perplexity and N-gram accuracy, two simple and scalable metrics that
gauge a model's prediction precision on benchmark, to identify potential data
leakages. By analyzing 31 LLMs under the context of mathematical reasoning, we
reveal substantial instances of training even test set misuse, resulting in
potentially unfair comparisons. These findings prompt us to offer several
recommendations regarding model documentation, benchmark setup, and future
evaluations. Notably, we propose the "Benchmark Transparency Card" to encourage
clear documentation of benchmark utilization, promoting transparency and
healthy developments of LLMs. we have made our leaderboard, pipeline
implementation, and model predictions publicly available, fostering future
research.


  In this paper we consider a singular wave equation with distributional and
more singular non-distributional coefficients and develop tools and techniques
for the phase-space analysis of such problems. In particular we provide a
detailed analysis for the interaction of singularities of solutions with strong
singularities of the coefficient in a model problem of recent interest.


  Automated animal censuses with aerial imagery are a vital ingredient towards
wildlife conservation. Recent models are generally based on supervised learning
and thus require vast amounts of training data. Due to their scarcity and
minuscule size, annotating animals in aerial imagery is a highly tedious
process. In this project, we present a methodology to reduce the amount of
required training data by resorting to self-supervised pretraining. In detail,
we examine a combination of recent contrastive learning methodologies like
Momentum Contrast (MoCo) and Cross-Level Instance-Group Discrimination (CLD) to
condition our model on the aerial images without the requirement for labels. We
show that a combination of MoCo, CLD, and geometric augmentations outperforms
conventional models pretrained on ImageNet by a large margin. Meanwhile,
strategies for smoothing label or prediction distribution in supervised
learning have been proven useful in preventing the model from overfitting. We
combine the self-supervised contrastive models with image mixup strategies and
find that it is useful for learning more robust visual representations.
Crucially, our methods still yield favorable results even if we reduce the
number of training animals to just 10%, at which point our best model scores
double the recall of the baseline at similar precision. This effectively allows
reducing the number of required annotations to a fraction while still being
able to train high-accuracy models in such highly challenging settings.


  We consider a mesoscopic model for a spatially extended FitzHugh-Nagumo
neural network and prove that in the regime where short-range interactions
dominate, the probability density of the potential throughout the network
concentrates into a Dirac distribution whose center of mass solves the
classical non-local reaction-diffusion FitzHugh-Nagumo system. In order to
refine our comprehension of this regime, we focus on the blow-up profile of
this concentration phenomenon. Our main purpose here consists in deriving two
quantitative and strong convergence estimates proving that the profile is
Gaussian: the first one in a L1 functional framework and the second in a
weighted L2 functional setting. We develop original relative entropy techniques
to prove the first result whereas our second result relies on propagation of
regularity.


  Spectrum efficiency and energy efficiency are two critical issues in
designing wireless networks. Through dynamic spectrum access, cognitive radios
can improve the spectrum efficiency and capacity of wireless networks. On the
other hand, radio frequency (RF) energy harvesting has emerged as a promising
technique to supply energy to wireless networks and thereby increase their
energy efficiency. Therefore, to achieve both spectrum and energy efficiencies,
the secondary users in a cognitive radio network (CRN) can be equipped with the
RF energy harvesting capability and such a network can be referred to as an
RF-powered cognitive radio network. In this article, we provide an overview of
the RF-powered CRNs and discuss the challenges that arise for dynamic spectrum
access in these networks. Focusing on the tradeoff among spectrum sensing, data
transmission, and RF energy harvesting, then we discuss the dynamic channel
selection problem in a multi-channel RF-powered CRN. In the RF-powered CRN, a
secondary user can adaptively select a channel to transmit data when the
channel is not occupied by any primary user. Alternatively, the secondary user
can harvest RF energy for data transmission if the channel is occupied. The
optimal channel selection policy of the secondary user can be obtained by
formulating a Markov decision process (MDP) problem. We present some numerical
results obtained by solving this MDP problem.


  We study the possible limitations and sources of decoherence in the scheme
for the deterministic generation of polarization-entangled photons, recently
proposed by Gheri et al. [K. M. Gheri et al., Phys. Rev. A 58, R2627 (1998)],
based on an appropriately driven single atom trapped within an optical cavity.
We consider in particular the effects of laser intensity fluctuations, photon
losses, and atomic motion.


  Given a simple Lie group $H$ of real rank at least $2$ we show that the
maximum cardinality of a set of isospectral non-isometric $H$-locally symmetric
spaces of volume at most $x$ grows at least as fast as $x^{c\log x/ (\log\log
x)^2}$ where $c = c(H)$ is a positive constant. In contrast with the real rank
$1$ case, this bound comes surprisingly close to the total number of such
spaces as estimated in a previous work of Belolipetsky and Lubotzky [BL]. Our
proof uses Sunada's method, results of [BL], and some deep results from number
theory. We also discuss an open number-theoretical problem which would imply an
even faster growth estimate.


  Inspired by problems arising in the geometrical treatment of Yang-Mills
theories and Palatini's gravity, the covariant formulation of Hamiltonian
dynamical systems as a Hamiltonian field theory of dimension $1+0$ on a
manifold with boundary is discussed. After a precise statement of Hamilton's
variational principle in this context, the geometrical properties of the space
of solutions of the Euler-Lagrange equations of the theory are analyzed. A
sufficient condition is obtained that guarantees that the set of solutions of
the Euler-Lagrange equations at the boundary of the manifold, fill a Lagrangian
submanifold of the space of fields at the boundary. Finally a theory of
constraints is introduced that mimics the constraints arising in Palatini's
gravity.


  The AdS/CFT correspondence provides a unique way to study the vortex matter
phases in superconductors. We solved the nonlinear equations of motion for the
Abelain-Higgs theory living on the AdS$_4$ black hole boundary that is dual to
a two dimensional strongly coupled type II superconductor at temperature $T$
with a perpendicular external uniform magnetic field $B_0$. We found the
associated two critical magnetic fields, $B_{c1}(T)$ and $B_{c2}(T)$. For $B_0
< B_{c1}(T)$ the magnetic field will be expelled out by the superconductor
resembling the Meissner effect and the superconductivity will be destroyed when
$B_0 > B_{c2}(T)$. The Abrikosov lattice appears in the range $B_{c1}(T) < B_0
< B_{c2}(T)$ including, due to the finite size and boundary effect, several
kinds of configurations such as hexagonal, square and slightly irregular square
lattices, when the magnetic field is increased. The upper and lower critical
fields behave as inverse squares of coherence length and magnetic penetration
depth respectively which matches the well known consensus.


  Micromegas is a type of micro-pattern gaseous detector currently under R&D
for applications in rare event search experiments. Here we report the
performance of a Micromegas structure constructed with a micromesh
thermo-bonded to a readout plane, motivated by its potential application in
two-phase xenon detectors for dark matter and neutrinoless double beta decay
experiments. The study is carried out in pure xenon at room temperature.
Measurements with alpha particles from the Americium-241 source showed that gas
gains larger than 200 can be obtained at xenon pressure up to 3 atm. Gamma rays
down to 8 keV were observed with such a device.


  We describe a proposal for an extensible, component-based software
architecture for natural language engineering applications. Our model leverages
existing linguistic resource description and discovery mechanisms based on
extended Dublin Core metadata. In addition, the application design is flexible,
allowing disparate components to be combined to suit the overall application
functionality. An application specification language provides abstraction from
the programming environment and allows ease of interface with computational
grids via a broker.


  Evaluation plays a crucial role in development of Machine translation
systems. In order to judge the quality of an existing MT system i.e. if the
translated output is of human translation quality or not, various automatic
metrics exist. We here present the implementation results of different metrics
when used on Hindi language along with their comparisons, illustrating how
effective are these metrics on languages like Hindi (free word order language).


  We analyze the dynamics of a nano-mechanical resonator coupled to a
single-electron transistor (SET) in the regime where the resonator behaves
classically. A master equation is derived describing the dynamics of the
coupled system which is then used to obtain equations of motion for the average
charge state of the SET and the average position of the resonator. We show that
the action of the SET on the resonator is very similar to that of a thermal
bath, as it leads to a steady-state probability-distribution for the resonator
which can be described by mean values of the resonator position, a renormalized
frequency, an effective temperature and an intrinsic damping constant.
Including the effects of extrinsic damping and finite temperature, we find that
there remain experimentally accessible regimes where the intrinsic damping of
the resonator still dominates its behavior. We also obtain the average current
through the SET as a function of the coupling to the resonator.


  Non-Hermitian (NH) operators are gaining growing significance in all branches
of physics and beyond. However, NH quantum theory faces challenges with
singularities, instabilities, and violations of standard linear algebra and
differential geometry. Here, we propose a quantum theory that resolves these
instabilities by reassigning them to the expansion parameters of a suitably
defined basis state of a Hermitian operator. We discover a computational basis,
defined by the eigenspace of $H^\dagger H$, in which the exceptional points of
$H$ are positioned as vacua on the two boundaries. The theory also introduces a
generic dual space map that functions as a dynamical `space-time'
transformation within the computational space. When this transformation assumes
a static symmetry, it ensures real energies, unraveling a hidden symmetry
beyond hermiticity or parity-time reversal symmetries. Our formalism elucidates
the origin and interpretation of several features associated with NH operators,
including exceptional points, normal operators, dual-space mapping, dynamical
metric manifold, and emergent symmetry-enforced real eigenvalues. Our general
framework broadens the application of NH theory across numerous branches of
physics where NH operators manifest as ladder operators, order parameters,
self-energies, projectors, and other entities.


  I propose an alternative method for measuring the $CP$ violating phase
$\phi_2$ ($\alpha$) without ambiguity in an extended SU(2) isospin triangle
analysis, which can ultimately be achieved by exploiting interference effects
between $B^0 \to \rho^0 \rho^0$ and $B^0 \to a_1^\pm \pi^\mp$ in a
time-dependent flavour-tagged amplitude analysis. Under certain assumptions on
the effective $\phi_2$ in each channel, I demonstrate with an idealised
amplitude model that potential deviations in the measured $\phi_2$ due to
penguin contamination in $B^0 \to a_1^\pm \pi^\mp$ are sufficiently large
within current experimental uncertainties that this programme could be executed
with Run 3 data at LHCb and easily at Belle II.