  Nonparametric estimation of a mixing density based on observations from the
corresponding mixture is a challenging statistical problem. This paper surveys
the literature on a fast, recursive estimator based on the predictive recursion
algorithm. After introducing the algorithm and giving a few examples, I
summarize the available asymptotic convergence theory, describe an important
semiparametric extension, and highlight two interesting applications. I
conclude with a discussion of several recent developments in this area and some
open problems.


  Nuclear cluster physics implicitly assumes a distinction between groups of
degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated)
relative cluster motion. We formulate a realistic and practical method to
describe the coupled motion of these two sets of degrees-of-freedom. We derive
a coupled set of differential equations for the system using the
phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon
interaction. We select a two-nucleon plus core system where the mean-field
approximation corresponding to the Skyrme interaction is used for the core. A
hyperspherical adiabatic expansion of the Faddeev equations is used for the
relative cluster motion. We shall specifically compare both the structure and
the decay mechanism found from the traditional three-body calculations with the
result using the new boundary condition provided by the full microscopic
structure at small distance. The extended Hilbert space guaranties an improved
wave function compared to both mean-field and three-body solutions. We shall
investigate the structures and decay mechanism of $^{22}$C ($^{20}$C+n+n). In
conclusion, we have developed a method combining nuclear few- and many-body
techniques without losing the descriptive power of each approximation at
medium-to-large distances and small distances respectively. The coupled set of
equations are solved self-consistently, and both structure and dynamic
evolution are studied.


  Penetration testing is the process of searching for security weaknesses by
simulating an attack. It is usually performed by experienced professionals,
where scanning and attack tools are applied. By automating the execution of
such tools, the need for human interaction and decision-making could be
reduced. In this work, a Network Attack Simulator (NASim) was used as an
environment to train reinforcement learning agents to solve three predefined
security scenarios. These scenarios cover techniques of exploitation,
post-exploitation and wiretapping. A large hyperparameter grid search was
performed to find the best hyperparameter combinations. The algorithms
Q-learning, DQN and A3C were used, whereby A3C was able to solve all scenarios
and achieve generalization. In addition, A3C could solve these scenarios with
fewer actions than the baseline automated penetration testing. Although the
training was performed on rather small scenarios and with small state and
action spaces for the agents, the results show that a penetration test can
successfully be performed by the RL agent.


  [PhD thesis of FCP.] Nowadays, genetics studies large amounts of very diverse
variables. Mathematical statistics has evolved in parallel to its applications,
with much recent interest high-dimensional settings. In the genetics of human
common disease, a number of relevant problems can be formulated as tests of
independence. We show how defining adequate premetric structures on the support
spaces of the genetic data allows for novel approaches to such testing. This
yields a solid theoretical framework, which reflects the underlying biology,
and allows for computationally-efficient implementations. For each problem, we
provide mathematical results, simulations and the application to real data.


  BarraCUDA is a C program which uses the BWA algorithm in parallel with nVidia
CUDA to align short next generation DNA sequences against a reference genome.
The genetically improved (GI) code is up to three times faster on short paired
end reads from The 1000 Genomes Project and 60percent more accurate on a short
BioPlanet.com GCAT alignment benchmark. GPGPU Barracuda running on a single K80
Tesla GPU can align short paired end nextgen sequences up to ten times faster
than bwa on a 12 core CPU.


  In this paper, we have proved that for each cardinal number $\lambda$ such
that $\lambda=\lambda^{\aleph_0}$ a metric space of weight $\lambda$ admits a
bijective continuous mapping onto a Banach space of weight $\lambda$. Then, we
get that every metric space of weight continuum admits a bijective continuous
mapping onto the Hilbert cube. This resolves the famous Banach's Problem (when
does a metric (possibly Banach) space $X$ admit a bijective continuous mapping
onto a compact metric space?) in the class of metric spaces of weight
continuum. Also we get that every metric space of weight
$\lambda=\lambda^{\aleph_0}$ admits a bijective continuous mapping onto a
Hausdorff compact space. This resolves the Alexandroff Problem (when does a
Hausdorff space $X$ admit a bijective continuous mapping onto a Hausdorff
compact space?) in the class of metric spaces of weight
$\lambda=\lambda^{\aleph_0}$.


  In this paper we study the Hilbert function of $\gr_{\mathfrak{m}}(R)$, when
$R$ is a numerical semigroup ring or, equivalently, the coordinate ring of a
monomial curve. In particular, we prove a sufficient condition for a numerical
semigroup ring in order get a non-decreasing Hilbert function, without making
any assumption on its embedding dimension; moreover, we show how this new
condition allows to improve known results about this problem. To this aim we
use certain invariants of the semigroup, with particular regard to its
\Apery-set.


  Text-adventure games and text role-playing games are grand challenges for
reinforcement learning game playing agents. Text role-playing games are
open-ended environments where an agent must faithfully play a particular
character. We consider the distinction between characters and actors, where an
actor agent has the ability to play multiple characters. We present a framework
we call a thespian agent that can learn to emulate multiple characters along
with a soft prompt that can be used to direct it as to which character to play
at any time. We further describe an attention mechanism that allows the agent
to learn new characters that are based on previously learned characters in a
few-shot fashion. We show that our agent outperforms the state of the art agent
framework in multi-character learning and few-shot learning.


  We consider the one-dimensional propagation of electromagnetic waves in a
weakly nonlinear and low-contrast spatially inhomogeneous medium with no energy
dissipation. We focus on the case of a periodic medium, in which dispersion
enters only through the (Floquet-Bloch) spectral band dispersion associated
with the periodic structure; chromatic dispersion (time-nonlocality of the
polarization) is neglected. Numerical simulations show that for initial
conditions of wave-packet type (a plane wave of fixed carrier frequency
multiplied by a slow varying, spatially localized function) very long-lived
spatially localized coherent soliton-like structures emerge, whose character is
that of a slowly varying envelope of a train of shocks. We call this structure
an envelope carrier-shock train.
  The structure of the solution violates the oft-assumed nearly monochromatic
wave packet structure, whose envelope is governed by the nonlinear coupled mode
equations (NLCME). The inconsistency and inaccuracy of NLCME lies in the
neglect of all (infinitely many) resonances except for the principle resonance
induced by the initial carrier frequency. We derive, via a nonlinear
geometrical optics expansion, a system of nonlocal integro-differential
equations governing the coupled evolution of backward and forward propagating
waves. These equations incorporate effects of all resonances. In a periodic
medium, these equations may be expressed as a system of infinitely many coupled
mode equations, which we call the extended nonlinear coupled mode system
(xNLCME). Truncating xNLCME to include only the principle resonances leads to
the classical NLCME.
  Numerical simulations of xNLCME demonstrate that it captures both large scale
features, related to third harmonic generation, and fine scale carrier shocks
features of the nonlinear periodic Maxwell equations.


  A technique is described in this paper to avoid order reduction when
integrating reaction-diffusion initial boundary value problems with explicit
exponential Rosenbrock methods. The technique is valid for any Rosenbrock
method, without having to impose any stiff order conditions, and for general
time-dependent boundary values. An analysis on the global error is thoroughly
performed and some numerical experiments are shown which corroborate the
theoretical results, and in which a big gain in efficiency with respect to
applying the standard method of lines can be observed.


  By performing first-principles electronic structure calculations and
analyzing effective magnetic model of alkali-doped iron selenides, we show that
the materials without iron vacancies should approach a novel checkerboard phase
in which each four Fe sites group together in tetragonal structure. The
checkerboard phase is the ground state with a block antiferromagnetic (AFM)
order and a small charge density wave order in the absence of
superconductivity. Both of them can also coexist with superconductivity. The
results explain mysterious $2\times 2$ ordered patterns and hidden orders
observed in various different experiments, clarify the missing link between AFM
and superconducting phases, suggest that the block-AFM state is the parent
state, and unify the understanding of various observed phases in alkali-doped
iron selenides.


  The XENON experiment is looking for non-baryonic particle dark matter in the
universe. The setup is a dual phase time projection chamber (TPC) filled with
3200 kg of ultra-pure liquid xenon. The setup is operated at the Laboratori
Nazionali del Gran Sasso (LNGS) in Italy. We present a full overview of the
computing scheme for data distribution and job management in XENON1T. The
software package Rucio, which is developed by the ATLAS collaboration,
facilitates data handling on Open Science Grid (OSG) and European Grid
Infrastructure (EGI) storage systems. A tape copy at the Center for High
Performance Computing (PDC) is managed by the Tivoli Storage Manager (TSM).
Data reduction and Monte Carlo production are handled by CI Connect which is
integrated into the OSG network. The job submission system connects resources
at the EGI, OSG, SDSC's Comet, and the campus HPC resources for distributed
computing. The previous success in the XENON1T computing scheme is also the
starting point for its successor experiment XENONnT, which starts to take data
in autumn 2019.


  In this paper we prove a general homogenization result for monotone parabolic
problems with an arbitrary number of microscopic scales in space as well as in
time, where the scale functions are not necessarily powers of epsilon. The main
tools for the homogenization procedure are multiscale convergence and very weak
multiscale convergence, both adapted to evo lution problems. At the end of the
paper an example is given to concretize the use of the main result.


  Aims. Photodissociation by UV light is an important destruction mechanism for
CO in many astrophysical environments, ranging from interstellar clouds to
protoplanetary disks. The aim of this work is to gain a better understanding of
the depth dependence and isotope-selective nature of this process.
  Methods. We present a photodissociation model based on recent spectroscopic
data from the literature, which allows us to compute depth-dependent and
isotope-selective photodissociation rates at higher accuracy than in previous
work. The model includes self-shielding, mutual shielding and shielding by
atomic and molecular hydrogen, and it is the first such model to include the
rare isotopologues C17O and 13C17O. We couple it to a simple chemical network
to analyse CO abundances in diffuse and translucent clouds, photon-dominated
regions, and circumstellar disks.
  Results. The photodissociation rate in the unattenuated interstellar
radiation field is 2.6e-10 s^-1, 30% higher than currently adopted values.
Increasing the excitation temperature or the Doppler width can reduce the
photodissociation rates and the isotopic selectivity by as much as a factor of
three for temperatures above 100 K. The model reproduces column densities
observed towards diffuse clouds and PDRs, and it offers an explanation for both
the enhanced and the reduced N(12CO)/N(13CO) ratios seen in diffuse clouds. The
photodissociation of C17O and 13C17O shows almost exactly the same depth
dependence as that of C18O and 13C18O, respectively, so 17O and 18O are equally
fractionated with respect to 16O. This supports the recent hypothesis that CO
photodissociation in the solar nebula is responsible for the anomalous 17O and
18O abundances in meteorites.


  We show that all amenable, minimal actions of a large class of nonamenable
countable groups on compact metric spaces have dynamical comparison. This class
includes all nonamenable hyperbolic groups, many HNN-extensions, nonamenable
Baumslag-Solitar groups, a large class of amalgamated free products, lattices
in many Lie groups, $\widetilde{A}_2$-groups, as well as direct products of the
above with arbitrary countable groups. As a consequence, crossed products by
amenable, minimal and topologically free actions of such groups on compact
metric spaces are Kirchberg algebras in the UCT class, and are therefore
classified by $K$-theory.


  Soil moisture is a key hydrological parameter that has significant importance
to human society and the environment. Accurate modeling and monitoring of soil
moisture in crop fields, especially in the root zone (top 100 cm of soil), is
essential for improving agricultural production and crop yield with the help of
precision irrigation and farming tools. Realizing the full sensor data
potential depends greatly on advanced analytical and predictive domain-aware
models. In this work, we propose a physics-constrained deep learning (P-DL)
framework to integrate physics-based principles on water transport and water
sensing signals for effective reconstruction of the soil moisture dynamics. We
adopt three different optimizers, namely Adam, RMSprop, and GD, to minimize the
loss function of P-DL during the training process. In the illustrative case
study, we demonstrate the empirical convergence of Adam optimizers outperforms
the other optimization methods in both mini-batch and full-batch training.


  Surface Dirac cones in three-dimensional topological insulators have
generated tremendous and enduring interest for almost two decades owing to
hosting a multitude of exotic properties. In this work, we unveil the existence
of two types of anomalous surface Dirac cones in three-dimensional Dirac
semimetals. These surface Dirac cones are located at the surfaces perpendicular
to the rotation symmetry axis, and are found to display a number of features
remarkably different from that in topological insulators. The most prominent
one is the absence of singular Dirac node. In addition, the spin textures of
these nodeless surface Dirac cones are found to exhibit a unique
two-phase-angle dependence, leading to the presence of two different winding
numbers in the orbital-resolved spin textures, which is rather different from
the well-known spin-momentum locking in topological insulators. Despite the
absence of Dirac node, we find that the two types of surface Dirac cones are
also characterized by quantized $\pi$ Berry phases, even though one of them
takes a quadratic dispersion. In the presence of
time-reversal-symmetry-breaking fields, we find that the responses of the
surface and bulk Dirac cones display an interesting bulk-surface
correspondence. The uncovering of these nodeless surface Dirac cones broadens
our understanding of the topological surface states and bulk-boundary
correspondence in Dirac semimetals, and also lays down the basis for studying
unconventional Dirac physics.


  We propose equations governing the dissolution in inhomogeneous temperature
field in terms of the variational principle. The derived equations clarify that
the interface energy between solute and solvent has a significant effect on the
process of the dissolution. The interface energy restrains the dissolution, and
the moving interface involves the heat of dissolution.


  The use of motion capture has increased from last decade in a varied spectrum
of applications like film special effects, controlling games and robots,
rehabilitation system, animations etc. The current human motion capture
techniques use markers, structured environment, and high resolution cameras in
a dedicated environment. Because of rapid movement, elbow angle estimation is
observed as the most difficult problem in human motion capture system. In this
paper, we take elbow angle estimation as our research subject and propose a
novel, markerless and cost-effective solution that uses RGB camera for
estimating elbow angle in real time using part affinity field. We have
recruited five (5) participants to perform cup to mouth movement and at the
same time measured the angle by both RGB camera and Microsoft Kinect. The
experimental results illustrate that markerless and cost-effective RGB camera
has a median RMS errors of 3.06{\deg} and 0.95{\deg} in sagittal and coronal
plane respectively as compared to Microsoft Kinect.


  We propose quantum-mechanical model of a beam splitter with second-order
nonlinearity and show that non-classical features such as squeezing and
sub-Poissonian photon statistics of optical fields can be generated in output
fundamental and second harmonic modes when we mix coherent light beams via such
a nonlinear beam splitter.


  We propose the on-the-fly ensembling of a machine translation model with an
LLM, prompted on the same task and input. We perform experiments on 4 language
pairs (both directions) with varying data amounts. We find that a slightly
weaker-at-translation LLM can improve translations of a NMT model, and
ensembling with an LLM can produce better translations than ensembling two
stronger MT models. We combine our method with various techniques from LLM
prompting, such as in context learning and translation context.


  Recent theoretical works have shown that the NSGA-II efficiently computes the
full Pareto front when the population size is large enough. In this work, we
study how well it approximates the Pareto front when the population size is
smaller.
  For the OneMinMax benchmark, we point out situations in which the parents and
offspring cover well the Pareto front, but the next population has large gaps
on the Pareto front. Our mathematical proofs suggest as reason for this
undesirable behavior that the NSGA-II in the selection stage computes the
crowding distance once and then removes individuals with smallest crowding
distance without considering that a removal increases the crowding distance of
some individuals.
  We then analyze two variants not prone to this problem. For the NSGA-II that
updates the crowding distance after each removal (Kukkonen and Deb (2006)) and
the steady-state NSGA-II (Nebro and Durillo (2009)), we prove that the gaps in
the Pareto front are never more than a small constant factor larger than the
theoretical minimum. This is the first mathematical work on the approximation
ability of the NSGA-II and the first runtime analysis for the steady-state
NSGA-II. Experiments also show the superior approximation ability of the two
NSGA-II variants.


  We report a confocal interferometric mid-infrared photothermal (MIP)
microscope and its application to label-free detection of biological
nanoparticles down to single virus level. We apply the interferometric
scattering principle to detect the weak photothermal effect induced by infrared
absorption in a viral particle. We validated this method with two kinds of
viruses, namely the vesicular stomatitis virus (VSV) and poxvirus. The single
virus spectra generated by MIP microscopy show high consistency in the same
group, with dominant peaks contributed by the amide I and amide II vibrations.
The ratio of these two peaks are significantly different between VSV and
poxvirus, highlighting the potential of using MIP microscopy for label-free
differentiation of viral particles. This all-optical chemical imaging method
opens a new way for spectroscopic detection of biological nanoparticles in a
label-free manner and may facilitate in predicting and controlling outbreaks of
emerging virus strains.


  We demonstrate that the synchronization of an array of electrically coupled
spin torque nano-oscillators (STNO) modelled by
Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation can be enhanced appreciably
in the presence of a common external microwave magnetic field. The applied
microwave magnetic field stabilizes and enhances the regions of synchronization
in the parameter space of our analysis, where the oscillators are exhibiting
synchronized oscillations thereby emitting improved microwave power. To
characterize the synchronized oscillations we have calculated the locking range
in the domain of external source frequency.


  New optical spectra of the original narrow-line quasar 1E 0449.4-1823 show
that it now has broad emission lines of considerable strength, eliminating it
as a "type 2 QSO" candidate. We suggest that the behavior of 1E 0449.4-1823 is
the same as that of some Seyfert 1.8 and 1.9 galaxies, in which Goodrich
attributed long-term variations of their broad Balmer lines to dynamical
motions of obscuring material located in or around the broad-line region. The
optical continuum and broad emission-line regions of 1E 0449.4-1823 may still
be partly covered in our line of sight, which would explain its large
forbidden-line equivalent widths and flat alpha_ox relative to other
low-redshift QSOs. Also present are apparent absorption features in the broad
Balmer lines and in Mg II, which may be related to the past obscuration and
current emergence of the broad-line region. However, it is difficult to
distinguish absorption from broad emission-line peaks that are displaced in
velocity; we consider the latter a plausible competing interpretation of these
peculiar line profiles. An ASCA X-ray spectrum of 1E 0449.4-1823 can be fitted
with a power-law of Gamma = 1.63, intrinsic N_H < 9 x 10^20 cm-2, and no Fe
Kalpha line emission. Its 2-10 keV luminosity is 6.7 x 10^44 ergs/s. With
regard to the still hypothetical type 2 QSOs, we argue that there is little
evidence for the existence of any among X-ray selected samples.


  The aim of this paper is to consider the value distribution of a differential
monomial generated by a transcendental meromorphic function.


  We present the first results of our program to study a sample of local
luminous infrared galaxies (LIRGs, L_IR = 10^11-10^12 L_sun) with the Spitzer
infrared spectrograph (IRS). In these proceedings we investigate the behavior
of the 9.7 um silicate feature in LIRGs. As opposed to the extreme silicate
absorptions observed in ultraluminous infrared galaxies (ULIRGs, L_IR =
10^12-10^13 L_sun), LIRGs exhibit intermediate silicate absorption features,
comparable to those of starburst galaxies. We also find that most of the LIRGs
have the minima of the [NeIII]/[NeII] ratio located at their nuclei. It is
likely that increased densities in the nuclei are responsible for the smaller
nuclear ratios. In the nuclei, it is also possible that the most massive stars
are either absent, or still embedded in ultracompact HII regions. Finally we
discuss the possible contribution of an AGN to the nuclear mid-IR emission of
the galaxy, which in general is low in these local LIRGs.


  Identification of lymph nodes (LN) in T2 Magnetic Resonance Imaging (MRI) is
an important step performed by radiologists during the assessment of
lymphoproliferative diseases. The size of the nodes play a crucial role in
their staging, and radiologists sometimes use an additional contrast sequence
such as diffusion weighted imaging (DWI) for confirmation. However, lymph nodes
have diverse appearances in T2 MRI scans, making it tough to stage for
metastasis. Furthermore, radiologists often miss smaller metastatic lymph nodes
over the course of a busy day. To deal with these issues, we propose to use the
DEtection TRansformer (DETR) network to localize suspicious metastatic lymph
nodes for staging in challenging T2 MRI scans acquired by different scanners
and exam protocols. False positives (FP) were reduced through a bounding box
fusion technique, and a precision of 65.41\% and sensitivity of 91.66\% at 4 FP
per image was achieved. To the best of our knowledge, our results improve upon
the current state-of-the-art for lymph node detection in T2 MRI scans.


  We propose a general exact method of calculating dynamical correlation
functions in dual symplectic brick-wall circuits in one dimension. These are
deterministic classical many-body dynamical systems which can be interpreted in
terms of symplectic dynamics in two orthogonal (time and space) directions. In
close analogy with quantum dual-unitary circuits, we prove that two-point
dynamical correlation functions are non-vanishing only along the edges of the
light cones. The dynamical correlations are exactly computable in terms of a
one-site Markov transfer operator, which is generally of infinite
dimensionality. We test our theory in a specific family of dual-symplectic
circuits, describing the dynamics of a classical Floquet spin chain.
Remarkably, expressing these models in the form of a composition of rotations
leads to a transfer operator with a block diagonal form in the basis of
spherical harmonics. This allows us to obtain analytical predictions for simple
local observables. We demonstrate the validity of our theory by comparison with
Monte Carlo simulations, displaying excellent agreement with the latter for
different choices of observables.


  In coherent diffraction imaging (CDI) experiments, the intensity of the
scattered wave impinging on an object is measured on an array of detectors.
This signal can be interpreted as the square of the modulus of the Fourier
transform of the unknown scattering density. A beam-stop obstructs the forward
scattered wave and, hence, the modulus Fourier data from a neighborhood of k=0
cannot be measured. In this note, we describe a linear method for recovering
this unmeasured modulus Fourier data from the measured values and an estimate
of the support of the image's autocorrelation function without consideration of
phase retrieval. We analyze the conditioning of this problem, which grows
exponentially with the modulus of the maximum spatial frequency not measured,
and the effects of noise.


  Starting from two case histories, where only after thorough Failure Analysis
the suddenly appearance of a failure was linked to much earlier events, the
possibility of improving the reliability and of adjusting the reliability
prediction tools are discussed.


  We investigate bilayer graphene transport in the presence of electron-hole
puddles induced by long-range charged impurities in the environment. We explain
the insulating behavior observed in the temperature dependent conductivity of
low mobility bilayer graphene using an analytic statistical theory taking into
account the non-mean-field nature of transport in the highly inhomogeneous
density and potential landscape. We find that the puddles can induce, even far
from the charge neutrality point, a coexisting metallic and insulating
transport behavior due to the random local activation gap in the system.


  To predict high-resolution (HR) omnidirectional depth map, existing methods
typically leverage HR omnidirectional image (ODI) as the input via
fully-supervised learning. However, in practice, taking HR ODI as input is
undesired due to resource-constrained devices. In addition, depth maps are
often with lower resolution than color images. Therefore, in this paper, we
explore for the first time to estimate the HR omnidirectional depth directly
from a low-resolution (LR) ODI, when no HR depth GT map is available. Our key
idea is to transfer the scene structural knowledge from the HR image modality
and the corresponding LR depth maps to achieve the goal of HR depth estimation
without any extra inference cost. Specifically, we introduce ODI
super-resolution (SR) as an auxiliary task and train both tasks collaboratively
in a weakly supervised manner to boost the performance of HR depth estimation.
The ODI SR task extracts the scene structural knowledge via uncertainty
estimation. Buttressed by this, a scene structural knowledge transfer (SSKT)
module is proposed with two key components. First, we employ a cylindrical
implicit interpolation function (CIIF) to learn cylindrical neural
interpolation weights for feature up-sampling and share the parameters of CIIFs
between the two tasks. Then, we propose a feature distillation (FD) loss that
provides extra structural regularization to help the HR depth estimation task
learn more scene structural knowledge. Extensive experiments demonstrate that
our weakly-supervised method outperforms baseline methods, and even achieves
comparable performance with the fully-supervised methods.


  We study the conditional upper bounds and extreme values of derivatives of
the Riemann zeta function and Dirichlet $L$-functions near the 1-line. Let
$\ell$ be a fixed natural number. We show that, if $|\sigma-1|\ll1/\log_2t$,
then $|\zeta^{(\ell)}(\sigma+ it)|$ has the same maximal order (up to the
leading coefficients) as $|\zeta^{(\ell)}(1+ it)|$ when $t\to\infty$. The range
$1-\sigma\ll1/\log_2t$ is wide enough, since we also show that $(1-\sigma)
\log_2t \to \infty\; (t \to \infty)$ implies
$\limsup_{t\to\infty}|\zeta^{(\ell)}(\sigma+ it)| / (\log_2t)^{\ell+1} =
\infty$. Similar results can be obtained for Dirichlet $L$-functions
$L^{(\ell)}(\sigma,\chi)$ with $\chi\pmod q$.


  We have introduced a Pareto sorting algorithm into Synopsis, a de novo design
program that generates synthesizable molecules with desirable properties. We
give a detailed description of the algorithm and illustrate its working in 2
different de novo design settings: the design of putative dual and selective
FGFR and VEGFR inhibitors, and the successful design of organic structure
determining agents (OSDAs) for the synthesis of zeolites. We show that the
introduction of Pareto sorting not only enables the simultaneous optimization
of multiple properties but also greatly improves the performance of the
algorithm to generate molecules with hard-to-meet constraints. This in turn
allows us to suggest approaches to address the problem of false positive hits
in de novo structure based drug design by introducing structural and
physicochemical constraints in the designed molecules, and by forcing essential
interactions between these molecules and their target receptor.


  We explore a potential new probe of reionization: the cross-correlation of
high-redshift galaxies with maps of the thermal Sunyaev-Zel'dovich (tSZ)
effect. We consider two types of high redshift galaxies: Lyman break galaxies
(LBGs) and Lyman-$\alpha$ emitters (LAEs). LBGs and LAEs will be detected in
large numbers at high redshift ($z \approx$ 4 to 7) by ongoing and future
surveys. We consider a LBG sample like that expected from the The Rubin
Observatory Legacy Survey of Space and Time (LSST), and a selection of LAEs
modelled after the Subaru SILVERRUSH program, but covering a much larger sky
fraction. The tSZ effect is sensitive to a line-of-sight integral of the
ionized gas pressure, and can be measured across large patches of the sky using
multi-frequency CMB surveys. We consider forecast tSZ maps from CMB Stage 4 and
more futuristic observations. Using a suite of hydrodynamical simulations, we
show that the high-redshift galaxies are correlated with the tSZ signal from
reionization, with cross-power amplitude of order $10^{-15}$ at $\ell \sim
1000$. The cross-spectra between LBGs/LAEs with tSZ maps contain information
about the reionization history of the Universe, such as the distribution of
bubble sizes, and could in principle be used to directly measure the timing of
reionization. The amplitude of the signal is small, however, and its
detectability is hindered by low-redshift contributions to tSZ maps and by
instrumental noise. If the the low-redshift contribution to the observed tSZ
signal is suppressed by masking of massive halos, a combination of overlapping
futuristic CMB and galaxy surveys could potentially probe this signal.


  We derive the off-shell nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations,
corresponding to the (1-form) Yang-Mills (YM) and (2-form) tensorial gauge
symmetries of the four (3 + 1)-dimensional (4D) Freedman-Townsend (FT) model,
by exploiting the augmented version of Bonora-Tonin's (BT) superfield approach
to BRST formalism where the 4D flat Minkowskian theory is generalized onto the
(4, 2)-dimensional supermanifold. One of the novel observations is the fact
that we are theoretically compelled to go beyond the horizontality condition
(HC) to invoke an additional set of gauge-invariant restrictions (GIRs) for the
derivation of the full set of proper (anti-)BRST symmetries. To obtain the
(anti-)BRST symmetry transformations, corresponding to the tensorial (2-form)
gauge symmetries within the framework of augmented version of BT-superfield
approach, we are logically forced to modify the FT-model to incorporate an
auxiliary 1-form field and the kinetic term for the antisymmetric (2-form)
gauge field. This is also a new observation in our present investigation. We
point out some key differences between the modified FT-model and Lahiri-model
(LM) of the dynamical non-Abelian 2-form gauge theories.


  Google app market captures the school of thought of users via ratings and
text reviews. The critique's viewpoint regarding an app is proportional to
their satisfaction level. Consequently, this helps other users to gain insights
before downloading or purchasing the apps. The potential information from the
reviews can't be extracted manually, due to its exponential growth. Sentiment
analysis, by machine learning algorithms employing NLP, is used to explicitly
uncover and interpret the emotions. This study aims to perform the sentiment
classification of the app reviews and identify the university students'
behavior towards the app market. We applied machine learning algorithms using
the TF-IDF text representation scheme and the performance was evaluated on the
ensemble learning method. Our model was trained on Google reviews and tested on
students' reviews. SVM recorded the maximum accuracy(93.37\%), F-score(0.88) on
tri-gram + TF-IDF scheme. Bagging enhanced the performance of LR and NB with
accuracy of 87.80\% and 85.5\% respectively.


  In the present paper, we obtain new interesting relations and identities of
the Apostol-Bernoulli polynomials of higher order, which are derived using a
Bernoulli polynomial basis. Finally, by utilizing our method, we also derive
formulas for the convolutions of Bernoulli and Euler polynomials, expressed via
Apostol-Bernoulli polynomials of higher order.


  For a diffeomorphism which preserves a hyperbolic measure the potential
$\phi^u=-\log|{\rm Jac} df|_{E^u}|$ is studied. Various types of pressure of
$\phi^u$ are introduced. It is shown that these pressures satisfy a
corresponding variational principle.


  The Galactic centre - as the closest galactic nucleus - holds both intrinsic
interest and possibly represents a useful analogue to star-burst nuclei which
we can observe with orders of magnitude finer detail than these external
systems. The environmental conditions in the GC - here taken to mean the inner
200 pc in diameter of the Milky Way - are extreme with respect to those
typically encountered in the Galactic disk. The energy densities of the various
GC ISM components are typically ~two orders of magnitude larger than those
found locally and the star-formation rate density ~three orders of magnitude
larger. Unusually within the Galaxy, the Galactic centre exhibits
hard-spectrum, diffuse TeV (=10^12 eV) gamma-ray emission spatially coincident
with the region's molecular gas. Recently the nuclei of local star-burst
galaxies NGC 253 and M82 have also been detected in gamma-rays of such
energies. We have embarked on an extended campaign of modelling the broadband
(radio continuum to TeV gamma-ray), non- thermal signals received from the
inner 200 pc of the Galaxy. On the basis of this modelling we find that
star-formation and associated supernova activity is the ultimate driver of the
region's non-thermal activity. This activity drives a large-scale wind of hot
plasma and cosmic rays out of the GC. The wind advects the locally-accelerated
cosmic rays quickly, before they can lose much energy in situ or penetrate into
the densest molecular gas cores where star-formation occurs. The cosmic rays
can, however, heat/ionize the lower density/warm H2 phase enveloping the cores.
On very large scales (~10 kpc) the non-thermal signature of the escaping GC
cosmic rays has probably been detected recently as the spectacular 'Fermi
bubbles' and corresponding 'WMAP haze'.


  The unprecedented performance of deep neural networks (DNNs) has led to large
strides in various Artificial Intelligence (AI) inference tasks, such as object
and speech recognition. Nevertheless, deploying such AI models across commodity
devices faces significant challenges: large computational cost, multiple
performance objectives, hardware heterogeneity and a common need for high
accuracy, together pose critical problems to the deployment of DNNs across the
various embedded and mobile devices in the wild. As such, we have yet to
witness the mainstream usage of state-of-the-art deep learning algorithms
across consumer devices. In this paper, we provide preliminary answers to this
potentially game-changing question by presenting an array of design techniques
for efficient AI systems. We start by examining the major roadblocks when
targeting both programmable processors and custom accelerators. Then, we
present diverse methods for achieving real-time performance following a
cross-stack approach. These span model-, system- and hardware-level techniques,
and their combination. Our findings provide illustrative examples of AI systems
that do not overburden mobile hardware, while also indicating how they can
improve inference accuracy. Moreover, we showcase how custom ASIC- and
FPGA-based accelerators can be an enabling factor for next-generation AI
applications, such as multi-DNN systems. Collectively, these results highlight
the critical need for further exploration as to how the various cross-stack
solutions can be best combined in order to bring the latest advances in deep
learning close to users, in a robust and efficient manner.


  Electroweak symmetry breaking may be naturally induced by the observed quark
and gauge fields in extra dimensions without a fundamental Higgs field. We show
that a composite Higgs doublet can arise as a bound state of $(t, b)_L$ and a
linear combination of the Kaluza-Klein states of $t_R$, due to QCD in extra
dimensions. The top quark mass depends on the number of active $t_R$
Kaluza-Klein modes, and is consistent with the experimental value.


  Oxygen is a powerful tracer element of Galactic chemical evolution.
Unfortunately, only a few oxygen lines are available in the
ultraviolet-infrared stellar spectra for the reliable determination of its
abundance. Moreover, oxygen abundances obtained using different spectral lines
often disagree significantly. In this contribution we therefore investigate
whether the inadequate treatment of convection in 1D hydrostatic model
atmospheres used in the abundance determinations may be responsible for this
disagreement. For this purpose, we used VLT CRIRES spectra of three EMP giants,
as well as 3D hydrodynamical CO$^5$BOLD and 1D hydrostatic LHD model
atmospheres, to investigate the role of convection in the formation of infrared
(IR) OH lines. Our results show that the presence of convection leads to
significantly stronger IR OH lines. As a result, the difference in the oxygen
abundance determined from IR OH lines with 3D hydrodynamical and classical 1D
hydrostatic model atmospheres may reach -0.2 ... -0.3 dex. In case of the three
EMP giants studied here, we obtain a good agrement between the 3D LTE oxygen
abundances determined by us using vibrational-rotational IR OH lines in the
spectral range of 1514-1626 nm, and oxygen abundances determined from forbidden
[O I] 630 nm line in previous studies.


  The integration of Artificial Intelligence (AI) into automation systems has
the potential to enhance efficiency and to address currently unsolved existing
technical challenges. However, the industry-wide adoption of AI is hindered by
the lack of standardized documentation for the complex compositions of
automation systems, AI software, production hardware, and their
interdependencies. This paper proposes a formal model using standards and
ontologies to provide clear and structured documentation of AI applications in
automation systems. The proposed information model for artificial intelligence
in automation systems (AIAS) utilizes ontology design patterns to map and link
various aspects of automation systems and AI software. Validated through a
practical example, the model demonstrates its effectiveness in improving
documentation practices and aiding the sustainable implementation of AI in
industrial settings.


  We discuss three SYCL realisations of a simple Finite Volume scheme over
multiple Cartesian patches. The realisation flavours differ in the way how they
map the compute steps onto loops and tasks: We compare an implementation that
is exclusively using a sequence of for-loops to a version that uses nested
parallelism, and finally benchmark these against a version modelling the
calculations as task graph. Our work proposes realisation idioms to realise
these flavours within SYCL. The results suggest that a mixture of classic task
and data parallelism performs if we map this hybrid onto a solely data-parallel
SYCL implementation, taking into account SYCL specifics and the problem size.


  We report the discovery with XMM-Newton of an approximately 7 mHz X-ray
(0.3-10.0 keV) quasi-periodic oscillation (QPO) from the eclipsing,
high-inclination black hole binary IC 10 X-1. The QPO is significant at > 4.33
sigma confidence level and has a fractional amplitude (% rms) and a quality
factor, Q, of approximately 11 and 4, respectively. The overall X-ray (0.3-10.0
keV) power spectrum in the frequency range 0.0001 - 0.1 Hz can be described by
a power-law with an index of -2, and a QPO at 7 mHz. At frequencies > 0.02 Hz
there is no evidence for significant variability. The fractional amplitude
(rms) of the QPO is roughly energy-independent in the energy range of 0.3-1.5
keV. Above 1.5 keV the low signal to noise ratio of the data does not allow us
to detect the QPO. By directly comparing these properties with the wide range
of QPOs currently known from accreting black hole and neutron stars, we suggest
that the 7 mHz QPO of IC 10 X-1 may be linked to one of the following three
categories of QPOs: (1) the "heartbeat" mHz QPOs of the black hole sources GRS
1915+105 and IGR J17091-3624, or (2) the 0.6-2.4 Hz "dipper QPOs" of
high-inclination neutron star systems, or (3) the mHz QPOs of Cygnus X-3.


  We highlight several analogies between the Finsler (infinitesimal) properties
of Teichm\"uller's metric and Thurston's asymmetric metric on Teichm\"uller
space. Thurston defined his asymmetric metric in analogy with Teichm\"ullers'
metric, as a solution to an extremal problem, which consists, in the case of
the asymmetric metric, of finding the best Lipschitz maps in the hoomotopy
class of homeomorphisms between two hyperbolic surface. (In the Teichm\"uller
metric case, one searches for the best quasiconformal map between two conformal
surfaces.) It turns out also that some properties of Thurston's asymmetric
metric can be used to get new insight into Teichm\"uller's metric. In this
direction, in analogy with Thurston's formula for the Finsler norm of a vector
for the asymmetric metric that uses the hyperbolic length function, we give a
new formula for the Finsler norm of a vector for the Teichm\"uller metric that
uses the extremal length function. We also describe an embedding of projective
measured foliation space in the cotangent space to Teichm\"uller space whose
image is the boundary of the dual of the unit ball in the tangent space
representing vectors of norm one for the Finsler structure associated to the
Teichm\"uller metric.


  We develop a new formalism to study $K\bar{K}$ threshold phenomena with
resonances $f_0$, $a_0$ and $K^+K^-$ atom (kaonium) included. The approach
provides two possible scenarios for $f_0-a_0$ mixing. Drastic interference
patterns can be observed in $K^+K^-$electroproduction at CEBAF, $pd\to ~^3HeX$
reaction, and $N\bar N$ annihilation.


  Sequencing of pools of individuals (Pool-Seq) represents a reliable and cost-
effective approach for estimating genome-wide SNP and transposable element
insertion frequencies. However, Pool-Seq does not provide direct information on
haplotypes so that for example obtaining inversion frequencies has not been
possible until now. Here, we have developed a new set of diagnostic marker SNPs
for 7 cosmopolitan inversions in Drosophila melanogaster that can be used to
infer inversion frequencies from Pool-Seq data. We applied our novel marker set
to Pool-Seq data from an experimental evolution study and from North American
and Australian latitudinal clines. In the experimental evolution data, we find
evidence that positive selection has driven the frequencies of In(3R)C and
In(3R)Mo to increase over time. In the clinal data, we confirm the existence of
frequency clines for In(2L)t, In(3L)P and In(3R)Payne in both North America and
Australia and detect a previously unknown latitudinal cline for In(3R)Mo in
North America. The inversion markers developed here provide a versatile and
robust tool for characterizing inversion frequencies and their dynamics in
Pool- Seq data from diverse D. melanogaster populations.


  One of the most intriguing problems, in $q$-analogs of designs and codes, is
the existence question of an infinite family of $q$-analog of Steiner systems
(spreads not included) in general, and the existence question for the
$q$-analog of the Fano plane in particular.
  We exhibit a completely new method to attack this problem. In the process we
define a new family of designs whose existence is implied by the existence of
$q$-Steiner systems, but could exist even if the related $q$-Steiner systems do
not exist.
  The method is based on a possible system obtained by puncturing all the
subspaces of the $q$-Steiner system several times. We define the punctured
system as a new type of design and enumerate the number of subspaces of various
types that it might have. It will be evident that its existence does not imply
the existence of the related $q$-Steiner system. On the other hand, this type
of design demonstrates how close can we get to the related $q$-Steiner system.
  Necessary conditions for the existence of such designs are presented. These
necessary conditions will be also necessary conditions for the existence of the
related $q$-Steiner system. Trivial and nontrivial direct constructions and a
nontrivial recursive construction for such designs, are given. Some of the
designs have a symmetric structure, which is uniform in the dimensions of the
existing subspaces in the system. Most constructions are based on this uniform
structure of the design or its punctured designs. Finally, the structure of the
$q$-Fano plane for any given $q$, was considered based on this new approach.


  Data-driven modelling and scientific machine learning have been responsible
for significant advances in determining suitable models to describe data.
Within dynamical systems, neural ordinary differential equations (ODEs), where
the system equations are set to be governed by a neural network, have become a
popular tool for this challenge in recent years. However, less emphasis has
been placed on systems that are only partially-observed. In this work, we
employ a hybrid neural ODE structure, where the system equations are governed
by a combination of a neural network and domain-specific knowledge, together
with symbolic regression (SR), to learn governing equations of
partially-observed dynamical systems. We test this approach on two case
studies: A 3-dimensional model of the Lotka-Volterra system and a 5-dimensional
model of the Lorenz system. We demonstrate that the method is capable of
successfully learning the true underlying governing equations of unobserved
states within these systems, with robustness to measurement noise.


  Large language models (LLMs) can be prone to hallucinations - generating
unreliable outputs that are unfaithful to their inputs, external facts or
internally inconsistent. In this work, we address several challenges for
post-hoc hallucination detection in production settings. Our pipeline for
hallucination detection entails: first, producing a confidence score
representing the likelihood that a generated answer is a hallucination; second,
calibrating the score conditional on attributes of the inputs and candidate
response; finally, performing detection by thresholding the calibrated score.
We benchmark a variety of state-of-the-art scoring methods on different
datasets, encompassing question answering, fact checking, and summarization
tasks. We employ diverse LLMs to ensure a comprehensive assessment of
performance. We show that calibrating individual scoring methods is critical
for ensuring risk-aware downstream decision making. Based on findings that no
individual score performs best in all situations, we propose a multi-scoring
framework, which combines different scores and achieves top performance across
all datasets. We further introduce cost-effective multi-scoring, which can
match or even outperform more expensive detection methods, while significantly
reducing computational overhead.


  In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to
be able to find the apparent horizon(s) (AH) in each slice of a time evolution.
A number of AH finders are available, but they often take many minutes to run,
so they're too slow to be practically usable at each time step. Here I present
a new AH finder,_AHFinderDirect_, which is very fast and accurate: at typical
resolutions it takes only a few seconds to find an AH to $\sim 10^{-5} m$
accuracy on a GHz-class processor.
  I assume that an AH to be searched for is a Strahlk\"orper (star-shaped
region) with respect to some local origin, and so parameterize the AH shape by
$r = h(angle)$ for some single-valued function $h: S^2 \to \Re^+$. The AH
equation then becomes a nonlinear elliptic PDE in $h$ on $S^2$, whose
coefficients are algebraic functions of $g_{ij}$, $K_{ij}$, and the
Cartesian-coordinate spatial derivatives of $g_{ij}$. I discretize $S^2$ using
6 angular patches (one each in the neighborhood of the $\pm x$, $\pm y$, and
$\pm z$ axes) to avoid coordinate singularities, and finite difference the AH
equation in the angular coordinates using 4th order finite differencing. I
solve the resulting system of nonlinear algebraic equations (for $h$ at the
angular grid points) by Newton's method, using a "symbolic differentiation"
technique to compute the Jacobian matrix._AHFinderDirect_ is implemented as a
thorn in the_Cactus_ computational toolkit, and is freely available by
anonymous CVS checkout.


  We present a neural program synthesis approach integrating components which
write, execute, and assess code to navigate the search space of possible
programs. We equip the search process with an interpreter or a
read-eval-print-loop (REPL), which immediately executes partially written
programs, exposing their semantics. The REPL addresses a basic challenge of
program synthesis: tiny changes in syntax can lead to huge changes in
semantics. We train a pair of models, a policy that proposes the new piece of
code to write, and a value function that assesses the prospects of the code
written so-far. At test time we can combine these models with a Sequential
Monte Carlo algorithm. We apply our approach to two domains: synthesizing text
editing programs and inferring 2D and 3D graphics programs.


  We investigate how the Raychaudhuri equation behaves in the $k$-essence
geometry. As far as we are concerned, both the early and current epochs of the
universe are relevant to the $k$-essence theory. Here, we have studied the
$k$-essence geometry using the Dirac-Born-Infeld (DBI) variety of non-standard
action. The corresponding $k$-essence emergent spacetime is not conformally
equivalent to the usual gravitational metric. We assume that the background
gravitational metric is of the Friedmann-Lemaitre-Robertson-Walker (FLRW) type
in this case. We have found that both the conditional singular and non-singular
cosmological models of the universe through the modified Raychaudhuri equation
are possible where we have used the spacetime as the flat $k$-essence emergent
FLRW-type. We have also addressed to the Focusing theorem and conditional
caustic universe construction. These conditional effects are caused by the
additional interactions that arise as a result of the coupling that exists
between the gravity and the $k$-essence scalar field.


  We study theoretically the low-energy hole states of Ge/Si core/shell
nanowires. The low-energy valence band is quasidegenerate, formed by two
doublets of different orbital angular momenta, and can be controlled via the
relative shell thickness and via external fields. We find that direct (dipolar)
coupling to a moderate electric field leads to an unusually large spin-orbit
interaction of Rashba type on the order of meV which gives rise to pronounced
helical states enabling electrical spin control. The system allows for quantum
dots and spin qubits with energy levels that can vary from nearly zero to
several meV, depending on the relative shell thickness.


  While various covert botnets were proposed in the past, they still lack
complete anonymization for their servers/botmasters or suffer from slow
communication between the botmaster and the bots. In this paper, we first
propose a new generation hybrid botnet that covertly and efficiently
communicates over Bitcoin Lightning Network (LN), called LNBot. Exploiting
various anonymity features of LN, we show the feasibility of a scalable
two-layer botnet which completely anonymizes the identity of the botmaster. In
the first layer, the botmaster anonymously sends the commands to the command
and control (C&C) servers through regular LN payments. Specifically, LNBot
allows botmaster's commands to be sent in the form of surreptitious multi-hop
LN payments, where the commands are either encoded with the payments or
attached to the payments to provide covert communications. In the second layer,
C&C servers further relay those commands to the bots in their mini-botnets to
launch any type of attacks to victim machines. We further improve on this
design by introducing D-LNBot; a distributed version of LNBot that generates
its C&C servers by infecting users on the Internet and forms the C&C
connections by opening channels to the existing nodes on LN. In contrary to the
LNBot, the whole botnet formation phase is distributed and the botmaster is
never involved in the process. By utilizing Bitcoin's Testnet and the new
message attachment feature of LN, we show that D-LNBot can be run for free and
commands are propagated faster to all the C&C servers compared to LNBot. We
presented proof-of-concept implementations for both LNBot and D-LNBot on the
actual LN and extensively analyzed their delay and cost performance. Finally,
we also provide and discuss a list of potential countermeasures to detect LNBot
and D-LNBot activities and minimize their impacts.


  Dicke states form a class of entangled states that has attracted much
attention for their applications in various quantum algorithms. They emerge as
eigenstates of the Tavis-Cummings Hamiltonian, a simplification of the Dicke
model, which describes an assembly of two-level atoms trapped in an
electromagnetic cavity. In this letter, we show that in the regime where the
field energy is large with respect to the atomic energy splitting, precise
control of the ground state can be implemented. Specifically, pure Dicke states
can be selected and produced by appropriate tuning of the parameters. This
result may have important applications in quantum engineering and quantum
information theory.


  Abductive reasoning is the process of making educated guesses to provide
explanations for observations. Although many applications require the use of
knowledge for explanations, the utilization of abductive reasoning in
conjunction with structured knowledge, such as a knowledge graph, remains
largely unexplored. To fill this gap, this paper introduces the task of complex
logical hypothesis generation, as an initial step towards abductive logical
reasoning with KG. In this task, we aim to generate a complex logical
hypothesis so that it can explain a set of observations. We find that the
supervised trained generative model can generate logical hypotheses that are
structurally closer to the reference hypothesis. However, when generalized to
unseen observations, this training objective does not guarantee better
hypothesis generation. To address this, we introduce the Reinforcement Learning
from Knowledge Graph (RLF-KG) method, which minimizes differences between
observations and conclusions drawn from generated hypotheses according to the
KG. Experiments show that, with RLF-KG's assistance, the generated hypotheses
provide better explanations, and achieve state-of-the-art results on three
widely used KGs.


  It is feasible and practically-valuable to bridge the characteristics between
graph neural networks (GNNs) and logical reasoning. Despite considerable
efforts and successes witnessed to solve Boolean satisfiability (SAT), it
remains a mystery of GNN-based solvers for more complex predicate logic
formulae. In this work, we conjectures with some evidences, that
generally-defined GNNs present several limitations to certify the
unsatisfiability (UNSAT) in Boolean formulae. It implies that GNNs may probably
fail in learning the logical reasoning tasks if they contain proving UNSAT as
the sub-problem included by most predicate logic formulae.


  In this paper, we study an application of deep learning to uplink multiuser
detection (MUD) for non-orthogonal multiple access (NOMA) scheme based on Welch
bound equality spread multiple access (WSMA). Several non-cooperating users,
each with its own preassigned NOMA signature sequence (SS), transmit over the
same resource. These SSs have low correlation among them and aid in the user
separation at the receiver during MUD. Several subtasks such as equalizing,
combining, slicing, signal reconstruction and interference cancellation are
involved in MUD. The neural network (NN) considered in this paper replaces
these well-defined receiver blocks with a single black box, i.e., the NN
provides a one-shot approximation for these modules. We consider two different
supervised feed-forward NN implementations, namely, a deep NN and a
2D-Convolutional NN, for MUD. Performance of these two NNs is compared with the
conventional receivers. Simulation results show that by proper selection of the
NN parameters, it is possible for the black box approximation to provide faster
and better performance, compared to conventional MUD schemes, and it achieves
almost the same symbol error rate as the ultimate one obtained by the complex
maximum likelihood-based detectors.


  In the early days of methanol maser discoveries the 9(2)-10(1) A+ transition
at 23.1 GHz was found to exhibit maser characteristics in the northern
star-forming region W3(OH), and probable maser emission in two other sources.
Attention subsequently turned to the 6.6-GHz 5(1)-6(0) A+ methanol maser
transition, which has proved a valuable tracer of early high-mass star
formation. We have undertaken a new search for 23.1-GHz methanol masers in 50
southern star formation regions using the Parkes radiotelescope. The target
sources all exhibit class II methanol maser emission at 6.6 GHz, with 20
sources also displaying maser features in the 107.0-GHz 3(1)-4(0) A+ methanol
line. Strong emission at 23.1 GHz in NGC 6334F was confirmed, but no emission
was detected in the remaining sources. Thus the 23.1-GHz methanol masers are
rare. A maser model in which methanol molecules are pumped to the second
torsionally excited state by radiation from warm dust can account for class II
maser activity in all the transitions in which it is observed. According to
this model the 23.1-GHz maser is favoured by conditions representing low gas
temperature, high external dust temperature, low gas density, and high column
density of methanol; the scarcity of this maser indicates that such
combinations of conditions are uncommon. We have undertaken new model
calculations to examine the range of parameters compatible with the upper
limits on 23.1-GHz emission from our survey.


  The lattice Schwinger model (SM), the discrete version of QED in 1+1
dimensions, is a well-studied test bench for lattice gauge theories. Here we
study the fractal properties of the SM. We reveal the self-similarity of the
ground state, which allows one to develop a recurrent procedure for finding the
ground-state wave functions and predicting ground-state energies. We provide
the results of recurrently calculating ground-state wave functions using the
fractal ansatz and automized software package for fractal image processing. In
certain parameter regimes, just a few terms are enough for our recurrent
procedure to predict ground state energies close to the exact ones for several
hundreds of sites. Our findings pave the way to understanding the complexity of
calculating many-body wave functions in terms of their fractal properties as
well as finding new links between condensed matter and high-energy lattice
models.


  The ground state of an S=1/2 antiferromagnetic Heisenberg model on a
spatially anisotropic triangular lattice, which is an effective model of Mott
insulators on a triangular layer of organic charge transfer salts or Cs2CuCl4,
is numerically studied. We apply a numerical variational method by using a
tensor network with entanglement renormalization, which improves the capability
of describing a quantum state. Magnetic ground states are identified for 0.7 <=
J2/J1 <= 1 in the thermodynamic limit, where J1 and J2 denote the inner-chain
and inter-chain coupling constants, respectively. Except for the isotropic case
(J1=J2), the magnetic structure is spiral with an incommensurate wave vector
that is different from the classical one. The quantum fluctuation weakens the
effective coupling between chains, but the magnetic order remains in the
thermodynamic limit. In addition, the incommensurate wave number is in good
agreement with that of the series expansion method.


  Multiples zeta values (MZV's for short) in positive characteristic were
introduced by Thakur as analogues of classical multiple zeta values of Euler.
In this paper we give a systematic study of algebraic structures of MZV's in
positive characteristic. We construct both the stuffle algebra and the shuffle
algebra of these MZV's and equip them with algebra and Hopf algebra structures.
In particular, we completely solve a problem suggested by Deligne and Thakur
\cite{Del17} in 2017 and establish Shi's conjectures \cite{Shi18}. The
construction of the stuffle algebra is based on our recent work
\cite{IKLNDP22}.


  We obtain long series expansions for the bulk, surface and corner free
energies for several two-dimensional statistical models, by combining Enting's
finite lattice method (FLM) with exact transfer matrix enumerations. The models
encompass all integrable curves of the Q-state Potts model on the square and
triangular lattices, including the antiferromagnetic transition curves and the
Ising model (Q=2) at temperature T, as well as a fully-packed O(n) type loop
model on the square lattice. The expansions are around the trivial fixed points
at infinite Q, n or 1/T.
  By using a carefully chosen expansion parameter, q << 1, all expansions turn
out to be of the form \prod_{k=1}^\infty (1-q^k)^{\alpha_k + k \beta_k}, where
the coefficients \alpha_k and \beta_k are periodic functions of k. Thanks to
this periodicity property we can conjecture the form of the expansions to all
orders (except in a few cases where the periodicity is too large). These
expressions are then valid for all 0 <= q < 1.
  We analyse in detail the q \to 1^- limit in which the models become critical.
In this limit the divergence of the corner free energy defines a universal term
which can be compared with the conformal field theory (CFT) predictions of
Cardy and Peschel. This allows us to deduce the asymptotic expressions for the
correlation length in several cases.
  Finally we work out the FLM formulae for the case where some of the system's
boundaries are endowed with particular (non-free) boundary conditions. We apply
this in particular to the square-lattice Potts model with Jacobsen-Saleur
boundary conditions, conjecturing the expansions of the surface and corner free
energies to arbitrary order for any integer value of the boundary interaction
parameter r. These results are in turn compared with CFT predictions.


  Current research in synthesized speech detection primarily focuses on the
generalization of detection systems to unknown spoofing methods of noise-free
speech. However, the performance of anti-spoofing countermeasures (CM) system
is often don't work as well in more challenging scenarios, such as those
involving noise and reverberation. To address the problem of enhancing the
robustness of CM systems, we propose a transfer learning-based speech
enhancement front-end joint optimization (TL-SEJ) method, investigating its
effectiveness in improving robustness against noise and reverberation. We
evaluated the proposed method's performance through a series of comparative and
ablation experiments. The experimental results show that, across different
signal-to-noise ratio test conditions, the proposed TL-SEJ method improves
recognition accuracy by 2.7% to 15.8% compared to the baseline. Compared to
conventional data augmentation methods, our system achieves an accuracy
improvement ranging from 0.7% to 5.8% in various noisy conditions and from 1.7%
to 2.8% under different RT60 reverberation scenarios. These experiments
demonstrate that the proposed method effectively enhances system robustness in
noisy and reverberant conditions.


  We report theoretical and simulation studies of phase coexistence in model
globular protein solutions, based on short-range, central, pair potential
representations of the interaction among macro-particles. After reviewing our
previous investigations of hard-core Yukawa and generalised Lennard-Jones
potentials, we report more recent results obtained within a DLVO-like
description of lysozyme solutions in water and added salt. We show that a
one-parameter fit of this model based on Static Light Scattering and
Self-Interaction Chromatography data in the dilute protein regime, yields
demixing and crystallization curves in good agreement with experimental
protein-rich/protein-poor and solubility envelopes. The dependence of cloud and
solubility points temperature of the model on the ionic strength is also
investigated. Our findings highlight the minimal assumptions on the properties
of the microscopic interaction sufficient for a satisfactory reproduction of
the phase diagram topology of globular protein solutions.


  In this paper we present Scylla, a methodology for domain adaptation of
Neural Machine Translation (NMT) systems that make use of a multilingual
FrameNet enriched with qualia relations as an external knowledge base. Domain
adaptation techniques used in NMT usually require fine-tuning and in-domain
training data, which may pose difficulties for those working with
lesser-resourced languages and may also lead to performance decay of the NMT
system for out-of-domain sentences. Scylla does not require fine-tuning of the
NMT model, avoiding the risk of model over-fitting and consequent decrease in
performance for out-of-domain translations. Two versions of Scylla are
presented: one using the source sentence as input, and another one using the
target sentence. We evaluate Scylla in comparison to a state-of-the-art
commercial NMT system in an experiment in which 50 sentences from the Sports
domain are translated from Brazilian Portuguese to English. The two versions of
Scylla significantly outperform the baseline commercial system in HTER.


  While the density profiles (DPs) of $\Lambda$CDM haloes obey the NFW law out
to roughly one virial radius, $r_{\rm vir}$, the structure of their outer parts
is still poorly understood, since the 1-halo term describing the halo itself is
dominated by the 2-halo term representing the other haloes picked up. Using a
semi-analytical model, we measure the real-space `1-halo' number DP of groups
out to $20\,r_{\rm vir}$ by assigning each galaxy to its nearest group with
mass above $M_{\rm a}$, in units of the group $r_{\rm vir}$. If $M_{\rm a}$ is
small (large), the outer DP of groups falls rapidly (slowly). We find that
there is an optimal $M_{\rm a}$ for which the stacked DP resembles the NFW
model to $0.1$ dex accuracy out to $\simeq 13\,r_{\rm vir}$. We find similar
long-range NFW surface DPs (out to $\simeq 10\,r_{\rm vir}$) in the SDSS
observations using a galaxy assignment scheme that combines the non-linear
virialized regions of groups with their linear outer parts. The optimal $M_{\rm
a}$ scales as the minimum mass of the groups that are stacked to the power
$0.25-0.3$. Our results suggest that the NFW model does not solely originate
from violent relaxation. Moreover, populating haloes with galaxies using HOD
models must proceed out to larger radii than usually done.


  Motivated by the recent empirical success of policy-based reinforcement
learning (RL), there has been a research trend studying the performance of
policy-based RL methods on standard control benchmark problems. In this paper,
we examine the effectiveness of policy-based RL methods on an important robust
control problem, namely $\mu$ synthesis. We build a connection between robust
adversarial RL and $\mu$ synthesis, and develop a model-free version of the
well-known $DK$-iteration for solving state-feedback $\mu$ synthesis with
static $D$-scaling. In the proposed algorithm, the $K$ step mimics the
classical central path algorithm via incorporating a recently-developed
double-loop adversarial RL method as a subroutine, and the $D$ step is based on
model-free finite difference approximation. Extensive numerical study is also
presented to demonstrate the utility of our proposed model-free algorithm. Our
study sheds new light on the connections between adversarial RL and robust
control.


  The influence of a small perturbation on a cavity mode plays an important
role in fields like optical sensing, cavity quantum electrodynamics and cavity
optomechanics. Typically, the resulting cavity frequency shift directly relates
to the polarizability of the perturbation. Here we demonstrate that particles
perturbing a radiating cavity can induce strong frequency shifts that are
opposite to, and even exceed, the effects based on the particles'
polarizability. A full electrodynamic theory reveals that these anomalous
results rely on a non-trivial phase relation between cavity and nanoparticle
radiation, allowing back-action via the radiation continuum. In addition, an
intuitive model based on coupled mode theory is presented that relates the
phenomenon to retardation. Because of the ubiquity of dissipation, we expect
these findings to benefit the understanding and engineering of a wide class of
systems.


  The ordering of the three-dimensional isotropic {\it XY} spin glass with the
nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo
simulations. To investigate the ordering of the spin and the chirality, we
compute several independent physical quantities including the glass order
parameter, the Binder parameter, the correlation-length ratio, the overlap
distribution and the non-self-averageness parameter, {\it etc}, for both the
spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of the
spin-chirality decoupling, {\it i.e.}, the CG and the SG order occurring at two
separated temperatures, $0<T_{SG}<T_{CG}$, is obtained from the glass order
parameter, which is fully corroborated by the Binder parameter. By contrast,
the CG correlation-length ratio yields a rather pathological and inconsistent
result in the range of sizes we studied, which may originate from the
finite-size effect associated with a significant short-length drop-off of the
spatial CG correlations. Finite-size-scaling analysis yields the CG exponents
$\nu_{CG}=1.36^{+0.15}_{-0.37}$ and $\eta_{CG}=0.26^{+0.29}_{-0.26}$, and the
SG exponents $\nu_{SG}=1.22^{+0.26}_{-0.06}$ and
$\eta_{SG}=-0.54^{+0.24}_{-0.52}$. The obtained exponents are close to those of
the Heisenberg SG, but are largely different from those of the Ising SG. The
chiral overlap distribution and the chiral Binder parameter exhibit the feature
of a continuous one-step replica-symmetry breaking (1RSB), consistently with
the previous reports. Such a 1RSB feature is again in common with that of the
Heisenberg SG, but is different from the Ising one, which may be the cause of
the difference in the CG critical properties from the Ising SG ones despite of
a common $Z_2$ symmetry.


  M dwarfs are the most abundant stars in the Solar Neighborhood and they are
prime targets for searching for rocky planets in habitable zones. Consequently,
a detailed characterization of these stars is in demand. The spectral sub-type
is one of the parameters that is used for the characterization and it is
traditionally derived from the observed spectra. However, obtaining the spectra
of M dwarfs is expensive in terms of observation time and resources due to
their intrinsic faintness. We study the performance of four machine-learning
(ML) models: K-Nearest Neighbor (KNN), Random Forest (RF), Probabilistic Random
Forest (PRF), and Multilayer Perceptron (MLP), in identifying the spectral
sub-types of M dwarfs at a grand scale by deploying broadband photometry in the
optical and near-infrared. We trained the ML models by using the
spectroscopically identified M dwarfs from the Sloan Digital Sky Survey Data
Release (SDSS) 7, together with their photometric colors that were derived from
the SDSS, Two-Micron All-Sky Survey, and Wide-field Infrared Survey Explorer.
We found that the RF, PRF, and MLP give a comparable prediction accuracy, 74%,
while the KNN provides slightly lower accuracy, 71%. We also found that these
models can predict the spectral sub-type of M dwarfs with ~99% accuracy within
+/-1 sub-type. The five most useful features for the prediction are r-z, r-i,
r-J, r-H, and g-z, and hence lacking data in all SDSS bands substantially
reduces the prediction accuracy. However, we can achieve an accuracy of over
70% when the r and i magnitudes are available. Since the stars in this study
are nearby (d~1300 pc for 95% of the stars), the dust extinction can reduce the
prediction accuracy by only 3%. Finally, we used our optimized RF models to
predict the spectral sub-types of M dwarfs from the Catalog of Cool Dwarf
Targets for TESS, and we provide the optimized RF models for public use.


  We study a class of variational problems for regularized conservation laws
with Lax's entropy-entropy flux pairs. We first introduce a modified optimal
transport space based on conservation laws with diffusion. Using this space, we
demonstrate that conservation laws with diffusion are "flux--gradient flows".
We next construct variational problems for these flows, for which we derive
dual PDE systems for regularized conservation laws. Several examples, including
traffic flow and Burgers' equation, are presented. Incorporating both
primal-dual algorithms and monotone schemes, we successfully compute the
control of conservation laws.


  We discuss topological quantum field theories that compute topological
invariants which depend on additional structures (or decorations) on
three-manifolds. The $q$-series invariant $\hat{Z}(q)$ proposed by Gukov, Pei,
Putrov and Vafa is an example of such an invariant. We describe how to obtain
these decorated invariants by cutting and gluing, and make a proposal for
Hilbert spaces that are assigned to two-dimensional surfaces in the
$\hat{Z}$-TQFT.


  This paper presents new and efficient algorithms for matching stellar
catalogues where the transformation between the coordinate systems of the two
catalagoues is unknown and may include shearing. Finding a given object whether
a star or asterism from the first catalogue in the second is logarithmic in
time rather than polynomial, yielding a dramatic speed up relative to a naive
implementation. Both acceleration of the matching algorithm and the ability to
solve for arbitrary affine transformations not only will allow the registration
of stellar catalogues and images that are now impossible to use but also will
find applications in machine vision and other imaging applications.


  This paper clarifies the local structure of the energy representation of a
local gauge group. The group to be considered is a smooth map from a manifold
into a compact Lie group. It acts on a Boson Fock spaces generated by
connection 1-forms on the manifold. The irreduciblity depends on the
dimensionality of a manifold. However, we showed that even if the
representation is reducible(for example, dim=1 case) the commutant is very
small. The discussion is based on the support property of the function, which
is analogous to the algebraic Quantum Field Theory.


  In this paper, we present LiveMedQA, a question answering system that is
optimized for consumer health question. On top of the general QA system
pipeline, we introduce several new features that aim to exploit domain-specific
knowledge and entity structures for better performance. This includes a
question type/focus analyzer based on deep text classification model, a
tree-based knowledge graph for answer generation and a complementary
structure-aware searcher for answer retrieval. LiveMedQA system is evaluated in
the TREC 2017 LiveQA medical subtask, where it received an average score of
0.356 on a 3 point scale. Evaluation results revealed 3 substantial drawbacks
in current LiveMedQA system, based on which we provide a detailed discussion
and propose a few solutions that constitute the main focus of our subsequent
work.


  We derived galaxy colour selections from Euclid and ground-based photometry,
aiming to accurately define background galaxy samples in cluster weak-lensing
analyses. Given any set of photometric bands, we developed a method for the
calibration of optimal galaxy colour selections that maximises the selection
completeness, given a threshold on purity. We calibrated galaxy selections
using simulated ground-based $griz$ and Euclid $Y_{\rm E}J_{\rm E}H_{\rm E}$
photometry. Both selections produce a purity higher than 97%. The $griz$
selection completeness ranges from 30% to 84% in the lens redshift range
$z_{\rm l}\in[0.2,0.8]$. With the full $grizY_{\rm E}J_{\rm E}H_{\rm E}$
selection, the completeness improves by up to $25$ percentage points, and the
$z_{\rm l}$ range extends up to $z_{\rm l}=1.5$. The calibrated colour
selections are stable to changes in the sample limiting magnitudes and
redshift, and the selection based on $griz$ bands provides excellent results on
real external datasets. The $griz$ selection is also purer at high redshift and
more complete at low redshift compared to colour selections found in the
literature. We find excellent agreement in terms of purity and completeness
between the analysis of an independent, simulated Euclid galaxy catalogue and
our calibration sample, except for galaxies at high redshifts, for which we
obtain up to 50 percent points higher completeness. The combination of colour
and photo-$z$ selections applied to simulated Euclid data yields up to 95%
completeness, while the purity decreases down to 92% at high $z_{\rm l}$. We
show that the calibrated colour selections provide robust results even when
observations from a single band are missing from the ground-based data.
Finally, we show that colour selections do not disrupt the shear calibration
for stage III surveys.


  We derive the expression for the anisotropic heterogeneous matrices of
permittivity and permeability associated with two-dimensional polygonal and
star shaped cloaks. We numerically show using finite elements that the forward
scattering worsens when we increase the number of sides in the latter cloaks,
whereas it improves for the former ones. This antagonistic behavior is
discussed using a rigorous asymptotic approach. We use a symmetry group
theoretical approach to derive the cloaks design.


  This work presents an investigation of the stochastic X-ray variability from
the 164 Hz accreting millisecond pulsar IGR J17062-6143, based on regular
observations collected with the Neutron Star Interior Composition Explorer
between 2017 July and 2020 August. Over this period, the power density spectrum
showed a stable morphology, with broad $\sim25\%$ rms band-limited noise below
16 Hz. Quasi-periodic oscillations (QPOs) were occasionally observed, with the
most notably detections including a low-frequency QPO centered at 2.7 Hz and a
sharp QPO centered at 115 Hz that may be a 2:3 resonance with the spin
frequency. Further, the energy dependence of the band-limited noise is studied
through a spectroscopic analysis of the complex covariance in two frequency
intervals. It is found that the power law continuum is the primary driver for
the observed variability, although the thermal (blackbody) emission also
appears to be intrinsically variable in area ($5\%$ rms) and temperature ($1\%$
rms). Notably, the 1 keV emission feature seen in all X-ray spectra of IGR
J17062-6143 varies with the same amplitude as the power law, but systematically
lags behind that continuum emission. These results appear consistent with a
scenario in which a time variable Compton-scattering corona is the primary
source for the observed stochastic variability, with the variability observed
in the emission feature and at the lowest photon energies being due to the disk
reflection of the power law continuum.


  We study the ground-state properties of frustrated Heisenberg ferrimagnetic
ladders with antiferromagnetic exchange interactions and two types of
alternating sublattice spins. In the limit of strong rung couplings, we show
that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a
spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The
system is either in a ferrimagnetic state or in a critical spin-liquid state
depending on the competition between the spin exchanges along the legs and the
diagonal exchanges.


  In a hate speech detection model, we should consider two critical aspects in
addition to detection performance-bias and explainability. Hate speech cannot
be identified based solely on the presence of specific words: the model should
be able to reason like humans and be explainable. To improve the performance
concerning the two aspects, we propose Masked Rationale Prediction (MRP) as an
intermediate task. MRP is a task to predict the masked human
rationales-snippets of a sentence that are grounds for human judgment-by
referring to surrounding tokens combined with their unmasked rationales. As the
model learns its reasoning ability based on rationales by MRP, it performs hate
speech detection robustly in terms of bias and explainability. The proposed
method generally achieves state-of-the-art performance in various metrics,
demonstrating its effectiveness for hate speech detection.


  A manifestly S-dual, and `12 dimensional', IIB superstring action with an
$Sl(2;\bR)$ doublet of `Born-Infeld' fields is presented. The M-theory origin
of the 12th dimension is the M-2-brane tension, which can be regarded as the
flux of a 3-form worldvolume field strength. The latter is required by the fact
that the M-2-brane can have a boundary on an M-5-brane.


  Single-photon sources and detectors are key enabling technologies in quantum
information processing. Nanowire-based superconducting single-photon detectors
(SSPDs) offer single-photon detection from the visible well into the infrared
with low dark counts, low jitter and short dead times. We report on the high
fidelity characterization (via antibunching and spontaneous emission lifetime
measurements) of a cavity-coupled single-photon source at 902 nm using a pair
of SSPDs. The twin SSPD scheme reported here is well-suited to the
characterization of single-photon sources at telecom wavelengths (1310 nm, 1550
nm).


  In this work, we describe a logic device in which an act of computation is
associated with finding a path connecting input and output ports. The device is
based on an active ring circuit comprising electric and magnetic parts. The
electric part includes an amplifier, a phase shifter, and an attenuator. The
magnetic part is a multi-port magnetic matrix comprising delay lines and
frequency filters. Signals propagating on different paths may accumulate
different phase shifts. Auto-oscillations occur in the circuit when the
magnetic and electric parts match each other to meet the resonance amplitude
and phase conditions. The system naturally searches for a resonance path that
depends on the position of the electric phase shifter and amplification level.
The path is detected by the set of power sensors. The proposed logic device can
be used for solving a variety of computational problems. We present the results
of numerical modeling illustrating prime factorization and finding the shortest
path connected selected points on the mesh.


  Using a generalised version of Gershgorin's circle theorem, rigorous
boundaries on the energies of the lowest states of a broad class of line graphs
above a critical filling are derived for hardcore bosonic systems. Also a lower
boundary on the energy gap towards the next lowest states is established.
Additionally, it is shown that the corresponding eigenstates are dominated by a
subspace spanned by states containing a compactly localised pair and a lower
boundary for the overlap is derived as well. Overall, this strongly suggests
localised pair formationin the ground states of the broad class of line graphs
and rigorously proves it for some of the graphs in it, including the
inhomogeneous chequerboard chain as well as two novel examples of regular two
dimensional graphs.


  Zaremba's conjecture (1971) states that every positive integer number d can
be represented as a denominator of a finite continued fraction b/d =
[d1,d2,...,dk], with all partial quotients d1,d2,...,dk being bounded by an
absolute constant A. Several new theorems concerning this conjecture were
proved by Bourgain and Kontorovich in 2011. The easiest of them states that the
set of numbers satisfying Zaremba's conjecture with A = 50 has positive
proportion in natural numbers. In 2014 I. D. Kan and D. A. Frolenkov proved
this result with A = 5. In this paper the same theorem is proved with A = 4.


  We consider ultracold atoms in a far detuned optical lattice orientated
across a high-Q optical resonator. Applying an external driving laser to the
atoms, which is red detuned from the cavity mode by one vibrational quantum,
induces cavity-enhanced sideband cooling. For a dense and cold enough atomic
ensemble we predict an oscillation threshold for optical Raman sideband lasing
concurrent with coherent matter-wave amplification. Above this oscillation
threshold photons and atoms in the lowest band are dominantly created pairwise
via stimulated emission with a strong suppression of competing spontaneous
processes. In close analogy to a nondegenerate parametric oscillator we find
sub-Poissonian photon statistics and almost perfect nonclassical atom-photon
number correlations. Injecting atoms in higher vibrational bands via tunneling
or incoherent scattering then leads to continuous, simultaneous generation of a
coherent atom beam and laser light with nonclassical atom-field correlations.


  Evolutionary biology shares many concepts with statistical physics: both deal
with populations, whether of molecules or organisms, and both seek to simplify
evolution in very many dimensions. Often, methodologies have undergone parallel
and independent development, as with stochastic methods in population genetics.
We discuss aspects of population genetics that have embraced methods from
physics: amongst others, non-equilibrium statistical mechanics, travelling
waves, and Monte-Carlo methods have been used to study polygenic evolution,
rates of adaptation, and range expansions. These applications indicate that
evolutionary biology can further benefit from interactions with other areas of
statistical physics, for example, by following the distribution of paths taken
by a population through time.


  Developing a suggestion by Russell, Prawitz showed how the usual natural
deduction inference rules for disjunction, conjunction and absurdity can be
derived using those for implication and the second order quantifier in
propositional intuitionistic second order logic $NI^2$. It is however well
known that the translation does not preserve the relations of identity among
derivations induced by the permutative conversions and immediate expansions for
the definable connectives, at least when the equational theory of $NI^2$ is
assumed to consist only of $\beta$ and $\eta$ equations. On the basis of the
categorial interpretation of $NI^2$, we introduce a new class of equations
expressing what in categorial terms is a naturality condition satisfied by the
transformations interpreting $NI^2$-derivations. We show that the
Russell-Prawitz translation does preserve identity of proof with respect to the
enriched system by highlighting the fact that naturality corresponds to a
generalized permutation principle. We show that these result generalize some
facts which have gone so far unnoticed, namely that the Russell-Prawitz
translation maps particular classes of instances of the equations governing
disjunction (and the other definable connectives) onto equations which are
already included in the $\beta\eta$ equational theory of $NI^2$. Finally, we
compare our approach with the one proposed by Ferreira and Ferreira and show
that the naturality condition suggests a generalization of their methods to a
wider class of formulas.


  In supersymmetric quantum mechanics, exact-solvability of one-dimensional
quantum systems can be classified only with an additional assumption of
integrability, the so-called shape invariance condition. In this paper we show
that in the prepotential approach we proposed previously, shape invariance is
automatically satisfied and needs not be assumed.


  A well-known ansatz (`trace method') for soliton solutions turns the
equations of the (noncommutative) KP hierarchy, and those of certain
extensions, into families of algebraic sum identities. We develop an algebraic
formalism, in particular involving a (mixable) shuffle product, to explore
their structure. More precisely, we show that the equations of the
noncommutative KP hierarchy and its extension (xncKP) in the case of a
Moyal-deformed product, as derived in previous work, correspond to identities
in this algebra. Furthermore, the Moyal product is replaced by a more general
associative product. This leads to a new even more general extension of the
noncommutative KP hierarchy. Relations with Rota-Baxter algebras are
established.


  Using molecular dynamics simulations, we have determined that the nature of
dynamical heterogeneity in jammed liquids is very sensitive to short-ranged
attractions. Weakly attractive systems differ little from dense hard-sphere and
Lennard-Jones fluids: Particle motion is punctuated and tends to proceed in
steps of roughly a single particle diameter. Both of these basic features
change in the presence of appreciable attractions. Transient periods of
particle mobility and immobility cannot be discerned at intermediate attraction
strength, for which structural relaxation is greatly enhanced. Strong
attractions, known to dramatically inhibit relaxation, restore bimodality of
particle motion. But in this regime, transiently mobile particles move in steps
that are significantly more biased toward large displacements than in the case
of weak attractions. This modified feature of dynamic heterogeneity, which
cannot be captured by conventional mode coupling theory, verifies recent
predictions from a model of spatially correlated facilitating defects.


  We introduce the ARMA (autoregressive-moving-average) point process, which is
a Hawkes process driven by a Neyman-Scott process with Poisson immigration. It
contains both the Hawkes and Neyman-Scott process as special cases and
naturally combines self-exciting and shot-noise cluster mechanisms, useful in a
variety of applications. The name ARMA is used because the ARMA point process
is an appropriate analogue of the ARMA time series model for integer-valued
series. As such, the ARMA point process framework accommodates a flexible
family of models sharing methodological and mathematical similarities with ARMA
time series. We derive an estimation procedure for ARMA point processes, as
well as the integer ARMA models, based on an MCEM (Monte Carlo Expectation
Maximization) algorithm. This powerful framework for estimation accommodates
trends in immigration, multiple parametric specifications of excitement
functions, as well as cases where marks and immigrants are not observed.


  The pion superfluid and the corresponding Goldstone and soft modes are
investigated in two-flavor quark-meson model with functional renormalization
group. By solving the flow equations for the effective potential and the meson
two-point functions at finite temperature and isospin density, the critical
temperature for the superfluid increases sizeably in comparison with solving
the flow equation for the potential only. The spectral function for the soft
mode shows clearly a transition from meson gas to quark gas with increasing
temperature and a crossover from BEC to BCS pairing of quarks with increasing
isospin density.


  On-device training is currently the most common approach for training machine
learning (ML) models on private, distributed user data. Despite this, on-device
training has several drawbacks: (1) most user devices are too small to train
large models on-device, (2) on-device training is communication- and
computation-intensive, and (3) on-device training can be difficult to debug and
deploy. To address these problems, we propose Private Evolution-Text
(PrE-Text), a method for generating differentially private (DP) synthetic
textual data. First, we show that across multiple datasets, training small
models (models that fit on user devices) with PrE-Text synthetic data
outperforms small models trained on-device under practical privacy regimes
($\epsilon=1.29$, $\epsilon=7.58$). We achieve these results while using
9$\times$ fewer rounds, 6$\times$ less client computation per round, and
100$\times$ less communication per round. Second, finetuning large models on
PrE-Text's DP synthetic data improves large language model (LLM) performance on
private data across the same range of privacy budgets. Altogether, these
results suggest that training on DP synthetic data can be a better option than
training a model on-device on private distributed data. Code is available at
https://github.com/houcharlie/PrE-Text.


  We address the long time behavior of the Boussinesq system coupling the
Navier-Stokes equations driven by density with the non-diffusive equation for
the density. We construct solutions of the system justifying previously
obtained a priori bounds.


  Astrophysical events that occur in active galactic nucleus (AGN) disks are
believed to differ significantly from the ordinary in the interstellar medium.
We show that stars located in the outer region of the AGN disk would explode
near the original migration starting points instead of being accreted by the
central supermassive black hole due to the effect of viscosity. AGN disks
provide a dense environment for supernova (SN) explosions, which inevitably
involve ejecta-disk interactions. In this paper, we investigate the light
curves (LCs) of core-collapse SN exploded in AGN disks. In addition to the
fundamental energy source of $^{56} \mathrm{Ni}$--$^{56} \mathrm{Co}$--$^{56}
\mathrm{Fe}$ decay reaction powering the SN LCs, the forward-reverse shock
produced during interactions may contribute significantly to the observed flux.
If the stellar winds manage to create a cavity surrounded by a shell near the
star before the SN explosion, the ejecta-winds-disk configurations are
expected. We present various SN LCs from different types of progenitors and
find that the SN LCs are dominated by the radiation of ejecta-disk
interaction-induced shocks. The resulting SNe in the AGN disk is a promising
transient source for UV and optical band detection by the Neil Gehrels Swift
Observatory (Swift), the Ultraviolet Explorer (UVEX) and wide field survey
telescopes such as Ultraviolet Transient Astronomy Satellite (ULTRASAT), Wide
Field Survey Telescope (WFST) and Legacy Survey of Space and Time (LSST) at the
Vera C. Rubin Observatory. These detections could aid in the investigation of
AGN discs and the associated high-energy transient occurrences.