  This review concerns the resolution of a special case of
Knizhnik-Zamolodchikov equations ($KZ_3$) using our recent results on
combinatorial aspects of zeta functions on several variables and software on
noncommutative symbolic computations. In particular, we describe the actual
solution of $(KZ_3)$ leading to the unique noncommutative series, $\Phi_{KZ}$,
so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions
for series with rational coefficients, satisfying the same properties with
$\Phi_{KZ}$, are also explicitly provided due to the algebraic structure and
the singularity analysis of the polylogarithms and harmonic sums.


  For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write
R^{1/q} = R^{a_q} \oplus M_q, where M_q has no free direct summands over R. We
investigate the structure of F-finite, F-pure rings R by studying how the
numbers a_q grow with respect to q. This growth is quantified by the splitting
dimension and the splitting ratios of R which we study in detail. We also prove
the existence of a special prime ideal P(R) of R, called the splitting prime,
that has the property that R/P(R) is strongly F-regular. We show that this
ideal captures significant information with regard to the F-purity of R.


  We present an iterative algorithm for solving a class of \\nonlinear
Laplacian system of equations in $\tilde{O}(k^2m \log(kn/\epsilon))$
iterations, where $k$ is a measure of nonlinearity, $n$ is the number of
variables, $m$ is the number of nonzero entries in the graph Laplacian $L$,
$\epsilon$ is the solution accuracy and $\tilde{O}()$ neglects (non-leading)
logarithmic terms. This algorithm is a natural nonlinear extension of the one
by of Kelner et. al., which solves a linear Laplacian system of equations in
nearly linear time. Unlike the linear case, in the nonlinear case each
iteration takes $\tilde{O}(n)$ time so the total running time is
$\tilde{O}(k^2mn \log(kn/\epsilon))$. For sparse graphs where $m = O(n)$ and
fixed $k$ this nonlinear algorithm is $\tilde{O}(n^2 \log(n/\epsilon))$ which
is slightly faster than standard methods for solving linear equations, which
require approximately $O(n^{2.38})$ time. Our analysis relies on the
construction of a nonlinear "energy function" and a nonlinear extension of the
duality analysis of Kelner et. al to the nonlinear case without any explicit
references to spectral analysis or electrical flows. These new insights and
results provide tools for more general extensions to spectral theory and
nonlinear applications.


  In noisy and reverberant environments, the performance of deep learning-based
speech separation methods drops dramatically because previous methods are not
designed and optimized for such situations. To address this issue, we propose a
multi-stage end-to-end learning method that decouples the difficult speech
separation problem in noisy and reverberant environments into three
sub-problems: speech denoising, separation, and de-reverberation. The
probability and speed of searching for the optimal solution of the speech
separation model are improved by reducing the solution space. Moreover, since
the channel information of the audio sequence in the time domain is crucial for
speech separation, we propose a triple-path structure capable of modeling the
channel dimension of audio sequences. Experimental results show that the
proposed multi-stage triple-path method can improve the performance of speech
separation models at the cost of little model parameter increment.


  Data from experiments and direct simulations of turbulence have historically
been used to calibrate simple engineering models such as those based on the
Reynolds-averaged Navier--Stokes (RANS) equations. In the past few years, with
the availability of large and diverse datasets, researchers have begun to
explore methods to systematically inform turbulence models with data, with the
goal of quantifying and reducing model uncertainties. This review surveys
recent developments in bounding uncertainties in RANS models via physical
constraints, in adopting statistical inference to characterize model
coefficients and estimate discrepancy, and in using machine learning to improve
turbulence models. Key principles, achievements and challenges are discussed. A
central perspective advocated in this review is that by exploiting foundational
knowledge in turbulence modeling and physical constraints, data-driven
approaches can yield useful predictive models.


  We prove a deviation inequality for noncommutative martingales by extending
Oliveira's argument for random matrices. By integration we obtain a Burkholder
type inequality with satisfactory constant. Using continuous time, we establish
noncommutative Poincar\'e type inequalities for "nice" semigroups with a
positive curvature condition. These results allow us to prove a general
deviation inequality and a noncommutative transportation inequality due to
Bobkov and G\"otze in the commutative case. To demonstrate our setting is
general enough, we give various examples, including certain group von Neumann
algebras, random matrices and classical diffusion processes, among others.


  This primer is intended as an introduction to differential forms, a central
object in modern mathematical physics, for scientists and engineers.


  We consider the outer automorphism group Out(A_Gamma) of the right-angled
Artin group A_Gamma of a random graph Gamma on n vertices in the Erdos--Renyi
model. We show that the functions (log(n)+log(log(n)))/n and
1-(log(n)+log(log(n)))/n bound the range of edge probability functions for
which Out(A_Gamma) is finite: if the probability of an edge in Gamma is
strictly between these functions as n grows, then asymptotically Out(A_Gamma)
is almost surely finite, and if the edge probability is strictly outside of
both of these functions, then asymptotically Out(A_Gamma) is almost surely
infinite. This sharpens results of Ruth Charney and Michael Farber from their
preprint "Random groups arising as graph products", arXiv:1006.3378v1.


  Along the development of free-electron laser operating at the wavelength of
X-ray, the importance of investigation on the radiation has increased. A
theoretical simulation is an essential tool for studying existing and proposed
experiments. The available simulations preserve net energy conservation over
the timestep, upholding causality between the electrons' power and the radiated
energy flux. However, according to Wheeler-Feynman time-symmetric theory, the
timestep is too short to ensure this. Therefore, the time evolution of
electrons and radiation field predicted by the simulations should contradict
the correct physics, regardless of whether the stimulated emission dominates
over the spontaneous emission or not.


  In this paper, we provide a novel approach to capture causal interaction in a
dynamical system from time-series data. In \cite{sinha_IT_CDC2016}, we have
shown that the existing measures of information transfer, namely directed
information, granger causality and transfer entropy fail to capture true causal
interaction in dynamical system and proposed a new definition of information
transfer that captures true causal interaction. The main contribution of this
paper is to show that the proposed definition of information transfer in
\cite{sinha_IT_CDC2016}\cite{sinha_IT_ICC} can be computed from time-series
data. We use transfer operator theoretic framework involving Perron-Frobenius
and Koopman operators for the data-driven approximation of the system dynamics
and for the computation of information transfer. Several examples involving
linear and nonlinear system dynamics are presented to verify the efficiency of
the developed algorithm.


  We study a slight variation of the unimodular gauge condition which we call
"the derivative gauge condition". We show that at the classical level these
conditions are completely equivalent up to a surface term. At the quantum level
the derivative gauge condition can be easily implemented by analogy with gauge
fixing in a quantum gauge theory. This condition might have advantages and
disadvantages upon the context.


  The main focus of this paper is a nonparametric filtering technique for the
estimation of interface geometry in bulk materials obtainable from modern
imaging measurements. The filtering methodology relies on an assumed hierarchy
of topological features present in a typical interface network, such as foam
interfaces and grain boundary networks in polycrystalline materials. Each type
of topological feature is treated in order of rank in the hierarchy, with the
lower-level feature being filtered subject to the positional constraints
imposed by the higher-level features. Such a scheme is an alternative to
existing surface smoothing/estimation techniques in microstructural materials
science, in which the explicit treatment of different elements of the network
topology is absent, or at best arbitrarily parameterized. We describe the
ramifications of this technique in the usual microstructural applications in
which the computation of important physical quantities is predicated on the
precise estimation of the interface features. As an additional application, we
describe a novel front-tracking algorithm for quantifying the transport of such
interfaces.


  Icosahedral shells undergo a buckling transition as the ratio of Young's
modulus to bending stiffness increases. Strong bending stiffness favors smooth,
nearly spherical shapes, while weak bending stiffness leads to a sharply
faceted icosahedral shape. Based on the phonon spectrum of a simplified
mass-and-spring model of the shell, we interpret the transition from smooth to
faceted as a soft-mode transition. In contrast to the case of a disclinated
planar network where the transition is sharply defined, the mean curvature of
the sphere smooths the transitition. We define elastic susceptibilities as the
response to forces applied at vertices, edges and faces of an icosahedron. At
the soft-mode transition the vertex susceptibility is the largest, but as the
shell becomes more faceted the edge and face susceptibilities greatly exceed
the vertex susceptibility. Limiting behaviors of the susceptibilities are
analyzed and related to the ridge-scaling behavior of elastic sheets. Our
results apply to virus capsids, liposomes with crystalline order and other
shell-like structures with icosahedral symmetry.


  The non-local block is a popular module for strengthening the context
modeling ability of a regular convolutional neural network. This paper first
studies the non-local block in depth, where we find that its attention
computation can be split into two terms, a whitened pairwise term accounting
for the relationship between two pixels and a unary term representing the
saliency of every pixel. We also observe that the two terms trained alone tend
to model different visual clues, e.g. the whitened pairwise term learns
within-region relationships while the unary term learns salient boundaries.
However, the two terms are tightly coupled in the non-local block, which
hinders the learning of each. Based on these findings, we present the
disentangled non-local block, where the two terms are decoupled to facilitate
learning for both terms. We demonstrate the effectiveness of the decoupled
design on various tasks, such as semantic segmentation on Cityscapes, ADE20K
and PASCAL Context, object detection on COCO, and action recognition on
Kinetics.


  Neutral silicon clusters Si_n (up to n = 7) and their cations Si_n+ (up to n
= 10) have been produced by femtosecond laser ablation of bulk silicon in
vacuum and investigated using time-of-flight mass spectrometry. Two populations
of the Si_n+ clusters with different velocity and abundance distributions in
the ablation plume have been clearly distinguished. Possible mechanisms of
cluster formation (Coulomb explosion, gas-phase condensation, phase explosion)
are discussed.


  Artificial intelligence and data-driven networks will be integral part of 6G
systems. In this article, we comprehensively discuss implementation challenges
and need for architectural changes in 5G radio access networks for integrating
machine learning (ML) solutions. As an example use case, we investigate user
equipment (UE) positioning assisted by deep learning (DL) in 5G and beyond
networks. As compared to state of the art positioning algorithms used in
today's networks, radio signal fingerprinting and machine learning (ML)
assisted positioning requires smaller additional feedback overhead; and the
positioning estimates are made directly inside the radio access network (RAN),
thereby assisting in radio resource management. In this regard, we study
ML-assisted positioning methods and evaluate their performance using system
level simulations for an outdoor scenario. The study is based on the use of
raytracing tool, a 3GPP 5G NR compliant system level simulator and DL framework
to estimate positioning accuracy of the UE. We evaluate and compare performance
of various DL models and show mean positioning error in the range of 1-1.5m for
a 2-hidden layer DL architecture with appropriate feature-modeling. Building on
our performance analysis, we discuss pros and cons of various architectures to
implement ML solutions for future networks and draw conclusions on the most
suitable architecture.


  We present new observations of the field containing the z=3.786 protocluster,
PC217.96+32.3. We confirm that it is one of the largest and most overdense
high-redshift structures known. Such structures are rare even in the largest
cosmological simulations. We used the Mayall/MOSAIC1.1 imaging camera to image
a 1.2x0.6 deg area (~150x75 comoving Mpc) surrounding the protocluster's core
and discovered 165 candidate Lyman Alpha emitting galaxies (LAEs) and 788
candidate Lyman Break galaxies (LBGs). There are at least 2 overdense regions
traced by the LAEs, the largest of which shows an areal overdensity in its core
(i.e., within a radius of 2.5 comoving Mpc) of 14+/-7 relative to the average
LAE spatial density in the imaged field. Further, the average LAE spatial
density in the imaged field is twice that derived by other field LAE surveys.
Spectroscopy with Keck/DEIMOS yielded redshifts for 164 galaxies (79 LAEs and
85 LBGs); 65 lie at a redshift of 3.785+/-0.010. The velocity dispersion of
galaxies near the core is 350+/-40 km/s, a value robust to selection effects.
The overdensities are likely to collapse into systems with present-day masses
of >10^{15} solar masses and >6x10^{14} solar masses. The low velocity
dispersion may suggest a dynamically young protocluster. We find a weak trend
between narrow-band (Lyman Alpha) luminosity and environmental density: the
Lyman Alpha luminosity is enhanced on average by 1.35X within the protocluster
core. There is no evidence that the Lyman Alpha equivalent width depends on
environment. These suggest that star-formation and/or AGN activity is enhanced
in the higher density regions of the structure. PC217.96+32.3 is a Coma cluster
analog, witnessed in the process of formation.


  The spectral region between 1250 Angstroms - 3000 Angstroms contains
important spectral lines to understand the morphological structures and
evolution of planetary
  nebulae. This is the region sampled by UVIT through various filter bands both
in the continuum and in emission lines (e.g. C IV, He I, Mg II etc.). We have
mapped several planetary nebulae with different characteristics, ranging in
morphology from bipolar to wide and diffuse, and in various states of
ionization, comparing the UV with the x-ray morphologies wherever the x-ray
images were also available. The major unanticipated discovery with UVIT has
been the detection of previously undetected, cold, fluorescent, molecular
hydrogen gas surrounding some planetary nebulae. This may be a possible
solution to the missing mass problem. Here we present a review of our studies
so far done (both published and on going) with UVIT.


  The resampling algorithm of Moser \& Tardos is a powerful approach to develop
constructive versions of the Lov\'{a}sz Local Lemma (LLL). We generalize this
to partial resampling: when a bad event holds, we resample an
appropriately-random subset of the variables that define this event, rather
than the entire set as in Moser & Tardos. This is particularly useful when the
bad events are determined by sums of random variables. This leads to several
improved algorithmic applications in scheduling, graph transversals, packet
routing etc. For instance, we settle a conjecture of Szab\'{o} & Tardos (2006)
on graph transversals asymptotically, and obtain improved approximation ratios
for a packet routing problem of Leighton, Maggs, & Rao (1994).


  We discuss the minimum value of the zero-bias differential conductance
$G_{\textrm{min}}$ in a junction consisting of a normal metal and a nodal
superconductor preserving time-reversal symmetry. Using the quasiclassical
Green function method, we show that $G_{\textrm{min}}$ is quantized at $
(4e^2/h) N_{\mathrm{ZES}}$ in the limit of strong impurity scatterings in the
normal metal. The integer $N_{\mathrm{ZES}}$ represents the number of perfect
transmission channels through the junction. An analysis of the chiral symmetry
of the Hamiltonian indicates that $N_{\mathrm{ZES}}$ corresponds to the
Atiyah-Singer index in mathematics.


  We report the impact of hydrostatic pressure on the superconductivity and
normal state resistivity of FeTe0.5Se0.5 superconductor. At the ambient
pressure the FeTe0.5Se0.5 compound shows the superconducting transition
temperature Tconset at above 13K and TcR=0 at 11.5K. We measure pressure
dependent resistivity from 250K to 5K, which shows that the normal state
resistivity increases initially for the applied pressures of up to 0.55GPa and
then the same is decreased monotonically with increasing pressure of up to
1.97GPa. On the other hand the superconducting transition temperatures (Tconset
and TcR=0) increase monotonically with increasing pressure. Namely the Tconset
increases from 13K to 25K and TcR=0 from 11.5K to 20K for the pressures range
of 0-1.97GPa. Our results suggest that superconductivity in this class of
Fe-based compounds is very sensitive to pressure as the estimated pressure
coefficient dTc(onset)/dP is 5.8K/GPa. It may be suggested that FeTe0.5Se0.5
superconductor is a strong electron correlated system. The enhancement of Tc
with applying pressure is mainly attributed to an increase of charge carriers
at Fermi surface.


  The compact radio source Sagittarius~A$^*$ (Sgr~A$^*$)in the Galactic Center
is the primary supermassive black hole candidate. General relativistic
magnetohydrodynamical (GRMHD) simulations of the accretion flow around
Sgr\,A$^*$ predict the presence of sub-structure at observing wavelengths of
$\sim 3$\,mm and below (frequencies of 86\,GHz and above). For very long
baseline interferometry (VLBI) observations of Sgr\,A$^*$ at this frequency the
blurring effect of interstellar scattering becomes subdominant, and arrays such
as the High Sensitivity Array (HSA) and the global mm-VLBI Array (GMVA) are now
capable of resolving potential sub-structure in the source. Such investigations
improve our understanding of the emission geometry of the mm-wave emission of
Sgr\,A$^*$, which is crucial for constraining theoretical models and for
providing a background to interpret 1\,mm VLBI data from the Event Horizon
Telescope (EHT). We performed high-sensitivity very long baseline
interferometry (VLBI) observations of Sgr\,A$^*$ at 3\,mm using the Very Long
Baseline Array (VLBA) and the Large Millimeter Telescope (LMT) in Mexico on two
consecutive days in May 2015, with the second epoch including the Green Bank
Telescope (GBT). We find an overall source geometry that matches previous
findings very closely, showing a deviation in fitted model parameters less than
3\% over a time scale of weeks and suggesting a highly stable global source
geometry over time. The reported sub-structure in the 3\,mm emission of
Sgr\,A$^*$ is consistent with theoretical expectations of refractive noise on
long baselines. However, comparing our findings with recent results from 1\,mm
and 7\,mm VLBI observations, which also show evidence for east-west asymmetry,
an intrinsic origin cannot be excluded. Confirmation of persistent intrinsic
substructure will require further VLBI observations spread out over multiple
epochs.


  We present results from large-scale numerical simulations of a first order
thermal phase transition in the early universe, in order to explore the shape
of the acoustic gravitational wave and the velocity power spectra. We compare
the results with the predictions of the recently proposed sound shell model.
For the gravitational wave power spectrum, we find that the predicted $k^{-3}$
behaviour, where $k$ is the wavenumber, emerges clearly for detonations. The
power spectra from deflagrations show similar features, but exhibit a steeper
high-$k$ decay and an extra feature not accounted for in the model. There are
two independent length scales: the mean bubble separation and the thickness of
the sound shell around the expanding bubble of the low temperature phase. It is
the sound shell thickness which sets the position of the peak of the power
spectrum. The low wavenumber behaviour of the velocity power spectrum is
consistent with a causal $k^{3}$, except for the thinnest sound shell, where it
is steeper. We present parameters for a simple broken power law fit to the
gravitational wave power spectrum for wall speeds well away from the speed of
sound where this form can be usefully applied. We examine the prospects for the
detection, showing that a LISA-like mission has the sensitivity to detect a
gravitational wave signal from sound waves with an RMS fluid velocity of about
$0.05c$, produced from bubbles with a mean separation of about $10^{-2}$ of the
Hubble radius. The shape of the gravitational wave power spectrum depends on
the bubble wall speed, and it may be possible to estimate the wall speed, and
constrain other phase transition parameters, with an accurate measurement of a
stochastic gravitational wave background.


  We discuss several points regarding symmetries of the Duflo-Serganova
functor. In particular we give new constructions of Lie superalgebras, Lie
supergroups, and associative superalgebras which act on the Duflo-Serganova
functor. We connect our work to a computation of Heidersdorf and Weissauer
which computed $DS_x$ for a maximal rank $x$ on Kac-modules for $GL(n|n)$, and
extend the ideas and results to $P(n)$.


  The \emph{fractional matching preclusion number} of a graph $G$, denoted by
$fmp(G)$, is the minimum number of edges whose deletion results in a graph that
has no fractional perfect matchings. In this paper, we first give some sharp
upper and lower bounds of fractional matching preclusion number. Next, graphs
with large and small fractional matching preclusion number are characterized,
respectively. In the end, we investigate some extremal problems on fractional
matching preclusion number.


  It is shown that the two-gap approximation is applicable for describing the
$dV/dI(V)$ spectra of LuNi$_{2}$B$_{2}$C-Ag point contacts in a wide interval
of temperatures. The values and the temperature dependences of the large and
the small gaps in the $ab$ plane and in the $c$ direction were estimated using
the generalized BTK model and the equations of Beloborodko. In the BCS
extrapolation the critical temperature of the small gap is 10 $K$ in the $ab$
plane and 14.5 $K$ in the $c$ direction. The absolute values of the gaps are
$\Delta_0^{ab}=2.16$ $meV$ and $\Delta_0^c=1.94$ $meV$. For the large gaps the
critical temperature coincides with the bulk $T_c$, $T_c^{bulk}=16.8$ $K$, and
their absolute values are very close, being about 3 $meV$ in both orientations.
In the $c$ direction the contributions to the conductivity from the small and
the large gaps remain practically identical up to $10 \div 11$ $K$. In the $ab$
plane the contribution from the small gap is much smaller and decreases rapidly
as a temperature rises.


  We consider $N$ two-dimensional Ising models coupled in presence of quenched
disorder and use scale invariant scattering theory to exactly show the presence
of a line of renormalization group fixed points for any fixed value of $N$
other than 1. We show how this result relates to perturbative studies and sheds
light on numerical simulations. We also observe that the limit $N\to 1$ may be
of interest for the Ising spin glass, and point out potential relevance for
nonuniversality in other contexts of random criticality.


  Makkeh, Theis, and Vicente found in [8] that Cone Programming model is the
most robust to compute the Bertschinger et al. partial information decompostion
(BROJA PID) measure [1]. We developed a production-quality robust software that
computes the BROJA PID measure based on the Cone Programming model. In this
paper, we prove the important property of strong duality for the Cone Program
and prove an equivalence between the Cone Program and the original Convex
problem. Then describe in detail our software and how to use it.\newline\indent


  The behavior of long DNA molecules in a cell-sized confined space was
investigated. We prepared water-in-oil droplets covered by phospholipids, which
mimic the inner space of a cell, following the encapsulation of DNA molecules
with unfolded coil and folded globule conformations. Microscopic observation
revealed that the adsorption of coiled DNA onto the membrane surface depended
on the size of the vesicular space. Globular DNA showed a cell-size-dependent
unfolding transition after adsorption on the membrane. Furthermore, when DNA
interacted with a two-phase membrane surface, DNA selectively adsorbed on the
membrane phase, such as an ordered or disordered phase, depending on its
conformation. We discuss the mechanism of these trends by considering the free
energy of DNA together with a polyamine in the solution. The free energy of our
model was consistent with the present experimental data. The cooperative
interaction of DNA and polyamines with a membrane surface leads to the
size-dependent behavior of molecular systems in a small space. These findings
may contribute to a better understanding of the physical mechanism of molecular
events and reactions inside a cell.


  Under the background of the new media era with the rapid development of
interactive advertising, this paper used case study method based on the summary
of the research of the communication effect of interactive advertising from
both domestic and foreign academia. This paper divided interactive advertising
into three types to examine ---- interactive ads on official website,
interactive ads based on SNS and interactive ads based on mobile media.
Furthermore, this paper induced and summarized a self-enhanced dissemination
mechanism of the interactive advertising, including three parts which are micro
level, meso level and macro level mechanism, micro level embodies core
interaction, inner interaction and outer interaction which reveal the whole
process of interact with contents, with people and with computer, and the
communication approach and spread speed shown in meso level which is
self-fission-type spread, finally in macro level the communication effect of IA
achieved the spiral increasing. In a word, this article enriches research
procedure of the interactive advertising communication effects.


  It is well known that a unit sphere admits Sasakian 3-structure. Also,
Sasakian manifolds are locally isometric to a unit sphere under several
curvature and critical conditions. So, a natural question is: Does there exist
any curvature or critical condition under which a Sasakian 3-manifold
represents a geometrical object other than the unit sphere? In this regard, as
an extension of the $\ast$-Ricci soliton, the notion of $\ast$-Ricci-Yamabe
soliton is introduced and studied on two classes contact metric manifolds. A
$(2n + 1)$-dimensional non-Sasakian $N(k)$-contact metric manifold admitting
$\ast$-Ricci-Yamabe soliton is completely classified. Further, it is proved
that if a Sasakian 3-manifold $M$ admits $\ast$-Ricci-Yamabe soliton
$(g,V,\lambda,\alpha,\beta)$ under certain conditions on the soliton vector
field $V$, then $M$ is $\ast$-Ricci flat, positive Sasakian and the transverse
geometry of $M$ is Fano. In addition, the Sasakian 3-metric $g$ is homothetic
to a Berger sphere and the soliton is steady. Also, the potential vector field
$V$ is an infinitesimal automorphism of the contact metric structure.


  We consider learning problems where the training set consists of two types of
examples: private and public. The goal is to design a learning algorithm that
satisfies differential privacy only with respect to the private examples. This
setting interpolates between private learning (where all examples are private)
and classical learning (where all examples are public).
  We study the limits of learning in this setting in terms of private and
public sample complexities. We show that any hypothesis class of VC-dimension
$d$ can be agnostically learned up to an excess error of $\alpha$ using only
(roughly) $d/\alpha$ public examples and $d/\alpha^2$ private labeled examples.
This result holds even when the public examples are unlabeled. This gives a
quadratic improvement over the standard $d/\alpha^2$ upper bound on the public
sample complexity (where private examples can be ignored altogether if the
public examples are labeled). Furthermore, we give a nearly matching lower
bound, which we prove via a generic reduction from this setting to the one of
private learning without public data.


  A major impediment to the transition to context-aware machine translation is
the absence of good evaluation metrics and test sets. Sentences that require
context to be translated correctly are rare in test sets, reducing the utility
of standard corpus-level metrics such as COMET or BLEU. On the other hand,
datasets that annotate such sentences are also rare, small in scale, and
available for only a few languages. To address this, we modernize, generalize,
and extend previous annotation pipelines to produce CTXPRO, a tool that
identifies subsets of parallel documents containing sentences that require
context to correctly translate five phenomena: gender, formality, and animacy
for pronouns, verb phrase ellipsis, and ambiguous noun inflections. The input
to the pipeline is a set of hand-crafted, per-language, linguistically-informed
rules that select contextual sentence pairs using coreference, part-of-speech,
and morphological features provided by state-of-the-art tools. We apply this
pipeline to seven languages pairs (EN into and out-of DE, ES, FR, IT, PL, PT,
and RU) and two datasets (OpenSubtitles and WMT test sets), and validate its
performance using both overlap with previous work and its ability to
discriminate a contextual MT system from a sentence-based one. We release the
CTXPRO pipeline and data as open source.


  We discuss the application of recent results on generalized solutions to the
Cauchy problem for hyperbolic systems to Dirac equations with external fields.
In further analysis we focus on the question of existence of associated
distributional limits and derive their explicit form in case of free Dirac
fields with regularizations of initial values corresponding to point-like
probability densities.


  Among the diverse and important applications that networks currently have is
the modeling of infectious diseases. Immunization, or the process of protecting
nodes in the network, plays a key role in stopping diseases from spreading.
Hence the importance of having tools or strategies that allow the solving of
this challenge. In this work, we evaluate the effectiveness of the
DIL-W^{\alpha} ranking in immunizing nodes in an edge-weighted network. The
network is obtained from a real database and the spread of COVID-19 was modeled
with the classic SIR model. We apply the protection to the network, according
to the importance ranking list produced by DIL-W^{\alpha}.


  Models of prestellar cores often assume that the cores are isolated from
their environment - material outside the core boundary plays no role in the
subsequent evolution. This is unlikely to be the case in reality, where cores
are located within hierarchically substructured molecular clouds. We
investigate the dynamical and chemical evolution of prestellar cores, modelled
as Bonnor-Ebert spheres, and show that the density of the ambient medium has a
large impact on the resulting chemical properties of the cores. Models embedded
in high-density, low-temperature surroundings have greatly enhanced abundances
of several molecules, such as CO and CS, compared to models with more diffuse
surroundings, corresponding to relatively isolated cores. The predicted
intensities and profile shapes of molecular lines are also affected. The
density of the ambient medium has a stronger effect on the chemical evolution
than whether the cores are initially in or out of equilibrium. This suggests
that the impact of environment cannot be neglected when modelling chemistry in
prestellar cores; the results of these models are highly sensitive to the
assumptions made about the core surroundings.


  The power of high quality imaging combined with the large collecting area of
each VLT telescope is impressive, and there are clearly many exciting
discoveries waiting to be made. The study of resolved stellar populations will
certainly benefit greatly from this new observatory, as with Palomar before. We
will now be able to probe a much large range of star forming environment within
the Local Group, and specifically very low metallicity regions in nearby dwarf
irregular galaxies. The study of individual stars and star-formation regions in
the nearby universe is the only way we will understand the observations of
galaxy populations at high redshift. We present some initial results from the
BVI imaging of the Local Group galaxy Antlia made during FORS1 science
verification in January 1999.


  QCD confines quarks in all representations. From lattice calculations and fat
center vortices model, we discuss that the coefficient of the linear term in
the potential is proportional to both casimir scaling and the number of
fundamental strings.


  The history of the IMF in starburst regions is reviewed. The IMFs are no
longer believed to be top-heavy, although some superstar clusters, whether in
starburst regions or not, could be. General observations of the IMF are
discussed to put the starburst results in perspective. Observed IMF variations
seem to suggest that the IMF varies a little with environment in the sense that
denser and more massive clusters produce more massive stars, and perhaps more
brown dwarfs too, compared to intermediate mass stars.


  The fuzzy integral is a powerful parametric nonlin-ear function with utility
in a wide range of applications, from information fusion to classification,
regression, decision making,interpolation, metrics, morphology, and beyond.
While the fuzzy integral is in general a nonlinear operator, herein we show
that it can be represented by a set of contextual linear order statistics(LOS).
These operators can be obtained via sampling the fuzzy measure and clustering
is used to produce a partitioning of the underlying space of linear convex
sums. Benefits of our approach include scalability, improved integral/measure
acquisition, generalizability, and explainable/interpretable models. Our
methods are both demonstrated on controlled synthetic experiments, and also
analyzed and validated with real-world benchmark data sets.


  Let $X$ be a smooth projective variety defined over an algebraically closed
field, and let $L$ be an ample line bundle over $X$. We prove that for any
smooth hypersurface $D$ on $X$ in the complete linear system $| L^{\otimes
d}|$, the inclusion map $D\hookrightarrow X$ induces an isomorphism of
fundamental group schemes, provided $d$ is sufficiently large and $\dim X \geq
3$. If $\dim X = 2$, and $d$ is sufficiently large, then the induced
homomorphism of fundamental group schemes remains surjective. We give an
example to show that the homomorphism of fundamental group schemes induced by
the inclusion map of a reduced ample curve in a smooth projective surface is
not surjective in general.


  In this work, we present a quantum algorithm for ground-state energy
calculations of periodic solids on error-corrected quantum computers. The
algorithm is based on the sparse qubitization approach in second quantization
and developed for Bloch and Wannier basis sets. We show that Wannier functions
require less computational resources with respect to Bloch functions because:
(i) the L$_1$ norm of the Hamiltonian is considerably lower and (ii) the
translational symmetry of Wannier functions can be exploited in order to reduce
the amount of classical data that must be loaded into the quantum computer. The
resource requirements of the quantum algorithm are estimated for periodic
solids such as NiO and PdO. These transition metal oxides are industrially
relevant for their catalytic properties. We find that ground-state energy
estimation of Hamiltonians approximated using 200--900 spin orbitals requires
{\it ca.}~$10{}^{10}$--$10^{12}$ T gates and up to $3\cdot10^8$ physical qubits
for a physical error rate of $0.1\%$.


  A single very deep $10'$ field has been imaged to $r \sim 26$. There are 2682
galaxies with $23 \le r \le 26$ with a size significantly larger than the
seeing disk in the field. After correcting for telescope aberrations, possible
guiding errors, and signal degradation due to seeing, I find a polarization
signal of amplitude $|p|=2.7\%$, with an uncertainty of 1.2\% (95\% confidence
limit). For the 1773 galaxies with $23 \le r \le 25$, the measured amplitude is
2.4\% $\pm$ 1.2\% (95\% confidence limit). If this observed polarization is due
to gravitational lensing by large scale structure, cosmological inferences can
be made. The polarization amplitude would indicate that $\Omega_0 \times
\sigma_8 \approx 1$. The amplitude probability distribution is a Rayleigh
distribution with variance $\sigma_p^2$ so the probability $P(1/2 <
|p|/\sigma_p <2) = 75\%$, and $P(1/3 < |p|/\sigma_p < 3) = 93.5\%$. The
measurement of the polarization amplitude in a single field can be used to
constrain cosmological models since $\sigma_p \propto \Omega_0 \times
\sigma_8$.


  We study the kernel estimator of the transition density of bifurcating Markov
chains. Under some ergodic and regularity properties, we prove that this
estimator is consistent and asymptotically normal. Next, in the numerical
studies, we propose two data-driven methods to choose the bandwidth parameters.
These methods are based on the so-called two bandwidths approach.


  These proceedings discuss recent jet measurements by the STAR experiment at
RHIC to study jet substructure in p+p and jet quenching in Au+Au collisions at
$\sqrt{s_\mathrm{NN}}$ = 200 GeV. Furthermore, STAR's future plans for
precision jet measurements with the upcoming data-taking periods in 2023-2025
are presented.


  Following an analysis of the advantages of SQL-based Machine Learning (ML)
and a short literature survey of the field, we describe a novel method for
In-Database Machine Learning (IDBML). We contribute a process for SQL-code
generation in Python using template macros in Jinja2 as well as the prototype
implementation of the process. We describe our implementation of the process to
compute multidimensional histogram (MDH) probability estimation in SQL. For
this, we contribute and implement a novel discretization method called equal
quantized rank binning (EQRB) and equal-width binning (EWB). Based on this, we
provide data gathered in a benchmarking experiment for the quantitative
empirical evaluation of our method and system using the Covertype dataset. We
measured accuracy and computation time and compared it to Scikit Learn state of
the art classification algorithms. Using EWB, our multidimensional probability
estimation was the fastest of all tested algorithms, while being only 1-2% less
accurate than the best state of the art methods found (decision trees and
random forests). Our method was significantly more accurate than Naive Bayes,
which assumes independent one-dimensional probabilities and/or densities. Also,
our method was significantly more accurate and faster than logistic regression.
This motivates for further research in accuracy improvement and in IDBML with
SQL code generation for big data and larger-than-memory datasets.


  After exploring much on two-dimensional higher-order topological
superconductors (HOTSCs) hosting Majorana corner modes (MCMs) only, we propose
a simple fermionic model based on a three-dimensional topological insulator
proximized with $s$-wave superconductor to realize Majorana hinge modes (MHMs)
followed by MCMs under the application of appropriate Wilson-Dirac
perturbations. We interestingly find that the second-order topological
superconductor, hosting MHMs, appears above a threshold value of the first type
perturbation while the third-order topological superconducting phase,
supporting MCMs, immediately arises incorporating infinitesimal perturbation of
the second kind. Thus, a hierarchy of HOTSC phases can be realized in a single
three-dimensional model. Additionally, the application of bulk magnetic field
is found to be instrumental in manipulating the number of MHMs, leaving the
number for MCMs unaltered. We analytically understand these above-mentioned
numerical findings by resorting to the low energy model. We further
characterize these topological phases with a distinct structure of the Wannier
spectra. From the practical point of view, we manifest quantized transport
signatures of these higher-order modes. Finally, we construct Floquet
engineering to generate the hierarchy of HOTSC phases by kicking the same
perturbations as considered in their static counterpart.


  The state-of-the-art in current two-loop QCD amplitude calculations is at
five-particle scattering. Computing two-loop six-particle processes requires
knowledge of the corresponding one-loop amplitudes to higher orders in the
dimensional regulator. In this paper we compute analytically the one-loop
hexagon integral via differential equations. In particular we identify its
function alphabet for general $D$-dimensional external states. We also provide
integral representations for all one-loop integrals up to weight four. With
this, the one-loop integral basis is ready for two-loop amplitude applications.
We also study in detail the difference between the conventional dimensional
regularization and the four-dimensional helicity scheme at the level of the
master integrals and their function space.


  We study the cosmology of canonically normalized scalar fields that lead to
an equation of state parameter of w_\phi=p_\phi/\rho_\phi<-1 without violating
the weak energy condition: rho=\Sigma_i\rho_i \geq 0 and \rho_i+p_i\geq 0. This
kind of behavior requires a negative scalar potential V, widely predicted in
particle physics. We show that the energy density \rho_\phi=E_k+V takes
negative values with an equation of state with w_\phi < -1. However, the net
effect of the $\phi$ field on the scale factor is to decelerate it giving a
total equation of state parameter w=p/\rho> w_b=p_b/\rho_b, where \rho_b stands
for any kind of energy density with -1\leq w_b \leq 1. The fact that
\rho_\phi<0 allows, at least in principle, to have a small cosmological
constant or quintessence today as the cancellation of high energy scales such
as the electroweak or susy breaking scale. While V is negative |\rho_\phi| is
smaller than the sum of all other energy densities regardless of the functional
form of the potential V. We show that the existence of a negative potential
leads, inevitable, to a collapsing universe, i.e. to a would be "big crunch".
In this picture we would still be living in the expanding universe.


  We investigate number conserving cellular automata with up to five inputs and
two states with the goal of comparing their dynamics with diffusion. For this
purpose, we introduce the concept of decompression ratio describing expansion
of configurations with finite support. We find that a large number of
number-conserving rules exhibit abrupt change in the decompression ratio when
the density of the initial pattern is increasing, somewhat analogous to the
second order phase transition. The existence of this transition is formally
proved for rule 184. Small number of rules exhibit infinite decompression
ratio, and such rules may be useful for "engineering" of CA rules which are
good models of diffusion, although they will most likely require more than two
states.


  In the Priority $k$-Supplier problem the input consists of a metric space $(F
\cup C, d)$ over set of facilities $F$ and a set of clients $C$, an integer $k
> 0$, and a non-negative radius $r_v$ for each client $v \in C$. The goal is to
select $k$ facilities $S \subseteq F$ to minimize $\max_{v \in C}
\frac{d(v,S)}{r_v}$ where $d(v,S)$ is the distance of $v$ to the closes
facility in $S$. This problem generalizes the well-studied $k$-Center and
$k$-Supplier problems, and admits a $3$-approximation [Plesn\'ik, 1987, Bajpai
et al., 2022. In this paper we consider two outlier versions. The Priority
$k$-Supplier with Outliers problem [Bajpai et al., 2022] allows a specified
number of outliers to be uncovered, and the Priority Colorful $k$-Supplier
problem is a further generalization where clients are partitioned into $c$
colors and each color class allows a specified number of outliers. These
problems are partly motivated by recent interest in fairness in clustering and
other optimization problems involving algorithmic decision making.
  We build upon the work of [Bajpai et al., 2022] and improve their
$9$-approximation Priority $k$-Supplier with Outliers problem to a
$1+3\sqrt{3}\approx 6.196$-approximation. For the Priority Colorful
$k$-Supplier problem, we present the first set of approximation algorithms. For
the general case with $c$ colors, we achieve a $17$-pseudo-approximation using
$k+2c-1$ centers. For the setting of $c=2$, we obtain a $7$-approximation in
random polynomial time, and a $2+\sqrt{5}\approx 4.236$-pseudo-approximation
using $k+1$ centers.


  Using Ferromagnetic Fermi liquid theory, Bedell and Blagoev derived the
collective low-energy excitations of a weak ferromagnet. They obtained the
well-known magnon (Nambu-Goldstone) mode and found a new gapped mode that was
never studied in weak ferromagnetic metals. In this article we have identified
this mode as the Higgs boson (amplitude mode) of a ferromagnetic metal. This is
identified as the Higgs since it can be show that it corresponds to a
fluctuation of the amplitude of the order parameter. We use this model to
describe the itinerant-electron ferromagnetic material MnSi. By fitting the
model with the existing experimental results, we calculate the dynamical
structure function and see well-defined peaks contributed from the magnon and
the Higgs. Our estimates of the relative intensity of the Higgs amplitude mode
suggest that it can be seen in neutron scattering experiments on MnSi.


  On the basis of the confinement mechanism earlier proposed by author, the
electric form factor of $\eta$-meson is nonperturbatively calculated. The
latter is then applied to describe electromagnetic decay $\eta\to2\gamma$ which
entails estimates for parameters of the confining SU(3)-gluonic field in
$\eta$-meson. The corresponding estimates of the gluon concentrations, electric
and magnetic colour field strengths are also adduced for the mentioned field.


  The Support Vector Machine (SVM) is a popular classification paradigm in
machine learning and has achieved great success in real applications. However,
the standard SVM can not select variables automatically and therefore its
solution typically utilizes all the input variables without discrimination.
This makes it difficult to identify important predictor variables, which is
often one of the primary goals in data analysis. In this paper, we propose two
novel types of regularization in the context of the multicategory SVM (MSVM)
for simultaneous classification and variable selection. The MSVM generally
requires estimation of multiple discriminating functions and applies the argmax
rule for prediction. For each individual variable, we propose to characterize
its importance by the supnorm of its coefficient vector associated with
different functions, and then minimize the MSVM hinge loss function subject to
a penalty on the sum of supnorms. To further improve the supnorm penalty, we
propose the adaptive regularization, which allows different weights imposed on
different variables according to their relative importance. Both types of
regularization automate variable selection in the process of building
classifiers, and lead to sparse multi-classifiers with enhanced
interpretability and improved accuracy, especially for high dimensional low
sample size data. One big advantage of the supnorm penalty is its easy
implementation via standard linear programming. Several simulated examples and
one real gene data analysis demonstrate the outstanding performance of the
adaptive supnorm penalty in various data settings.


  We have conducted a deep multi-wavelength analysis (0.15-160 mum) to study
the outer region of the nearby galaxy M94. We show that the non-optical data
support the idea that the outskirts of this galaxy is not formed by a closed
stellar ring (as traditionally claimed in the literature) but by a spiral arm
structure. In this sense, M94 is a good example of a Type III (anti-truncated)
disk galaxy having a very bright outer disk. The outer disk of this galaxy
contains ~23% of the total stellar mass budget of the galaxy and contributes
~10% of the new stars created showing that this region of the galaxy is active.
In fact, the specific star formation rate of the outer disk (~0.012 Gyr^{-1})
is a factor of ~2 larger (i.e. the star formation is more efficient per unit
stellar mass) than in the inner disk. We have explored different scenarios to
explain the enhanced star formation in the outer disk. We find that the inner
disk (if considered as an oval distortion) can dynamically create a spiral arm
structure in the outer disk which triggers the observed relatively high star
formation rate as well as an inner ring similar to what is found in this
galaxy.


  In this paper, we study the decentralized parallel multiple access channel
(MAC) when transmitters selfishly maximize their individual spectral efficiency
by selecting a single channel to transmit. More specifically, we investigate
the set of Nash equilibria (NE) of decentralized networks comprising several
transmitters communicating with a single receiver that implements single user
decoding. This scenario is modeled as a one-shot game where the players (the
transmitters) have discrete action sets (the channels). We show that the
corresponding game has always at least one NE in pure strategies, but,
depending on certain parameters, the game might possess several NE. We provide
an upper bound for the maximum number of NE as a function of the number of
transmitters and available channels. The main contribution of this paper is a
mathematical proof of the existence of a Braess-type paradox. In particular, it
is shown that under the assumption of a fully loaded network, when transmitters
are allowed to use all the available channels, the corresponding sum spectral
efficiency achieved at the NE is lower or equal than the sum spectral
efficiency achieved when transmitters can use only one channel. A formal proof
of this observation is provided in the case of small networks. For general
scenarios, we provide numerical examples that show that the same effect holds
as long as the network is kept fully loaded. We conclude the paper by
considering the case of successive interference cancellation at the receiver.
In this context, we show that the power allocation vectors at the NE are
capacity maximizers. Finally, simulations are presented to verify our
theoretical results.


  Size-selected anionic silicon clusters, Sin- (n=14-20), have been
investigated by photoelectron spectroscopy and density functional theory (DFT)
calculations. Low-energy structures of the clusters are globally searched for
by using a genetic algorithm based on DFT calculations. The electronic density
of states and VDEs have been simulated by using ten DFT functionals and
compared to the experimental results. We systematically evaluated the DFT
functionals for the calculation of the energetics of silicon clusters. CCSD(T)
single-point energies based on MP2 optimized geometries for selected isomers of
Sin- are also used as benchmark for the energy sequence. The HSE06 functional
with aug-cc-pVDZ basis set is found to show the best performance. Our global
minimum search corroborates that most of the lowest-energy structures of Sin-
(n=14-20) clusters can be derived from assembling tricapped trigonal prisms
(TTP) in various ways. For most sizes previous structures are confirmed,
whereas for Si20- a new structure has been found.


  Depth cameras are emerging as a cornerstone modality with diverse
applications that directly or indirectly rely on measured depth, including
personal devices, robotics, and self-driving vehicles. Although time-of-flight
(ToF) methods have fueled these applications, the precision and robustness of
ToF methods is limited by relying on photon time-tagging or modulation after
photo-conversion. Successful optical modulation approaches have been restricted
fiber-coupled modulation with large coupling losses or interferometric
modulation with sub-cm range, and the precision gap between interferometric
methods and ToF methods is more than three orders of magnitudes. In this work,
we close this gap and propose a computational imaging method for all-optical
free-space correlation before photo-conversion that achieves micron-scale depth
resolution with robustness to surface reflectance and ambient light with
conventional silicon intensity sensors. To this end, we solve two technical
challenges: modulating at GHz rates and computational phase unwrapping. We
propose an imaging approach with resonant polarization modulators and devise a
novel optical dual-pass frequency-doubling which achieves high modulation
contrast at more than 10GHz. At the same time, centimeter-wave modulation
together with a small modulation bandwidth render existing phase unwrapping
methods ineffective. We tackle this problem with a neural phase unwrapping
method that exploits that adjacent wraps are often highly correlated. We
validate the proposed method in simulation and experimentally, where it
achieves micron-scale depth precision. We demonstrate precise depth sensing
independently of surface texture and ambient light and compare against existing
analog demodulation methods, which we outperform across all tested scenarios.


  In this study, we analyze the various arrangements that droplets can form
within dispersed buoyant emulsions, which we refer to as the study of
microstructure. To this end, we have developed a novel algorithm that
effectively prevents numerical coalescence between drops while maintaining a
reasonable computational cost. This algorithm is integrated into the Volume of
Fluid (VoF) method and implemented using the open-source code
http://basilisk.fr. Subsequently, we perform Direct Numerical Simulations (DNS)
of statistically steady state mono-disperse buoyant emulsion over a broad range
of dimensionless parameters, including the particle volume fraction ($\phi$),
the Galileo number ($Ga$) and the viscosity ratio ($\lambda$). We make use of
nearest particle statistics to quantify the microstructure properties. As
predicted by Zhang et al. (2023), it is demonstrated that the second moment of
the nearest particle pair distribution can effectively quantify microstructural
features such as particle clusters and layers. Specifically, the findings are:
(1) In moderately inertial flows ($Ga = 10$), droplets form isotropic clusters.
In high inertial regimes ($Ga = 100$), non-isotropic clusters, such as
horizontal layers, are more likely to form. (3) The viscosity ratio plays a
significant role in determining the microstructure, with droplets that are less
viscous or equally viscous as the surrounding fluid tending to form layers
preferentially. Overall, our study provides a quantitative measure of the
microstructure in terms of $Ga$, $\phi$ and $\lambda$.


  The first nontrivial eigenfunction of the Neumann eigenvalue problem for the
$p$-Laplacian, suitable normalized, converges as $p$ goes to $\infty$ to a
viscosity solution of an eigenvalue problem for the $\infty$-Laplacian. We show
among other things that the limit of the eigenvalue, at least for convex sets,
is in fact the first nonzero eigenvalue of the limiting problem. We then derive
a number of consequences, which are nonlinear analogues of well-known
inequalities for the linear (2-)Laplacian.


  Unmanned aerial vehicle (UAV)-enabled positioning that uses UAVs as aerial
anchor nodes is a promising solution for providing positioning services in
harsh environments. In previous research, the state sensing and control of UAVs
were either ignored or simply set to be performed continuously, resulting in
system instability or waste of wireless resources. Therefore, in this article,
we propose a quality-of-service (QoS)-oriented UAV-enabled positioning system
based on the concept of sensing-communication-control (SCC) co-design. We first
establish the mathematical models of UAV state sensing and control. Then, the
influence of sensing scheduling and transmission failure on UAV stability, as
well as the performance of positioning services in the presence of UAV control
error, are analyzed. Based on these models and analysis results, we further
study the problem of minimizing the amount of data transmitted by optimizing
the sensing scheduling and blocklength allocation under the condition of
satisfying each user's demand. Finally, an efficient scheme is developed to
solve this mixed-integer nonlinear problem. Numerical results show that the
proposed system could work efficiently and meet users' requirements. In
addition, compared with two benchmark schemes, our scheme reduces the failure
rate or resource consumption of positioning services by more than 76.2% or
82.7%.


  A quasiparticle model of the quark-gluon plasma is compared with lattice QCD
data for purely imaginary chemical potential. Net quark number density,
susceptibility as well as the deconfinement border line in the phase diagram of
strongly interacting matter are investigated. In addition, the impact of
baryo-chemical potential dependent quasiparticle masses is discussed. This
accomplishes a direct test of the model for non-zero baryon density. The found
results are compared with lattice QCD data for real chemical potential by means
of analytic continuation and with a different (independent) set of lattice QCD
data at zero chemical potential.


  In this work we consider quantum cascade networks in which quantum systems
are connected through unidirectional channels that can mutually interact giving
rise to interference effects. In particular we show how to compute master
equations for cascade systems in an arbitrary interferometric configuration by
means of a collisional model. We apply our general theory to two specific
examples: the first consists in two systems arranged in a Mach-Zender-like
configuration; the second is a three system network where it is possible to
tune the effective chiral interactions between the nodes exploiting
interference effects.


  Connection management is an important problem for any wireless network to
ensure smooth and well-balanced operation throughout. Traditional methods for
connection management (specifically user-cell association) consider sub-optimal
and greedy solutions such as connection of each user to a cell with maximum
receive power. However, network performance can be improved by leveraging
machine learning (ML) and artificial intelligence (AI) based solutions. The
next generation software defined 5G networks defined by the Open Radio Access
Network (O-RAN) alliance facilitates the inclusion of ML/AI based solutions for
various network problems. In this paper, we consider intelligent connection
management based on the O-RAN network architecture to optimize user association
and load balancing in the network. We formulate connection management as a
combinatorial graph optimization problem. We propose a deep reinforcement
learning (DRL) solution that uses the underlying graph to learn the weights of
the graph neural networks (GNN) for optimal user-cell association. We consider
three candidate objective functions: sum user throughput, cell coverage, and
load balancing. Our results show up to 10% gain in throughput, 45-140% gain
cell coverage, 20-45% gain in load balancing depending on network deployment
configurations compared to baseline greedy techniques.


  We measure the conductance of amine-terminated molecules by breaking Au point
contacts in a molecular solution at room temperature. We find that the
variability of the observed conductance for the diamine molecule-Au junctions
is much less than the variability for diisonitrile and dithiol-Au junctions.
This narrow distribution enables unambiguous conductance measurements of single
molecules. For an alkane diamine series with 2-8 carbon atoms in the
hydrocarbon chain, our results show a systematic trend in the conductance from
which we extract a tunneling decay constant of 0.91 +/- 0.03 per methylene
group. We hypothesize that the diamine link binds preferentially to
undercoordinated Au atoms in the junction. This is supported by density
functional theory-based calculations that show the amine binding to a gold
adatom with sufficient angular flexibility for easy junction formation but
well-defined electronic coupling of the N lone pair to the Au. Therefore, the
amine linkage leads to well-defined conductance measurements of a single
molecule junction in a statistical study.


  Surface gravity is one of a star's basic properties, but it is difficult to
measure accurately, with typical uncertainties of 25-50 per cent if measured
spectroscopically and 90-150 per cent photometrically. Asteroseismology
measures gravity with an uncertainty of about two per cent but is restricted to
relatively small samples of bright stars, most of which are giants. The
availability of high-precision measurements of brightness variations for
>150,000 stars provides an opportunity to investigate whether the variations
can be used to determine surface gravities. The Fourier power of granulation on
a star's surface correlates physically with surface gravity; if brightness
variations on timescales of hours arise from granulation, then such variations
should correlate with surface gravity. Here we report an analysis of archival
data that reveals an observational correlation between surface gravity and the
root-mean-square brightness variations on timescales of less than eight hours
for stars with temperatures of 4500-6750K, log of surface gravities of 2.5-4.5
(cgs units), and having overall brightness variations <3 parts per thousand. A
straightforward observation of optical brightness variations therefore allows a
determination of the surface gravity with a precision of <25 percent for
inactive Sun-like stars at main-sequence to giant stages of evolution.


  We construct p-brane solutions with non-trivial world volume metrics and show
that applied to supergravity theories, they will lead to threshold BPS bound
states of intersecting solutions. However applied to certain specific values of
the couplings in cosmological (a,b)-models non-trivial solutions can be
constructed.


  Recently, various encoder-only and encoder-decoder pre-trained models like
BERT and T5 have been applied to automatic essay scoring (AES) as small
language models. However, existing studies have primarily treated this task
akin to a classification problem, focusing solely on outputting scores in the
target text without offering interpretations for the generated scores.
Departing from the approaches, we introduce Reasoning Distillation-Based
Evaluation (RDBE), which integrates interpretability to elucidate the rationale
behind model scores while enhancing performance through initial reasoning. This
interpretive capability is acquired during training by leveraging generated
reasoning from a large language model (LLM) to distill a small language model
(SLM). Our experimental results demonstrate the efficacy of RDBE across all
scoring rubrics considered in the dataset. RDBE outperforms both zero-shot LLM
generation and generation from a baseline fine-tuned model, establishing itself
as state-of-the-art in the corresponding dataset. This highlights its practical
interpretative output and enhanced performance.


  We introduce a notion of morphism of CohFT algebras, based on the analogy
with A-infinity morphisms. We discuss a "quantization" of the classical Kirwan
morphism to a morphism of CohFT algebras from the equivariant quantum
cohomology of a G-variety to the quantum cohomology of its git or symplectic
quotient, and an example relating to the orbifold quantum cohomology of a
compact toric orbifold. Finally we identify the space of Cartier divisors on
the moduli space of scaled marked curves; these appear in the splitting axiom.


  We prove that the Ricci scalar curvature and the Berwald scalar curvature of
a two-dimensional Finsler space, considered over a vector field on the
3-dimensional flat space, are naturally related to 2-dimensional
electro-capillary phenomena effects observed for a compressed monolayer. The
Cartan tensor and the nonlinear Barthel connection of the Finsler model are
determined, and the geometric objects which depend on compression speed and on
the characteristics of the electrically charged double layer are used in order
to reveal several classes of structure formation within the phase transition of
the first order.


  In this paper we present a cut-free sequent calculus, called SeqS, for some
standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus
uses labels and transition formulas and can be used to prove decidability and
space complexity bounds for the respective logics. We also present CondLean, a
theorem prover for these logics implementing SeqS calculi written in SICStus
Prolog.


  It has recently been shown that in single field slow-roll inflation the total
volume cannot grow by a factor larger than e^(S_dS/2) without becoming
infinite. The bound is saturated exactly at the phase transition to eternal
inflation where the probability to produce infinite volume becomes non zero. We
show that the bound holds sharply also in any space-time dimensions, when
arbitrary higher-dimensional operators are included and in the multi-field
inflationary case. The relation with the entropy of de Sitter and the
universality of the bound strengthen the case for a deeper holographic
interpretation. As a spin-off we provide the formalism to compute the
probability distribution of the volume after inflation for generic multi-field
models, which might help to address questions about the population of vacua of
the landscape during slow-roll inflation.


  Despite the growing body of work on explainable machine learning in time
series classification (TSC), it remains unclear how to evaluate different
explainability methods. Resorting to qualitative assessment and user studies to
evaluate explainers for TSC is difficult since humans have difficulties
understanding the underlying information contained in time series data.
Therefore, a systematic review and quantitative comparison of explanation
methods to confirm their correctness becomes crucial. While steps to
standardized evaluations were taken for tabular, image, and textual data,
benchmarking explainability methods on time series is challenging due to a)
traditional metrics not being directly applicable, b) implementation and
adaption of traditional metrics for time series in the literature vary, and c)
varying baseline implementations. This paper proposes XTSC-Bench, a
benchmarking tool providing standardized datasets, models, and metrics for
evaluating explanation methods on TSC. We analyze 3 perturbation-, 6 gradient-
and 2 example-based explanation methods to TSC showing that improvements in the
explainers' robustness and reliability are necessary, especially for
multivariate data.


  Fundamental sensitivity of an optical interferometric gravitational wave
detector increases with increase of the optical power which, in turn, limited
because of the opto-mechanical parametric instabilities of the interferometer.
We propose to optimize geometrical shape of the mirrors of the detector to
reduce the diffraction-limited finesse of unessential optical modes of the
interferometer resulting in increase of the threshold of the opto-mechanical
instabilities and subsequent increase of the measurement sensitivity. Utilizing
parameters of the LIGO interferometer we found that the proposed technique
allows constructing a Fabry-Perot interferometer with round trip diffraction
loss of the fundamental mode not exceeding $5$~ppm, whereas the loss of the
first dipole as well as the other high order modes exceed $1,000$~ppm and
$8,000$~ppm, respectively. The optimization comes at the price of tighter
tolerances on the mirror tilt stability, but does not result in a significant
modification of the optical beam profile and does not require changes in the
the gravity detector read-out system. The cavity with proposed mirrors is also
stable with respect to the slight modification of the mirror shape.


  We provide a canonical form of mixed states in bipartite quantum systems in
terms of a convex combination of a separable state and a, so-called, edge
state. We construct entanglement witnesses for all edge states. We present a
canonical form of nondecomposable entanglement witnesses and the corresponding
positive maps. We provide constructive methods for their optimization in a
finite number of steps. We present a characterization of separable states using
a special class of entanglement witnesses. Finally, we present a nontrivial
necessary condition for entanglement witnesses and positive maps to be
extremal.


  Despite the modeling power for problems under uncertainty, robust
optimization (RO) and adaptive robust optimization (ARO) can exhibit too
conservative solutions in terms of objective value degradation compared to the
nominal case. One of the main reasons behind this conservatism is that, in many
practical applications, uncertain constraints are directly designed as
constraint-wise without taking into account couplings over multiple
constraints. In this paper, we define a coupled uncertainty set as the
intersection between a constraint-wise uncertainty set and a coupling set. We
study the benefit of coupling in alleviating conservatism in RO and ARO. We
provide theoretical tight and computable upper and lower bounds on the
objective value improvement of RO and ARO problems under coupled uncertainty
over constraint-wise uncertainty. In addition, we relate the power of
adaptability over static solutions with the coupling of uncertainty set.
Computational results demonstrate the benefit of coupling in applications.


  We present a kinematic study of six dwarf spheroidal galaxies (dSph)
satellites of the Milky Way (MW), namely Carina, Draco, Fornax, Sculptor,
Sextans, and Ursa Minor. We combine proper motions (PMs) from the $Gaia$ Data
Release 3 (DR3) and line-of-sight velocities ($v_{\mathrm{los}}$) from the
literature to derive their 3D internal kinematics and to study the presence of
internal velocity gradients. We find velocity gradients along the line-of-sight
for Carina, Draco, Fornax, and Ursa Minor, at $\geq 1\sigma$ level of
significance . The value of such gradients appears to be related to the orbital
history of the dwarfs, indicating that the interaction with the MW is causing
them. Dwarfs that are close to the MW and moving towards their orbits
pericentres show, on average, larger velocity gradients. On the other hand,
dwarfs that have recently left their orbits pericentres show no significant
gradients. Lastly, dwarfs located at large Galactocentric distances show
gradients with an intermediate intensity. Our results would indicate that the
torque caused by the strong tidal forces exerted by the MW induces a strong
velocity gradient when the dwarfs approach their orbits pericentres. During the
pericentre passage, the rapid change in the forces direction would disrupt such
gradient, which may steadily recover as the galaxies recede. We assess our
findings by analysing dwarfs satellites from the TNG50 simulation. We find a
significant increase in the intensity of the detected gradients as the
satellites approach their pericentre, followed by a sharp drop as they abandon
it, supporting our results for the dSphs of the MW.


  Recently, Memory-based Neural Recommenders (MNR) have demonstrated superior
predictive accuracy in the task of sequential recommendations, particularly for
modeling long-term item dependencies. However, typical MNR requires complex
memory access operations, i.e., both writing and reading via a controller
(e.g., RNN) at every time step. Those frequent operations will dramatically
increase the network training time, resulting in the difficulty in being
deployed on industrial-scale recommender systems. In this paper, we present a
novel general Chunk framework to accelerate MNR significantly. Specifically,
our framework divides proximal information units into chunks, and performs
memory access at certain time steps, whereby the number of memory operations
can be greatly reduced. We investigate two ways to implement effective
chunking, i.e., PEriodic Chunk (PEC) and Time-Sensitive Chunk (TSC), to
preserve and recover important recurrent signals in the sequence. Since
chunk-accelerated MNR models take into account more proximal information units
than that from a single timestep, it can remove the influence of noise in the
item sequence to a large extent, and thus improve the stability of MNR. In this
way, the proposed chunk mechanism can lead to not only faster training and
prediction, but even slightly better results. The experimental results on three
real-world datasets (weishi, ml-10M and ml-latest) show that our chunk
framework notably reduces the running time (e.g., with up to 7x for training &
10x for inference on ml-latest) of MNR, and meantime achieves competitive
performance.


  Multiple-scale mobility is ubiquitous in nature and has become instrumental
for understanding and modeling animal foraging behavior. However, the impact of
individual movements on the long-term stability of populations remains largely
unexplored. We analyze deterministic and stochastic Lotka Volterra systems,
where mobile predators consume scarce resources (prey) confined in patches. In
fragile systems (that is, those unfavorable to species coexistence), the
predator species has a maximized abundance and is resilient to degraded prey
conditions when individual mobility is multiple scaled. Within the L\'evy
flight model, highly superdiffusive foragers rarely encounter prey patches and
go extinct, whereas normally diffusing foragers tend to proliferate within
patches, causing extinctions by overexploitation. L\'evy flights of
intermediate index allow a sustainable balance between patch exploitation and
regeneration over wide ranges of demographic rates. Our analytical and
simulated results can explain field observations and suggest that scale-free
random movements are an important mechanism by which entire populations adapt
to scarcity in fragmented ecosystems.


  Bilingual word embeddings, which representlexicons of different languages in
a shared em-bedding space, are essential for supporting se-mantic and knowledge
transfers in a variety ofcross-lingual NLP tasks. Existing approachesto
training bilingual word embeddings requireoften require pre-defined seed
lexicons that areexpensive to obtain, or parallel sentences thatcomprise coarse
and noisy alignment. In con-trast, we propose BilLex that leverages pub-licly
available lexical definitions for bilingualword embedding learning. Without the
needof predefined seed lexicons, BilLex comprisesa novel word pairing strategy
to automati-cally identify and propagate the precise fine-grained word
alignment from lexical defini-tions. We evaluate BilLex in word-level
andsentence-level translation tasks, which seek tofind the cross-lingual
counterparts of wordsand sentences respectively.BilLex signifi-cantly
outperforms previous embedding meth-ods on both tasks.


  On a separable C*-algebra A every (completely) bounded map, which preserves
closed two sided ideals, can be approximated uniformly by elementary operators
if and only if A is a finite direct sum of C*-algebras of continuous sections
vanishing at infinity of locally trivial C*-bundles of finite type.


  We numericaly demonstrate that, in double well models, the autocorrelation
time of open path integral Monte Carlo simulations can be much smaller compared
to standard ones using ring polymers. We also provide an intuitive explanation
based on the role of instantons as transition states of the path integral
pseudodynamics. Therefore we propose that, in all cases when the ground state
approximation to the finite temperature partition function holds, open path
integral simulations can be used to accelerate the sampling in realistic
simulations aimed to explore nuclear quantum effects.


  We suggest the inclusive detection at the LHC of a light charged hadron and
of a jet widely separated in rapidity as a new probe channel for the study of
the BFKL resummation. Predictions for cross section and azimuthal correlations,
shaped on the CMS and CASTOR acceptances, are presented.


  In this article, we introduce an algebraic setup of non-strict multiple zeta
values (NMZVs, for short) and prove some relations of NMZVs, which are
analogous to Hoffman's relations of multiple zeta values, by using this
algebraic setup of NMZVs.


  Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good
parameters as well as efficient encoding and decoding procedures. However, RS
codes suffer from having a fixed length. In many applications where the length
is static, the appropriate length can be obtained by an RS code by shortening
or puncturing. Generalized Reed-Solomon (GRS) codes are a generalization of RS
codes, whose subfield-subcodes are extensively studied. In this paper we show
that a particular class of GRS codes produces many subfield-subcodes with large
dimension. An algorithm for searching through the codes is presented as well as
a list of new codes obtained from this method.


  A common hope of many physics educators and researchers is that students
leave the course with a stronger sense that physics is relevant to them than
when they entered the course. Multiple survey measures have attempted to
measure shifts in students' beliefs on the relevance of physics but frequently
the results show a negative shift in students' beliefs and are often reported
as a failure of students to "see the relevance." We challenge this
interpretation by first operationalizing relevance as a construct by using
existing theories on beliefs and attitudes. We utilize ecological systems
theory to identify rich sites of relevance in students lives and present
evidence to demonstrate the rich ways students are able to make relevant
connections to physics. We then reflect on the implications of this expanded
view on the limitations of past measures of relevance. We articulate how
incorporating students' disciplinary ideas and expertise into the classroom can
challenge previous deficit-framed narratives of students' abilities to find the
relevance of physics.


  Acoustic wave heating is believed to contribute significantly to the missing
energy input required to maintain the solar chromosphere in its observed state.
We studied the propagation of waves above the acoustic cutoff in the upper
photosphere into the chromosphere with ultraviolet and optical spectral
observations interpreted through comparison with three dimensional radiative
magnetohydrodynamic (rMHD) \emph{Bifrost} models to constrain the heating
contribution from acoustic waves in the solar atmosphere. Sit-and-stare
observations taken with the Interface Region Imaging Spectrograph (IRIS) and
data from the Interferometric BIdimensional Spectrograph (IBIS) were used to
provide the observational basis of this work. We compared the observations with
synthetic observables derived from the Bifrost solar atmospheric model. Our
analysis of the \emph{Bifrost} simulations show that internetwork and enhanced
network regions exhibit significantly different wave propagation properties,
which are important for the accurate wave flux estimates. The inferred wave
energy fluxes based on our observations are not sufficient to maintain the
solar chromosphere. We point out that the systematics of the modeling
approaches in the literature lead to differences which could determine the
conclusions of this type of studies, based on the same observations.


  Distances and extinction values are usually degenerate. To refine the
distance to the general Galactic Center region, a carefully determined
extinction law (taking into account the prevailing systematic errors) is
urgently needed. We collected data for 55 classical Cepheids projected toward
the Galactic Center region to derive the near- to mid-infrared extinction law
using three different approaches. The relative extinction values obtained are
AJ/AKs = 3.005, AH/AKs = 1.717, A[3.6]/AKs = 0.478, A[4.5]/AKs = 0.341,
A[5.8]/AKs = 0.234, A[8.0]/AKs = 0.321, AW1/AKs = 0.506, and AW2/AKs = 0.340.
We also calculated the corresponding systematic errors. Compared with previous
work, we report an extremely low and steep mid-infrared extinction law. Using a
seven-passband 'optimal distance' method, we improve the mean distance
precision to our sample of 55 Cepheids to 4%. Based on four confirmed Galactic
Center Cepheids, a solar Galactocentric distance of R_0 = 8.10\pm0.19\pm0.22
kpc is determined, featuring an uncertainty that is close to the limiting
distance accuracy (2.8%) for Galactic Center Cepheids.


  Interactive visualization via direct manipulation has inherent design
trade-offs in flexibility, discoverability, and ease-of-use. Scripting
languages can support a vast range of user queries and tasks, but may be more
cumbersome for free-form exploration. Embedding interactive visualization in a
scripting environment, such as a computational notebook, provides an
opportunity for leveraging the strengths of both direct manipulation and
scripting. We conduct a design study investigating this opportunity in the
context of calling context trees as used for performance analysis of parallel
software. Our collaborators make new performance analysis functionality
available to users via Jupyter notebook examples, making the project setting
conducive to such an investigation. Through a series of semi-structured
interviews and regular meetings with project stakeholders, we produce a formal
task analysis grounded in the expectation that tasks may be supported by
scripting, interactive visualization, or both paradigms. We then design an
interactive bivariate calling context tree visualization for embedding in
Jupyter notebooks with features to pass data and state between the scripting
and visualization contexts. We evaluated our embedded design with seven high
performance computing experts. The experts were able to complete tasks and
provided further feedback on the visualization and the notebook-embedded
interactive visualization paradigm. We reflect upon the project and discuss
factors in both the process and the design of the embedded visualization.


  The Submillimetre Common-User Bolometer Array (SCUBA) is a new continuum
camera operating on the James Clerk Maxwell Telescope (JCMT) on Mauna Kea,
Hawaii. It consists of two arrays of bolometric detectors; a 91 pixel 350/450
micron array and a 37 pixel 750/850 micron array. Both arrays can be used
simultaneously and have a field-of-view of approximately 2.4 arcminutes in
diameter on the sky.
  Ideally, performance should be limited solely by the photon noise from the
sky background at all wavelengths of operation. However, observations at
submillimetre wavelengths are hampered by ``sky-noise'' which is caused by
spatial and temporal fluctuations in the emissivity of the atmosphere above the
telescope. These variations occur in atmospheric cells that are larger than the
array diameter, and so it is expected that the resultant noise will be
correlated across the array and, possibly, at different wavelengths.
  In this paper we describe our initial investigations into the presence of
sky-noise for all the SCUBA observing modes, and explain our current technique
for removing it from the data.


  We present rigorous results for the SU($n$) Fermi-Hubbard models with
finite-range hopping in $d$ ($\ge 2$) dimensions. The models are defined on a
class of decorated lattices. We first study the models with flat bands at the
bottom of the single-particle spectrum and prove that the ground states exhibit
SU($n$) ferromagnetism when the number of particles is equal to the number of
unit cells. We then perturb the models by adding particular hopping terms and
make the bottom bands dispersive. Under the same filling condition, it is
proved that the ground states remain SU($n$) ferromagnetic when the bottom
bands are sufficiently flat and the Coulomb repulsion is sufficiently large.


  We investigate the thermodynamic uncertainty relation for the $(1+1)$
dimensional Kardar-Parisi-Zhang equation on a finite spatial interval. In
particular, we extend the results for small coupling strengths obtained
previously to large values of the coupling parameter. It will be shown that,
due to the scaling behavior of the KPZ equation, the TUR product displays two
distinct regimes which are separated by a critical value of an effective
coupling parameter. The asymptotic behavior below and above the critical
threshold is explored analytically. For small coupling, we determine this
product perturbatively including the fourth order; for strong coupling we
employ a dynamical renormalization group approach. Whereas the TUR product
approaches a value of $5$ in the weak coupling limit, it asymptotically
displays a linear increase with the coupling parameter for strong couplings.
The analytical results are then compared to direct numerical simulations of the
KPZ equation showing convincing agreement.


  In a recent paper by Gomes and Adhikari (J.Phys B30 5987(1997)) a matrix
formulation of the Bohr-Sommerfield quantization rule has been applied to the
study of bound states in one dimension quantum wells. Here we study these
potentials in the frame work of supersymmetric WKB (SWKB) quantization
approximation and find that SWKB quantization rule is superior to the modified
Bohr-Sommerfield or WKB rules as it exactly reproduces the eigenenergies.


  We continue to study $\alpha$-times integrated semigroups. Essentially, we
characterize the different spectrums of $\alpha$-times integrated semigroups by
the spectrums of their generators. Particulary quasi-Fredholm, Kato,
essentially Kato, Saphar and essentially Saphar spectrums.


  We explore the feasibility of Multiple-Input-Multiple-Output (MIMO)
communication through vibrations over human skin. Using off-the-shelf motors
and piezo transducers as vibration transmitters and receivers, respectively, we
build a 2x2 MIMO testbed to collect and analyze vibration signals from real
subjects. Our analysis reveals that there exist multiple independent vibration
channels between a pair of transmitter and receiver, confirming the feasibility
of MIMO. Unfortunately, the slow ramping of mechanical motors and rapidly
changing skin channels make it impractical for conventional channel sounding
based channel state information (CSI) acquisition, which is critical for
achieving MIMO capacity gains. To solve this problem, we propose Skin-MIMO, a
deep learning based CSI acquisition technique to accurately predict CSI
entirely based on inertial sensor (accelerometer and gyroscope) measurements at
the transmitter, thus obviating the need for channel sounding. Based on
experimental vibration data, we show that Skin-MIMO can improve MIMO capacity
by a factor of 2.3 compared to Single-Input-Single-Output (SISO) or open-loop
MIMO, which do not have access to CSI. A surprising finding is that gyroscope,
which measures the angular velocity, is found to be superior in predicting skin
vibrations than accelerometer, which measures linear acceleration and used
widely in previous research for vibration communications over solid objects.


  For a cofibrantly generated Quillen model category, we show that the
cofibrant replacement functor constructed using the small object argument
admits a cotriple structure. If all acyclic cofibrations are monomorphisms, the
fibrant replacement functor constructed using the small object argument admits
a triple structure. For a triple in the base category, the associated
cosimplicial resolution is not necessarily homotopy invariant. However using a
mix of the triple with the cofibrant replacement cotriple we construct a
'homotopically correct' version of the cosimplicial resolution of the triple.
This allows us to construct a Bousfield-Kan completion functor with respect to
a triple, and for pointed cofibrantly-generated model categories a
Bousfield-Kan spectral sequence that computes the relative homotopy groups of
the Bousfield-Kan completion of an object.
  This is the text of my PhD thesis, worked under the supervision of Prof.
Haynes Miller, submitted on Feb. 1999 at MIT.


  We introduce a new parameterization of four-fermion matrix elements which
does not involve quark masses and thus allows a reduction of systematic
uncertainties in physical amplitudes. As a result the apparent quadratic
dependence of e'/e on m_s is removed. To simplify the matching between lattice
and continuum renormalization schemes, we express our results in terms of
Renormalization Group Invariant B-parameters which are renormalization-scheme
and scale independent. As an application of our proposal, matrix elements of
DeltaI=3/2 and SUSY DeltaF=2 (F=S,C,B) four-fermion operators have been
computed.


  Approximate solutions of the chemical master equation and the chemical
Fokker-Planck equation are an important tool in the analysis of biomolecular
reaction networks. Previous studies have highlighted a number of problems with
the moment-closure approach used to obtain such approximations, calling it an
ad-hoc method. In this article, we give a new variational derivation of
moment-closure equations which provides us with an intuitive understanding of
their properties and failure modes and allows us to correct some of these
problems. We use mixtures of product-Poisson distributions to obtain a flexible
parametric family which solves the commonly observed problem of divergences at
low system sizes. We also extend the recently introduced entropic matching
approach to arbitrary ansatz distributions and Markov processes, demonstrating
that it is a special case of variational moment closure. This provides us with
a particularly principled approximation method. Finally, we extend the above
approaches to cover the approximation of multi-time joint distributions,
resulting in a viable alternative to process-level approximations which are
often intractable.


  The observed chemical diversity of Milky Way stars places important
constraints on Galactic chemical evolution and the mixing processes that
operate within the interstellar medium. Recent works have found that the
chemical diversity of disk stars is low. For example, the APOGEE "chemical
doppelganger rate," or the rate at which random pairs of field stars appear as
chemically similar as stars born together, is high, and the chemical
distributions of APOGEE stars in some Galactic populations are well-described
by two-dimensional models. However, limited attention has been paid to the
heavy elements (Z > 30) in this context. In this work, we probe the potential
for neutron-capture elements to enhance the chemical diversity of stars by
determining their effect on the chemical doppelganger rate. We measure the
doppelganger rate in GALAH DR3, with abundances rederived using The Cannon, and
find that considering the neutron-capture elements decreases the doppelganger
rate from 2.2% to 0.4%, nearly a factor of 6, for stars with -0.1 < [Fe/H] <
0.1. While chemical similarity correlates with similarity in age and dynamics,
including neutron-capture elements does not appear to select stars that are
more similar in these characteristics. Our results highlight that the
neutron-capture elements contain information that is distinct from that of the
lighter elements and thus add at least one dimension to Milky Way abundance
space. This work illustrates the importance of considering the neutron-capture
elements when chemically characterizing stars and motivates ongoing work to
improve their atomic data and measurements in spectroscopic surveys.


  We analyze the symmetry of all possible magnetic structures of bilayered
manganites La_{2-2x}Sr_{1+2x}Mn_2O_7 with doping 0.3 <= x < 0.5 and formulate a
corresponding Landau theory of the phase transitions involved. It is shown that
canting of spins is not allowed at x=0.3 though is at x=0.4. The observed
magnetic reflections from the sample with x=0.3 may be described as arising
from two spatially distributed phases with close transition temperatures but
different easy axes and ranges of stability. Experimental results are revisited
on the basis of the theoretical findings.


  We have developed a new numerical code to simulate the joint evolution of a
massive black hole (MBH) and a surrounding stellar cluster at the center of a
galaxy. The physics treated in the simulations include: 2-body relaxation,
stellar collisions (using a large set of "SPH" hydrodynamical simulations) and
tidal disruption of stars by the MBH. In particular, we investigate the rates
of star disruptive events that provide the MBH with gas to accrete.


  We present an analytic solution to the problem of the Rashba spin-orbit
coupling in semiconductor quantum dots. We calculate the exact energy spectrum,
wave-functions, and spin--flip relaxation times. We discuss various effects
inaccessible via perturbation theory. In particular, we find that the effective
gyromagnetic ratio is strongly suppressed by the spin-orbit coupling. The
spin-flip relaxation rate has a maximum as a function of the spin-orbit
coupling and is therefore suppressed in both the weak- and strong coupling
limits.


  In the context of MSSM, a novel improving procedure based on the
renormalization group equation is applied to the effective potential in the
Higgs sector. We focus on the one-loop radiative corrections computed in Landau
gauge by using the mass independent renormalization scheme $\bar{DR}$. Thanks
to the decoupling theorem, the well-known multimass scale problem is
circumvented by switching to a new effective field theory every time a new
particle threshold is encountered. We find that, for any field configuration,
there is a convenient renormalization scale $\tilde{Q}^*$ at which the loop
expansion respects the perturbation series hierarchy and the theory retains the
vital property of stability.


  Over the past few years, neural networks have re-emerged as powerful
machine-learning models, yielding state-of-the-art results in fields such as
image recognition and speech processing. More recently, neural network models
started to be applied also to textual natural language signals, again with very
promising results. This tutorial surveys neural network models from the
perspective of natural language processing research, in an attempt to bring
natural-language researchers up to speed with the neural techniques. The
tutorial covers input encoding for natural language tasks, feed-forward
networks, convolutional networks, recurrent networks and recursive networks, as
well as the computation graph abstraction for automatic gradient computation.


  Steganography involves hiding a secret message or image inside another cover
image. Changes are made in the cover image without affecting visual quality of
the image. In contrast to cryptography, Steganography provides complete secrecy
of the communication. Security of very sensitive data can be enhanced by
combining cryptography and steganography. A new technique that uses the concept
of Steganography to obtain the position values from an image is suggested. This
paper proposes a new method where no change is made to the cover image, only
the pixel position LSB (Least Significant Bit) values that match with the
secret message bit values are noted in a separate position file. At the sending
end the position file along with the cover image is sent. At the receiving end
the position file is opened only with a secret key. The bit positions are taken
from the position file and the LSB values from the positions are combined to
get ASCII values and then form characters of the secret message


  Assume $k$ is a positive integer, $\lambda=\{k_1, k_2, \ldots, k_q\}$ is a
partition of $k$ and $G$ is a graph. A $\lambda$-list assignment of $G$ is a
$k$-list assignment $L$ of $G$ such that the colour set $\cup_{v\in V(G)}L(v)$
can be partitioned into $q$ subsets $C_1 \cup C_2 \ldots \cup C_q$ and for each
vertex $v$ of $G$, $|L(v) \cap C_i| \ge k_i$. We say $G$ is $\lambda$-choosable
if for each $\lambda$-list assignment $L$ of $G$, $G$ is $L$-colourable. It
follows from the definition that if $\lambda =\{k\}$, then $\lambda$-choosable
is the same as $k$-choosable, if $\lambda =\{1,1,\ldots, 1\}$, then
$\lambda$-choosable is equivalent to $k$-colourable. For the other partitions
of $k$ sandwiched between $\{k\}$ and $\{1,1,\ldots, 1\}$ in terms of
refinements, $\lambda$-choosability reveals a complex hierarchy of
colourability of graphs.
  We prove that for two partitions $\lambda, \lambda'$ of $k$, every
$\lambda$-choosable graph is $\lambda'$-choosable if and only if $\lambda'$ is
a refinement of $\lambda$.
  Then we concentrate on $\lambda$-choosability of planar graphs for partitions
$\lambda$ of $4$.
  Several conjectures concerning colouring of generalized signed planar graphs
are proposed and relations between these conjectures and list colouring
conjectures for planar graphs are explored. In particular, it is proved that a
conjecture of K\"{u}ndgen and Ramamurthi on list colouring of planar graphs is
implied by the conjecture that every planar graph is $\{2,2\}$-choosable, and
also implied by the conjecture of M\'{a}\v{c}ajov\'{a}, Raspaud and
\v{S}koviera which asserts that every planar graph is signed
MRS-$4$-colourable, and that a conjecture of Kang and Steffen asserting that
every planar graph is signed KS-$4$-colourable implies that every planar graph
is $\{1,1,2\}$-choosable.