  As large language models continue to scale up, the imperative for fault
tolerance in distributed deep learning systems intensifies, becoming a focal
area of AI infrastructure research. Checkpoint has emerged as the predominant
fault tolerance strategy, with extensive studies dedicated to optimizing its
efficiency. However, the advent of the sparse Mixture-of-Experts (MoE) model
presents new challenges for traditional checkpoint techniques due to the
substantial increase in model size, despite comparable computational demands to
dense models. Breaking new ground in the realm of efficient fault tolerance for
MoE model training, we introduce a novel Partial Experts Checkpoint (PEC)
mechanism alongside a corresponding PEC fault-tolerant system. Our approach
strategically checkpoints a selected subset of experts, thereby significantly
reducing the checkpoint size for MoE models to a level comparable with that of
dense models. The empirical analysis on our 8-expert GPT-MoE model demonstrates
that the proposed PEC approach facilitates a substantial 54.2% decrease in the
size of non-redundant checkpoint (no data-parallel duplication), without
compromising the final model quality. Moreover, our PEC fault-tolerant system
achieves a 76.9% reduction in checkpoint workload per data-parallel distributed
rank, thereby correspondingly diminishing the checkpointing time and
facilitating complete overlap with the training process.


  We prove that the cubic nonlinear Schr\"odinger equation (both focusing and
defocusing) is globally well-posed in $H^s(\mathbb R)$ for any regularity
$s>-\frac12$. Well-posedness has long been known for $s\geq 0$, see [55], but
not previously for any $s<0$. The scaling-critical value $s=-\frac12$ is
necessarily excluded here, since instantaneous norm inflation is known to occur
[11, 40, 48].
  We also prove (in a parallel fashion) well-posedness of the real- and
complex-valued modified Korteweg-de Vries equations in $H^s(\mathbb R)$ for any
$s>-\frac12$. The best regularity achieved previously was $s\geq \frac14$; see
[15, 24, 33, 39].
  To overcome the failure of uniform continuity of the data-to-solution map, we
employ the method of commuting flows introduced in [37]. In stark contrast with
our arguments in [37], an essential ingredient in this paper is the
demonstration of a local smoothing effect for both equations. Despite the
non-perturbative nature of the well-posedness, the gain of derivatives matches
that of the underlying linear equation. To compensate for the local nature of
the smoothing estimates, we also demonstrate tightness of orbits. The proofs of
both local smoothing and tightness rely on our discovery of a new one-parameter
family of coercive microscopic conservation laws that remain meaningful at this
low regularity.


  For Ising spin models which bear the spin-ice type macroscopic
(quasi-)degeneracy, conventional classical Monte Carlo (MC) simulation using
single spin flips suffers from dynamical freezing at low temperatures ($T$). A
similar difficulty is seen also in a family of Heisenberg spin models with
easy-axis anisotropy or biquadratic interactions. In the Ising case, the
difficulty is avoided by introducing a non-local update based on the loop
algorithm. We present an extension of the loop algorithm to the Heisenberg
case. As an example of its application, we review our recent study on
spin-glass (SG) transition in a bond-disordered Heisenberg antiferromagnet
coupled to local lattice distortions.


  We present fore-optics and calibration unit design of Devasthal Optical
Telescope Integral Field Spectrograph (DOTIFS). DOTIFS fore-optics is designed
to modify the focal ratio of the light and to match its plate scale to the
physical size of Integral Field Units (IFUs). The fore-optics also delivers a
telecentric beam to the IFUs on the telescope focal plane. There is a
calibration unit part of which is combined with the fore-optics to have a light
and compact system. We use Xenon-arc lamp as a continuum source and
Krypton/Mercury-Neon lamps as wavelength calibration sources. Fore-optics and
calibration unit shares two optical lenses to maintain compactness of the
overall subsystem. Here we present optical and opto-mechanical design of the
calibration unit and fore-optics as well as calibration scheme of DOTIFS.


  The Product of Exponentials (PoE) formula is a mathematical tool that is used
extensively in robotics. The virtue of using the exponential mapping, Lie
Algebra and screw theory is that it allows an elegant and concise way of
describing the orientation and position of a body with respect to another body
in a multi-body system. Although the PoE formula is mainly used in robotics,
this work aims to demonstrate the utility of the PoE formula as an alternative
method for defining and drawing orbits given an orbital elements set. The work
also explores the first derivative of the adapted PoE formula in the framework
of orbital mechanics, which allows obtaining the state of the satellite
(position and velocity) from the orbital elements set using the developed
formulation.


  In this work we prove that the 5-qubit quantum error correcting code does not
fix qubit independent errors, even assuming that the correction circuit does
not introduce new errors. We say that a quantum code does not fix a quantum
computing error if its application does not reduce the variance of the error.
We also prove for qubit independent errors that if the correction circuit of
the 5-qubit quantum code detects an error, the corrected state has central
symmetry and, as a consequence, its variance is maximum. We have been able to
obtain these results thanks to the high symmetry of the 5-qubit quantum code
and we believe that the necessary calculations for less symmetric codes are
extremely complicated but that, despite this, the results obtained for the
5-qubit quantum code reveal a general behavior pattern of quantum error
correcting codes against qubit independent errors.


  Using surface-templated electrophoretic deposition, we have created arrays of
polymer beads (photonic units) incorporating photo-switchable DAE molecules,
which can be reversibly and individually switched between high and low emission
states by direct photo-excitation, without any energy or electron transfer
processes within the molecular system. The micropatterned array of these
photonic units is spectroscopically characterized in detail and optimized with
respect to both signal contrast and cross-talk. The optimum optical parameters
including laser intensity, wavelength and duration of irradiation are
elucidated and ideal conditions for creating reversible on/off cycles in a
micropatterned array are determined. 500 such cycles are demonstrated with no
obvious on/off contrast attenuation. The ability to process binary information
is demonstrated by selectively writing information to the given photonic unit,
reading the resultant emissive signal pattern and finally erasing the
information again, which in turn demonstrates the possibility of continuous
recording. This basic study paves the way for building complex circuits using
spatially well-arranged photonic units.


  The main focus of the present work is to study the Feynman's proof of the
Maxwell equations using the NC geometry framework. To accomplish this task, we
consider two kinds of noncommutativity formulations going along the same lines
as Feynman's approach. This allows us to go beyond the standard case and
discover non-trivial results. In fact, while the first formulation gives rise
to the static Maxwell equations, the second formulation is based on the
following assumption $m[x_{j},\dot{x_{k}}]=i\hbar \delta_{jk}+im\theta_{jk}f.$
The results extracted from the second formulation are more significant since
they are associated to a non trivial $\theta $-extension of the Bianchi-set of
Maxwell equations. We find $div_{\theta}B=\eta_{\theta}$ and $\frac{\partial
B_{s}}{\partial t}+\epsilon_{kjs}\frac{\partial E_{j}}{\partial
x_{k}}=A_{1}\frac{d^{2}f}{dt^{2}}+A_{2}\frac{df}{dt}+A_{3},$ where
$\eta_{\theta}$, $A_{1}$, $A_{2}$ and $A_{3}$ are local functions depending on
the NC $\theta $-parameter. The novelty of this proof in the NC space is
revealed notably at the level of the corrections brought to the previous
Maxwell equations. These corrections correspond essentially to the possibility
of existence of magnetic charges sources that we can associate to the magnetic
monopole since $div_{\theta}B=\eta_{\theta}$ is not vanishing in general.


  Studies on the new MgB2 superconductor, with a critical temperature Tc ~ 39
K, have evidenced its potential for applications although intense magnetic
relaxation effects limit the critical current density, Jc, at high magnetic
fields. This means that effective pinning centers must be added into the
material microstructure, in order to halt dissipative flux movements.
Concerning the basic microscopic mechanism to explain the superconductivity in
MgB2, several experimental and theoretical works have pointed to the relevance
of a phonon-mediated interaction, in the framework of the BCS theory. Questions
have been raised about the relevant phonon modes, and the gap and Fermi surface
anisotropies, in an effort to interpret spectroscopic and thermal data that
give values between 2.4 and 4.5 for the gap energy ratio. Preliminary results
on the anisotropy of Hc2 have shown a ratio, between the in-plane and
perpendicular directions, around 1.7 for aligned MgB2 crystallites and 1.8 for
epitaxial thin films. Here we show a study on the angular dependence of Hc2
pointing to a Fermi velocity anisotropy around 2.5. This anisotropy certainly
implies the use of texturization techniques to optimize Jc in MgB2 wires and
other polycrystalline components.


  The problem of asymptotic expansions of Green functions in perturbative QFT
is studied for the class of Euclidean asymptotic regimes. Phenomenological
applications are analyzed to obtain a meaningful mathematical formulation of
the problem. It is shown that the problem reduces to studying asymptotic
expansions of products of a class of singular functions in the sense of the
distribution theory. Existence, uniqueness and explicit expressions for such
expansions ("asymptotic operation for products of singular functions") in
dimensionally regularized form are obtained using the so-called extension
principle.


  We introduce Clapp-Puppe type generalized Lusternik-Schnirelmann (co)category
in a Quillen model category. We establish some of their basic properties and
give various characterizations of them. As the first application of these
characterizations, we show that our generalized (co)category is invariant under
Quillen modelization equivalences. In particular, generalized (co)category of
spaces and simplicial sets coincide. Another application of these
characterizations is to define and study rational cocategory. Various other
applications are also given.


  We investigate the heat transport through a rare earth multilayer system
composed of Yttrium (Y), Dysprosium (Dy) and Niobium (Nb) by ultrafast X-ray
diffraction. This is an example of a complex heat flow problem on the
nanoscale, where several different quasi-particles carry the heat. The Bragg
peak positions of each layer represent layer-specific thermometers that measure
the energy flow through the sample after excitation of the Y top-layer with
fs-laser pulses. In an experiment-based analytic solution to the nonequilibrium
heat transport problem, we derive the individual contributions of the spins and
the coupled electron-lattice system to the heat conduction. The full
characterization of the spatiotemporal energy flow at different starting
temperatures reveals that the spin excitations of antiferromagnetic Dy speed up
the heat transport into the Dy layer at low temperatures, whereas the heat
transport through this layer and further into the Y and Nb layers underneath is
slowed down. The experimental findings are compared to the solution of the heat
equation using macroscopic temperature-dependent material parameters without
separation of spin- and phonon contributions to the heat. We explain, why the
simulated energy density matches our experiment-based derivation of the heat
transport, although the simulated thermoelastic strain in this simulation is
not even in qualitative agreement.


  The mixed spin-(1/2,1) Ising chain with axial and rhombic zero-field
splitting parameters in a presence of the longitudinal magnetic field is
exactly solved within the framework of decoration-iteration transformation and
transfer-matrix method. Our particular emphasis is laid on an investigation of
the influence of the rhombic term, which is responsible for an onset of quantum
entanglement between two magnetic states S_k^z = 1 and -1 of the spin-1 atoms.
It is shown that the rhombic term gradually destroys a classical ferrimagnetic
order in the ground state and simultaneously causes diversity in magnetization
curves including intermediate plateau regions, regions with a continuous change
in the magnetization as well as several unusual field-induced transitions
accompanied with magnetization jumps. Another interesting findings concern with
an appearance of the round minimum in the temperature dependence of
susceptibility times temperature data, the double-peak zero-field specific heat
curves and the enhanced magnetocaloric effect. The temperature dependence of
the specific heat with three separate maxima may also be detected when driving
the system through the axial and rhombic zero-field splitting parameters close
enough to a phase boundary between the ferrimagnetic and disordered states and
applying sufficiently small longitudinal magnetic field.


  We show that the Fibered Isomorphism Conjecture (FIC) of Farrell and Jones
corresponding to the stable topological pseudoisotopy functor is true for the
fundamental groups of a large class of 3-manifolds. We also prove that if the
FIC is true for irreducible 3-manifold groups then it is true for all
3-manifold groups. In fact, this follows from a more general result we prove
here, namely we show that if the FIC is true for each vertex group of a graph
of groups with trivial edge groups then the FIC is true for the fundamental
group of the graph of groups. This result is part of a program to prove FIC for
the fundamental group of a graph of groups where all the vertex and edge groups
satisfy FIC. A consequence of the first result gives a partial solution to a
problem in the problem list of R. Kirby. We also deduce that the FIC is true
for a class of virtually PD_3-groups.
  Another main aspect of this article is to prove the FIC for all Haken
3-manifold groups assuming that the FIC is true for B-groups. By definition a
B-group contains a finite index subgroup isomorphic to the fundamental group of
a compact irreducible 3-manifold with incompressible nonempty boundary so that
each boundary component is of genus \geq 2. We also prove the FIC for a large
class of B-groups and moreover, using a recent result of L.E. Jones we show
that the surjective part of the FIC is true for any B-group.


  We consider the consequences for future neutrino factory experiments of small
CPT-odd interactions in neutrino oscillations. The \nu_\mu\to\nu_\mu and
\bar\nu_\mu\to\bar\nu_\mu survival probabilities at a baseline L=732 km can
test for CPT-odd contributions at orders of magnitude better sensitivity than
present limits. Interference between the CPT-violating interaction and CPT-even
mass terms in the Lagrangian can lead to a resonant enhancement of the
oscillation amplitude. For oscillations in matter, a simultaneous enhancement
of both neutrino and antineutrino oscillation amplitudes is possible.


  Precise control of an open quantum system is critical to quantum information
processing, but is challenging due to inevitable interactions between the
quantum system and the environment. We demonstrated experimentally at room
temperature a type of dynamically corrected gates on the nitrogen-vacancy
centers in diamond. The infidelity of quantum gates caused by environment
nuclear spin bath is reduced from being the second-order to the sixth-order of
the noise to control field ratio, which offers greater efficiency in reducing
the infidelity by reducing the noise level. The decay time of the coherent
oscillation driven by dynamically corrected gates is shown to be two orders of
magnitude longer than the dephasing time, and is essentially limited by
spin-lattice relaxation. The infidelity of DCG, which is actually constrained
by the decay time, reaches $4\times 10^{-3}$ at room temperature and is further
reducible by 2-3 orders of magnitudes via lowering temperature. The greatly
reduced noise dependence of infidelity and the uttermost extension of the
coherent time mark an important step towards fault-tolerant quantum computation
in realistic systems.


  We obtain new combinatorial formulae for modified Hall--Littlewood
polynomials, for matrix elements of the transition matrix between the
elementary symmetric functions and Hall-Littlewood's ones, and for the number
of rational points over the finite field of unipotent partial flag variety. The
definitions and examples of generalized mahonian statistic on the set of
transport matrices and dual mahonian statistic on the set of transport
(0,1)-matrices are given. We also review known q-analogues of
Littlewood-Richardson numbers and consider their possible generalizations.
Several conjectures about multinomial fermionic formulae for homogeneous
unrestricted one dimensional sums and generalized Kostka-Foulkes polynomials
are formulated. Finally we suggest two parameters deformations of polynomials
$P_{\lambda\mu}(t)$ and one dimensional sums.


  We propose a new method for the estimation of a semiparametric tempered
stable L\'{e}vy model. The estimation procedure combines iteratively an
approximate semiparametric method of moment estimator, Truncated Realized
Quadratic Variations (TRQV), and a newly found small-time high-order
approximation for the optimal threshold of the TRQV of tempered stable
processes. The method is tested via simulations to estimate the volatility and
the Blumenthal-Getoor index of the generalized CGMY model as well as the
integrated volatility of a Heston-type model with CGMY jumps. The method
outperforms other efficient alternatives proposed in the literature when
working with a L\'evy process (i.e., the volatility is constant), or when the
index of jump intensity $Y$ is larger than $3/2$ in the presence of stochastic
volatility.


  A novel algorithm to solve the quadratic programming problem over ellipsoids
is proposed. This is achieved by splitting the problem into two optimisation
sub-problems, quadratic programming over a sphere and orthogonal projection.
Next, an augmented-Lagrangian algorithm is developed for this multiple
constraint optimisation. Benefit from the fact that the QP over a single sphere
can be solved in a closed form by solving a secular equation, we derive a
tighter bound of the minimiser of the secular equation. We also propose to
generate a new psd matrix with a low condition number from the matrices in the
quadratic constraints. This correction method improves convergence of the
proposed augmented-Lagrangian algorithm. Finally, applications of the
quadratically constrained QP to bounded linear regression and tensor
decompositions are presented.


  Recently, several promising approximate message passing (AMP) based
algorithms have been developed for bilinear recovery with model
$\boldsymbol{Y}=\sum_{k=1}^K b_k \boldsymbol{A}_k \boldsymbol{C}
+\boldsymbol{W} $, where $\{b_k\}$ and $\boldsymbol{C}$ are jointly recovered
with known $\boldsymbol{A}_k$ from the noisy measurements $\boldsymbol{Y}$. The
bilinear recover problem has many applications such as dictionary learning,
self-calibration, compressive sensing with matrix uncertainty, etc. In this
work, we propose a new bilinear recovery algorithm based on AMP with unitary
transformation. It is shown that, compared to the state-of-the-art message
passing based algorithms, the proposed algorithm is much more robust and
faster, leading to remarkably better performance.


  Classical autoencoders are neural networks that can learn efficient low
dimensional representations of data in higher dimensional space. The task of an
autoencoder is, given an input $x$, is to map $x$ to a lower dimensional point
$y$ such that $x$ can likely be recovered from $y$. The structure of the
underlying autoencoder network can be chosen to represent the data on a smaller
dimension, effectively compressing the input. Inspired by this idea, we
introduce the model of a quantum autoencoder to perform similar tasks on
quantum data. The quantum autoencoder is trained to compress a particular
dataset of quantum states, where a classical compression algorithm cannot be
employed. The parameters of the quantum autoencoder are trained using classical
optimization algorithms. We show an example of a simple programmable circuit
that can be trained as an efficient autoencoder. We apply our model in the
context of quantum simulation to compress ground states of the Hubbard model
and molecular Hamiltonians.


  We continue here the exam \cite{LuMa} of a theory of gravity that satisfies
the Einstein Equivalence Principle (EEP) for any kind of matter/energy, except
for the gravitational energy. This is part of a research program that intends
to re-examine the standard Feynman-Deser approach of field theoretical
derivation of Einstein\rq s General Relativity. The hypothesis implicit in such
precedent derivations \cite{Feynman} \cite{Deser} concerns the universality of
gravity interaction. Although there is a strong observational basis supporting
the universality of matter to gravity interaction, there is not an equivalent
situation that supports the hypothesis that gravity interacts with gravity as
any other form of non-gravitational energy. We analyse here a kind of
gravity-gravity interaction distinct from GR but, as we shall see, that
conforms with the actual status of observation. We exhibit the gravitational
field produced by a spherically symmetric static configuration as described in
this field theory of gravity. The values that we obtain for the standard PPN
parameters ($\alpha = \beta = \gamma = 1$) coincide with those of General
Relativity. Thus, as we pointed out in a previous paper, the main different
aspect of our theory and GR concerns the velocity of the gravitational waves.
Since there is a large expectation that the detection of gravitational waves
will occur in the near future, the question of which theory describes Nature
better will probably be settled soon.


  In this paper we embed $m$-dimensional Euclidean space in the geometric
algebra $Cl_m $ to extend the operators of incidence in ${R^m}$ to operators of
incidence in the geometric algebra to generalize the notion of separator to a
decision boundary hyperconic in the Clifford algebra of hyperconic sections
denoted as ${Cl}({Co}_{2})$. This allows us to extend the concept of a linear
perceptron or the spherical perceptron in conformal geometry and introduce the
more general conic perceptron, namely the {elliptical perceptron}. Using
Clifford duality a vector orthogonal to the decision boundary hyperplane is
determined. Experimental results are shown in 2-dimensional Euclidean space
where we separate data that are naturally separated by some typical plane conic
separators by this procedure. This procedure is more general in the sense that
it is independent of the dimension of the input data and hence we can speak of
the hyperconic elliptic perceptron.


  In this work we investigate stochastic non-convex optimization problems where
the objective is an expectation over smooth loss functions, and the goal is to
find an approximate stationary point. The most popular approach to handling
such problems is variance reduction techniques, which are also known to obtain
tight convergence rates, matching the lower bounds in this case. Nevertheless,
these techniques require a careful maintenance of anchor points in conjunction
with appropriately selected "mega-batchsizes". This leads to a challenging
hyperparameter tuning problem, that weakens their practicality. Recently,
[Cutkosky and Orabona, 2019] have shown that one can employ recursive momentum
in order to avoid the use of anchor points and large batchsizes, and still
obtain the optimal rate for this setting. Yet, their method called STORM
crucially relies on the knowledge of the smoothness, as well a bound on the
gradient norms. In this work we propose STORM+, a new method that is completely
parameter-free, does not require large batch-sizes, and obtains the optimal
$O(1/T^{1/3})$ rate for finding an approximate stationary point. Our work
builds on the STORM algorithm, in conjunction with a novel approach to
adaptively set the learning rate and momentum parameters.


  A technique using RF bucket reduction for acquiring information about the
particle distribution in longitudinal phase space has been applied in the
Fermilab Booster. Data sets were obtained at six important time intervals of a
Booster cycle for three different beam intensities. Controlled RF bucket
reduction also provides other opportunities for beam manipulation.


  The Bell basis, a set of maximally entangled biphoton state, is a critical
prerequisite towards quantum information processing, and many quantum
applications have highlighted the requirement for the manipulation of
high-dimensional Bell basis. While the Bell states can be created by using
ingenious single-photon quantum gates, its implementation complexity in higher
dimensions is significantly increased. Here we present an elaborate approach to
show that the adaptive pump modulation enable the efficient preparation of Bell
basis in arbitrary-dimensional Hilbert space. A complete set of
four-dimensional orbital angular momentum Bell states are experimentally
created, yielding high fidelities for certifying the entanglement
dimensionality. Our strategy can be simply generalized to prepare more complex
forms of quantum states even exploiting other physical degrees of freedom.
Also, it can facilitate the use of high-dimensional entanglement in a variety
of quantum protocols, in particular those requiring quantum dense coding.


  In this paper we develop a boundary $\varepsilon$-regularity theory for
optimal transport maps between bounded open sets with $C^{1,\alpha}$-boundary.
Our main result asserts sharp $C^{1,\alpha}$-regularity of transport maps at
the boundary in form of a linear estimate under certain assumptions: The main
quantitative assumptions are that the local nondimensionalized transport cost
is small and that the boundaries are locally almost flat in $C^{1,\alpha}$. Our
method is completely variational and builds on the recently developed interior
regularity theory.


  This paper describes the machine translation system developed jointly by
Baidu Research and Oregon State University for WMT 2019 Machine Translation
Robustness Shared Task. Translation of social media is a very challenging
problem, since its style is very different from normal parallel corpora (e.g.
News) and also include various types of noises. To make it worse, the amount of
social media parallel corpora is extremely limited. In this paper, we use a
domain sensitive training method which leverages a large amount of parallel
data from popular domains together with a little amount of parallel data from
social media. Furthermore, we generate a parallel dataset with pseudo noisy
source sentences which are back-translated from monolingual data using a model
trained by a similar domain sensitive way. We achieve more than 10 BLEU
improvement in both En-Fr and Fr-En translation compared with the baseline
methods.


  Studies involving colourising images has been garnering researchers' keen
attention over time, assisted by significant advances in various Machine
Learning techniques and compute power availability. Traditionally, colourising
images have been an intricate task that gave a substantial degree of freedom
during the assignment of chromatic information. In our proposed method, we
attempt to colourise images using Vision Transformer - Inception - Generative
Adversarial Network (ViT-I-GAN), which has an Inception-v3 fusion embedding in
the generator. For a stable and robust network, we have used Vision Transformer
(ViT) as the discriminator. We trained the model on the Unsplash and the COCO
dataset for demonstrating the improvement made by the Inception-v3 embedding.
We have compared the results between ViT-GANs with and without Inception-v3
embedding.


  Three Tidal Disruption Event (TDE) candidates (AT2019dsg, AT2019fdr,
AT2019aalc) have been associated with high energy astrophysical neutrinos in
multi-messenger follow-ups. In all cases, the neutrino observation occurred
O(100) days after the maximum of the optical-ultraviolet (OUV) luminosity. We
discuss unified fully time-dependent interpretations of the neutrino signals
where the neutrino delays are not a statistical effect, but rather the
consequence of a physical scale of the post-disruption system. Noting that
X-rays flares and infrared (IR) dust echoes have been observed in all cases, we
consider three models in which quasi-isotropic neutrino emission is due to the
interactions of accelerated protons of moderate, medium, and ultra-high
energies with X-rays, OUV, and IR photons, respectively. We find that the
neutrino time delays can be well described in the X-ray model assuming magnetic
confinement of protons in a calorimetric approach if the unobscured X-ray
luminosity is roughly constant over time, and in the IR model, where the delay
is directly correlated with the time evolution of the echo luminosity (for
which a model is developed here). The OUV model exhibits the highest neutrino
production efficiency. In all three models, the highest neutrino fluence is
predicted for AT2019aalc, due to its high estimated supermassive black hole
mass and low redshift. All models result in diffuse neutrino fluxes that are
consistent with observations.


  As big spatial data becomes increasingly prevalent, classical spatiotemporal
(ST) methods often do not scale well. While methods have been developed to
account for high-dimensional spatial objects, the setting where there are
exceedingly large samples of spatial observations has had less attention. The
variational autoencoder (VAE), an unsupervised generative model based on deep
learning and approximate Bayesian inference, fills this void using a latent
variable specification that is inferred jointly across the large number of
samples. In this manuscript, we compare the performance of the VAE with a more
classical ST method when analyzing longitudinal visual fields from a large
cohort of patients in a prospective glaucoma study. Through simulation and a
case study, we demonstrate that the VAE is a scalable method for analyzing ST
data, when the goal is to obtain accurate predictions. R code to implement the
VAE can be found on GitHub: https://github.com/berchuck/vaeST.


  We present evidence that infant mortality of stellar clusters is likely to be
a major and very efficient process for the dissolution of young clusters in the
spiral galaxy NGC 1313. Performing stellar PSF photometry on archival HST/ACS
images of the galaxy, we find that a large fraction of early B-type stars are
seen outside of star clusters and well spread within the galactic disk,
consistent with the scenario of infant mortality. We also calculate the UV flux
produced by the stars in and out the clusters and find that 75 to 90% of the UV
flux in NGC 1313 is produced by stars outside the clusters. These results
suggest that the infant mortality of star clusters is probably the underlying
cause of the diffuse UV emission in starburst galaxies. Infant mortality would
also explain the numerous B-type stars observed in the background field of our
Galaxy as well. We exclude the possibility that unresolved low-mass star
clusters and scaled OB associations might be the main source for the diffuse UV
emission.


  Random bond Ising systems on a general hierarchical lattice are considered.
The inequality between the specific heat exponent of the pure system,
$\alpha_p$, and the crossover exponent $\phi$, $\alpha_p<=\phi$, gives rise to
a possibility of a negative $\alpha_p$ along with a positive $\phi$, leading to
random criticality in disagreement with the Harris criterion. An explicit
example where this really happens for an Ising system is presented and
discussed. In addition to that, it is shown that in presence of full long-range
correlations, the crossover exponent is larger than in the uncorrelated case.


  The pervasive spread of misinformation and disinformation in social media
underscores the critical importance of detecting media bias. While robust Large
Language Models (LLMs) have emerged as foundational tools for bias prediction,
concerns about inherent biases within these models persist. In this work, we
investigate the presence and nature of bias within LLMs and its consequential
impact on media bias detection. Departing from conventional approaches that
focus solely on bias detection in media content, we delve into biases within
the LLM systems themselves. Through meticulous examination, we probe whether
LLMs exhibit biases, particularly in political bias prediction and text
continuation tasks. Additionally, we explore bias across diverse topics, aiming
to uncover nuanced variations in bias expression within the LLM framework.
Importantly, we propose debiasing strategies, including prompt engineering and
model fine-tuning. Extensive analysis of bias tendencies across different LLMs
sheds light on the broader landscape of bias propagation in language models.
This study advances our understanding of LLM bias, offering critical insights
into its implications for bias detection tasks and paving the way for more
robust and equitable AI systems


  We use the two fluid model to determine the conditions under which the
nuclear spin-lattice lattice relaxation rate, $T_1$, of candidate heavy quantum
critical superconductors can exhibit scaling behavior and find that it can
occur if and only if their "hidden" quantum critical spin fluctuations give
rise to a temperature-independent intrinsic heavy electron spin-lattice
relaxation rate. The resulting scaling of $T_1$ with the strength of the heavy
electron component and the coherence temperature, $T^*$, provides a simple test
for their presence at pressures at which the superconducting transition
temperature, $T_c$, is maximum and is proportional to $T^*$. These findings
support the previously noted partial scaling of the spin-lattice relaxation
rate with $T_c$ in a number of important heavy electron materials and provide
additional evidence that in these materials their optimal superconductivity
originates in the quantum critical spin fluctuations associated with a nearby
phase transition from partially localized to fully itinerant quasiparticles.


  Reduced rank regression (RRR) is a widely employed model for investigating
the linear association between multiple response variables and a set of
predictors. While RRR has been extensively explored in various works, the focus
has predominantly been on continuous response variables, overlooking other
types of outcomes. This study shifts its attention to the Bayesian perspective
of generalized linear models (GLM) within the RRR framework. In this work, we
relax the requirement for the link function of the generalized linear model to
be canonical. We examine the properties of fractional posteriors in GLM within
the RRR context, where a fractional power of the likelihood is utilized. By
employing a spectral scaled Student prior distribution, we establish
consistency and concentration results for the fractional posterior. Our results
highlight adaptability, as they do not necessitate prior knowledge of the rank
of the parameter matrix. These results are in line with those found in
frequentist literature. Additionally, an examination of model mis-specification
is undertaken, underscoring the effectiveness of our approach in such
scenarios.


  A method of expansion of solutions of singularly perturbed nonlinear systems
in power series of small parameters is applied to the popular Lorenz model in
synergetics.Simple asymptotic expressions for the solution to the model in
consideration is obtained for some extreme cases.The times for achieving of
quasistationary and stationary states are estimated.


  We present a determination of the perturbative QCD (pQCD) coupling using the
V+A channel ALEPH $\tau$-decay data. The determination involves the
double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules. The
theoretical basis is the Operator Product Expansion (OPE) of the V+A channel
Adler function in which the higher order terms of the leading-twist part
originate from a model based on the known structure of the leading renormalons
of this quantity. The applied evaluation methods are contour-improved
perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and
Principal Value of the Borel resummation (PV). All the methods involve
truncations in the order of the coupling. In contrast to the truncated CIPT
method, the truncated FOPT and PV methods account correctly for the suppression
of various renormalon contributions of the Adler function in the mentioned sum
rules. The extracted value of the ${\overline {\rm MS}}$ coupling is
$\alpha_s(m_{\tau}^2) = 0.3116 \pm 0.0073$ [$\alpha_s(M_Z^2)=0.1176 \pm
0.0010$] for the average of the FOPT and PV methods, which we regard as our
main result. On the other hand, if we include in the average also the CIPT
method, the resulting values are significantly higher, $\alpha_s(m_{\tau}^2) =
0.3194 \pm 0.0167$ [$\alpha_s(M_Z^2)=0.1186 \pm 0.0021$].


  In this review article, we first briefly introduce the transport theory and
quantum molecular dynamics model applied in the study of the heavy ion
collisions from low to intermediate energies. The developments of improved
quantum molecular dynamics model (ImQMD) and ultra-relativistic quantum
molecular dynamics model (UrQMD), are reviewed. The reaction mechanism and
phenomena related to the fusion, multinucleon transfer, fragmentation,
collective flow and particle production are reviewed and discussed within the
framework of the two models. The constraints on the isospin asymmetric nuclear
equation of state and in-medium nucleon-nucleon cross sections by comparing the
heavy ion collision data with transport models calculations in last decades are
also discussed, and the uncertainties of these constraints are analyzed as
well. Finally, we discuss the future direction of the development of the
transport models for improving the understanding of the reaction mechanism, the
descriptions of various observables, the constraint on the nuclear equation of
state, as well as for the constraint on in-medium nucleon-nucleon cross
sections.


  Dynamical screening in the magnetic part of the one-gluon exchange
interaction is included in the study of radiative energy loss of a fast parton
propagating inside a quark-gluon plasma. As a result the final radiative energy
loss is about twice as large as when only the electric part of one-gluon
exchange interaction is considered. A non-perturbative magnetic screening mass
is also used in the estimate of the mean-free-path of parton scattering in a
hot QCD matter.


  In this paper we obtain a necessary and sufficient condition for the
canonical solution operator to $\overline \partial $ restricted to radial
symmetric Bergman spaces to be a Hilbert-Schmidt operator. We also discuss
compactness of the solution operator in spaces of entire functions in one
variable. In the sequel we consider several examples and also treat the case of
weighted spaces of entire functions in several variables.


  In this letter, we present a high pulse energy Raman laser at 1946 nm
wavelength directly pumped with a 1533 nm custom-made fiber laser. The Raman
laser is based on the stimulated Raman scattering (SRS) in an 8-meter carbon
dioxide (CO2) filled nested anti-resonant hollow-core fiber (ARHCF). The low
energy phonon emission combined with the inherent SRS process along the
low-loss fiber allows the generation of high pulse energy up to 15.4 {\mu}J at
atmospheric CO2 pressure. The Raman laser exhibits good long-term stability and
low relative intensity noise (RIN) of less than 4%. We also investigate the
pressure-dependent overlap of the Raman laser line with the absorption band of
CO2 at 2 {\mu}m spectral range. Our results constitute a novel and promising
technology towards high energy 2 {\mu}m lasers.


  We reduce the leading term in Lehman's theorem. This improved estimate allows
us to refine the main theorem of Bays and Hudson. Entering $2,000,000$ Riemann
zeros, we prove that there exists $x$ in the interval $[exp(727.951858),
exp(727.952178)]$ for which $\pi(x)-\li(x) > 3.2 \times 10^{151}$. There are at
least $10^{154}$ successive integers $x$ in this interval for which
$\pi(x)>\li(x)$. This interval is strictly a sub-interval of the interval in
Bays and Hudson, and is narrower by a factor of about 12.


  A chiral sculptured thin film is fabricated from patinal titanium oxide using
the serial bideposition technique. Axial transmittance spectrums are measured
over a spectral region encompassing the Bragg regime for axial excitation. The
same spectrums are calculated using a nominal structure-property relationship
model and the parameter space of the model is explored for best fits of the
calculated and measured transmittances. Ambiguity arising on calibrating the
model against axial transmittance measurements is shown to be resolvable using
non--axial transmittance measurements.


  Photonics chips on which one can perform Gaussian Boson Sampling have become
accessible on the cloud, in particular the X8 chip of Xanadu. In this technical
report, we study its potential use as a first step towards graph classification
on quantum devices. In order to achieve this goal, we study the generated
samples of the graph embedding method which leads to feature vectors. This is
done on a restricted class of unweighted, undirected and loop-free graphs.
Hardware constraints are matched to properties of graphs that can be encoded.
We report experiments on the X8 chip as well as comparisons to numerical
simulations on a classical computer and analytical solutions. We conclude this
technical report by trying to take photon loss into account and explain the
observed results accordingly.


  We report on electronic collective excitations in RMn2O5 (R= Pr, Sm, Gd, Tb)
showing condensation starting at and below TN\simTC\sim40-50 K. Its origin is
understood as partial delocalized eg electron orbitals in the Jahn-Teller
distortion of the pyramids dimmer with strong hybridized Mn3+-O bonds. Our
local probes, Raman, infrared, and X-ray absorption, back the conclusion by
which there is no structural phase transition at TN\simTC. Ferroelectricity is
magnetically assisted by electron localization triggering lattice
polarizability by unscreening. We have also found phonon hardening as the rare
earth is sequentially replaced. This is understood as consequence of lanthanide
contraction. It is suggested that partially f-electron screened Rare Earth
nuclei might be introducing a perturbation to eg electrons prone to delocalize
as the superexchange interaction takes place.


  We demonstrate the physical generation of random bits at high bit rates (>
100 Gb/s) using optical chaos from a solitary laser diode and therefore without
the complex addition of either external optical feedback or injection. This
striking result is obtained despite the low dimension and relatively small
bandwidth of the laser chaos, i.e. two characteristics that have been so far
considered as limiting the performances of optical chaos-based applications. We
unambiguously attribute the successful randomness at high speed to the physics
of the laser chaotic polarization dynamics and the resulting growth rate of the
dynamical entropy.


  Using numerical simulations of magnetically interacting vortices in
disordered layered superconductors we obtain the static vortex phase diagram as
a function of magnetic field and temperature. For increasing field or
temperature, we find a transition from ordered straight vortices to disordered
decoupled vortices. This transition is associated with a peak effect in the
critical current. For samples with increasing disorder strength the field at
which the decoupling occurs decreases. Long range, nonlinear interactions in
the c-axis are required to observe the effect.


  In this paper, we analyze the lower bound property of the discrete
eigenvalues by the rectangular Morley elements of the biharmonic operators in
both two and three dimensions. The analysis relies on an identity for the
errors of eigenvalues. We explore a refined property of the canonical
interpolation operators and use it to analyze the key term in this identity. In
particular, we show that such a term is of higher order for two dimensions, and
is negative and of second order for three dimensions, which causes a main
difficulty. To overcome it, we propose a novel decomposition of the first term
in the aforementioned identity. Finally, we establish a saturation condition to
show that the discrete eigenvalues are smaller than the exact ones. We present
some numerical results to demonstrate the theoretical results.


  A function of two variables F(x,y)is universal iff for every other function
G(x,y) there exists functions h(x) and k(y) with G(x,y) = F(h(x),k(y))
Sierpinski showed that assuming the continuum hypothesis there exists a Borel
function F(x,y) which is universal. Assuming Martin's Axiom there is a
universal function of Baire class 2. A universal function cannot be of Baire
class 1. We show that it is consistent that for each countable ordinal alpha>2
there is a universal function of class alpha but none of smaller class.
  We show that it is consistent with ZFC that there is no universal function
(Borel or not) on the reals, and we show that it is consistent that there is a
universal function but no Borel universal function. We also prove some results
concerning higher arity universal functions. For example, the existence of an F
such that for every G there are unary h,k,j such that G(x,y,z) =
F(h(x),k(y),j(z)) is equivalent to the existence of a 2-ary universal F.
However the existence of an F such that for every G there are h,k,j such that
G(x,y,z) = F(h(x,y),k(x,z),j(y,z)) follows from a 2-ary universal F but is
strictly weaker. Results obtained Mar-June 2009, Nov 2010. Last revised April
2012 LaTex2e: 28 pages Latest version at: www.math.wisc.edu/~miller


  Effective oscillator strength distributions are systematically generated and
tabulated for the alkali atoms, the alkaline-earth atoms, the alkaline-earth
ions, the rare gases and some miscellaneous atoms. These effective
distributions are used to compute the dipole, quadrupole and octupole static
polarizabilities, and are then applied to the calculation of the dynamic
polarizabilities at imaginary frequencies. These polarizabilities can be used
to determine the long-range $C_6$, $C_8$ and $C_{10}$ atom-atom interactions
for the dimers formed from any of these atoms and ions, and we present tables
covering all of these combinations.


  We discuss the possible signals of the degenerate BESS model at the LHC. This
model describes a strongly interacting scenario responsible of the spontaneous
breaking of the electroweak symmetry. It predicts two triplets of extra gauge
bosons which are almost degenerate in mass. Due to this feature, the model has
the property of decoupling and therefore, at low energies (below or of the
order of $100 GeV$) it is nearly indistinguishable from the Standard Model.
However the new resonances, both neutral and charged, should give quite
spectacular signals at the LHC, where the c.o.m. energy will allow to produce
these gauge bosons directly.


  In situ neutron diffraction of the uniaxial tension test was used to study
the effect of the surrounding matrix microstructure on the mechanical stability
of retained austenite in high-carbon bearing steels. Comparing the samples with
bainitic microstructures to those with martensitic ones it was found that the
retained austenite in a bainitic matrix starts transforming into martensite at
a lower strain compared to that within a martensitic matrix. On the other hand,
the rate of transformation of the austenite was found to be higher within a
martensitic microstructure. Crystal plasticity modeling was used to analyze the
transformation phenomenon in these two microstructures and determine the effect
of surrounding microstructure on elastic, plastic and transformation components
of the strain. The results showed that the predominant difference in the
deformation accumulated was from the transformation strain and the critical
transformation driving force within the two microstructures. The retained
austenite was more stable for identical loading conditions in case of
martensitic matrix compared to the bainitic one. It was also observed that the
initial volume fraction of retained austenite within the bainitic matrix would
alter the onset of transformation to martensite but not the rate of
transformation.


  We show that each Saletan (linear) contraction can be realized, up to change
of bases of the initial and the target Lie algebras, by a matrix-function that
is completely defined by a partition of the dimension of Fitting component of
its value at the limit value of the contraction parameter. The codimension of
the Fitting component and this partition constitute the signature of the
Saletan contraction. We study Saletan contractions with Fitting component of
maximal dimension and trivial one-part partition. All contractions of such kind
in dimension three are completely classified.


  During outbreaks of emerging infectious diseases, internationally connected
cities often experience large and early outbreaks, while rural regions follow
after some delay. This hierarchical structure of disease spread is influenced
primarily by the multiscale structure of human mobility. However, during the
COVID-19 epidemic, public health responses typically did not take into
consideration the explicit spatial structure of human mobility when designing
non-pharmaceutical interventions (NPIs). NPIs were applied primarily at
national or regional scales. Here we use weekly anonymized and aggregated human
mobility data and spatially highly resolved data on COVID-19 cases, deaths and
hospitalizations at the municipality level in Mexico to investigate how
behavioural changes in response to the pandemic have altered the spatial scales
of transmission and interventions during its first wave (March - June 2020). We
find that the epidemic dynamics in Mexico were initially driven by SARS-CoV-2
exports from Mexico State and Mexico City, where early outbreaks occurred. The
mobility network shifted after the implementation of interventions in late
March 2020, and the mobility network communities became more disjointed while
epidemics in these communities became increasingly synchronised. Our results
provide actionable and dynamic insights into how to use network science and
epidemiological modelling to inform the spatial scale at which interventions
are most impactful in mitigating the spread of COVID-19 and infectious diseases
in general.


  The age, evolution, and chemical properties of the Galactic disk can be
effectively ascertained using open clusters. Within the large program Stellar
Populations Astrophysics at the Telescopio Nazionale Galileo, we specifically
focused on stars in open clusters, to investigate various astrophysical topics,
from the chemical content of very young systems to the abundance patterns of
lesser studied intermediate-age and old open clusters. We investigate the
astrophysically interesting element fluorine (F), which has an uncertain and
intriguing cosmic origin. We also determine the abundance of cerium (Ce), as F
abundance is expected to correlate with the s-process elements. High-resolution
near-infrared spectra were obtained using the GIANO-B spectrograph. The Python
version of Spectroscopy Made Easy (PySME), was used to derive atmospheric
parameters and abundances. The stellar parameters were determined using OH, CN,
and CO molecular lines along with Fe I lines. This paper presents the first F
Galactic radial abundance gradient. Our results are also compared with
literature estimates and with Galactic chemical evolution models that have been
generated using different F production channels. Our results indicate a
constant, solar pattern in the [F/Fe] ratios across clusters of different ages,
supporting the latest findings that fluorine levels do not exhibit any
secondary behavior for stars with solar or above-solar metallicity. By
comparing our sample stars with the predictions of Galactic chemical evolution
models, we came to the conclusion that both asymptotic giant branch stars and
massive stars, including a fraction of fast rotators that increase with
decreasing metallicity, are needed to explain the cosmic origin of F.


  A Hom-type generalization of non-commutative Poisson algebras, called
non-commutative Hom-Poisson algebras, are studied. They are closed under
twisting by suitable self-maps. Hom-Poisson algebras, in which the
Hom-associative product is commutative, are closed under tensor products.
Through (de)polarization Hom-Poisson algebras are equivalent to admissible
Hom-Poisson algebras, each of which has only one binary operation.
Multiplicative admissible Hom-Poisson algebras are Hom-power associative.


  We study the Spohn conditional independence (CI) variety $C_X$ of an
$n$-player game $X$ for undirected graphical models on $n$ binary random
variables consisting of one edge. For a generic game, we show that $C_X$ is a
smooth irreducible complete intersection curve (Nash conditional independence
curve) in the Segre variety $(\mathbb{P}^{1})^{n-2} \times \mathbb{P}^3$ and we
give an explicit formula for its degree and genus. We prove two universality
theorems for $C_X$: The product of any affine real algebraic variety with the
real line or any affine real algebraic variety in $\mathbb{R}^m$ defined by at
most $m-1$ polynomials is isomorphic to an affine open subset of $C_X$ for some
game $X$.


  We discuss the current status of the investigations of the conformal symmetry
breaking contributions to three forms for the QCD generalizations of the
Crewther relation. The new third form of the extension of this relation is
considered in more detail. Particular attention is paid to the discussions of
the applications of the $\beta$-expansion formalism proposed previously by one
of us (SVM). Several relations between 5-loop contributions to the Adler
D-function $D^{NS}_{A}$ and to the polarized Bjorken sum rule $S_\text{Bjp}$
are presented. One of them gives the additional confirmation of the correctness
of the advanced analytical computer calculations of order $\alpha_s^4$
contributions to $D^{NS}_{A}$ and $S_\text{Bjp}$ in the general $SU(N_c)$ gauge
group.


  In this PhD thesis we analyze the medium modification of the pi-omega-rho
coupling and subsequently discuss its possible influence on the dilepton
production rate in relativistic heavy-ion collisions. The first part of the
thesis is devoted to the medium modifications of the Dalitz decays from the
omega and rho mesons in nuclear matter. We use the relativistic field theory
formalism describing modifications of the coupling by one-loop Feynman diagrams
with nucleons and Delta(1232) isobars. We consider cases when the decaying
particle is at rest or at motion with respect to the medium. We investigate the
dependence of medium effects on the dilepton invariant mass and observe a
sizeable increase of the effective coupling constants compared to their vacuum
values. The effect grows with density. In the second part of the thesis we
apply our model to evaluate the influence of the medium effects on the dilepton
production from the Dalitz decays. In the calculations of the dilepton spectrum
we use the model of the hydrodynamic expansion of the fire cylinder. In our
comparison to the CERES dilepton data we take into account the experimental
cuts. The medium modifications enhance the effect of the Dalitz decays. It is
worth to point out that in the medium the rho decay due to the isospin
degeneracy becomes as important as the omega decay. The main new and original
results of the thesis are: 1. Significant in-medium increase of the
pi-omega-rho coupling constant. 2. Large enhancement of the Dalitz decays from
the omega and rho mesons in the range 0.2-0.6 GeV of the dilepton invariant
mass.


  We study the volume of the intersection of two unit balls from one of the
classical matrix ensembles GOE, GUE and GSE, as the dimension tends to
infinity. This can be regarded as a matrix analogue of a result of Schechtman
and Schmuckenschl\"ager for classical $\ell_p$-balls [Schechtman and
Schmuckenschl\"ager, GAFA Lecture Notes, 1991]. The proof of our result is
based on two ingredients, which are of independent interest. The first one is a
weak law of large numbers for a point chosen uniformly at random in the unit
ball of such a matrix ensemble. The second one is an explicit computation of
the asymptotic volume of such matrix unit balls, which in turn is based on the
theory of logarithmic potentials with external fields.


  Sharpness-aware minimization (SAM) was proposed to reduce sharpness of minima
and has been shown to enhance generalization performance in various settings.
In this work we show that perturbing only the affine normalization parameters
(typically comprising 0.1% of the total parameters) in the adversarial step of
SAM can outperform perturbing all of the parameters.This finding generalizes to
different SAM variants and both ResNet (Batch Normalization) and Vision
Transformer (Layer Normalization) architectures. We consider alternative sparse
perturbation approaches and find that these do not achieve similar performance
enhancement at such extreme sparsity levels, showing that this behaviour is
unique to the normalization layers. Although our findings reaffirm the
effectiveness of SAM in improving generalization performance, they cast doubt
on whether this is solely caused by reduced sharpness.


  The observation of long-lived particles at the LHC would reveal physics
beyond the Standard Model, could account for the many open issues in our
understanding of our universe, and conceivably point to a more complete theory
of the fundamental interactions. Such long-lived particle signatures are
fundamentally motivated and can appear in virtually every theoretical construct
that address the Hierarchy Problem, Dark Matter, Neutrino Masses and the Baryon
Asymmetry of the Universe. We describe in this document a large detector,
MATHUSLA, located on the surface above an HL-LHC $pp$ interaction point, that
could observe long-lived particles with lifetimes up to the Big Bang
Nucleosynthesis limit of 0.1 s. We also note that its large detector area
allows MATHUSLA to make important contributions to cosmic ray physics. Because
of the potential for making a major breakthrough in our conceptual
understanding of the universe, long-lived particle searches should have the
highest level of priority.


  Relaying can improve the coverage and performance of wireless access
networks. In presence of a localisation system at the mobile nodes, the use of
such location estimates for relay node selection can be advantageous as such
information can be collected by access points in linear effort with respect to
number of mobile nodes (while the number of links grows quadratically).
However, the localisation error and the chosen update rate of location
information in conjunction with the mobility model affect the performance of
such location-based relay schemes; these parameters also need to be taken into
account in the design of optimal policies. This paper develops a Markov model
that can capture the joint impact of localisation errors and inaccuracies of
location information due to forwarding delays and mobility; the Markov model is
used to develop algorithms to determine optimal location-based relay policies
that take the aforementioned factors into account. The model is subsequently
used to analyse the impact of deployment parameter choices on the performance
of location-based relaying in WLAN scenarios with free-space propagation
conditions and in an measurement-based indoor office scenario.


  Nematic polymer networks (NPNs) are nematic elastomers within which the
nematic director is enslaved to the elastic deformation. The elastic free
energy of a NPN sheet of thickness $h$ has both stretching and bending
components (the former scaling like h, the latter scaling like $h^3$). NPN
sheets bear a director field $\mathbf{m}$ imprinted in them (usually, uniformly
throughout their thickness); they can be activated by changing the nematic
order (e.g. by illumination or heating). This paper illustrates an attempt to
compute the bending energy of a NPN sheet and to show which role it can play in
determining the activated shape. Our approach is approximate: the activated
surface consists of flat sectors connected by ridges, where the unit normal
jumps and the bending energy is concentrated. By increasing the number of
ridges, we should get closer to the real situation, where the activated surface
is smooth and the bending energy is distributed on it. The method is applied to
a disk with imprinted a spiraling hedgehog. It is shown that upon activation
the disk, like a tiny hand, is able to grab a rigid lamina.


  In this paper we review and extend our earlier recent work on thermostated
systems. A description of nano-biological systems by Markov chains in
coordinate space in the strongly overdamped limit is presented.
Characterization of the most probable path is given and a new formula for the
probability of this special path is provided from recursion formulae. The
deterministic limit is derived and the significance of Lagrange multipliers
introduced when constructing the most probable path is elucidated. The
characterization of the generation of path entropy by the most probable path is
given an equivalent interpretation relating to the rate of entropy production
by the most probable path. The paper concludes with an account of the
biological implications. Here we address why the origin of life and its
subsequent evolution took place, not the particular chemical details of how it
happened.


  A nonhydrostatic dynamical core has been developed by using the multi-moment
finite volume method that ensures the rigorous numerical conservation. To
represent the spherical geometry free of polar problems, the cubed-sphere grid
is adopted. A fourth-order multi-moment discretization formulation is applied
to solve the governing equations cast in the local curvilinear coordinates on
each patch of cubed sphere through a gnomonic projection. In vertical
direction, the height-based terrain-following grid is used to deal with the
topography and a conservative finite difference scheme is adopted for the
spatial discretization. The dynamical core adopts the nonhydrostatic governing
equations. To get around the CFL stability restriction imposed by sound wave
propagation and relatively small grid spacing in the vertical direction, the
dimensional-splitting time integration algorithm using the HEVI
(horizontally-explicit and vertically-implicit) strategy is implemented by
applying the IMEX (implicit-explicit) Runge-Kutta method. The proposed model
was checked by the widely-used benchmark tests in this study. The numerical
results show that the multi-moment model has superior solution quality and
great practical potential as a numerical platform for development of the
atmospheric general circulation models.


  We consider the viability of dark energy (DE) models in the framework of the
scalar-tensor theory of gravity, including the possibility to have a phantom DE
at small redshifts $z$ as admitted by supernova luminosity-distance data. For
small $z$, the generic solution for these models is constructed in the form of
a power series in $z$ without any approximation. Necessary constraints for DE
to be phantom today and to cross the phantom divide line $p=-\rho$ at small $z$
are presented. Considering the Solar System constraints, we find for the
post-Newtonian parameters that $\gamma_{PN}<1$ and $\gamma_{PN,0}\approx 1$ for
the model to be viable, and $\beta_{PN,0}>1$ (but very close to 1) if the model
has a significantly phantom DE today. However, prospects to establish the
phantom behaviour of DE are much better with cosmological data than with Solar
System experiments. Earlier obtained results for a $\Lambda$-dominated universe
with the vanishing scalar field potential are extended to a more general DE
equation of state confirming that the cosmological evolution of these models
rule them out. Models of currently fantom DE which are viable for small $z$ can
be easily constructed with a constant potential; however, they generically
become singular at some higher $z$. With a growing potential, viable models
exist up to an arbitrary high redshift.


  Origami has shown the potential to approximate three-dimensional curved
surfaces by folding through designed crease patterns on flat materials. The
Miura-ori tessellation is a widely used pattern in engineering and tiles the
plane when partially folded. Based on constrained optimization, this paper
presents the construction of generalized Miura-ori patterns that can
approximate three-dimensional parametric surfaces of varying curvatures while
preserving the inherent properties of the standard Miura-ori, including
developability, flat-foldability and rigid-foldability. An initial
configuration is constructed by tiling the target surface with triangulated
Miura-like unit cells and used as the initial guess for the optimization. For
approximation of a single target surface, a portion of the vertexes on the one
side is attached to the target surface; for fitting of two target surfaces, a
portion of vertexes on the other side is also attached to the second target
surface. The parametric coordinates are adopted as the unknown variables for
the vertexes on the target surfaces whilst the Cartesian coordinates are the
unknowns for the other vertexes. The constructed generalized Miura-ori
tessellations can be rigidly folded from the flat state to the target state
with a single degree of freedom.


  The generation of large-scale urban layouts has garnered substantial interest
across various disciplines. Prior methods have utilized procedural generation
requiring manual rule coding or deep learning needing abundant data. However,
prior approaches have not considered the context-sensitive nature of urban
layout generation. Our approach addresses this gap by leveraging a canonical
graph representation for the entire city, which facilitates scalability and
captures the multi-layer semantics inherent in urban layouts. We introduce a
novel graph-based masked autoencoder (GMAE) for city-scale urban layout
generation. The method encodes attributed buildings, city blocks, communities
and cities into a unified graph structure, enabling self-supervised masked
training for graph autoencoder. Additionally, we employ scheduled iterative
sampling for 2.5D layout generation, prioritizing the generation of important
city blocks and buildings. Our approach achieves good realism, semantic
consistency, and correctness across the heterogeneous urban styles in 330 US
cities. Codes and datasets are released at https://github.com/Arking1995/COHO.


  In this paper we present quaternary and ternary routing tracks for FPGAs, and
their implementation in 28nm FDSOI technology. We discuss the transistor level
design of multi-valued repeaters, multiplexers and translators, and specific
features of FDSOI technology which make it possible. Next we compare the
multi-valued routing architectures with equivalent single driver two-valued
routing architectures. We show that for long tracks, it is possible to achieve
upto 3x reduction in dynamic switching energy, upto 2x reduction in routing
wire area and 10% reduction in area dedicated to routing resources. The
multi-valued tracks are slightly more susceptible to process variation. We
present a layout method for multivalued standard cells and determine the layout
overhead.We conclude with various usage scenarios of these tracks.


  Quantum cascade lasers (QCLs) are high-power coherent light sources in the
midinfrared and terahertz parts of the electromagnetic spectrum. They are
devices in which the electronic and lattice systems are far from equilibrium,
strongly coupled to one another, and the problem bridges disparate spatial
scales. We present our ongoing work on the multiphysics and multiscale
simulation of far-from-equilibrium transport of charge and heat in midinfrared
QCLs.


  Stochastic solutions provide new rigorous results for nonlinear PDE's and,
through its local non-grid nature, are a natural tool for parallel computation.
There are two different approaches for the construction of stochastic
solutions: MacKean's and superprocesses. However, when restricted to measures,
superprocesses can only be used to generate solutions for a limited class of
nonlinear PDE's. A new class of superprocesses, namely superprocesses on signed
measures and on distributions, is proposed to extend the stochastic solution
approach to a wider class of PDE's.


  We develop an effective generation of adversarial attacks on neural models
that output a sequence of probability distributions rather than a sequence of
single values. This setting includes the recently proposed deep probabilistic
autoregressive forecasting models that estimate the probability distribution of
a time series given its past and achieve state-of-the-art results in a diverse
set of application domains. The key technical challenge we address is
effectively differentiating through the Monte-Carlo estimation of statistics of
the joint distribution of the output sequence. Additionally, we extend prior
work on probabilistic forecasting to the Bayesian setting which allows
conditioning on future observations, instead of only on past observations. We
demonstrate that our approach can successfully generate attacks with small
input perturbations in two challenging tasks where robust decision making is
crucial: stock market trading and prediction of electricity consumption.


  The new water-soluble gold cluster Au146(pMBA)57, the structure of which has
been recently determined at sub-atomic resolution by Vergara et al. [1], is the
largest aqueous gold cluster ever structurally determined and likewise the
smallest cluster with a stacking fault. The core presents a twinned truncated
octahedron, while additional peripheral gold atoms follow a C2 rotational
symmetry. According to the usual counting rules of the superatom complex (SAC)
model, the compound attains a number of 92 SAC electrons if the overall net
charge is 3- (three additional electrons). As this is the number of electrons
required for a major shell closing, the question arises if Au146(pMBA)57 should
be regarded as a superatom complex. Starting from the experimental coordinates
we have analyzed the structure using density-functional theory. The optimized
(relaxed) structure retains all the connectivity of the experimental
coordinates, while removing much of its irregularities in interatomic
distances, thereby enhancing the C2-symmetry feature. Analyzing the
angular-momentum projected states, we show that, despite a small gap, the
electronic structure does not exhibit SAC model character. In addition, optical
absorption spectra are found to be relatively smooth compared to the example of
the Au144(SR)60 cluster. The Au146(SR)57 cluster does not derive its stability
from SAC character; it cannot be considered a superatom complex.


  In this paper we derive the Wiener-Hopf factorization for a finite-state
time-inhomogeneous Markov chain. To the best of our knowledge, this study is
the first attempt to investigate the Wiener-Hopf factorization for
time-inhomogeneous Markov chains. In this work we only deal with a special
class of time-inhomogeneous Markovian generators, namely piece-wise constant,
which allows to use an appropriately tailored randomization technique. Besides
the mathematical importance of the Wiener-Hopf factorization methodology, there
is also an important computational aspect: it allows for efficient computation
of important functionals of Markov chains.


  We consider surfaces with a double elliptic fibration, with two sections. We
study the orbits under the induced translation automorphisms proving that,
under natural conditions, the finite orbits are confined to a curve. This goes
in a similar direction of (and is motivated by) recent work by Cantat-Dujardin,
although we use very different methods and obtain related but different
results. As a sample of application of similar arguments, we prove a new case
of the Zilber-Pink conjecture, namely Theorem 1.5, for certain schemes over a
2-dimensional base, which was known to lead to substantial difficulties. Most
results rely, among other things, on recent theorems by Bakker and the second
author of `Ax-Schanuel Type'; we also relate a functional condition with a
theorem of Shioda on ramified sections of the Legendre scheme. For one of our
proofs, we also use recent height inequalities by Yuan-Zhang. Finally, in an
appendix, we show that the Relative Manin-Mumford Conjecture over the complex
number field is equivalent to its version over the field of algebraic numbers.


  We compare the discovery potential of the LHC for lepton number violating
(LNV) signals with the sensitivity of current and future double beta decay
experiments, assuming 0\nu\beta\beta decay is dominated by heavy particle
exchange. We consider charged scalar, leptoquark and diquark mechanisms of
0\nu\beta\beta-decay, covering the 0\nu\beta\beta-decay operators with both,
the smallest and largest, possible rates. We demonstrate, if
0\nu\beta\beta-decay were found with a half-life below $10^{26}-10^{27}$ ys a
positive signal should show up at the LHC, except for some particular cases of
the leptoquark mechanism, and vice versa, if the LHC does not find any hints
for LNV, a "short-range" explanation for a finite 0\nu\beta\beta-decay
half-life will be ruled out in most cases. We argue, if a positive LNV signal
were found at the LHC, it is possible to identify the dominant contribution to
0\nu\beta\beta. Two different kinds of observables which could provide such
"model discriminating" power are discussed: Different invariant mass peaks and
the charge asymmetry.


  Our peculiar motion with respect to the CMB rest frame represents a preferred
direction in the observed CMB sky since it induces an apparent deflection of
the observed CMB photons (aberration) and a shift in their frequency (Doppler).
Both effects distort the multipoles $a_{\ell m}$'s at all $\ell$'s. Such
effects are real as it has been recently measured for the first time by Planck
according to what was forecast in some recent papers. However, the common lore
when estimating a power spectrum from CMB is to consider that Doppler affects
only the $\ell=1$ multipole, neglecting any other corrections. In this work we
use simulations of the CMB sky in a boosted frame with a peculiar velocity
$\beta = v/c = 1.23 \times 10^{-3}$ in order to assess the impact of such
effect on power spectrum estimations in different regions of the sky. We show
that the boost induces a north-south asymmetry in the power spectrum which is
highly significant and non-negligible, of about (0.58 $\pm$ 0.10)% for half-sky
cuts when going up to $\ell$ = 2500. We suggest that these effects are relevant
and may account for some of the north-south asymmetries seen in the Planck
data, being especially important at small scales. Finally we analyze the
particular case of the ACT experiment, which observed only a small fraction of
the sky and show that it suffers a bias of about 1% on the power spectrum and
of similar size on some cosmological parameters: for example the position of
the peaks shifts by 0.5% and the overall amplitude of the spectrum is about
0.4% lower than a full-sky case.


  Recently, deep learning techniques have enjoyed success in various multimedia
applications, such as image classification and multi-modal data analysis. Large
deep learning models are developed for learning rich representations of complex
data. There are two challenges to overcome before deep learning can be widely
adopted in multimedia and other applications. One is usability, namely the
implementation of different models and training algorithms must be done by
non-experts without much effort especially when the model is large and complex.
The other is scalability, that is the deep learning system must be able to
provision for a huge demand of computing resources for training large models
with massive datasets. To address these two challenges, in this paper, we
design a distributed deep learning platform called SINGA which has an intuitive
programming model based on the common layer abstraction of deep learning
models. Good scalability is achieved through flexible distributed training
architecture and specific optimization techniques. SINGA runs on GPUs as well
as on CPUs, and we show that it outperforms many other state-of-the-art deep
learning systems. Our experience with developing and training deep learning
models for real-life multimedia applications in SINGA shows that the platform
is both usable and scalable.


  An automaton is history-deterministic if its nondeterminism can be resolved
on the fly, only using the prefix of the word read so far. This mild form of
nondeterminism has attracted particular attention for its applications in
synthesis problems. An automaton $A$ is guidable with respect to a class $C$ of
automata if it can fairly simulate every automaton in $C$ whose language is
contained in that of $A$. In other words, guidable automata are those for which
inclusion and simulation coincide, making them particularly interesting for
model-checking.
  We study the connection between these two notions, and specifically the
question of when they coincide. For classes of automata on which they do,
deciding guidability, an otherwise challenging decision problem, reduces to
deciding history-determinism, a problem that is starting to be well-understood
for many classes.
  We provide a selection of sufficient criteria for a class of automata to
guarantee the coincidence of the notions, and use them to show that the notions
coincide for the most common automata classes, among which are $\omega$-regular
automata and many infinite-state automata with safety and reachability
acceptance conditions, including vector addition systems with states,
one-counter nets, pushdown-, Parikh-, and timed-automata.
  We also demonstrate that history-determinism and guidability do not always
coincide, for example, for the classes of timed automata with a fixed number of
clocks.


  Numerical stability is a crucial requirement of reliable scientific
computing. However, despite the pervasiveness of Python in data science,
analyzing large Python programs remains challenging due to the lack of scalable
numerical analysis tools available for this language. To fill this gap, we
developed PyTracer, a profiler to quantify numerical instability in Python
applications. PyTracer transparently instruments Python code to produce
numerical traces and visualize them interactively in a Plotly dashboard. We
designed PyTracer to be agnostic to numerical noise model, allowing for tool
evaluation through Monte-Carlo Arithmetic, random rounding, random data
perturbation, or structured noise for a particular application. We illustrate
PyTracer's capabilities by testing the numerical stability of key functions in
both SciPy and Scikit-learn, two dominant Python libraries for mathematical
modeling. Through these evaluations, we demonstrate PyTracer as a scalable,
automatic, and generic framework for numerical profiling in Python.


  In this paper, we introduce polynomials (in $t$) of signed relative
derangements that track the number of signed elements. The polynomials are
clearly seen to be in a sense symmetric. Note that relative derangements are
those without any signed elements, i.e., the evaluations of the polynomials at
$t=0$. Also, the numbers of all signed relative derangements are given by the
evaluations at $t=1$. Then the coefficients of the polynomials connect unsigned
and signed relative derangements and show how putting elements with signs
affects the formation of derangements. We first prove a recursion satisfied by
these polynomials which results in a recursion satisfied by the coefficients. A
combinatorial proof of the latter is provided next. We also show that the
sequences of the coefficients are unimodal. Moreover, other results are
obtained. For instance, a kind of dual of a relation between signed
derangements and signed relative derangements previously proved by Chen and
Zhang is presented.


  Using the recently proposed ALPHA algorithm (and the resulting code) I
compute the rate (at tree level) for the process
$\gamma\gamma\rightarrow\bar\nu_e e^- u \bar d$. The bulk of the contribution
is due to W pair production and decay. However a non negligible ($\sim10 \%$)
contribution comes from other channels, mainly the production and decay of a W
and a collinear charged fermion. Requiring that the reconstructed invariant $u
\bar d$ mass lies in the intervals $M_W\pm 5 $ GeV and $M_W\pm 20 $ GeV one
obtains a rate which is lower, by 25 \% and 4 \% respectively, than the rate
obtained in the $narrow$ $width$ approximation, thus demonstrating the
relevance of the finite W width.


  Scalar dark matter can interact with Standard Model (SM) particles, altering
the fundamental constants of Nature in the process. Changes in the fundamental
constants during and prior to Big Bang nucleosynthesis (BBN) produce changes in
the primordial abundances of the light elements. By comparing the measured and
calculated (within the SM) primordial abundance of $^{4}$He, which is
predominantly determined by the ratio of the neutron-proton mass difference to
freeze-out temperature at the time of weak interaction freeze-out prior to BBN,
we are able to derive stringent constraints on the mass of a scalar dark matter
particle $\phi$ together with its interactions with the photon, light quarks
and massive vector bosons via quadratic couplings in $\phi$, as well as its
interactions with massive vector bosons via linear couplings in $\phi$. We also
derive a stringent constraint on the quadratic interaction of $\phi$ with the
photon from recent atomic dysprosium spectroscopy measurements.


  We examine critically how tightly the density dependence of nuclear symmetry
energy \esym is constrained by the universal equation of state (EOS) of the
unitary Fermi gas $E_{\rm{UG}}(\rho)$ considering currently known uncertainties
of higher order parameters describing the density dependence of the Equation of
State of isospin-asymmetric nuclear matter. We found that $E_{\rm{UG}}(\rho)$
does provide a useful lower boundary for the \esym. However, it does not
tightly constrain the correlation between the magnitude $E_{\rm{sym}}(\rho_0)$
and slope $L$ unless the curvature $K_{\rm{sym}}$ of the symmetry energy at
saturation density $\rho_0$ is more precisely known. The large uncertainty in
the skewness parameters affects the $E_{\rm{sym}}(\rho_0)$ versus $L$
correlation by the same almost as significantly as the uncertainty in
$K_{\rm{sym}}$.


  We consider three a priori totally different setups for Hopf algebras from
number theory, mathematical physics and algebraic topology. These are the Hopf
algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for
renormalization, and a Hopf algebra constructed by Baues to study double loop
spaces. We show that these examples can be successively unified by considering
simplicial objects, co-operads with multiplication and Feynman categories at
the ultimate level. These considerations open the door to new constructions and
reinterpretations of known constructions in a large common framework which is
presented step-by-step with examples throughout. In this second part of two
papers, we give the general categorical formulation.


  We construct finite size, supersymmetric, tubular D-brane configurations with
three charges, two angular momenta and several brane dipole moments. In type
IIA string theory these are tubular configurations with D0, D4 and F1 charge,
as well as D2, D6 and NS5 dipole moments. These multi-charge generalizations of
supertubes might have interesting consequences for the physics of the D1-D5-P
black hole. We study the relation of the tubes to the spinning BMPV black hole,
and find that they have properties consistent with describing some of the hair
of this black hole.


  Context: The internal rotation of the Sun constitutes a fundamental
constraint when modelling angular momentum transport in stellar interiors. In
addition to the more external regions of the solar radiative zone probed by
pressure modes, measurements of rotational splittings of gravity modes would
offer an invaluable constraint on the rotation of the solar core. Aims: We
study the constraints that a measurement of the core rotation rate of the Sun
could bring on magnetic angular momentum transport in stellar radiative zones.
Results: We first show that models computed with angular momentum transport by
magnetic instabilities and a recent prescription for the braking of the stellar
surface by magnetized winds can reproduce the observations of surface
velocities of stars in open clusters. These solar models predict both a flat
rotation profile in the external part of the solar radiative zone probed by
pressure modes and an increase in the rotation rate in the solar core, where
the stabilizing effect of chemical gradients plays a key role. A rapid rotation
of the core of the Sun, as suggested by reported detections of gravity modes,
is thus found to be compatible with angular momentum transport by magnetic
instabilities. Moreover, we show that the efficiency of magnetic angular
momentum transport in regions of strong chemical gradients can be calibrated by
the solar core rotation rate independently from the unknown rotational history
of the Sun. In particular, we find that a recent revised prescription for the
transport of angular momentum by the Tayler instability can be easily
distinguished from the original Tayler-Spruit dynamo, with a faster rotating
solar core supporting the original prescription.


  The adsorption and self-assembly of vanadyl phthalocyanine molecules on
Ag(100) has been investigated using a combination of scanning tunneling
microscopy and density functional theory. At sub-monolayer coverage, we observe
two distinct adsorption configurations of isolated molecules, corresponding to
the central O atom pointing toward (O-down) or away (O-up) from the substrate.
Upon adsorption in the O-up orientation, the otherwise achiral molecules take
on a windmill-like chiral appearance due to their interaction with the
substrate. At monolayer coverage, we observe a self-assembled square lattice
with a mixture of O-up and O-down molecules. At higher coverage we find a
strong preference for bilayer formation with O-up and O-down molecules in
alternating layers, suggesting stabilization by dipolar interactions. Close
inspection of the multi-layer surface reveals grain boundaries separating
domains of opposite organizational chirality, and long-range ordering.


  In this paper, we focus on the problem of item matching using only the
description. Those specific items not only lack a unique code but also contain
short text descriptions, making the item matching process difficult. Our goal
is to compare products using only the description provided by the purchase
process. Therefore, evaluating other characteristics and differences can
uncover possible flaws during the acquiring phase. However, the text of the
items that we were working on was very small, with numbers due to the nature of
the products and we have a limited amount of time to develop the solution which
was 8 weeks. As result, we showed that working using a well-oriented
methodology we were able to deliver a successful MVP and achieve the results
expected with up to 55% match.


  We show that much of the structure of the 2-sphere as a complex curve
survives the q-deformation and has natural generalizations to the quantum
2-sphere - which, with additional structures, we identify with the quantum
projective line. Notably among these is the identification of a quantum
homogeneous coordinate ring with the coordinate ring of the quantum plane. In
parallel with the fact that positive Hochschild cocycles on the algebra of
smooth functions on a compact oriented 2-dimensional manifold encode the
information for complex structures on the surface, we formulate a notion of
twisted positivity for twisted Hochschild and cyclic cocycles and exhibit an
explicit twisted positive Hochschild cocycle for the complex structure on the
sphere.


  Let $F$ be a number field. Let $p$ be a prime number. Washington proved the
$\ell$-part of the class numbers in cyclotomic $\mathbb{Z}_p$ extension of $F$
is bounded when $F$ is an abelian number field and $\ell\neq p$ is a prime. By
class number formula, this is essentially a mod $\ell$ nonvanishing property of
Drichlet L-functions at $s=0$. In \cite{Sinnot}, Sinnot gave a different proof
by algebraic methods. In this article, we show that Sinnot's method can prove
nonvanishing properties of Drichlet L-functions at $s=-k$, where $k\geq 0$ is
an integer. Since the Lichtenbaurn conjecture which relates the Dedekind zeta
functions at $s=-k$ and higher K-groups is proved for abelian number fields, we
give some bounded results on non-$p$ part of higher K-groups in cyclotomic
$\mathbb{Z}_p$ extensions of a real abelian number field.


  Motivated by the problem of colocalization analysis in fluorescence
microscopic imaging, we study in this paper structured detection of correlated
regions between two random processes observed on a common domain. We argue that
although intuitive, direct use of the maximum log-likelihood statistic suffers
from potential bias and substantially reduced power, and introduce a simple
size-based normalization to overcome this problem. We show that scanning with
the proposed size-corrected likelihood ratio statistics leads to optimal
correlation detection over a large collection of structured correlation
detection problems.


  In this paper, we have shown the improvement of English to Bharti Braille
machine translation system. We have shown how we can improve a baseline NMT
model by adding some linguistic knowledge to it. This was done for five
language pairs where English sentences were translated into five Indian
languages and then subsequently to corresponding Bharti Braille. This has been
demonstrated by adding a sub-module for translating multi-word expressions. The
approach shows promising results as across language pairs, we could see
improvement in the quality of NMT outputs. The least improvement was observed
in English-Nepali language pair with 22.08% and the most improvement was
observed in the English-Hindi language pair with 23.30%.


  We study weak anti-localization (WAL) effect in topological insulator Bi2Te3
thin films at low temperatures. Two-dimensional WAL effect associated with
surface carriers is revealed in the tilted magnetic field dependence of
magneto-conductance. Our data demonstrates that the observed WAL is robust
against deposition of non-magnetic Au impurities on the surface of the thin
films. But it is quenched by deposition of magnetic Fe impurities which destroy
the pi Berry's phase of the topological surface states. The magneto-conductance
data of a 5 nm Bi2Te3 film suggests that a crossover from symplectic to unitary
classes is observed with the deposition of Fe impurities.


  Whether or not space-time is fundamentally discrete is of central importance
for the development of the theory of quantum gravity. If the fundamental
description of space-time is discrete, typically represented in terms of a
graph or network, then the apparent smoothness of geometry on large scales
should be imperfect -- it should have defects. Here, we review a model for
space-time defects and summarize the constraints on the prevalence of these
defects that can be derived from observation.


  We propose a method of testing source evolution theories that is independent
of the effects of inhomogeneity, and thus complementary to other studies of
evolution. It is suitable for large scale sky surveys, and the new generation
of large telescopes.
  In an earlier paper it was shown that basic cosmological observations -
luminosity versus redshift, area distance versus redshift and number counts
versus redshift - cannot separate the effects of cosmic inhomogeneity, cosmic
evolution and source evolution. We here investigate multicolour observations,
and show that by comparing luminosity versus redshift in two or more colours,
contraints can be placed on source evolution even if unknown source evolution
is present, providing an important test of evolution theories that is
complementary to present methods. However, number counts in different colours
versus redshift are not useful in separating the effects of source evolution
and inhomogeneity.


  The geometric form of standard quantum mechanics is compatible with the two
postulates: 1) The laws of physics are invariant under the choice of
experimental setup and 2) Every quantum observation or event is intrinsically
statistical. These postulates remain compatible within a background independent
extension of quantum theory with a local intrinsic time implying the relativity
of the concept of a quantum event. In this extension the space of quantum
events becomes dynamical and only individual quantum events make sense
observationally. At the core of such a general theory of quantum relativity is
the three-way interplay between the symplectic form, the dynamical metric and
non-integrable almost complex structure of the space of quantum events. Such a
formulation provides a missing conceptual ingredient in the search for a
background independent quantum theory of gravity and matter. The crucial new
technical element in our scheme derives from a set of recent mathematical
results on certain infinite dimensional almost Kahler manifolds which replace
the complex projective spaces of standard quantum mechanics.


  Birman--Murakami--Wenzl (BMW) algebra was introduced in connection with knot
theory. We treat here interaction round the face solvable (IRF) lattice models.
We assume that the face transfer matrix obeys a cubic polynomial equation,
which is called the three block case. We prove that the three block theories
all obey the BMW algebra. We exemplify this result by treating in detail the
$SU(2)$ $2\times 2$ fused models, and showing explicitly the BMW structure. We
use the connection between the construction of solvable lattice models and
conformal field theory. This result is important to the solution of IRF lattice
models and the development of new models, as well as to knot theory.


  The oxygen (O/H) and N/O abundance ratios along the bar of 16 barred spiral
starburst galaxies are determined using long-slit spectroscopy. The abundance
gradients and the spatial distribution of the ionized gas along the bar are
used to understand the role of bars in starburst galaxies.
  The oxygen abundance gradients are steeper than in normal barred galaxies,
while the intersects are low. This excludes the possibility that these are
chemically evolved galaxies rejuvenated by the effect of a bar. The
nitrogen-to-oxygen abundance gradients are flatter than the oxygen ones. But
N/O intersects are high, which rules out the possibility that a large quantity
of gas was recently funneled by a bar toward the center of a young galaxy.
Bars, therefore, cannot be at the origin of the bursts in the nuclei of our
sample galaxies.
  The oxygen and N/O abundance gradients are generally stronger in the bar than
in the disk and are linked together by a linear relation. This can be fully
explained in terms of star formation history: the gradients build up from the
inside out, becoming stronger as the oxygen and N/O abundances increase in the
bulge while staying low in the disk.
  In many of the sample galaxies, star formation occurs at one or both ends of
the bar. The low level of chemical enrichment in these regions suggests that
they recently experienced bar-triggered star formation: this is the only
visible effect of bars. Our analysis shows that bars probably appeared very
recently (a few 10^7 years) in the starburst galaxies, which are relatively
"young" galaxies still in the process of formation.(Abridged)


  For a 1-tough graph $G$ we define $\sigma_3(G) = \min\{\deg(u) + \deg(v)+
\deg(w):$ $\{u, v, w\}$ is an independent set of vertices$\}$ and $NC2(G)=\min
\{|N(u)\cup N(v)|: d(u,v)=2\}$. D. Bauer, G. Fan and H.J.Veldman proved that
$c(G)\geq \min\{n,2NC2(G)\}$ for any 1-tough graph $G$ with $\sigma_3(G)\geq
n\geq 3$, where $c(G)$ is the circumference of $G$ (D. Bauer, G. Fan and
H.J.Veldman,Hamiltonian properties of graphs with large neighborhood
unions,Discrete Mathematics, 1991). They also conjectured a stronger upper
bound for the circumference: $c(G)\geq\min\{n,2NC2(G)+4\}$.In this paper, we
prove this conjecture.


  This article studies how to form CUR decompositions of low-rank matrices via
primarily random sampling, though deterministic methods due to previous works
are illustrated as well. The primary problem is to determine when a column
submatrix of a rank $k$ matrix also has rank $k$. For random column sampling
schemes, there is typically a tradeoff between the number of columns needed to
be chosen and the complexity of determining the sampling probabilities. We
discuss several sampling methods and their complexities as well as stability of
the method under perturbations of both the probabilities and the underlying
matrix. As an application, we give a high probability guarantee of the exact
solution of the Subspace Clustering Problem via CUR decompositions when columns
are sampled according to their Euclidean lengths.