  In the quantum statistical parton distributions approach proposed more than
one decade ago, one imposes relations between quarks and antiquarks
expressions, which lead to very specific properties for the antiquarks. These
properties have been verified up to now by recent data and it is a real
challenge also for forthcoming experimental results, mainly in the high $x$
region.


  Our work is at the crossroads of two categories of technologies. On the one
hand, omnichannel digit services, to address the needs of users in the most
seamless way. On the other hand, low code approaches, to build simply even
complex software applications. In this twofold context, we propose DSUL
(Digital Service Universal Language). It allows to build omnichannel services
with minimal work from their designers. We describe precisely how DSUL
operates, and its innovation in regard to the state of the art. We also
consider the various methods to evaluate this framework.


  The counter-rotation phenomenon in disc galaxies directly indicates a complex
galaxy assembly history which is crucial for our understanding of galaxy
physics. Here we present the complex data analysis for a lenticular galaxy NGC
448, which has been recently suspected to host a counter-rotating stellar
component. We collected deep long-slit spectroscopic observations using the
Russian 6-m telescope and performed the photometric decomposition of Sloan
Digital Sky Survey (SDSS) archival images. We exploited (i) a non-parametric
approach in order to recover stellar line-of-sight velocity distributions and
(ii) a parametric spectral decomposition technique in order to disentangle
stellar population properties of both main and counter-rotating stellar discs.
Our spectral decomposition stays in perfect agreement with the photometric
analysis. The counter-rotating component contributes $\approx$30 per cent to
the total galaxy light. We estimated its stellar mass to be
$9.0^{+2.7}_{-1.8}\cdot10^{9}M_\odot$. The radial scale length of
counter-rotating disc is $\approx$3 times smaller than that of the main disc.
Both discs harbour old stars but the counter-rotating components reveals a
detectable negative age gradient that might suggest an extended inside-out
formation during $3\dots4$ Gyrs. The counter-rotating disc hosts more
metal-rich stars and possesses a shallower metallicity gradient with respect to
the main disc. Our findings rule out cosmological filaments as a source of
external accretion which is considered as a potential mechanism of the
counter-rotating component formation in NGC 448, and favour the satellite
merger event with the consequent slow gas accretion.


  The concept of Virtual Monte Carlo (VMC) has been developed by the ALICE
Software Project to allow different Monte Carlo simulation programs to run
without changing the user code, such as the geometry definition, the detector
response simulation or input and output formats. Recently, the VMC classes have
been integrated into the ROOT framework, and the other relevant packages have
been separated from the AliRoot framework and can be used individually by any
other HEP project. The general concept of the VMC and its set of base classes
provided in ROOT will be presented. Existing implementations for Geant3, Geant4
and FLUKA and simple examples of usage will be described.


  Recently, there are increasing interests in inferring mirco-expression from
facial image sequences. Due to subtle facial movement of micro-expressions,
feature extraction has become an important and critical issue for spontaneous
facial micro-expression recognition. Recent works usually used spatiotemporal
local binary pattern for micro-expression analysis. However, the commonly used
spatiotemporal local binary pattern considers dynamic texture information to
represent face images while misses the shape attribute of face images. On the
other hand, their works extracted the spatiotemporal features from the global
face regions, which ignore the discriminative information between two
micro-expression classes. The above-mentioned problems seriously limit the
application of spatiotemporal local binary pattern on micro-expression
recognition. In this paper, we propose a discriminative spatiotemporal local
binary pattern based on an improved integral projection to resolve the problems
of spatiotemporal local binary pattern for micro-expression recognition.
Firstly, we develop an improved integral projection for preserving the shape
attribute of micro-expressions. Furthermore, an improved integral projection is
incorporated with local binary pattern operators across spatial and temporal
domains. Specifically, we extract the novel spatiotemporal features
incorporating shape attributes into spatiotemporal texture features. For
increasing the discrimination of micro-expressions, we propose a new feature
selection based on Laplacian method to extract the discriminative information
for facial micro-expression recognition. Intensive experiments are conducted on
three availably published micro-expression databases. We compare our method
with the state-of-the-art algorithms. Experimental results demonstrate that our
proposed method achieves promising performance for micro-expression
recognition.


  While many languages possess processes of joining two or more words to create
compound words, previous studies have been typically limited only to languages
with excessively productive compound formation (e.g., German, Dutch) and there
is no public dataset containing compound and non-compound words across a large
number of languages. In this work, we systematically study decompounding, the
task of splitting compound words into their constituents, at a wide scale. We
first address the data gap by introducing a dataset of 255k compound and
non-compound words across 56 diverse languages obtained from Wiktionary. We
then use this dataset to evaluate an array of Large Language Models (LLMs) on
the decompounding task. We find that LLMs perform poorly, especially on words
which are tokenized unfavorably by subword tokenization. We thus introduce a
novel methodology to train dedicated models for decompounding. The proposed
two-stage procedure relies on a fully self-supervised objective in the first
stage, while the second, supervised learning stage optionally fine-tunes the
model on the annotated Wiktionary data. Our self-supervised models outperform
the prior best unsupervised decompounding models by 13.9% accuracy on average.
Our fine-tuned models outperform all prior (language-specific) decompounding
tools. Furthermore, we use our models to leverage decompounding during the
creation of a subword tokenizer, which we refer to as CompoundPiece.
CompoundPiece tokenizes compound words more favorably on average, leading to
improved performance on decompounding over an otherwise equivalent model using
SentencePiece tokenization.


  In this paper, we give a complete topological and smooth classification of
non-invertible Anosov maps on torus. We show that two non-invertible Anosov
maps on torus are topologically conjugate if and only if their corresponding
periodic points have the same Lyapunov exponents on the stable bundles. As a
corollary, if two $C^r$ non-invertible Anosov maps on torus are topologically
conjugate, then the conjugacy is $C^r$-smooth along the stable foliation.
Moreover, we show that the smooth conjugacy class of a non-invertible Anosov
map on torus is completely determined by the Jacobians of return maps at
periodic points.


  In this paper, we consider the problem of sequentially optimizing a black-box
function $f$ based on noisy samples and bandit feedback. We assume that $f$ is
smooth in the sense of having a bounded norm in some reproducing kernel Hilbert
space (RKHS), yielding a commonly-considered non-Bayesian form of Gaussian
process bandit optimization. We provide algorithm-independent lower bounds on
the simple regret, measuring the suboptimality of a single point reported after
$T$ rounds, and on the cumulative regret, measuring the sum of regrets over the
$T$ chosen points. For the isotropic squared-exponential kernel in $d$
dimensions, we find that an average simple regret of $\epsilon$ requires $T =
\Omega\big(\frac{1}{\epsilon^2} (\log\frac{1}{\epsilon})^{d/2}\big)$, and the
average cumulative regret is at least $\Omega\big( \sqrt{T(\log T)^{d/2}}
\big)$, thus matching existing upper bounds up to the replacement of $d/2$ by
$2d+O(1)$ in both cases. For the Mat\'ern-$\nu$ kernel, we give analogous
bounds of the form $\Omega\big( (\frac{1}{\epsilon})^{2+d/\nu}\big)$ and
$\Omega\big( T^{\frac{\nu + d}{2\nu + d}} \big)$, and discuss the resulting
gaps to the existing upper bounds.


  Multimodal sentiment analysis is an important research area that predicts
speaker's sentiment tendency through features extracted from textual, visual
and acoustic modalities. The central challenge is the fusion method of the
multimodal information. A variety of fusion methods have been proposed, but few
of them adopt end-to-end translation models to mine the subtle correlation
between modalities. Enlightened by recent success of Transformer in the area of
machine translation, we propose a new fusion method, TransModality, to address
the task of multimodal sentiment analysis. We assume that translation between
modalities contributes to a better joint representation of speaker's utterance.
With Transformer, the learned features embody the information both from the
source modality and the target modality. We validate our model on multiple
multimodal datasets: CMU-MOSI, MELD, IEMOCAP. The experiments show that our
proposed method achieves the state-of-the-art performance.


  Certain concrete "ontological models" for quantum mechanics (models in which
measurement outcomes are deterministic and quantum states are equivalent to
classical probability distributions over some space of `hidden variables') are
examined. The models are generalizations of Kochen and Specker's such model for
a single 2-dimensional system - in particular a model for a three dimensional
quantum system is considered in detail. Unfortunately, it appears the models do
not quite reproduce the quantum mechanical statistics. They do, however, come
close to doing so, and in as much as they simply involve probability
distributions over the complex projective space they do reproduce pretty much
everything else in quantum mechanics.
  The Kochen-Specker theorem is examined in the light of these models, and the
rather mild nature of the manifested contextuality is discussed.


  Generating accurate 3D models is a challenging problem that traditionally
requires explicit learning from 3D datasets using supervised learning. Although
recent advances have shown promise in learning 3D models from 2D images, these
methods often rely on well-structured datasets with multi-view images of each
instance or camera pose information. Furthermore, these datasets usually
contain clean backgrounds with simple shapes, making them expensive to acquire
and hard to generalize, which limits the applicability of these methods. To
overcome these limitations, we propose a method for reconstructing 3D geometry
from the diverse and unstructured Imagenet dataset without camera pose
information. We use an efficient triplane representation to learn 3D models
from 2D images and modify the architecture of the generator backbone based on
StyleGAN2 to adapt to the highly diverse dataset. To prevent mode collapse and
improve the training stability on diverse data, we propose to use multi-view
discrimination. The trained generator can produce class-conditional 3D models
as well as renderings from arbitrary viewpoints. The class-conditional
generation results demonstrate significant improvement over the current
state-of-the-art method. Additionally, using PTI, we can efficiently
reconstruct the whole 3D geometry from single-view images.


  This paper introduces new parameterizations of equilibrium neural networks,
i.e. networks defined by implicit equations. This model class includes standard
multilayer and residual networks as special cases. The new parameterization
admits a Lipschitz bound during training via unconstrained optimization: no
projections or barrier functions are required. Lipschitz bounds are a common
proxy for robustness and appear in many generalization bounds. Furthermore,
compared to previous works we show well-posedness (existence of solutions)
under less restrictive conditions on the network weights and more natural
assumptions on the activation functions: that they are monotone and slope
restricted. These results are proved by establishing novel connections with
convex optimization, operator splitting on non-Euclidean spaces, and
contracting neural ODEs. In image classification experiments we show that the
Lipschitz bounds are very accurate and improve robustness to adversarial
attacks.


  Motivated by the recent experimental observations of the DNA loop extrusion
by protein motors, in this paper we investigate the statistical properties of
the growing polymer loops within the ideal chain model. The loop conformation
is characterized statistically by the mean gyration radius and the pairwise
contact probabilities. It turns out that a single dimensionless parameter,
which is given by the ratio of the loop relaxation time over the time elapsed
since the start of extrusion, controls the crossover between near-equilibrium
and highly non-equilibrium asymptotics in statistics of the extruded loop.
Besides, we show that two-sided and one-sided loop extruding motors produce the
loops with almost identical properties. Our predictions are based on two
rigorous semi-analytical methods accompanied by asymptotic analysis of slow and
fast extrusion limits.


  Computational virtual high-throughput screening (VHTS) with density
functional theory (DFT) and machine-learning (ML)-acceleration is essential in
rapid materials discovery. By necessity, efficient DFT-based workflows are
carried out with a single density functional approximation (DFA). Nevertheless,
properties evaluated with different DFAs can be expected to disagree for the
cases with challenging electronic structure (e.g., open shell transition metal
complexes, TMCs) for which rapid screening is most needed and accurate
benchmarks are often unavailable. To quantify the effect of DFA bias, we
introduce an approach to rapidly obtain property predictions from 23
representative DFAs spanning multiple families and "rungs" (e.g., semi-local to
double hybrid) and basis sets on over 2,000 TMCs. Although computed properties
(e.g., spin-state ordering and frontier orbital gap) naturally differ by DFA,
high linear correlations persist across all DFAs. We train independent ML
models for each DFA and observe convergent trends in feature importance; these
features thus provide DFA-invariant, universal design rules. We devise a
strategy to train ML models informed by all 23 DFAs and use them to predict
properties (e.g., spin-splitting energy) of over 182k TMCs. By requiring
consensus of the ANN-predicted DFA properties, we improve correspondence of
these computational lead compounds with literature-mined, experimental
compounds over the single-DFA approach typically employed. Both feature
analysis and consensus-based ML provide efficient, alternative paths to
overcome accuracy limitations of practical DFT.


  We analyze the time series of Ca II H-line obtained from Hinode/SOT on the
solar limb. We follow three cases of upwardly propagating kink waves along a
spicule and inverted Y-shaped structures at the cusp of it. The time-distance
analysis shows that the axis of spicule undergoes quasi-periodic transverse
displacement at different heights from the photosphere. The mean period of
transverse displacement is ~ 175 s and the mean amplitude is 1 arc\,sec. The
oscillation periods are increasing linearly with height which may be counted as
the signature that the spicule is working as a low pass filter and allows only
the low frequencies to propagate towards higher heights. The oscillations
amplitude is increasing with height due to decrease in density. The phase
speeds are increasing until some heights and then decreasing which may be
related to the small scale reconnection at the spicule basis. We conclude that
transversal displacement of spicules axis can be related to the propagation of
kink waves along them. Moreover, we observe signatures of small-scale magnetic
reconnection at the cusp of spicules which may excite kink waves.


  The observation of the Hong-Ou-Mandel (HOM)-type two-photon interference
(TPI) has played an important role in the development of photonic quantum
technologies. The time-resolved coincidence-detection technique has been
effectively used to identify and characterize the TPI phenomena of
long-coherence optical fields. Here, we report on the experimental
demonstration of the TPI of two phase-randomized weak coherent pulses with
time-resolved coincidence detection. The mutual coherence time between the two
weak coherent lights is determined by applying a frequency noise to one of the
two interfering lights. We analyze the HOM-type TPI-fringe visibility according
to the ratio of the coherence time to the pulse duration.


  In two recent papers we explored the modifications to primordial black hole
physics when one moves to the simplest braneworld model, Randall--Sundrum type
II. Both the evaporation law and the cosmological evolution of the population
can be modified, and additionally accretion of energy from the background can
be dominant over evaporation at high energies. In this paper we present a
detailed study of how this impacts upon various astrophysical constraints,
analyzing constraints from the present density, from the present high-energy
photon background radiation, from distortion of the microwave background
spectrum, and from processes affecting light element abundances both during and
after nucleosynthesis. Typically, the constraints on the formation rate of
primordial black holes weaken as compared to the standard cosmology if black
hole accretion is unimportant at high energies, but can be strengthened in the
case of efficient accretion.


  On the occasion of the 70th birthday of Prof. Adriano Di Giacomo we report on
recent numerical computations of the Landau gauge gluon and ghost propagators
as well as of a non-symmetric MOM-scheme ghost-gluon vertex in quenched and
full lattice QCD. Special emphasis is paid to the Gribov copy problem and to
the unquenching effect. The corresponding running coupling \alpha_s(q^2) is
found and shown to decrease for q^2 \le 0.3 GeV^2 in the infrared limit. No
indication for a non-trivial infrared fixed point is seen in agreement with
findings from truncated systems of Dyson-Schwinger equations treated on a
four-dimensional torus.


  Rapid progress has been made towards question answering (QA) systems that can
extract answers from text. Existing neural approaches make use of expensive
bi-directional attention mechanisms or score all possible answer spans,
limiting scalability. We propose instead to cast extractive QA as an iterative
search problem: select the answer's sentence, start word, and end word. This
representation reduces the space of each search step and allows computation to
be conditionally allocated to promising search paths. We show that globally
normalizing the decision process and back-propagating through beam search makes
this representation viable and learning efficient. We empirically demonstrate
the benefits of this approach using our model, Globally Normalized Reader
(GNR), which achieves the second highest single model performance on the
Stanford Question Answering Dataset (68.4 EM, 76.21 F1 dev) and is 24.7x faster
than bi-attention-flow. We also introduce a data-augmentation method to produce
semantically valid examples by aligning named entities to a knowledge base and
swapping them with new entities of the same type. This method improves the
performance of all models considered in this work and is of independent
interest for a variety of NLP tasks.


  Among the problems yet to be solved by current theories of solar system
formation is the origin of the Jupiter-family comets. Several possibilities are
examined using a fifth-order Runge-Kutta algorithm.


  Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) are
promising candidates for optoelectronic applications due to their efficient
light emission properties, and strong dielectric confinement effects. Raman
spectroscopy is a versatile, non-contact and often non-destructive technique,
widely used to characterize crystalline materials. However, the inherently weak
phonon scattering, strong background, and complex nature of the Raman signals
from HOIPs present challenges in obtaining reliable signals. Further, the
fragile nature of the 2D HOIP crystals results in rapid degradation upon
exposure to heat, light and moisture, which presents further difficulty in
enhancing Raman scattered photon signals. Herein, we report a novel approach to
enhance the weak Raman scattering signals in Ruddlesden-Popper (RP) phase HOIPs
by introducing an open-cavity comprising HOIP crystals on a gold substrate. We
observe 15x enhancement of the Raman signals due to the Purcell effect inside
the high-index HOIP crystals. Our simple approach can be extended to enhance
the study of phonon scattering in other HOIP and van der Waals layered
crystals.


  This paper grew out of the observation that the possibilities of proof by
induction and definition by recursion are often confused. The paper reviews the
distinctions. The von Neumann construction of the ordinal numbers includes a
construction of natural numbers as a special kind of ordinal. In any case, the
natural numbers can be understood as composing a free algebra in a certain
signature, {0,s}. The paper here culminates in a construction of, for each
algebraic signature S, a class ON_S that is to the class of ordinals as S is to
{0,s}. In particular, ON_S has a subclass that is a free algebra in the
signature S.


  Improving the resistance of deep neural networks against adversarial attacks
is important for deploying models to realistic applications. However, most
defense methods are designed to defend against intensity perturbations and
ignore location perturbations, which should be equally important for deep model
security. In this paper, we focus on adversarial deformations, a typical class
of location perturbations, and propose a flow gradient regularization to
improve the resistance of models. Theoretically, we prove that, compared with
input gradient regularization, regularizing flow gradients is able to get a
tighter bound. Over multiple datasets, architectures, and adversarial
deformations, our empirical results indicate that models trained with flow
gradients can acquire a better resistance than trained with input gradients
with a large margin, and also better than adversarial training. Moreover,
compared with directly training with adversarial deformations, our method can
achieve better results in unseen attacks, and combining these two methods can
improve the resistance further.


  We introduce a refinement of the standard continuous variable teleportation
measurement and displacement strategies. This refinement makes use of prior
knowledge about the target state and the partial information carried by the
classical channel when entanglement is non-maximal. This gives an improvement
in the output quality of the protocol. The strategies we introduce could be
used in current continuous variable teleportation experiments.


  The center determination of a galaxy cluster from an optical cluster finding
algorithm can be offset from theoretical prescriptions or $N$-body definitions
of its host halo center. These offsets impact the recovered cluster statistics,
affecting both richness measurements and the weak lensing shear profile around
the clusters. This paper models the centering performance of the \RM~cluster
finding algorithm using archival X-ray observations of \RM-selected clusters.
Assuming the X-ray emission peaks as the fiducial halo centers, and through
analyzing their offsets to the \RM~centers, we find that $\sim 75\pm 8 \%$ of
the \RM~clusters are well centered and the mis-centered offset follows a Gamma
distribution in normalized, projected distance. These mis-centering offsets
cause a systematic underestimation of cluster richness relative to the
well-centered clusters, for which we propose a descriptive model. Our results
enable the DES Y1 cluster cosmology analysis by characterizing the necessary
corrections to both the weak lensing and richness abundance functions of the
DES Y1 redMaPPer cluster catalog.


  It is shown that the homogeneous cooling state (HCS) for a heavy impurity
particle in a granular fluid supports two distinct phases. The order parameter
$\phi$ is the mean square velocity of the impurity particle relative to that of
a fluid particle, and the control parameter $\xi$ is the fluid cooling rate
relative to the impurity collision rate. For $\xi<1$ there is a ``normal''
phase for which $\phi$ scales as the fluid/impurity mass ratio, just as for a
system with elastic collisions. For $\xi>1$ an ``ordered'' phase occurs in
which $\phi$ is finite even for vanishingly small mass ratio, representing an
extreme violation of energy equipartition. The phenomenon can be described in
terms of a Landau-like free energy for a second order phase transition. The
dynamics leading to the HCS is studied in detail using an asymptotic analysis
of the Enskog-Lorentz kinetic equation near each phase and the critical domain.
Critical slowing is observed with a divergent relaxation time at the critical
point. The stationary velocity distributions are determined in each case,
showing a crossover from Maxwellian in the normal phase to an exponential
quartic function of the velocity that is sharply peaked about the non-zero
$\phi$ for the ordered phase. It is shown that the diffusion coefficient in the
normal phase diverges at the critical point and remains so in the ordered
phase. This is interpreted as a transition from diffusive to ballistic dynamics
between the normal and ordered phases.


  Semantic objects are unevenly distributed over images. In this paper, we
study the spatial disequilibrium problem of modern object detectors and propose
to quantify this ``spatial bias'' by measuring the detection performance over
zones. Our analysis surprisingly shows that the spatial imbalance of objects
has a great impact on the detection performance, limiting the robustness of
detection applications. This motivates us to design a more generalized
measurement, termed Spatial equilibrium Precision (SP), to better characterize
the detection performance of object detectors. Furthermore, we also present a
spatial equilibrium label assignment (SELA) to alleviate the spatial
disequilibrium problem by injecting the prior spatial weight into the
optimization process of detectors. Extensive experiments on PASCAL VOC, MS
COCO, and 3 application datasets on face mask/fruit/helmet images demonstrate
the advantages of our method. Our findings challenge the conventional sense of
object detectors and show the indispensability of spatial equilibrium. We hope
these discoveries would stimulate the community to rethink how an excellent
object detector should be. All the source code, evaluation protocols, and the
tutorials are publicly available at https://github.com/Zzh-tju/ZoneEval


  These lectures give a topical review of heavy flavour physics, in particular
\CP violation and rare decays, from an experimental point of view. They
describe the ongoing motivation to study heavy flavour physics in the LHC era,
the current status of the field emphasising key results from previous
experiments, some selected topics in which new results are expected in the near
future, and a brief look at future projects.


  The large size of the ASKAP HI surveys DINGO and WALLABY necessitates
automated 3D source finding. A performance difference of a few percent
corresponds to a significant number of galaxies being detected or undetected.
As such, the performance of the automated source finding is of paramount
importance to both of these surveys. We have analysed the performance of
various source finders to determine which will allow us to meet our survey
goals during the DINGO and WALLABY design studies. Here we present a comparison
of the performance of five different methods of automated source finding. These
source finders are Duchamp, the Gamma-finder, CNHI, a 2D-1D Wavelet
Reconstruction and S+C finder, a sigma clipping method. Each source finder was
applied on the same three-dimensional data cubes containing (a) point sources
with a Gaussian velocity profile and (b) spatially extended model-galaxies with
inclinations and rotation profiles. We focus on the completeness and
reliability of each algorithm when comparing the performance of the different
source finders.


  This paper concerns the paraconsistent logic LPQ$^{\supset,\mathsf{F}}$ and
an application of it in the area of relational database theory. The notions of
a relational database, a query applicable to a relational database, and a
consistent answer to a query with respect to a possibly inconsistent relational
database are considered from the perspective of this logic. This perspective
enables among other things the definition of a consistent answer to a query
with respect to a possibly inconsistent database without resort to database
repairs. In a previous paper, LPQ$^{\supset,\mathsf{F}}$ is presented with a
sequent-style natural deduction proof system. In this paper, a sequent calculus
proof system is presented because it is common to use a sequent calculus proof
system as the basis of proof search procedures and such procedures may form the
core of algorithms for computing consistent answers to queries.


  It is shown that 3D part of a spherically symmetric solution in conformal
Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well.
The Yamabe flow describes the transition from a horn of an initial wormhole to
a 3D Euclidean space both filled with a radial electric field. It is supposed
that such transition may describe appearing/disappearing quantum wormholes in a
spacetime foam.


  Recent developments have renewed the demand for solar cells with increased
tolerance to radiation damage. To investigate the specific irradiation damage
of 1 MeV electron irradiation in GaInAsP lattice matched to InP for varying In
and P contents, a simulation based analysis is employed: by fitting the quantum
efficiency and open-circuit voltage simultaneously before and after
irradiation, the induced changes in lifetime are detected. Furthermore, the
reduction of irradiation damage during regeneration under typical satellite
operating conditions for GEO missions (60{\deg}C and AM0 illumination) is
investigated. A clear decrease of the radiation damage is observed after post
irradiation regeneration. This regeneration effect is stronger for increasing
InP-fraction. It is demonstrated that the irradiation induced defect
recombination coefficient for irradiation with 1 MeV electrons after
regeneration for 216 hours can be described with a linear function of
InP-fraction between 1*10$^{-5}$ cm$^2$/s for GaAs and 7*10$^{-7}$ cm$^2$/s for
InP. The results show that GaInAsP is a promising material for radiation hard
space solar cells.


  The string landscape suggests that the supersymmetry breaking scale can be
high, and then the simplest low energy effective theory is the Standard Model
(SM). We show that gauge coupling unification can be achieved at about
10^{16-17} GeV in the SM with suitable normalizations of the U(1)_Y. Assuming
grand unification scale supersymmetry breaking, we predict that the Higgs mass
range is 127 GeV to 165 GeV, with the precise value strongly correlated with
the top quark mass and SU(3)_C gauge coupling. We also present 7-dimensional
orbifold grand unified theories in which such normalizations for the U(1)_Y and
charge quantization can be realized.


  Virtualization technology is widely used for sharing the abilities of
computer systems by splitting the resources among various virtual PCs. In
traditional computer systems, the utilization of hardware is not maximized and
the resources are not fully consumed. By using the virtualization technology,
the maximum utilization of computer system hardware is possible. Today, many
organizations especially educational institutes are adopting virtualization
technology to minimize the costs and increase the flexibility, responsiveness,
and efficiency. In this paper, we built a virtual educational lab in which we
successfully implemented Virtual Desktop Infrastructure (VDI) and created more
than 30 virtual desktops. The virtual desktops are created on the Citrix
XenServer hypervisor using the Citrix XenDesktop. Finally, we used benchmarking
software tool called Login VSI in order to measure the performance of the
virtual desktop infrastructure and the XenServer hypervisor. The results have
shown that the system performs well with 30 virtual desktops without reaching
the saturation point.


  In systems of multiple agents, identifying the cause of observed agent
dynamics is challenging. Often, these agents operate in diverse, non-stationary
environments, where models rely on hand-crafted environment-specific features
to infer influential regions in the system's surroundings. To overcome the
limitations of these inflexible models, we present GP-LAPLACE, a technique for
locating sources and sinks from trajectories in time-varying fields. Using
Gaussian processes, we jointly infer a spatio-temporal vector field, as well as
canonical vector calculus operations on that field. Notably, we do this from
only agent trajectories without requiring knowledge of the environment, and
also obtain a metric for denoting the significance of inferred causal features
in the environment by exploiting our probabilistic method. To evaluate our
approach, we apply it to both synthetic and real-world GPS data, demonstrating
the applicability of our technique in the presence of multiple agents, as well
as its superiority over existing methods.


  We present an efficient method of calculating the vibrational spectrum of a
magnetic molecule adsorbed on a superconductor, directly related to the first
derivative of the tunneling $IV$ curve. The work is motivated by a recent
scanning-tunneling spectroscopy of lead phthalocyanine on superconducting
Pb(100), showing a wealth of vibrational excitations, the number of which
highly exceeds molecular vibrations typically encountered on normal metals. We
design a minimal model which represents the inelastic transitions by the
spectral function of a frontier orbital of the molecule in isolation. The model
allows for an exact solution; otherwise the full correlated superconducting
problem would be hard to treat. The model parameters are supplied from an
ab-initio calculation, where the presence of the surface on the deformation of
molecular geometry can be taken into account. The spectral function of the
highest-occupied molecular orbital of the anionic PbPc$^{1-}$ shows the best
agreement with the experimental reference among other molecular charge states
and orbitals. The method allows to include multiple vibrational transitions
straightforwardly.


  We use an analytic model to study how inhomogeneous hydrogen reionization
affects the temperature distribution of the intergalactic medium (IGM). During
this process, the residual energy of each ionizing photon is deposited in the
IGM as heat, increasing its temperature to 20,000-30,000 K; subsequent
expansion of the Universe then cools the gas. Because reionization most likely
proceeds from high to low densities, underdense voids are ionized last, have
less time to cool, and are (on average) warmer than mean-density gas
immediately after reionization is complete (an "inverted" equation of state).
  From this initial configuration, the low-density gas cools quickly and
eventually returns to a more normal equation of state. The rapidly evolving
temperature introduces systematic uncertainties in measurements of the ionizing
background at z~6. For example, late reionization implies rapid cooling, so
that the ionizing background would have to evolve even more rapidly at z ~5-6
than typically claimed. This degeneracy is difficult to disentangle, because
the Lyman-alpha forest probes only a narrow range in densities (over which the
gas is nearly isothermal). However, higher Lyman-series transitions probe wider
density ranges, sampling different effective temperatures, and offer a new way
to measure the IGM equation of state that should work where nearly saturated
absorption precludes other methods. This will help to separate evolution in
temperature from that in the ionizing background. While more detailed study
with hydrodynamic simulations is needed, we show that such measurements could
potentially distinguish early and late reionization using only a handful of
lines of sight.


  We performed Monte Carlo simulations of two-dimensional $q$-state Potts
models with $q=10,15$, and $20$ and measured the spin-spin correlation function
at the first-order transition point $\beta_t$ in the disordered and ordered
phase. Our results for the correlation length $\xi_d(\beta_t)$ in the
disordered phase are compatible with an analytic formula. Estimates of the
correlation length $\xi_o(\beta_t)$ in the ordered phase yield strong numerical
evidence that $R \equiv \xi_o(\beta_t)/\xi_d(\beta_t) = 1$.


  We introduce a simple and very fast algorithm that computes Weil-Petersson
metrics on moduli spaces of polarized Calabi-Yau manifolds. Also, by using
Donaldson's quantization link between the infinite and finite dimensional G.I.T
quotients that describe moduli spaces of varieties, we define a natural
sequence of Kaehler metrics. We prove that the sequence converges to the
Weil-Petersson metric. We also develop an algorithm that numerically
approximates such metrics, and hence the Weil-Petersson metric itself. Explicit
examples are provided on a family of Calabi-Yau Quintic hypersurfaces in CP^4.
The scope of our second algorithm is much broader; the same techniques can be
used to approximate metrics on null spaces of Dirac operators coupled to
Hermite Yang-Mills connections.


  I review certain results in harmonic analysis for systems whose configuration
space is a compact Lie group. The results described involve a heat kernel
measure, which plays the same role as a Gaussian measure on Euclidean space.
The main constructions are group analogs of the Hermite expansion, the
Segal-Bargmann transform, and the Taylor expansion. The results are related to
geometric quantization, to stochastic analysis, and to the quantization of
1+1-dimensional Yang-Mills theory.


  In this article, we investigate monoidal, braided, sylleptic centralizers of
monoidal, braided, sylleptic 2-functors. We specifically focus on multifusion
2-categories and show that monoidal, braided, sylleptic centralizers are
multifusion again, via studying the corresponding enveloping algebras. We
provide a characterization of the non-degeneracy condition for monoidal,
braided, and sylleptic fusion 2-categories, via vanishing of their centers.
Applying Double Centralizer Theorems, we establish the relationship between
monoidal, braided, symmetric local modules and free modules. In particular, we
obtain factorization properties of non-degenerate monoidal, braided, and
sylleptic fusion 2-categories. Main results in this article will be used to
study higher Witt equivalences of non-degenerate monoidal, braided, sylleptic
2-categories in the sequential articles.


  We introduce the Lagrangian for a multi-scalar field configuration in a
$N$-dimensional internal space endowed with a constant metric $Q_{ik}$ and
generalize the quintom cosmological scenario. We find the energy momentum
tensor of the model and show that the set of dual transformations, that
preserve the form of the Einstein equations in the Friedmann-Robertson-Walker
(FRW) cosmology, is enlarged. We show that the stability of the power law
solutions leads to an exponential potential which is invariant under linear
transformations in the internal space. Moreover, we obtain the general exact
solution of the Einstein-Klein-Gordon equations for that potential. There exist
solutions that cross the phantom divide and solutions that blow up at a finite
time, exhibiting a superaccelerated behavior and ending in a big rip. We show
that the quintom model with a separable potential can be identified with a
mixture of several fluids. This framework includes the $\Lambda$CDM model, a
bouncing model, and a setting sourced by a cosmic string network plus a
cosmological constant. The we concentrate on the case where the dimension of
the internal quintessence sector $N_{q}$ exceeds the dimension of the internal
phantom sector $N_{ph}$. For $(N_q,N_{ph})=(2,1)$ the dark energy density
derived from the 3-scalar field crosses the phantom divide and its negative
component plays the role of the negative part of a classical Dirac Field.


  In this work, we investigate the production of $X_b$ in the process
$\Upsilon(5S,6S)\to \gamma X_b$, where $X_b$ is assumed to be the counterpart
of $X(3872)$ in the bottomonium sector as a $B {\bar B}^*$ molecular state. We
use the effective Lagrangian based on the heavy quark symmetry to explore the
rescattering mechanism and calculate their production ratios. Our results have
shown that the production ratios for the $\Upsilon(5S,6S) \to \gamma X_b$ are
orders of $10^{-5}$ with reasonable cutoff parameter range $\alpha \simeq 2\sim
3$. The sizeable production ratios may be accessible at the future experiments
like forthcoming BelleII, which will provide important clues to the inner
structures of the exotic state $X_b$.


  Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra,
which are superpartners of Hermitian Hamiltonians, must be
$\eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular
$\eta$ operators. We show that despite the fact that an $\eta$ operator
produced by a supersymmetric transformation, corresponding to the exact
supersymmetry, is singular, it can be used to find the eigenfunctions of a
Hermitian operator equivalent to the given pseudo-Hermitian Hamiltonian. Once
the eigenfunctions of the Hermitian operator are found the operator may be
reconstructed with the help of the spectral decomposition.


  We describe a film of highly-aligned single-walled carbon nanotubes that acts
as an excellent terahertz linear polarizer. There is virtually no attenuation
(strong absorption) when the terahertz polarization is perpendicular (parallel)
to the nanotube axis. From the data we calculated the reduced linear dichrosim
to be 3, corresponding to a nematic order parameter of 1, which demonstrates
nearly perfect alignment as well as intrinsically anisotropic terahertz
response of single-walled carbon nanotubes in the film.


  This paper presents an empirical analysis of Steemit, a key representative of
the emerging incentivized social media platforms over Blockchains, to
understand and evaluate the actual level of decentralization and the practical
effects of cryptocurrency-driven reward system in these modern social media
platforms. Similar to Bitcoin, Steemit is operated by a decentralized
community, where 21 members are periodically elected to cooperatively operate
the platform through the Delegated Proof-of-Stake (DPoS) consensus protocol.
Our study performed on 539 million operations performed by 1.12 million Steemit
users during the period 2016/03 to 2018/08 reveals that the actual level of
decentralization in Steemit is far lower than the ideal level, indicating that
the DPoS consensus protocol may not be a desirable approach for establishing a
highly decentralized social media platform. In Steemit, users create contents
as posts which get curated based on votes from other users. The platform
periodically issues cryptocurrency as rewards to creators and curators of
popular posts. Although such a reward system is originally driven by the desire
to incentivize users to contribute to high-quality contents, our analysis of
the underlying cryptocurrency transfer network on the blockchain reveals that
more than 16% transfers of cryptocurrency in Steemit are sent to curators
suspected to be bots and also finds the existence of an underlying supply
network for the bots, both suggesting a significant misuse of the current
reward system in Steemit. Our study is designed to provide insights on the
current state of this emerging blockchain-based social media platform including
the effectiveness of its design and the operation of the consensus protocols
and the reward system.


  In this paper, we compute the Chevalley-Eilenberg cohomology of the
three-dimensionnal Heisenberg Lie algebra with values in its universal
enveloping algebra. We also compte the Schouten brackets on cochains and
cohomology level in order to write the formality equations. It turns out that
there is no formality, ans that the perturbed L-infinity structure on the
cohomology has non-trivial terms in infinitely manu degrees.


  Electron beam induced deposition (EBID) currently provides the only direct
writing technique for truly three-dimensional nanostructures with geometrical
features below 50 nm. Unfortunately, the depositions from metal-organic
precursors suffer from a substantial carbon content. This hinders many
applications, especially in plasmonics where the metallic nature of the
geometric surfaces is mandatory. To overcome this problem a post-deposition
treatment with oxygen plasma at room temperature was investigated for the
purification of gold containing EBID structures. Upon plasma treatment, the
structures experience a shrinkage in diameter of about 18 nm but entirely keep
their initial shape. The proposed purification step results in a core-shell
structure with the core consisting of mainly unaffected EBID material and a
gold shell of about 20 nm in thickness. These purified structures are
plasmonically active in the visible wavelength range as shown by dark field
optical microscopy on helical nanostructures. Most notably, electromagnetic
modeling of the corresponding scattering spectra verified that the thickness
and quality of the resulting gold shell ensures an optical response equal to
that of pure gold nanostructures.


  We discuss necessary conditions for the existence of probability distribution
on particle configurations in $d$-dimensions i.e. a point process, compatible
with a specified density $\rho$ and radial distribution function $g({\bf r})$.
In $d=1$ we give necessary and sufficient criteria on $\rho g({\bf r})$ for the
existence of such a point process of renewal (Markov) type. We prove that these
conditions are satisfied for the case $g(r) = 0, r < D$ and $g(r) = 1, r > D$,
if and only if $\rho D \leq e^{-1}$: the maximum density obtainable from
diluting a Poisson process. We then describe briefly necessary and sufficient
conditions, valid in every dimension, for $\rho g(r)$ to specify a
determinantal point process for which all $n$-particle densities, $\rho_n({\bf
r}_1, ..., {\bf r}_n)$, are given explicitly as determinants. We give several
examples.


  In this paper we obtain some new estimates for multilinear exponential sums
in prime fields with a more general class of weights than previously
considered. Our techniques are based on some recent progress of Shkredov on
multilinear sums which has roots in Rudnev's point plane incidence bound. We
apply our estimates to obtain new results concerning exponential sums with
sparse polynomials and Weyl sums over small generalized arithmetic
progressions.


  A large body of work has investigated the properties of graph neural networks
and identified several limitations, particularly pertaining to their expressive
power. Their inability to count certain patterns (e.g., cycles) in a graph lies
at the heart of such limitations, since many functions to be learned rely on
the ability of counting such patterns. Two prominent paradigms aim to address
this limitation by enriching the graph features with subgraph or homomorphism
pattern counts. In this work, we show that both of these approaches are
sub-optimal in a certain sense and argue for a more fine-grained approach,
which incorporates the homomorphism counts of all structures in the ``basis''
of the target pattern. This yields strictly more expressive architectures
without incurring any additional overhead in terms of computational complexity
compared to existing approaches. We prove a series of theoretical results on
node-level and graph-level motif parameters and empirically validate them on
standard benchmark datasets.


  Temporal graph is an abstraction for modeling dynamic systems that consist of
evolving interaction elements. In this paper, we aim to solve an important yet
neglected problem -- how to learn information from high-order neighbors in
temporal graphs? -- to enhance the informativeness and discriminativeness for
the learned node representations. We argue that when learning high-order
information from temporal graphs, we encounter two challenges, i.e.,
computational inefficiency and over-smoothing, that cannot be solved by
conventional techniques applied on static graphs. To remedy these deficiencies,
we propose a temporal propagation-based graph neural network, namely TPGNN. To
be specific, the model consists of two distinct components, i.e., propagator
and node-wise encoder. The propagator is leveraged to propagate messages from
the anchor node to its temporal neighbors within $k$-hop, and then
simultaneously update the state of neighborhoods, which enables efficient
computation, especially for a deep model. In addition, to prevent
over-smoothing, the model compels the messages from $n$-hop neighbors to update
the $n$-hop memory vector preserved on the anchor. The node-wise encoder adopts
transformer architecture to learn node representations by explicitly learning
the importance of memory vectors preserved on the node itself, that is,
implicitly modeling the importance of messages from neighbors at different
layers, thus mitigating the over-smoothing. Since the encoding process will not
query temporal neighbors, we can dramatically save time consumption in
inference. Extensive experiments on temporal link prediction and node
classification demonstrate the superiority of TPGNN over state-of-the-art
baselines in efficiency and robustness.


  Each classical public-coin protocol for coin flipping is naturally associated
with a quantum protocol for weak coin flipping. The quantum protocol is
obtained by replacing classical randomness with quantum entanglement and by
adding a cheat detection test in the last round that verifies the integrity of
this entanglement. The set of such protocols defines a family which contains
the protocol with bias 0.192 previously found by the author, as well as
protocols with bias as low as 1/6 described herein. The family is analyzed by
identifying a set of optimal protocols for every number of messages. In the
end, tight lower bounds for the bias are obtained which prove that 1/6 is
optimal for all protocols within the family.


  We prove new lower bounds on the modularity of graphs. Specifically, the
modularity of a graph $G$ with average degree $\bar d$ is
$\Omega(\bar{d}^{-1/2})$, under some mild assumptions on the degree sequence of
$G$. The lower bound $\Omega(\bar{d}^{-1/2})$ applies, for instance, to graphs
with a power-law degree sequence or a near-regular degree sequence.
  It has been suggested that the relatively high modularity of the
Erd\H{o}s-R\'enyi random graph $G_{n,p}$ stems from the random fluctuations in
its edge distribution, however our results imply high modularity for any graph
with a degree sequence matching that typically found in $G_{n,p}$.
  The proof of the new lower bound relies on certain weight-balanced bisections
with few cross-edges, which build on ideas of Alon [Combinatorics, Probability
and Computing (1997)] and may be of independent interest.


  In this paper we show that the supergravity equations describing both cosmic
billiards and a large class of black-holes are, generically, both Liouville
integrable as a consequence of the same universal mechanism. This latter is
provided by the Liouville integrable Poissonian structure existing on the dual
Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive
the explicit integration algorithm associated with all symmetric spaces U/H^{*}
relevant to the description of time-like and space-like p-branes. The most
important consequence of our approach is the explicit construction of a
complete set of conserved involutive hamiltonians h_{\alpha} that are
responsible for integrability and provide a new tool to classify flows and
orbits. We believe that these will prove a very important new tool in the
analysis of supergravity black holes and billiards.


  A general Hamiltonian approach to black hole thermodynamics is used to study
entropy and conserved charges for Kerr-AdS solutions in general relativity.
These thermodynamic variables are first consistently defined by choosing
suitable boundary conditions, and then, they are shown to satisfy the first law
of black hole dynamics


  We experimentally investigate the transient dynamics of an optical cavity
field interacting with large ion Coulomb crystals in a situation of
electromagnetically induced transparency (EIT). EIT is achieved by injecting a
probe field at the single photon level and a more intense control field with
opposite circular polarization into the same mode of an optical cavity to
couple Zeeman substates of a metastable level in 40Ca+ ions. The EIT
interaction dynamics are investigated both in the frequency-domain - by
measuring the probe field steady state reflectivity spectrum - and in the
time-domain - by measuring the progressive buildup of transparency. The
experimental results are observed to be in excellent agreement with theoretical
predictions taking into account the inhomogeneity of the control field in the
interaction volume, and confirm the high degree of control on light-matter
interaction that can be achieved with ion Coulomb crystals in optical cavities.


  We prove that the category of generalized holomorphically contractible
families possesses maximal and minimal objects. Moreover, we present basic
properties of these extremal families.


  Let $\mbox{IG}(k,2n+1)$ be the odd symplectic Grassmannian. It is a
quasi-ho\-mo\-ge\-neous space with homogeneous-like behavior. A very limited
description of curve neighborhoods of Schubert varieties in $\mbox{IG}(k,2n+1)$
was used by Mihalcea and the second named author to prove an (equivariant)
quantum Chevalley rule. In this paper we give a full description of the
irreducible components of curve neighborhoods in terms of the Hecke product of
(appropriate) Weyl group elements, $k$-strict partitions, and BC-partitions.
The latter set of partitions respect the Bruhat order with inclusions. Our
approach follows the philosophy of Buch and Mihalcea's curve neighborhood
calculations of Schubert varieties in the homogeneous cases.


  The $\mathcal{KS}$ map is revisited in terms of an $S^1$-action in
$T^*\mathbb{H}_0$ with the bilinear function as the associated momentum map.
Indeed, the $\mathcal{KS}$ transformation maps the $S^1$-fibers related to the
mentioned action to single points. By means of this perspective a second
twin-bilinear function is obtained with an analogous $S^1$-action. We also show
that the connection between the 4-D isotropic harmonic oscillator and the
spatial Kepler systems can be done in a straightforward way after
regularization and through the extension to 4 degrees of freedom of the Euler
angles, when the bilinear relation is imposed. This connection incorporates
both bilinear functions among the variables. We will show that an alternative
regularization separates the oscillator expressed in Projective Euler
variables. This setting takes advantage of the two bilinear functions and
another integral of the system including them among a new set of variables that
allows to connect the 4-D isotropic harmonic oscillator and the planar Kepler
system. In addition, our approach makes transparent that only when we refer to
rectilinear solutions, both bilinear relations defining the $\mathcal{KS}$
transformations are needed.


  Respiratory ailments afflict a wide range of people and manifests itself
through conditions like asthma and sleep apnea. Continuous monitoring of
chronic respiratory ailments is seldom used outside the intensive care ward due
to the large size and cost of the monitoring system. While Electrocardiogram
(ECG) based respiration extraction is a validated approach, its adoption is
limited by access to a suitable continuous ECG monitor. Recently, due to the
widespread adoption of wearable smartwatches with in-built Photoplethysmogram
(PPG) sensor, it is being considered as a viable candidate for continuous and
unobtrusive respiration monitoring. Research in this domain, however, has been
predominantly focussed on estimating respiration rate from PPG. In this work, a
novel end-to-end deep learning network called RespNet is proposed to perform
the task of extracting the respiration signal from a given input PPG as opposed
to extracting respiration rate. The proposed network was trained and tested on
two different datasets utilizing different modalities of reference respiration
signal recordings. Also, the similarity and performance of the proposed network
against two conventional signal processing approaches for extracting
respiration signal were studied. The proposed method was tested on two
independent datasets with a Mean Squared Error of 0.262 and 0.145. The
Cross-Correlation coefficient of the respective datasets were found to be 0.933
and 0.931. The reported errors and similarity was found to be better than
conventional approaches. The proposed approach would aid clinicians to provide
comprehensive evaluation of sleep-related respiratory conditions and chronic
respiratory ailments while being comfortable and inexpensive for the patient.


  The time delay between appearances of multiple images of a gravitationally
lensed supernova (glSN) is sensitive to the Hubble constant, $H_0$. As well as
time delays, a lensed host galaxy is needed to enable precise inference of
$H_0$. In this work we investigate the connection between discoverable lensed
transients and their host galaxies. We find that LSST will discover 88 glSNe
per year, of which $54\%$ will also have a strongly lensed host. The rates can
change by approximately 30 percent uncertainty depending primarily on the
choice of unlensed SN population and uncertainties in the redshift evolution of
the deflector population, but the fraction of glSNe with a lensed host is
consistently around a half. LSST will discover 20 glSNe per year in systems
that could plausibly have been identified by Euclid as galaxy-galaxy lenses
before the discovery of the glSN. Such systems have preferentially longer time
delays and therefore are well suited for cosmography. We define a golden sample
of glSNe Ia with time delays over 10 days, image separations greater than 0.8
arcseconds, and a multiply imaged host. For this golden sample, we find $91\%$
occur in systems that should already be discoverable as galaxy-galaxy lenses in
Euclid. For cosmology with glSNe, monitoring Euclid lenses is a plausible
alternative to searching the entire LSST alert stream.


  Due to feedback from accretion onto supermassive black holes (SMBHs), Active
Galactic Nuclei (AGNs) are believed to play a key role in LambdaCDM cosmology
and galaxy formation. However, AGNs' extreme luminosities and the small angular
size of their accretion flows create a challenging imaging problem. We show
James Webb Space Telescope's Near Infrared Imager and Slitless Spectrograph
(JWST-NIRISS) Aperture Masking Interferometry (AMI) mode will enable true
imaging (i.e. without any requirement of prior assumptions on source geometry)
at ~65 mas angular resolution at the centers of AGNs. This is advantageous for
studying complex extended accretion flows around SMBHs, and in other areas of
angular-resolution-limited astrophysics. By simulating data sequences
incorporating expected sources of noise, we demonstrate that JWST-NIRISS AMI
mode can map extended structure at a pixel-to-pixel contrast of ~10^{-2} around
an L=7.5 point source, using short exposure times (minutes). Such images will
test models of AGN feedback, fuelling and structure (complementary with ALMA
observations), and are not currently supported by any ground-based IR
interferometer or telescope. Binary point source contrast with NIRISS is
~10^{-4} (for observing binary nuclei in merging galaxies), significantly
better than current ground-based optical or IR interferometry. JWST-NIRISS'
seven-hole non-redundant mask has a throughput of 15%, and utilizes NIRISS'
F277W (2.77\micron), F380M (3.8\micron), F430M (4.3\micron), and F480M
(4.8\micron) filters. NIRISS' square pixels are 65mas per side, with a field of
view ~2\arcmin x 2\arcmin. We also extrapolate our results to AGN science
enabled by non-redundant masking on future 2.4m and 16m space telescopes
working at long-UV to near-IR wavelengths.


  In this paper, we undertake a comprehensive survey of key trends and
innovations in the development of research-based and commercial micropayment
systems. Based on our study, we argue that past solutions have largely failed
because research has focused heavily on cryptographic and engineering
innovation, whereas fundamental issues pertaining to usability, psychology, and
economics have been neglected. We contextualize the range of existing
challenges for micropayments systems, discuss potential deployment strategies,
and identify critical stumbling blocks, some of which we believe researchers
and developers have yet to fully recognize. We hope this effort will motivate
and guide the development of micropayments systems.


  In this work, we introduce SureFED, a novel framework for byzantine robust
federated learning. Unlike many existing defense methods that rely on
statistically robust quantities, making them vulnerable to stealthy and
colluding attacks, SureFED establishes trust using the local information of
benign clients. SureFED utilizes an uncertainty aware model evaluation and
introspection to safeguard against poisoning attacks. In particular, each
client independently trains a clean local model exclusively using its local
dataset, acting as the reference point for evaluating model updates. SureFED
leverages Bayesian models that provide model uncertainties and play a crucial
role in the model evaluation process. Our framework exhibits robustness even
when the majority of clients are compromised, remains agnostic to the number of
malicious clients, and is well-suited for non-IID settings. We theoretically
prove the robustness of our algorithm against data and model poisoning attacks
in a decentralized linear regression setting. Proof-of Concept evaluations on
benchmark image classification data demonstrate the superiority of SureFED over
the state of the art defense methods under various colluding and non-colluding
data and model poisoning attacks.


  Many network applications, especially the multimedia applications, often
deliver flows with high QoS, like end-to-end delay constraint. Flows of these
applications usually need to traverse a series of different network functions
orderly before reaching to the host in the customer end, which is called the
service function chain (SFC). The emergence of network function virtualization
(NFV) increases the deployment flexibility of such network functions. In this
paper, we present heuristics to embed the SFC for a given flow considering: i)
bounded end-to-end delay along the path, and ii) minimum cost of the SFC
embedding, where cost and delay can be independent metrics and be attached to
both links and nodes. This problem of embedding SFC is NP-hard, which can be
reduced to the Knapsack problem. We then design a greedy algorithm which is
applied to a multilevel network. The simulation results demonstrate that the
multilevel greedy algorithm can efficiently solve the NP-hard problem.


  In this paper we shall focus on one-dimensional strictly local operators, the
notion of which naturally arises in the context of discrete-time quantum walks
on the one-dimensional integer lattice. In particular, we give an elementary
constructive approach to the following two topological invariants associated
with such operators: Fredholm index and essential spectrum. As a direct
application, we shall explicitly compute and fully classify these topological
invariants for a well-known quantum walk model.


  We present a class of Lie algebraic similarity transformations generated by
exponentials of two-body on-site hermitian operators whose Hausdorff series can
be summed exactly without truncation. The correlators are defined over the
entire lattice and include the Gutzwiller factor
$n_{i\uparrow}n_{i\downarrow}$, and two-site products of density
$(n_{i\uparrow} + n_{i\downarrow})$ and spin $(n_{i\uparrow}-n_{i\downarrow})$
operators. The resulting non-hermitian many-body Hamiltonian can be solved in a
biorthogonal mean-field approach with polynomial computational cost. The
proposed similarity transformation generates locally weighted orbital
transformations of the reference determinant. Although the energy of the model
is unbound, projective equations in the spirit of coupled cluster theory lead
to well-defined solutions. The theory is tested on the 1D and 2D repulsive
Hubbard model where we find accurate results across all interaction strengths.


  Point cloud analysis has received much attention recently; and segmentation
is one of the most important tasks. The success of existing approaches is
attributed to deep network design and large amount of labelled training data,
where the latter is assumed to be always available. However, obtaining 3d point
cloud segmentation labels is often very costly in practice. In this work, we
propose a weakly supervised point cloud segmentation approach which requires
only a tiny fraction of points to be labelled in the training stage. This is
made possible by learning gradient approximation and exploitation of additional
spatial and color smoothness constraints. Experiments are done on three public
datasets with different degrees of weak supervision. In particular, our
proposed method can produce results that are close to and sometimes even better
than its fully supervised counterpart with 10$\times$ fewer labels.


  This is an empirical study to investigate the impact of scanner effects when
using machine learning on multi-site neuroimaging data. We utilize structural
T1-weighted brain MRI obtained from two different studies, Cam-CAN and UK
Biobank. For the purpose of our investigation, we construct a dataset
consisting of brain scans from 592 age- and sex-matched individuals, 296
subjects from each original study. Our results demonstrate that even after
careful pre-processing with state-of-the-art neuroimaging pipelines a
classifier can easily distinguish between the origin of the data with very high
accuracy. Our analysis on the example application of sex classification
suggests that current approaches to harmonize data are unable to remove
scanner-specific bias leading to overly optimistic performance estimates and
poor generalization. We conclude that multi-site data harmonization remains an
open challenge and particular care needs to be taken when using such data with
advanced machine learning methods for predictive modelling.


  We prove that the universal covering $\Wi M$ of an $n$-dimensional closed
spin PSC manifold $M$ whose fundamental group $\pi_1(M)$ is a right-angled
Artin group has macroscopic dimension $\dim_{mc}\Wi M\le n-2$. This confirms
Gromov's conjecture in the case of right-angled Artin groups.


  We extend the algebra of local observables in topological conformal field
theories by nonlocal operators. This allows to construct parameter-dependent
operations realized via certain integrals over the compactified moduli spaces,
satisfying analogues of the Leibniz and higher order Leibniz identities holding
up to homotopy. We conjecture that one can construct a complete set of such
operations which lead to a parameter-dependent version of Loday's homotopy
Leibniz algebras.


  We study large time behavior of quantum walks (QWs) with self-dependent
(nonlinear) coin. In particular, we show scattering and derive the reproducing
formula for inverse scattering in the weak nonlinear regime. The proof is based
on space-time estimate of (linear) QWs such as dispersive estimates and
Strichartz estimate. Such argument is standard in the study of nonlinear
Schr\"odinger equations and discrete nonlinear Schr\"odinger equations but it
seems to be the first time to be applied to QW.


  We consider scattering amplitudes in string models in the Regge limit of high
energies and fixed momentum transfers with the use of the unitarity in direct
channels. Intermediate states are taken in the multi-Regge kinematics
corresponding to the production of resonances with fixed invariant masses and
large relative rapidities. In QCD such kinematics leads to the BFKL equation
for the Pomeron wave function in the leading logarithmic approximation. We
derive a similar equation in the string theory and discuss its properties. The
purpose of this investigation is to find a generalization of the BFKL approach
to the region of small momentum transfers where non-perturbative corrections to
the gluon Regge trajectory and reggeon couplings are essential. The BFKL
equation in the string theory contains additional contributions coming from a
linear part of the Regge trajectory and from the soft Pomeron singularity
appearing already in the tree approximation. In higher dimensions in addition,
a non-multi-Regge kinematics corresponding to production of particles with
large masses is important. We solve the equation for the Pomeron wave function
in the string theory for D=4 and discuss integrability properties of analogous
equations for composite states of several reggeised gluons in the multi-colour
limit.


  Exclusive rho^0 electroproduction at HERA has been studied with the ZEUS
detector using 120 pb^{-1} of integrated luminosity collected during 1996-2000.
The analysis was carried out in the kinematic range of photon virtuality 2 <
Q^2 < 160 GeV$^2, and gamma^* p centre-of-mass energy 32 < W < 180 GeV. The
results include the Q^2 and W dependence of the gamma^* p --> rho^0 p cross
section and the distribution of the squared-four-momentum transfer to the
proton. The helicity analysis of the decay-matrix elements of the rho^0 was
used to study the ratio of the gamma^* p cross section for longitudinal and
transverse photon as a function of Q^2 and W. Finally, an effective Pomeron
trajectory was extracted. The results are compared to various theoretical
predictions.


  In the Best-$k$-Arm problem, we are given $n$ stochastic bandit arms, each
associated with an unknown reward distribution. We are required to identify the
$k$ arms with the largest means by taking as few samples as possible. In this
paper, we make progress towards a complete characterization of the
instance-wise sample complexity bounds for the Best-$k$-Arm problem. On the
lower bound side, we obtain a novel complexity term to measure the sample
complexity that every Best-$k$-Arm instance requires. This is derived by an
interesting and nontrivial reduction from the Best-$1$-Arm problem. We also
provide an elimination-based algorithm that matches the instance-wise lower
bound within doubly-logarithmic factors. The sample complexity of our algorithm
strictly dominates the state-of-the-art for Best-$k$-Arm (module constant
factors).


  The output of persistent homology is an algebraic object called a persistence
module. This object admits a decomposition into a direct sum of interval
persistence modules described entirely by the barcode invariant. In this paper
we investigate when a morphism $\Phi \colon V \to W$ of persistence modules
admits an analogous direct sum decomposition. Jacquard et al. showed that a
ladder decomposition can be obtained whenever the barcodes of $V$ and $W$ do
not have any strictly nested bars. We refine this result and show that even in
the presence of nested bars, a ladder decomposition exists when the morphism is
sufficiently close to being invertible relative to the scale of the nested
bars.


  Representations of polynomial covariance commutation relations by pairs of
linear integral and differential operators are constructed in the space of
infinitely continuously differentiable functions. Representations of polynomial
covariance commutation relations by pairs consisting of a differential and
linear integral operator are considered including conditions on kernels and
coefficients of operators, and examples.


  Fintech business models based on distributed ledgers -- and their
smart-contract variants in particular -- offer the prospect of democratizing
access to faster, anywhere-accessible, lower cost, reliable-and-secure
high-quality financial services. In addition to holding great, economically
transformative promise, these business models pose new, little-studied risks
and transaction costs. However, these risks and transaction costs are not
evident during the demonstration and testing phases of development, when
adopters and users are drawn from the community of developers themselves, as
well as from among non-programmer fintech evangelists. Hence, when the new
risks and transaction costs become manifest -- as the fintech business models
are rolled out across the wider economy -- the consequences may also appear to
be new and surprising. The present study represents an effort to get ahead of
these developments by delineating risks and transaction costs inherent in
distributed-ledger- and smart-contracts-based fintech business models. The
analysis focuses on code risk and moral-hazard risk, as well as on
mixed-economy risks and the unintended consequences of replicating
bricks-and-mortar-generation contract forms within the ultra-low
transaction-cost environment of fintech.


  Sums-of-squares formulas over the integers have been studied extensively
using their equivalence to consistently signed intercalate matrices. This
representation, combined with combinatorial arguments, has been used to produce
sums-of-squares formulas and to show that formulas of certain types cannot
exist. In this paper, we introduce an algorithm that produces consistently
signed intercalate matrices, or proves their nonexistence, extending previous
methods beyond what is computationally feasible by hand.


  In the general accretion disk model theory, the accretion disk surrounding an
astronomical object comprises fluid rings obeying Keplerian motion. However, we
should consider relativistic and rotational effects as we close in toward the
center of accretion disk surrounding spinning compact massive objects such as a
black hole or a neutron star. In this study, we explore the geometry of the
inner portion of the accretion disk in the context of Mukhopadhyay's pseudo
Newtonian potential approximation for the full general relativity theory. We
found that the shape of the accretion disk "puffs up" or becomes thicker and
the luminosity of the disk could exceed the Eddington luminosity near the
surface of the compact spinning black hole.


  The flux-line lattice in the compound $ErNi_2B_2C$, which has a tendency to
ferromagnetic order in the a-b plane is studied with external magnetic field
direction close to the c-axis. We show the existence of an instability where
the direction of flux-lines spontaneously tilts away from that of the applied
field near the onset of ferromagnetic order. The enhanced fluctuations in the
flux lattice and the square flux lattice recently observed are explained and
further experiments suggested.


  Carbon ion is the mostly common used particle in heavy ion radiotherapy. In
this paper, carbon ion dose in tumor treatment for human eye was simulated with
FLUKA code, 80 MeV/u carbon beam was irradiated into the human eye from two
directions, The first is from the lateral-forward direction which was a typical
therapeutic condition, maximum dose was deposited in the tumor volume. The
second one was that beam irradiated into eyes from the forward direction which
may cause certain medical accident. The calculated results are compared with
other reports. The agreement indicates that this method can be used for
treatment plan in heavy ion radiotherapy.


  The explosive BN/KL outflow emerging from OMC1 behind the Orion Nebula may
have been powered by the dynamical decay of a non-hierarchical multiple system
$\sim$500 years ago that ejected the massive stars I, BN, and source n, with
velocities of about 10 to 30 km s$^{-1}$. New proper motion measurements of
H$_2$ features show that within the errors of measurement, the outflow
originated from the site of stellar ejection. Combined with published data,
these measurements indicate an outflow age of $\sim$500 years, similar to the
time since stellar ejection. The total kinetic energy of the ejected stars and
the outflow is about 2 to $6 \times 10^{47}$ ergs. It is proposed that the
gravitational potential energy released by the formation of a short-period
binary, most likely source I, resulted in stellar ejection and powered the
outflow. A scenario is presented for the formation of a compact,
non-hierarchical multiple star system, its decay into an ejected binary and two
high-velocity stars, and launch of the outflow. Three mechanisms may have
contributed to the explosion in the gas: (i) Unbinding of the circum-cluster
envelope following stellar ejection, (ii) disruption of circumstellar disks and
high-speed expulsion of the resulting debris during the final stellar
encounter, and (iii) the release of stored magnetic energy. Plausible
proto-stellar disk end envelope properties can produce the observed outflow
mass, velocity, and kinetic energy distributions. The ejected stars may have
acquired new disks by fall-back or Bondi-Hoyle accretion with axes roughly
orthogonal to their velocities. The expulsion of gas and stars from OMC1 may
have been driven by stellar interactions.


  A tunable quantum point contact with modes occupied in both transverse
directions is studied by magnetotransport experiments. We use conductance
quantization of the one-dimensional subbands as a tool to determine the mode
spectrum. A magnetic field applied along the direction of the current flow
couples the modes. This can be described by an extension of the Darwin-Fock
model. Anticrossings are observed as a function of the magnetic field, but not
for zero field or perpendicular field directions, indicating coupling of the
subbands due to nonparabolicity in the electrical confinement.


  It is shown by explicit construction of new metrics, that General Relativity
can solve the exact Poinc$\acute{a}$re recurrence problem. In these solutions,
the light cone, flips periodically between past and future, due to a
periodically alternating arrow of the proper time. The geodesics in these
universes show periodic Loschmidt's velocity reversion $v \to -v$, at critical
points, which leads to recurrence. However, the matter tensors of some of these
solutions exhibit unusual properties - such as, periodic variations in density
and pressure. While this is to be expected in periodic models, the physical
basis for such a variation is not clear. Present paper therefore can be
regarded as an extension of Tipler's "no go theorem for recurrence in an
expanding universe", to other space-time geometries.


  Federated Semi-Supervised Learning (FedSSL) has gained rising attention from
both academic and industrial researchers, due to its unique characteristics of
co-training machine learning models with isolated yet unlabeled data. Most
existing FedSSL methods focus on the classical scenario, i.e, the labeled and
unlabeled data are stored at the client side. However, in real world
applications, client users may not provide labels without any incentive. Thus,
the scenario of labels at the server side is more practical. Since unlabeled
data and labeled data are decoupled, most existing FedSSL approaches may fail
to deal with such a scenario. To overcome this problem, in this paper, we
propose FedCon, which introduces a new learning paradigm, i.e., contractive
learning, to FedSSL. Experimental results on three datasets show that FedCon
achieves the best performance with the contractive framework compared with
state-of-the-art baselines under both IID and Non-IID settings. Besides,
ablation studies demonstrate the characteristics of the proposed FedCon
framework.


  We propose a novel test to assess the unitarity of the
Cabibbo-Kobayashi-Maskawa matrix, $V_{\scriptscriptstyle{\rm CKM}}$, at present
and future collider experiments. Our strategy makes use of the $W^+W^-$
production cross section to directly probe the $V_{\scriptscriptstyle{\rm
CKM}}^{\dagger} V_{\scriptscriptstyle{\rm CKM}}$ product, which regulates the
high-energy behavior of the observable. The violation of unitarity is signalled
by an anomalous behavior of the cross section that grows quadratically with the
$W^+W^-$ invariant mass with respect to the Standard Model prediction. By using
the recent ATLAS measurements of the $W^+W^-$ cross section we are able to
constrain the maximal unitarity violation allowed by current data, producing a
bound complementary to the results of flavor physics experiments. Forecasts for
the high luminosity phase of the LHC and for the future 100 TeV hadron collider
are also discussed.


  The quantum nature of matter lies in the wave function phases that accumulate
while particles move along their trajectories. A prominent example is the
Aharonov-Bohm phase, which has been studied in connection with the conductance
of nanostructures. However, optical response in solids is determined by neutral
excitations, for which no sensitivity to magnetic flux would be expected. We
propose a new mechanism for the topological phase of a neutral particle, a
polarized exciton confined to a semiconductor quantum ring. We predict that
this magnetic-field induced phase may strongly affect excitons in a system with
cylindrical symmetry, resulting in switching between `bright' exciton ground
states and novel `dark' states with nearly infinite lifetimes. Since excitons
determine the optical response of semiconductors, the predicted phase can be
used to tailor photon emission from quantum nanostructures.


  A star approaching a supermassive black hole (SMBH) can be torn apart in a
tidal disruption event (TDE). We examine ultra-deep TDEs, a new regime in which
the disrupted debris approaches close to the black hole's Schwarzschild radius,
and the leading part intersects the trailing part at the first pericenter
passage. We calculate the range of penetration factors $\beta$ vs SMBH masses
$M$ that produce these prompt self-intersections using a Newtonian analytic
estimate and a general relativistic (GR) geodesic model. We find that
significant self-intersection of Solar-type stars requires $\beta \sim 50 -
127$ for $M/M_\odot = 10^4$, down to $\beta \sim 5.6 - 5.9$ for $M/M_\odot =
10^6$. We run smoothed-particle hydrodynamic (SPH) simulations to corroborate
our calculations and find close agreement, with a slightly shallower dependence
on $M$. We predict that the shock from the collision emits an X-ray flare
lasting $t \sim 2$ s with $L \sim 10^{47}$ ergs/s at $E \sim 2$ keV, and the
debris has a prompt accretion episode lasting $t \sim$ several min. The events
are rare and occur with a rate $\dot{N} \lesssim 10^{-7}$ Mpc$^{-3}$ yr$^{-1}$.
Ultra-deep TDEs can probe the strong gravity and demographics of low-mass
SMBHs.


  Non-Hermitian non-reciprocal systems are known to be extremely sensitive to
boundary conditions, exhibiting diverse localizing behaviors and spectrum
structures when translational invariance is locally broken, either by tuning
the boundary coupling strength, or by introducing an effective boundary using
impurities or defects. In this work, we consider the single impurity problem in
the Hatano-Nelson model and the Su-Schreieffer-Heeger model, which can be
exactly solved with the single impurity being treated as an effective boundary
of the system. From our exact solutions for finite-size systems, we unveil that
increasing the impurity strength can lead to a transition of the bulk states
from non-skin states to skin states, accompanied by the change of the spectrum
structure from an ellipse in the complex plane to a segment along the real
axis. These exact results indicate that the critical value of impurity strength
is size-dependent, and increases exponentially with the lattice size when the
impurity is strong or the system is large enough. OUr exact solutions are also
useful for determining the point-gap topological transition in the concerned
models.


  Semantic knowledge can be a great asset to natural language processing
systems, but it is usually hand-coded for each application. Although some
semantic information is available in general-purpose knowledge bases such as
WordNet and Cyc, many applications require domain-specific lexicons that
represent words and categories for a particular topic. In this paper, we
present a corpus-based method that can be used to build semantic lexicons for
specific categories. The input to the system is a small set of seed words for a
category and a representative text corpus. The output is a ranked list of words
that are associated with the category. A user then reviews the top-ranked words
and decides which ones should be entered in the semantic lexicon. In
experiments with five categories, users typically found about 60 words per
category in 10-15 minutes to build a core semantic lexicon.


  The influence of high magnetic fields on coherent transport is investigated.
A monolayer graphene quantum ring is fabricated and the Aharonov-Bohm effect is
observed. For increased magnitude of the magnetic field higher harmonics
appear. This phenomenon is attributed to an increase of the phase coherence
length due to reduction of spin flip scattering.


  Self-supervised pre-training has been successful in both text and speech
processing. Speech and text offer different but complementary information. The
question is whether we are able to perform a speech-text joint pre-training on
unpaired speech and text. In this paper, we take the idea of self-supervised
pre-training one step further and propose token2vec, a novel joint pre-training
framework for unpaired speech and text based on discrete representations of
speech. Firstly, due to the distinct characteristics between speech and text
modalities, where speech is continuous while text is discrete, we first
discretize speech into a sequence of discrete speech tokens to solve the
modality mismatch problem. Secondly, to solve the length mismatch problem,
where the speech sequence is usually much longer than text sequence, we convert
the words of text into phoneme sequences and randomly repeat each phoneme in
the sequences. Finally, we feed the discrete speech and text tokens into a
modality-agnostic Transformer encoder and pre-train with token-level masking
language modeling (tMLM). Experiments show that token2vec is significantly
superior to various speech-only pre-training baselines, with up to 17.7%
relative WER reduction. Token2vec model is also validated on a non-ASR task,
i.e., spoken intent classification, and shows good transferability.


  We study gamma-ray observations of NGC 4151 by GRO/OSSE contemporaneous with
X-ray observations by ROSAT and Ginga in 1991 June and with ASCA in 1993 May.
The spectra are well modeled by thermal Comptonization and a dual neutral
absorber. We also find, for the first time for NGC 4151, a Compton-reflection
spectral component in the Ginga/OSSE data. The OSSE spectra of those and other
observations of NGC 4151 are statistically undistinguishable from the average
OSSE spectrum of radio-quiet Seyfert 1s. NGC 4151 observed in 1991 and 1993 has
the intrinsic X-ray/gamma-ray spectrum typical for Seyfert 1s, and the main
property distinguishing it from other Seyfert 1s is a large absorbing column of
$\sim 10^{23}$ cm$^{-2}$. We find no evidence for a strong, broad and
redshifted, Fe K$\alpha$ line component in the ASCA spectrum of 1993 May.
  On the other hand, we confirm previous studies in that archival X-ray data do
imply strong intrinsic X-ray variability and hardness of the intrinsic spectrum
in low X-ray states. An observed softening of the intrinsic X-ray spectrum with
the increasing flux implies variability in gamma-rays weaker than in X-rays,
which agrees with the 100 keV flux changing only within a factor of 2 in
archival OSSE and Granat/SIGMA observations.
  The relative hardness of the intrinsic X-ray spectrum rules out the
homogeneous hot corona/cold disk model for this source. Instead, the hot plasma
has to subtend a small solid angle as seen from the source of UV radiation. If
the hot plasma is purely thermal, it consists of electrons rather than $e^+e^-$
pairs. On the other hand, the plasma can be pair-dominated if a small fraction
of the power is nonthermal.


  We present a theorem that allows to simplify linear stability analysis of
periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems
(both conservative and dissipative) with different kinds of discrete symmetry.
This theorem suggests a decomposition of the linearized system arising in the
standard stability analysis into a number of subsystems whose dimensions can be
considerably less than that of the full system. As an example of such
simplification, we discuss the stability of bushes of modes (invariant
manifolds) for the Fermi-Pasta-Ulam chains and prove another theorem about the
maximal dimension of the above mentioned subsystems.


  For the multi-peg Tower of Hanoi problem with $k \geqslant 4$ pegs, so far
the best solution is obtained by the Stewart's algorithm based on the the
following recurrence relation: $\mathrm{S}\_k(n)=\min\_{1 \leqslant t \leqslant
n} \left\{2 \cdot \mathrm{S}\_k(n-t) + \mathrm{S}\_{k-1}(t)\right\}$,
$\mathrm{S}\_3(n) = 2^n -- 1$. In this paper, we generalize this recurrence
relation to $\mathrm{G}\_k(n) = \min\_{1\leqslant t\leqslant n}\left\{
p\_k\cdot \mathrm{G}\_k(n-t) + q\_k\cdot \mathrm{G}\_{k-1}(t) \right\}$,
$\mathrm{G}\_3(n) = p\_3\cdot \mathrm{G}\_3(n-1) + q\_3$, for two sequences of
arbitrary positive integers $\left(p\_i\right)\_{i \geqslant 3}$ and
$\left(q\_i\right)\_{i \geqslant 3}$ and we show that the sequence of
differences $\left(\mathrm{G}\_k(n)- \mathrm{G}\_k(n-1)\right)\_{n \geqslant
1}$ consists of numbers of the form $\left(\prod\_{i=3}^{k}q\_i\right) \cdot
\left(\prod\_{i=3}^{k}{p\_i}^{\alpha\_i}\right)$, with $\alpha\_i\geqslant 0$
for all $i$, arranged in nondecreasing order. We also apply this result to
analyze recurrence relations for the Tower of Hanoi problems on several graphs.


  We consider a parabolic-like systems of differential equations involving
geometrical quantities to examine uniformization theorems for two- and
three-dimensional closed orientable manifolds. We find that in the
two-dimensional case there is a simple gauge theoretic flow for a connection
built from a Riemannian structure, and that the convergence of the flow to the
fixed points is consistent with the Poincare Uniformization Theorem. We
construct a similar system for the three-dimensional case. Here the connection
is built from a Riemannian geometry, an SO(3) connection and two other 1-form
fields which take their values in the SO(3) algebra. The flat connections
include the eight homogeneous geometries relevant to the three-dimensional
uniformization theorem conjectured by W. Thurston. The fixed points of the flow
include, besides the flat connections (and their local deformations), non-flat
solutions of the Yang-Mills equations. These latter "instanton" configurations
may be relevant to the fact that generic 3-manifolds do not admit one of the
homogeneous geometries, but may be decomposed into "simple 3-manifolds" which
do.


  The electronic structure of pentacene decorated with dipole groups
(d-pentacene) and adsorbed onto a graphene substrate has been studied within
the density functional theory. Three reference configurations have been
considered, namely the ideal molecule without distortions, the actual molecule
including intramolecular distortions and the molecule adsorbed onto graphene.
Calculations show a noticeable charge redistribution within the d-pentacene +
graphene system due to molecular distortion, as well as the formation of weak
$\pi$-bonds between the molecule and the substrate. Additionally, the effect of
the chemical modification of the terminal saturation with --H by --OH and =O is
checked to explore the possibility of "levels engineering". The imaginary part
of the dielectric function of d-pentacene in the ideal and distorted
conformations and the molecule adsorbed at graphene were calculated within the
random phase approximation. Results show that, even though molecular
distortions change apreciably the absorption spectrum of isolated d-pentacene,
the adsorbed molecule exhibits an optical spectrum which mimics quite much that
of single graphene.


  The critical baryon chemical potential for the onset of nuclear matter is a
function of the vacuum mass and the binding energy. Both quantities are
affected by an external magnetic field. We show within two relativistic
mean-field models - including magnetic catalysis, but omitting the anomalous
magnetic moment - that a magnetic field increases both the vacuum mass and the
binding energy. For sufficiently large magnetic fields, the effect on the
vacuum mass dominates and as a result the critical baryon chemical potential is
increased.


  We report possible evidence of non-Fermi liquid (NFL) observed at room
temperature from the quasi one-dimensional (1D) indium (In) nanowires
self-assembled on Si(111)-7$\times$7 surface. Using high-resolution
electron-energy-loss spectroscopy, we have measured energy and width
dispersions of a low energy intrasubband plasmon excitation in the In
nanowires. We observe the energy-momentum dispersion $\omega$(q) in the low q
limit exactly as predicted by both NFL theory and the
random-phase-approximation. The unusual non-analytic width dispersion $\zeta(q)
\sim q^{\alpha}$ measured with an exponent ${\alpha}$=1.40$\pm$0.24, however,
is understood only by the NFL theory. Such an abnormal width dispersion of low
energy excitations may probe the NFL feature of a non-ideal 1D interacting
electron system despite the significantly suppressed spin-charge separation
($\leq$40 meV).


  Self Consistent Normal Mode Analysis (SCNMA) is applied to heme c type
cytochrome f to study temperature dependent protein motion. Classical Normal
Mode Analysis (NMA) assumes harmonic behavior and the protein Mean Square
Displacement (MSD) has a linear dependence on temperature. This is only
consistent with low temperature experimental results. To connect the protein
vibrational motions between low temperature and physiological temperature, we
have incorporated a fitted set of anharmonic potentials into SCNMA. In
addition, Quantum Harmonic Oscillator (QHO) theory has been used to calculate
the displacement distribution for individual vibrational modes. We find that
the modes involving soft bonds exhibit significant non-Gaussian dynamics at
physiological temperature, which suggests it may be the cause of the
non-Gaussian behavior of the protein motions probed by Elastic Incoherent
Neutron Scattering (EINS). The combined theory displays a dynamical transition
caused by the softening of few "torsional" modes in the low frequency regime (<
50cm-1or < 6meVor > 0.6ps). These modes change from Gaussian to a classical
distribution upon heating. Our theory provides an alternative way to understand
the microscopic origin of the protein dynamical transition.


  The usual path integral formulation for scalar particles at finite density
involves a sign problem, making numerical simulation impractical. We present
alternative methods free of this difficulty. We apply these approaches to phi^4
theory in 2+1 dimensions, presenting preliminary numerical results for physical
quantities in the vicinity of the phase transition in the T-mu plane.


  We determine a next-to-leading order result for the correlator of the shear
stress operator in high-temperature Yang-Mills theory. The computation is
performed via an ultraviolet expansion, valid in the limit of small distances
or large momenta, and the result is used for writing operator product
expansions for the Euclidean momentum and coordinate space correlators as well
as for the Minkowskian spectral density. In addition, our results enable us to
confirm and refine a shear sum rule originally derived by Romatschke, Son and
Meyer.


  The complexity of glasses makes it challenging to explain their dynamics.
Machine Learning (ML) has emerged as a promising pathway for understanding
glassy dynamics by linking their structural features to rearrangement dynamics.
Support Vector Machine (SVM) was one of the first methods used to detect such
correlations. Specifically, a certain output of SVMs trained to predict
dynamics from structure, the distance from the separating hyperplane, was
interpreted as being linearly related to the activation energy for the
rearrangement. By numerical analysis of toy models, we explore under which
conditions it is possible to infer the energy barrier to rearrangements from
the distance to the separating hyperplane. We observe that such successful
inference is possible only under very restricted conditions. Typical tests,
such as the apparent Arrhenius dependence of the probability of rearrangement
on the inferred energy and the temperature, or high cross-validation accuracy
do not guarantee success. We propose practical approaches for measuring the
quality of the energy inference and for modifying the inferred model to improve
the inference, which should be usable in the context of realistic datasets.


  Fusion reactions relevant for the carbon and oxygen burning cycles in highly
evolved stars are investigated in a standard approach to fusion. We employ the
double folding method to evaluate the ion-ion interactions with Gogny-D1 and
M3Y-Paris $n-n$ effective forces. The cross-section evaluation do not indicate
a possible hindrance even at the lowest energies under the barrier. Reaction
rates at temperatures relevant for the stellar processes are estimated and
compared to the traditional and modern extrapolation formulas.