  With the help of conditioning mechanisms, the state-of-the-art diffusion
models have achieved tremendous success in guided image generation,
particularly in text-to-image synthesis. To gain a better understanding of the
training process and potential risks of text-to-image synthesis, we perform a
systematic investigation of backdoor attack on text-to-image diffusion models
and propose BadT2I, a general multimodal backdoor attack framework that tampers
with image synthesis in diverse semantic levels. Specifically, we perform
backdoor attacks on three levels of the vision semantics: Pixel-Backdoor,
Object-Backdoor and Style-Backdoor. By utilizing a regularization loss, our
methods efficiently inject backdoors into a large-scale text-to-image diffusion
model while preserving its utility with benign inputs. We conduct empirical
experiments on Stable Diffusion, the widely-used text-to-image diffusion model,
demonstrating that the large-scale diffusion model can be easily backdoored
within a few fine-tuning steps. We conduct additional experiments to explore
the impact of different types of textual triggers, as well as the backdoor
persistence during further training, providing insights for the development of
backdoor defense methods. Besides, our investigation may contribute to the
copyright protection of text-to-image models in the future.


  Precision gauge coupling unification is one of the primary quantitative
successes of low energy or split supersymmetry. Preserving this success puts
severe restrictions on possible matter and gauge sectors that might appear at
collider-accessible energies. In this work we enumerate new gauge sectors which
are compatible with unification, consisting of horizontal gauge groups acting
on vector-like matter charged under the Standard Model. Interestingly, almost
all of these theories are in the supersymmetric conformal window at high
energies and confine quickly after the superpartners are decoupled. For a range
of scalar masses compatible with both moderately tuned and minimally split
supersymmetry, the confining dynamics happen at the multi-TeV scale, leading to
a spectrum of multiple spin-0 and spin-1 resonances accessible to the LHC, with
unusual quantum numbers and striking decay patterns.


  We give rigidity results for the discrete Bonnet-Myers diameter bound and the
Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if
the underlying graph is a hypercube. The proofs use well-known semigroup
methods as well as new direct methods which translate curvature to
combinatorial properties. Our results can be seen as first known discrete
analogues of Cheng's and Obata's rigidity theorems.


  Structure is the most distinctive feature of nanoporous metals. The intricate
maze of rounded shapes, where ligaments and pores run after each other
disorderly, strikes imagination no less than it imparts properties that, tuned
by size effects, have no counterpart in the bulk form. Indisputably, nanoporous
Au has been the absolute protagonist of the field of study, unveiling the
disrupting potential of nanoporous metals in areas ranging from catalysis to
energy and sensing. Here, we still focus on nanoporous Au, addressing the
long-standing issue of mechanical properties in nanoporous metals. In
particular, we investigate how Young's modulus changes with ligament size,
being the porosity the same. Based on atomistic replicas generated starting
from experimental tomographic evidence, atomistic simulations reveal that
nanoporous Au stiffens as ligaments become finer, reproducing experimental
findings obtained by nanoindentation of dealloyed samples. Ruled out surface
stress effects, theoretical considerations relate stiffening to the dislocation
density increase.


  The Branching Brownian Motions (BBM) are particles performing independent
Brownian motions in $\mathbb R$ and each particle at rate 1 creates a new
particle at her current position; the newborn particle increments and
branchings are independent of the other particles. The $N$-BBM starts with $N$
particles and at each branching time, the leftmost particle is removed so that
the total number of particles is $N$ for all times. The $N$-BBM was proposed by
Maillard and belongs to a family of processes introduced by Brunet and Derrida.
We fix a density $\rho$ with a left boundary $L=\sup\{r\in\mathbb R:
\int_r^\infty \rho(x)dx=1\}>-\infty$ and let the initial particle positions be
iid continuous random variables with density $\rho$. We show that the empirical
measure associated to the particle positions at a fixed time $t$ converges to
an absolutely continuous measure with density $\psi(\cdot,t)$, as $N\to\infty$.
The limit $\psi$ is solution of a free boundary problem (FBP) when this
solution exists. The existence of solutions for finite time-intervals has been
recently proved by Lee.


  The retarded gravitation produced by the matter and energy content of the
observable universe is formulated and shown how this cosmological gravity gives
rise to inertial forces in accelerated frames of reference. The model is
developed for spatially flat Friedman-Robertson-Walker (FRW) universes. The
retarded potential of cosmological gravity is determined first in fundamental
frames of reference, in Einstein-de Sitter (ES)and in LambdaCDM models. Despite
the expansion, the observable universe gives rise to a static, retarded
gravitational potential equal to c2 in ES universe, while gravity is weakening
during the expansion in LambdaCDM model.
  In the locally Minkowski spacetime occurring in a small domain of the
universe, a covariant Lagrangian of a test body moving in the cosmological
gravitational field is derived. Inertial forces are determined from a test
body's Euler-Lagrange equation, in Newtonian approximation. The model
calculation indicates, that the inertial forces meet exactly the ones observed
in ES universe and Mach's principle holds there. In the present-day standard,
LambdaCDM model inertial forces are weaker by 10 % than expected.


  We study a special class of diamond channels which was introduced by Schein
in 2001. In this special class, each diamond channel consists of a transmitter,
a noisy relay, a noiseless relay and a receiver. We prove the capacity of this
class of diamond channels by providing an achievable scheme and a converse. The
capacity we show is strictly smaller than the cut-set bound. Our result also
shows the optimality of a combination of decode-and-forward (DAF) and
compress-and-forward (CAF) at the noisy relay node. This is the first example
where a combination of DAF and CAF is shown to be capacity achieving. Finally,
we note that there exists a duality between this diamond channel coding problem
and the Kaspi-Berger source coding problem.


  The magnetorotational instability (MRI), also known as the Balbus -- Hawley
instability, is thought to have an important role on the initiation of
turbulence and angular momentum transport in accretion discs. In this work, we
investigate the effect of the magnetic field gradient in the azimuthal
direction on MRI. We solve the magnetohydrodynamic equations by including the
azimuthal component of the field gradient. We find the dispersion relation and
calculate the growth rates of the instability numerically. The inclusion of the
azimuthal magnetic field gradient produces a new unstable region on wavenumber
space. It also modifies the growth rate and the wavelength range of the
unstable mode: the higher the magnitude of the field gradient, the greater the
growth rate and the wider the unstable wavenumber range. Such a gradient in the
magnetic field may be important in T Tauri discs where the stellar magnetic
field has an axis which is misaligned with respect to the rotation axis of the
disc.


  We prove that the condition \begin{equation}
\sum_{n=1}^\infty\frac{1}{nw(n)}<\infty \end{equation} is necessary for an
increasing sequence of numbers $w(n)$ to be an almost everywhere unconditional
convergence Weyl multiplier for the trigonometric system. This property for
Haar, Walsh, Franklin and some other classical orthogonal systems was known
long ago. The proof of this result is based on a new sharp logarithmic lower
bound on $L^2$ of the majorant operator related to the rearranged trigonometric
system.


  Precursors provide important clues to the nature of gamma-ray burst (GRB)
central engines and can be used to contain GRB physical processes. In this
letter, we study the self-organized criticality in precursors of long GRBs in
the third Swift/BAT Catalog. We investigate the differential and cumulative
size distributions of 100 precursors, including peak flux, duration, rise time,
decay time, and quiescent time with the Markov Chain Monte Carlo technique. It
is found that all of the distributions can be well described by power-law
models and understood within the physical framework of a self-organized
criticality system. In addition, we inspect the cumulative distribution
functions of the size differences with a q-Gaussian function. The
scale-invariance structures of precursors further strengthen our findings.
Particularly, similar analyses are made in 127 main bursts. The results show
that both precursors and main bursts can be attributed to an self-organized
criticality system with the spatial dimension S = 3 and driven by the similar
magnetically dominated process.


  Designing effective emergency response management (ERM) systems to respond to
incidents such as road accidents is a major problem faced by communities. In
addition to responding to frequent incidents each day (about 240 million
emergency medical services calls and over 5 million road accidents in the US
each year), these systems also support response during natural hazards.
Recently, there has been a consistent interest in building decision support and
optimization tools that can help emergency responders provide more efficient
and effective response. This includes a number of principled subsystems that
implement early incident detection, incident likelihood forecasting and
strategic resource allocation and dispatch policies. In this paper, we
highlight the key challenges and provide an overview of the approach developed
by our team in collaboration with our community partners.


  We study the dynamical and critical behavior of a model for irreversible
opinion spreading on Barab\'asi-Albert (BA) scale-free networks by performing
extensive Monte Carlo simulations. The opinion spreading within an
inhomogeneous society is investigated by means of the magnetic Eden model, a
nonequilibrium kinetic model for the growth of binary mixtures in contact with
a thermal bath. The deposition dynamics, which is studied as a function of the
degree of the occupied sites, shows evidence for the leading role played by
hubs in the growth process. Systems of finite size grow either ordered or
disordered, depending on the temperature. By means of standard finite-size
scaling procedures, the effective order-disorder phase transitions are found to
persist in the thermodynamic limit. This critical behavior, however, is absent
in related equilibrium spin systems such as the Ising model on BA scale-free
networks, which in the thermodynamic limit only displays a ferromagnetic phase.
The dependence of these results on the degree exponent is also discussed for
the case of uncorrelated scale-free networks.


  Oxygen vacancies (VO), a common type of point defects in metal oxides
materials, play important roles on the physical and chemical properties. To
obtain stoichiometric oxide crystal, the pre-existing VO is always removed via
careful post-annealing treatment at high temperature in air or oxygen
atmosphere. However, the annealing conditions is difficult to control and the
removal of VO in bulk phase is restrained due to high energy barrier of VO
migration. Here, we selected VO2 crystal film as the model system and developed
an alternative annealing treatment aided by controllable hydrogen doping, which
can realizes effective removal of VO defects in VO2-{\delta} crystal at lower
temperature. This finding is attributed to the hydrogenation accelerated oxygen
vacancies recovery in VO2-{\delta} crystal. Theoretical calculations revealed
that the H-doping induced electrons are prone to accumulate around the oxygen
defects in VO2-{\delta} film, which facilitates the diffusion of VO and thus
makes it easier to be removed. The methodology is expected to be applied to
other metal oxides for oxygen-related point defects control.


  Using two-dimensional radiation hydrodynamic simulations, we investigate
origin of the ultra fast outflows (UFOs) that are often observed in luminous
active galactic nuclei (AGNs). We found that the radiation force due to the
spectral lines generates strong winds (line-driven disk winds) that are
launched from the inner region of accretion disks (~30 Schwarzschild radii). A
wide range of black hole masses ($M_{\rm BH}$) and Eddington ratios
($\varepsilon$) was investigated to study conditions for causing the
line-driven winds. For $M_{\rm BH} = 10^6-10^9 M_\odot$ and $\varepsilon =
0.1-0.7$, funnel-shaped disk winds appear, in which dense matter is accelerated
outward with an opening angle of 70-80 deg and with 10% of the light speed. If
we observe the wind along its direction, the velocity, the column density, and
the ionization state are consistent with those of the observed UFOs. As long as
the obscuration by the torus does not affect the observations of X-ray bands,
the UFOs could be statistically observed in about 13-28% of the luminous AGNs,
which is not inconsistent with the observed ratio (~40%). We also found that
the results are insensitive to the X-ray luminosity and the density of the disk
surface. Thus, we can conclude that the UFOs could exist in any luminous AGNs,
such as narrow-line Seyfert 1s (NLS1s) and quasars with $\varepsilon > 0.1$, in
which fast line-driven winds are associated.


  We investigate the effects of isocurvature perturbations on the 21cm
radiation from minihaloes (MHs) at high redshifts and examine constraints on
the isocurvature amplitude and power spectrum using the next generation of
radio telescopes such as the Square Kilometre Array. We find that there is a
realistic prospect of observing the isocurvature imprints in the 21cm emission
from MHs, but only if the isocurvature spectral index is close to $3$ (i.e.,
the spectrum is blue). When the isocurvature fraction increases beyond $\sim
10\%$ of the adiabatic component, we observe an unexpected decline in the 21cm
fluctuations from small-mass MHs, which can be explained by the incorporation
small MHs into larger haloes. We perform a detailed Fisher-matrix analysis, and
conclude that the combination of future CMB and 21cm experiments (such as
CMBPol and the Fast-Fourier-Transform Telescope) is ideal in constraining the
isocurvature parameters, but will stop short of distinguishing between CDM and
baryon types of isocurvature perturbations, unless the isocurvature fraction is
large and the spectrum is blue.


  We test the consistency of the data on the nucleon structure functions with
analyticity and the Regge asymptotics of the virtual Compton amplitude. By
solving a functional extremal problem, we derive an optimal lower bound on the
maximum difference between the exact amplitude and the dominant Reggeon
contribution for energies $\nu$ above a certain high value $\nu_h(Q^2)$.
Considering in particular the difference of the amplitudes $T_1^\inel(\nu,
Q^2)$ for the proton and neutron, we find that the lower bound decreases in an
impressive way when $\nu_h(Q^2)$ is increased, and represents a very small
fraction of the magnitude of the dominant Reggeon. While the method cannot rule
out the hypothesis of a fixed Regge pole, the results indicate that the data on
the structure function are consistent with an asymptotic behaviour given by
leading Reggeon contributions. We also show that the minimum of the lower bound
as a function of the subtraction constant $S_1^\inel(Q^2)$ provides a
reasonable estimate of this quantity, in a frame similar, but not identical to
the Reggeon dominance hypothesis.


  Let $S = \{q_1, \ldots , q_s\}$ be a finite, non-empty set of distinct prime
numbers. For a non-zero integer $m$, write $m = q_1^{r_1} \ldots q_s^{r_s} M$,
where $r_1, \ldots , r_s$ are non-negative integers and $M$ is an integer
relatively prime to $q_1 \ldots q_s$. We define the $S$-part $[m]_S$ of $m$ by
$[m]_S := q_1^{r_1} \ldots q_s^{r_s}$. Let $(u_n)_{n \ge 0}$ be a linear
recurrence sequence of integers. Under certain necessary conditions, we
establish that for every $\varepsilon > 0$, there exists an integer $n_0$ such
that $[u_n]_S\leq |u_n|^{\varepsilon}$ holds for $n > n_0$. Our proof is
ineffective in the sense that it does not give an explicit value for $n_0$.
Under various assumptions on $(u_n)_{n \ge 0}$, we also give effective, but
weaker, upper bounds for $[u_n]_S$ of the form $|u_n|^{1 -c}$, where $c$ is
positive and depends only on $(u_n)_{n \ge 0}$ and $S$.


  This paper reviews recent results on hybrid inverse problems, which are also
called coupled-physics inverse problems of multi-wave inverse problems. Inverse
problems tend to be most useful in, e.g., medical and geophysical imaging, when
they combine high contrast with high resolution. In some settings, a single
modality displays either high contrast or high resolution but not both. In
favorable situations, physical effects couple one modality with high contrast
with another modality with high resolution. The mathematical analysis of such
couplings forms the class of hybrid inverse problems.
  Hybrid inverse problems typically involve two steps. In a first step, a
well-posed problem involving the high-resolution low-contrast modality is
solved from knowledge of boundary measurements. In a second step, a
quantitative reconstruction of the parameters of interest is performed from
knowledge of the point-wise, internal, functionals of the parameters
reconstructed during the first step. This paper reviews mathematical techniques
that have been developed in recent years to address the second step.
  Mathematically, many hybrid inverse problems find interpretations in terms of
linear and nonlinear (systems of) equations. In the analysis of such equations,
one often needs to verify that qualitative properties of solutions to elliptic
linear equations are satisfied, for instance the absence of any critical
points. This paper reviews several methods to prove that such qualitative
properties hold, including the method based on the construction of complex
geometric optics solutions.


  We provide a mathematically rigorous framework for supersymmetric fermion
lattice systems.
  We construct supersymmetric C*-dynamics in terms of a nilpotent
superderivation
  and a one-parameter group of automorphisms on the CAR-algebra. (We do not
make use of Grassmann numbers.) We establish several basic properties of
superderivations on the fermion lattice system. Among others, we obtain a
criterion of superderivations to yield supersymmetic dynamics.


  The AI for Experimental Controls project is developing an AI system to
control and calibrate detector systems located at Jefferson Laboratory.
Currently, calibrations are performed offline and require significant time and
attention from experts. This work would reduce the amount of data and the
amount of time spent calibrating in an offline setting. The first use case
involves the Central Drift Chamber (CDC) located inside the GlueX spectrometer
in Hall D. We use a combination of environmental and experimental data, such as
atmospheric pressure, gas temperature, and the flux of incident particles as
inputs to a Sequential Neural Network (NN) to recommend a high voltage setting
and the corresponding calibration constants in order to maintain consistent
gain and optimal resolution throughout the experiment. Utilizing AI in this
manner represents an initial shift from offline calibration towards near real
time calibrations performed at Jefferson Laboratory.


  We give a capacity formula for the classical information transmission over a
noisy quantum channel, with separable encoding by the sender and limited
resources provided by the receiver's pre-shared ancilla. Instead of a pure
state, we consider the signal-ancilla pair in a mixed state, purified by a
"witness". Thus, the signal-witness correlation limits the resource available
from the signal-ancilla correlation. Our formula characterizes the utility of
different forms of resources, including noisy or limited entanglement
assistance, for classical communication. With separable encoding, the sender's
signals across multiple channel uses are still allowed to be entangled, yet our
capacity formula is additive. In particular, for generalized covariant channels
our capacity formula has a simple closed-form. Moreover, our additive capacity
formula upper bounds the general coherent attack's information gain in various
two-way quantum key distribution protocols. For Gaussian protocols, the
additivity of the formula indicates that the collective Gaussian attack is the
most powerful.


  Braidoids generalize the classical braids and form a counterpart theory to
the theory of planar knotoids, just as the theory of braids does for the theory
of knots. In this paper, we introduce basic notions of braidoids, a closure
operation for braidoids, we prove an analogue of the Alexander theorem, that
is, an algorithm that turns a knotoid into a braidoid, and we formulate and
prove a geometric analogue of the Markov theorem for braidoids using the
$L$-moves.


  A search for the decay Bs -> D*-+ \pi+- is presented using a data sample
corresponding to an integrated luminosity of 1.0 fb-1 of pp collisions
collected by LHCb. This decay is expected to be mediated by a W-exchange
diagram, with little contribution from rescattering processes, and therefore a
measurement of the branching fraction will help to understand the mechanism
behind related decays such as Bs -> \pi+ \pi- and Bs -> D Dbar. Systematic
uncertainties are minimised by using B0 -> D*-+ \pi+- as a normalisation
channel. We find no evidence for a signal, and set an upper limit on the
branching fraction of BR(Bs -> D*-+ \pi+-) < 6.1 (7.8) x10^(-6) at 90% (95%)
confidence level.


  We model the kinematics of the high- and intermediate- velocity clouds (HVCs
and IVCs) observed in absorption towards a sample of 55 Galactic halo stars
with accurate distance measurements. We employ a simple model of a thick disc
whose main free parameters are the gas azimuthal, radial and vertical
velocities ($v_\phi$, $v_{\rm R}$ and $v_{\rm z}$), and apply it to the data by
fully accounting for the distribution of the observed features in the
distance-velocity space. We find that at least two separate components are
required to reproduce the data. A scenario where the HVCs and the IVCs are
treated as distinct populations provides only a partial description of the
data, which suggests that a pure velocity-based separation may give a biased
vision of the gas physics at the Milky Way's disc-halo interface. Instead, the
data are best described by a combination of an inflow and an outflow
components, both characterised by rotation with $v_\phi$ comparable to that of
the disc and $v_{\rm z}$ of 50-100 km/s. Features associated with the inflow
appear to be diffused across the sky, while those associated with the outflow
are mostly confined within a bi-cone pointing towards ($l\!=\!220^{\circ}$,
$b\!=\!+40^{\circ}$) and ($l\!=\!40^{\circ}$, $b\!=\!-40^{\circ}$). Our
findings indicate that the lower ($|z|\!\lesssim\!10$ kpc) Galactic halo is
populated by a mixture of diffuse inflowing gas and collimated outflowing
material, which are likely manifestations of a galaxy-wide gas cycle triggered
by stellar feedback, that is, the galactic fountain.


  Let $X$ be a compact connected hyperbolic surface, that is, a closed
connected orientable smooth surface with a Riemannian metric of constant
curvature -1. For each $n\in\mathbf{N}$, let $X_{n}$ be a random degree-$n$
cover of $X$ sampled uniformly from all degree-$n$ Riemannian covering spaces
of $X$. An eigenvalue of $X$ or $X_{n}$ is an eigenvalue of the associated
Laplacian operator $\Delta_{X}$ or $\Delta_{X_{n}}$. We say that an eigenvalue
of $X_n$ is new if it occurs with greater multiplicity than in $X$. We prove
that for any $\varepsilon>0$, with probability tending to 1 as $n\to\infty$,
there are no new eigenvalues of $X_n$ below $\frac{3}{16}-\varepsilon$. We
conjecture that the same result holds with $\frac{3}{16}$ replaced by
$\frac{1}{4}$.


  An important problem of optimization analysis surges when parameters such as
$ \{\theta_j\}_{j=1,\, \dots \,,k }$, determining a function $
y=f(x\given\{\theta_j\}) $, must be estimated from a set of observables $ \{
x_i,y_i\}_{i=1,\, \dots \,,m} $. Where $ \{x_i\} $ are independent variables
assumed to be uncertainty-free. It is known that analytical solutions are
possible if $ y=f(x\given\theta_j) $ is a linear combination of $
\{\theta_{j=1,\, \dots \,,k} \}.$ Here it is proposed that determining the
uncertainty of parameters that are not \textit{linearly independent} may be
achieved from derivatives $ \tfrac{\partial f(x \given \{\theta_j\})}{\partial
\theta_j} $ at an optimum, if the parameters are \textit{stochastically
independent}.


  We study the Josephson effect in a trijunction formed by two topological
superconductor (TS) wires and a conventional $s$-wave superconductor. Using a
boundary Green's function formalism, analytical results for the current-phase
relation are obtained in various limiting cases by modeling the TS wires via
the low-energy limit of a Kitaev chain. We show that Josephson transport
critically depends on the spin canting angle $\theta$ between the boundary spin
polarizations of the TS wires, which in turn suggests that the spin structure
of Majorana states can be accessed through supercurrent measurements. We also
extend the boundary Green's function approach to a more microscopic spinful
wire model and thereby compute the dependence of $\theta$ on experimentally
accessible parameters such as the Zeeman field and/or the chemical potential.
Furthermore, we show that the equilibrium current-phase relation between both
TS wires exhibits a robust $4\pi$-periodicity since the conventional
superconducting lead effectively locks the fermion parity of the trijunction.


  In this paper, we focus on the analysis of discrete versions of the Calderon
problem with partial boundary data in dimension d >= 3. In particular, we
establish logarithmic stability estimates for the discrete Calderon problem on
an arbitrarily small portion of the boundary under suitable a priori bounds.
For this end, we will use CGO solutions and derive a new discrete Carleman
estimate and a key unique continuation estimate. Unlike the continuous case, we
use a new strategy inspired by [32] to prove the key discrete unique
continuation estimate by utilizing the new Carleman estimate with boundary
observations for a discrete Laplace operator.


  We investigate Brownian motion with diffusivity alternately fluctuating
between fast and slow states. We assume that sojourn-time distributions of
these two states are given by exponential or power-law distributions. We
develop a theory of alternating renewal processes to study a relaxation
function which is expressed with an integral of the diffusivity over time. This
relaxation function can be related to a position correlation function if the
particle is in a harmonic potential, and to the self-intermediate scattering
function if the potential force is absent. It is theoretically shown that, at
short times, the exponential relaxation or the stretched-exponential relaxation
are observed depending on the power law index of the sojourn-time
distributions. In contrast, at long times, a power law decay with an
exponential cutoff is observed. The dependencies on the initial ensembles
(i.e., equilibrium or non-equilibrium initial ensembles) are also elucidated.
These theoretical results are consistent with numerical simulations.


  Delay-and-Sum (DAS) beamformer is the most common beamforming algorithm in
Photoacoustic imaging (PAI) due to its simple implementation and real time
imaging. However, it provides poor resolution and high levels of sidelobe. A
new algorithm named Delay-Multiply-and-Sum (DMAS) was introduced. Using DMAS
leads to lower levels of sidelobe compared to DAS, but resolution is not
satisfying yet. In this paper, a novel beamformer is introduced based on the
combination of Minimum Variance (MV) adaptive beamforming and DMAS, so-called
Minimum Variance-Based DMAS (MVB-DMAS). It is shown that expanding the DMAS
equation leads to some terms which contain a DAS equation. It is proposed to
use MV adaptive beamformer instead of existing DAS inside the DMAS algebra
expansion. MVB-DMAS is evaluated numerically compared to DAS, DMAS and MV and
Signal-to-noise ratio (SNR) metric is presented. It is shown that MVB-DMAS
leads to higher image quality and SNR for about 13 dB, 3 dB and 2 dB in
comparison with DAS, DMAS and MV, respectively.


  Here we use large-scale molecular dynamics (MD) simulations of the high-rate
deformation of nanocrystalline tantalum to investigate the processes associated
with plastic deformation for strains up to 100%. We use initial atomic
configurations that were produced through simulations of solidification in the
work of Streitz et al [Phys. Rev. Lett. 96, (2006) 225701]. These 3D
polycrystalline systems have typical grain sizes of 10-20 nm. We also study a
rapidly quenched liquid (amorphous solid) tantalum. We apply a constant volume
(isochoric), constant temperature (isothermal) shear deformation over a range
of strain rates, and compute the resulting stress-strain curves to large
strains for both uniaxial and biaxial compression. We study the rate dependence
and identify plastic deformation mechanisms. The identification of the
mechanisms is facilitated through a novel technique that computes the local
grain orientation, returning it as a quaternion for each atom. We find both
dislocation and twinning processes are important, and they interact in the weak
strain hardening in these extremely fine-grained microstructures.


  Composed of a large variety of technologies and applications with
unprecedented complexity, the smart grid, as a cyber-physical energy system,
needs careful investigation of the interactions between the various domains
involved, especially the coupling between the power and information systems. In
this paper, two modern ways of modeling and simulating complex cyber-physical
energy systems are considered: Co-simulation and Power-Hardware-in-the-Loop
experiments. An analysis of these two approaches shows that a complementary and
joint setup with realistic behaviors of hardware equipment under a variety of
complex environments, co-simulated by several simulators from different
domains, create a complete and high performance environment to achieve a
holistic approach for smart grid validation and roll out. In the scope of
coupling these two techniques, major technical challenges are identified and
advanced solutions are outlined.


  The global star formation rate has decreased significantly since z ~ 1, for
reasons that are not well understood. Red-sequence galaxies, dominating in
galaxy clusters, represent the population that have had their star formation
shut off, and may therefore be the key to this problem. In this work, we select
127 rich galaxy clusters at 0.17<z<0.36, from 119 square degrees of the
Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) optical imaging data, and
construct the r'-band red-sequence luminosity functions (LFs). We show that the
faint end of the LF is very sensitive to how red-sequence galaxies are
selected, and an optimal way to minimise the contamination from the blue cloud
is to mirror galaxies on the redder side of the colour-magnitude relation
(CMR). The LFs of our sample have a significant inflexion centred at Mr' ~-
18.5, suggesting a mixture of two populations. Combining our survey with low
redshift samples constructed from the Sloan Digital Sky Survey, we show that
there is no strong evolution of the faint end of the LF (or the red-sequence
dwarf-to-giant ratio) over the redshift range 0.2 < z < 0.4, but from z ~ 0.2
to z ~ 0 the relative number of red-sequence dwarf galaxies has increased by a
factor of ~3, implying a significant build-up of the faint end of the cluster
red-sequence over the last 2.5 Gyr.


  In this paper we provide new methodology for inference of the geometric
features of a multivariate density in deconvolution. Our approach is based on
multiscale tests to detect significant directional derivatives of the unknown
density at arbitrary points in arbitrary directions. The multiscale method is
used to identify regions of monotonicity and to construct a general procedure
for the detection of modes of the multivariate density. Moreover, as an
important application a significance test for the presence of a local maximum
at a pre-specified point is proposed. The performance of the new methods is
investigated from a theoretical point of view and the finite sample properties
are illustrated by means of a small simulation study.


  This paper is devoted to the study of generalized subdifferentials of
spectral functions over Euclidean Jordan algebras. Spectral functions appear
often in optimization problems playing the role of "regularizer", "barrier",
"penalty function" and many others. We provide formulae for the regular,
approximate and horizon subdifferentials of spectral functions. In addition,
under local lower semicontinuity, we also furnish a formula for the Clarke
subdifferential, thus extending an earlier result by Baes. As application, we
compute the generalized subdifferentials of the function that maps an element
to its k-th largest eigenvalue. Furthermore, in connection with recent
approaches for nonsmooth optimization, we present a study of the
Kurdyka-Lojasiewicz (KL) property for spectral functions and prove a transfer
principle for the KL-exponent. In our proofs, we make extensive use of recent
tools such as the commutation principle of Ram\'irez, Seeger and Sossa and
majorization principles developed by Gowda.


  Planar functions, introduced by Dembowski and Ostrom, have attracted much
attention in the last decade. As shown in this paper, we present a new class of
planar functions of the form $\operatorname{Tr}(ax^{q+1})+\ell(x^2)$ on an
extension of the finite field $\mathbb F_{q^n}/\mathbb F_q$. Specifically, we
investigate those functions on $\mathbb F_{q^2}/\mathbb F_q$ and construct
several typical kinds of planar functions. We also completely characterize them
on $\mathbb F_{q^3}/\mathbb F_q$. When the degree of extension is higher, it
will be proved that such planar functions do not exist given certain
conditions.


  The forward physics program of the CMS experiment at the LHC spans a broad
range of diverse physics topics including studies of low-x QCD and diffractive
scattering, multi-parton interactions and underlying event structure,
gamma-mediated processes and luminosity determination, Monte Carlo tuning and
even MSSM Higgs discovery in central exclusive production. In this article, the
forward detector instrumentation around the CMS interaction point is described
and the prospects for diffractive and forward physics using the CMS forward
detectors are summarized. In addition, first observation of forward jets as
well as early measurements of the forward energy flow in the pseudorapidity
range 3.15<|\eta|<4.9 at \sqrt{s}=0.9 TeV, 2.36 TeV and 7 TeV are presented.


  How does one measure the failure of Hochschild homology to commute with
colimits?
  Here I relate this question to a major open problem about dynamics in contact
manifolds -- the assertion that Reeb orbits exist and are detected by
symplectic homology. More precisely, I show that for polarizably Weinstein
fillable contact manifolds, said property is equivalent to the failure of
Hochschild homology to commute with certain colimits of representation
categories of tree quivers.
  So as to be intelligible to algebraists, I try to include or black-box as
much of the geometric background as possible.


  The entanglement at finite temperatures are analyzed by using thermal models
for colored quarks making up the hadron physical states. We have found that
these quantum correlations entirely vanish at $T_c\geq m_q/\ln(1.5)$. For
temperatures larger than $T_c$ the correlations are classical. Also we worked
out the entanglement for the transverse Ising spin chain. In dependence on both
temperature $T$ and transverse field $\lambda$ we can identify a certain
region, where the quantum effects are likely to dominate the system. We suggest
the mutual information as a quantitative measure for the correlations in ground
state.


  A variety of oscillations are observed in pancreatic islets.We establish a
model, incorporating two oscillatory systems of different time scales: One is
the well-known bursting model in pancreatic beta-cells and the other is the
glucose-insulin feedback model which considers direct and indirect feedback of
secreted insulin. These two are coupled to interact with each other in the
combined model, and two basic assumptions are made on the basis of biological
observations: The conductance g_{K(ATP)} for the ATP-dependent potassium
current is a decreasing function of the glucose concentration whereas the
insulin secretion rate is given by a function of the intracellular calcium
concentration. Obtained via extensive numerical simulations are complex
oscillations including clusters of bursts, slow and fast calcium oscillations,
and so on. We also consider how the intracellular glucose concentration depends
upon the extracellular glucose concentration, and examine the inhibitory
effects of insulin.


  We investigate the ground state properties of the spin S=1 Kitaev honeycomb
model under a magnetic field based on the density matrix renormalization group
(DMRG) calculation. With the time reversal symmetry breaking due to the
magnetic field, a gapped Kitaev spin liquid is identified for both
ferromagnetic (FM) and antiferromagnetic (AFM) Kitaev couplings. The
topological nature of such Kitaev spin liquid is manifested by the nearly
quantized Wilson loop, degeneracy in the entanglement spectra and existence of
edge modes. While the FM Kitaev spin liquid is destroyed by a weaker magnetic
field $H_*^\text{FM}$, the AFM one demonstrates a robustness up to an order of
magnitude larger critical field $H_*^\text{AFM}$. Moreover, an intermediate
nonmagnetic phase appears only for the AFM case at larger fields,
$H_*^\text{AFM} < H < H_{**}^\text{AFM}$, before the transition to a high-field
polarized paramagnet. The stability of the Kitaev spin liquid against the
Heisenberg interactions is also examined. Our findings may further inspire the
investigation of recently proposed S=1 Kitaev materials.


  Let $\varphi (x_{1}, \ldots, x_{h})=c_{1} x_{1}+\cdots+c_{h} x_{h}$ be a
linear form with coefficients in a field $\mathbf{F}$, and let $V$ be a vector
space over $\mathbf{F}$. A nonempty subset $A$ of $V$ is a $\varphi$-Sidon set
if $\varphi\left(a_{1}, \ldots, a_{h}\right)=\varphi\left(a_{1}^{\prime},
\ldots, a_{h}^{\prime}\right)$ implies $\left(a_{1}, \ldots, a_{h}\right)=$
$\left(a_{1}^{\prime}, \ldots, a_{h}^{\prime}\right)$ for all $h$-tuples
$\left(a_{1}, \ldots, a_{h}\right) \in A^{h}$ and $\left(a_{1}^{\prime},
\ldots, a_{h}^{\prime}\right) \in A^{h}$. We call $A$ a polynomial perturbation
of $B$ if for some $r>0$ and positive integer $k_0$, $|a_k-b_k|< k^r$ holds for
all integers $k \geq k_0$. In this paper, for a given set $B$, we prove that
there exists a $\varphi$-Sidon set $A$ of integers that is a polynomial
perturbation of $B$. This gives an affirmative answer to a recent problem of
Nathanson. Some other results are also proved.


  The present contribution contains a quite extensive theory for the stability
analysis of plane periodic waves of general Schr{\"o}dinger equations. On one
hand, we put the one-dimensional theory, or in other words the stability theory
for longitudinal perturbations, on a par with the one available for systems of
Korteweg type, including results on co-periodic spectral instability, nonlinear
co-periodic orbital stability, side-band spectral instability and linearized
large-time dynamics in relation with modulation theory, and resolutions of all
the involved assumptions in both the small-amplitude and large-period regimes.
On the other hand, we provide extensions of the spectral part of the latter to
the multi-dimensional context. Notably, we provide suitable multi-dimensional
modulation formal asymptotics, validate those at the spectral level and use
them to prove that waves are always spectrally unstable in both the
small-amplitude and the large-period regimes.


  We study flat space cosmologies in two dimensions by taking the flat space
limit of the Achucarro-Ortiz model. We unravel a phase transition between hot
flat space and flat space cosmologies, and derive a new dilaton-dependent
counterterm required for the consistency of the Euclidean partition function.
Our results generalize to asymptotically mass-dominated 2-dimensional dilaton
gravity models, whose thermodynamical properties we discuss. The novel case of
asymptotic mass-domination is neither covered by the comprehensive discussion
of hep-th/0703230 nor by the more recent generalization to dilaton gravity with
confining U(1) charges in 1406.7007.


  Recent experiments have shown that the edge states of a quantum Hall sample
can be coupled to a superconductor, so that incoming electrons in the edge
states can be Andreev converted on the superconductor as coherent
superpositions of an electron and a hole. In addition to this, single-electron
emitters that operate in the gigahertz regime have been realized. Motivated by
this remarkable experimental progress, we here analyze the Andreev reflections
of incoming charge pulses on the interface with a superconductor. To this end,
we employ a Wigner function representation that allows us to visualize the
response function of the interface both in the time and in the frequency
domain. We analyze the response of an interface between a normal-metal and a
singlet or triplet superconductor with and without an insulating barrier in
between them. As a special case, we analyze the Andreev reflections of clean
single-particle excitations that are generated by the application of
lorentzian-shaped voltage pulses to the contacts of the inputs. Our predictions
may be tested in future experiments with edge states coupled to
superconductors.


  Machines are possible to have some artificial intelligence like human beings
owing to particular algorithms or software. Such machines could learn knowledge
from what people taught them and do works according to the knowledge. In
practical learning cases, the data is often extremely complicated and large,
thus classical learning machines often need huge computational resources.
Quantum machine learning algorithm, on the other hand, could be exponentially
faster than classical machines using quantum parallelism. Here, we demonstrate
a quantum machine learning algorithm on a four-qubit NMR test bench to solve an
optical character recognition problem, also known as the handwriting
recognition. The quantum machine learns standard character fonts and then
recognize handwritten characters from a set with two candidates. To our best
knowledge, this is the first artificial intelligence realized on a quantum
processor. Due to the widespreading importance of artificial intelligence and
its tremendous consuming of computational resources, quantum speedup would be
extremely attractive against the challenges from the Big Data.


  A classical phase space with a suitable symplectic structure is constructed
together with functions which have Poisson brackets algebraically identical to
the Lie algebra structure of the Lie group SU(n). In this phase space we show
that the orbit of the generators corresponding to the simple roots of the Lie
algebra give rise to fibres that are complex lines containing spheres. There
are n-1 spheres on a fibre and they intersect in exactly the same way as the
Cartan matrix of the Lie algebra. This classical phase space bundle,being
compact,has a description as a variety.Our construction shows that the variety
containing the intersecting spheres is exactly the one obtained by resolving
the singularities of the variety {x_0}{x_1}-{{x_2}^n}=0 in {C^3}. A direct
connection between this singular variety and the classical phase space
corresponding to the Lie group SU(n) is thus established.


  Lattice models with non-hermitian, parity and time-reversal ($\mathcal{PT}$)
symmetric Hamiltonians, realized most readily in coupled optical systems, have
been intensely studied in the past few years. A $\mathcal{PT}$-symmetric dimer
lattice consists of dimers with intra-dimer coupling $\nu$, inter-dimer
coupling $\nu'$, and balanced gain and loss potentials $\pm i\gamma$ within
each dimer. This model undergoes two independent transitions, namely a
$\mathcal{PT}$-breaking transition and a topological transition. We numerically
and analytically investigate the signatures of these transitions in the
time-evolution of states that are initially localized on the gain-site or the
loss-site.


  L\'evai and Pyber proposed the following as a conjecture: Let $G$ be a
profinite group such that the set of solutions of the equation $x^n=1$ has
positive Haar measure. Then $G$ has an open subgroup $H$ and an element $t$
such that all elements of the coset $tH$ have order dividing $n$ (see Problem
14.53 of [The Kourovka Notebook, No. 19, 2019]). The validity of the conjecture
has been proved in [Arch. Math. (Basel) 75 (2000) 1-7] for $n=2$. Here we study
the conjecture for compact groups $G$ which are not necessarily profinite and
$n=3$; we show that in the latter case the group $G$ contains an open normal
$2$-Engel subgroup.


  We have analyzed deep narrow-band H$\alpha$ images and high-resolution
long-slit spectra for a sample of the nearest and brightest late-type galaxies
to study the morphology, physical state, and kinematics of the `Diffuse Ionized
Medium' (`DIM'). We find that the DIM covers most of the star-forming disk, and
is morphologically related to the presence of the giant HII regions. In
addition, the DIM and the giant HII regions differ systematically in their
physical and dynamical state. The DIM is characterized by enhanced emission in
the low-ionization forbidden lines ([OI], [NII], and [SII]), and even the
high-ionization [OIII]$\lambda$5007 line is moderately strong in the DIM. We
verify the inference made by Lehnert & Heckman that the DIM contributes
significantly to the global emission-line ratios measured in late-type
galaxies. We also find that the DIM is more disturbed kinematically than the
gas in the giant HII regions. The intrinsic FWHMs of the H$\alpha$ and
[NII]$\lambda$6584 lines range from 30 to 100 km s$^{-1}$ in the DIM compared
to 20-50 km s$^{-1}$ in HII regions. The high-ionization gas in the DIM is even
more kinematically disturbed than the low-ionization gas: the
[OIII]$\lambda$5007 lines have intrinsic FWHMs of 70-150 km s$^{-1}$. The
differing kinematics implies that `the DIM' is not a single monolithic phase of
the ISM. Instead, it may consist of a `quiescent DIM' with a low
ionization-state and small scale-height (few hundred pc) and a `disturbed DIM'
with a high ionization state and moderate scale-height (0.5 to 1 kpc). We argue
that the quiescent DIM is most likely photoionized by radiation leaking out of
giant HII regions, while the disturbed DIM is most likely heated by the
mechanical energy supplied by supernovae and stellar winds.


  Understanding transformer-based language models is becoming increasingly
crucial, particularly as they play pivotal roles in advancing towards
artificial general intelligence. However, language model research faces
significant challenges, especially for academic research groups with
constrained resources. These challenges include complex data structures,
unknown target functions, high computational costs and memory requirements, and
a lack of interpretability in the inference process, etc. Drawing a parallel to
the use of simple models in scientific research, we propose the concept of an
anchor function. This is a type of benchmark function designed for studying
language models in learning tasks that follow an "anchor-key" pattern. By
utilizing the concept of an anchor function, we can construct a series of
functions to simulate various language tasks. The anchor function plays a role
analogous to that of mice in diabetes research, particularly suitable for
academic research. We demonstrate the utility of the anchor function with an
example, revealing two basic operations by attention structures in language
models: shifting tokens and broadcasting one token from one position to many
positions. These operations are also commonly observed in large language
models. The anchor function framework, therefore, opens up a series of valuable
and accessible research questions for further exploration, especially for
theoretical study.


  The energy super-critical Gross--Pitaevskii equation with a harmonic
potential is revisited in the particular case of cubic focusing nonlinearity
and dimension d > 4. In order to prove the existence of a ground state (a
positive, radially symmetric solution in the energy space), we develop the
shooting method and deal with a one-parameter family of classical solutions to
an initial-value problem for the stationary equation. We prove that the
solution curve (the graph of the eigenvalue parameter versus the supremum) is
oscillatory for d <= 12 and monotone for d >= 13. Compared to the existing
literature, rigorous asymptotics are derived by constructing three families of
solutions to the stationary equation with functional-analytic rather than
geometric methods.


  This work mainly presents a preliminary design for a pendulum experiment with
both the source mass and the test mass in a striped pattern to amplify the
Lorentz-violation signal, since the signal is sensitive to edge effects.


  When long-range interactions are present the usual definition of temperature
implies that two systems in thermal equilibrium can be at different
temperatures. This local temperature has physical significance, if the
sub-systems cease to interact, each system will be at their different local
temperatures. This is formally related to redshifting of temperature in general
relativity. We propose experiments to test this effect which are feasible using
current microfabrication techniques. It is also possible to display
thermodynamical analogues to black-hole space-time.


  The instabilities of the nontrivial phase elliptic solutions in a repulsive
Bose-Einstein condensate (BEC) with a periodic potential are investigated.
Based on the defocusing nonlinear Schr\"{o}dinger (NLS) equation with an
elliptic function potential, the well-known modulational instability (MI), the
more recently identified high-frequency instability, and an unprecedented -- to
our knowledge -- variant of the MI, the so-called isola instability are
identified numerically. Upon varying parameters of the solutions, instability
transitions occur through the suitable bifurcations, such as the Hamiltonian
Hope one. Specifically, (i) increasing the elliptic modulus $k$ of the
solutions, we find that MI switches to the isola instability and the dominant
disturbance has twice the elliptic wave's period, corresponding to a Floquet
exponent $\mu=\frac{\pi}{2K(k)}$. The isola instability arises from the
collision of spectral elements at the origin of the spectral plane. (ii) Upon
varying $V_{0}$, the transition between MI and the high-frequency instability
occurs. Differently from the MI and isola instability where the collisions of
eigenvalues happen at the origin, high-frequency instability arises from
pairwise collisions of nonzero, imaginary elements of the stability spectrum;
(iii) In the limit of sinusoidal potential, we show that MI occurs from a
collision of eigenvalues with $\mu=\frac{\pi}{2K(k)}$ at the origin; (iv) we
also examine the dynamic byproducts of the instability in chaotic fields
generated by its manifestation. An interesting observation is that, in addition
to MI, the isola instability could also lead to dark localized events in the
scalar defocusing NLS equation.


  In this paper, we consider the convergence problem of Schr\"odinger equation.
Firstly, we show the almost everywhere pointwise convergence of Schr\"odinger
equation in Fourier-Lebesgue spaces
$\hat{H}^{\frac{1}{p},\frac{p}{2}}(\mathbb{R})(4\leq p<\infty),$
$\hat{H}^{\frac{3 s_{1}}{p},\frac{2p}{3}}(\mathbb{R}^2)(s_{1}>\frac{1}{3},3\leq
p<\infty),$ $\hat{H}^{\frac{2
s_{1}}{p},p}(\mathbb{R}^n)(s_{1}>\frac{n}{2(n+1)},2\leq p<\infty,n\geq3)$ with
rough data. Secondly, we show that the maximal function estimate related to one
Schr\"odinger equation can fail with data in
$\hat{H}^{s,\frac{p}{2}}(\mathbb{R})(s<\frac{1}{p})$. Finally, we show the
stochastic continuity of Schr\"odinger equation with random data in
$\hat{L}^{r}(\mathbb{R}^n)(2\leq r<\infty)$ almost surely. The main ingredients
are Lemmas 2.4, 2.5, 3.2-3.4.


  We present in this paper a library to compute with Taylor models, a technique
extending interval arithmetic to reduce decorrelation and to solve differential
equations. Numerical software usually produces only numerical results. Our
library can be used to produce both results and proofs. As seen during the
development of Fermat's last theorem reported by Aczel 1996, providing a proof
is not sufficient. Our library provides a proof that has been thoroughly
scrutinized by a trustworthy and tireless assistant. PVS is an automatic proof
assistant that has been fairly developed and used and that has no internal
connection with interval arithmetic or Taylor models. We built our library so
that PVS validates each result as it is produced. As producing and validating a
proof, is and will certainly remain a bigger task than just producing a
numerical result our library will never be a replacement to imperative
implementations of Taylor models such as Cosy Infinity. Our library should
mainly be used to validate small to medium size results that are involved in
safety or life critical applications.


  The boundary control problem is a non-convex optimization and control problem
in many scientific domains, including fluid mechanics, structural engineering,
and heat transfer optimization. The aim is to find the optimal values for the
domain boundaries such that the enclosed domain adhering to the governing
equations attains the desired state values. Traditionally, non-linear
optimization methods, such as the Interior-Point method (IPM), are used to
solve such problems.
  This project explores the possibilities of using deep learning and
reinforcement learning to solve boundary control problems. We adhere to the
framework of iterative optimization strategies, employing a spatial neural
network to construct well-informed initial guesses, and a spatio-temporal
neural network learns the iterative optimization algorithm using policy
gradients. Synthetic data, generated from the problems formulated in the
literature, is used for training, testing and validation. The numerical
experiments indicate that the proposed method can rival the speed and accuracy
of existing solvers. In our preliminary results, the network attains costs
lower than IPOPT, a state-of-the-art non-linear IPM, in 51\% cases. The overall
number of floating point operations in the proposed method is similar to that
of IPOPT. Additionally, the informed initial guess method and the learned
momentum-like behaviour in the optimizer method are incorporated to avoid
convergence to local minima.


  NICMOS observations of the complex gravitational lens system B1933+503 reveal
infrared counterparts to two of the inverted spectrum radio images. The
infrared images have arc-like structures. The corresponding radio images are
also detected in a VLBA map made at 1.7 GHz with a resolution of 6 mas. We fail
to detect two of the four inverted radio spectrum components with the VLBA even
though they are clearly visible in a MERLIN map at the same frequency at a
different epoch. The absence of these two components could be due to rapid
variability on a time-scale less than the time delay, or to broadening of the
images during propagation of the radio waves through the ISM of the lensing
galaxy to an extent that they fall below the surface brightness detectability
threshold of the VLBA observations. The failure to detect the same two images
with NICMOS is probably due to extinction in the ISM of the lensing galaxy.


  The aim of our paper is twofold. First, we thoroughly study the set of meager
elements M(E), the center C(E) and the compatibility center B(E)in the setting
of atomic Archimedean lattice effect algebras E. The main result is that in
this case the center C(E) is bifull (atomic) iff the compatibility center B(E)
is bifull (atomic) whenever E is sharply dominating. As a by-product, we give a
new descriciption of the smallest sharp element over x in E via the basic
decomposition of x. Second, we prove the Triple Representation Theorem for
sharply dominating atomic Archimedean lattice effect algebras.


  We consider the embedding problem in coding theory: given an independence (a
code-related property) and an independent language $L$, find a maximal
independent language containing $L$. We consider the case where the
code-related property is defined via a rational binary relation that is
decreasing with respect to any fixed total order on the set of words. Our
method works by iterating a max-min operator that has been used before for the
embedding problem for properties defined by length-increasing-and-transitive
binary relations. By going to order-decreasing rational relations, represented
by input-decreasing transducers, we are able to include many known properties
from both the noiseless and noisy domains of coding theory, as well as any
combination of such properties. Moreover, in many cases the desired maximal
embedding is effectively computable.


  Transformer has become the new standard method in natural language processing
(NLP), and it also attracts research interests in computer vision area. In this
paper we investigate the application of Transformer in Image Quality (TRIQ)
assessment. Following the original Transformer encoder employed in Vision
Transformer (ViT), we propose an architecture of using a shallow Transformer
encoder on the top of a feature map extracted by convolution neural networks
(CNN). Adaptive positional embedding is employed in the Transformer encoder to
handle images with arbitrary resolutions. Different settings of Transformer
architectures have been investigated on publicly available image quality
databases. We have found that the proposed TRIQ architecture achieves
outstanding performance. The implementation of TRIQ is published on Github
(https://github.com/junyongyou/triq).


  In this paper we introduce new characterizations of spectral fractional
Laplacian to incorporate nonhomogeneous Dirichlet and Neumann boundary
conditions. The classical cases with homogeneous boundary conditions arise as a
special case. We apply our definition to fractional elliptic equations of order
$s \in (0,1)$ with nonzero Dirichlet and Neumann boundary condition. Here the
domain $\Omega$ is assumed to be a bounded, quasi-convex Lipschitz domain. To
impose the nonzero boundary conditions, we construct fractional harmonic
extensions of the boundary data. It is shown that solving for the fractional
harmonic extension is equivalent to solving for the standard harmonic extension
in the very-weak form. The latter result is of independent interest as well.
The remaining fractional elliptic problem (with homogeneous boundary data) can
be realized using the existing techniques. We introduce finite element
discretizations and derive discretization error estimates in natural norms,
which are confirmed by numerical experiments. We also apply our
characterizations to Dirichlet and Neumann boundary optimal control problems
with fractional elliptic equation as constraints.


  We present a method to combine the all-order treatment of the High Energy
Jets exclusive partonic Monte Carlo (HEJ) with the parton shower of Pythia8,
while retaining the logarithmic accuracy of both. This procedure enables the
generation of fully realistic and hadronised events with HEJ. Furthermore, the
combination of the two all-order treatments leads to improvements in the
quality of the description of observables, in particular for regions with
disparate transverse scales.


  The effective action for QED in curved spacetime includes equivalence
principle violating interactions between the electromagnetic field and the
spacetime curvature. These interactions admit the possibility of superluminal
yet causal photon propagation in gravitational fields. In this paper, we extend
our analysis of photon propagation in gravitational backgrounds to the Kerr
spacetime describing a rotating black hole. The results support two general
theorems -- a polarisation sum rule and a `horizon theorem'. The implications
for the stationary limit surface bounding the ergosphere are also discussed.


  The minimal surface equation $Q$ in the second order contact bundle of $R^3$,
modulo translations, is provided with a complex structure and a canonical
vector-valued holomorphic differential form $Omega$ on $Q\0$. The minimal
surfaces $M$ in $R^3$ correspond to the complex analytic curves $C$ in $Q$,
where the derivative of the Gauss map sends $M$ to $C$, and $M$ is equal to the
real part of the integral of $\Omega$ over $C$. The complete minimal surfaces
of finite topological type and with flat points at infinity correspond to the
algebraic curves in $Q$.


  In this paper, necessary and sufficient conditions on terms of monotone
Fourier coefficients for a function to belong to a Nikol'ski\u{\i}--Besov type
class are given.


  We analyze the cut-off dependence of mesonic spectral functions calculated at
finite temperature on Euclidean lattices with finite temporal extent. In the
infinite temperature limit we present analytic results for lattice spectral
functions calculated with standard Wilson fermions as well as a truncated
perfect action. We explicitly determine the influence of `Wilson doublers' on
the high momentum structure of the mesonic spectral functions and show that
this cut-off effect is strongly suppressed when using an improved fermion
action.


  In order to annihilate in the early Universe to levels well below the
measured dark matter density, asymmetric dark matter must possess large
couplings to the Standard Model. In this paper, we consider effective operators
which allow asymmetric dark matter to annihilate into quarks. In addition to a
bound from requiring sufficient annihilation, the energy scale of such
operators can be constrained by limits from direct detection and monojet
searches at colliders. We show that the allowed parameter space for these
operators is highly constrained, leading to non-trivial requirements that any
model of asymmetric dark matter must satisfy.


  We revisit residual algorithms in both model-free and model-based
reinforcement learning settings. We propose the bidirectional target network
technique to stabilize residual algorithms, yielding a residual version of DDPG
that significantly outperforms vanilla DDPG in the DeepMind Control Suite
benchmark. Moreover, we find the residual algorithm an effective approach to
the distribution mismatch problem in model-based planning. Compared with the
existing TD($k$) method, our residual-based method makes weaker assumptions
about the model and yields a greater performance boost.


  Many approaches for estimation of Remaining Useful Life (RUL) of a machine,
using its operational sensor data, make assumptions about how a system degrades
or a fault evolves, e.g., exponential degradation. However, in many domains
degradation may not follow a pattern. We propose a Long Short Term Memory based
Encoder-Decoder (LSTM-ED) scheme to obtain an unsupervised health index (HI)
for a system using multi-sensor time-series data. LSTM-ED is trained to
reconstruct the time-series corresponding to healthy state of a system. The
reconstruction error is used to compute HI which is then used for RUL
estimation. We evaluate our approach on publicly available Turbofan Engine and
Milling Machine datasets. We also present results on a real-world industry
dataset from a pulverizer mill where we find significant correlation between
LSTM-ED based HI and maintenance costs.


  We study the low-energy excitations of the spin-1/2 antiferromagnetic
Heisenberg chain and $N$-leg ($N$=2, 3, 4) ladders in a staggered magnetic
field $h_s$. We show that $h_s$ induces gap and midgap states in all the cases
and examine their field scaling behavior. A modified boundary scheme is devised
to extract accurate bulk excitation behavior. The gap values converge rapidly
as $N$ increases, leading to a field scaling exponent $\gamma=1/2$ for both the
longitudinal and transverse gaps of the square lattice ($N \to \infty$). The
midgap states induced by the boundary edge effects share the bulk gap scaling
exponents but their overall scaling behavior in the large-N limit needs further
investigation.


  Online social networks are more and more studied. The links between users of
a social network are important and have to be well qualified in order to detect
communities and find influencers for example. In this paper, we present an
approach based on the theory of belief functions to estimate the degrees of
cognitive independence between users in a social network. We experiment the
proposed method on a large amount of data gathered from the Twitter social
network.


  It has been shown that maximum distance profile (MDP) convolutional codes
have optimal recovery rate for windows of a certain length, when transmitting
over an erasure channel. In addition, the subclass of complete MDP
convolutional codes has the ability to reduce the waiting time during decoding.
In this paper, we derive upper bounds on the necessary field size for the
existence of MDP and complete MDP convolutional codes and show that these
bounds improve the already existing ones. Moreover, we derive lower bounds for
the probability that a random code is MDP respective complete MDP.


  We report on the creation of ultracold 84Sr2 molecules in the electronic
ground state. The molecules are formed from atom pairs on sites of an optical
lattice using stimulated Raman adiabatic passage (STIRAP). We achieve a
transfer efficiency of 30% and obtain 4x10^4 molecules with full control over
the external and internal quantum state. STIRAP is performed near the narrow
1S0-3P1 intercombination transition, using a vibrational level of the 0u
potential as intermediate state. In preparation of our molecule association
scheme, we have determined the binding energies of the last vibrational levels
of the 0u, 1u excited-state, and the 1\Sigma_g^+ ground-state potentials. Our
work overcomes the previous limitation of STIRAP schemes to systems with
Feshbach resonances, thereby establishing a route that is applicable to many
systems beyond bi-alkalis.


  Neutrinos from core collapse supernovae can excite nuclei of some detector
materials beyond their neutron emission thresholds. Detection of these neutrons
can give valuable information about the supernova explosion mechanism and
possibly also throw light on neutrino properties. In this article, we give a
brief review of the basic physics of neutrino induced neutron emission and
describe the results of some recent calculations of supernova neutrino induced
neutrons for some specific target detector materials due to charged current
(CC) interactions of the electron flavored neutrinos and antineutrinos as well
as due to neutral current (NC) interactions of neutrinos and antineutrinos of
all flavors with the detector nuclei. We highlight the fact that a detector
material such as lead with a relatively large neutron excess produces neutrons
dominantly through the CC interaction of the $\nu_e$s, whereas a material such
as iron with small neutron excess produces neutrons dominantly through the
combined NC interaction of all the six neutrino and antineutrino species. This
raises the interesting possibility of probing the fraction of mu- and tau
flavored neutrinos (which interact only through NC interaction) in the
supernova neutrino flux by means of simultaneous detection of a supernova in a
lead and an iron detector, for example.


  \noindent A formalism based on path-integral expression of time-evolution
operator during tunneling at a finite energy proposed by the authors is applied
to $SU(2)$ gauge-Higgs system to produce Higgs particles with $\Delta B=1$.
Instead of starting from instanton tunneling at the zero energy, a classical
bounce solution giving sphaleron (instanton) action at high (low) energies is
used as the tunneling configuration. Fourier transform of the bounce
configuration in coherent state expression at the entrance and exit of the
tunneling plays an important role. Numerical results at various energies for
$M_H/M_W=1 \sim 2 $ are given. Though the cross section with $\Delta B=1$
results from a severe cancellation of several large quantities in the leading
order as occured in the instanton calculus, it seems unlikely that the cross
section grows as largely as to reach unitarity bound at energies $E \leq
E_{sph}$. It is pointed out that the actual value $g^2=0.418$ of the $SU(2)$
gauge coupling constant may be too large to take the weak coupling limit.}


  We introduce a notion of weak Denjoy subsystem (WDS) that generalizes the
Aubry-Mather Cantor sets to diffeomorphisms of manifolds. We explain how a
rotation number can be associated to such a WDS. Then we build in any horseshoe
a continuous one parameter family of such WDS that is indexed by its rotation
number. Looking at the inverse problem in the setting of Aubry-Mather theory,
we also prove that for a generic conservative twist map of the annulus, the
majority of the Aubry-Mather sets are contained in some horseshoe that is
associated to a Aubry-Mather set with a rational rotation number.


  We evaluate the amplitude of Bethe-Heitler process: \gamma^* p -> \gamma
\Delta^+ -electron bremsstrahlung of photon accompanied by the excitation of
\Delta$ isobar. We show that this background is suppressed at small momentum
transfer squared t to a proton relative to that for \gamma^* p -> \gamma p and
\gamma^* p\to -> \Delta^+ - DVCS processes. From experimental point of view,
this means that N -> N and N -> \Delta skewed quark distributions (SQD's) might
be measurable at small momentum transfer. Several implications and applications
of the QCD factorization theorem for the processes \gamma_{L}^* + p -> h_f +h_s
are discussed where h_f - the particle produced along photon momentum $\vec q$
maybe either a meson or a baryon. We discuss also t dependence of DVCS and
exclusive meson production as the practical criteria to distinguish between
soft and hard regime. Basing on the large-N_c picture of the nucleon as a
soliton of the effective chiral Lagrangian we derive relations between N -> N
and N ->\Delta SQD's which can be used to estimate amplitude of N -> \Delta
DVCS .


  Water resources are essential for sustaining human livelihoods and
environmental well being. Accurate water quality prediction plays a pivotal
role in effective resource management and pollution mitigation. In this study,
we assess the effectiveness of five distinct predictive models linear
regression, Random Forest, XGBoost, LightGBM, and MLP neural network, in
forecasting pH values within the geographical context of Georgia, USA. Notably,
LightGBM emerges as the top performing model, achieving the highest average
precision. Our analysis underscores the supremacy of tree-based models in
addressing regression challenges, while revealing the sensitivity of MLP neural
networks to feature scaling. Intriguingly, our findings shed light on a
counterintuitive discovery: machine learning models, which do not explicitly
account for time dependencies and spatial considerations, outperform spatial
temporal models. This unexpected superiority of machine learning models
challenges conventional assumptions and highlights their potential for
practical applications in water quality prediction. Our research aims to
establish a robust predictive pipeline accessible to both data science experts
and those without domain specific knowledge. In essence, we present a novel
perspective on achieving high prediction accuracy and interpretability in data
science methodologies. Through this study, we redefine the boundaries of water
quality forecasting, emphasizing the significance of data driven approaches
over traditional spatial temporal models. Our findings offer valuable insights
into the evolving landscape of water resource management and environmental
protection.


  We propose a K-sparse exhaustive search (ES-K) method and a K-sparse
approximate exhaustive search method (AES-K) for selecting variables in linear
regression. With these methods, K-sparse combinations of variables are tested
exhaustively assuming that the optimal combination of explanatory variables is
K-sparse. By collecting the results of exhaustively computing ES-K, various
approximate methods for selecting sparse variables can be summarized as density
of states. With this density of states, we can compare different methods for
selecting sparse variables such as relaxation and sampling. For large problems
where the combinatorial explosion of explanatory variables is crucial, the
AES-K method enables density of states to be effectively reconstructed by using
the replica-exchange Monte Carlo method and the multiple histogram method.
Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the
conventional understanding in astronomy when an appropriate K is given
beforehand. However, we found the difficulty to determine K from the data.
Using virtual measurement and analysis, we argue that this is caused by data
shortage.


  The new field of adaptive data analysis seeks to provide algorithms and
provable guarantees for models of machine learning that allow researchers to
reuse their data, which normally falls outside of the usual statistical
paradigm of static data analysis. In 2014, Dwork, Feldman, Hardt, Pitassi,
Reingold and Roth introduced one potential model and proposed several solutions
based on differential privacy. In previous work in 2016, we described a problem
with this model and instead proposed a Bayesian variant, but also found that
the analogous Bayesian methods cannot achieve the same statistical guarantees
as in the static case.
  In this paper, we prove the first positive results for the Bayesian model,
showing that with a Dirichlet prior, the posterior mean algorithm indeed
matches the statistical guarantees of the static case. The main ingredient is a
new theorem showing that the $\mathrm{Beta}(\alpha,\beta)$ distribution is
subgaussian with variance proxy $O(1/(\alpha+\beta+1))$, a concentration result
also of independent interest. We provide two proofs of this result: a
probabilistic proof utilizing a simple condition for the raw moments of a
positive random variable and a learning-theoretic proof based on considering
the beta distribution as a posterior, both of which have implications to other
related problems.


  We study the direct detection rate for SUSY cold dark m atter (CDM) predicted
by the minimal supersymmetric standard model with universal boundary conditions
and large values for tan\beta. The relic abundance of the lightest
supersymmetric particle (LSP), assumed to be approximately a bino, is obtained
by including its coannihilations with the next-to-lightest supersymmetric
particle (NLSP), which is the lightest s-tau. We find detectable rates in the
currently planned experiments for a sector of the parameter space consistent
with the cosmological constraint on the LSP relic abundance and the ones
imposed by b->s gamma and the Higgs searches.


  When designing agents for operation in uncertain environments, designers need
tools to automatically reason about what agents ought to do, how that conflicts
with what is actually happening, and how a policy might be modified to remove
the conflict. These obligations include ethical and social obligations,
permissions and prohibitions, which constrain how the agent achieves its
mission and executes its policy. We propose a new deontic logic, Expected Act
Utilitarian deontic logic, for enabling this reasoning at design time: for
specifying and verifying the agent's strategic obligations, then modifying its
policy from a reference policy to meet those obligations. Unlike approaches
that work at the reward level, working at the logical level increases the
transparency of the trade-offs. We introduce two algorithms: one for
model-checking whether an RL agent has the right strategic obligations, and one
for modifying a reference decision policy to make it meet obligations expressed
in our logic. We illustrate our algorithms on DAC-MDPs which accurately
abstract neural decision policies, and on toy gridworld environments.


  In this research, we do a software writing in Python to calculate the
efforts, bending moments and deformations in beams of different materials. This
computational tool, that we developed, is of great help in area of
computational physical, more exactly in resistance of materials, which serves
as support for researchers and teachers especially in physics and civil
engineering, of the part of statics, who wish to carry out the modeling of the
functions, involved in the calculation of resistance in beams in a practical
and simple way, using the software presented in this article. In order to carry
out this software, we are going to use the following methods: the
double-integration method and the conjugate-beam method, which will serve as
the basis of calculation to find the mathematical expressions involved in the
analysis of resistance in beams, then we will perform the implementation of the
aforementioned methods, using Python as the programming language. As a final
step in this project, the graphical interface of said calculation tool will be
made using the Python 3.0 Tkinter library. In this work, we show the results of
the graphs of the stress profiles, bending moments and deformations, for the
case of different types of beams, load and force distributions applied to them.
Where we were also able to conclude that a calculation software was
successfully built, dedicated to the analysis of efforts and deformations in
beams made of different materials.


  We analyze a set of volume limited samples from SDSS DR12 to quantify the
degree of inhomogeneity at different length scales using Shannon entropy. We
find that the galaxy distributions exhibit a higher degree of inhomogeneity as
compared to a Poisson point process at all length scales. Our analysis
indicates that signatures of inhomogeneities in the galaxy distributions
persist at least upto a length scale of $120 \, h^{-1}\, {\rm Mpc}$. The galaxy
distributions appear to be homogeneous on a scale of $140 \, h^{-1}\, {\rm
Mpc}$ and beyond. Analyzing a set of mock galaxy samples from a semi analytic
galaxy catalogue from the Millennium simulation we find a scale of transition
to homogeneity at $\sim 100 \, h^{-1}\, {\rm Mpc}$.


  We measured the linear polarization of Sagittarius A* to be 7.2 +/- 0.6 % at
230 GHzusing the BIMA array with a resolution of 3.6 x 0.9 arcsec. This
confirms the previously reported detection with the JCMT 14-m antenna. Our high
resolution observations demonstrate that the polarization does not arise from
dust but from a synchrotron source associated with Sgr A*. We see no change in
the polarization position angle and only a small change in the polarization
fraction in four observations distributed over 60 days. We find a position
angle 139 +/- 4 degrees that differs substantially from what was found in
earlier JCMT observations at the same frequency. Polarized dust emission cannot
account for this discrepancy leaving variability and observational error as the
only explanations. The BIMA observations alone place an upper limit on the
magnitude of the rotation measure of 2 x 10^6 rad m^-2. These new observations
when combined with the JCMT observations at 150, 375 and 400 GHz suggest RM
=-4.3 +/- 0.1 x 10^5 rad m^-2. This RM may be caused by an external Faraday
screen. Barring a special geometry or a high number of field reversals, this RM
rules out accretion rates greater than ~ 10^-7 M_sun y^-1. This measurement is
inconsistent with high accretion rates necessary in standard advection
dominated accretion flow and Bondi-Hoyle models for Sgr A*. It argues for low
accretion rates as a major factor in the overall faintness of Sgr A*.


  Visual servoing enables robotic systems to perform accurate closed-loop
control, which is required in many applications. However, existing methods
either require precise calibration of the robot kinematic model and cameras or
use neural architectures that require large amounts of data to train. In this
work, we present a method for unsupervised learning of visual servoing that
does not require any prior calibration and is extremely data-efficient. Our key
insight is that visual servoing does not depend on identifying the veridical
kinematic and camera parameters, but instead only on an accurate generative
model of image feature observations from the joint positions of the robot. We
demonstrate that with our model architecture and learning algorithm, we can
consistently learn accurate models from less than 50 training samples (which
amounts to less than 1 min of unsupervised data collection), and that such
data-efficient learning is not possible with standard neural architectures.
Further, we show that by using the generative model in the loop and learning
online, we can enable a robotic system to recover from calibration errors and
to detect and quickly adapt to possibly unexpected changes in the robot-camera
system (e.g. bumped camera, new objects).


  This article addresses the problem of Cooperative Coverage Path Planning
(C-CPP) for the inspection of complex infrastructures (offline 3D
reconstruction) by utilizing multiple Unmanned Autonomous Vehicles (UAVs). The
proposed scheme, based on a priori 3D model of the infrastructure under
inspection, is able to generate multiple paths for UAVs in order to achieve a
complete cooperative coverage in a short time. Initially the infrastructure
under inspection is being sliced by horizontal planes, which has the capability
of recognizing the branches of the structure and these branches will be handled
as breaking points for the path planning of the UAVs to collaboratively execute
the coverage task in less time and more realistically, based on the current
flying times of the UAVs. The multiple data sets collected from the coverage
are merged for the offline sparse and dense 3D reconstruction of the
infrastructure by utilizing SLAM and Structure from Motion approaches, with
either monocular or stereo sensors. The performance of the proposed C-CPP has
been experimentally evaluated in multiple indoor and realistic outdoor
infrastructure inspection experiments.


  The high-temperature superconducting cuprates host unidirectional spin- and
charge-density-wave orders that can intertwine with superconductivity in
non-trivial ways. While the charge components of these stripes have now been
observed in nearly all cuprate families, their detailed evolution with doping
varies across different materials and at high and low temperatures. We address
this problem using non-perturbative determinant quantum Monte Carlo
calculations for the three-band Hubbard model. Using an efficient
implementation, we can resolve the model's fluctuating spin and charge
modulations and map their evolution as a function of the charge transfer energy
and doping. We find that the incommensurability of the charge modulations is
decoupled from the spin modulations and decreases with hole doping, consistent
with experimental measurements at high temperatures. These findings support the
proposal that the high-temperature charge correlations are distinct from the
intertwined stripe order observed at low-temperature and in the single-band
Hubbard model.


  Video-to-speech is the process of reconstructing the audio speech from a
video of a spoken utterance. Previous approaches to this task have relied on a
two-step process where an intermediate representation is inferred from the
video, and is then decoded into waveform audio using a vocoder or a waveform
reconstruction algorithm. In this work, we propose a new end-to-end
video-to-speech model based on Generative Adversarial Networks (GANs) which
translates spoken video to waveform end-to-end without using any intermediate
representation or separate waveform synthesis algorithm. Our model consists of
an encoder-decoder architecture that receives raw video as input and generates
speech, which is then fed to a waveform critic and a power critic. The use of
an adversarial loss based on these two critics enables the direct synthesis of
raw audio waveform and ensures its realism. In addition, the use of our three
comparative losses helps establish direct correspondence between the generated
audio and the input video. We show that this model is able to reconstruct
speech with remarkable realism for constrained datasets such as GRID, and that
it is the first end-to-end model to produce intelligible speech for LRW (Lip
Reading in the Wild), featuring hundreds of speakers recorded entirely `in the
wild'. We evaluate the generated samples in two different scenarios -- seen and
unseen speakers -- using four objective metrics which measure the quality and
intelligibility of artificial speech. We demonstrate that the proposed approach
outperforms all previous works in most metrics on GRID and LRW.


  In the geometry of quantum evolutions, a geodesic path is viewed as a path of
minimal statistical length connecting two pure quantum states along which the
maximal number of statistically distinguishable states is minimum. In this
paper, we present an explicit geodesic analysis of the dynamical trajectories
that emerge from the quantum evolution of a single-qubit quantum state. The
evolution is governed by an Hermitian Hamiltonian operator that achieves the
fastest possible unitary evolution between given initial and final pure states.
Furthermore, in addition to viewing geodesics in ray space as paths of minimal
length, we also verify the geodesicity of paths in terms of unit geometric
efficiency and vanishing geometric phase. Finally, based on our analysis, we
briefly address the main hurdles in moving to the geometry of quantum
evolutions for open quantum systems in mixed quantum states.


  Many of the affect modelling tasks present an asymmetric distribution of
information between training and test time; additional information is given
about the training data, which is not available at test time. Learning under
this setting is called Learning Under Privileged Information (LUPI). At the
same time, due to the ordinal nature of affect annotations, formulating affect
modelling tasks as supervised learning ranking problems is gaining ground
within the Affective Computing research community. Motivated by the two facts
above, in this study, we introduce a ranking model that treats additional
information about the training data as privileged information to accurately
rank affect states. Our ranking model extends the well-known RankNet model to
the LUPI paradigm, hence its name AffRankNet+. To the best of our knowledge, it
is the first time that a ranking model based on neural networks exploits
privileged information. We evaluate the performance of the proposed model on
the public available Afew-VA dataset and compare it against the RankNet model,
which does not use privileged information. Experimental evaluation indicates
that the AffRankNet+ model can yield significantly better performance.


  We show that the Ehresmann-Schauenburg bialgebroid of a quantum principal
bundle $P$ or Hopf Galois extension with structure quantum group $H$ is in fact
a left Hopf algebroid $L(P,H)$. We show further that if $H$ is
coquasitriangular then $L(P,H)$ has an antipode map $S$ obeying certain minimal
axioms. Trivial quantum principal bundles or cleft Hopf Galois extensions with
base $B$ are known to be cocycle cross products $B\#_\sigma H$ for a
cocycle-action pair ($\vartriangleright$,$\sigma$) and we look at these of a
certain `associative type' where $ \vartriangleright$ is an actual action. In
this case also, we show that the associated left Hopf algebroid has an antipode
obeying our minimal axioms. We show that if $L$ is any left Hopf algebroid then
so is its cotwist $L^\varsigma$ as an extension of the previous bialgebroid
Drinfeld cotwist theory. We show that in the case of associative type,
$L(B\#_\sigma H,H)=L(B\# H)^{\tilde\sigma}$ for a Hopf algebroid cotwist
$\varsigma=\tilde\sigma$. Thus, switching on $\sigma$ of associative type
appears at the Hopf algebroid level as a Drinfeld cotwist. We view the affine
quantum group $\hat{U_q(sl_2)}$ and the quantum Weyl group of $u_q(sl_2)$ as
examples of associative type.


  Photo-polymerization of a reactive mesogen mixed with a mesogenic dimer,
shown to exhibit the twist-bend nematic phase ($N_{TB}$), reveals the complex
structure of the self-deformation patterns observed in planar cells. The
polymerized reactive mesogen retains the structure formed by liquid crystalline
molecules in the twist bend phase, thus enabling observation by Scanning
Electron Microscope (SEM). Hierarchical ordering scales from tens of nanometers
to micrometers are imaged in detail. Submicron features, anticipated from
earlier X-ray experiments, are visualized directly. In the self-deformation
stripes formed in the $N_{TB}$ phase, the average director field is found
tilted in the cell plane by an angle of up to 45$^{\circ}$ from the cell
rubbing direction. This tilting explains the sign inversion being observed in
the electro-optical studies.


  The classical Schur polynomials form a natural basis for the ring of
symmetric polynomials, and have geometric significance since they represent the
Schubert classes in the cohomology ring of Grassmannians. Moreover, these
polynomials enjoy rich combinatorial properties. In the last decade, an exact
analogue of this picture has emerged in the symplectic and orthogonal Lie
types, with the Schur polynomials replaced by the theta and eta polynomials of
Buch, Kresch, and the author. This expository paper gives an overview of what
is known to date about this correspondence, with examples.


  This article introduces a modeling framework to characterize evacuee response
to environmental stimuli during emergency egress. The model is developed in
consistency with stress theory, which explains how an organism reacts to
environmental stressors. We integrate the theory into the well-known
social-force model, and develop a framework to simulate crowd evacuation
behavior in multi-compartment buildings. Our method serves as a theoretical
basis to study crowd movement at bottlenecks, and simulate their herding and
way-finding behavior in normal and hazardous conditions. The pre-movement
behavior is also briefly investigated by using opinion dynamics with social
group model. The algorithms have been partly tested in FDS+EVAC as well as our
simulation platform crowdEgress.


  We review the basic features of transition radiation and how they are used
for the design of modern Transition Radiation Detectors (TRD). The discussion
will include the various realizations of radiators as well as a discussion of
the detection media and aspects of detector construction. With regard to
particle identification we assess the different methods for efficient
discrimination of different particles and outline the methods for the
quantification of this property. Since a number of comprehensive reviews
already exist, we predominantly focus on the detectors currently operated at
the LHC. To a lesser extent we also cover some other TRDs, which are planned or
are currently being operated in balloon or space-borne astro-particle physics
experiments.


  In this paper we show how the prediction of CMBR angular power spectra $C_l$
in non-Gaussian theories is affected by a cosmic covariance problem, that is
$(C_l,C_{l'})$ correlations impart features on any observed $C_l$ spectrum
which are absent from the average $C^l$ spectrum. Therefore the average
spectrum is rendered a bad observational prediction, and two new prediction
strategies, better adjusted to these theories, are proposed. In one we search
for hidden random indices conditional to which the theory is released from the
correlations. Contact with experiment can then be made in the form of the
conditional power spectra plus the random index distribution. In another
approach we apply to the problem a principal component analysis. We discuss the
effect of correlations on the predictivity of non-Gaussian theories. We finish
by showing how correlations may be crucial in delineating the borderline
between predictions made by non-Gaussian and Gaussian theories. In fact, in
some particular theories, correlations may act as powerful non-Gaussianity
indicators.


  If the originally flat bottom of a wide quantum well with multiple
eigenstates is periodically modulated, its eigenvalues rearrange into denser
groups separated by wider gaps. We show that this effect, if implemented in an
elongated bottle microresonator (also called a SNAP microresonator) allows to
design microwave photonic tunable filters with an outstanding performance.


  We introduce new homomorphisms relative to additive convolutions and
max-convolutions in free, boolean and classical cases. Crucial roles are played
by the limit distributions for free multiplicative law of large numbers.


  This paper deals with the following fractional Schr$ \ddot{\textrm{o}}$dinger
equations with Choquard-type nonlinearities \begin{equation*}
\left\{\begin{array}{r@{\ \ }c@{\ \ }ll}
  (-\Delta)^{\frac{\alpha}{2}}u + u - C_{n,-\beta} \,(|x|^{\beta-n}\ast
u^{p})\, u^{p-1}& = &0 & \mbox{in}\ \ \mathbb{R}^{n}\,, \\[0.05cm]
  u & > & 0 & \mbox{on}\ \ \mathbb{R}^{n}, \end{array}\right. \end{equation*}
where $ 0< \alpha,\beta < 2, 1\leq p <\infty \,\,and\,\, n\geq 2. $ First we
construct a decay result at infinity and a narrow region principle for related
equations. Then we establish the radial symmetry of positive solutions for the
above equation with the generalized direct method of moving planes.


  A theory of symbolic dynamic systems with long-range correlations based on
the consideration of the binary N-step Markov chains developed earlier in Phys.
Rev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal
numbers of zeros and unities in the chain). In the model, the conditional
probability that the i-th symbol in the chain equals zero (or unity) is a
linear function of the number of unities (zeros) among the preceding N symbols.
The correlation and distribution functions as well as the variance of number of
symbols in the words of arbitrary length L are obtained analytically and
verified by numerical simulations. A self-similarity of the studied stochastic
process is revealed and the similarity group transformation of the chain
parameters is presented. The diffusion Fokker-Planck equation governing the
distribution function of the L-words is explored. If the persistent
correlations are not extremely strong, the distribution function is shown to be
the Gaussian with the variance being nonlinearly dependent on L. An equation
connecting the memory and correlation function of the additive Markov chain is
presented. This equation allows reconstructing a memory function using a
correlation function of the system. Effectiveness and robustness of the
proposed method is demonstrated by simple model examples. Memory functions of
concrete coarse-grained literary texts are found and their universal power-law
behavior at long distances is revealed.


  The projected gravitational potential of galaxy clusters is reflected in both
their X-ray emission and their imprint on the images of background sources due
to their gravitational lensing effects. Since these projections of the
potential are weighted differently along the line-of-sight, we propose a method
to combine them and remove the degeneracy between two cases: (i) a cluster
consisting of a single potential well, or (ii) an apparent cluster composed of
several potential wells projected onto each other. We demonstrate with
simulated data of potential models that this method indeed allows to
significantly distinguish multiple from single clusters. The confidence limit
for this distinction depends on the mass ratio between the clusters. It ranges
from ~ 15 sigma for mass ratio 1:1 to ~ 4 sigma for mass ratio 1:6.
Furthermore, the method reconstructs the correct cluster mass, the correct mass
ratio of the two clusters, and the correct scale radii with typical fractional
accuracies of a few percent at 3 sigma confidence. As an aside, our method
allows to accurately determine gas fractions in clusters, also with 3 sigma
fractional accuracies of order a few percent. We argue that our method provides
an alternative to the commonly used beta-fit technique, and yields more
reliable results in a broader range of cases.


  We present a new efficient OpenCL-based Accelerator for large scale
Convolutional Neural Networks called Fast Inference on FPGAs for Convolution
Neural Network (FFCNN). FFCNN is based on a deeply pipelined OpenCL kernels
architecture. As pointed out before, high-level synthesis tools such as the
OpenCL framework can easily port codes originally designed for CPUs and GPUs to
FPGAs, but it is still difficult to make OpenCL codes run efficiently on FPGAs.
This work aims to propose an efficient FPGA implementation of OpenCL
High-Performance Computing Applications. To do so, a Data reuse and task
mapping techniques are also presented to improve design efficiency. In
addition, the following motivations were taken into account when developing
FFCNN: 1) FFCNN has been designed to be easily implemented on Intel OpenCL SDK
based FPGA design flow. 2) In FFFCN, different techniques have been integrated
to improve the memory band with and throughput. A performance analysis is
conducted on two deep CNN for Large-Scale Images classification. The obtained
results, and the comparison with other works designed to accelerate the same
types of architectures, show the efficiency and the competitiveness of the
proposed accelerator design by significantly improved performance and resource
utilization.