  In this paper, we consider band-structure calculations governed by the
Helmholtz or Maxwell equations in piecewise homogeneous periodic materials.
Methods based on boundary integral equations are natural in this context, since
they discretize the interface alone and can achieve high order accuracy in
complicated geometries. In order to handle the quasi-periodic conditions which
are imposed on the unit cell, the free-space Green's function is typically
replaced by its quasi-periodic cousin. Unfortunately, the quasi-periodic
Green's function diverges for families of parameter values that correspond to
resonances of the empty unit cell. Here, we bypass this problem by means of a
new integral representation that relies on the free-space Green's function
alone, adding auxiliary layer potentials on the boundary of the unit cell
itself. An important aspect of our method is that by carefully including a few
neighboring images, the densities may be kept smooth and convergence rapid.
This framework results in an integral equation of the second kind, avoids
spurious resonances, and achieves spectral accuracy. Because of our image
structure, inclusions which intersect the unit cell walls may be handled easily
and automatically. Our approach is compatible with fast-multipole acceleration,
generalizes easily to three dimensions, and avoids the complication of
divergent lattice sums.


  Video sequences exhibit significant nuisance variations (undesired effects)
of speed of actions, temporal locations, and subjects' poses, leading to
temporal-viewpoint misalignment when comparing two sets of frames or evaluating
the similarity of two sequences. Thus, we propose Joint tEmporal and cAmera
viewpoiNt alIgnmEnt (JEANIE) for sequence pairs. In particular, we focus on 3D
skeleton sequences whose camera and subjects' poses can be easily manipulated
in 3D. We evaluate JEANIE on skeletal Few-shot Action Recognition (FSAR), where
matching well temporal blocks (temporal chunks that make up a sequence) of
support-query sequence pairs (by factoring out nuisance variations) is
essential due to limited samples of novel classes. Given a query sequence, we
create its several views by simulating several camera locations. For a support
sequence, we match it with view-simulated query sequences, as in the popular
Dynamic Time Warping (DTW). Specifically, each support temporal block can be
matched to the query temporal block with the same or adjacent (next) temporal
index, and adjacent camera views to achieve joint local temporal-viewpoint
warping. JEANIE selects the smallest distance among matching paths with
different temporal-viewpoint warping patterns, an advantage over DTW which only
performs temporal alignment. We also propose an unsupervised FSAR akin to
clustering of sequences with JEANIE as a distance measure. JEANIE achieves
state-of-the-art results on NTU-60, NTU-120, Kinetics-skeleton and UWA3D
Multiview Activity II on supervised and unsupervised FSAR, and their
meta-learning inspired fusion.


  The main goal of this paper is to introduce the notion of $3$-L-dendriform
algebras which are the dendriform version of $3$-pre-Lie algebras. In fact they
are the algebraic structures behind the $\mathcal{O}$-operator of $3$-pre-Lie
algebras. They can be also regarded as the ternary analogous of L-dendriform
algebras. Moreover, we study the generalized derivations of $3$-L-dendriform
algebras. Finally, we explore the spaces of quasi-derivations, the centroids
and the quasi-centroids and give some properties.


  Improving Transformer efficiency has become increasingly attractive recently.
A wide range of methods has been proposed, e.g., pruning, quantization, new
architectures and etc. But these methods are either sophisticated in
implementation or dependent on hardware. In this paper, we show that the
efficiency of Transformer can be improved by combining some simple and
hardware-agnostic methods, including tuning hyper-parameters, better design
choices and training strategies. On the WMT news translation tasks, we improve
the inference efficiency of a strong Transformer system by 3.80X on CPU and
2.52X on GPU. The code is publicly available at
https://github.com/Lollipop321/mini-decoder-network.


  The Local Density Approximation combined with Dynamical Mean-Field Theory
(LDA+DMFT method) is applied to the study of the paramagnetic and magnetically
ordered phases of hematite Fe$_2$O$_3$ as a function of volume. As the volume
is decreased, a simultaneous 1st order insulator-metal and high-spin to
low-spin transition occurs close to the experimental value of the critical
volume. The high-spin insulating phase is destroyed by a progressive reduction
of the charge gap with increasing pressure, upon closing of which the high spin
phase becomes unstable. We conclude that the transition in Fe$_2$O$_3$ at
$\approx$50 GPa can be described as an electronically driven volume collapse.


  We look at the eigenvalues of the Hessian of a loss function before and after
training. The eigenvalue distribution is seen to be composed of two parts, the
bulk which is concentrated around zero, and the edges which are scattered away
from zero. We present empirical evidence for the bulk indicating how
over-parametrized the system is, and for the edges that depend on the input
data.


  In pursuit of infrared (IR) radiation absorbers, we examine quasicrystal
structures made of graphite wires. An array of graphitic cages and
cage-within-cage, and whose overall dimensions is smaller than the radiation
wavelength exhibit a flat absorption spectrum, A~0.83 between 10-30 microns and
a quality loss factor of L~0.83 (L=A/Q, with Q, the quality factor).
Simulations at microwave frequencies show multiple absorption lines. In the
case of a cage within cage, energy is funneled towards the inner cage which
result in a rather hot structure. Applications are envisioned as anti-fogging
surfaces, EM shields and energy harvesting.


  We derive a BPS-type bound for four-dimensional Born-Infeld action with
constant B field background. The supersymmetric configuration saturates this
bound and is regarded as an analog of instanton in U(1) gauge theory.
Furthermore, we find the explicit solutions of this BPS condition. These
solutions have a finite action proportional to the instanton number and
represent D(p-4)-branes within a Dp-brane although they have a singularity at
the origin. Some relations to the noncommutative U(1) instanton are discussed.


  The tetragonal compound Sr2RuO4 exhibits a chiral p-wave superconducting (SC)
state of its three t2g-type conduction bands. The characteristics of
unconventional gap structure are known from experiment, in particular
field-angle resolved specific heat measurements and from microscopic theories.
A rotated extremal structure on the main active SC band with respect to the
nodal gaps on the passive bands was concluded. We propose that this gap
structure can be further specified by applying the STM- quasiparticle
interference (QPI) method. We calculate the QPI spectrum within a three band
and chiral three gap model and give closed analytical expressions. We show that
as function of bias voltage the chiral three gap model will lead to
characteristic changes in QPI that may be identified and may be used for more
quantitative gap determination of the chiral gap structure.


  We review the status of Bell's inequalities in quantum information, stressing
mainly the links with quantum key distribution and distillation of
entanglement. We also prove that for all the eavesdropping attacks using one
qubit, and for a family of attacks of two qubits, acting on half of a maximally
entangled state of two qubits, the violation of a Bell inequality implies the
possibility of an efficient secret-key extraction.


  A non-extreme dilatonic charged (by two ``color electric'' charges) black
hole solution is examined within a four-dimensional gravity model that
incorporates two scalar (dilaton) fields and two Abelian vector fields. The
scalar and vector fields interact through exponential terms containing two
dilatonic coupling vectors. The solution is characterized by a dimensionless
parameter $a$ $(0 < a < 2)$, which is a specific function of dilatonic coupling
vectors. The paper presents solutions for timelike and null circular geodesics
that may play a crucial role in different astrophysical scenarios, including
quasinormal modes of various test fields in the eikonal approximation. For $a =
1/2, 1, 3/2, 2$, the radii of the innermost stable circular orbit are presented
and analyzed.


  In this article, we study the weak and strong Lefschetz of higher dimensional
quotients and dimension 1 almost complete intersections. We then apply the
obtained results to the study of the Jacobian algebra of hyperplane
arrangements.


  A long-standing conjecture asserts that any Anosov diffeomorphism of a closed
manifold is finitely covered by a diffeomorphism which is topologically
conjugate to a hyperbolic automorphism of a nilpotent manifold. In this paper,
we show that any closed 4-manifold that carries a Thurston geometry and is not
finitely covered by a product of two aspherical surfaces does not support
(transitive) Anosov diffeomorphisms.


  Indium-doped SnTe has been of interest because the system can exhibit both
topological surface states and bulk superconductivity. While the enhancement of
the superconducting transition temperature is established, the character of the
electronic states induced by indium doping remains poorly understood. We report
a study of magneto-transport in a series of Sn$_{1-x}$In$_x$Te single crystals
with $0.1\le x \le 0.45$. From measurements of the Hall effect, we find that
the dominant carrier type changes from hole-like to electron-like at
$x\sim0.25$; one would expect electron-like carriers if the In ions have a
valence of $+3$. For single crystals with $x = 0.45$, corresponding to the
highest superconducting transition temperature, pronounced Shubnikov-de Haas
oscillations are observed in the normal state. In measurements of
magnetoresistance, we find evidence for weak anti-localization (WAL). We
attribute both the quantum oscillations and the WAL to bulk Dirac-like hole
pockets, previously observed in photoemission studies, which coexist with the
dominant electron-like carriers.


  We present the first-principles investigation of the structural, electronic,
and magnetic properties of SrCoO$_{3-\delta}$ ($\delta=0, 0.25, 0.5$) to
understand the multivalent nature of Co ions in SrCoO$_{3-\delta}$ along the
line of topotactic transition between perovskite SrCoO$_{3}$ and brownmillerite
SrCoO$_{2.5}$. From the on-site Coulomb interaction $U$-dependent ground state
of stoichiometric SrCoO$_{3}$, we show the proximity of its metallic
ferromagnetic ground state to other antiferromagnetic states. The structural
and magnetic properties of SrCoO$_{3-\delta}$ depending on their oxygen-content
provide an interesting insight into the relationship between the Co-Co
distances and the magnetic couplings so that the spin-state transition of Co
spins can understood by the change of $pd$-hybridization depending on the Co-Co
distances. The \emph{strong} suppression of the $dp\sigma$-hybridization
between Co $d$ and O $p$ orbitals in brownmillerite SrCoO$_{2.5}$ brings on the
high-spin state of Co$^{3+}$ $d^{6}$ and is responsible for the
antiferromagnetically ordered insulating ground state. The increase of
effective Co-Co distances driven by the presence of oxygen vacancies in
SrCoO$_{3-\delta}$ is consistent with the reduction of the effective
$pd$-hybridization between Co $d$ and O $p$ orbitals. We conclude that the
configuration of neighboring Co spins is shown to be crucial to their local
electronic structure near the metal-to-insulator transition along the line of
the topotactic transition in SrCoO$_{3-\delta}$. Incidentally, we also find
that the \textit{I2mb} symmetry of SrCoO$_{2.5}$ is energetically stable and
exhibits ferroelectricity via the ordering of CoO$_{4}$ tetrahedra, where this
polar lattice can be stabilized by the presence of a large activation barrier.


  We recall some abstract connectivity concepts, and apply them to special
chains in partially ordered sets, called veins, that are defined as
order-convex chains that are contained in every maximal chain they meet. Veins
enable us to define a new partial order on the same underlying set, called the
pruning order. The associated pruned poset is simpler than the initial poset,
but irreducible, coirreducible, and doubly-irreducible elements are preserved
by the operation of pruning.


  We consider a class of nonlinear Schrodinger / Gross-Pitaevskii (NLS/GP)
equations with periodic potentials, having an even symmetry. We construct
"solitons", centered about any point of symmetry of the potential. For focusing
(attractive) nonlinearities, these solutions bifurcate from the zero state at
the lowest band edge frequency, into the semi-infinite spectral gap. Our
results extend to bifurcations into finite spectral gaps, for focusing or
defocusing (repulsive) nonlinearities under more restrictive hypotheses.
Soliton nonlinear bound states with frequencies near a band edge are
well-approximated by a slowly decaying solution of a homogenized NLS/GP
equation, with constant homogenized effective mass tensor and effective
nonlinear coupling coefficient, modulated by a Bloch state. For the critical
NLS equation with a periodic potential, e.g. the cubic two dimensional NLS/GP
with a periodic potential, our results imply that the limiting soliton power,
as the spectral band edge frequency is approached, is equal to a constant
\zeta_* times the minimal mass soliton of the translation invariant critical
NLS equation. \zeta_* is expressible in terms of the band edge Bloch
eigenfunction and the determinant of the effective mass tensor; and
0<\zeta_*<1$ for any non-constant potential. The results are confirmed by
numerical computation of bound states with frequencies near the spectral band
edge. Finally, these results have implications for the control of nonlinear
waves using periodic structures.


  Enhanced efforts in the transportation sector should be implemented to
mitigate the adverse effects of CO2 emissions resulting from zoning-based
planning paradigms. The innovative concept of the 15-minute city, with a focus
on proximity-based planning, holds promise in minimizing unnecessary travel and
advancing the progress toward achieving carbon neutrality. However, an
important research question that remains insufficiently explored is: to what
extent is a 15-minute city concept within reach for US cities? This paper
establishes a comprehensive framework to evaluate the 15-minute city concept
using SafeGraph Point of Interest (POI) check-in data in the 12 most populous
US cities. The results reveal that residents are more likely to rely on cars
due to the fact that most of their essential activities are located beyond
convenient walking, cycling, and public transit distances. However, there is
significant potential for the implementation of the 15-minute city concept, as
most residents' current activities can be accommodated within a 15-minute
radius by the aforementioned low-emission modes of transportation. Our findings
can offer policymakers insight into how far US cities are away from the
15-minute city and the potential CO2 emission reduction they can expect if the
concept is successfully implemented.


  In substations, the presence of random transient impulsive interference
sources makes noise highly non-Gaussian. In this paper, the primary interest is
to provide a general model for wireless channel in presence of these transient
impulsive noise for space-time signal processing problems. We assume a
superposition of independent interference sources randomly distributed in
space-time in a Poisson field of interferers. By using stochastic geometry
approach, first order and second order statistics can be derived from basic
waveforms of impulsive interferers. We use discrete-time series model to
simulate the random transient impulsive waveforms. It is demonstrated that the
amplitude distribution and density of the proposed model converges to
$\alpha$-stable distributions and their power spectral densities are $\sim
1/(f-f_{0})^{k}$ where $f_{0}\geq 0$ is a resonant frequency and $k > 0$.
Measurements and computer simulations are provided where impulsive noise are to
demonstrate the efficiency of the analysis.


  In recent years, a lot of research has been conducted within the area of
causal inference and causal learning. Many methods have been developed to
identify the cause-effect pairs in models and have been successfully applied to
observational real-world data to determine the direction of causal
relationships. Yet in bivariate situations, causal discovery problems remain
challenging. One class of such methods, that also allows tackling the bivariate
case, is based on Additive Noise Models (ANMs). Unfortunately, one aspect of
these methods has not received much attention until now: what is the impact of
different noise levels on the ability of these methods to identify the
direction of the causal relationship. This work aims to bridge this gap with
the help of an empirical study. We test Regression with Subsequent Independence
Test (RESIT) using an exhaustive range of models where the level of additive
noise gradually changes from 1\% to 10000\% of the causes' noise level (the
latter remains fixed). Additionally, the experiments in this work consider
several different types of distributions as well as linear and non-linear
models. The results of the experiments show that ANMs methods can fail to
capture the true causal direction for some levels of noise.


  We present an approach for pricing European call options in presence of
proportional transaction costs, when the stock price follows a general
exponential L\'{e}vy process. The model is a generalization of the celebrated
work of Davis, Panas and Zariphopoulou (1993), where the value of the option is
defined as the utility indifference price. This approach requires the solution
of two stochastic singular control problems in finite horizon, satisfying the
same Hamilton-Jacobi-Bellman equation, with different terminal conditions. We
introduce a general formulation for these portfolio selection problems, and
then we focus on the special case in which the probability of default is
ignored. We solve numerically the optimization problems using the Markov chain
approximation method and show results for diffusion, Merton and Variance Gamma
processes. Option prices are computed for both the writer and the buyer.


  Recent research has shown that incorporating equivariance into neural network
architectures is very helpful, and there have been some works investigating the
equivariance of networks under group actions. However, as digital images and
feature maps are on the discrete meshgrid, corresponding
equivariance-preserving transformation groups are very limited. In this work,
we deal with this issue from the connection between convolutions and partial
differential operators (PDOs). In theory, assuming inputs to be smooth, we
transform PDOs and propose a system which is equivariant to a much more general
continuous group, the $n$-dimension Euclidean group. In implementation, we
discretize the system using the numerical schemes of PDOs, deriving
approximately equivariant convolutions (PDO-eConvs). Theoretically, the
approximation error of PDO-eConvs is of the quadratic order. It is the first
time that the error analysis is provided when the equivariance is approximate.
Extensive experiments on rotated MNIST and natural image classification show
that PDO-eConvs perform competitively yet use parameters much more efficiently.
Particularly, compared with Wide ResNets, our methods result in better results
using only 12.6% parameters.


  Based on earlier work of the latter two named authors on the higher
super-Teichmueller space with $\mathcal{N}=1$, a component of the flat
$OSp(1|2)$ connections on a punctured surface, here we extend to the case
$\mathcal{N}=2$ of flat $OSp(2|2)$ connections. Indeed, we construct here
coordinates on the higher super-Teichmueller space of a surface $F$ with at
least one puncture associated to the supergroup $OSp(2|2)$, which in particular
specializes to give another treatment for $\mathcal{N}=1$ simpler than the
earlier work. The Minkowski space in the current case, where the corresponding
super Fuchsian groups act, is replaced by the superspace $\mathbb{R}^{2,2|4}$,
and the familiar lambda lengths are extended by odd invariants of triples of
special isotropic vectors in $\mathbb{R}^{2,2|4}$ as well as extra bosonic
parameters, which we call ratios, defining a flat $\mathbb{R}_{+}$-connection
on $F$. As in the pure bosonic or $\mathcal{N}=1$ cases, we derive the analogue
of Ptolemy transformations for all these new variables.


  Rearrangement effects in light hypernuclei are investigated in the framework
of the Brueckner theory. We can estimate without detailed numerical
calculations that the energy of the $\alpha$-core is reduced by more than 2.5
MeV when the $\Lambda$ adheres to $^4$He to form $^5_\Lambda$He. Similar
assessment of rearrangement contributions is essential to deduce the strength
of $\Lambda\Lambda$ interaction from experimentally observed $\Delta
B_{\Lambda\Lambda}$. The recently observed experimental value of $\sim$ 1 MeV
for the $\Delta B_{\Lambda\Lambda}$ of \hll suggests that the matrix element of
$<\Lambda \Lambda |v|\Lambda \Lambda>$ in \hll is around -2 MeV.


  In this work we present a method for lung nodules segmentation, their texture
classification and subsequent follow-up recommendation from the CT image of
lung. Our method consists of neural network model based on popular U-Net
architecture family but modified for the joint nodule segmentation and its
texture classification tasks and an ensemble-based model for the follow-up
recommendation. This solution was evaluated within the LNDb medical imaging
challenge and produced the best nodule segmentation result on the final
leaderboard.


  Motivated by various applications and examples, the standard notion of
potential for dynamical systems has been generalized to almost additive and
asymptotically additive potential sequences, and the corresponding
thermodynamic formalism, dimension theory and large deviations theory have been
extensively studied in the recent years. In this paper, we show that every such
potential sequence is actually equivalent to a standard (additive) potential in
the sense that there exists a continuous potential with the same topological
pressure, equilibrium states, variational principle, weak Gibbs measures, level
sets (and irregular set) for the Lyapunov exponent and large deviations
properties. In this sense, our result shows that almost and asymptotically
additive potential sequences do not extend the scope of the theory compared to
standard potentials, and that many results in the literature about such
sequences can be recovered as immediate consequences of their counterpart in
the additive case. A corollary of our main result is that all quasi-Bernoulli
measures are weak Gibbs.


  Deep learning-based methods have pushed the limits of the state-of-the-art in
face analysis. However, despite their success, these models have raised
concerns regarding their bias towards certain demographics. This bias is
inflicted both by limited diversity across demographics in the training set, as
well as the design of the algorithms. In this work, we investigate the
demographic bias of deep learning models in face recognition, age estimation,
gender recognition and kinship verification. To this end, we introduce the most
comprehensive, large-scale dataset of facial images and videos to date. It
consists of 40K still images and 44K sequences (14.5M video frames in total)
captured in unconstrained, real-world conditions from 1,045 subjects. The data
are manually annotated in terms of identity, exact age, gender and kinship. The
performance of state-of-the-art models is scrutinized and demographic bias is
exposed by conducting a series of experiments. Lastly, a method to debias
network embeddings is introduced and tested on the proposed benchmarks.


Withdrawn by the authors due to submitting policy required by some journals.


  Isotopy classes of diffeomorphisms of the 4-sphere can be described either
from a Cerf theoretic perspective in terms of loops of 5-dimensional handle
attaching data, starting and ending with handles in cancelling position, or via
certain twists along submanifolds analogous to Dehn twists in dimension two.
The subgroup of the smooth mapping class group of the 4-sphere coming from
loops of 5-dimensional handles of index 1 and 2 coincides with the subgroup
generated by twists along Montesinos twins (pairs of 2-spheres intersecting
transversely twice) in which one of the two 2-spheres in the twin is unknotted.
In this paper we show that this subgroup is in fact trivial or cyclic of order
two.


  Numerous formulations of finite volume schemes for the Euler and
Navier-Stokes equations exist, but in the majority of cases they have been
developed for structured and stationary meshes. In many applications, more
flexible mesh geometries that can dynamically adjust to the problem at hand and
move with the flow in a (quasi) Lagrangian fashion would, however, be highly
desirable, as this can allow a significant reduction of advection errors and an
accurate realization of curved and moving boundary conditions. Here we describe
a novel formulation of viscous continuum hydrodynamics that solves the
equations of motion on a Voronoi mesh created by a set of mesh-generating
points. The points can move in an arbitrary manner, but the most natural motion
is that given by the fluid velocity itself, such that the mesh dynamically
adjusts to the flow. Owing to the mathematical properties of the Voronoi
tessellation, pathological mesh-twisting effects are avoided. Our
implementation considers the full Navier-Stokes equations and has been realized
in the AREPO code both in 2D and 3D. We propose a new approach to compute
accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a
finite volume solver of the Navier-Stokes equations. Through a number of test
problems, including circular Couette flow and flow past a cylindrical obstacle,
we show that our new scheme combines good accuracy with geometric flexibility,
and hence promises to be competitive with other highly refined Eulerian
methods. This will in particular allow astrophysical applications of the AREPO
code where physical viscosity is important, such as in the hot plasma in galaxy
clusters, or for viscous accretion disk models.


  Several uncertainty estimation methods have been recently proposed for
machine translation evaluation. While these methods can provide a useful
indication of when not to trust model predictions, we show in this paper that
the majority of them tend to underestimate model uncertainty, and as a result
they often produce misleading confidence intervals that do not cover the ground
truth. We propose as an alternative the use of conformal prediction, a
distribution-free method to obtain confidence intervals with a theoretically
established guarantee on coverage. First, we demonstrate that split conformal
prediction can ``correct'' the confidence intervals of previous methods to
yield a desired coverage level. Then, we highlight biases in estimated
confidence intervals, both in terms of the translation language pairs and the
quality of translations. We apply conditional conformal prediction techniques
to obtain calibration subsets for each data subgroup, leading to equalized
coverage.


  We report on the polarization measure, obtained with IBIS on board INTEGRAL,
of the prompt emission of GRB 061122. Over an 8 s interval containing the
brightest part of the Gamma-Ray Burst we put a lower limit on its polarization
fraction of 60% at 68% c.l. and of 33% at 90% c.l. on the 250-800 keV energy
range.
  We performed late time optical and near infra-red imaging observations of the
GRB field using the Telescopio Nazionale Galileo (TNG), and the
Canada-France-Hawaii Telescope (CFHT). Our multi-band (ugrizYJHK) photometry
allowed us to identify the host galaxy of GRB 061122 and to build its SED.
Using a photometric redshift code we fitted these data, and derived the basic
properties of the galaxy, including its type and redshift, that we could
constrain to the interval [0.57, 2.10] at a 90% c.l., with a best fit value of
z=1.33.
  The polarization measurement in different energy bands, together with the
distance determination, allowed us to put the most stringent limit (xi <
3.4x10-16) to date to a possible Lorentz Invariance Violation based on the
vacuum birefringence effect, predicted by some quantum-gravity theories.


  The effective potential of massless standard model (SM) is calculated up to
three-loop order. The stability of the effective potential and the Higgs boson
mass are investigated up to three-loop order. We found that, Higgs boson mass
$m_{H}$ of one-loop order is large. The two-loop and three-loop results are not
appreciably different from each other. The two-loop and three-loop radiative
corrections have led to an improvement of Higgs boson mass and the value of the
scalar coupling. For the value $m_{t}=170$ GeV at the energy scale $\mu\approx
5.68\times10^2$GeV, we get $m_{H2-loop}\approx 125.4$ GeV. At the energy scale
$\mu\geq28\times10^2$, the scalar coupling $\lambda$ at two-loop becomes
negative and leads to metastable vacuum while the three-loop level is stable
even at high $\mu$ $\approx 10^{19}$ GeV. For the larger $\mu$-range $(3 \times
10^{3} \text{GeV}\leq \mu \leq 20 \times 10^{3} \text{GeV})$ spontaneous
symmetry breaking for one-loop and three-loop occurs at approximately the same
scalar coupling values. We get $m_{H1-loop}\approx 126.14$ GeV at $\mu \approx
6.5 \times 10^{3}$ GeV while for three-loop $m_{H3-loop}\approx 126$ GeV at
$\mu \approx 20 \times 10^{3}$ GeV.


  If space, time and mass-energy expand outward from the Big Bang along the
time axis equally in the (+) and (-) directions, then time is symmetric by
Weyl's definition. In the Feynman-Stueckelberg Interpretation, antimatter is
identical to matter but moves backward in time. This paper argues this
interpretation is physically real, leading to the universe containing dark
matter with mass accumulations similar to ordinary matte. As time expands, in
both directions away from the origin, quantum uncertainty allows a brief,
decreasing leakage of mass between (+) and (-) universes. Matter leaking from
(-) to (+) time moves forward in time, producing preponderance of matter in (+)
time. Antimatter leakage from (+) time to (-) time in the same way produces
antimatter preponderance in the (-) time universe. The remaining opposite
partner particles left by the leakage, (antimatter and matter respectively)
proceeding outward in antitime and time respectively, after many annihilations
also increase the two preponderances in the two universes. The anti-universe
should be observable by gravitational lensing, predicting "MACHOS" of
approximately stellar mass, and multiple micro-lensing of quasars.
Non-existence of primordial antimatter of Z>1, and a large variation in the
quantities of dark matter associated with different individual galaxies are
predicted. A symmetry is provided for Nodland and Ralston's observed maximum
axis of rotation of polarization of galactic synchrotron radiation. A new
solution of the horizon problem at times close to the origin is indicated.
Collapse of the wave function and time's arrow are explained and non-locality
and instantaneity of quantum interaction required. Extension of the hypothesis
to six dimensions gives an 83.3% dark matter share of the universe.


  The prediction for the quartic coupling of the SM-like Higgs boson constrains
the parameter space of SUSY models, even in scenarios where all of the
new-particle masses are above the scale probed so far by the LHC. We study the
implications of the Higgs-mass prediction on a recently-proposed SUSY model
that features two pairs of Higgs doublets, and provides a solution to the g-2
anomaly thanks to a suitable enhancement of the muon Yukawa coupling.


  The Maximum Likelihood Estimator (MLE) serves an important role in statistics
and machine learning. In this article, for i.i.d. variables, we obtain
constant-specified and sharp concentration inequalities and oracle inequalities
for the MLE only under exponential moment conditions. Furthermore, in a robust
setting, the sub-Gaussian type oracle inequalities of the log-truncated maximum
likelihood estimator are derived under the second-moment condition.


  Diabetic Retinopathy (DR) is a prominent cause of blindness in the world. The
early treatment of DR can be conducted from detection of microaneurysms (MAs)
which appears as reddish spots in retinal images. An automated microaneurysm
detection can be a helpful system for ophthalmologists. In this paper, deep
learning, in particular convolutional neural network (CNN), is used as a
powerful tool to efficiently detect MAs from fundus images. In our method a new
technique is used to utilise a two-stage training process which results in an
accurate detection, while decreasing computational complexity in comparison
with previous works. To validate our proposed method, an experiment is
conducted using Keras library to implement our proposed CNN on two standard
publicly available datasets. Our results show a promising sensitivity value of
about 0.8 at the average number of false positive per image greater than 6
which is a competitive value with the state-of-the-art approaches.


  The relationship between the properties of a dynamical system and the
structure of its defining equations has long been studied in many contexts.
Here we study this problem for the class of conjunctive (resp. disjunctive)
Boolean networks, that is, Boolean networks in which all Boolean functions are
constructed with the AND (resp. OR) operator only. The main results of this
paper describe network dynamics in terms of the structure of the network
dependency graph (topology). For a given such network, all possible limit cycle
lengths are computed and lower and upper bounds for the number of cycles of
each length are given. In particular, the exact number of fixed points is
obtained. The bounds are in terms of structural features of the dependency
graph and its partially ordered set of strongly connected components. For
networks with strongly connected dependency graph, the exact cycle structure is
computed.


  In a space of 4-dimensions, I will examine constrained variational problems
in which the Lagrangian, and constraint scalar density, are concomitants of a
(pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange
multiplier for these constrained extremal problems will be a scalar field. For
suitable choices of the Lagrangian, and constraint, we can obtain
Euler-Lagrange equations which are second order in the scalar field and third
order in the metric tensor. The effect of disformal transformations on the
constraint Lagrangians, and their generalizations, is examined. This will yield
other second order scalar-tensor Lagrangians which yield field equations which
are at most of third order. No attempt is made to construct all possible third
order scalar-tensor Euler-Lagrange equations in a 4-space, although nine
classes of such field equations are presented. Two of these classes admit
subclasses which yield conformally invariant field equations. A few remarks on
scalar-tensor-connection theories are also presented.


  If X and Y are real valued random variables such that the first moments of X,
Y, and XY exist and the conditional expectation of Y given X is an affine
function of X, then the intercept and slope of the conditional expectation
equal the intercept and slope of the least squares linear regression function,
even though Y may not have a finite second moment. As a consequence, the affine
in X form of the conditional expectation and zero covariance imply mean
independence.


  Video detection and human action recognition may be computationally
expensive, and need a long time to train models. In this paper, we were
intended to reduce the training time and the GPU memory usage of video
detection, and achieved a competitive detection accuracy. Other research works
such as Two-stream, C3D, TSN have shown excellent performance on UCF101. Here,
we used a LSTM structure simply for video detection. We used a simple structure
to perform a competitive top-1 accuracy on the entire validation dataset of
UCF101. The LSTM structure is named Context-LSTM, since it may process the deep
temporal features. The Context-LSTM may simulate the human recognition system.
We cascaded the LSTM blocks in PyTorch and connected the cell state flow and
hidden output flow. At the connection of the blocks, we used ReLU, Batch
Normalization, and MaxPooling functions. The Context-LSTM could reduce the
training time and the GPU memory usage, while keeping a state-of-the-art top-1
accuracy on UCF101 entire validation dataset, show a robust performance on
video action detection.


  Presented here are the results of a broadband spectral line survey of the Sgr
B2(N) - LMH region from 260 - 286 GHz using the Caltech Submillimeter
Observatory. The data were taken over the course of a single night (May 26,
2013) during the course of science testing of the remote observational
capabilities of the facility. The data are freely available to public both as
raw, double-side band observational data and as a minimally-reduced ascii
spectrum. The procedural scripts used for the preliminary data reduction using
CLASS are provided as well. The observational parameters and preliminary data
reduction procedures are detailed. Finally, we provide instructions for
accessing the data as well as comment on the robustness of the preliminary
reduction.


  We study the ages of a large sample (1,802) of nearly face-on disk low
surface brightness galaxies (LSBGs) by using the evolutionary population
synthesis (EPS) model PEGASE with exponential decreasing star formation rate to
fit their multiwavelength spectral energy distributions (SEDs) from
far-ultraviolet (FUV) to near-infrared (NIR). The derived ages of LSBGs are 1-5
Gyr for most of the sample no matter the constant or varying dust extinction is
adopted, which are similar to most of the previous studies on smaller samples.
This means that these LSBGs formed their majority of stars quite recently.
However, a small part of the sample (~2-3%) have larger ages as 5-8 Gyr,
meaning their major star forming process may occur earlier. At the same time, a
large sample (5,886) of high surface brightness galaxies (HSBGs) are selected
and studied in the same method for comparisons. The derived ages are 1-5 Gyr
for most of the sample (97%) as well. These may mean that probably these LSBGs
have no much different star formation history from their HSBGs counterparts.
But we should notice that the HSBGs are about 0.2 Gyr younger generally, which
could mean that the HSBGs may have more recent star forming activities than the
LSBGs.


  We prove uniform $L^p$ estimates for resolvents of higher order elliptic
self-adjoint differential operators on compact manifolds without boundary,
generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami
operators on Riemannian manifolds. In doing so, we follow the methods,
developed in [1] very closely. We also show that spectral regions in our $L^p$
resolvent estimates are optimal.


  Let $Q(n)$ denote the number of integers $1 \leq q \leq n$ whose prime
factorization $q= \prod^{t}_{i=1}p^{a_i}_i$ satisfies $a_1\geq a_2\geq \ldots
\geq a_t$. Hardy and Ramanujan proved that $$ \log Q(n) \sim
\frac{2\pi}{\sqrt{3}} \sqrt{\frac{\log(n)}{\log\log(n)}}\;. $$ Before proving
the above precise asymptotic formula, they studied in great detail what can be
obtained concerning $Q(n)$ using purely elementary methods, and were only able
to obtain much cruder lower and upper bounds using such methods.
  In this paper we show that it is in fact possible to obtain a purely
elementary (and much shorter) proof of the Hardy--Ramanujan Theorem. Towards
this goal, we first give a simple combinatorial argument, showing that $Q(n)$
satisfies a (pseudo) recurrence relation. This enables us to replace almost all
the hard analytic part of the original proof with a short inductive argument.


  Humans perceive and interact with hundreds of objects every day. In doing so,
they need to employ mental models of these objects and often exploit symmetries
in the object's shape and appearance in order to learn generalizable and
transferable skills. Active inference is a first principles approach to
understanding and modeling sentient agents. It states that agents entertain a
generative model of their environment, and learn and act by minimizing an upper
bound on their surprisal, i.e. their Free Energy. The Free Energy decomposes
into an accuracy and complexity term, meaning that agents favor the least
complex model, that can accurately explain their sensory observations. In this
paper, we investigate how inherent symmetries of particular objects also emerge
as symmetries in the latent state space of the generative model learnt under
deep active inference. In particular, we focus on object-centric
representations, which are trained from pixels to predict novel object views as
the agent moves its viewpoint. First, we investigate the relation between model
complexity and symmetry exploitation in the state space. Second, we do a
principal component analysis to demonstrate how the model encodes the principal
axis of symmetry of the object in the latent space. Finally, we also
demonstrate how more symmetrical representations can be exploited for better
generalization in the context of manipulation.


  We demonstrate the use of the 3D Monte Carlo radiative transfer code PHAETHON
to model infrared-dark clouds (IRDCs) that are externally illuminated by the
interstellar radiation field (ISRF). These clouds are believed to be the
earliest observed phase of high-mass star formation, and may be the high-mass
equivalent of lower-mass prestellar cores. We model three different cases as
examples of the use of the code, in which we vary the mass, density, radius,
morphology and internal velocity field of the IRDC. We show the predicted
output of the models at different wavelengths chosen to match the observing
wavebands of Herschel and Spitzer. For the wavebands of the long- wavelength
SPIRE photometer on Herschel, we also pass the model output through the SPIRE
simulator to generate output images that are as close as possible to the ones
that would be seen using SPIRE. We then analyse the images as if they were real
observations, and compare the results of this analysis with the results of the
radiative transfer models. We find that detailed radiative transfer modelling
is necessary to accurately determine the physical parameters of IRDCs (e.g.
dust temperature, density profile). This method is applied to study
G29.55+00.18, an IRDC observed by the Herschel Infrared Galactic Plane survey
(Hi-GAL), and in the future it will be used to model a larger sample of IRDCs
from the same survey.


  The restricted invertibility theorem was originally introduced by Bourgain
and Tzafriri in $1987$ and has been considered as one of the most celebrated
theorems in geometry and analysis. In this note, we present weighted versions
of this theorem with slightly better estimates. Particularly, we show that for
any $A\in\mathbb{R}^{n\times m}$ and $k,r\in\mathbb{N}$ with $k\leq r\leq
\mbox{rank}(A)$, there exists a subset $\mathcal{S}$ of size $k$ such that
$\sigma_{\min}(A_{\mathcal{S}}W_{\mathcal{S}})^2\geq
\frac{(\sqrt{r}-\sqrt{k-1})^2}{\|W^{-1}\|_F^{2}}\cdot\frac{r}{\sum_{i=1}^{r}\sigma_{i}(A)^{-2}}$,
where $W=\mbox{diag}(w_1,\ldots,w_m)$ with $w_i$ being the weight of the $i$-th
column of $A$. Our constructions are algorithmic and employ the interlacing
families of polynomials developed by Marcus, Spielman, and Srivastava.


  A radial probability measure is a probability measure with a density (with
respect to the Lebesgue measure) which depends only on the distances to the
origin. Consider the Euclidean space enhanced with a radial probability
measure. A correlation problem concerns showing whether the radial measure of
the intersection of two symmetric convex bodies is greater than the product of
the radial measures of the two convex bodies. A radial measure satisfying this
property is said to satisfy the correlation property. A major question in this
field is about the correlation property of the (standard) Gaussian measure. The
main result in this paper is a theorem suggesting a sufficient condition for a
radial measure to satisfy the correlation property. A consequence of the main
theorem will be a proof of the correlation property of the Gaussian measure.


  Given two orthornormal bases A and B, the basic form of the entropic
uncertainty principle is stated in terms of the sum of the Shannon entropies of
the probabilities of measuring A and B onto a given quantum state. State
independent lower bounds for this sum encapsulate the degree of incompatibility
of the observables diagonal in the A and B bases, and are usually derived by
extracting as much information as possible from the unitary operator U
connecting the two bases. Here we show a strategy to derive sequences of lower
bounds based on alternating sequences of measurements onto A and B. The problem
can be mapped into the multiple application of bistochastic processes that can
be described by the powers of the unistochastic matrices directly derivable
from U. By means of several examples we study the applicability of the method.
The results obtained show that the strategy can allow for an advantage both in
the pure state and in the mixed state scenario. The sequence of lower bounds is
obtained with resources which are polynomial in the dimension of the underlying
Hilbert space, and it is thus suitable for studying high dimensional cases.


  Laser-induced nuclear recollisions following $\alpha$ decay in the presence
of an intense laser field are investigated theoretically. We show that while an
intense optical laser does not influence notably the tunneling rate in $\alpha$
decay, it can completely change the $\alpha$ particle spectrum. For intensities
of $10^{22}-10^{23}$ W/cm$^{2}$, the field is strong enough to induce
recollisions between the emitted $\alpha$ particle and the daughter nucleus.
The energy gained by the $\alpha$ particle in the field can reach 20 MeV and
suffice to trigger several types of nuclear reactions on a femtosecond time
scale. Similar conclusions can be drawn about laser-induced recollisions after
proton emission. Prospects for the experimental realization of laser-induced
nuclear recollisions are discussed.


  The so-called ``symplectic method'' is used for studying the linear stability
of a self-gravitating collisionless stellar system, in which the particles are
also submitted to an external potential. The system is steady and spherically
symmetric, and its distribution function $f_0$ thus depends only on the energy
$E$ and the squarred angular momentum $L^2$ of a particle. Assuming that
$\partial f_0 / \partial E < 0$, it is first shown that stability holds with
respect to all the spherical perturbations -- a statement which turns out to be
also valid for a rotating spherical system. Thus it is proven that the energy
of an arbitrary aspherical perturbation associated to a ``preserving generator"
$\delta g_1$ [i.e., one satisfying $\partial f_0 / \partial L^2 \{ \delta g_1,
L^2 \} = 0$] is always positive if $\partial f_0 / \partial L^2 \leq 0$ and the
external mass density is a decreasing function of the distance $r$ to the
center. This implies in particular (under the latter condition) the stability
of an isotropic system with respect to all the perturbations. Some new remarks
on the relation between the symmetry of the system and the form of $f_0$ are
also reported. It is argued in particular that a system with a distribution
function of the form $f_0 = f_0 (E,L^2)$ is necessarily spherically symmetric.


  The link between chirality in the fermion sector and (anti-)self-duality in
the boson sector is reexamined in the light of Connes' noncommutative geometry
approach to the Standard Model. We find it to impose that the noncommutative
Yang-Mills action be symmetrized in an analogous way to the Dirac-Yukawa
operator itself.


  We study the reduced fidelity and reduced fidelity susceptibility in the
Kitaev honeycomb model. It is shown that the reduced fidelity susceptibility of
two nearest site manifest itself a peak at the quantum phase transition point,
although the one-site reduced fidelity susceptibility vanishes. Our results
directly reveal that the reduced fidelity susceptibility can be used to
characterize the quantum phase transition in the Kitaev honeycomb model, and
thus suggest that the reduced fidelity susceptibility is an accurate marker of
the topological phase transition when it is properly chosen, despite of its
local nature.


  The diffusion of gas through porous material is important to understand the
physical processes underlying cometary activity. We study the diffusion of a
rarefied gas (Knudsen regime) through a packed bed of monodisperse spheres via
experiments and numerical modelling, providing an absolute value of the
diffusion coefficient and compare it to published analytical models. The
experiments are designed to be directly comparable to numerical simulations, by
using precision steel beads, simple geometries, and a trade-off of the sample
size between small boundary effects and efficient computation. For direct
comparison, the diffusion coefficient is determined in Direct Simulation Monte
Carlo (DSMC) simulations, yielding a good match with experiments. This model is
further-on used on a microscopic scale, which cannot be studied in experiments,
to determine the mean path of gas molecules and its distribution, and compare
it against an analytical model. Scaling with sample properties (particle size,
porosity) and gas properties (molecular mass, temperature) is consistent with
analytical models. As predicted by these, results are very sensitive on sample
porosity and we find that a tortuosity $q(\varepsilon)$ depending linearly on
the porosity $\varepsilon$ can well reconcile the analytical model with
experiments and simulations. Mean paths of molecules are close to those
described in the literature, but their distribution deviates from the
expectation for small path lengths. The provided diffusion coefficients and
scaling laws are directly applicable to thermophysical models of idealised
cometary material.


  Recently, calculations which consider the implications of anomalous trilinear
gauge-boson couplings, both at tree-level and in loop-induced processes, have
been criticized on the grounds that the lagrangians employed are not \gwk gauge
invariant. We prove that, in fact, the general Lorentz-invariant and $U(1)_\em$
invariant but {\it not} $SU_L(2)\times U_Y(1)$ invariant action is equivalent
to the general lagrangian in which $SU_L(2)\times U_Y(1)$ appears but is
nonlinearly realized. We demonstrate this equivalence in an explicit
calculation, and show how it is reconciled with loop calculations in which the
different formulations can (superficially) appear to give different answers. In
this sense any effective theory containing light spin-one particles is seen to
be automatically gauge invariant.


  Boundary conditions defining a non-rotating isolated horizon are given in
Einstein-Maxwell theory. A spacetime representing a black hole which itself is
in equilibrium but whose exterior contains radiation admits such a horizon.
Inspired by Hamiltonian mechanics, a (quasi-)local definition of isolated
horizon mass is formulated. Although its definition does not refer to infinity,
this mass takes the standard value in a Reissner-Nordstrom solution.
Furthermore, under certain technical assumptions, the mass of an isolated
horizon is shown to equal the future limit of the Bondi energy.


  Deep learning has become the dominant approach in coping with various tasks
in Natural LanguageProcessing (NLP). Although text inputs are typically
represented as a sequence of tokens, there isa rich variety of NLP problems
that can be best expressed with a graph structure. As a result, thereis a surge
of interests in developing new deep learning techniques on graphs for a large
numberof NLP tasks. In this survey, we present a comprehensive overview onGraph
Neural Networks(GNNs) for Natural Language Processing. We propose a new
taxonomy of GNNs for NLP, whichsystematically organizes existing research of
GNNs for NLP along three axes: graph construction,graph representation
learning, and graph based encoder-decoder models. We further introducea large
number of NLP applications that are exploiting the power of GNNs and summarize
thecorresponding benchmark datasets, evaluation metrics, and open-source codes.
Finally, we discussvarious outstanding challenges for making the full use of
GNNs for NLP as well as future researchdirections. To the best of our
knowledge, this is the first comprehensive overview of Graph NeuralNetworks for
Natural Language Processing.


  We show that coloring properties of a simplicial complex K are reflected by
splitting properties of a bundle over the associated Davis-Januszkiewicz space
whose Chern classes are given by the elementary symmetric polynomials in the
generators of the Stanley-Reisner algebra of K.


  We present the discovery of the first Neptune analog exoplanet or super-Earth
with Neptune-like orbit, MOA-2013-BLG-605Lb. This planet has a mass similar to
that of Neptune or a super-Earth and it orbits at $9\sim 14$ times the expected
position of the snow-line, $a_{\rm snow}$, which is similar to Neptune's
separation of $ 11\,a_{\rm snow}$ from the Sun. The planet/host-star mass ratio
is $q=(3.6\pm0.7)\times 10^{-4}$ and the projected separation normalized by the
Einstein radius is $s=2.39\pm0.05$. There are three degenerate physical
solutions and two of these are due to a new type of degeneracy in the
microlensing parallax parameters, which we designate "the wide degeneracy". The
three models have (i) a Neptune-mass planet with a mass of $M_{\rm
p}=21_{-7}^{+6} M_{Earth}$ orbiting a low-mass M-dwarf with a mass of $M_{\rm
h}=0.19_{-0.06}^{+0.05} M_\odot$, (ii) a mini-Neptune with $M_{\rm p}=
7.9_{-1.2}^{+1.8} M_{Earth}$ orbiting a brown dwarf host with $M_{\rm
h}=0.068_{-0.011}^{+0.019} M_\odot$ and (iii) a super-Earth with $M_{\rm p}=
3.2_{-0.3}^{+0.5} M_{Earth}$ orbiting a low-mass brown dwarf host with $M_{\rm
h}=0.025_{-0.004}^{+0.005} M_\odot$ which is slightly favored. The 3-D
planet-host separations are 4.6$_{-1.2}^{+4.7}$ AU, 2.1$_{-0.2}^{+1.0}$ AU and
0.94$_{-0.02}^{+0.67}$ AU, which are $8.9_{-1.4}^{+10.5}$, $12_{-1}^{+7}$ or
$14_{-1}^{+11}$ times larger than $a_{\rm snow}$ for these models,
respectively. The Keck AO observation confirm that the lens is faint. This
discovery suggests that low-mass planets with Neptune-like orbit are common. So
processes similar to the one that formed Neptune in our own Solar System or
cold super-Earth may be common in other solar systems.


  We show that each entanglement witness detecting given bipartite entangled
state provides an estimation of its concurrence. We illustrate our result with
several well known examples of entanglement witnesses and compare the
corresponding estimation of concurrence with other estimations provided by the
trace norm of partial transposition and realignment.


  We establish quadratic asymptotics for solutions to special Lagrangian
equations with supercritical phases in exterior domains. The method is based on
an exterior Liouville type result for general fully nonlinear elliptic
equations toward constant asymptotics of bounded Hessian, and also certain
rotation arguments toward Hessian bound. Our unified approach also leads to
quadratic asymptotics for convex solutions to Monge-Amp\`{e}re equations
(previously known), quadratic Hessian equations, and inverse harmonic Hessian
equations over exterior domains.


  This review covers applications of quantum Monte Carlo methods to quantum
mechanical problems in the study of electronic and atomic structure, as well as
applications to statistical mechanical problems both of static and dynamic
nature. The common thread in all these applications is optimization of
many-parameter trial states, which is done by minimization of the variance of
the local or, more generally for arbitrary eigenvalue problems, minimization of
the variance of the configurational eigenvalue.


  Nanomechanical resonators having small mass, high resonance frequency and low
damping rate are widely employed as mass detectors. We study the performances
of such a detector when the resonator is driven into a region of nonlinear
oscillations. We predict theoretically that in this region the system acts as a
phase-sensitive mechanical amplifier. This behavior can be exploited to achieve
noise squeezing in the output signal when homodyne detection is employed for
readout. We show that mass sensitivity of the device in this region may exceed
the upper bound imposed by thermomechanical noise upon the sensitivity when
operating in the linear region. On the other hand, we show that the high mass
sensitivity is accompanied by a slowing down of the response of the system to a
change in the mass.


  We derive the structure of the Higgs branch of 5d superconformal field
theories or gauge theories from their realization as a generalized toric
polygon (or dot diagram). This approach is motivated by a dual, tropical curve
decomposition of the $(p,q)$ 5-brane-web system. We define an edge coloring,
which provides a decomposition of the generalized toric polygon into a refined
Minkowski sum of sub-polygons, from which we compute the magnetic quiver. The
Coulomb branch of the magnetic quiver is then conjecturally identified with the
5d Higgs branch. Furthermore, from partial resolutions, we identify the
symplectic leaves of the Higgs branch and thereby the entire foliation
structure. In the case of strictly toric polygons, this approach reduces to the
description of deformations of the Calabi-Yau singularities in terms of
Minkowski sums.


  Non-diagonal couplings to a bosonic bath completely change polaronic
dynamics, from the usual diagonally-coupled paradigm of smoothly-varying
properties. We study, using analytic and numerical methods, a model having both
diagonal Holstein and non-diagonal Su-Schrieffer-Heeger (SSH) couplings. The
critical coupling found previously in the pure SSH model, at which the $k=0$
effective mass diverges, now becomes a transition line in the coupling constant
plane - the form of the line depends on the adiabaticity parameter. Detailed
results are given for the quasiparticle and ground state properties, over a
wide range of couplings and adiabaticity ratios. The new paradigm involves a
destabilization, at the transition line, of the simple Holstein polaron to one
with a finite ground-state momentum, but with everywhere a continuously
evolving band shape. No 'self-trapping transition' exists in any of these
models. The physics may be understood entirely in terms of competition between
different hopping terms in a simple renormalized effective band theory. The
possibility of further transitions is suggested by the results.


  Lack of self-averaging originates in many disordered models from a
fragmentation of the phase space where the sizes of the fragments remain
sample-dependent in the thermodynamic limit. On the basis of new results in
percolation theory, we give here an argument in favour of the conjecture that
critical two dimensional percolation on the square lattice lacks of
self-averaging.


  A path in a vertex-colored graph is a {\it vertex-proper path} if any two
internal adjacent vertices differ in color. A vertex-colored graph is {\it
proper vertex $k$-connected} if any two vertices of the graph are connected by
$k$ disjoint vertex-proper paths of the graph. For a $k$-connected graph $G$,
the {\it proper vertex $k$-connection number} of $G$, denoted by $pvc_{k}(G)$,
is defined as the smallest number of colors required to make $G$ proper vertex
$k$-connected. A vertex-colored graph is {\it strong proper vertex-connected},
if for any two vertices $u,v$ of the graph, there exists a vertex-proper
$u$-$v$ geodesic. For a connected graph $G$, the {\it strong proper
vertex-connection number} of $G$, denoted by $spvc(G)$, is the smallest number
of colors required to make $G$ strong proper vertex-connected. In this paper,
we study the proper vertex $k$-connection number and the strong proper
vertex-connection number on the join of two graphs, the Cartesian,
lexicographic, strong and direct product, and present exact values or upper
bounds for these operations of graphs.


  We consider max-weighted matching with costs for learning the weights,
modeled as a "Pandora's Box" on each endpoint of an edge. Each vertex has an
initially-unknown value for being matched to a neighbor, and an algorithm must
pay some cost to observe this value. The goal is to maximize the total matched
value minus costs. Our model is inspired by two-sided settings, such as
matching employees to employers. Importantly for such settings, we allow for
negative values which cause existing approaches to fail.
  We first prove upper bounds for algorithms in two natural classes. Any
algorithm that "bundles" the two Pandora boxes incident to an edge is an
$o(1)$-approximation. Likewise, any "vertex-based" algorithm, which uses
properties of the separate Pandora's boxes but does not consider the
interaction of their value distributions, is an $o(1)$-approximation. Instead,
we utilize Pandora's Nested-Box Problem, i.e. multiple stages of inspection. We
give a self-contained, fully constructive optimal solution to the nested-boxes
problem, which may have structural observations of interest compared to prior
work. By interpreting each edge as a nested box, we leverage this solution to
obtain a constant-factor approximation algorithm. Finally, we show any
``edge-based'' algorithm, which considers the interactions of values along an
edge but not with the rest of the graph, is also an $o(1)$-approximation.


  Let W be a Weyl group. We define a new basis for the Grothendieck group of
representations of W. This basis contains on the one hand the special
representations of W and on the other hand the representations carried by the
left cells of W. We show that the representations in the new basis have a
certain bipositivity property.


  Machine learning models that first learn a representation of a domain in
terms of human-understandable concepts, then use it to make predictions, have
been proposed to facilitate interpretation and interaction with models trained
on high-dimensional data. However these methods have important limitations: the
way they define concepts are not inherently interpretable, and they assume that
concept labels either exist for individual instances or can easily be acquired
from users. These limitations are particularly acute for high-dimensional
tabular features. We propose an approach for learning a set of transparent
concept definitions in high-dimensional tabular data that relies on users
labeling concept features instead of individual instances. Our method produces
concepts that both align with users' intuitive sense of what a concept means,
and facilitate prediction of the downstream label by a transparent machine
learning model. This ensures that the full model is transparent and intuitive,
and as predictive as possible given this constraint. We demonstrate with
simulated user feedback on real prediction problems, including one in a
clinical domain, that this kind of direct feedback is much more efficient at
learning solutions that align with ground truth concept definitions than
alternative transparent approaches that rely on labeling instances or other
existing interaction mechanisms, while maintaining similar predictive
performance.


  Safe memory reclamation (SMR) schemes are an essential tool for lock-free
data structures and concurrent programming. However, manual SMR schemes are
notoriously difficult to apply correctly, and automatic schemes, such as
reference counting, have been argued for over a decade to be too slow for
practical purposes. A recent wave of work has disproved this long-held notion
and shown that reference counting can be as scalable as hazard pointers, one of
the most common manual techniques. Despite these tremendous improvements, there
remains a gap of up to 2x or more in performance between these schemes and
faster manual techniques such as epoch-based reclamation (EBR).
  In this work, we first advance these ideas and show that in many cases,
automatic reference counting can in fact be as fast as the fastest manual SMR
techniques. We generalize our previous Concurrent Deferred Reference Counting
(CDRC) algorithm to obtain a method for converting any standard manual SMR
technique into an automatic reference counting technique with a similar
performance profile. Our second contribution is extending this framework to
support weak pointers, which are reference-counted pointers that automatically
break pointer cycles by not contributing to the reference count, thus
addressing a common weakness in reference-counted garbage collection.
  Our experiments with a C++-library implementation show that our automatic
techniques perform in line with their manual counterparts, and that our weak
pointer implementation outperforms the best known atomic weak pointer library
by up to an order of magnitude on high thread counts. All together, we show
that the ease of use of automatic memory management can be achieved without
significant cost to practical performance or general applicability.


  We describe the properties and kinematics of the neutral gas in the two dwarf
elliptical galaxies NGC 185 and NGC 205, companions of M31. The kinematics of
the HI suggest that an internal origin for the gas (i.e. stellar mass loss)
should be considered, at least in the case of NGC 185. The molecular clouds in
these dwarf ellipticals are similar to Galactic giant molecular clouds in many
ways. However, the HI column density in the dwarf ellipticals is surprisingly
low. A lower interstellar UV field may make it easier to form and retain
molecular gas in the dwarf ellipticals than in the solar neighborhood.


  Growth of atomic indium chains - 1D islands - on the Si(100)-2x1 surface was
observed by scanning tunneling microscopy (STM) at room temperature and
simulated by means of a kinetic Monte Carlo method. Density of indium islands
and island size distribution were obtained for various deposition rates and
coverage. STM observation of growth during deposition of indium provided
information on growth kinetics and relaxation of grown layers. Important role
of C-type defects at adsorption of metal atoms was observed. Measured growth
characteristics were simulated using a microscopic model with anisotropic
surface diffusion and forbidden zones along the metal chains. An analysis of
experimental and simulation data shows that detachment of indium adatoms from
the chains substantially influences a growth scenario and results in
monotonously decreasing chain length distribution function at low coverage.
Diffusion barriers determined from the simulations correspond to almost
isotropic diffusion of indium adatoms on the surface. The results are discussed
with respect to data reported in earlier papers for other metals.


  We report a novel technique for launching broadband laser light into
liquid-filled hollow-core photonic crystal fiber (HC-PCF). It uniquely offers
self-alignment and self-stabilization via optomechanical trapping of a fused
silica nanospike, fabricated by thermally tapering and chemically etching a
single mode fiber into a tip diameter of 350 nm. We show that a trapping laser,
delivering ~300 mW at 1064 nm, can be used to optically align and stably
maintain the nanospike at the core center. Once this is done, a broadband
supercontinuum beam (~575 to 1064 nm) can be efficiently and close to
achromatically launched in the HC-PCF. The system is robust against liquid-flow
in either direction inside the HC-PCF and the Fresnel back-reflections are
reduced to negligible levels compared to free-space launching or butt-coupling.
The results are of potential relevance for any application where the efficient
delivery of broadband light into liquid-core waveguides is desired.


  In the context of the modified Becke-Johnson (mBJ) potential, we recently
underlined that $\bar{g}$, the average of
$\left\vert\nabla\rho\right\vert/\rho$ in the unit cell, has markedly different
values in transition-metal oxides and pure transition metals [Tran et al., J.
Appl. Phys. 126, 110902 (2019)]. However, since $\bar{g}$ is a constant it is
not able to provide local information about a particular atom in the system.
Furthermore, while $\overline{g}$ can be used only for periodic bulk solids, a
local (i.e., position-dependent) version would allow us to consider also
low-dimensional systems and interfaces. Such a local function has been proposed
by Rauch et al. [J. Chem. Theory Comput. 16, 2654 (2020)] for the local mBJ
potential. Actually, a local version of $\overline{g}$, or of another similar
quantity like the reduced density gradient $\overline{s}$, could also be used
in the framework of other methods. Here, we explored the idea to use such a
local function $\tilde{g}$ (or $\tilde{s}$), defined as the average of $g$ (or
$s$) over a certain region around a transition-metal atom, to estimate the
degree of on-site correlation on this atom. We found a large difference in our
correlation estimators between non-correlated and correlated materials, proving
its usefulness and reliability. Our estimators can subsequently be used to
determine whether or not a Hubbard $U$ on-site correction in the DFT+$U$ method
should be applied to a particular atom. This is particularly interesting in
cases where the degree of correlation of the transition-metal atoms is not
clear, like interfaces between correlated and non-correlated materials or
oxygen-covered metal surfaces. In such cases, our estimators could also be used
for an interpolation of $U$ between correlated and non-correlated atoms.


  Measuring the primordial power spectrum on small scales is a powerful tool in
inflation model building, yet constraints from Cosmic Microwave Background
measurements alone are insufficient to place bounds stringent enough to be
appreciably effective. For the very small scale spectrum, those which subtend
angles of less than 0.3 degrees on the sky, an upper bound can be extracted
from the astrophysical constraints on the possible production of primordial
black holes in the early universe. A recently discovered observational
by-product of an enhanced power spectrum on small scales, induced gravitational
waves, have been shown to be within the range of proposed space based
gravitational wave detectors; such as NASA's LISA and BBO detectors, and the
Japanese DECIGO detector. In this paper we explore the impact such a detection
would have on models of inflation known to lead to an enhanced power spectrum
on small scales, namely the Hilltop-type and running mass models. We find that
the Hilltop-type model can produce observable induced gravitational waves
within the range of BBO and DECIGO for integral and fractional powers of the
potential within a reasonable number of e-folds. We also find that the running
mass model can produce a spectrum within the range of these detectors, but
require that inflation terminates after an unreasonably small number of
e-folds. Finally, we argue that if the thermal history of the Universe were to
accomodate such a small number of e-folds the Running Mass Model can produce
Primordial Black Holes within a mass range compatible with Dark Matter, i.e.
within a mass range 10^{20}g< M_{BH}<10^{27}g.


  The proliferation and ubiquity of temporal data across many disciplines has
sparked interest for similarity, classification and clustering methods
specifically designed to handle time series data. A core issue when dealing
with time series is determining their pairwise similarity, i.e., the degree to
which a given time series resembles another. Traditional distance measures such
as the Euclidean are not well-suited due to the time-dependent nature of the
data. Elastic metrics such as dynamic time warping (DTW) offer a promising
approach, but are limited by their computational complexity,
non-differentiability and sensitivity to noise and outliers. This thesis
proposes novel elastic alignment methods that use parametric \& diffeomorphic
warping transformations as a means of overcoming the shortcomings of DTW-based
metrics. The proposed method is differentiable \& invertible, well-suited for
deep learning architectures, robust to noise and outliers, computationally
efficient, and is expressive and flexible enough to capture complex patterns.
Furthermore, a closed-form solution was developed for the gradient of these
diffeomorphic transformations, which allows an efficient search in the
parameter space, leading to better solutions at convergence. Leveraging the
benefits of these closed-form diffeomorphic transformations, this thesis
proposes a suite of advancements that include: (a) an enhanced temporal
transformer network for time series alignment and averaging, (b) a
deep-learning based time series classification model to simultaneously align
and classify signals with high accuracy, (c) an incremental time series
clustering algorithm that is warping-invariant, scalable and can operate under
limited computational and time resources, and finally, (d) a normalizing flow
model that enhances the flexibility of affine transformations in coupling and
autoregressive layers.


  We study the strong and electromagnetic decay properties of scalar mesons
above 1 GeV within a chiral approach. The scalar-isoscalar states are treated
as mixed states of quarkonia and glueball configurations. A fit to the
experimental decay rates listed by the Particle Data group is performed to
extract phenomenological constraints on the nature of the scalar resonances. A
comparison to other theoretical approaches in the scalar meson sector is
discussed.


  We report the detection of a compact (of order 5 arcsec; about 1800 AU
projected size) CO outflow from L1148-IRS. This confirms that this Spitzer
source is physically associated with the nearby (about 325 pc) L1148 dense
core. Radiative transfer modeling suggests an internal luminosity of 0.08 to
0.13 L_sun. This validates L1148-IRS as a Very Low Luminosity Object (VeLLO; L
< 0.1 L_sun). The L1148 dense core has unusually low densities and column
densities for a star-forming core. It is difficult to understand how L1148-IRS
might have formed under these conditions. Independent of the exact final mass
of this VeLLO (which is likely < 0.24 M_sun), L1148-IRS and similar VeLLOs
might hold some clues about the isolated formation of brown dwarfs.


  Language is an outcome of our complex and dynamic human-interactions and the
technique of natural language processing (NLP) is hence built on human
linguistic activities. Bidirectional Encoder Representations from Transformers
(BERT) has recently gained its popularity by establishing the state-of-the-art
scores in several NLP benchmarks. A Lite BERT (ALBERT) is literally
characterized as a lightweight version of BERT, in which the number of BERT
parameters is reduced by repeatedly applying the same neural network called
Transformer's encoder layer. By pre-training the parameters with a massive
amount of natural language data, ALBERT can convert input sentences into
versatile high-dimensional vectors potentially capable of solving multiple NLP
tasks. In that sense, ALBERT can be regarded as a well-designed
high-dimensional dynamical system whose operator is the Transformer's encoder,
and essential structures of human language are thus expected to be encapsulated
in its dynamics. In this study, we investigated the embedded properties of
ALBERT to reveal how NLP tasks are effectively solved by exploiting its
dynamics. We thereby aimed to explore the nature of human language from the
dynamical expressions of the NLP model. Our short-term analysis clarified that
the pre-trained model stably yields trajectories with higher dimensionality,
which would enhance the expressive capacity required for NLP tasks. Also, our
long-term analysis revealed that ALBERT intrinsically shows transient chaos, a
typical nonlinear phenomenon showing chaotic dynamics only in its transient,
and the pre-trained ALBERT model tends to produce the chaotic trajectory for a
significantly longer time period compared to a randomly-initialized one. Our
results imply that local chaoticity would contribute to improving NLP
performance, uncovering a novel aspect in the role of chaotic dynamics in human
language behaviors.


  De Broglie - Bohm (dBB) theory is a deterministic theory, built for
reproducing almost all Quantum Mechanics (QM) predictions, where position plays
the role of a hidden variable. It was recently shown that different coincidence
patterns are predicted by QM and dBB when a double slit experiment is realised
under specific conditions and, therefore, an experiment can test the two
theories. In this letter we present the first realisation of such a double slit
experiment by using correlated photons produced in type I Parametric Down
Conversion. Our results confirm QM contradicting dBB predictions.


  While surface temperature gradients have been highlighted as drivers of
low-level atmospheric circulation, the underlying physical mechanisms remain
unclear. Lindzen and Nigam (1987) noted that sea level pressure (SLP) gradients
are proportional to surface temperature gradients if isobaric height (the
height where pressure does not vary in the horizontal plane) is constant; their
own model of low-level circulation assumed that isobaric height in the tropics
is around 3 km. Recently Bayr and Dommenget (2013) proposed a simple model of
temperature-driven air redistribution from which they derived that the isobaric
height in the tropics again varies little but occurs higher (at the height of
the troposphere). Here investigations show that neither the empirical
assumption of Lindzen and Nigam (1987) nor the theoretical derivations of Bayr
and Dommenget (2013) are plausible. Observations show that isobaric height is
too variable to determine a universal spatial or temporal relationship between
local values of air temperature and SLP. Since isobaric height cannot be
determined from independent considerations, the relationship between SLP and
temperature is not evidence that differential heating drives low-level
circulation. An alternative theory suggests SLP gradients are determined by the
condensation of water vapor as moist air converges towards the equator. This
theory quantifies the meridional SLP differences observed by season across the
Hadley cells reasonably well. Higher temperature of surface air where SLP is
low may be determined by equatorward transport and release of latent heat below
the trade wind inversion layer. The relationship between atmospheric
circulation and moisture dynamics merits further investigation.


  Multi-socket multi-core servers are used for solving some of the important
problems in computing. Remote DRAM accesses can impact performance of certain
applications running on such servers. This paper presents a new near linear
operating system (OS) scheduling algorithm to reduce the impact of such remote
DRAM accesses. By keeping track of the number of local and remote DRAM
accesses, using performance counters, for every thread and applying this
algorithm, I come up with a new schedule of threads for the next quantum. This
new schedule reduces remote DRAM accesses and improves overall performance. I
also show that this algorithm is actually linear in the best case. As the
algorithm is near-linear it is amenable for implementation in a real operating
system.


  In this work, an operator superquadratic function (in operator sense) for
positive Hilbert space operators is defined. Several examples with some
important properties together with some observations which are related to the
operator convexity are pointed out. Equivalent statements of a non-commutative
version of Jensen's inequality for operator superquadratic function are
established. A generalization of the main result to any positive unital linear
map is also provided.


  We compute the spatial-volume dependence of the spectrum of 4D SU(3 <= N <=
6) gauge theories by lattice Monte-Carlo techniques. Setting the scale with the
string tension, the spatial volume is L^3 with 0.78fm <= L <= 2.3fm. The
Euclidean `time' direction is kept large enough to be considered infinite and
the boundary conditions are periodic in all four dimensions. We study the
mixing of torelon pairs with the scalar and tensor glueballs, using a 2x2
Hamiltonian based on large-N counting rules. Looking to the other symmetry
channels, finite-volume effects on the glueball spectrum are already
surprisingly small in SU(3), and they become rapidly smaller as N is increased:
several low-lying SU(6) states have no finite-volume corrections at the 1-2%
level, at least down to L=0.9fm. We discuss the relation of this work with
analytic calculations in small and intermediate volume, and with Eguchi-Kawai
reduction in the planar limit.


  The optical data transport system of the KM3NeT neutrino telescope at the
bottom of the Mediterranean Sea will provide each of the more than 6000 optical
modules in the detector arrays with a point-to-point optical connection to the
control stations onshore. The ARCA and ORCA detectors of KM3NeT are being
installed at a depth of about 3500 m and 2500 m, respectively; their distance
to the control stations is about 100 kilometers and 40 kilometers. The expected
maximum data rate is 200 Mbps per optical module. The implemented optical data
transport system matches the layouts of the networks of electro-optical cables
and junction boxes in the deep sea. For efficient use of the fibres in the
system the technology of Dense Wavelength Division Multiplexing is applied. The
performance of the optical system in terms of measured bit error rates, optical
budget and the next steps in the implementation of the system are presented.


  Krivine and Maurey proved in 1981 that every stable Banach space contains
almost isometric copies of $\ell_p$, for some $p\in[1,\infty)$. In 1983,
Raynaud showed that if a Banach space uniformly embeds into a superstable
Banach space, then $X$ must contain an isomorphic copy of $\ell_p$, for some
$p\in[1,\infty)$. In these notes, we show that if a Banach space coarsely
embeds into a superstable Banach space, then $X$ has a spreading model
isomorphic to $\ell_p$, for some $p\in[1,\infty)$. In particular, we obtain
that there exist reflexive Banach spaces which do not coarsely embed into any
superstable Banach space.


  Gene transcription is a critical step in gene expression. The currently
accepted physical model of transcription predicts the existence of a physical
limit on the maximal rate of transcription, which does not depend on the
transcribed gene. This limit appears as a result of polymerase "traffic jams"
forming in the bulk of the 1D DNA chain at high polymerase concentrations.
Recent experiments have, for the first time, allowed one to access live gene
expression dynamics in the Drosophila fly embryo in vivo under the conditions
of heavy polymerase load and test the predictions of the model. Our analysis of
the data shows that the maximal rate of transcription is indeed the same for
the Hunchback, Snail and Knirps gap genes, and modified gene constructs in
nuclear cycles 13, 14, but the experimentally observed value of the maximal
transcription rate corresponds to only 40 % of the one predicted by this model.
We argue that such a decrease must be due to a slower polymerase elongation
rate in the vicinity of the promoter region. This effectively shifts the
bottleneck of transcription from the bulk to the promoter region of the gene.
We suggest a quantitative explanation of the difference by taking into account
abortive transcription initiation. Our calculations based on the independently
measured abortive initiation constant in vitro confirm this hypothesis and find
quantitative agreement with MS2 fluorescence live imaging data in the early
fruit fly embryo. If our explanation is correct, then the transcription rate
cannot be increased by replacing "slow codons" in the bulk with synonymous
codons, and experimental efforts must be focused on the promoter region
instead. This study extends our understanding of transcriptional regulation,
re-examines physical constraints on the kinetics of transcription and
re-evaluates the validity of the standard TASEP model of transcription.


  Extrapolation codes in Cartesian geometry for modelling the magnetic field in
the corona do not take the curvature of the Sun's surface into account and can
only be applied to relatively small areas, e.g., a single active region. We
compare the analysis of the photospheric magnetic field and subsequent
force-free modeling based on full-disk vector maps from Helioseismic and
Magnetic Imager (HMI) on board solar dynamics observatory (SDO) and Vector
Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of
the Sun (SOLIS). We use Helioseismic and Magnetic Imager and Vector
Spectromagnetograph photospheric magnetic field measurements to model the
force-free coronal field above multiple solar active regions, assuming magnetic
forces to dominate. We solve the nonlinear force-free field equations by
minimizing a functional in spherical coordinates over a full disk excluding the
poles. After searching for the optimum modeling parameters for the particular
data sets, we compare the resulting nonlinear force-free model fields. We
compare quantities like the total magnetic energy content and free magnetic
energy, the longitudinal distribution of the magnetic pressure and surface
electric current density using our spherical geometry extrapolation code. The
magnetic field lines obtained from nonlinear force-free extrapolation based on
Helioseismic and Magnetic Imager and Vector Spectromagnetograph data have good
agreement. However, the nonlinear force-free extrapolation based on
Helioseismic and Magnetic Imager data have more contents of total magnetic
energy, free magnetic energy, the longitudinal distribution of the magnetic
pressure and surface electric current density compared to the one from Vector
Spectromagnetograph data.


  The $\frac{1}{2}^+ \rightarrow \frac{1}{2}^+$ superallowed mixed mirror decay
of $^{19}$Ne to $^{19}$F is excellently suited for high precision studies of
the weak interaction. However, there is some disagreement on the value of the
half-life. In a new measurement we have determined this quantity to be
$T_{1/2}$ = $17.2832 \pm 0.0051_{(stat)}$ $\pm 0.0066_{(sys)}$ s, which differs
from the previous world average by 3 standard deviations. The impact of this
measurement on limits for physics beyond the standard model such as the
presence of tensor currents is discussed.


  We present a study of rest-frame UV-to-optical color distributions for z~4
galaxies based on the combination of deep HST/ACS+WFC3/IR data with
Spitzer/IRAC imaging. In particular, we use new, ultra-deep data from the IRAC
Ultradeep Field program (IUDF10). Our sample contains a total of ~2600 galaxies
selected as B-dropout Lyman Break Galaxies (LBGs) in the HUDF and one of its
deep parallel fields, the HUDF09-2, as well as GOODS-North and South. This
sample is used to investigate the UV continuum slopes beta and Balmer break
colors (J_125-[4.5]) as a function of rest-frame optical luminosity. The [4.5]
filter is chosen to avoid potential contamination by strong rest-frame optical
emission lines. We find that galaxies at M_z<-21.5 (roughly corresponding to
L*[z~4]) are significantly redder than their lower luminosity counterparts. The
UV continuum slopes and the J_125-[4.5] colors are well correlated. The most
simple explanation for this correlation is that the dust reddening at these
redshifts is better described by an SMC-like extinction curve, rather than the
typically assumed Calzetti reddening. After correcting for dust, we find that
the galaxy population shows mean stellar population ages in the range 10^8.5 to
10^9 yr, with a dispersion of ~0.5 dex, and only weak trends as a function of
luminosity. In contrast to some results from the literature, we find that only
a small fraction of galaxies shows Balmer break colors which are consistent
with extremely young ages, younger than 100 Myr. Under the assumption of smooth
star-formation histories, this fraction is only 12-19% for galaxies at
M_z<-19.75. Our results are consistent with a gradual build-up of stars and
dust in galaxies at z>4, with only a small fraction of stars being formed in
short, intense bursts of star-formation.


  We show that $\mathbb{Z}_3$-valued particle-vortex braiding phases are
present in high density quark matter. Certain mesonic and baryonic excitations,
in the presence of a superfluid vortex, have orbital angular momentum quantized
in units of $\hbar/3$. Such non-local topological features can distinguish
phases whose realizations of global symmetries, as probed by local order
parameters, are identical. If $\mathbb{Z}_3$ braiding phases and angular
momentum fractionalization are absent in lower density hadronic matter, as is
widely expected, then the quark matter and hadronic matter regimes of dense QCD
must be separated by at least one phase transition.


  Let $\Lambda$ be a dominant integral weight of level $k$ for the affine Lie
algebra $\mathfrak g$ and let $\alpha$ be a non-negative integral combination
of simple roots. We address the question of whether the weight
$\eta=\Lambda-\alpha$ lies in the set $P(\Lambda)$ of weights in the
irreducible highest-weight module with highest weight $\Lambda$. We give a
non-recursive criterion in terms of the coefficients of $\alpha$ modulo an
integral lattice $kM$, where $M$ is the lattice parameterizing the abelian
normal subgroup $T$ of the Weyl group. The criterion requires the preliminary
computation of a set no larger than the fundamental region for $kM$, and we
show how this set can be efficiently calculated.


  The top quark is the heaviest known elementary particle, with a mass about 40
times larger than the mass of its isospin partner, the bottom quark. It decays
almost 100% of the time to a $W$ boson and a bottom quark. Using top-antitop
pairs at the Tevatron proton-antiproton collider, the CDF and {\dzero}
collaborations have measured the top quark's mass in different final states for
integrated luminosities of up to 5.8 fb$^{-1}$. This paper reports on a
combination of these measurements that results in a more precise value of the
mass than any individual decay channel can provide. It describes the treatment
of the systematic uncertainties and their correlations. The mass value
determined is $173.18 \pm 0.56 \thinspace ({\rm stat}) \pm 0.75 \thinspace
({\rm syst})$ GeV or $173.18 \pm 0.94$ GeV, which has a precision of $\pm
0.54%$, making this the most precise determination of the top quark mass.


  Let \Sigma be a minimal submanifold of \R^{n+m} that can be represented as
the graph of a smooth map f:\R^n-->\R^m. We apply a formula we derived in the
study of mean curvature flow to obtain conditions under which \Sigma must be an
affine subspace. Our result covers all known ones in the general case. The
conditions are stated in terms of the singular values of $df$.


  We give a proper fractional extension of the classical calculus of
variations. Necessary optimality conditions of Euler-Lagrange type for
variational problems containing both classical and fractional derivatives are
proved. The fundamental problem of the calculus of variations with mixed
integer and fractional order derivatives as well as isoperimetric problems are
considered.


  The uncertainty principle can be understood as constraining the probability
of winning a game in which Alice measures one of two conjugate observables,
such as position or momentum, on a system provided by Bob, and he is to guess
the outcome. Two variants are possible: either Alice tells Bob which observable
she measured, or he has to furnish guesses for both cases. Here I derive new
uncertainty relations for both, formulated directly in terms of Bob's guessing
probabilities. For the former these relate to the entanglement that can be
recovered by action on Bob's system alone. This gives a condition for
approximate quantum error correction in terms of the recoverability of
"amplitude" and "phase" information, implicitly used in the recent construction
of efficient quantum polar codes. I also find a tight relation on the guessing
probabilities for the latter game, which has application to wave-particle
duality relations.


  We study a social choice setting of manipulation in elections and extend the
usual model in two major ways: first, instead of considering a single
manipulating agent, in our setting there are several, possibly competing ones;
second, instead of evaluating an election after the first manipulative action,
we allow several back-and-forth rounds to take place. We show that in certain
situations, such as in elections with only a few candidates, optimal strategies
for each of the manipulating agents can be computed efficiently.
  Our algorithmic results rely on formulating the problem of finding an optimal
strategy as sentences of Presburger arithmetic that are short and only involve
small coefficients, which we show is fixed-parameter tractable -- indeed, one
of our contributions is a general result regarding fixed-parameter tractability
of Presburger arithmetic that might be useful in other settings. Following our
general theorem, we design quite general algorithms; in particular, we describe
how to design efficient algorithms for various settings, including settings in
which we model diffusion of opinions in a social network, complex budgeting
schemes available to the manipulating agents, and various realistic
restrictions on adversary actions.


  The present paper is devoted to the study of resonances for a $1$D
Schr\"{o}dinger operator with truncated periodic potential. Precisely, we
consider the half-line operator $H^{\mathbb N}=-\Delta +V$ and $H^{\mathbb
N}_{L}= -\Delta + V1_{[0, L]}$ acting on $\ell^{2}(\mathbb N)$ with Dirichlet
boundary condition at $0$ with $L \in \mathbb N$. We describe the resonances of
$H^{\mathbb N}_{L}$ near the boundary of the essential spectrum of $H^{\mathbb
N}$ as $L \rightarrow +\infty$ under a special assumption.\\ The present paper
is in a series of our research papers on resonances


  We propose a new mechanism of spontaneous gauge symmetry breaking in the
world-volume theory of revolving D-branes around a fixed point of orbifolds. In
this paper, we consider a simple model of the T6/Z3 orbifold on which we put
D3-branes, D7-branes and their anti-branes. The configuration breaks
supersymmetry, but the R-R tadpole cancellation conditions are satisfied. A set
of three D3-branes at an orbifold fixed point can separate from the point, but
when they move perpendicular to the anti-D7-branes put on the fixed point, they
are forced to be pulled back due to an attractive interaction between the D3
and anti-D7 branes. In order to stabilize the separation of the D3-branes at
nonzero distance, we consider revolution of the D3-branes around the fixed
point. Then the gauge symmetry on D3-branes is spontaneously broken, and the
rank of the gauge group is reduced. The distance can be set at our will by
appropriately choosing the angular momentum of the revolving D3-branes, which
should be determined by the initial condition of the cosmological evolution of
D-brane configurations. The distance corresponds to the vacuum expectation
values of brane moduli fields in the world-volume theory and, if it is written
as M/Ms^2 in terms of the string scale Ms, the scale of gauge symmetry breaking
is given by M. Angular momentum conservation of revolving D3-branes assures the
stability of the scale M against Ms.


  We review the dispersion-theoretical analysis of the electromagnetic form
factors of the nucleon. We emphasize in particular the role of unitarity and
analyticity in the construction of the isoscalar and isovector spectral
functions. We present new results on the extraction of the nucleon radii, the
electric and magnetic form factors and the extraction of $\omega$-meson
couplings. All this is supplemented by a detailed calculation of the
theoretical uncertainties, using bootstrap and Bayesian methods to pin down the
statistical errors, while systematic errors are determined from variations of
the spectral functions. We also discuss the physics of the time-like form
factors and point out further issues to be addressed in this framework.


  As originally defined by Ashraf and Mozumder, multiplicative
(generalized)-skew derivations must satisfy two identities. In this short note
we show that, as a consequence of the simultaneous satisfaction of both
identities, a multiplicative (generalized)-skew derivation of a prime ring is
either a multiplicative (generalized) derivation (i.e., not skew), or a
generalized skew derivation (i.e., additive). Therefore only one of the
identities should be taken in the definition of multiplicative
(generalized)-skew derivations in order to get a new class of derivations in
prime rings.


  In a previous paper we study the neutrino-electron scattering in the
framework of a left-right symmetric model (LRSM). Constraints on the LRSM
parameters $M_{Z_{2}}$ and $\phi$ were obtained. Based on new measurements we
present an update to these constraints and also include in the calculation the
radiative corrections.