  The loop quantization of Brans-Dicke theory (with coupling parameter
$\omega\neq-3/2$) is studied. In the geometry-dynamical formalism, the
canonical structure and constraint algebra of this theory are similar to those
of general relativity coupled with a scalar field. The connection dynamical
formalism of the Brans-Dicke theory with real $su(2)$-connections as
configuration variables is obtained by canonical transformations. The quantum
kinematical Hilbert space of Brans-Dicke theory is constituted as of that loop
quantum gravity coupled with a polymer-like scalar field. The Hamiltonian
constraint is promoted as a well defined operator to represent quantum
dynamics. This formalism enable us to extend the scheme of non-perturbative
loop quantum gravity to the Brans-Dicke theory.


  In our paper "Dendroidal sets as models for homotopy operads" (J. Topol. 4
(2011), no. 2, 257-299, and arXiv:0902.1954), we made the wrong claim about the
behaviour of the tensor product with respect to cofibrations of dendroidal
sets. We added an erratum at the end of the arXiv version of loc. cit. This
short note contains the proof of a technical lemma used in the erratum.


  Based on regularities in rotational splittings, we seek possible multiplets
for the observed frequencies of CoRoT 102749568. Twenty-one sets of multiplets
are identified, including four sets of multiplets with $l=1$, nine sets of
multiplets with $l=2$, and eight sets of multiplets with $l=3$. In particular,
there are three complete triplets ($f_{10}$, $f_{12}$, $f_{14}$), ($f_{31}$,
$f_{34}$, $f_{35}$), and ($f_{41}$, $f_{43}$, $f_{44}$). The rotational period
of CoRoT 102749568 is estimated to be $1.34^{+0.04}_{-0.05}$ days. When doing
model fittings, three $l=1$ modes ($f_{12}$, $f_{34}$, and $f_{43}$) and the
radial first overtone $f_{13}$ are used. Our results shows that the three
nonradial modes ($f_{12}$, $f_{34}$, and $f_{43}$) are mixed modes, which
mainly provide constraints on the helium core. The radial first overtone
$f_{13}$ mainly provides constraint on the stellar envelope. Hence the size of
the helium core of CoRoT 102749568 is determined to be $M_{\rm He}$ = 0.148
$\pm$ 0.003 $M_{\odot}$ and $R_{\rm He}$ = 0.0581 $\pm$ 0.0007 $R_{\odot}$. The
fundamental parameters of CoRoT 102749568 are determined to be $M$ = 1.54 $\pm$
0.03 $M_{\odot}$, $Z=$ 0.006, $f_{\rm ov}$ = 0.004 $\pm$ 0.002, $\log g$ =
3.696 $\pm$ 0.003, $T_{\rm eff}$ = 6886 $\pm$ 70 K, $R$ = 2.916 $\pm$ 0.039
$R_{\odot}$, and $L$ = 17.12 $\pm$ 1.13 $L_{\odot}$.


  The local chromatic number of a graph G is the number of colors appearing in
the most colorful closed neighborhood of a vertex minimized over all proper
colorings of G. We show that two specific topological obstructions that have
the same implications for the chromatic number have different implications for
the local chromatic number. These two obstructions can be formulated in terms
of the homomorphism complex Hom(K_2,G) and its suspension, respectively.
  These investigations follow the line of research initiated by Matousek and
Ziegler who recognized a hierarchy of the different topological expressions
that can serve as lower bounds for the chromatic number of a graph.
  Our results imply that the local chromatic number of 4-chromatic Kneser,
Schrijver, Borsuk, and generalized Mycielski graphs is 4, and more generally,
that 2r-chromatic versions of these graphs have local chromatic number at least
r+2. This lower bound is tight in several cases by results in an earlier paper
of the first two authors.


  A more precise determination of the effective fine structure constant
alpha_eff(E) is mandatory for confronting data from future precision
experiments with precise SM predictions. At a future e+e- collider like the
ILC, as at LEP before, alpha_eff(E) plays the role the static zero momentum
alpha=alpha_eff(0) plays in low energy physics. However, by going to the
effective version of alpha one loses about a factor 2 times 10^2 at E=m_mu to
10^5 at E=M_Z in precision, such that for physics at the gauge boson mass scale
and beyond alpha_eff(E) is the least known basic parameter, about a factor 20
less precise than the neutral gauge boson mass M_Z and by about a factor 60
less precise than the Fermi constant G_F. We discuss a strategy which should be
able to reach a factor 10 improvement by appropriate efforts in performing
dedicated measurements of sigma_hadronic in a wide energy range as well as
efforts in theory and in particular improving the precision of the QCD
parameters alpha_s, m_c and m_b. Projects at VEPP-2000 (Novosibirsk) and
DANAE/KLOE-2 (Frascati) are particularly important for improving on
alpha_eff(M_Z) as well as alpha_eff(m_mu). We present an up-to-date analysis
including the recent data from KLOE, SND, CMD-2 and BABAR. The analysis based
on e+e- data yields Delta alpha_had^(5)(M_Z) = 0.027593 +/- 0.000169
[alpha^-1(M_Z) = 128.938 +/- 0.023] and a_mu^had=(692.1 +/- 5.6) x 10^{-10}. We
emphasize the very high improvement potential of the VEPP-2000 and DANAE/KLOE-2
projects.


  We study the modification of the far-field cross sections and the near-field
enhancement for gold and silver nanospheres illuminated by a tightly focused
beam. Using a multipole-expansion approach we obtain an analytical solution to
the scattering problem and provide insight on the effects of focusing on the
optical response. Large differences with respect to Mie theory are found
especially when the nanoparticle supports quadrupole or higher-order
resonances.


  We prove that under any projective embedding of an abelian variety A of
dimension g, a complete system of addition laws has cardinality at least g+1,
generalizing of a result of Bosma and Lenstra for the Weierstrass model of an
elliptic curve in P^2. In contrast with this geometric constraint, we moreover
prove that if k is any field with infinite absolute Galois group, then there
exists, for every abelian variety A/k, a projective embedding and an addition
law defined for every pair of k-rational points. For an abelian variety of
dimension 1 or 2, we show that this embedding can be the classical Weierstrass
model or embedding in P^15, respectively, up to a finite number of
counterexamples for |k| less or equal to 5.


  We introduce "weakly chained spaces", which need not be locally connected or
path connected, but for which one has a reasonable notion of generalized
fundamental group and associated generalized universal cover. We show that in
the compact metric case, weakly chained is equivalent to the concept of
"pointed 1-movable" from classical shape theory. We use this fact and a theorem
of Geoghegan-Swenson to give criteria on the metric spheres in a CAT(0) space
that imply that the boundary is has semistable fundamental group at infinity.


  Recently, Neuhaeuser et al. (2005) presented evidence for a sub-stellar,
common proper motion companion to GQ Lup. With two theoretical mass estimates,
both below the Deuterium burning minimum mass limit, the companion is probably
a planet imaged directly. We present here a more detailed astrometric analysis
of the GQ Lup system, using all the (different) proper motions published for
the primary. The common proper motion is significant in all cases, also when
taking into account the error in parallax or distance (140 +- 50 pc). When
using the weighted mean, the significance for common proper motion of GQ Lup
and its companion is 7 + 4 sigma for no change in separation plus 8 sigma for
no change in position angle. We also discuss the question, whether GQ Lup and
its common-proper motion companion are not bound, but share the same or similar
proper motion as two independent members of the Lupus T association, which is a
moving group, where most members should have the same motion anyway. Given our
discussion, this hypothesis can be rejected by several sigma: The probability
to find by chance an L-dwarf fainter than Ks = 14 mag within 0.7325 arcsec with
(almost) the same proper motion of GQ Lup is only < 3 10^{-10}. The orbital
motion of the system is not yet detected (1.4 +- 2.2 mas/yr), but is probably
smaller than the escape velocity (5.3 +- 2.1 mas/yr), so that the system may
well be gravitationally bound and stable. This is different for the
2MASSWJ1207334-393254 system, as we also show.


  The Natural Language Inference (NLI) task is an important task in modern NLP,
as it asks a broad question to which many other tasks may be reducible: Given a
pair of sentences, does the first entail the second? Although the
state-of-the-art on current benchmark datasets for NLI are deep learning-based,
it is worthwhile to use other techniques to examine the logical structure of
the NLI task. We do so by testing how well a machine-oriented controlled
natural language (Attempto Controlled English) can be used to parse NLI
sentences, and how well automated theorem provers can reason over the resulting
formulae. To improve performance, we develop a set of syntactic and semantic
transformation rules. We report their performance, and discuss implications for
NLI and logic-based NLP.


  We study the problem of learning a good set of policies, so that when
combined together, they can solve a wide variety of unseen reinforcement
learning tasks with no or very little new data. Specifically, we consider the
framework of generalized policy evaluation and improvement, in which the
rewards for all tasks of interest are assumed to be expressible as a linear
combination of a fixed set of features. We show theoretically that, under
certain assumptions, having access to a specific set of diverse policies, which
we call a set of independent policies, can allow for instantaneously achieving
high-level performance on all possible downstream tasks which are typically
more complex than the ones on which the agent was trained. Based on this
theoretical analysis, we propose a simple algorithm that iteratively constructs
this set of policies. In addition to empirically validating our theoretical
results, we compare our approach with recently proposed diverse policy set
construction methods and show that, while others fail, our approach is able to
build a behavior basis that enables instantaneous transfer to all possible
downstream tasks. We also show empirically that having access to a set of
independent policies can better bootstrap the learning process on downstream
tasks where the new reward function cannot be described as a linear combination
of the features. Finally, we demonstrate how this policy set can be useful in a
lifelong reinforcement learning setting.


  Intercalation of magnetic atoms into the van der Waals gaps of layered
transition metal dichalcogenides offers an excellent platform to produce exotic
physical properties. Here, we report a detailed study of magnetic and
electrical transport properties of Co$_{0.28}$TaS$_2$. The temperature
dependent resistivity measurements display anomalous upturn below 11 K, which
persists in presence of magnetic field even up to 14 T. In the low temperature
region, the resistivity upturn exhibits a unique $T^{1/2}$ scaling behavior,
which remains unchanged when an external magnetic field is applied. The
$T^{1/2}$ dependence of resistivity upturn is the hallmark of non-Fermi liquid
state in orbital two-channel Kondo effect(2CK). This anomalous resistivity
upturn in Co$_{0.28}$TaS$_2$ can be attributed to the orbital two-channel Kondo
mechanism.


  We describe some instances of the appearance of Chern's mathematical ideas in
physics. By means of simple examples, we bring out the geometric and
topological ideas which have found application in describing the physical
world. These applications range from magnetic monopoles in electrodynamics to
instantons in quantum chromodynamics to the geometric phase of quantum
mechanics. The first part of this article is elementary and addressed to a
general reader. The second part is somewhat more demanding and is addressed to
advanced students of mathematics and physics.


  In the last decade matrix polynomials have been investigated with the primary
focus on adequate linearizations and good scaling techniques for computing
their eigenvalues and eigenvectors. In this article we propose a new method for
computing a factored Schur form of the associated companion pencil. The
algorithm has a quadratic cost in the degree of the polynomial and a cubic one
in the size of the coefficient matrices. Also the eigenvectors can be computed
at the same cost.
  The algorithm is a variant of Francis's implicitly shifted QR algorithm
applied on the companion pencil. A preprocessing unitary equivalence is
executed on the matrix polynomial to simultaneously bring the leading matrix
coefficient and the constant matrix term to triangular form before forming the
companion pencil. The resulting structure allows us to stably factor each
matrix of the pencil as a product of $k$ matrices of unitary-plus-rank-one
form, admitting cheap and numerically reliable storage. The problem is then
solved as a product core chasing eigenvalue problem. A backward error analysis
is included, implying normwise backward stability after a proper scaling.
Computing the eigenvectors via reordering the Schur form is discussed as well.
  Numerical experiments illustrate stability and efficiency of the proposed
methods.


  Gaussian processes (GP) for machine learning have been studied systematically
over the past two decades and they are by now widely used in a number of
diverse applications. However, GP kernel design and the associated
hyper-parameter optimization are still hard and to a large extend open
problems. In this paper, we consider the task of GP regression for time series
modeling and analysis. The underlying stationary kernel can be approximated
arbitrarily close by a new proposed grid spectral mixture (GSM) kernel, which
turns out to be a linear combination of low-rank sub-kernels. In the case where
a large number of the sub-kernels are used, either the Nystr\"{o}m or the
random Fourier feature approximations can be adopted to deal efficiently with
the computational demands. The unknown GP hyper-parameters consist of the
non-negative weights of all sub-kernels as well as the noise variance; their
estimation is performed via the maximum-likelihood (ML) estimation framework.
Two efficient numerical optimization methods for solving the unknown
hyper-parameters are derived, including a sequential majorization-minimization
(MM) method and a non-linearly constrained alternating direction of multiplier
method (ADMM). The MM matches perfectly with the proven low-rank property of
the proposed GSM sub-kernels and turns out to be a part of efficiency, stable,
and efficient solver, while the ADMM has the potential to generate better local
minimum in terms of the test MSE. Experimental results, based on various
classic time series data sets, corroborate that the proposed GSM kernel-based
GP regression model outperforms several salient competitors of similar kind in
terms of prediction mean-squared-error and numerical stability.


  We prove a generalization of Tur\'{a}n's theorem proposed by Balogh and
Lidick\'{y}.


  The WISSH quasars project aims at studying the nuclear and host galaxy
properties of the most luminous quasars ($L_{bol}>10^{47}$ erg/s, $1.8<z<4.6$).
Nuclear winds are manifested as UV broad ($\geq$ 2,000 km/s) absorption lines
(BAL) in $\sim$ 15\% of quasars. We aim at studying the incidence and
properties of such winds in the WISSH sample, to investigate possible
differences with respect to lower luminosity AGN regimes. We collected optical
spectra from the SDSS data release 12, and identified those showing absorption
troughs in the region between \siiv and \civ emission lines. We find a higher
observed fraction of \civ BAL quasars in the WISSH sample (24\%) with respect
to previous catalogues (10-15\%). These WISSH BAL quasars are also
characterized by a larger average BI ($\sim$4,000 km/s) and maximum velocity
($\sim$17,000 km/s). Moreover, for two objects we discovered BAL features
bluewards of the \siiv peak, which can be associated to \civ absorption with
velocity of 0.15c. Finally, we updated previous studies on the dependence of
maximum outflow velocity upon bolometric luminosity, showing that BAL winds
have intermediate properties compared to molecular/ionized winds and ultra fast
outflows (UFOs). Finally, the radio properties of the WISSH BAL quasars as a
whole are in line with those of samples at lower luminosities from previous
studies. Our results suggest that the higher $L_{\rm bol}$ of the WISSH quasars
likely favours the acceleration of BAL outflows and that their most likely
driving mechanism is radiation pressure. Furthermore we estimate that the
kinetic power associated to these winds in hyperluminous quasars is sufficient,
for the highest column density and fastest winds, to provide efficient feedback
onto the host galaxy.


  In order to learn quickly with few samples, meta-learning utilizes prior
knowledge learned from previous tasks. However, a critical challenge in
meta-learning is task uncertainty and heterogeneity, which can not be handled
via globally sharing knowledge among tasks. In this paper, based on
gradient-based meta-learning, we propose a hierarchically structured
meta-learning (HSML) algorithm that explicitly tailors the transferable
knowledge to different clusters of tasks. Inspired by the way human beings
organize knowledge, we resort to a hierarchical task clustering structure to
cluster tasks. As a result, the proposed approach not only addresses the
challenge via the knowledge customization to different clusters of tasks, but
also preserves knowledge generalization among a cluster of similar tasks. To
tackle the changing of task relationship, in addition, we extend the
hierarchical structure to a continual learning environment. The experimental
results show that our approach can achieve state-of-the-art performance in both
toy-regression and few-shot image classification problems.


  This paper presents a statistical analysis of the structure of Peer-to-Peer
(P2P) social networks that captures social associations of distributed peers in
resource sharing. Peer social networks appear to be mainly composed of pure
resource providers that guarantee high resource availability and reliability of
P2P systems. The major peers that both provide and request resources are only a
small fraction. The connectivity between peers, including undirected, directed
(out and in) and weighted connections, is scale-free and the social networks of
all peers and major peers are small world networks. The analysis also confirms
that peer social networks show in general disassortative correlations, except
that active providers are connected between each other and by active
requesters. The study presented in this paper gives a better understanding of
peer relationships in resource sharing, which may help a better design of
future P2P networks and open the path to the study of transport processes on
top of real P2P topologies.


  Soft x-ray radiation from the sun is responsible for the production of high
energy photoelectrons in the D and E regions of the ionosphere, where they
deposit most of their ionization energy. The photoelectrons created by this
process are the main drivers for dissociation of Nitrogen molecule ($N_2$)
below 200 km. The dissociation of N2 is one of main mechanisms of the
production of Nitric Oxide (NO), an important minor constituent at these
altitudes. In order to estimate the dissociation rate of N2 we need its
dissociation cross-sections. The dissociation cross-sections for N2 by
photoelectrons are primarily estimated from the cross-sections of its
excitation states using predissociation factors and dissociative ionization
channels. The lack of cross-sections data, particularly at high electron
energies and of higher excited states of $N_2$ and $N_2^+$, introduces
uncertainty in the dissociation rate calculation, which subsequently leads to
uncertainties in the NO production rate from this source. In this work, we have
fitted updated electron impact cross-sections data and by applying
predissociation factors obtained, updated dissociation rates of N2 due to high
energy photoelectrons. The new dissociation rates of N2 are compared to the
dissociation rates obtained from Solomon and Qian [2005]. The new dissociation
cross-sections and rates are estimated to be about 30% lower than the Solomon
and Qian [2005] model. Simulations using a parameterized version of the updated
dissociation rates in the Atmospheric Chemistry and Energetics (ACE1D) model
leads to a $20%$ increase in NO density at the altitudes below 100 km is
observed.


  Recently, a minimal kinetic model for fluid flow, known as entropic lattice
Boltzmann method, has been proposed for the simulation of isothermal
hydrodynamic flows. At variance with previous Lattice Boltzmann methods, the
entropic version permits to describe the non-linear dynamics of short scales in
a controlled and stable way. In this paper, we provide the first numerical
evidence that the entropic lattice Boltzmann scheme provides a quantitatively
correct description of the large-scale structures of two-dimensional
turbulence, free of numerical instabilities. This indicates that the entropic
lattice Boltzmann method might provide a starting basis for the formulation of
a new class of turbulence models based on genuinely kinetic principles.


  In Phys. Rev. Lett. 91, 157404 (2003) Yong Zhang et al. study light
propagation through an interface between two identical but differently oriented
uniaxial crystals. The authors show that the light refraction at the interface
at some region of incident angles is negative. The observed effect of negative
refraction resembles the analogous effect in left-handed materials (LHM)
although the physics is different. In LHM the negative refraction is caused by
a negative group velocity, whereas in the considered case one deals with the
special properties of wave propagation in uniaxial anisotropic media.


  The method of calculating a distributed system imbalance based on the
calculation of node system load was proposed in the work. Calculation of node
system load is carried out by calculating the average coefficient of
utilization of CPU, memory, bandwidth of each system node, taking into account
multifractal properties of input data flows. The simulation of the proposed
method for different multifractal parameters was conducted. The simulation
showed that the characteristics of multifractal traffic have a considerable
effect on the system imbalance. Using the proposed method allows to distribute
requests across the servers so that the deviation of the load servers from the
average value was minimal, which allows to get higher system performance
metrics and faster processing flows.


  In this paper, we introduce the concept of circular Pythagorean fuzzy set
(value) (C-PFS(V)) as a new generalization of both circular intuitionistic
fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs)
proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle
that represents the membership degree and the non-membership degree and whose
center consists of non-negative real numbers $\mu$ and $\nu$ with the condition
$\mu^2+\nu^2\leq 1$. A C-PFS models the fuzziness of the uncertain information
more properly thanks to its structure that allows modelling the information
with points of a circle of a certain center and a radius. Therefore, a C-PFS
lets decision makers to evaluate objects in a larger and more flexible region
and thus more sensitive decisions can be made. After defining the concept of
C-PFS we define some fundamental set operations between C-PFSs and propose some
algebraic operations between C-PFVs via general $t$-norms and $t$-conorms. By
utilizing these algebraic operations, we introduce some weighted aggregation
operators to transform input values represented by C-PFVs to a single output
value. Then to determine the degree of similarity between C-PFVs we define a
cosine similarity measure based on radius. Furthermore, we develop a method to
transform a collection of Pythagorean fuzzy values to a PFS. Finally, a method
is given to solve multi-criteria decision making problems in circular
Pythagorean fuzzy environment and the proposed method is practiced to a problem
about selecting the best photovoltaic cell from the literature. We also study
the comparison analysis and time complexity of the proposed method.


  Soft or Deformable Plate Tectonics in the sphere must follow geometric rules
inferred from the orthographic projection. An analytic equivalent of this
geometry can be derived by the application of Potential Field Methods in the
case of Atlantic type oceans. Laplace equation must be obeyed by the velocity
field between the ridge and the passive margin if we neglect the very slight
compressibility of ocean lithosphere. A strain wave propagates in the sphere
analogous to the behaviour of a free harmonic oscillator. Combining zonal
harmonics of order one and sectorial harmonics of degree one we obtain a
tesseral harmonic equivalent to the orthographic solution. This potential field
approach is valid for homogeneous deformation regime in oceanic lithosphere.
Above a compression threshold of 5 to 10% buckling and simultaneous faulting
occurs. In Pacific type oceans a dynamic approach, similar to a forced
oscillation, must be applied because there are sinks in subduction zones.


  The Feynman-Kac equations are a type of partial differential equations
describing the distribution of functionals of diffusive motion. The probability
density function (PDF) of Brownian functionals satisfies the Feynman-Kac
formula, being a Schr\"{o}dinger equation in imaginary time. The functionals of
no-Brownian motion, or anomalous diffusion, follow the fractional Feynman-Kac
equation [J. Stat. Phys. 141, 1071-1092, 2010], where the fractional
substantial derivative is involved. Based on recently developed discretized
schemes for fractional substantial derivatives [arXiv:1310.3086], this paper
focuses on providing algorithms for numerically solving the forward and
backward fractional Feynman-Kac equations; since the fractional substantial
derivative is non-local time-space coupled operator, new challenges are
introduced comparing with the general fractional derivative. Two ways (finite
difference and finite element) of discretizing the space derivative are
considered. For the backward fractional Feynman-Kac equation, the numerical
stability and convergence of the algorithms with first order accuracy are
theoretically discussed; and the optimal estimates are obtained. For all the
provided schemes, including the first order and high order ones, of both
forward and backward Feynman-Kac equations, extensive numerical experiments are
performed to show their effectiveness.


  We consider the ANTS problem [Feinerman et al.] in which a group of agents
collaboratively search for a target in a two-dimensional plane. Because this
problem is inspired by the behavior of biological species, we argue that in
addition to studying the {\em time complexity} of solutions it is also
important to study the {\em selection complexity}, a measure of how likely a
given algorithmic strategy is to arise in nature due to selective pressures. In
more detail, we propose a new selection complexity metric $\chi$, defined for
algorithm ${\cal A}$ such that $\chi({\cal A}) = b + \log \ell$, where $b$ is
the number of memory bits used by each agent and $\ell$ bounds the fineness of
available probabilities (agents use probabilities of at least $1/2^\ell$). In
this paper, we study the trade-off between the standard performance metric of
speed-up, which measures how the expected time to find the target improves with
$n$, and our new selection metric.
  In particular, consider $n$ agents searching for a treasure located at
(unknown) distance $D$ from the origin (where $n$ is sub-exponential in $D$).
For this problem, we identify $\log \log D$ as a crucial threshold for our
selection complexity metric. We first prove a new upper bound that achieves a
near-optimal speed-up of $(D^2/n +D) \cdot 2^{O(\ell)}$ for $\chi({\cal A})
\leq 3 \log \log D + O(1)$. In particular, for $\ell \in O(1)$, the speed-up is
asymptotically optimal. By comparison, the existing results for this problem
[Feinerman et al.] that achieve similar speed-up require $\chi({\cal A}) =
\Omega(\log D)$. We then show that this threshold is tight by describing a
lower bound showing that if $\chi({\cal A}) < \log \log D - \omega(1)$, then
with high probability the target is not found within $D^{2-o(1)}$ moves per
agent. Hence, there is a sizable gap to the straightforward $\Omega(D^2/n + D)$
lower bound in this setting.


  The magnetooptic Kerr effect (MOKE) is a well known and handy tool to
characterize ferro-, ferri- and antiferromagnetic materials. Many of the MOKE
techniques employ effects solely linear in magnetization $\bm{M}$.
Nevertheless, a higher-order term being proportional to $\bm{M}^2$ and called
quadratic MOKE (QMOKE) can additionally contribute to the experimental data.
Here, we present detailed QMOKE spectroscopy measurements in the range of 0.8
-- 5.5\,eV based on a modified 8-directional method applied on ferromagnetic
bcc Fe thin films grown on MgO substrates. From the measured QMOKE spectra, two
further complex spectra of the QMOKE parameters $G_s$ and $2G_{44}$ are
yielded. The difference between those two parameters, known as $\Delta G$,
denotes the strength of the QMOKE anisotropy. Those QMOKE parameters give rise
to the QMOKE tensor $\bm{G}$, fully describing the perturbation of the
permittivity tensor in the second order in $\bm{M}$ for cubic crystal
structures. We further present experimental measurements of ellipsometry and
linear MOKE spectra, wherefrom permittivity in the zeroth and the first order
in $\bm{M}$ are obtained, respectively. Finally, all those spectra are
described by ab-initio calculations.


  We study classes of ultradifferentiable functions defined in terms of small
weight sequences violating standard growth and regularity requirements. First,
we show that such classes can be viewed as weighted spaces of entire functions
for which the crucial weight is given by the associated weight function of the
so-called conjugate weight sequence. Moreover, we generalize results from M.
Markin from the so-called small Gevrey-setting to arbitrary convenient families
of (small) sequences and show how the corresponding ultradifferentiable
function classes can be used to detect boundedness of normal linear operators
on Hilbert spaces (associated to an evolution equation problem). Finally, we
study the connection between small sequences and the recent notion of dual
sequences introduced in the PhD-thesis of J. Jim\'{e}nez-Garrido.


  Selling a single item to $n$ self-interested buyers is a fundamental problem
in economics, where the two objectives typically considered are welfare
maximization and revenue maximization. Since the optimal mechanisms are often
impractical and do not work for sequential buyers, posted pricing mechanisms,
where fixed prices are set for the item for different buyers, have emerged as a
practical and effective alternative. This paper investigates how many samples
are needed from buyers' value distributions to find near-optimal posted prices,
considering both independent and correlated buyer distributions, and welfare
versus revenue maximization. We obtain matching upper and lower bounds (up to
logarithmic factors) on the sample complexity for all these settings.


  Low-dose computed tomography (LDCT) image reconstruction techniques can
reduce patient radiation exposure while maintaining acceptable imaging quality.
Deep learning is widely used in this problem, but the performance of testing
data (a.k.a. target domain) is often degraded in clinical scenarios due to the
variations that were not encountered in training data (a.k.a. source domain).
Unsupervised domain adaptation (UDA) of LDCT reconstruction has been proposed
to solve this problem through distribution alignment. However, existing UDA
methods fail to explore the usage of uncertainty quantification, which is
crucial for reliable intelligent medical systems in clinical scenarios with
unexpected variations. Moreover, existing direct alignment for different
patients would lead to content mismatch issues. To address these issues, we
propose to leverage a probabilistic reconstruction framework to conduct a joint
discrepancy minimization between source and target domains in both the latent
and image spaces. In the latent space, we devise a Bayesian uncertainty
alignment to reduce the epistemic gap between the two domains. This approach
reduces the uncertainty level of target domain data, making it more likely to
render well-reconstructed results on target domains. In the image space, we
propose a sharpness-aware distribution alignment to achieve a match of
second-order information, which can ensure that the reconstructed images from
the target domain have similar sharpness to normal-dose CT images from the
source domain. Experimental results on two simulated datasets and one clinical
low-dose imaging dataset show that our proposed method outperforms other
methods in quantitative and visualized performance.


  We consider the application of Abelian orbifold constructions in Meromorphic
Conformal Field Theory (MCFT) towards an understanding of various aspects of
Monstrous Moonshine and Generalised Moonshine. We review some of the basic
concepts in MCFT and Abelian orbifold constructions of MCFTs and summarise some
of the relevant physics lore surrounding such constructions including aspects
of the modular group, the fusion algebra and the notion of a self-dual MCFT.
The FLM Moonshine Module, $V^\natural$, is historically the first example of
such a construction being a $Z_2$ orbifolding of the Leech lattice MCFT,
$V^\Lambda$. We review the usefulness of these ideas in understanding Monstrous
Moonshine, the genus zero property for Thompson series which we have shown is
equivalent to the property that the only meromorphic $Z_n$ orbifoldings of
$V^\natural$ are $V^\Lambda$ and $V^\natural$ itself (assuming that
$V^\natural$ is uniquely determined by its characteristic function $J(\tau)$.
We show that these constraints on the possible $Z_n$ orbifoldings of
$V^\natural$ are also sufficient to demonstrate the genus zero property for
Generalised Moonshine functions in the simplest non-trivial prime cases by
considering $Z_p\times Z_p$ orbifoldings of $V^\natural$. Thus Monstrous
Moonshine implies Generalised Moonshine in these cases.


  Environmental statistics provide a necessary means of comparing the
properties of galaxies in different environments and a vital test of models of
galaxy formation within the prevailing, hierarchical cosmological model. We
explore counts-in-cylinders, a common statistic defined as the number of
companions of a particular galaxy found within a given projected radius and
redshift interval. Galaxy distributions with the same two-point correlation
functions do not necessarily have the same companion count distributions. We
use this statistic to examine the environments of galaxies in the Sloan Digital
Sky Survey, Data Release 4. We also make preliminary comparisons to four models
for the spatial distributions of galaxies, based on N-body simulations, and
data from SDSS DR4 to study the utility of the counts-in-cylinders statistic.
There is a very large scatter between the number of companions a galaxy has and
the mass of its parent dark matter halo and the halo occupation, limiting the
utility of this statistic for certain kinds of environmental studies. We also
show that prevalent, empirical models of galaxy clustering that match observed
two- and three-point clustering statistics well fail to reproduce some aspects
of the observed distribution of counts-in-cylinders on 1, 3 and 6-Mpc/h scales.
All models that we explore underpredict the fraction of galaxies with few or no
companions in 3 and 6-Mpc/h cylinders. Roughly 7% of galaxies in the real
universe are significantly more isolated within a 6 Mpc/h cylinder than the
galaxies in any of the models we use. Simple, phenomenological models that map
galaxies to dark matter halos fail to reproduce high-order clustering
statistics in low-density environments.


  Given an $r$-uniform hypergraph $H$, the multicolor Ramsey number $r_k(H)$ is
the minimum $n$ such that every $k$-coloring of the edges of the complete
$r$-uniform hypergraph $K_n^r$ yields a monochromatic copy of $H$. We
investigate $r_k(H)$ when $k$ grows and $H$ is fixed. For nontrivial 3-uniform
hypergraphs $H$, the function $r_k(H)$ ranges from $\sqrt{6k}(1+o(1))$ to
double exponential in $k$.
  We observe that $r_k(H)$ is polynomial in $k$ when $H$ is $r$-partite and at
least single-exponential in $k$ otherwise. Erd\H{o}s, Hajnal and Rado gave
bounds for large cliques $K_s^r$ with $s\ge s_0(r)$, showing its correct
exponential tower growth. We give a proof for cliques of all sizes, $s>r$,
using a slight modification of the celebrated stepping-up lemma of Erd\H{o}s
and Hajnal.
  For 3-uniform hypergraphs, we give an infinite family with
sub-double-exponential upper bound and show connections between graph and
hypergraph Ramsey numbers. Specifically, we prove that $$r_k(K_3)\le
r_{4k}(K_4^3-e)\le r_{4k}(K_3)+1,$$ where $K_4^3-e$ is obtained from $K_4^3$ by
deleting an edge.
  We provide some other bounds, including single-exponential bounds for
$F_5=\{abe,abd,cde\}$ as well as asymptotic or exact values of $r_k(H)$ when
$H$ is the bow $\{abc,ade\}$, kite $\{abc,abd\}$, tight path $\{abc,bcd,cde\}$
or the windmill $\{abc,bde,cef,bce\}$. We also determine many new "small"
Ramsey numbers and show their relations to designs. For example, the lower
bound for $r_6(kite)=8$ is demonstrated by decomposing the triples of $[7]$
into six partial STS (two of them are Fano planes).


  In this paper we investigate the Sunyaev-Zel'dovich (SZ) effect and the X-ray
surface brightness for clusters of galaxies with a non-spherical mass
distribution. In particular, we consider the influence of the shape and the
finite extension of a cluster as well as of a polytropic thermal profile on the
Compton parameter, the X-ray surface brightness and on the determination of the
Hubble constant. We find that the the non-inclusion of such effects can induce
errors up to 30 per cent in the various parameters and in particular on the
Hubble constant value, when compared with results obtained under the
isothermal, infinitely extended and spherical shape assumptions.


  We study ZZ instanton corrections in the $(2,4k)$ $N=1$ minimal superstring
theory with the type 0B GSO projection, which becomes the type 0B $N=1$
super-JT gravity in the $k \to \infty$ limit. Each member of the $(2,4k)$
family of theories has two phases distinguished by the sign of the Liouville
bulk cosmological constant. The worldsheet method for computing the one-loop
normalization constant multiplying the instanton corrections gives an
ill-defined answer in both phases. We fix these divergences using insights from
string field theory and find finite, unambiguous results. Each member of the
$(2,4k)$ family of theories is dual to a double-scaled one-matrix integral,
where the double-scaling limit can be obtained starting either from a unitary
matrix integral with a leading one-cut saddle point, or from a hermitian matrix
integral with a leading two-cut saddle point. The matrix integral exhibits a
gap-closing transition, which is the same as the double-scaled
Gross-Witten-Wadia transition when $k=1$. We also compute instanton corrections
in the double-scaled matrix integral for all $k$ and in both phases, and find
perfect agreement with the string theory results.


  In this paper, we give a combinatorial rule to calculate the decomposition of
the tensor product (Kronecker product) of two irreducible complex
representations of the symmetric group ${\mathfrak S}_n$, when one of the
representations corresponds to a hook $(n-m, 1^m)$.


  Chiral effective field theory ($\chi$EFT) is a powerful tool for studying
electroweak processes in nuclei. I discuss $\chi$EFT calculations of three key
nuclear electroweak processes: primordial deuterium production, proton-proton
fusion, and magnetic dipole excitations of $^{48}\mathrm{Ca}$. This article
showcases $\chi$EFT's ability to quantify theory uncertainties at the
appropriate level of rigor for addressing the different precision demands of
these three processes.


  We describe detailed simulations of X-ray-emitting populations to evaluate
the levels of contamination by both Galactic and extragalactic X-ray sources
unrelated to a star-forming region under study. For Galactic contaminations, we
consider contribution from main-sequence stars and giants (not including
cataclysmic variables and other classes of accretion-driven X-ray binary
systems) as they make the dominant contribution at the position of the Carina
Nebula. The simulations take into consideration a variety of technical factors
involving a Galactic population synthesis model, stellar X-ray luminosity
functions, Chandra telescope response, source detection methodology, and
possible spatial variations in the X-ray background and absorption through
molecular clouds. When applied to the 1.42 square-degree field of the Chandra
Carina Complex Project (CCCP), the simulations predict ~5000 contaminating
sources (1 source per square arcminute of the survey), evenly distributed
across the field. The results of the simulations are further employed in a
companion CCCP study to assign membership probabilities to individual sources.


  We study an attractive version of the East model using the real-space
renormalization group (RG) introduced by Stella et al. The former is a
kinetically constrained model with an Ising-like interaction between
excitations, and shows striking agreement with the phenomonology of attractive
colloidal systems. We find that the RG predicts two nonuniversal dynamic
exponents, which suggests that in the out-of-equilibrium regime the model
coarsens via a two-stage mechanism. We explain this mechanism physically, and
verify this prediction numerically. In addition, we find that the
characteristic relaxation time of the model is a non-monotonic function of
attraction strength, again in agreement with numerical results.


  Tip-driven growth processes underlie the development of many plants. To date,
tip-driven growth processes have been modelled as an elongating path or series
of segments without taking into account lateral expansion during elongation.
Instead, models of growth often introduce an explicit thickness by expanding
the area around the completed elongated path. Modelling expansion in this way
can lead to contradictions in the physical plausibility of the resulting
surface and to uncertainty about how the object reached certain regions of
space. Here, we introduce "fiber walks" as a self-avoiding random walk model
for tip-driven growth processes that includes lateral expansion. In 2D, the
fiber walk takes place on a square lattice and the space occupied by the fiber
is modelled as a lateral contraction of the lattice. This contraction
influences the possible follow-up steps of the fiber walk. The boundary of the
area consumed by the contraction is derived as the dual of the lattice faces
adjacent to the fiber. We show that fiber walks generate fibers that have
well-defined curvatures, enable the identification of the process underlying
the occupancy of physical space. Hence, fiber walks provide a base from which
to model both the extension and expansion of physical biological objects with
finite thickness.


  In this article we extend evaluations of the Kauffman bracket on regular
isotopy classes of knots and links to a variety of functors defined on the
category of framed tangles. We show that many such functors exist, and that
they correspond up to equivalence to bilinear forms on free, finitely-generated
modules over commutative rings.


  The gold-assisted exfoliation is a very effective method to produce
large-area ($cm^2$-scale) membranes of molybdenum disulfide ($MoS_2$) for
electronics. However, the strong $MoS_2/Au$ interaction, beneficial for the
exfoliation process, has a strong impact on the vibrational and light emission
properties of $MoS_2$. Here, we report an atomic force microscopy (AFM),
micro-Raman ($\mu-R$) and micro-Photoluminescence ($\mu-PL$) investigation of
$MoS_2$ with variable thickness exfoliated on Au and subsequently transferred
on an $Al_2O_3/Si$ substrate. The $E_{2g}$ - $A_{1g}$ vibrational modes
separation $\Delta\mu$ (typically used to estimate $MoS_2$ thickness) exhibits
an anomalous large value ($\Delta\mu=21.2 cm^{-1}$) for monolayer (1L) $MoS_2$
on Au as compared to the typical one ($\Delta\mu=18.5 cm^{-1}$) measured on 1L
$MoS_2$ on $Al_2O_3/Si$. Such substrate-related differences, explained in terms
of tensile strain and p-type doping arising from the $MoS_2/Au$ interaction,
were found to gradually decrease while increasing the number of $MoS_2$ layers.
Furthermore, $\mu-PL$ spectra for 1L $MoS_2$ on Au exhibit a strong quenching
and an overall red-shift of the main emission peak at 1.79 eV, compared to the
1.84 eV peak for 1L $MoS_2$ on $Al_2O_3$. After PL spectra deconvolution, such
red shift was explained in terms of a higher trion/exciton intensity ratio,
probably due to the higher polarizability of the metal substrate, as well as to
the smaller equilibrium distance at $MoS_2/Au$ interface.


  The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues
of the reduced density matrix, contains more information than the conventional
entanglement entropy and has been studied recently in several many-particle
systems. We compute the disorder-averaged entanglement spectrum, in the form of
the disorder-averaged moments of the reduced density matrix, for a contiguous
block of many spins at the random-singlet quantum critical point in one
dimension. The result compares well in the scaling limit with numerical studies
on the random XX model and is also expected to describe the (interacting)
random Heisenberg model. Our numerical studies on the XX case reveal that the
dependence of the entanglement entropy and spectrum on the geometry of the
Hilbert space partition is quite different than for conformally invariant
critical points.


  Bayesian networks provide an elegant formalism for representing and reasoning
about uncertainty using probability theory. Theyare a probabilistic extension
of propositional logic and, hence, inherit some of the limitations of
propositional logic, such as the difficulties to represent objects and
relations. We introduce a generalization of Bayesian networks, called Bayesian
logic programs, to overcome these limitations. In order to represent objects
and relations it combines Bayesian networks with definite clause logic by
establishing a one-to-one mapping between ground atoms and random variables. We
show that Bayesian logic programs combine the advantages of both definite
clause logic and Bayesian networks. This includes the separation of
quantitative and qualitative aspects of the model. Furthermore, Bayesian logic
programs generalize both Bayesian networks as well as logic programs. So, many
ideas developed


  We introduce s.n where n is the unit vector in the direction of the radius
vector and s is the spin, which along with the velocity forms a spin-orbit
interaction of the order of v/c whereas the usual spin-orbit interaction is of
the order of the square of v/c. The effective fractional charges obtained from
this interaction are in good agreement with the experimental data of the
quantum Hall effect. The energy of the system diverges as L tends to infinity
indicating that there is a phase transformation at the half-filled Landau
level.


  We have constructed a quantum field theory in a finite box, with periodic
boundary conditions, using the hypothesis that particles living in a finite box
are created and/or annihilated by the creation and/or annihilation operators,
respectively, of a quantum harmonic oscillator on a circle. An expression for
the effective coupling constant is obtained showing explicitly its dependence
on the dimension of the box.


  Electronic excitations in atomic, molecular, and crystal targets are at the
forefront of the ongoing search for light, sub-GeV dark matter (DM). In many
light DM-electron interactions the energy and momentum deposited is much
smaller than the electron mass, motivating a non-relativistic (NR) description
of the electron. Thus, for any target, light DM-electron phenomenology relies
on understanding the interactions between the DM and electron in the NR limit.
In this work we derive the NR effective field theory (EFT) of general
DM-electron interactions from a top-down perspective, starting from general
high-energy DM-electron interaction Lagrangians. This provides an explicit
connection between high-energy theories and their low-energy phenomenology in
electron excitation based experiments. Furthermore, we derive Feynman rules for
the DM-electron NR EFT, allowing observables to be computed diagrammatically,
which can systematically explain the presence of in-medium screening effects in
general DM models. We use these Feynman rules to compute absorption,
scattering, and dark Thomson scattering rates for a wide variety of high-energy
DM models.


  We analyze theoretical constraints on the consistency of brane inflation
leading to cosmic superstring formation and on the subsequent radiation of
these cosmic superstrings. We first investigate the implications of recently
elucidated supergravity constraints on models of brane inflation. We show that
both D3/D7 and D3/anti-D3 brane inflation are subject to non-trivial
constraints. Both models can be shown to satisfy those constraints, but for the
case of D3/D7 there may be important consequences for the inflationary
mechanism. We then analyze the strong theoretical constraints on the types of
allowed radiation by cosmic superstrings, should they be formed; such
constraints do not apply to their field theoretical analogues. We argue that in
a warped background where one might expect axionic radiation to be enhanced
relative to gravitational radiation, neithe F-strings nor D-strings can emit
axionic radiation, while FD-strings cannot give rise to
Neveu-Schwarz--Neveu-Schwarz particle emission, and their Ramond-Ramond
particle emission is not well-defined.


  Hydrogen is an efficient energy carrier that can be produced from renewable
sources, enabling the transition towards CO2-free energy. Hydrogen can be
stored for a long period in the solid-state, with suitable alloys. Ti-rich
TiFe0.90 compound exhibits a mild activation process for the first
hydrogenation, and Ti(Fe,Mn)0.90 substituted alloys can lead to the fine tuning
of equilibrium pressure as a function of the final application. In this study,
the crystal structure of TiFe(0.90-x)Mnx alloys (x = 0, 0.05 and 0.10) and
their deuterides has been determined by in-situ neutron diffraction, while
recording Pressure-Composition Isotherms at room temperature. The investigation
aims at analysing the influence of Mn for Fe substitution in Ti-rich
Ti(Fe,Mn)0.90 alloys on structural properties during reversible deuterium
loading, which is still unsolved and seldom explored. After activation, samples
have been transferred into custom-made stainless-steel and aluminium alloy
cells used for in-situ neutron diffraction experiments during deuterium loading
at ILL and ISIS neutron facilities, respectively. The study enables remarkable
understanding on hydrogen storage, basic structural knowledge, and support to
the industrial application of TiFe-type alloys for integrated hydrogen tank in
energy storage systems by determining the volume expansion during deuteration.
Furthermore, the study demonstrates that different contents of Mn do not
significantly change the volumetric expansion during phase transitions,
affecting only the deuterium content for the {\gamma} phase and the cell
evolution for the \b{eta} phase. The study confirms that the deuterated
structures of the {\gamma} phase upon absorption, \b{eta} and {\alpha} phase
upon desorption, correspond to S.G. Cmmm, P2221 and Pm-3m, respectively.


  Designing and implementing efficient, provably correct parallel neural
network processing is challenging. Existing high-level parallel abstractions
like MapReduce are insufficiently expressive while low-level tools like MPI and
Pthreads leave ML experts repeatedly solving the same design challenges.
However, the diversity and large-scale data size have posed a significant
challenge to construct a flexible and high-performance implementation of deep
learning neural networks. To improve the performance and maintain the
scalability, we present CNNLab, a novel deep learning framework using GPU and
FPGA-based accelerators. CNNLab provides a uniform programming model to users
so that the hardware implementation and the scheduling are invisible to the
programmers. At runtime, CNNLab leverages the trade-offs between GPU and FPGA
before offloading the tasks to the accelerators. Experimental results on the
state-of-the-art Nvidia K40 GPU and Altera DE5 FPGA board demonstrate that the
CNNLab can provide a universal framework with efficient support for diverse
applications without increasing the burden of the programmers. Moreover, we
analyze the detailed quantitative performance, throughput, power, energy, and
performance density for both approaches. Experimental results leverage the
trade-offs between GPU and FPGA and provide useful practical experiences for
the deep learning research community.


  The selection of best variables is a challenging problem in supervised and
unsupervised learning, especially in high dimensional contexts where the number
of variables is usually much larger than the number of observations. In this
paper, we focus on two multivariate statistical methods: principal components
analysis and partial least squares. Both approaches are popular linear
dimension-reduction methods with numerous applications in several fields
including in genomics, biology, environmental science, and engineering. In
particular, these approaches build principal components, new variables that are
combinations of all the original variables. A main drawback of principal
components is the difficulty to interpret them when the number of variables is
large. To define principal components from the most relevant variables, we
propose to cast the best subset solution path method into principal component
analysis and partial least square frameworks. We offer a new alternative by
exploiting a continuous optimization algorithm for best subset solution path.
Empirical studies show the efficacy of our approach for providing the best
subset solution path. The usage of our algorithm is further exposed through the
analysis of two real datasets. The first dataset is analyzed using the
principle component analysis while the analysis of the second dataset is based
on partial least square framework.


  Current-induced spin-orbit torques (SOTs) are of interest for fast and
energy-efficient manipulation of magnetic order in spintronic devices. To be
deterministic, however, switching of perpendicularly magnetized materials by
SOT requires a mechanism for in-plane symmetry breaking. Existing methods to do
so involve the application of an in-plane bias magnetic field, or incorporation
of in-plane structural asymmetry in the device, both of which can be difficult
to implement in practical applications. Here, we reported bias-field-free SOT
switching in a single perpendicular CoTb layer with an engineered vertical
composition gradient. The vertical structural inversion asymmetry induces
strong intrinsic SOTs and a gradient-driven Dzyaloshinskii-Moriya interaction
(g-DMI), which breaks the in-plane symmetry during the switching process.
Micromagnetic simulations are in agreement with experimental results, and
elucidate the role of g-DMI in the deterministic switching. This
bias-field-free switching scheme for perpendicular ferrimagnets with g-DMI
provides a strategy for efficient and compact SOT device design.


  Image deconvolution is still to be a challenging ill-posed problem for
recovering a clear image from a given blurry image, when the point spread
function is known. Although competitive deconvolution methods are numerically
impressive and approach theoretical limits, they are becoming more complex,
making analysis, and implementation difficult. Furthermore, accurate estimation
of the regularization parameter is not easy for successfully solving image
deconvolution problems. In this paper, we develop an effective approach for
image restoration based on one explicit image filter - guided filter. By
applying the decouple of denoising and deblurring techniques to the
deconvolution model, we reduce the optimization complexity and achieve a simple
but effective algorithm to automatically compute the parameter in each
iteration, which is based on Morozov's discrepancy principle. Experimental
results demonstrate that the proposed algorithm outperforms many
state-of-the-art deconvolution methods in terms of both ISNR and visual
quality.


  The crystal plasticity finite element method (CPFEM) is used to investigate
the coupling between the cylindrical void growth or collapse and grain
refinement in face-centered cubic (FCC) single crystals. A 2D plane strain
model with one void is used. The effect of the initial lattice orientation,
similarities, and differences between stress- and strain-driven loading
scenarios are explored. To this end, boundary conditions are enforced in two
different ways. The first one is based on maintaining constant in-plane stress
biaxiality via a dedicated truss element, while the second one is imposing a
constant displacement biaxiality factor. Uniaxial and biaxial loading cases are
studied. For the uniaxial loading case a special configuration, which enforces
an equivalent pattern of plastic deformation in the pristine crystal, is
selected in order to investigate the mutual interactions between the evolving
void and the developed lattice rotation heterogeneity. Next, biaxial loading
cases are considered for three crystal orientations, one of which is not
symmetric with respect to loading directions. It is analysed how stress or
strain biaxility factors and initial lattice orientation influence the void
evolution in terms of its size and shape. Moreover, the consequences of
variations in the resulting heterogeneity of lattice rotation are studied in
the context of the grain refinement phenomenon accompanying the void evolution.
Scenarios that may lead to more advanced grain fragmentation are identified.


  The tree-level S-matrix of type II supergravity can be computed in scattering
equation form by correlators in a worldsheet theory analogous to a chiral,
infinite tension limit of the pure spinor formalism. By defining a non-minimal
version of this theory, we give a prescription for computing correlators on
higher genus worldsheets which manifest space-time supersymmetry. These
correlators are conjectured to provide the loop integrands of supergravity
scattering amplitudes, supported on the scattering equations. We give
non-trivial evidence in support of this conjecture at genus one and two with
four external states. Throughout, we find a close correspondence with the pure
spinor formalism of superstring theory, particularly regarding regulators and
zero-mode counting.


  A knowledge graph is an essential and trending technology with great
applications in entity recognition, search, or question answering. There are a
plethora of methods in natural language processing for performing the task of
Named entity recognition; however, there are very few methods that could
provide triples for a domain-specific text. In this paper, an effort has been
made towards developing a system that could convert the text from a given
textbook into triples that can be used to visualize as a knowledge graph and
use for further applications. The initial assessment and evaluation gave
promising results with an F1 score of 82%.


  Our approach views the thermodynamics and kinetics in general relativity and
extended gravitational theories (with generic local anisotropy) from the
perspective of the theory of stochastic differential equations on curved
spaces.
  Nonequilibrium and irreversible processes in black hole thermodynamics are
considered. The paper summarizes the author's contribution to Journees
Relativistes 99 (12--17 September 1999), Weimar, Germany.


  Subradiant excited states in finite chains of two-level quantum emitters
coupled to a one-dimensional reservoir are a resource for superior photon
storage and controlled photon manipulation. Typically, states storing multiple
excitations exhibit fermionic correlations and are thus characterized by an
anti-symmetric wavefunction, which makes them hard to prepare experimentally.
Here we identify a class of quasi-localized dark states with up to half of the
qubits excited, which appear for lattice constants that are an integer multiple
of the guided-mode wavelength. They allow for a high-fidelity preparation and
minimally invasive read out in state-of-the-art setups. In particular, we
suggest an experimental implementation using a coplanar wave-guide coupled to
superconducting transmon qubits on a chip. As free space and intrinsic losses
are minimal, virtually perfect dark states can be achieved even for a low
number of qubits, enabling fast preparation and manipulation with high
fidelity.


  The X-ray Integral Field Unit (X-IFU) is the high resolution X-ray
spectrometer of ESA's Athena X-ray observatory. It will deliver X-ray data in
the 0.2-12 keV band with an unprecedented spectral resolution of 2.5 eV up to 7
keV. During the observation of very bright X-ray sources, the X-IFU detectors
will receive high photon rates. The count rate capability of the X-IFU will be
improved by using the defocusing option, which will enable the observations of
extremely bright sources with fluxes up to $\simeq 1$ Crab. In the defocused
mode, the point spread function (PSF) of the telescope will be spread over a
large number of pixels. In this case, each pixel receives a small fraction of
the overall flux. Due to the energy dependence of the PSF, this mode will
generate energy dependent artefacts increasing with count rate if not analysed
properly. To account for the degradation of the energy resolution with pulse
separation in a pixel, a grading scheme (here four grades) will be defined to
affect the proper energy response to each event. This will create selection
effects preventing the use of the nominal Auxiliary Response File (ARF) for all
events. We present a new method for the reconstruction of the spectra obtained
from observations performed with a PSF that varies as a function of energy. We
apply our method to the case of the X-IFU spectra obtained during the defocused
observations. We use the end-to-end SIXTE simulator to model defocused X-IFU
observations. Then we estimate new ARF for each of the grades by calculating
the effective area at the level of each pixel. Our method allows us to
successfully reconstruct the spectra of bright sources when employed in the
defocused mode, without any bias. Finally, we address how various sources of
uncertainty related to our knowledge of the PSF as a function of energy affect
our results.


  Power spectral density measurements of any sampled signal are typically
restricted by both acquisition rate and frequency response limitations of
instruments, which can be particularly prohibitive for video-based
measurements. We have developed a new method called Intensity Modulation
Spectral Analysis (IMSA) that circumvents these limitations, dramatically
extending the effective detection bandwidth. We demonstrate this by
video-tracking an optically-trapped microsphere while oscillating an LED
illumination source. This approach allows us to quantify fluctuations of the
microsphere at frequencies over 10 times higher than the Nyquist frequency,
mimicking a significantly higher frame rate.


  This paper introduces Okapi, a new hardware/software cross-layer architecture
designed to mitigate Transient Execution Side Channel (TES) attacks in modern
computing systems. Okapi enforces sandboxing for speculative execution,
providing a hardware basis that can replace expensive speculation barriers in
software.
  At its core, Okapi allows for speculative data accesses to a memory page only
after the page has been accessed non-speculatively at least once by the current
trust domain. The granularity of the trust domains can be controlled in
software to achieve different security and performance trade-offs. For
environments with less stringent security needs, Okapi's features can be
deactivated to remove all performance overhead.
  Without relying on any software modification, the Okapi hardware features
already provide full protection against TES breakout attacks at a thread-level
granularity. This incurs an average performance overhead of only 3.17% for the
SPEC CPU2017 benchmark suite.
  Okapi introduces the OkapiReset instruction for additional software-level
security support. This instruction allows for fine-grained sandboxing with
custom program sizes smaller than a thread, resulting in 1.68% performance
overhead in our WebAssembly runtime experiment.
  On top, Okapi provides the possibility to eliminate poisoning attacks. For
the highest level of security, the OkapiLoad instruction prevents confidential
data from being added to the trust domain after a sequential access, thereby
enforcing weak speculative non-interference. In addition, we present a hardware
extension that limits the exploitable code space for Spectre gadgets to
well-defined sections of the program. By ensuring the absence of gadgets in
these sections, developers can tailor their software towards achieving
beneficial trade-offs between the size of a trust domain and performance.


  We study a multicomponent $CP^N$ model's scalar electrodynamics. The model
contains Q-balls/shells, which are non-topological compact solitons with time
dependency $e^{i\omega t}$. Two coupled $CP^N$ models can decouple locally if
one of their $CP^N$ fields takes the vacuum value. Because of the compacton
nature of solutions, Q-shells can shelter another compact Q-ball or Q-shell
within their hollow region. Even if compactons do not overlap, they can
interact through the electromagnetic field. We investigate how the size of
multi-compacton formations is affected by electric charge. We are interested in
structures with non-zero or zero total net charge.


  Specific heat data for the quasi one dimensional quantum magnet Copper
Benzoate (Cu(C_6D_5COO)_2 \cdot 3D_2O) is analyzed in the framework of an
effective low-energy description in terms of a Sine-Gordon theory.


  Traditional approaches to automatic emotion recognition are relying on the
application of handcrafted features. More recently however the advent of deep
learning enabled algorithms to learn meaningful representations of input data
automatically. In this paper, we investigate the applicability of transferring
knowledge learned from large text and audio corpora to the task of automatic
emotion recognition. To evaluate the practicability of our approach, we are
taking part in this year's Interspeech ComParE Elderly Emotion Sub-Challenge,
where the goal is to classify spoken narratives of elderly people with respect
to the emotion of the speaker. Our results show that the learned feature
representations can be effectively applied for classifying emotions from spoken
language. We found the performance of the features extracted from the audio
signal to be not as consistent as those that have been extracted from the
transcripts. While the acoustic features achieved best in class results on the
development set, when compared to the baseline systems, their performance
dropped considerably on the test set of the challenge. The features extracted
from the text form, however, are showing promising results on both sets and are
outperforming the official baseline by 5.7 percentage points unweighted average
recall.


  The paper deals with jump generators with a convolution kernel. Assuming that
the kernel decays either exponentially or polynomially we prove a number of
lower and upper bounds for the resolvent of such operators. We consider two
applications of these results. First we obtain pointwise estimates for
principal eigenfunction of jump generators perturbed by a compactly supported
potential (so-called nonlocal Schr\"odinger operators). Then we consider the
Cauchy problem for the corresponding inhomogeneous evolution equations and
study the behaviour of its solutions.


  We derive a full set of exact, analytic expressions for the annihilation of
the lightest neutralino pairs into all two-body tree-level final states in the
framework of minimal supersymmetry. We make no simplifying assumptions about
the neutralino nor about sfermion masses and mixings other than the absence of
explicit CP--violating terms. The expressions should be particularly useful in
computing the neutralino WIMP relic abundance without the usual approximation
of partial wave expansion.


  We obtain best possible upper and lower bounds for the Lodge-Ramanujan and
DeTemple-Wang approximations to the nth Harmonic Number


  The gamma-ray pulsar PSR B1706-44 and the adjacent supernova remnant (SNR)
candidate G343.1-2.3 were observed by H.E.S.S. during a dedicated observation
campaign in 2007. As a result of this observation campaign, a new source of
very-high-energy (VHE; E > 100 GeV) gamma-ray emission, HESS J1708-443, was
detected with a statistical significance of 7 sigma, although no significant
point-like emission was detected at the position of the energetic pulsar
itself. In this paper, the morphological and spectral analyses of the
newly-discovered TeV source are presented. The centroid of HESS J1708-443 is
considerably offset from the pulsar and located near the apparent center of the
SNR, at RA(J2000) = 17h08m11s +/- 17s and Dec(J2000) = -44d20' +/- 4'. The
source is found to be significantly more extended than the H.E.S.S. point
spread function (~0.1 deg), with an intrinsic Gaussian width of 0.29 deg +/-
0.04 deg. Its integral flux between 1 and 10 TeV is ~ 3.8 x 10^-12 ph cm^-2
s^-1, equivalent to 17% of the Crab Nebula flux in the same energy range. The
measured energy spectrum is well-fit by a power law with a relatively hard
photon index Gamma = 2.0 +/- 0.1 (stat) +/- 0.2 (sys). Additional
multi-wavelength data, including 330 MHz VLA observations, were used to
investigate the VHE gamma-ray source's possible associations with the pulsar
wind nebula of PSR B1706-44 and/or with the complex radio structure of the
partial shell-type SNR G343.1-2.3.


  Quark contributions to the proton spin as deduced from polarized DIS of
leptons off a nucleon target, and the octet baryon magnetic moments, can be
used to deduce the antiquark polarizations $\Delta_{\overline{q}}$ inside the
proton. In this way, the 1992 analysis by Karl is shown to imply
$\Delta_{\overline{q}}\simeq 0.$ Such a spin structure fits nicely into the
chiral quark interpretation of the proton spin and flavor puzzles.


  A possibility of a quark spin polarization originated from a pseudovector
condensate is investigated in the three-flavor Nambu-Jona-Lasinio model with
the Kobayashi-Maskawa-'t Hooft interaction which leads to flavor mixing. It is
shown that a pseudovector condensate related to the strange quark easily occurs
compared with pseudovector condensate related to light quarks. Further, it is
shown that the pseudovector condensate related to the strange quark appears at
a slightly small chemical potential by the effect of the flavor mixing due to
the Kobayashi-Maskawa-'t Hooft interaction.


  We prove that a finite torsion-free conformal Lie algebra with a splitting
solvable radical has a finite faithful conformal representation.


  Quasars are complex sources, characterized by broad band spectra from radio
through optical to X-ray band, with numerous emission and absorption features.
However, Boroson & Green (1992) used Principal Component Analysis (PCA), and
with this analysis they were able to show significant correlations between the
measured parameters. The leading component, related to Eigenvector 1 (EV1) was
dominated by the anticorrelation between the Fe${\mathrm{II}}$ optical emission
and [OIII] line and EV1 alone contained 30% of the total variance. It opened a
way in defining a quasar main sequence, in close analogy to the stellar main
sequence on the Hertzsprung-Russel (HR) diagram (Sulentic et al. 2001). The
question still remains which of the basic theoretically motivated parameters of
an active nucleus (Eddington ratio, black hole mass, accretion rate, spin, and
viewing angle) is the main driver behind the EV1. Here we limit ourselves to
the optical waveband, and concentrate on theoretical modelling the
Fe${\mathrm{II}}$ to H$\mathrm{\beta}$ ratio, and we test the hypothesis that
the physical driver of EV1 is the maximum of the accretion disk temperature,
reflected in the shape of the spectral energy distribution (SED). We performed
computations of the H$\mathrm{\beta}$ and optical Fe${\mathrm{II}}$ for a broad
range of SED peak position using CLOUDY photoionisation code. We assumed that
both H$\mathrm{\beta}$ and Fe${\mathrm{II}}$ emission come from the Broad Line
Region represented as a constant density cloud in a plane-parallel geometry. We
expected that a hotter disk continuum will lead to more efficient production of
Fe${\mathrm{II}}$ but our computations show that the Fe${\mathrm{II}}$ to
H$\mathrm{\beta}$ ratio actually drops with the rise of the disk temperature.
Thus either hypothesis is incorrect, or approximations used in our paper for
the description of the line emissivity is inadequate.


  Educational robots allow experimenting with a variety of principles from
mechanics, electronics, and informatics. Here we propose ClipBot, a low-cost,
do-it-yourself, robot whose skeleton is made of two paper clips. An Arduino
nano microcontroller actuates two servo motors that move the paper clips.
However, such mechanical configuration confers physical impairments to
movement. This creates the need for and allows experimenting with artificial
intelligence methods to overcome hardware limitations. We report our experience
in the usage of this robot during the study week 'fascinating informatics',
organized by the Swiss Foundation Schweizer Jugend Forscht (www.sjf.ch).
Students at the high school level were asked to implement a genetic algorithm
to optimize the movements of the robot until it learned to walk. Such a
methodology allowed the robot to learn the motor actuation scheme yielding
straight movement in the forward direction using less than 20 iterations.


  We investigate dynamically and statistically diffusive motion in a chain of
linearly coupled 2-dimensional symplectic McMillan maps and find evidence of
subdiffusion in weakly and strongly chaotic regimes when all maps of the chain
possess a saddle point at the origin and the central map is initially excited.
In the case of weak coupling, there is either absence of diffusion or
subdiffusion with $q>1$-Gaussian probability distributions, characterizing weak
chaos. However, for large enough coupling and already moderate number of maps,
the system exhibits strongly chaotic ($q\approx 1$) subdiffusive behavior,
reminiscent of the subdiffusive energy spreading observed in a disordered
Klein-Gordon Hamiltonian. Our results provide evidence that coupled symplectic
maps can exhibit physical properties similar to those of disordered Hamiltonian
systems, even though the local dynamics in the two cases is significantly
different.


  The second order method as Newton Step is a suitable technique in Online
Learning to guarantee regret bound. The large data is a challenge in Newton
method to store second order matrices as hessian. In this paper, we have
proposed an modified online Newton step that store first and second order
matrices of dimension m (classes) by d (features). we have used element wise
arithmetic operation to retain matrices size same. The modified second order
matrix size results in faster computations. Also, the mistake rate is at par
with respect to popular methods in literature. The experiments outcome indicate
that proposed method could be helpful to handle large multi class datasets in
common desktop machines using second order method as Newton step.


  We consider a double quantum dot whose energy detuning is controlled by an ac
electric field. We demonstrate an energy configuration for which the ac-induced
current flowing through the double dot directly probes the spin-orbit
anticrossing point for small ac field amplitudes. On the contrary, as the ac
amplitude increases a current antiresonance is formed, and the direct
information about the spin-orbit interaction is lost. This result indicates
that a large ac amplitude is not necessarily advantageous for the spectroscopy
of spin-orbit coupled two-spin states. Moreover, we investigate the ac-induced
current peaks versus the ac amplitude and show a current suppression when the
ac field forms spin blocked states. This effect gives rise to a characteristic
pattern for the current which can be controlled at will by tuning the ac
amplitude. Our results can be explored by performing electronic transport
measurements in the spin blockade regime.


  In many chemical and biological applications, systems of differential
equations containing unknown parameters are used to explain empirical
observations and experimental data. The DEs are typically nonlinear and
difficult to analyze, requiring numerical methods to approximate the solutions.
Compounding this difficulty are the unknown parameters in the DE system, which
must be given specific numerical values in order for simulations to be run.
  Estrogen receptor protein dimerization is used as an example to demonstrate
model construction, reduction, simulation, and parameter estimation.
Mathematical, computational, and statistical methods are applied to empirical
data to deduce kinetic parameter estimates and guide decisions regarding future
experiments and modeling. The process demonstrated serves as a pedagogical
example of quantitative methods being used to extract parameter values from
biochemical data models.


  There exist non-degenerate 3-form $d\omega_I$, $\omega_I(X,Y)=g(IX,Y)$, for
each leftinvariant almost Hermitian structure $(g,I)$, where $g$ is
Killing-Cartan metric on the $M=S^3\times S^3=SU(2)\times SU(2)$. Known
\cite{H1}, that arbitrary non-degenerate 3-form on the 6-dimensional manifold,
with some additional properties defines the almost complex structure. Condition
for $I$ to define almost complex structure $J_I$ by $d\omega_I$ is obtained.
Properties of $J_I$ are researched.


  Quantum graphs with leads to infinity serve as convenient models for studying
various aspects of systems which are usually attributed to chaotic scattering.
They are also studied in several experimental systems and practical
applications. In the present manuscript we investigate the effect of a time
dependent random noise on the transmission of such graphs, and in particular on
the resonances which dominate the scattering observable such as e.g., the
transmission and reflection intensities. We model the noise by a potential
$\alpha \delta (x-(x_0 +\gamma(t)))$ localized at an arbitrary point $x_0$ on
any of the graph bonds, that fluctuates in time as a Brownian particle bounded
in a harmonic potential described by the Ornstein-Uhlenbeck statistics. This
statistics, which binds the Brownian motion within a finite interval, enables
the use of a second order time-dependent perturbation theory, which can be
applied whenever the strength parameter $\alpha$ is sufficiently small. The
theoretical frame-work will be explained in full generality, and will be
explicitly solved for a simple, yet nontrivial example.


  Random Forest's performance can be matched by a single slow-growing tree
(SGT), which uses a learning rate to tame CART's greedy algorithm. SGT exploits
the view that CART is an extreme case of an iterative weighted least square
procedure. Moreover, a unifying view of Boosted Trees (BT) and Random Forests
(RF) is presented. Greedy ML algorithms' outcomes can be improved using either
"slow learning" or diversification. SGT applies the former to estimate a single
deep tree, and Booging (bagging stochastic BT with a high learning rate) uses
the latter with additive shallow trees. The performance of this tree ensemble
quaternity (Booging, BT, SGT, RF) is assessed on simulated and real regression
tasks.


  Supertagging is conventionally regarded as an important task for combinatory
categorial grammar (CCG) parsing, where effective modeling of contextual
information is highly important to this task. However, existing studies have
made limited efforts to leverage contextual features except for applying
powerful encoders (e.g., bi-LSTM). In this paper, we propose attentive graph
convolutional networks to enhance neural CCG supertagging through a novel
solution of leveraging contextual information. Specifically, we build the graph
from chunks (n-grams) extracted from a lexicon and apply attention over the
graph, so that different word pairs from the contexts within and across chunks
are weighted in the model and facilitate the supertagging accordingly. The
experiments performed on the CCGbank demonstrate that our approach outperforms
all previous studies in terms of both supertagging and parsing. Further
analyses illustrate the effectiveness of each component in our approach to
discriminatively learn from word pairs to enhance CCG supertagging.


  We introduce a Bayesian optimization approach to guide the sputter deposition
of molybdenum thin films, aiming to achieve desired residual stress and sheet
resistance while minimizing susceptibility to stochastic fluctuations during
deposition. Thin films are pivotal in numerous technologies, including
semiconductors and optical devices, where their properties are critical.
Sputter deposition parameters, such as deposition power, vacuum chamber
pressure, and working distance, influence physical properties like residual
stress and resistance. Excessive stress and high resistance can impair device
performance, necessitating the selection of optimal process parameters.
Furthermore, these parameters should ensure the consistency and reliability of
thin film properties, assisting in the reproducibility of the devices. However,
exploring the multidimensional design space for process optimization is
expensive. Bayesian optimization is ideal for optimizing inputs/parameters of
general black-box functions without reliance on gradient information. We
utilize Bayesian optimization to optimize deposition power and pressure using a
custom-built objective function incorporating observed stress and resistance
data. Additionally, we integrate prior knowledge of stress variation with
pressure into the objective function to prioritize films least affected by
stochastic variations. Our findings demonstrate that Bayesian optimization
effectively explores the design space and identifies optimal parameter
combinations meeting desired stress and resistance specifications.


  Many data have an underlying dependence on spatial location; it may be
weather on the Earth, a simulation on a mesh, or a registered image. Yet this
feature is rarely taken advantage of, and violates common assumptions made by
many neural network layers, such as translation equivariance. Further, many
works that do incorporate locality fail to capture fine-grained structure. To
address this, we introduce the Spatial Mixture-of-Experts (SMoE) layer, a
sparsely-gated layer that learns spatial structure in the input domain and
routes experts at a fine-grained level to utilize it. We also develop new
techniques to train SMoEs, including a self-supervised routing loss and damping
expert errors. Finally, we show strong results for SMoEs on numerous tasks, and
set new state-of-the-art results for medium-range weather prediction and
post-processing ensemble weather forecasts.


  This work focuses on quantitative representation of transport in systems with
quenched disorder. Explicit mapping of the quenched trap model to continuous
time random walk is presented. Linear temporal transformation: $t\to
t/\Lambda^{1/\alpha}$ for transient process on translationally invariant
lattice, in the sub-diffusive regime, is sufficient for asymptotic mapping.
Exact form of the constant $\Lambda^{1/\alpha}$ is established. Disorder
averaged position probability density function for quenched trap model is
obtained and analytic expressions for the diffusion coefficient and drift are
provided.


  The aim of the paper is to study some dynamic aspects coming from a tangent
form, i.e. a time dependent differential form on a tangent bundle. The action
on curves of a tangent form is natural associated with that of a second order
Lagrangian linear in accelerations, while the converse association is not
unique. An equivalence relation of tangent form, compatible with gauge
equivalent Lagrangians, is considered. We express the Euler-Lagrange equation
of the Lagrangian as a second order Lagrange derivative of a tangent form,
considering controlled and higher order tangent forms. Hamiltonian forms of the
dynamics generated are given, extending some quantization formulas given by
Lukierski, Stichel and Zakrzewski. Using semi-sprays, local solutions of the
E-L equations are given in some special particular cases.


  Phase transition of decay rate from quantum tunneling to thermal activity
regimes is investigated in (3+1)-dimensional field theories with symmetry
breaking term $f\phi$. By applying the two independent criteria for the sharp
first-order transition to the same model, the upper and lower bounds of
critical value of the symmetry breaking parameter are obtained. Unlike two
dimensional case continuum states of the fluctuation operator near sphaleron
solution play an important role to determine the type of transition.


  Understanding, finding, or even deciding on the existence of real solutions
to a system of equations is a very difficult problem with many applications.
While it is hopeless to expect much in general, we know a surprising amount
about these questions for systems which possess additional structure.
Particularly fruitful--both for information on real solutions and for
applicability--are systems whose additional structure comes from geometry. Such
equations from geometry for which we have information about their real
solutions are the subject of these lecture notes, which focuses on bounds, both
upper and lower, as well as situations in which all solutions can be real.


  Non-adiabatic holonomic quantum computation in decoherence-free subspaces
protects quantum information from control imprecisions and decoherence. For the
non-collective decoherence that each qubit has its own bath, we show the
implementations of two non-commutable holonomic single-qubit gates and one
holonomic nontrivial two-qubit gate that compose a universal set of
non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the
decoupling group, with an encoding rate of $\frac{N-2}{N}$. The proposed scheme
is robust against control imprecisions and the non-collective decoherence, and
its non-adiabatic property ensures less operation time. We demonstrate that our
proposed scheme can be realized by utilizing only two-qubit interactions rather
than many-qubit interactions. Our results reduce the complexity of practical
implementation of holonomic quantum computation in experiments. We also discuss
the physical implementation of our scheme in coupled microcavities.


  Under the assumption of infinitely many Siegel zeroes $s$ with
$Re(s)>1-\frac{1}{(\log q)^{R}}$ for a sufficiently large value of $R$, we
prove that there exist infinitely many $m$-tuples of primes that are $\ll
e^{1.9828m}$ apart. This "improves" (in some sense) on the bounds of
Maynard-Tao, Baker-Irving, and Polymath 8b, who found bounds of $e^{3.815m}$
unconditionally and $me^{2m}$ assuming the Elliott-Halberstam conjecture; it
also generalizes a 1983 result of Heath-Brown that states that infinitely many
Siegel zeroes would imply infinitely many twin primes. Under this assumption of
Siegel zeroes, we also improve the upper bounds for the gaps between prime
triples, quadruples, quintuples, and sextuples beyond the bounds found via
Elliott-Halberstam.


  In this review, we provide a concrete overview of the Raychaudhuri equation,
Focusing theorem and Convergence conditions in a plethora of backgrounds and
discuss the consequences. We also present various classical and quantum
approaches suggested in the literature that could potentially mitigate the
initial big-bang singularity and the black-hole singularity.


  M\"uger proved in 2003 that the center of a spherical fusion category C of
non-zero dimension over an algebraically closed field is a modular fusion
category whose dimension is the square of that of C. We generalize this theorem
to a pivotal fusion category C over an arbitrary commutative ring K, without
any condition on the dimension of the category. (In this generalized setting,
modularity is understood as 2-modularity in the sense of Lyubashenko.) Our
proof is based on an explicit description of the Hopf algebra structure of the
coend of the center of C. Moreover we show that the dimension of C is
invertible in K if and only if any object of the center of C is a retract of a
`free' half-braiding. As a consequence, if K is a field, then the center of C
is semisimple (as an abelian category) if and only if the dimension of C is
non-zero. If in addition K is algebraically closed, then this condition implies
that the center is a fusion category, so that we recover M\"uger's result.


  We construct integral forms containing the conformal vector $\omega$ in
certain tensor powers of the Virasoro vertex operator algebra
$L(\frac{1}{2},0)$, and we construct integral forms in certain modules for
these algebras. When a triple of modules for a tensor power of
$L(\frac{1}{2},0)$ have integral forms, we classify which intertwining
operators among these modules respect the integral forms. As an application, we
explore how these results might be used to obtain integral forms in framed
vertex operator algebras.


  Quantum information, computation and communication, will have a great impact
on our world. One important subfield will be quantum networking and the quantum
Internet. The purpose of a quantum Internet is to enable applications that are
fundamentally out of reach for the classical Internet. Quantum networks enable
new capabilities to communication systems. This allows the parties to generate
long distance quantum entanglement, which serves a number of tasks including
the generation of multiparty shared secrets whose security relies only on the
laws of physics, distributed quantum computing, improved sensing, quantum
computing on encrypted data, and secure private-bid auctions. However, quantum
signals are fragile, and, in general, cannot be copied or amplified. In order
to enable widespread use and application development, it is essential to
develop methods that allow quantum protocols to connect to the underlying
hardware implementation transparently and to make fast and reactive decisions
for generating entanglement in the network to mitigate limited qubit lifetimes.
Architectures for large-scale quantum internetworking are in development,
paralleling theoretical and experimental work on physical layers and low-level
error management and connection technologies. This chapter aims to present the
main concepts, challenges, and opportunities for research in quantum
information, quantum computing and quantum networking.


  Efficient and versatile Out-of-Distribution (OOD) detection is essential for
the safe deployment of AI yet remains challenging for existing algorithms.
Inspired by Neural Collapse, we discover that features of in-distribution (ID)
samples cluster closer to the weight vectors compared to features of OOD
samples. In addition, we reveal that ID features tend to expand in space to
structure a simplex Equiangular Tight Framework, which nicely explains the
prevalent observation that ID features reside further from the origin than OOD
features. Taking both insights from Neural Collapse into consideration, we
propose to leverage feature proximity to weight vectors for OOD detection and
further complement this perspective by using feature norms to filter OOD
samples. Extensive experiments on off-the-shelf models demonstrate the
efficiency and effectiveness of our method across diverse classification tasks
and model architectures, enhancing the generalization capability of OOD
detection.


  Static gesture recognition is an effective non-verbal communication channel
between a user and their devices; however many modern methods are sensitive to
the relative pose of the user's hands with respect to the capture device, as
parts of the gesture can become occluded. We present two methodologies for
gesture recognition via synchronized recording from two depth cameras to
alleviate this occlusion problem. One is a more classic approach using
iterative closest point registration to accurately fuse point clouds and a
single PointNet architecture for classification, and the other is a dual
Point-Net architecture for classification without registration. On a manually
collected data-set of 20,100 point clouds we show a 39.2% reduction in
misclassification for the fused point cloud method, and 53.4% for the dual
PointNet, when compared to a standard single camera pipeline.


  We study the problem of domain adaptation for neural abstractive
summarization. We make initial efforts in investigating what information can be
transferred to a new domain. Experimental results on news stories and opinion
articles indicate that neural summarization model benefits from pre-training
based on extractive summaries. We also find that the combination of in-domain
and out-of-domain setup yields better summaries when in-domain data is
insufficient. Further analysis shows that, the model is capable to select
salient content even trained on out-of-domain data, but requires in-domain data
to capture the style for a target domain.


  Previously we have demonstrated that, on a torus, the abelian quantum hall
liquid is adiabatically connected to a charge density wave as the smaller
dimension of the torus is varied. In this work we extend this result to the
non-abelian bosonic Hall state. The outcome of these works is the realization
that the paradigms of quantum number fractionalization in one dimension
(polyacetylene) and two dimensions (fractional quantum Hall effect) are in fact
equivalent.


  The attack of novel avian influenza (H7N9) in east China caused a serious
health crisis and public panic. In this paper, we empirically analyze the onset
patterns of human cases of the novel avian influenza and observe several
spatial and temporal properties that are similar to other infective diseases.
More deeply, using the empirical analysis and modeling studies, we find that
the spatio-temporal network that connects the cities with human cases along the
order of outbreak timing emerges two-section-power-law edge-length
distribution, indicating the picture that several islands with higher and
heterogeneous risk straggle in east China. The proposed method is applicable to
the analysis on the spreading situation in early stage of disease outbreak
using quite limited dataset.


  The reliability and security of a user in an interconnected system depends on
all users' collective effort in security. Consequently, investments in security
technologies by strategic users is typically modeled as a public good problem,
known as the Interdependent Security (IDS) game. The equilibria for such games
are often inefficient, as selfish users free-ride on positive externalities of
others' contributions. In this paper, we present a mechanism that implements
the socially optimal equilibrium in an IDS game through a message exchange
process, in which users submit proposals about the security investment and
tax/price profiles of one another. This mechanism is different from existing
solutions in that (1) it results in socially optimal levels of investment,
closing the Price of Anarchy gap in the IDS game, (2) it is applicable to a
general model of user interdependencies. We further consider the issue of
individual rationality, often a trivial condition to satisfy in many resource
allocation problems, and argue that with positive externality, the incentive to
stay out and free-ride on others' investment can make individual rationality
much harder to satisfy in designing a mechanism.


  We examine those matrix rings whose entries lie in periodic rings equipped
with some additional properties. Specifically, we prove that the famous Diesl's
question whether or not $R$ being nil-clean implies that $\mathbb{M}_n(R)$ is
nil-clean for all $n\geq 1$ is paralleling to the corresponding implication for
(Abelian, local) periodic rings. Besides, we study when the endomorphism ring
$\mathrm{E}(G)$ of an Abelian group $G$ is periodic. Concretely, we establish
that $\mathrm{E}(G)$ is periodic exactly when $G$ is finite as well as we find
a complete necessary and sufficient condition when the endomorphism ring over
an Abelian group is strongly $m$-nil clean for some natural number $m$ thus
refining an "old" result concerning strongly nil-clean endomorphism rings.
Responding to a question when a group ring is periodic, we show that if $R$ is
a right (resp., left) perfect periodic ring and $G$ is a locally finite group,
then the group ring $RG$ is periodic, too. We finally find some criteria under
certain conditions when the tensor product of two periodic algebras over a
commutative ring is again periodic. In addition, some other sorts of rings very
close to periodic rings, namely the so-called weakly periodic rings, are also
investigated.


  We compare calculations of the three-point correlation functions of BMN
operators at the one-loop (next-to-leading) order in the scalar SU(2) sector
from the integrability expression recently suggested by Gromov and Vieira, and
from the string field theory expression based on the effective interaction
vertex by Dobashi and Yoneya. A disagreement is found between the form-factors
of the correlation functions in the one-loop contributions. The order-of-limits
problem is suggested as a possible explanation of this discrepancy.