  We study the N=1 supersymmetric solutions of D=11 supergravity obtained as a
warped product of four-dimensional anti-de-Sitter space with a
seven-dimensional Riemannian manifold M. Using the octonion bundle structure on
M we reformulate the Killing spinor equations in terms of sections of the
octonion bundle on M. The solutions then define a single complexified
G2-structure on M or equivalently two real G2-structures. We then study the
torsion of these G2-structures and the relationships between them.


  We develop a combined hydro-kinetic approach which incorporates a
hydrodynamical expansion of the systems formed in \textit{A}+\textit{A}
collisions and their dynamical decoupling described by escape probabilities.
The method corresponds to a generalized relaxation time ($\tau_{\text{rel}}$)
approximation for the Boltzmann equation applied to inhomogeneous expanding
systems; at small $\tau_{\text{rel}}$ it also allows one to catch the viscous
effects in hadronic component - hadron-resonance gas. We demonstrate how the
approximation of sudden freeze-out can be obtained within this dynamical
picture of continuous emission and find that hypersurfaces, corresponding to a
sharp freeze-out limit, are momentum dependent. The pion $m_{T}$ spectra are
computed in the developed hydro-kinetic model, and compared with those obtained
from ideal hydrodynamics with the Cooper-Frye isothermal prescription. Our
results indicate that there does not exist a universal freeze-out temperature
for pions with different momenta, and support an earlier decoupling of higher
$p_{T}$ particles. By performing numerical simulations for various initial
conditions and equations of state we identify several characteristic features
of the bulk QCD matter evolution preferred in view of the current analysis of
heavy ion collisions at RHIC energies.


  We derive the optimal $\epsilon$-differentially private mechanism for a
general two-dimensional real-valued (histogram-like) query function under a
utility-maximization (or cost-minimization) framework for the $\ell^1$ cost
function. We show that the optimal noise probability distribution has a
correlated multidimensional staircase-shaped probability density function.
Compared with the Laplacian mechanism, we show that in the high privacy regime
(as $\epsilon \to 0$), the Laplacian mechanism is approximately optimal; and in
the low privacy regime (as $\epsilon \to +\infty$), the optimal cost is
$\Theta(e^{-\frac{\epsilon}{3}})$, while the cost of the Laplacian mechanism is
$\frac{2\Delta}{\epsilon}$, where $\Delta$ is the sensitivity of the query
function. We conclude that the gain is more pronounced in the low privacy
regime. We conjecture that the optimality of the staircase mechanism holds for
vector-valued (histogram-like) query functions with arbitrary dimension, and
holds for many other classes of cost functions as well.


  We present modeling and design of singly-resonant optical parametric
oscillator (SR-OPO) with an intracavity idler absorber to enhance the
conversion efficiency for the signal, by suppressing the back conversion of the
signal and idler to the pump. Following plane wave analysis, we arrive at the
optimum parameters of the OPO to achieve high conversion efficiency for the
signal. For a given pump intensity, we have analyzed the effect of position and
number of absorbers required for optimum performance of the device. The model
is also extended to the case in which the signal is absorbed, yielding higher
conversion efficiency for the idler (in mid-IR region). The magnitude of
absorption and the effect of inter-crystal phase shift on the conversion
efficiency are also discussed. We also present an analytical solution for
twin-crystal SR-OPO with an absorber in between; taking into account the
variation of signal amplitude inside the cavity, we re-affirm that the often
used 'constant signal-wave approximation' is valid if the reflectivity of the
output coupler is high for the signal.


  Nowadays, mobile telephony interruptions in our daily life activities are
common because of the inappropriate ringing notifications of incoming phone
calls in different contexts. Such interruptions may impact on the work
attention not only for the mobile phone owners but also the surrounding people.
Decision tree is the most popular machine learning classification technique
that is used in existing context-aware mobile intelligent interruption
management (MIIM) model to overcome such issues. However, a single decision
tree based context-aware model may cause overfitting problem and thus decrease
the prediction accuracy of the inferred model. Therefore, in this paper, we
propose an ensemble machine learning based context-aware mobile telephony model
for the purpose of intelligent interruption management by taking into account
multi-dimensional contexts and name it "E-MIIM". The experimental results on
individuals' real life mobile telephony datasets show that our E-MIIM model is
more effective and outperforms existing MIIM model for predicting and managing
individual's mobile telephony interruptions based on their relevant contextual
information.


  We present the detection of a broad 8 $\mu$m feature in newly formed dust
around the carbon-rich Wolf-Rayet (WC) binary WR 125 from N-band low-resolution
(NL; R$\sim$250) spectroscopy between 7.3-13.6 $\mu$m and N-band (11.7 $\mu$m)
and Q-band (18.8 $\mu$m) imaging with Subaru/COMICS in 2019 October. WR 125 is
a colliding wind binary (${\rm WC7+O9}$) that exhibited renewed dust formation
starting in 2018, $\sim$28 years after its first dust formation episode had
been observed. We also compare our infrared photometry with historical
observations and revise the dust-formation period of WR 125 to 28.1 years.
Archival infrared spectra of five dusty WC stars, WR 48a, WR 98a, WR 104, WR
112 and WR 118, obtained with ISO/SWS are reanalyzed and compared with the WR
125 spectrum to search for a similar feature. We analyze the dusty WC spectra
using two different extinction curves to investigate the impact of interstellar
extinction correction on the presence and/or properties of the 8 $\mu$m
feature. All of the dusty WC spectra dereddened with the two different
extinction curves show a broad feature around 8 $\mu$m (FWHM$\sim$1-2 $\mu$m).
We suggest that these 8 $\mu$m features seen in the dusty WC spectra are
related to the Class C unidentified infrared (UIR) features.


  In his the Comment, P. Ao affirms that his vortex many-body theory explains
the observations reported in G. D'Anna et al., Phys. Rev. Lett. 81, 2530
(1998). Indeed, we provide here some arguments to show the lack of a
satisfactory explanation within the known theoretical frameworks.


  Convolutions are the core operation of deep learning applications based on
Convolutional Neural Networks (CNNs). Current GPU architectures are highly
efficient for training and deploying deep CNNs, and hence, these are largely
used in production for this purpose. State-of-the-art implementations, however,
present a lack of efficiency for some commonly used network configurations.
  In this paper we propose a GPU-based implementation of the convolution
operation for CNN inference that favors coalesced accesses, without requiring
prior data transformations. Our experiments demonstrate that our proposal
yields notable performance improvements in a range of common CNN forward
propagation convolution configurations, with speedups of up to 2.29x with
respect to the best implementation of convolution in cuDNN, hence covering a
relevant region in currently existing approaches.


  An ab-initio calculation scheme for finite nuclei based on self-consistent
Green's functions in the Gorkov formalism is developed. It aims at describing
properties of doubly-magic and semi-magic nuclei employing state-of-the-art
microscopic nuclear interactions and explicitly treating pairing correlations
through the breaking of U(1) symmetry associated with particle number
conservation. The present paper introduces the formalism, necessary to
undertake applications at (self-consistent) second-order using two-nucleon
interactions, in a detailed and self-contained fashion. First applications of
such a scheme will be reported soon in a forthcoming publication. Future works
will extend the present scheme to include three-nucleon interactions and
implement more advanced truncation schemes.


  We show that for an elliptic curve E defined over a number field K, the group
E(A) of points of E over the adele ring A of K is a topological group that can
be analyzed in terms of the Galois representation associated to the torsion
points of E. An explicit description of E(A) is given, and we prove that for K
of degree n, almost all elliptic curves over K have an adelic point group
topologically isomorphic to a universal group depending on n. We also show that
there exist infinitely many elliptic curves over K having a different adelic
point group.


  A classical theorem in conformal geometry states that on a manifold with
non-positive Yamabe invariant, a smooth metric achieving the invariant must be
Einstein. In this work, we extend it to the singular case and show that in all
dimension, if a continuous metric is smooth outside a compact set of high
co-dimension and achieves the Yamabe invariant, then the metric is Einstein
away from the singularity and can be extended to be smooth on the manifold in a
suitable sense. As an application of the method, we prove a Positive Mass
Theorem for asymptotically flat manifolds with analogous singularities.


  Exploration policies in Bayesian bandits maximize the average reward over
problem instances drawn from some distribution $\mathcal{P}$. In this work, we
learn such policies for an unknown distribution $\mathcal{P}$ using samples
from $\mathcal{P}$. Our approach is a form of meta-learning and exploits
properties of $\mathcal{P}$ without making strong assumptions about its form.
To do this, we parameterize our policies in a differentiable way and optimize
them by policy gradients, an approach that is general and easy to implement. We
derive effective gradient estimators and introduce novel variance reduction
techniques. We also analyze and experiment with various bandit policy classes,
including neural networks and a novel softmax policy. The latter has regret
guarantees and is a natural starting point for our optimization. Our
experiments show the versatility of our approach. We also observe that neural
network policies can learn implicit biases expressed only through the sampled
instances.


  We present the analytic foundation of a unified B-D-F extension functor
$\operatorname{Ext}_\tau$ on the category of noncommutative smooth algebras,
for any Fr\'echet operator ideal $\Cal K_\tau$. Combining the techniques
devised by Arveson and Voiculescu, we generalize Voiculescu's theorem to smooth
algebras and Fr\'echet operator ideals. A key notion involved is
$\tau$-smoothness, which is verified for the algebras of smooth functions, via
a noncommutative Sobolev lemma. The groups $\operatorname{Ext}_\tau$ are
computed for many examples.


  We consider four-dimensional gravity coupled to a non-linear sigma model
whose scalar manifold is a non-compact geometrically finite surface $\Sigma$
endowed with a Riemannian metric of constant negative curvature. When the
space-time is an FLRW universe, such theories produce a very wide
generalization of two-field $\alpha$-attractor models, being parameterized by a
positive constant $\alpha$, by the choice of a finitely-generated surface group
$\Gamma\subset \mathrm{PSL}(2,\mathbb{R})$ (which is isomorphic with the
fundamental group of $\Sigma$) and by the choice of a scalar potential defined
on $\Sigma$. The traditional two-field $\alpha$-attractor models arise when
$\Gamma$ is the trivial group, in which case $\Sigma$ is the Poincar\'e disk.
We give a general prescription for the study of such models through
uniformization in the so-called "non-elementary" case and discuss some of their
qualitative features in the gradient flow approximation, which we relate to
Morse theory. We also discuss some aspects of the SRST approximation in these
models, showing that it is generally not well-suited for studying dynamics near
cusp ends. When $\Sigma$ is non-compact and the scalar potential is
"well-behaved" at the ends, we show that, in the {\em naive} local one-field
truncation, our generalized models have the same universal behavior as ordinary
one-field $\alpha$-attractors if inflation happens near any of the ends of
$\Sigma$ where the extended potential has a local maximum, for trajectories
which are well approximated by non-canonically parameterized geodesics near the
ends, we also discuss spiral trajectories near the ends.


  We show that in a weak commutative inverse property loop, such as a Bruck
loop, if $\alpha$ is a right [left] pseudoautomorphism with companion $c$, then
$c$ [$c^2$] must lie in the left nucleus. In particular, for any such loop with
trivial left nucleus, every right pseudoautomorphism is an automorphism and if
the squaring map is a permutation, then every left pseudoautomorphism is an
automorphism as well. We also show that every pseudoautomorphism of a
commutative inverse property loop is an automorphism, generalizing a well-known
result of Bruck.


  We characterize the statistical law according to which Italian primary
school-size distributes. We find that the school-size can be approximated by a
log-normal distribution, with a fat lower tail that collects a large number of
very small schools. The upper tail of the school-size distribution decreases
exponentially and the growth rates are distributed with a Laplace PDF. These
distributions are similar to those observed for firms and are consistent with a
Bose-Einstein preferential attachment process. The body of the distribution
features a bimodal shape suggesting some source of heterogeneity in the school
organization that we uncover by an in-depth analysis of the relation between
schools-size and city-size. We propose a novel cluster methodology and a new
spatial interaction approach among schools which outline the variety of
policies implemented in Italy. Different regional policies are also discussed
shedding lights on the relation between policy and geographical features.


  A major challenge in matching images and text is that they have intrinsically
different data distributions and feature representations. Most existing
approaches are based either on embedding or classification, the first one
mapping image and text instances into a common embedding space for distance
measuring, and the second one regarding image-text matching as a binary
classification problem. Neither of these approaches can, however, balance the
matching accuracy and model complexity well. We propose a novel framework that
achieves remarkable matching performance with acceptable model complexity.
Specifically, in the training stage, we propose a novel Multi-modal Tensor
Fusion Network (MTFN) to explicitly learn an accurate image-text similarity
function with rank-based tensor fusion rather than seeking a common embedding
space for each image-text instance. Then, during testing, we deploy a generic
Cross-modal Re-ranking (RR) scheme for refinement without requiring additional
training procedure. Extensive experiments on two datasets demonstrate that our
MTFN-RR consistently achieves the state-of-the-art matching performance with
much less time complexity. The implementation code is available at
https://github.com/Wangt-CN/MTFN-RR-PyTorch-Code.


  Using sample surveys as a cost effective tool to provide estimates for
characteristics of interest at population and sub-populations (area/domain)
level has a long tradition in "small area estimation". However, the existence
of outliers in the sample data can significantly affect the estimation for
areas in which they occur, especially where the domain-sample size is small.
Based on existing robust estimators for small area estimation we propose two
novel approaches for bias calibration. A series of simulations shows that our
methods lead to more efficient estimators in comparison with other existing
bias-calibration methods. As a real data example we apply our estimators to
obtain \textit{Gini} coefficients in labour market areas of the Tuscany region
of Italy, where our sources of information are the EU-SILC survey and the
Italian census. This analysis shows that the new methods reveal a different
picture than existing methods. We extend our ideas to predictions for
non-sampled areas.


  We study the transverse momentum resummation for dijet correlation in hadron
collisions based on the Collins-Soper-Sterman formalism. The complete one-loop
calculations are carried out in the collinear factorization framework for the
differential cross sections at low imbalance transverse momentum between the
two jets. Important cross checks are performed to demonstrate that the soft
divergences cancelled out between different diagrams, and in particular, those
associated with final state jets. The leading and sub-leading logarithms are
identified. All order resummation is derived following the transverse momentum
dependent factorization at this order. Its phenomenological applications are
also presented.


  We report detector characteristics and background measurements from two
prototype imaging CZT detectors flown on a scientific balloon payload in May
2001. The detectors are both platinum-contact 10mm x 10mm x 5mm CZT crystals,
each with a 4 $\times$ 4 array of pixels tiling the anode. One is made from
IMARAD horizontal Bridgman CZT, the other from eV Products high-pressure
Bridgman material. Both detectors were mounted side-by-side in a flip-chip
configuration and read out by a 32-channel IDE VA/TA ASIC preamp/shaper. We
enclosed the detectors in the same 40deg field-of-view collimator (comprisinga
graded passive shield and plastic scintillator) used in our previously-reported
September 2000 flight. I-V curves for the detectors are diode-like, and we find
that the platinum contacts adhere significantly better to the CZT surfaces than
gold to previous detectors. The detectors and instrumentation performed well in
a 20-hour balloon flight on 23/24 May 2001. Although we discovered a
significant instrumental background component in flight, it was possible to
measure and subtract this component from the spectra. The resulting IMARAD
detector background spectrum (from 30 keV to ~450 keV) reaches ~5 x 10^{-3}$
counts/cm^2 -sec-keV at 100 keV and has a power-law index of ~2 at high
energies. The eV Products detector has a similar spectrum, although there is
more uncertainty in the energy scale because of calibration complications.


  This paper presents a curvature-free version of the Log(2k-1) Theorem of
Anderson, Canary, Culler & Shalen [ACCS96]. It generalizes a result by Hou
[Hou01] and its proof is rather straightforward once we know the work by Lim
[Lim08] on volume entropy for graphs. As a byproduct we obtain a curvature-free
version of the Collar Lemma in all dimensions.


  We make Bayesian Additive Regression Networks (BARN) available as a Python
package, \texttt{barmpy}, with documentation at
\url{https://dvbuntu.github.io/barmpy/} for general machine learning
practitioners. Our object-oriented design is compatible with SciKit-Learn,
allowing usage of their tools like cross-validation. To ease learning to use
\texttt{barmpy}, we produce a companion tutorial that expands on reference
information in the documentation. Any interested user can \texttt{pip install
barmpy} from the official PyPi repository. \texttt{barmpy} also serves as a
baseline Python library for generic Bayesian Additive Regression Models.


  The $k$-means is one of the most important unsupervised learning techniques
in statistics and computer science. The goal is to partition a data set into
many clusters, such that observations within clusters are the most homogeneous
and observations between clusters are the most heterogeneous. Although it is
well known, the investigation of the asymptotic properties is far behind,
leading to difficulties in developing more precise $k$-means methods in
practice. To address this issue, a new concept called clustering consistency is
proposed. Fundamentally, the proposed clustering consistency is more
appropriate than the previous criterion consistency for the clustering methods.
Using this concept, a new $k$-means method is proposed. It is found that the
proposed $k$-means method has lower clustering error rates and is more robust
to small clusters and outliers than existing $k$-means methods. When $k$ is
unknown, using the Gap statistics, the proposed method can also identify the
number of clusters. This is rarely achieved by existing $k$-means methods
adopted by many software packages.


  Reflectance spectrometry is a fast and reliable method for the
characterisation of human skin if the spectra are analysed with respect to a
physical model describing the optical properties of human skin. For a field
study performed at the Institute of Legal Medicine and the Freiburg Materials
Research Center of the University of Freiburg an electronic laboratory notebook
has been developed, which assists in the recording, management, and analysis of
reflectance spectra. The core of the electronic laboratory notebook is a MySQL
database. It is filled with primary data via a web interface programmed in
Java, which also enables the user to browse the database and access the results
of data analysis. These are carried out by Matlab, Tcl and
  Python scripts, which retrieve the primary data from the electronic
laboratory notebook, perform the analysis, and store the results in the
database for further usage.


  Nuclear magnetic resonance (NMR) has enormous applications. Two-dimensional
NMR is an essential technique to characterize correlations between nuclei and,
hence, molecule structures. Towards the ultimate goal of single-molecule NMR,
dynamical-decoupling- (DD) enhanced diamond quantum sensing enables the
detection of single nuclear spins and nanoscale NMR. However, there is still
the lack of a standard method in DD-based quantum sensing to characterize
correlations between nuclear spins in single molecules. Here we present a
scheme of two-dimensional DD-based quantum sensing, as a universal method for
correlation spectroscopy of single molecules. We design two-dimensional DD
sequences composed of two sets of periodic DD sequences with different periods,
which can be independently set to match two different transition frequencies
for resonant DD. We find that under the resonant DD condition the sensor
coherence patterns, as functions of the two independent pulse numbers of DD
subsequences, can fully determine different types of correlations between
nuclear spin transitions. This work offers a systematic approach to correlation
spectroscopy for single-molecule NMR.


  The symmetric group S_n possesses a nontrivial central extension, whose
irreducible representations, different from the irreducible representations of
S_n itself, coincide with the irreducible representations of a certain algebra
A_n. Recently M.~Nazarov realized irreducible representations of A_n and Young
symmetrizers by means of the Howe duality between the Lie superalgebra q(n) and
the Hecke algebra H_n, the semidirect product of S_n with the Clifford algebra
C_n on n indeterminates.
  Here I construct one more analog of Young symmetrizers in H_n as well as the
analogs of Specht modules for A_n and H_n.


  We study the formation of cosmic strings by confining a stochastic magnetic
field into flux tubes in a numerical simulation. We use overdamped evolution in
a potential that is minimized when the flux through each face in the simulation
lattice is a multiple of the fundamental flux quantum. When the typical number
of flux quanta through a correlation-length-sized region is initially about 1,
we find a string network similar to that generated by the Kibble-Zurek
mechanism. With larger initial flux, the loop distribution and the Brownian
shape of the infinite strings remain unchanged, but the fraction of length in
infinite strings is increased. A 2D slice of the network exhibits bundles of
strings pointing in the same direction, as in earlier 2D simulations. We find,
however, that strings belonging to the same bundle do not stay together in 3D
for much longer than the correlation length. As the initial flux per
correlation length is decreased, there is a point at which infinite strings
disappear, as in the Hagedorn transition.


  In many cases, unconventional superconductivity are realized by suppressing
another order parameter, such as charge density wave (CDW) or spin density wave
(SDW). This suggests that the fluctuations of these order parameters play an
important role in producing superconductivity. LaPt$_2$Ge$_2$ undergoes a
tetragonal-to-monoclinic structural phase transition (SPT) at $T_{\rm s}$ = 394
K, accompanying a double period modulation in the $a$-axis direction, and
superconducts at $T_{\rm c}$ = 0.41 K. We performed band calculations and found
2D (two dimensional)-like Fermi surfaces with partial nesting. A reduction in
the density of states in the monoclinic phase was found in the calculation and
confirmed by $^{195}$Pt-NMR. We suggest a CDW as a possible cause for the SPT.
By changing the stoichiometry between Pt and Ge, we succeeded in suppressing
$T_{\rm s}$ and increasing $T_{\rm c}$ in LaPt$_{2-x}$Ge$_{2+x}$. Comparison of
$^{139}$La- and $^{195}$Pt-NMR data reveals moderate fluctuations associated
with SPT. From $^{139}$La-NQR measurements at zero field, we found that an
isotropic superconducting gap is realized in LaPt$_{2-x}$Ge$_{2+x}$ ($x$ =
0.20). We discuss the relationship between superconductivity and the SPT
order/fluctuations.


  Let $\mathcal{X} : y^2 = f(x)$ be a hyperelliptic curve over $\mathbb{Q}(T)$
of genus $g\geq 1$. Assume that the jacobian of $\mathcal{X}$ over
$\mathbb{Q}(T)$ has no subvariety defined over $\mathbb{Q}$. Denote by
$\mathcal{X}_t$ the specialization of $\mathcal{X}$ to an integer $T=t$, let
$a_{\mathcal{X}_t}(p)$ be its trace of Frobenius, and $A_{\mathcal{X},r}(p) =
\frac{1}{p}\sum_{t=1}^p a_{\mathcal{X}_t}(p)^r$ its $r$-th moment. The first
moment is related to the rank of the jacobian
$J_\mathcal{X}\left(\mathbb{Q}(T)\right)$ by a generalization of a conjecture
of Nagao: $$\lim_{X \to \infty} \frac{1}{X} \sum_{p \leq X} -
A_{\mathcal{X},1}(p) \log p = \operatorname{rank}
J_\mathcal{X}(\mathbb{Q}(T)).$$ Generalizing a result of S. Arms, \'A.
Lozano-Robledo, and S.J. Miller, we compute first moments for various families
resulting in infinitely many hyperelliptic curves over $\mathbb{Q}(T)$ having
jacobian of moderately large rank $4g+2$, where $g$ is the genus; by
Silverman's specialization theorem, this yields hyperelliptic curves over
$\mathbb{Q}$ with large rank jacobian. Note that Shioda has the best record in
this directon: he constructed hyperelliptic curves of genus $g$ with jacobian
of rank $4g+7$. In the case when $\mathcal{X}$ is an elliptic curve, Michel
proved $p\cdot A_{\mathcal{X},2} = p^2 + O\left(p^{3/2}\right)$. For the
families studied, we observe the same second moment expansion. Furthermore, we
observe the largest lower order term that does not average to zero is on
average negative, a bias first noted by S.J. Miller in the elliptic curve case.
We prove this bias for a number of families of hyperelliptic curves.


  The multiple root loci among univariate polynomials of degree $n$ are indexed
by partitions of $n$. We study these loci and their conormal varieties. The
projectively dual varieties are joins of such loci where the partitions are
hooks. Our emphasis lies on equations and parametrizations that are useful for
Euclidean distance optimization. We compute the ED degrees for hooks. Among the
dual hypersurfaces are those that demarcate the set of binary forms whose real
rank equals the generic complex rank.


  Scale has been a major driving force in improving machine learning
performance, and understanding scaling laws is essential for strategic planning
for a sustainable model quality performance growth, long-term resource planning
and developing efficient system infrastructures to support large-scale models.
In this paper, we study empirical scaling laws for DLRM style recommendation
models, in particular Click-Through Rate (CTR). We observe that model quality
scales with power law plus constant in model size, data size and amount of
compute used for training. We characterize scaling efficiency along three
different resource dimensions, namely data, parameters and compute by comparing
the different scaling schemes along these axes. We show that parameter scaling
is out of steam for the model architecture under study, and until a
higher-performing model architecture emerges, data scaling is the path forward.
The key research questions addressed by this study include: Does a
recommendation model scale sustainably as predicted by the scaling laws? Or are
we far off from the scaling law predictions? What are the limits of scaling?
What are the implications of the scaling laws on long-term hardware/system
development?


  We report measurements of the evolution of the diffuse scattering in a single
crystal PbMg1/3Nb2/3O3 as a function of hydrostatic pressure. Upon applying
pressure the diffuse scattering intensity decreases and is suppressed at about
3 GPa, while no change in the line shape is observed. Correlations between Pb
displacements, diffuse scattering and relaxor properties are discussed.


  In this paper, we consider the steps to be followed in the analysis and
interpretation of the quantization problem related to the $C_{2,8}$ channel,
where the Fuchsian differential equations, the generators of the Fuchsian
groups, and the tessellations associated with the cases $g=2$ and $g=3$,
related to the hyperbolic case, are determined. In order to obtain these
results, it is necessary to determine the genus $g$ of each surface on which
this channel may be embedded. After that, the procedure is to determine the
algebraic structure (Fuchsian group generators) associated with the fundamental
region of each surface. To achieve this goal, an associated linear second-order
Fuchsian differential equation whose linearly independent solutions provide the
generators of this Fuchsian group is devised. In addition, the tessellations
associated with each analyzed case are identified. These structures are
identified in four situations, divided into two cases $(g=2$ and $g=3)$,
obtaining, therefore, both algebraic and geometric characterizations associated
with quantizing the $C_{2,8}$ channel.


  We survey recent results on ample cones and birational contractions of
holomorphic symplectic varieties of K3 type, focusing on explicit constructions
and concrete examples.


  The expressions for entropy production, free energy, and entropy extraction
rates are derived for a Brownian particle that walks in an underdamped medium.
Our analysis indicates that as long as the system is driven out of equilibrium,
it constantly produces entropy at the same time it extracts entropy out of the
system. At steady state, the rate of entropy production ${\dot e}_{p}$ balances
the rate of entropy extraction ${\dot h}_{d}$. At equilibrium both entropy
production and extraction rates become zero. The entropy production and entropy
extraction rates are also sensitive to time. As time progresses, both entropy
production and extraction rates increase in time and saturate to constant
values. Moreover employing microscopic stochastic approach, several
thermodynamic relations for different model systems are explored analytically
and via numerical simulations by considering a Brownian particle that moves in
overdamped medium. Our analysis indicates that the results obtained for
underdamped cases quantitatively agree with overdamped cases at steady state.
The fluctuation theorem is also discussed in detailed.


  Let k be a finite base field. In this note, making use of topological
periodic cyclic homology and of the theory of noncommutative motives, we prove
that the numerical Grothendieck group of every smooth proper dg k-linear
category is a finitely generated free abelian group. Along the way, we prove
moreover that the category of noncommutative numerical motives over k is
abelian semi-simple, as conjectured by Kontsevich. Furthermore, we show that
the zeta functions of endomorphisms of noncommutative Chow motives are rational
and satisfy a functional equation.


  We present the calculation of the $\mathcal{O}(\alpha_s^2 C_F T_F)$ massive
quark corrections to the soft function for the double hemisphere jet mass
distribution in $e^+ e^-$ collisions, a necessary ingredient for the
calculation of several event shape distributions at N${}^3$LL order. Using the
mass as an infrared regulator allows us to derive an expression for the
massless momentum space limit, which has not been given so far in the
literature. Furthermore, we compute the corresponding corrections in the soft
function for thrust, the most prominent projection of the double hemisphere
mass distribution. Finally we give expressions for the corresponding renormalon
subtractions in the gap scheme.


  Modularity, since its introduction, has remained one of the most widely used
metrics to assess the quality of community structure in a complex network.
However the resolution limit problem associated with modularity limits its
applicability to networks with community sizes smaller than a certain scale. In
the past various attempts have been made to solve this problem. More recently a
new metric, modularity density, was introduced for the quality of community
structure in networks in order to solve some of the known problems with
modularity, particularly the resolution limit problem. Modularity density
resolves some communities which are otherwise undetectable using modularity.
However, we find that it does not solve the resolution limit problem completely
by investigating some cases where it fails to detect expected community
structures. To address this problem, we introduce a variant of this metric and
show that it further reduces the resolution limit problem, effectively
eliminating the problem in a wide range of networks.


  We study a diluted mean-field spin glass model with a quadratic Hamiltonian.
Our main result establishes the limiting free energy in terms of an integral of
a family of random variables that are the weak limits of the quenched variances
of the spins in the system with varying edge connectivity. The key ingredient
in our argument is played by the identification of these random variables as
the unique solution to a recursive distributional equation. Our results in
particular provide the first example of the diluted Shcherbina-Tirozzi model,
whose limiting free energy can be derived at any inverse temperature and
external field.


  We explore UV and optical variability signatures for several hundred members
of NGC 2264 (3 Myr). We performed simultaneous u- and r-band monitoring over
two full weeks with CFHT/MegaCam. About 750 young stars are probed; 40% of them
are accreting. Statistically distinct variability properties are observed for
accreting and non-accreting cluster members. The accretors exhibit a
significantly higher level of variability than the non-accretors, especially in
the UV. The amount of u-band variability correlates statistically with UV
excess in disk-bearing objects, which suggests that accretion and star-disk
interaction are the main sources of variability. Cool magnetic spots, several
hundred degrees colder than the photosphere and covering from 5 to 30% of the
stellar surface, appear to be the leading factor of variability for the
non-accreting stars. In contrast, accretion spots, a few thousand degrees
hotter than the photosphere and covering a few percent of the stellar surface,
best reproduce the variability of accreting objects. The color behavior is also
found to be different between accreting and non-accreting stars. Typical
variability amplitudes for accreting members rapidly increase from r to u,
which indicates a much stronger contrast at short wavelengths; a lower color
dependence in the amplitudes is instead measured for diskless stars. We find
that u-band variability on hour timescales is typically about 10% of the
peak-to-peak variability on day timescales, while longer term (years)
variability is consistent with amplitudes measured over weeks. We conclude that
for both accreting and non-accreting stars, the mid-term rotational modulation
by spots is the leading timescale for a variability of up to several years. In
turn, this suggests that the accretion process is essentially stable over
years, although it exhibits low-level shorter term variations in single
accretion events.


  There is a reformulation of magnetohydrodynamics in which the fundamental
dynamical quantities are the positions and velocities of the lines of magnetic
flux in the plasma, which turn out to obey equations of motion very much like
ideal strings. We use this approach to study the evolution of a primordial
magnetic field generated during the radiation-dominated era in the early
Universe. Causality dictates that the field lines form a tangled random
network, and the string-like equations of motion, plus the assumption of
perfect reconnection, inevitably lead to a self-similar solution for the
magnetic field power spectrum. We present the predicted form of the power
spectrum, and discuss insights gained from the string approximation, in
particular the implications for the existence or not of an inverse cascade.


  The low temperature specific heat of annealed single crystal samples of
Ba(Fe1-xCox)2As2 with compositions spanning the entire superconducting phase
diagram was measured. Effort was made to discover the best annealing schedule
to maximize Tc and minimize transition width in these samples. Values of
deltaC/Tc normalized to 100% superconducting volume fractions varied
proportionally to Tc^alpha. Within a rather narrow error bar of +-0.15, the
exponent alpha was the same (approximately 2) over a range of compositions
(0.055 < x < 0.15) around the optimal concentration, x=0.08, where Tc is the
maximum in the phase diagram. Thus, whether the superconductivity was
coexistent with magnetism (underdoped) or not (overdoped) did not affect the
non-BCS variation (alpha nearly 2 instead of 0.8-0.9 for BCS superconductors)
of deltaC/Tc with Tc. The annealed samples in the present work, with increased
deltaC/Tc and Tc values compared to previous results for the Ba(Fe1-xCox)2As2
alloy system, suggest that the intrinsic value of the exponent alpha for the
iron superconductors, when the samples are annealed, with fewer defects, may
indeed be even further from the BCS value of 0.8-0.9 than previously thought.


  Online availability and diffusion of New Psychoactive Substances (NPS)
represent an emerging threat to healthcare systems. In this work, we analyse
drugs forums, online shops, and Twitter. By mining the data from these sources,
it is possible to understand the dynamics of drugs diffusion and their
endorsement, as well as timely detecting new substances. We propose a set of
visual analytics tools to support analysts in tackling NPS spreading and
provide a better insight about drugs market and analysis.


  The current ongoing advancements in AI have shed light on the landscape of
numerical analysis in science. Inspired by the path of achievement of AI, we
have developed a method to construct accurate ground state wave functions of
multiquark configurations within a quark model. We successfully tested our
method through comparisons with meson-type two-body systems with analytic and
numerical solutions. We then applied our method to find the ground-state
solutions of $T_{cc}$($ud\bar{c}\bar{c}$) and $T_{bb}$($ud\bar{b}\bar{b}$)
states. Our findings indicate that our approach outperforms existing methods,
achieving greater accuracy in reproducing highly intricate configurations.
Within the model parameters, we find that the $T_{cc}$ is a compact multiquark
configuration.


  By the introduction of locally constant prefactorization algebras at a fixed
scale, we show a mathematical incarnation of the fact that observables at a
given scale of a topological field theory propagate to every scale over
euclidean spaces. The key is that these prefactorization algebras over
$\mathbb{R}^n$ are equivalent to algebras over the little $n$-disc operad. For
topological field theories with defects, we get analogous results by replacing
$\mathbb{R}^n$ with the spaces modelling corners
$\mathbb{R}^p\times\mathbb{R}^{q}_{\geq 0}$. As a toy example in $1d$, we
quantize, once more, constant Poisson structures.


  As Internet of Things (IoT) and Cyber-Physical systems become more ubiquitous
and an integral part of our daily lives, it is important that we are able to
trust the data aggregate from such systems. However, the interpretation of
trustworthiness is contextual and varies according to the risk tolerance
attitude of the concerned application and varying levels of uncertainty
associated with the evidence upon which trust models act. Hence, the data
integrity scoring mechanisms should have provisions to adapt to varying risk
attitudes and uncertainties. In this paper, we propose a Bayesian inference
model and a prospect theoretic framework for data integrity scoring that
quantify the trustworthiness of data collected from IoT devices in the presence
of an adversaries who manipulate the data. We consider an imperfect anomaly
monitoring mechanism that monitors the data being sent from each device and
classifies the outcome as not compromised, compromised, and cannot be inferred.
These outcomes are conceptualized as a multinomial hypothesis of a Bayesian
inference model with three parameters which are then used for calculating a
utility value on how reliable the aggregate data is. We use a prospect theory
inspired approach to quantify this data integrity score and evaluate the
trustworthiness of the aggregate data from the IoT framework. Furthermore, we
also model the system using the traditionally used expected utility theory and
compare the results with that obtained using prospect theory. As decisions are
based on how the data is fused, we propose two measuring models: one optimistic
and another conservative. The proposed framework is validated using extensive
simulation experiments. We show how data integrity scores vary under a variety
of system factors like attack intensity and inaccurate detection.


  As a cheap and safe antimalarial agent, chloroquine (CQ) has been used in the
battle against malaria for more than half century. However, the mechanism of CQ
action and resistance in Plasmodium falciparum remains elusive. Based on
further analysis of our published experimental results, we propose that the
mechanism of CQ action and resistance might be closely linked with
cell-cycle-associated amplified genomic-DNA fragments (CAGFs, singular form =
CAGF) as CQ induces CAGF production in P. falciparum, which could affect
multiple biological processes of the parasite, and thus might contribute to
parasite death and CQ resistance. Recently, we found that CQ induced one of
CAGFs, UB1- CAGF, might downregulate a probable P. falciparum cystine
transporter (Pfct) gene expression, which could be used to understand the
mechanism of CQ action and resistance in P. falciparum.


  Let $\mathbb{F}_q$ be a field with $q$ elements. In this note, we study some
generalized arcs, that is, sets of $\mathbb{F}_q$-points in the projective
plane $\mathbb{P}^2(\mathbb{F}_q)$ such that no six of them are on a conic.
First, we consider the geometric configurations of such generalized arcs for
small values of $q$ and then we give some upper and lower bounds for the
cardinality of complete generalized arcs, i.e. generalized arcs which are not
contained in a bigger one.


  We study the effects of substructure in the Galactic halo on direct detection
of dark matter, on searches for energetic neutrinos from WIMP annihilation in
the Sun and Earth, and on the enhancement in the WIMP annihilation rate in the
halo. Our central result is a probability distribution function (PDF) P(\rho)
for the local dark-matter density. This distribution must be taken into account
when using null dark-matter searches to constrain the properties of dark-matter
candidates. We take two approaches to calculating the PDF. The first is an
analytic model that capitalizes on the scale-invariant nature of the
structure--formation hierarchy in order to address early stages in the
hierarchy (very small scales; high densities). Our second approach uses
simulation-inspired results to describe the PDF that arises from lower-density
larger-scale substructures which formed in more recent stages in the merger
hierarchy. The distributions are skew positive, and they peak at densities
lower than the mean density. The local dark-matter density may be as small as
1/10th the canonical value of ~ 0.4 GeV/cm^3, but it is probably no less than
0.2 GeV/cm^3.


  This paper addresses the modeling of fracture in quasi-brittle materials
using a phase-field approach to the description of crack topology. Within the
computational mechanics community, several studies have treated the issue of
modeling fracture using phase fields. Most of these studies have used an
approach that implies the lack of a damage threshold. We herein explore an
alternative model that includes a damage threshold and study how it compares
with the most popular approach. The formulation is systematically explained
within a rigorous variational framework. Subsequently, we present the
corresponding three-dimensional finite element discretization that leads to a
straightforward numerical implementation. Benchmark simulations in two
dimensions and three dimensions are then presented. The results show that while
an elastic stage and a damage threshold are ensured by the present model, good
agreement with the results reported in the literature can be obtained, where
such features are generally absent.


  While it is well-known that electrode conductivity has a critical impact on
rate-performance in battery electrodes, this relationship has been quantified
only by computer simulations. Here we investigate the relationship between
electrode conductivity and rate-performance in
Lithium-Nickel-Manganese-Cobalt-Oxide (NMC) cathodes filled with various
quantities of carbon black, single-walled carbon nanotubes and graphene. The
electrode conductivity is always extremely anisotropic with the out-of-plane
conductivity, which is most relevant to rate-performance, roughly 1000 smaller
than the in-plane conductivity. For all fillers the conductivity increases with
filler loading although the nanotube-filled electrodes show by far the most
rapid increase. Fitting capacity versus rate curves yielded the characteristic
time associated with charge/discharge. This parameter increased linearly with
the inverse of the out-of-plane conductivity, with all data points falling on
the same master curve. Using a simple mechanistic model for the characteristic
time, we develop an equation which matches the experimental data almost
perfectly with no adjustable parameters. This implies that increasing the
electrode conductivity improves the rate-performance by decreasing the RC
charging time of the electrode. This model shows the effect of electrode
resistance on the rate-performance to become negligible in almost all cases
once the out-of-plane conductivity of the electrode exceeds 1 S/m. Our results
show that this can be achieved by including <1wt% single-walled carbon
nanotubes in the electrode.


  We propose an indistinguishability measure for assessment of ansatz
wavefunctions with numerically determined wavefunctions. The measure
efficiently compares all correlation functions of two states and can therefore
be used to distinguish phases by defining correlator classes for ansatz
wavefunctions. It also allows identification of quantum critical points. We
demonstrate the approach for the transverse Ising model, using the matrix
product state formalism with the time evolving block decimation algorithm.


  Optical metasurfaces are planar substrates with custom-designed, nanoscale
features that selectively modulate incident light with respect to direction,
wavelength, and polarization. When coupled with photodetectors and appropriate
post-capture processing, they provide a means to create computational imagers
and sensors that are exceptionally small and have distinctive capabilities. We
introduce D-Flat, a framework in TensorFlow that renders physically-accurate
images induced by metasurface optical systems. This framework is fully
differentiable with respect to metasurface shape and post-capture computational
parameters and allows simultaneous optimization with respect to almost any
measure of sensor performance. D-Flat enables simulation of millimeter to
centimeter diameter metasurfaces on commodity computers, and it is modular in
the sense of accommodating a variety of wave optics models for scattering at
the metasurface and for propagation to photosensors. We validate D-Flat against
symbolic calculations and previous experimental measurements, and we provide
simulations that demonstrate its ability to discover novel computational sensor
designs for two applications: single-shot depth sensing and single-shot spatial
frequency filtering.


  We explore the interplay of electron-electron correlations and surface
effects in the prototypical correlated insulating material, NiO. In particular,
we compute the electronic structure, magnetic properties, and surface energies
of the $(001)$ and $(110)$ surfaces of paramagnetic NiO using a fully charge
self-consistent DFT+DMFT method. Our results reveal a complex interplay between
electronic correlations and surface effects in NiO, with the electronic
structure of the $(001)$ and $(110)$ NiO surfaces being significantly different
from that in bulk NiO. We obtain a sizeable reduction of the band gap at the
surface of NiO, which is most significant for the $(110)$ NiO surface. This
suggests a higher catalytic activity of the $(110)$ NiO surface than that of
the $(001)$ NiO one. Our results reveal a charge-transfer character of the
$(001)$ and $(110)$ surfaces of NiO. Most notably, for the $(110)$ NiO surface
we observe a remarkable electronic state characterized by an alternating
charge-transfer and Mott-Hubbard character of the band gap in the surface and
subsurface NiO layers, respectively. This novel form of electronic order
stabilized by strong correlations is not driven by lattice reconstructions but
of purely electronic origin. We notice the importance of
orbital-differentiation of the Ni $e_g$ states to characterize the Mott-Hubbard
insulating state of the $(001)$ and $(110)$ NiO surfaces. The unoccupied Ni
$e_g$ surface states are seen to split from the lower edge of the conduction
band to form strongly localized states in the fundamental gap of bulk NiO. Our
results for the surface energies of the $(001)$ and $(110)$ NiO surfaces show
that the $(001)$ facet of NiO has significantly lower energy. This implies that
the relative stability of different surfaces, at least from a purely energetic
point of view, does not depend on the presence or absence of magnetic order in
NiO.


  Causality has been often confused with the notion of determinism. It is
mandatory to separate the two notions in view of the debate about quantum
foundations. Quantum theory provides an example of causal not-deterministic
theory. Here we introduce a toy operational theory that is deterministic and
non-causal, thus proving that the two notions of causality and determinism are
totally independent.


  In this paper, we present a data-driven approach to generate realistic
steering behaviors for virtual crowds in crowd simulation. We take advantage of
both rule-based models and data-driven models by applying the interaction
patterns discovered from crowd videos. Unlike existing example-based models in
which current states are matched to states extracted from crowd videos
directly, our approach adopts a hierarchical mechanism to generate the steering
behaviors of agents. First, each agent is classified into one of the
interaction patterns that are automatically discovered from crowd video before
simulation. Then the most matched action is selected from the associated
interaction pattern to generate the steering behaviors of the agent. By doing
so, agents can avoid performing a simple state matching as in the traditional
example-based approaches, and can perform a wider variety of steering behaviors
as well as mimic the cognitive process of pedestrians. Simulation results on
scenarios with different crowd densities and main motion directions demonstrate
that our approach performs better than two state-of-the-art simulation models,
in terms of prediction accuracy. Besides, our approach is efficient enough to
run at interactive rates in real time simulation.


  It was argued in the past that bulges of galaxies cannot be formed through
collisionless secular evolution because that would violate constraints on the
phase-space density: the phase-space density in bulges is several times larger
than in the inner parts of discs. We show that these arguments against secular
evolution are not correct. Observations give estimates of the coarsely grained
phase-space densities of galaxies, f'=rho_s/(sigma_R sigma_phi sigma_z), where
rho_s is stellar density and sigma_R, sigma_phi, sigma_z are the radial,
tangential, and vertical rms velocities of stars. Using high-resolution N-body
simulations, we study the evolution of f' in discs of Galaxy-size models.
During the secular evolution, the discs, which are embedded in live CDM haloes,
form a bar and then a thick, dynamically hot, central mass concentration. In
the course of evolution f' declines at all radii, not just in the central
region. However, the decline is different in different parts of the disc. In
the inner disc, f'(R) develops a valley with a minimum around the end of the
central mass concentration. The final result is that the values of f' in the
central regions are significantly larger than those in the inner disc. The
minimum, which gets deeper with time, seems to be due to a large phase mixing
produced by the outer bar. We find that the shape and the amplitude of f'(R)
for different simulations agree qualitatively with the observed f'(R) in our
Galaxy. Curiously enough, the fact that the coarsely grained phase-space
density of the bulge is significantly larger than the one of the inner disc
turns out to be an argument in favor of secular formation of bulges, not
against it.


  We study solutions of type IIB string theory dual to ${\cal N}=4$
supersymmetric Yang-Mills theory on half of $\mathbb{R}^{3,1}$ coupled to
holographic three-dimensional superconformal field theories (SCFTs) at the edge
of this half-space. The dual geometries are asymptotically $AdS^5 \times S^5$
with boundary geometry $\mathbb{R}^{2,1} \times \mathbb{R}^+$, with a
geometrical end-of-the-world (ETW) brane cutting off the other half of the
asymptotic region of the would-be Poincar\'e $AdS^5 \times S^5$. We show that
by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily
far towards the missing asymptotic region, recovering the "missing" half of
Poincar\'e $AdS^5 \times S^5$. We also show that there are 3D SCFTs whose dual
includes a wedge of Poincar\'e $AdS^5 \times S^5$ with an angle arbitrarily
close to $\pi$, with geometrical ETW branes on either side.


  It is well known that the completeness theorem for
$\mathrm{L}_{\omega_1\omega}$ fails with respect to Tarski semantics. Mansfield
showed that it holds for $\mathrm{L}_{\infty\infty}$ if one replaces Tarski
semantics with boolean valued semantics. We use forcing to improve his result
in order to obtain a stronger form of boolean completeness (but only for
$\mathrm{L}_{\infty\omega}$). Leveraging on our completeness result, we
establish the Craig interpolation property and a strong version of the omitting
types theorem for $\mathrm{L}_{\infty\omega}$ with respect to boolean valued
semantics. We also show that a weak version of these results holds for
$\mathrm{L}_{\infty\infty}$ (if one leverages instead on Mansfield's
completeness theorem). Furthermore we bring to light (or in some cases just
revive) several connections between the infinitary logic
$\mathrm{L}_{\infty\omega}$ and the forcing method in set theory.


  Four-dimensional cylindrically symmetric spacetimes with homothetic
self-similarity are studied in the context of Einstein's Theory of Gravity, and
a class of exact solutions to the Einstein-massless scalar field equations is
found. Their local and global properties are investigated and found that they
represent gravitational collapse of a massless scalar field. In some cases the
collapse forms black holes with cylindrical symmetry, while in the other cases
it does not. The linear perturbations of these solutions are also studied and
given in closed form. From the spectra of the unstable eigen-modes, it is found
that there exists one solution that has precisely one unstable mode, which may
represent a critical solution, sitting on a boundary that separates two
different basins of attraction in the phase space.


  We introduce a new algorithm called {\sc Rec-Gen} for reconstructing the
genealogy or \textit{pedigree} of an extant population purely from its genetic
data. We justify our approach by giving a mathematical proof of the
effectiveness of {\sc Rec-Gen} when applied to pedigrees from an idealized
generative model that replicates some of the features of real-world pedigrees.
Our algorithm is iterative and provides an accurate reconstruction of a large
fraction of the pedigree while having relatively low \emph{sample complexity},
measured in terms of the length of the genetic sequences of the population. We
propose our approach as a prototype for further investigation of the pedigree
reconstruction problem toward the goal of applications to real-world examples.
As such, our results have some conceptual bearing on the increasingly important
issue of genomic privacy.


  We discuss a model of motion of substance through the nodes of a channel of a
network. The channel can be modeled by a chain of urns where each urn can
exchange substance with the neighboring urns. In addition the urns can exchange
substance with the network nodes and the new point is that we include in the
model the possibility for exchange of substance among the urns (nodes) and the
environment of the network. We consider stationary regime of motion of
substance through a finite channel (stationary regime of exchange of substance
along the chain of urns) and obtain a class of statistical distributions of
substance in the nodes of the channel. Our attention is focused on this class
of distributions and we show that for the case of finite channel the obtained
class of distributions contains as particular cases truncated versions of the
families of distributions of Katz, Ord, Kemp, etc. The theory for the case of
infinite chain of urns is presented in the Appendix.


  Let ${\mathcal M}$ be a von Neumann algebra without central summands of type
$I_1$ and $\xi\in{\mathbb C}$ a scalar. It is shown that an additive map $L$ on
$\mathcal M$ satisfies $L(AB-\xi BA)=L(A)B-\xi BL(A)+L(B)A-\xi AL(B)$ whenever
$A,B\in{\mathcal M}$ with $AB=0$ if and only if one of the following statements
holds: (1) $\xi=1$, $L=\varphi+f$, where $\varphi$ is an additive derivation on
$\mathcal M$ and $f$ is an additive map from $\mathcal M$ into its center
vanishing on $[A,B]$ with $AB=0$; (2)
  $\xi=0$, $L(I)\in{\mathcal Z}({\mathcal M})$ and there exists an additive
derivation $\varphi$ such that $L(A)=\varphi(A)+L(I)A$ for all $A$; (3)
$\xi=-1$, $L$ is a Jordan derivation; (4) $\xi$ is rational and $\xi\not=0,
\pm1$, $L$ is an additive derivation; (5) $\xi$ is not rational, there exists
an additive derivation $\varphi$ satisfying $\varphi(\xi I)=\xi L(I)$ such that
$L(A)=\varphi(A) + L(I)A$ for all $A \in{\mathcal M}$. A linear map $L$ on
$\mathcal M$ satisfies $L(AB-\xi BA)=L(A)B-\xi BL(A)+L(B)A-\xi AL(B)$ whenever
$A,B\in{\mathcal M}$ with $AB=0$ if and only if there exists a $T\in\mathcal M$
and a linear map $f:{\mathcal M}\rightarrow{\mathcal Z}({\mathcal M})$
vanishing on $[A,B]$ with $AB=0$ such that (i) $\xi=1$, $L(A)=AT-TA+f(A)$ for
all $A\in\mathcal M$; (ii) $\xi=0$, $L(I)\in{\mathcal Z}({\mathcal M})$ and
$L(A)=AT-(T-L(I))A$ for all $A\in{\mathcal M}$; (iii) $\xi\not=0,1$,
$L(A)=AT-TA$ for all $A \in{\mathcal M}$.


  We focus on the following natural question: is it possible to influence the
outcome of a voting process through the strategic provision of information to
voters who update their beliefs rationally? We investigate whether it is
computationally tractable to design a signaling scheme maximizing the
probability with which the sender's preferred candidate is elected. We focus on
the model recently introduced by Arieli and Babichenko (2019) (i.e., without
inter-agent externalities), and consider, as explanatory examples, $k$-voting
rule and plurality voting. There is a sharp contrast between the case in which
private signals are allowed and the more restrictive setting in which only
public signals are allowed. In the former, we show that an optimal signaling
scheme can be computed efficiently both under a $k$-voting rule and plurality
voting. In establishing these results, we provide two general (i.e., applicable
to settings beyond voting) contributions. Specifically, we extend a well known
result by Dughmi and Xu (2017) to more general settings, and prove that, when
the sender's utility function is anonymous, computing an optimal signaling
scheme is fixed parameter tractable w.r.t. the number of receivers' actions. In
the public signaling case, we show that the sender's optimal expected return
cannot be approximated to within any factor under a $k$-voting rule. This
negative result easily extends to plurality voting and problems where utility
functions are anonymous.


  Wireless sensor networks take a major part in our everyday lives by enhancing
systems for home automation, healthcare, temperature control, energy
consumption monitoring, and so forth. In this paper we focus on a system used
for temperature regulation for residential, educational, industrial, and
commercial premises, and so forth. We propose a framework for indoor
temperature regulation and optimization using wireless sensor networks based on
ZigBee platform. This paper considers architectural design of the system, as
well as implementation guidelines. The proposed system favors methods that
provide energy savings by reducing the amount of data transmissions through the
network. Furthermore, the framework explores techniques for localization, such
that the location of the nodes can be used by algorithms that regulate
temperature settings.


  In this paper, some points to the convergence analysis performed in the paper
[A new computing approach for power signal modeling using fractional adaptive
algorithms, ISA Transactions 68 (2017) 189-202] are presented. It is
highlighted that the way the authors prove convergence, suffers lack of correct
and valid mathematical justifications.


  We employ a fiber-based optical microcavity with high finesse to study the
enhancement of phonon sideband fluorescence of nitrogen-vacancy centers in
nanodiamonds. Harnessing the full tunability and open access of the resonator,
we explicitly demonstrate the scaling laws of the Purcell enhancement by
varying both the mode volume and the quality factor over a large range. While
changes in the emission lifetime remain small in the regime of a broadband
emitter, we observe an increase of the emission spectral density by up to a
factor of 300. This gives a direct measure of the Purcell factor that could be
achieved with this resonator and an emitter whose linewidth is narrower than
the cavity linewidth. Our results show a method for the realization of
wavelength-tunable narrow-band single-photon sources and demonstrate a system
that has the potential to reach the strong-coupling regime.


  The explanation of the small neutrino mass can be depicted using some
handsome models like type-I and inverse seesaw where the Standard Model gauge
singlet heavy right handed neutrinos are deployed. The common thing in these
two models is a lepton number violating parameter, however, its order of
magnitude creates a striking difference between them making the nature of the
right handed heavy neutrinos a major play factor. In the type-I seesaw a large
lepton number violating parameter involves the heavy right handed neutrinos in
the form of Majorana fermions while a small lepton number violating parameter
being involved in the inverse seesaw demands the pseudo-Dirac nature of the
heavy right handed neutrinos. Such heavy neutrinos are accommodated in these
models through the sizable mixings with the Standard Model light neutrinos. In
this paper we consider the purely inverse seesaw scenario to study the pair
production of the pseudo-Dirac heavy neutrinos followed by their various
multilepton decay modes through the leading branching fraction at the Leading
Order and Next-to-Leading Order QCD at the LHC with a center of mass energy of
13 TeV and a luminosity of 3000 fb$^{-1}$. We also consider a prospective 100
TeV hadron collider with luminosities of 3000 fb$^{-1}$ and 30000 fb$^{-1}$
respectively to study the process. Using anomalous multilepton search performed
by the CMS at the 8 TeV with 19.5 fb$^{-1}$ luminosity we show prospective
search reaches of the mixing angles for the three lepton and four lepton events
at the 13 TeV LHC and 100 TeV hadron collider.


  HCI increasingly employs Machine Learning and Image Recognition, in
particular for visual analysis of user interfaces (UIs). A popular way for
obtaining human-labeled training data is Crowdsourcing, typically using the
quality control methods ground truth and majority consensus, which necessitate
redundancy in the outcome. In our paper we propose a non-redundant method for
prediction of crowdworkers' output quality in web UI labeling tasks, based on
homogeneity of distributions assessed with two-sample Kolmogorov-Smirnov test.
Using a dataset of about 500 screenshots with over 74,000 UI elements located
and classified by 11 trusted labelers and 298 Amazon Mechanical Turk
crowdworkers, we demonstrate the advantage of our approach over the baseline
model based on mean Time-on-Task. Exploring different dataset partitions, we
show that with the trusted set size of 17-27% UIs our "distributional ground
truth" model can achieve R2s of over 0.8 and help to obviate the ancillary work
effort and expenses.


  We prove that there are rational homology balls $B_p$ smoothly embedded in
the $2$-handlebodies associated to certain knots. Furthermore we show that, if
we rationally blow up the $2$-handlebody along the embedded rational homology
ball $B_p$, then the resulting $4$-manifold cannot be obtained just by a
sequence of ordinary blow ups from the $2$-handlebody under a certain mild
condition.


  When building state-of-the-art speech translation models, the need for large
computational resources is a significant obstacle due to the large training
data size and complex models. The availability of pre-trained models is a
promising opportunity to build strong speech translation systems efficiently.
In a first step, we investigate efficient strategies to build cascaded and
end-to-end speech translation systems based on pre-trained models. Using this
strategy, we can train and apply the models on a single GPU. While the
end-to-end models show superior translation performance to cascaded ones, the
application of this technology has a limitation on the need for additional
end-to-end training data. In a second step, we proposed an additional
similarity loss to encourage the model to generate similar hidden
representations for speech and transcript. Using this technique, we can
increase the data efficiency and improve the translation quality by 6 BLEU
points in scenarios with limited end-to-end training data.


  Suppose that $\Omega = \{0, 1\}^ {\mathbb {N}}$ and $ {\sigma}$ is the
one-sided shift. The Birkhoff spectrum $ \displaystyle S_{f}(
{\alpha})=\dim_{H}\Big \{ {\omega}\in {\Omega}:\lim_{N \to \infty} \frac{1}{N}
\sum_{n=1}^N f(\sigma^n \omega) = \alpha \Big \},$ where $\dim_{H}$ is the
Hausdorff dimension. It is well-known that the support of $S_{f}( {\alpha})$ is
a bounded and closed interval $L_f = [\alpha_{f, \min}^*, \alpha_{f, \max}^*]$
and $S_{f}( {\alpha})$ on $L_{f}$ is concave and upper semicontinuous. We are
interested in possible shapes/properties of the spectrum, especially for
generic/typical $f\in C( {\Omega})$ in the sense of Baire category. For a dense
set in $C( {\Omega})$ the spectrum is not continuous on $ {\mathbb {R}}$,
though for the generic $f\in C( {\Omega})$ the spectrum is continuous on $
{\mathbb {R}}$, but has infinite one-sided derivatives at the endpoints of
$L_{f}$. We give an example of a function which has continuous $S_{f}$ on $
{\mathbb {R}}$, but with finite one-sided derivatives at the endpoints of
$L_{f}$. The spectrum of this function can be as close as possible to a
"minimal spectrum". We use that if two functions $f$ and $g$ are close in $C(
{\Omega})$ then $S_{f}$ and $S_{g}$ are close on $L_{f}$ apart from
neighborhoods of the endpoints.


  We study the asymptotics of the higher dimensional Reidemeister torsion for
torus knot exteriors, which is related to the results by W. M\"uller and P.
Menal-Ferrer and J. Porti on the asymptotics of the Reidemeister torsion and
the hyperbolic volumes for hyperbolic 3-manifolds. We show that the sequence of
log |the higher dimensional Reidemeister torsion of a torus knot exterior with
SL(2N,C)-representation| / (2N)^2 converges to zero when N goes to infinity. We
also give a classification for SL(2,C)-representations of torus knot groups,
which induce acyclic SL(2N,C)-representations.


  We study the specific dependence of the periodic Anderson Model (PAM) in the
limit of $U=\infty$ employing the X-boson treatment in two fifferent regimes of
the PAM: the heavy fermion Kondo (HF-K) and the heavy fermion local magnetic
regime (HF-LMM). We obtain a multiple peak structure for the specific heat in
agreement with experimental results as well as the increase of the electronic
effective mass at low temperatures associated with the HF-K regime. The entropy
per site at low T tends to zero in the HF-K regime, corresponding to a singlet
ground state, and it tends to $k_{B}ln(2)$ in the HF-LMM, corresponding to a
doublet ground state at each site. The linear coefficient $\gamma(T)=C_{v}/T$
of the specific heat qualitatively agrees with the experimental results
obtained for differents materials in the two regimes considered here.


  In classical thermodynamics, irreversible processes are accomplished with an
increase of entropy and a release of heat into the environment. In the case of
black hole thermodynamics, instead, the increase of entropy is related with the
absorption of energy from the outside of the black hole. Based on this analogy,
the black hole is considered as a thermodynamic open system in the
non-equilibrium regime during the absorption. Applying a novel result, we
obtain a detailed balance relation for the macroscopic absorption of an
astronomical object by an static spherically symmetric black hole. Because of
the special characteristic of the thermodynamic system, it is necessary to
include an additional term for the entropy produced by the absorption, allowing
us to set a lower bound for the entropy production due to internal processes
associated to the fluctuation.


  A. R\'enyi \cite{Renyi} made a definition that gives a generalization of
simple normality in the context of $Q$-Cantor series. In \cite{Mance}, a
definition of $Q$-normality was given that generalizes the notion of normality
in the context of $Q$-Cantor series. In this work, we examine both
$Q$-normality and $Q$-distribution normality, treated in \cite{Laffer} and
\cite{Salat}. Specifically, while the non-equivalence of these two notions is
implicit in \cite{Laffer}, in this paper, we give an explicit construction
witnessing the nontrivial direction. That is, we construct a base $Q$ as well
as a real $x$ that is $Q$-normal yet not $Q$-distribution normal. We next
approach the topic of simultaneous normality by constructing an explicit
example of a base $Q$ as well as a real $x$ that is both $Q$-normal and
$Q$-distribution normal.


  In this article we consider $SU(2)$ Chern-Simons/Higgs theory coupled to
gravity in three-dimensions. It is shown that for a cylindrically symmetric
vortex both the Einstein equations and the field equations can be reduced to a
set of first-order Bogomol'nyi equations provided that we choose a specific
eighth-order potential.


  We establish new estimates for the constant $J_a(k,\alpha)$ in the
Brudnyi-Jackson inequality for approximation of $f \in C[-1,1]$ by algebraic
polynomials:
  $$ E_{n}^a (f) \le J_a(k, \alpha) \ \omega_k (f, \alpha \pi /n ), \quad
\alpha >0 $$
  The main result of the paper implies the following inequalities
  $$ 1/2< J_a (2k, \alpha) < 10, \quad n \ge 2k(2k-1), \quad
  \alpha \ge 2 $$


  We develop a new 1D photochemical kinetics code to address stratospheric
chemistry and stratospheric heating in hot Jupiters. Here we address optically
active S-containing species and CO2 at 1200 < T < 2000 K. HS (mercapto) and S2
are highly reactive species that are generated photochemically and
thermochemically from H2S with peak abundances between 1-10 mbar. S2 absorbs UV
between 240 and 340 nm and is optically thick for metallicities [SH] > 0 at T >
1200 K. HS is probably more important than S2, as it is generally more abundant
than S2 under hot Jupiter conditions and it absorbs at somewhat redder
wavelengths. We use molecular theory to compute an HS absorption spectrum from
sparse available data and find that HS should absorb strongly between 300 and
460 nm, with absorption at the longer wavelengths being temperature sensitive.
When the two absorbers are combined, radiative heating (per kg of gas) peaks at
100 microbars, with a total stratospheric heating of about 8 x 10^4 W/m^2 for a
jovian planet orbiting a solar-twin at 0.032 AU. Total heating is insensitive
to metallicity. The CO2 mixing ratio is a well-behaved quadratic function of
metallicity, ranging from 1.6 x 10^-8 to 1.6 x 10^-4 for -0.3 < [M/H] < 1.7.
CO2 is insensitive to insolation, vertical mixing, temperature (1200 < T <2000
K), and gravity. The photochemical calculations confirm that CO2 should prove a
useful probe of planetary metallicity.


  Diacritical marks play a crucial role in meeting the criteria of usability of
typographic text, such as: homogeneity, clarity and legibility. To change the
diacritic of a letter in a word could completely change its semantic. The
situation is very complicated with multilingual text. Indeed, the problem of
design becomes more difficult by the presence of diacritics that come from
various scripts; they are used for different purposes, and are controlled by
various typographic rules. It is quite challenging to adapt rules from one
script to another. This paper aims to study the placement and sizing of
diacritical marks in Arabic script, with a comparison with the Latin's case.
The Arabic script is cursive and runs from right-to-left; its criteria and
rules are quite distinct from those of the Latin script. In the beginning, we
compare the difficulty of processing diacritics in both scripts. After, we will
study the limits of Latin resolution strategies when applied to Arabic. At the
end, we propose an approach to resolve the problem for positioning and resizing
diacritics. This strategy includes creating an Arabic font, designed in
OpenType format, along with suitable justification in TEX.


  The increasing use of autonomous robot systems in hazardous environments
underscores the need for efficient search and rescue operations. Despite
significant advancements, existing literature on object search often falls
short in overcoming the difficulty of long planning horizons and dealing with
sensor limitations, such as noise. This study introduces a novel approach that
formulates the search problem as a belief Markov decision processes with
options (BMDP-O) to make Monte Carlo tree search (MCTS) a viable tool for
overcoming these challenges in large scale environments. The proposed
formulation incorporates sequences of actions (options) to move between regions
of interest, enabling the algorithm to efficiently scale to large environments.
This approach also enables the use of customizable fields of view, for use with
multiple types of sensors. Experimental results demonstrate the superiority of
this approach in large environments when compared to the problem without
options and alternative tools such as receding horizon planners. Given compute
time for the proposed formulation is relatively high, a further approximated
"lite" formulation is proposed. The lite formulation finds objects in a
comparable number of steps with faster computation.


  We present two protocols for classical verification of quantum depth. Our
protocols allow a purely classical verifier to distinguish devices with
different quantum circuit depths even in the presence of classical computation.
We show that a device with quantum circuit depth at most d will be rejected by
the verifier even if the prover applies additional polynomial-time classical
computation to cheat. On the other hand, the verifier accepts a device which
has quantum circuit depth d' for some d'>d. In our first protocol, we introduce
an additional untrusted quantum machine which shares entanglements with the
target machine. Applying a robust self-test, our first protocol certifies the
depth of the target machine with information theoretic security and nearly
optimal separation. The protocol relies on the oracle separation problem for
quantum depth by Chia, Chung and Lai [STOC 2020] and a transformation from an
oracle separation problem to a two-player non-local game. Our second protocol
certifies the quantum depth of a single device based on quantum hardness of
learning with errors. The protocol relies on the noisy trapdoor claw-free
function family and the idea of pointer chasing to force the prover to keep
quantum coherence until all preceding message exchanges are completed. To our
knowledge, we give the first constructions for distinguishing hybrid
quantum-classical computers with different circuit depths in unrelativized
models.


  This paper theoretically proposes a multichannel functional metasurface
computer characterized by Generalized Sheet Transition Conditions (GSTCs) and
surface susceptibility tensors. The study explores a polarization- and
angle-multiplexed metasurfaces enabling multiple and independent parallel
analog spatial computations when illuminated by differently polarized incident
beams from different directions. The proposed synthesis overcomes substantial
restrictions imposed by previous designs such as large architectures arising
from the need of additional subblocks, slow responses, and most importantly,
supporting only the even reflection symmetry operations for normal incidences,
working for a certain incident angle or polarization, and executing only single
mathematical operation. The versatility of the design is demonstrated in a way
that an ultra-compact, integrable and planar metasurface-assisted platform can
execute a variety of optical signal processing operations such as spatial
differentiation and integration. It is demonstrated that a metasurface
featuring non-reciprocal property can be thought of as a new paradigm to break
the even symmetry of reflection and perform both even- and odd-symmetry
mathematical operations at normal incidences. Numerical simulations also
illustrate different aspects of multichannel edge detection scheme through
projecting multiple images on the metasurface from different directions. Such
appealing findings not only circumvent the major potential drawbacks of
previous designs but also may offer an efficient, easy-to-fabricate, and
flexible approach in wave-based signal processing, edge detection, image
contrast enhancement, hidden object detection, and equation solving without any
Fourier lens.


  Means to increase water resources are essential in regions grappling with
water scarcity and growing populations. Soil aquifer treatment (SAT) is a
cheap, low maintenance, low-energy method to supply water for irrigation of
crops consumed raw or even for drinking purposes. However, the most expensive
cost-component of SATs is the land use, the infiltration basins the area of
which is inversely proportional to the infiltration rate, the most important
characteristic of SAT basins design and operation, which until now was believed
to be time-dependent and, therefore, difficult to predict. Focusing on the
Shafdan SAT in Israel as a showcase and using a decade's worth of data from 50
recharge basins, we study the time dependence of the infiltration rates. The
study reveals a noteworthy consistency in the decline of effluent levels during
the drainage phase across various flooding events, signifying a constant,
head-independent infiltration rate. 97% of over 40,000 flooding events showed
this behavior. Furthermore, the infiltration rate calculated in this manner
provides good predictions of the average infiltration rate during the entire
wetting phase.
  The water-level-independent infiltration rate is a general feature. It was
found in all the 50 studied basins, regardless of the soil sand content,
commissioning year, operation conditions and season. The constant infiltration
rate law revealed in this study simplifies the prediction of the flooding cycle
duration and will facilitate simplified predictive modeling of multiple basins
SAT systems. Our research may extend beyond SAT systems, offering insights
applicable to other managed aquifer recharge methods, crucial for effective
water resource management, ensuring environmental compatibility.


  For an integer $m\geq 1$, a combinatorial manifold $\widetilde{M}$ is defined
to be a geometrical object $\widetilde{M}$ such that for $\forall
p\in\widetilde{M}$, there is a local chart $(U_p,\phi_p)$ enable $\phi_p:U_p\to
B^{n_{i_1}}\bigcup B^{n_{i_2}}\bigcup...\bigcup B^{n_{i_{s(p)}}}$ with
$B^{n_{i_1}}\bigcap B^{n_{i_2}}\bigcap...\bigcap
B^{n_{i_{s(p)}}}\not=\emptyset$, where $B^{n_{i_j}}$ is an $n_{i_j}$-ball for
integers $1\leq j\leq s(p)\leq m$. Topological and differential structures such
as those of $d$-pathwise connected, homotopy classes, fundamental $d$-groups in
topology and tangent vector fields, tensor fields, connections, {\it Minkowski}
norms in differential geometry on these finitely combinatorial manifolds are
introduced. Some classical results are generalized to finitely combinatorial
manifolds. Euler-Poincare characteristic is discussed and geometrical
inclusions in Smarandache geometries for various geometries are also presented
by the geometrical theory on finitely combinatorial manifolds in this paper.


  Protein aggregation is of particular interest due to its connection with many
diseases and disorders. Many factors can alter the dynamics and result of this
process, one of them being the diffusivity of the monomers and aggregates in
the system. Here, we study experimentally and theoretically an aggregation
process in cells, and we identify two distinct physical timescales that set the
number and size of aggregates. The first timescale involves fast aggregation of
small clusters freely diffusing in the cytoplasm, while, in the second one, the
aggregates are larger than the pore size of the cytoplasm and thus barely
diffuse, and the aggregation process is slowed down. However, the process is
not entirely halted, potentially reflecting a myriad of active but random
forces forces that stir the aggregates. Such slow timescale is essential to
account for the experimental results of the aggregation process. These results
could also have implications in other processes of spatial organization in cell
biology, such as phase-separated droplets.


  The electronic and magnetic properties of zigzag graphene nanoribbons with
asymmetric notches along their edges are investigated by first principle
density functional theory calculations. It is found that the electronic and
magnetic properties of the asymmetrically-notched graphene nanoribbons are
closely related with the depth of notches, but weekly dependent on the length
of notches. As the relative depth of notch increases, the energy level of
spin-up and spin-down becomes greatly shifted, associated with the gradual
increase of magnetic momentum. The asymmetric band shift allows the
asymmetrically notched graphene nanoribbons to be a spintronic semiconductor,
through which an N- or P-type spin-semiconductor can be obtained by doping B or
N atoms.


  Game theory is the mathematical framework for analyzing strategic
interactions in conflict and competition situations. In recent years quantum
game theory has earned the attention of physicists, and has emerged as a branch
of quantum information theory [1]. With the aid of entanglement and linear
superposition of strategies, quantum games are shown to yield signifcant
advantage over their classical counterparts. In this paper we explore optimal
and equilibrium solutions to quantum minority games. Initial states with
different level of entanglement are investigated. Focus will be on 4 and 6
player games with some N-player generalizations.


  We perform a detailed comparison of next-to-next-to-leading order (NNLO) QCD
predictions for the W+jet and Z+jet processes with 7 TeV experimental data from
ATLAS and CMS. We observe excellent agreement between theory and data for most
studied observables, which span several orders of magnitude in both cross
section and energy. For some observables, such as the $H_T$ distribution, the
NNLO QCD corrections are essential for resolving existing discrepancies between
theory and data.


  There are four division algebras over $\mathbb{R}$, namely real numbers,
complex numbers, quaternions, and octonions. Lack of commutativity and
associativity make it difficult to investigate algebraic and geometric
properties of octonions. It does not make sense to ask, for example, whether
the equation $x^2+1=0$ is solvable, without specifying the field in which we
want the solutions to be lie. The equation $x^2+1=0$ has no solutions in
$\mathbb{R}$, which is to say, there are no real numbers satisfying this
equation. On the other hand, there are complex numbers which do satisfy this
equation in the field $\mathbb{C}$ of all complex numbers. How about if we
extend the same idea to other two normed division algebras quaternions and
octonions. Liping Huang and Wasin So derive explicit formulas for computing the
roots of quaternionic quadratic equations. We extend their work to octonionic
case and solve monic left octonionic quadratic equation of the form
$x^2+bx+c=0$, where $a,b$ are octonions in general.[ We called this form of
quadratic equation as left octonion quadratic equation because we can consider
$x^2+xb+c=0$ as a different case due to non-commutativity of octonions].
Finally, we represent the left spectrum of $2\times2$ octonionic matrix as a
set of solutions to a corresponding octonionic quadratic equation, which is an
application of deriving explicit formulas for computing the roots of octonionic
quadratic equations.


  McCammond and Wise have introduced the perimeter of 2-complexes, and they
have used it to obtain a sufficient criterion for coherence. We present a new
exposition of their main result, as well as some applications.


  In this paper, we deal with the solutions of systems of PDEs with bilateral
inter-connected obstacles of min-max and max-min types. These systems arise
naturally in stochastic switching zero-sum game problems. We show that when the
switching costs of one side are regular, the solutions of the min-max and
max-min systems coincide. Then, this common viscosity solution is related to a
multi-dimensional doubly reflected BSDE with bilateral interconnected
obstacles. Finally, its relationship with the the values of a zero-sum
switching game is studied.


  Breast cancer ranks as the most prevalent form of cancer diagnosed in women,
and diagnosis faces several challenges, a change in the size, shape and
appearance of breasts, dense breast tissue, lumps or thickening in the breast
especially if in only one breast, lumps and nodules in the breast. The major
challenge that faces deep learning diagnosis of breast cancer was its shape,
size and position non-uniformity especially malignant cancer. This work
proposed a deep learning system that increased the accuracy of classification
of breast cancer types from ultrasound images. It reaches 99.29% accuracy,
exceeding other previous work. First, image processing was applied to in
enhance the quality of input images. Second, the image segmentation was
performed using U-Net architecture. Third, many features are extracted using
Mobilenet. Finally, the accuracy of proposed system was evaluated.


  Calculating the trace of the product of $m$ $n$-qubit density matrices
(multivariate trace) is a crucial subroutine in quantum error mitigation and
information measures estimation. We propose an unified multivariate trace
estimation (UMT) which conceptually unifies the previous qubit-optimal and
depth-optimal approaches with tunable quantum circuit depth and the number of
qubits. The constructed circuits have $\lceil(m-1)/s\rceil$ or
$n\lceil(m-1)/s\rceil$ depth corresponding to $(s+m)n$ or $s+mn$ qubits for
$s\in\{1,\cdots,\lfloor m/2\rfloor\}$, respectively. Such flexible circuit
structures enable people to choose suitable circuits according different
hardware devices. We apply UMT to virtual distillation for achieving
exponential error suppression and design a family of concrete circuits to
calculate the trace of the product of $8$ and $9$ $n$-qubit density matrices.
Numerical example shows that the additional circuits still mitigate the noise
expectation value under the global depolarizing channel.


  Within the conformally reduced gravity model, where the metric is
parametrised by a function $f(\phi)$ of the conformal factor $\phi$, we keep
dependence on both the background and fluctuation fields, to local potential
approximation and $\mathcal{O}(\partial^2)$ respectively, making no other
approximation. Explicit appearances of the background metric are then dictated
by realising a remnant diffeomorphism invariance. The standard non-perturbative
Renormalization Group (RG) scale $k$ is inherently background dependent, which
we show in general forbids the existence of RG fixed points with respect to
$k$. By utilising transformations that follow from combining the flow equations
with the modified split Ward identity, we uncover a unique background
independent notion of RG scale, $\hat k$. The corresponding RG flow equations
are then not only explicitly background independent along the entire RG flow
but also explicitly independent of the form of $f$. In general $f(\phi)$ is
forced to be scale dependent and needs to be renormalised, but if this is
avoided then $k$-fixed points are allowed and furthermore they coincide with
$\hat k$-fixed points.


  Matrix weighted rational B\'{e}zier curves can represent complex curve shapes
using small numbers of control points and clear geometric definitions of matrix
weights. Explicit formulae are derived to convert matrix weighted rational
B\'{e}zier curves in 2D or 3D space to rational B\'{e}zier curves. A method for
computing the convex hulls of matrix weighted rational B\'{e}zier curves is
given as a conjecture.


  The nonequilibrium dynamic phase transition, in the kinetic Ising model in
presence of an oscillating magnetic field, has been studied by Monte Carlo
simulation. The fluctuation of dynamic order parameter has been studied as a
function of temperature near the dynamic transition point. The temperature
variation of appropriately defined `susceptibility' has also been studied near
the dynamic transition point. Similarly, fluctuation of energy and
appropriately defined `specific-heat' have been studied as a function of
temperature near the dynamic transition point. In both the cases, the
fluctuations (of dynamic order parameter and energy) and the corresponding
responses diverge (as power law fashion) near the dynamic transition point with
similar critical behavior (with identical exponent values).


  Deep reinforcement learning (DRL) is poised to revolutionise the field of
artificial intelligence (AI) by endowing autonomous systems with high levels of
understanding of the real world. Currently, deep learning (DL) is enabling DRL
to effectively solve various intractable problems in various fields. Most
importantly, DRL algorithms are also being employed in audio signal processing
to learn directly from speech, music and other sound signals in order to create
audio-based autonomous systems that have many promising application in the real
world. In this article, we conduct a comprehensive survey on the progress of
DRL in the audio domain by bringing together the research studies across
different speech and music-related areas. We begin with an introduction to the
general field of DL and reinforcement learning (RL), then progress to the main
DRL methods and their applications in the audio domain. We conclude by
presenting challenges faced by audio-based DRL agents and highlighting open
areas for future research and investigation.


  We present a simple model to study micellization of amphiphiles condensed on
a rodlike polyion. Although the mean field theory leads to a first order
micellization transition for sufficiently strong hydrophobic interactions, the
simulations show that no such thermodynamic phase transition exists. Instead,
the correlations between the condensed amphiphiles can result in a structure
formation very similar to micelles.


  A novel algorithm was recently presented to utilize emerging time dependent
probability density data to extract molecular potential energy surfaces. This
paper builds on the previous work and seeks to enhance the capabilities of the
extraction algorithm: An improved method of removing the generally ill-posed
nature of the inverse problem is introduced via an extended Tikhonov
regularization and methods for choosing the optimal regularization parameters
are discussed. Several ways to incorporate multiple data sets are investigated,
including the means to optimally combine data from many experiments exploring
different portions of the potential. Results are presented on the stability of
the inversion procedure, including the optimal combination scheme, under the
influence of data noise. The method is applied to the simulated inversion of a
double well system.


  Sparse coding is a core building block in many data analysis and machine
learning pipelines. Typically it is solved by relying on generic optimization
techniques, that are optimal in the class of first-order methods for
non-smooth, convex functions, such as the Iterative Soft Thresholding Algorithm
and its accelerated version (ISTA, FISTA). However, these methods don't exploit
the particular structure of the problem at hand nor the input data
distribution. An acceleration using neural networks was proposed in
\cite{Gregor10}, coined LISTA, which showed empirically that one could achieve
high quality estimates with few iterations by modifying the parameters of the
proximal splitting appropriately.
  In this paper we study the reasons for such acceleration. Our mathematical
analysis reveals that it is related to a specific matrix factorization of the
Gram kernel of the dictionary, which attempts to nearly diagonalise the kernel
with a basis that produces a small perturbation of the $\ell_1$ ball. When this
factorization succeeds, we prove that the resulting splitting algorithm enjoys
an improved convergence bound with respect to the non-adaptive version.
Moreover, our analysis also shows that conditions for acceleration occur mostly
at the beginning of the iterative process, consistent with numerical
experiments. We further validate our analysis by showing that on dictionaries
where this factorization does not exist, adaptive acceleration fails.


  Open-World Compositional Zero-shot Learning (OW-CZSL) aims to recognize novel
compositions of state and object primitives in images with no priors on the
compositional space, which induces a tremendously large output space containing
all possible state-object compositions. Existing works either learn the joint
compositional state-object embedding or predict simple primitives with separate
classifiers. However, the former heavily relies on external word embedding
methods, and the latter ignores the interactions of interdependent primitives,
respectively. In this paper, we revisit the primitive prediction approach and
propose a novel method, termed Progressive Cross-primitive Compatibility
(ProCC), to mimic the human learning process for OW-CZSL tasks. Specifically,
the cross-primitive compatibility module explicitly learns to model the
interactions of state and object features with the trainable memory units,
which efficiently acquires cross-primitive visual attention to reason
high-feasibility compositions, without the aid of external knowledge. Moreover,
considering the partial-supervision setting (pCZSL) as well as the imbalance
issue of multiple task prediction, we design a progressive training paradigm to
enable the primitive classifiers to interact to obtain discriminative
information in an easy-to-hard manner. Extensive experiments on three widely
used benchmark datasets demonstrate that our method outperforms other
representative methods on both OW-CZSL and pCZSL settings by large margins.


  Dynamic operation of biological processes, such as anaerobic digestion (AD),
requires reliable process monitoring to guarantee stable operating conditions
at all times. Unscented Kalman filters (UKF) are an established tool for
nonlinear state estimation, and there exist numerous variants of UKF
implementations, treating state constraints, improvements of numerical
performance and different noise cases. So far, however, a unified comparison of
proposed methods emphasizing the algorithmic details is lacking. The present
study thus examines multiple unconstrained and constrained UKF variants,
addresses aspects crucial for direct implementation and applies them to a
simplified AD model. The constrained UKF considering additive noise delivered
the most accurate state estimations. The long run time of the underlying
optimization could be vastly reduced through pre-calculated gradients and
Hessian of the associated cost function, as well as by reformulation of the
cost function as a quadratic program. However, unconstrained UKF variants
showed lower run times at competitive estimation accuracy. This study provides
useful advice to practitioners working with nonlinear Kalman filters by paying
close attention to algorithmic details and modifications crucial for successful
implementation.