  Cognitive radio technology is an innovative radio design concept which aims
to increase spectrum utilization by exploiting unused spectrum in dynamically
changing environments. By extending previous results, we investigate the
capacity gains achievable with this dynamic spectrum approach in asymmetric
fading channels. More specifically, we allow the secondary-to-primary and
secondary-to-secondary user channels to undergo Rayleigh or Rician fading, with
arbitrary link power. In order to compute the capacity, we derive the
distributions of ratios of Rayleigh and Rician variables. Compared to the
symmetric fading scenario, our results indicate several interesting features of
the capacity behaviour under both average and peak received power constraints.
Finally, the impact of multiple primary users on the capacity under asymmetric
fading has also been studied.


  Spectroscopic observations for a new survey of 250 000 galaxy redshifts are
underway, using the 2dF instrument at the AAT. The input galaxy catalogue and
commissioning data are described. The first result from the preliminary data is
a new estimate of the galaxy luminosity function at <z>=0.1.


  Optical/UV photons and even harder radiation components in galaxies are
absorbed and scattered by dust and re-emitted at infrared wavelengths. For a
better understanding of the obscured regions of the galaxies detailed models of
the interaction of photons with dust grains and the propagation of light are
required. A problem which can only be solved by means of numerical solution of
the radiative transfer equation. As a prologue we present high angular mid IR
observations of galactic nuclei in the spirit of future ELT instrumentation.
Dust models are discussed, which are suited to fit the extinction curves and
relevant to compute the emission of external galaxies. Self-consistent
radiative transfer models have been presented in spherical symmetry for
starburst nuclei, in two dimensions for disk galaxies (spirals) and, more
recently, in three dimensional configuration of the dust density distribution.
For the latter, a highlighting example is the clumpy dust tori around AGN.
Modern advances in the field are reviewed which are either based on a more
detailed physical picture or progress in computational sciences.


  The p-type doping efficiency of 4H silicon carbide (4H-SiC) is rather low due
to the large ionization energies of p-type dopants. Such an issue impedes the
exploration of the full advantage of 4H-SiC for semiconductor devices. In this
letter, we show that co-doping group-IVB elements effectively decreases the
ionization energy of the most widely used p-type dopant, i. e., aluminum (Al),
through the Coulomb repulsion between the energy levels of group-IVB elements
and that of Al in 4H-SiC. Among group-IVB elements Ti has the most prominent
effectiveness. Ti decreases the ionization energy of Al by nearly 50%, leading
to a value as low as ~ 0.13 eV. As a result, the ionization rate of Al with Ti
co-doping is up to ~ 5 times larger than that without co-doping at room
temperature when the doping concentration is up to 1018 cm-3. This work may
encourage the experimental co-doping of group-IB elements such as Ti and Al to
significantly improve the p-type doping efficiency of 4H-SiC.


  The foremost challenge to causal inference with real-world data is to handle
the imbalance in the covariates with respect to different treatment options,
caused by treatment selection bias. To address this issue, recent literature
has explored domain-invariant representation learning based on different domain
divergence metrics (e.g., Wasserstein distance, maximum mean discrepancy,
position-dependent metric, and domain overlap). In this paper, we reveal the
weaknesses of these strategies, i.e., they lead to the loss of predictive
information when enforcing the domain invariance; and the treatment effect
estimation performance is unstable, which heavily relies on the characteristics
of the domain distributions and the choice of domain divergence metrics.
Motivated by information theory, we propose to learn the Infomax and
Domain-Independent Representations to solve the above puzzles. Our method
utilizes the mutual information between the global feature representations and
individual feature representations, and the mutual information between feature
representations and treatment assignment predictions, in order to maximally
capture the common predictive information for both treatment and control
groups. Moreover, our method filters out the influence of instrumental and
irrelevant variables, and thus it effectively increases the predictive ability
of potential outcomes. Experimental results on both the synthetic and
real-world datasets show that our method achieves state-of-the-art performance
on causal effect inference. Moreover, our method exhibits reliable prediction
performances when facing data with different characteristics of data
distributions, complicated variable types, and severe covariate imbalance.


  We study information gathering in ad-hoc radio networks. Initially, each node
of the network has a piece of information called a rumor, and the overall
objective is to gather all these rumors in the designated target node. The
ad-hoc property refers to the fact that the topology of the network is unknown
when the computation starts. Aggregation of rumors is not allowed, which means
that each node may transmit at most one rumor in one step.
  We focus on networks with tree topologies, that is we assume that the network
is a tree with all edges directed towards the root, but, being ad-hoc, its
actual topology is not known. We provide two deterministic algorithms for this
problem. For the model that does not assume any collision detection nor
acknowledgement mechanisms, we give an $O(n\log\log n)$-time algorithm,
improving the previous upper bound of $O(n\log n)$. We also show that this
running time can be further reduced to $O(n)$ if the model allows for
acknowledgements of successful transmissions.


  This is the first of a two part paper investigating the geometry of the
integrator reach sets, and the applications thereof. In this Part I, assuming
box-valued input uncertainties, we establish that this compact convex reach set
is semialgebraic, translated zonoid, and not a spectrahedron. We derive the
parametric as well as the implicit representation of the boundary of this reach
set. We also deduce the closed form formula for the volume and diameter of this
set, and discuss their scaling with state dimension and time. We point out that
these results may be utilized in benchmarking the performance of the reach set
over-approximation algorithms.


  We prove the irreducibility of moduli spaces of rational curves on a general
del Pezzo threefold of Picard rank $1$ and degree $1$. As corollaries, we
confirm Geometric Manin's conjecture and enumerativity of certain Gromov-Witten
invariants for these threefolds.


  Clustering is a class of unsupervised learning methods that has been
extensively applied and studied in computer vision. Little work has been done
to adapt it to the end-to-end training of visual features on large scale
datasets. In this work, we present DeepCluster, a clustering method that
jointly learns the parameters of a neural network and the cluster assignments
of the resulting features. DeepCluster iteratively groups the features with a
standard clustering algorithm, k-means, and uses the subsequent assignments as
supervision to update the weights of the network. We apply DeepCluster to the
unsupervised training of convolutional neural networks on large datasets like
ImageNet and YFCC100M. The resulting model outperforms the current state of the
art by a significant margin on all the standard benchmarks.


  In this article we construct the Hamiltonian description of the closed vortex
filament dynamics in terms of non-standard variables, phase space and
constraints. The suggested approach makes obvious interpretation of considered
system as a quasiparticle that possess certain external and internal degrees of
the freedom. The constructed theory is invariant under the transformation of
Galilei group. The appearance of this group allows for a new viewpoint on the
energy of a closed vortex filament with zero thickness. The explicit formula
for the effective mass of the quasiparticle 'closed vortex filament' is
suggested.


  The study of word hyperbolic groups is a prominent topic in geometric group
theory; however word hyperbolic groups are defined by a geometric condition
which does not extend naturally to semigroups. We propose a linguistic
definition. Roughly speaking a semigroup is word hyperbolic if its
multiplication table is a context free language. For groups this definition is
equivalent to the original geometric one. We also briefly consider word
problems of semigroups.


  We study the group of volume-preserving diffeomorphisms on a manifold. We
develop a general theory of implicit generating forms. Our results generalize
the classical formulas for generating functions of symplectic twist maps.


  We introduce a conceptual framework that associates syntax and semantics with
vertical and horizontal directions in principal bundles and related
constructions. This notion of geometry corresponds to a mechanism for
performing goal-directed file transformations such as "eliminate unsafe syntax"
and suggests various engineering practices.


  The measurements of heavy quarkonium suppression at RHIC and LHC urge theory
to develop intuitive as well as quantitative methods for the description of
$Q\bar{Q}$ melting in the quark-gluon plasma. Here I will present a brief
sketch on the effective field theory strategies underlying the definition of
the heavy quark static potential and report on two recent advances in the
extraction and interpretation of such a potential. On the one side, progress
has been made in obtaining its values from lattice QCD, which promises to make
possible investigating its real and imaginary part non-perturbatively. On the
other side, the existence of an imaginary part emphasizes the dynamical nature
of the melting process and invites us to make a direct connection to the
framework of open quantum systems.


  Model-free data-driven computational mechanics, first proposed by
Kirchdoerfer and Ortiz, replaces phenomenological models with numerical
simulations based on sample data sets in strain-stress space. Recent literature
extended the approach to inelastic problems using structured data sets, tangent
space information, and transition rules. From an application perspective, the
coverage of qualified data states and calculating the corresponding tangent
space is crucial. In this respect, material symmetry significantly helps to
reduce the amount of necessary data. This study applies the data-driven
paradigm to elasto-plasticity with isotropic hardening. We formulate our
approach employing Haigh-Westergaard coordinates, providing information on the
underlying material yield surface. Based on this, we use a combined
tension-torsion test to cover the knowledge of the yield surface and a single
tensile test to calculate the corresponding tangent space. The resulting
data-driven method minimizes the distance over the Haigh-Westergaard space
augmented with directions in the tangent space subject to compatibility and
equilibrium constraints.


  The paper addresses the hydrodynamic behavior of a sphere close to a
micro-patterned superhydrophobic surface described in terms of alternated
no-slip and perfect-slip stripes. Physically, the perfect-slip stripes model
the parallel grooves where a large gas cushion forms between fluid and solid
wall, giving rise to slippage at the gas-liquid interface. The potential of the
boundary element method (BEM) in dealing with mixed no-slip/perfect-slip
boundary conditions is exploited to systematically calculate the mobility
tensor for different particle-to-wall relative positions and for different
particle radii. The particle hydrodynamics is characterized by a non trivial
mobility field which presents a distinct near wall behavior where the wall
patterning directly affects the particle motion. In the far field, the effects
of the wall pattern can be accurately represented via an effective description
in terms of a homogeneous wall with a suitably defined apparent slippage. The
trajectory of the sphere under the action of an external force is also
described in some detail. A resonant regime is found when the frequency of the
transversal component of the force matches a characteristic crossing frequency
imposed by the wall pattern. It is found that, under resonance, the particle
undergoes a mean transversal drift. Since the resonance condition depends on
the particle radius the effect can in principle be used to conceive devices for
particle sorting based on superhydrophobic surfaces.


  In this work it is continued the investigation of the space-time scales of
the hadronization process in the framework of string model. The average
formation lengths of several widely using species of baryons (antibaryons) such
as $p$ ($\bar{p}$), $n$ ($\bar{n}$), $\Delta$ ($\bar{\Delta}$), $\Lambda$
($\bar{\Lambda}$) and $\Sigma$ ($\bar{\Sigma}$) are studied. It is shown that
they depend from electrical charges or, more precise, from quark contents of
the hadrons. In particular, the average formation lengths of positively charged
hadrons, for example protons, are considerably larger than of their negatively
charged antiparticles, antiprotons. This statement is fulfilled for all nuclear
targets and any value of the Bjorken scaling variable $x_{Bj}$. The main
mechanism is direct production. Additional production mechanism in result of
decay of resonances gives small contribution. It is shown that the average
formation lengths of protons (antiprotons) are slowly rising (decreasing)
functions of $x_{Bj}$, the ones of neutrons and antineutrons are slowly
decreasing functions of $x_{Bj}$. The shape and behavior of average formation
lengths for baryons qualitatively coincide with the ones for pseudoscalar
mesons obtained earlier.


  XGBoost is one of the most widely used machine learning models in the
industry due to its superior learning accuracy and efficiency. Targeting at
data isolation issues in the big data problems, it is crucial to deploy a
secure and efficient federated XGBoost (FedXGB) model. Existing FedXGB models
either have data leakage issues or are only applicable to the two-party setting
with heavy communication and computation overheads. In this paper, a lossless
multi-party federated XGB learning framework is proposed with a security
guarantee, which reshapes the XGBoost's split criterion calculation process
under a secret sharing setting and solves the leaf weight calculation problem
by leveraging distributed optimization. Remarkably, a thorough analysis of
model security is provided as well, and multiple numerical results showcase the
superiority of the proposed FedXGB compared with the state-of-the-art models on
benchmark datasets.


  For positive functions $u\in C^{2}(\Omega) $, where $\Omega$ is an open
subset of $\mathbb{R}^{n}$, the Symmetric Minimal Surface Equation (SME), is
$\sum_{i=1}^{n}D_{i}\bigl(\frac{D_{i}u}{\sqrt{1+|Du|^{2}}}\bigr)=\frac{m-1}{u\sqrt{1+|Du|^{2}}}$.
Geometrically, the SME expresses the fact that the ``symmetric graph'' $SG(u)$,
defined by $SG(u)=\bigl\{(x,\xi)\in
\Omega\times\mathbb{R}^{m}:|\xi|=u(x)\bigr\}$, is a minimal (i.e.\ zero mean
curvature) hypersurface in $\Omega\times\mathbb{R}^{m}$. A function $u\in
C^{1}(\Omega)$ is said to be a singular solution if $u^{-1}\{0\}\neq
\emptyset$, and if $u=\lim_{j\to\infty}u_{j}$, uniformly on each compact subset
of $\Omega$, where each $u_{j}$ is a positive $C^{2}(\Omega)$ solution of the
SME. The present paper develops are theory of singular solutions of the SME,
including existence, H\"older and Lipschitz estimates for bounded solutions,
and a compactness and regularity theory. We also prove that the singular set
$u^{-1}{\{0\}}$ is codimension at most 2.


  We consider paradigmatic quenched disordered quantum spin models, viz., the
XY spin glass and random-field XY models, and show that quenched averaged
quantum correlations can exhibit the order-from-disorder phenomenon for
finite-size systems as well as in the thermodynamic limit. Moreover, we find
that the order-from-disorder can get more pronounced in the presence of
temperature by suitable tuning of the system parameters. The effects are found
for entanglement measures as well as for information-theoretic quantum
correlation ones, although the former show them more prominently. We also
observe that the equivalence between the quenched averages and their
self-averaged cousins -- for classical and quantum correlations -- is related
to the quantum critical point in the corresponding ordered system.


  We show that there is a measure-preserving system $(X,\mathscr{B}, \mu, T)$
together with functions $F_0, F_1, F_2 \in L^{\infty}(\mu)$ such that the
correlation sequence $C_{F_0, F_1, F_2}(n) = \int_X F_0 \cdot T^n F_1 \cdot
T^{2n} F_2 d\mu$ is not an approximate integral combination of $2$-step
nilsequences.


  Coherently moving flocks of birds, beasts or bacteria are examples of living
matter with spontaneous orientational order. How do these systems differ from
thermal equilibrium systems with such liquid-crystalline order? Working with a
fluidized monolayer of macroscopic rods in the nematic liquid crystalline
phase, we find giant number fluctuations consistent with a standard deviation
growing linearly with the mean, in contrast to any situation where the Central
Limit Theorem applies. These fluctuations are long-lived, decaying only as a
logarithmic function of time. This shows that flocking, coherent motion and
large-scale inhomogeneity can appear in a system in which particles do not
communicate except by contact.


  Inelastic neutron scattering studies in single crystals of TbInO3 and
TbIn0.95Mn0.05O3 with nearly-triangular antiferromagnetic lattice are reported.
At low energies, a broad and apparently gapless continuum of magnetic
excitations, located at the triangular lattice (TL) Brillouin zone boundary, is
observed. The data are well described by the uncorrelated nearest-neighbor
valence bonds model. At higher energies, a broad excitation branch dispersing
from the TL zone boundary is observed. No signs of static magnetic order are
found down to the temperatures two orders of magnitude smaller than the
effective interaction energy. The fluctuating magnetic moment exceeds two
thirds of the Tb3+ free-ion value and is confined to the TL plane. These
observations are consistent with a TL-based spin liquid state in TbInO3.


  The first Indian lunar mission Chandrayaan-1 was launched on 22 October 2008.
The Sub-keV Atom Reflecting Analyzer (SARA) instrument onboard Chandrayaan-1
consists of an energetic neutral atom (ENA) imaging mass analyzer called CENA
(Chandrayaan-1 Energetic Neutrals Analyzer), and an ion-mass analyzer called
SWIM (Solar wind Monitor). CENA performed the first ever experiment to study
the solar wind-planetary surface interaction via detection of sputtered neutral
atoms and neutralized backscattered solar wind protons in the energy range
~0.01-3.0 keV. SWIM measures solar wind ions, magnetosheath and magnetotail
ions, as well as ions scattered from lunar surface in the ~0.01-15 keV energy
range. The neutral atom sensor uses conversion of the incoming neutrals to
positive ions, which are then analyzed via surface interaction technique. The
ion mass analyzer is based on similar principle. This paper presents the SARA
instrument and the first results obtained by the SWIM and CENA sensors. SARA
observations suggest that about 20% of the incident solar wind protons are
backscattered as neutral hydrogen and ~1% as protons from the lunar surface.
These findings have important implications for other airless bodies in the
solar system.


  Although current deep learning methods have achieved impressive results for
semantic segmentation, they incur high computational costs and have a huge
number of parameters. For real-time applications, inference speed and memory
usage are two important factors. To address the challenge, we propose a
lightweight feature pyramid encoding network (FPENet) to make a good trade-off
between accuracy and speed. Specifically, we use a feature pyramid encoding
block to encode multi-scale contextual features with depthwise dilated
convolutions in all stages of the encoder. A mutual embedding upsample module
is introduced in the decoder to aggregate the high-level semantic features and
low-level spatial details efficiently. The proposed network outperforms
existing real-time methods with fewer parameters and improved inference speed
on the Cityscapes and CamVid benchmark datasets. Specifically, FPENet achieves
68.0\% mean IoU on the Cityscapes test set with only 0.4M parameters and 102
FPS speed on an NVIDIA TITAN V GPU.


  We consider maximization of stochastic monotone continuous submodular
functions (CSF) with a diminishing return property. Existing algorithms only
guarantee the performance \textit{in expectation}, and do not bound the
probability of getting a bad solution. This implies that for a particular run
of the algorithms, the solution may be much worse than the provided guarantee
in expectation. In this paper, we first empirically verify that this is indeed
the case. Then, we provide the first \textit{high-probability} analysis of the
existing methods for stochastic CSF maximization, namely PGA, boosted PGA, SCG,
and SCG++. Finally, we provide an improved high-probability bound for SCG,
under slightly stronger assumptions, with a better convergence rate than that
of the expected solution. Through extensive experiments on non-concave
quadratic programming (NQP) and optimal budget allocation, we confirm the
validity of our bounds and show that even in the worst-case, PGA converges to
$OPT/2$, and boosted PGA, SCG, SCG++ converge to $(1 - 1/e)OPT$, but at a
slower rate than that of the expected solution.


  Photovoltaic (PV) response of epitaxial BiFe0.95Mn0.05O3 thin film grown by
pulsed laser deposition has been investigated on a broad range of temperature.
Wavelength dependent photovoltaic effect shows the contribution of in gap level
states most likely connected to the manganese doping on the B-site of the
perovskite unit cells and presence of defects (Bi and O vacancies). The
temperature dependent response of the PV response rules out electromigration
and/or Schottky barriers as dominant mechanisms. This is corroborated with the
observed switchable photovoltaic effect that can be explained either by the
depolarizing field or bulk photovoltaic effect. In addition the PV response
shows strong correlation with the low temperature polaronic like conduction
mechanism and high open circuit voltage (2.5V) is detected in the investigated
vertical capacitive geometry.


  We consider the model describing the vertical motion of a ball falling with
constant acceleration on a wall and elastically reflected. The wall is supposed
to move in the vertical direction according to a given periodic function $f$.
We apply the Aubry-Mather theory to the generating function in order to prove
the existence of bounded motions with prescribed mean time between the bounces.
As the existence of unbounded motions is known, it is possible to find a class
of functions $f$ that allow both bounded and unbounded motions.


  We present a conjecture (and a proof for G=SL(2)) generalizing a result of J.
Arthur which expresses a character value of a cuspidal representation of a
$p$-adic group as a weighted orbital integral of its matrix coefficient. It
also generalizes a conjecture by the second author proved by Schneider-Stuhler
and (independently) the first author. The latter statement expresses an
elliptic character value as an orbital integral of a pseudo-matrix coefficient
defined via the Chern character map taking value in zeroth Hochschild homology
of the Hecke algebra. The present conjecture generalizes the construction of
pseudo-matrix coefficient using compactly supported Hochschild homology, as
well as a modification of the category of smooth representations, the so called
compactified category of smooth $G$-modules. This newly defined "compactified
pseudo-matrix coefficient" lies in a certain space on which the weighted
orbital integral is a conjugation invariant linear functional, our conjecture
states that evaluating a weighted orbital integral on the compactified
pseudo-matrix coefficient one recovers the corresponding character value of the
representation. We also discuss general properties of that space, building on
works of Waldspurger and Beuzart-Plessis.


  French regulation allows consumers in low-voltage networks to form
collectives to produce, share, and consume local energy under the collective
self-consumption framework. A natural consequence of collectively-owned
generation projects is the need to allocate production among consumers. In
long-term plans, production allocation determines each of the consumers'
benefits of joining the collective. In the short-term, energy should be
dynamically allocated to reflect operation. This paper presents a framework
that integrates long and short-term planning of a collective that shares a
solar plus energy storage system. In the long-term planning stage, we maximize
the collective's welfare and equitably allocate expected energy to each
consumer. For operation, we propose a model predictive control algorithm that
minimizes short-term costs and allocates energy to each consumer on a 30-minute
basis (as required by French regulation). We adjust the energy allotment
ex-post operation to reflect the materialization of uncertainty. We present a
case study where we showcase the framework for a 15 consumer collective.


  We focus on \emph{row sampling} based approximations for matrix algorithms,
in particular matrix multipication, sparse matrix reconstruction, and
\math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in
\math{d\ll m} dimensions), and appropriate row-sampling probabilities, which
typically depend on the norms of the rows of the \math{m\times d} left singular
matrix of \math{\matA} (the \emph{leverage scores}), we give row-sampling
algorithms with linear (up to polylog factors) dependence on the stable rank of
\math{\matA}. This result is achieved through the application of
non-commutative Bernstein bounds. Keywords: row-sampling; matrix
multiplication; matrix reconstruction; estimating spectral norm; linear
regression; randomized


  This paper is devoted to the mathematical analysis of a time-domain
electromagnetic scattering by periodic structures which are known as
diffraction gratings. The scattering problem is reduced equivalently into an
initial-boundary value problem in a bounded domain by using an exact
transparent boundary condition. The well-posedness and stability of the
solution are established for the reduced problem. Moreover, a priori energy
estimates are obtained with minimum regularity requirement for the data and
explicit dependence on the time.


  Reliable autonomous navigation requires adapting the control policy of a
mobile robot in response to dynamics changes in different operational
conditions. Hand-designed dynamics models may struggle to capture model
variations due to a limited set of parameters. Data-driven dynamics learning
approaches offer higher model capacity and better generalization but require
large amounts of state-labeled data. This paper develops an approach for
learning robot dynamics directly from point-cloud observations, removing the
need and associated errors of state estimation, while embedding Hamiltonian
structure in the dynamics model to improve data efficiency. We design an
observation-space loss that relates motion prediction from the dynamics model
with motion prediction from point-cloud registration to train a Hamiltonian
neural ordinary differential equation. The learned Hamiltonian model enables
the design of an energy-shaping model-based tracking controller for rigid-body
robots. We demonstrate dynamics learning and tracking control on a real
nonholonomic wheeled robot.


  Categorical compositional distributional model of Coecke et al. (2010)
suggests a way to combine grammatical composition of the formal, type logical
models with the corpus based, empirical word representations of distributional
semantics. This paper contributes to the project by expanding the model to also
capture entailment relations. This is achieved by extending the representations
of words from points in meaning space to density operators, which are
probability distributions on the subspaces of the space. A symmetric measure of
similarity and an asymmetric measure of entailment is defined, where lexical
entailment is measured using von Neumann entropy, the quantum variant of
Kullback-Leibler divergence. Lexical entailment, combined with the composition
map on word representations, provides a method to obtain entailment relations
on the level of sentences. Truth theoretic and corpus-based examples are
provided.


  We propose and demonstrate a system that produces squeezed vacuum using a
pair of optical parametric amplifiers. This scheme allows the production of
phase sidebands on the squeezed vacuum which facilitate phase locking in
downstream applications. We observe strong, stably locked, continuous wave
vacuum squeezing at frequencies as low as 220 kHz. We propose an alternative
resonator configuration to overcome low frequency squeezing degradation caused
by the optical parametric amplifiers.


  In Conspiracy Santa, a variant of Secret Santa, a group of people offer each
other Christmas gifts, where each member of the group receives a gift from the
other members of the group. To that end, the members of the group form
conspiracies, to decide on appropriate gifts, and usually divide the cost of
each gift among all participants of that conspiracy. This requires to settle
the shared expenses per conspiracy, so Conspiracy Santa can actually be seen as
an aggregation of several shared expenses problems. First, we show that the
problem of finding a minimal number of transaction when settling shared
expenses is NP-complete. Still, there exist good greedy approximations. Second,
we present a greedy distributed secure solution to Conspiracy Santa. This
solution allows a group of n people to share the expenses for the gifts in such
a way that no participant learns the price of his gift, but at the same time
notably reduces the number of transactions to 2 $\times$ n + 1 with respect to
a na{\"i}ve aggregation of n $\times$ (n -- 2). Furthermore, our solution does
not require a trusted third party, and can either be implemented physically
(the participants are in the same room and exchange money using envelopes) or,
over Internet, using a cryptocurrency.


  We show that the Street nerve of a strict $\omega$-category $C$ is a Kan
complex (respectively a quasi-category) if and only if the $n$-cells of $C$ for
$n\geq 1$ (respectively $n> 1$) are weakly invertible. Moreover, we equip
$\mathcal{N}(C)$ with a structure of saturated complicial set where the
$n$-simplices correspond to morphisms from the $n^{th}$ oriental to $C$ sending
the unique non-trivial $n$-cell of the domain to a weakly invertible cell of
$C$.


  We computationally investigate the active transport of tangentially-driven
polymers with varying degrees of flexibility and activity in two-dimensional
square lattices of obstacles. Tight periodic confinement induces notable
conformational changes and distinct modes of transport for flexible and stiff
active filaments. It leads to localization and caging of flexible polymers
inside the inter-obstacle pores, while promoting more elongated conformations
and enhanced diffusion for stiff polymers at low to moderate activity levels.
The migration of flexible active polymers occurs via hopping events, where they
unfold to move from one cage to another. In contrast, stiff chains travel
mainly in straight paths within inter-obstacle channels, while occasionally
changing their direction of motion. Both the duration of caging and persistent
directed migration within the channels decrease with increasing the activity
level. As a consequence, at high active forces polymers overcome confinement
effects and transport within inter-obstacle pores as swiftly as those in free
space. We explain the center of mass dynamics of semiflexible polymers in terms
of active force and obstacle packing fraction by developing an approximate
analytical theory.


  Astrophysical lensing has typically been studied in two regimes: diffractive
optics and refractive optics. Diffractive optics is characterized by a
perturbative expansion of the Kirchhoff-Fresnel diffraction integral, while
refractive optics is characterized by the stationary phase approximation.
Previously, it has been assumed that the Fresnel scale, $R_F$ , is the relevant
physical scale that separates these two regimes. With the recent introduction
of Picard-Lefschetz theory to the field of lensing, it has become possible to
generalize the refractive description of discrete images to all wave
parameters, and, in particular, exactly evaluate the diffraction integral at
all frequencies. In this work, we assess the regimes of validity of refractive
and diffractive approximations for a simple one-dimensional lens model through
comparison with this exact evaluation. We find that, contrary to previous
assumptions, the true separation scale between these regimes is given by $R_F /
\sqrt{\kappa}$, where $\kappa$ is the convergence of the lens. Thus, when the
lens is strong, refractive optics can hold for arbitrarily small scales. We
also argue that intensity variations in diffractive optics are generically
small, which has implications for the study of strong diffractive scintillation
(DISS).


  We discuss the results of recent 3D simulations of first structure formation
in relationship to the formation of the first stars. On the basis of a new,
high-resolution AMR simulation (spatial dynamic range = 30,000,000), we
conclude that the first stars are likely to be massive.


  During M phase, Endosulfine (Endos) family proteins are phosphorylated by
Greatwall kinase (Gwl), and the resultant pEndos inhibits the phosphatase
PP2A-B55, which would otherwise prematurely reverse many CDK-driven
phosphorylations. We show here that PP2A-B55 is the enzyme responsible for
dephosphorylating pEndos during M phase exit. The kinetic parameters for
PP2A-B55's action on pEndos are orders of magnitude lower than those for
CDK-phosphorylated substrates, suggesting a simple model for PP2A-B55
regulation that we call inhibition by unfair competition. As the name suggests,
during M phase PP2A-B55's attention is diverted to pEndos, which binds much
more avidly and is dephosphorylated more slowly than other substrates. When Gwl
is inactivated during the M phase-to-interphase transition, the dynamic balance
changes: pEndos dephosphorylated by PP2A-B55 cannot be replaced, so the
phosphatase can refocus its attention on CDK-phosphorylated substrates. This
mechanism explains simultaneously how PP2A-B55 and Gwl together regulate
pEndos, and how pEndos controls PP2A-B55.


  Although species longevity is subject to a diverse range of selective forces,
the mortality curves of a wide variety of organisms are rather similar. We
argue that aging and its universal characteristics may have evolved by means of
a gradual increase in the systemic interdependence between a large collection
of biochemical or mechanical components. Modeling the organism as a dependency
network which we create using a constructive evolutionary process, we age it by
allowing nodes to be broken or repaired according to a probabilistic algorithm
that accounts for random failures/repairs and dependencies. Our simulations
show that the network slowly accumulates damage and then catastrophically
collapses. We use our simulations to fit experimental data for the time
dependent mortality rates of a variety of multicellular organisms and even
complex machines such as automobiles. Our study suggests that aging is an
emergent finite-size effect in networks with dynamical dependencies and that
the qualitative and quantitative features of aging are not sensitively
dependent on the details of system structure.


  We compute the shear viscosity of the non-commutative N=4 super Yang-Mills
quantum field theory at strong coupling using the dual supergravity background.
Special interest derives from the fact that the background presents an
intrinsic anisotropy in space through the distinction of commutative and
non-commutative directions. Despite this anisotropy the analysis exhibits the
ubiquitous result \eta/s = 1/4\pi for two different shear channels. In order to
derive this result, we show that the boundary energy momentum tensor must
couple to the open string metric. As a byproduct we compute the renormalised
holographic energy momentum tensor and show that it coincides with one in the
commutative theory.


  We prove that many, but not all injective factors arise as crossed products
by nonsingular Bernoulli actions of the group $\mathbb{Z}$. We obtain this
result by proving a completely general result on the ergodicity, type and
Krieger's associated flow for Bernoulli shifts with arbitrary base spaces. We
prove that the associated flow must satisfy a structural property of infinite
divisibility. Conversely, we prove that all almost periodic flows, as well as
many other ergodic flows, do arise as associated flow of a weakly mixing
Bernoulli action of any infinite amenable group. As a byproduct, we prove that
all injective factors with almost periodic flow of weights are infinite tensor
products of $2 \times 2$ matrices. Finally, we construct Poisson suspension
actions with prescribed associated flow for any locally compact second
countable group that does not have property (T).


  We define the Z/2Z Hodge spaces H_{pq}(\Sigma) of a fan \Sigma.
  If \Sigma is the normal fan of a reflexive polytope \Delta then we use
polyhedral duality to compute the Z/2Z Hodge Spaces of \Sigma. In particular,
if the cones of dimension at most e in the face fan \Sigma^* of \Delta are
smooth then we compute H_{pq}(\Sigma) for p<e-1. If \Sigma^* is a smooth fan
then we completely determine the spaces H_{pq}(\Sigma) and we show the toric
variety X associated to \Sigma is maximal, meaning that the sum of the Z/2Z
Betti numbers of X(R) is equal to the sum of the Z/2Z Betti numbers of X(C).


  The low replication rate of published studies has long concerned the social
science community, making understanding the replicability a critical problem.
Several studies have shown that relevant research communities can make
predictions about the replicability of individual studies with above-chance
accuracy. Follow-up work further indicates that laypeople can also achieve
above-chance accuracy in predicting replicability when experts interpret the
studies into short descriptions that are more accessible for laypeople. The
involvement of scarce expert resources may make these methods expensive from
financial and time perspectives. In this work, we explored whether laypeople
can predict the replicability of social science studies without expert
intervention. We presented laypeople with raw materials truncated from
published social science papers and elicited their answers to questions related
to the paper. Our results suggested that laypeople were engaged in this
technical task, providing reasonable and self-contained answers. The majority
of them also demonstrated a good understanding of the material. However, the
solicited information had limited predictive power on the actual replication
outcomes. We further discuss several lessons we learned compared to the
approach with expert intervention to inspire future works.


  We introduce an equilibrium formulation of the functional renormalization
group (fRG) for inhomogeneous systems capable of dealing with spatially
finite-ranged interactions. In the general third order truncated form of fRG,
the dependence of the two-particle vertex is described by O(N^4) independent
variables, where N is the dimension of the single-particle system. In a
previous paper [Phys. Rev. B 89, 045128 (2014)], the so-called coupled-ladder
approximation (CLA) was introduced and shown to admit a consistent treatment
for models with a purely onsite interaction, reducing the vertex to O(N^2)
independent variables. Here, we extend this scheme to the extended coupled
ladder approximation (eCLA), which includes a spatially extended feedback
between the individual channels, measured by a feedback length L, using O(N^2
L^2) independent variables for the vertex. We apply the eCLA to three types of
one-dimensional models : First, to a quantum point contact (QPC) with a
parabolic barrier top and short-ranged interactions. Here eCLA achieves
convergence for L equal to the characteristic length l_x of the QPC. It also
turns out that the additional feedback stabilizes the fRG-flow. This enables
us, second, to study the crossover between a QPC and a quantum dot, again for a
model with short-ranged interactions. Third, the enlarged feedback also enables
the treatment of a finite-ranged interaction extending over up to L sites.
Estimating the form of such a finite-ranged interaction in a QPC, we study its
effects on the conductance and the density. For low densities and sufficiently
large interaction ranges the conductance develops additional oscillatory
features, and the corresponding density shows fluctuations that can be
interpreted as Friedel oscillations arising from a renormalized barrier shape
with a rather flat top and steep flanks.


  This paper examines the problem of testing whether a discrete time-series
vector contains a periodic signal or is merely noise. To do this we examine the
stochastic behaviour of the maximum intensity of the observed time-series
vector and formulate a simple hypothesis test that rejects the null hypothesis
of exchangeability if the maximum intensity spike in the Fourier domain is "too
big" relative to its null distribution. This comparison is undertaken by
simulating the null distribution of the maximum intensity using random
permutations of the time-series vector. We show that this test has a p-value
that is uniformly distributed for an exchangeable time-series vector, and that
the p-value increases when there is a periodic signal present in the observed
vector. We compare our test to Fisher's spectrum test, which assumes normality
of the underlying noise terms. We show that our test is more robust than this
test, and accommodates noise vectors with fat tails.


  We present high resolution (R=55,000) optical spectra obtained with MIKE on
the 6.5 m Magellan Clay Telescope as well as Spitzer MIPS photometry and IRS
low resolution (R~60) spectroscopy of the close (14 AU separation) binary, HD
101088, a member of the ~12 Myr old southern region of the Lower Centaurus Crux
(LCC) subgroup of the Scorpius-Centaurus OB association. We find that the
primary and/or secondary is accreting from a tenuous circumprimary and/or
circumsecondary disk despite the apparent lack of a massive circumbinary disk.
We estimate a lower limit to the accretion rate of > 1x10^-9 solar masses per
year, which our multiple observation epochs show varies over a timescale of
months. The upper limit on the 70 micron flux allows us to place an upper limit
on the mass of dust grains smaller than several microns present in a
circumbinary disk of 0.16 moon masses. We conclude that the classification of
disks into either protoplanetary or debris disks based on fractional infrared
luminosity alone may be misleading.


  In this contribution we first summarize how contour integration methods can
be used to derive closed formulae for functional determinants of ordinary
differential operators. We then generalize our considerations to partial
differential operators. Examples are used to show that also in higher
dimensions closed answers can be obtained as long as the eigenvalues of the
differential operators are determined by transcendental equations. Examples
considered comprise of the finite temperature Casimir effect on a ball and the
functional determinant of the Laplacian on a two-dimensional torus.


  5G cellular networks are particularly vulnerable against narrowband jammers
that target specific control sub-channels in the radio signal. One mitigation
approach is to detect such jamming attacks with an online observation system,
based on machine learning. We propose to detect jamming at the physical layer
with a pre-trained machine learning model that performs binary classification.
Based on data from an experimental 5G network, we study the performance of
different classification models. A convolutional neural network will be
compared to support vector machines and k-nearest neighbors, where the last two
methods are combined with principal component analysis. The obtained results
show substantial differences in terms of classification accuracy and
computation time.


  Data verbalisation is a task of great importance in the current field of
natural language processing, as there is great benefit in the transformation of
our abundant structured and semi-structured data into human-readable formats.
Verbalising Knowledge Graph (KG) data focuses on converting interconnected
triple-based claims, formed of subject, predicate, and object, into text.
Although KG verbalisation datasets exist for some KGs, there are still gaps in
their fitness for use in many scenarios. This is especially true for Wikidata,
where available datasets either loosely couple claim sets with textual
information or heavily focus on predicates around biographies, cities, and
countries. To address these gaps, we propose WDV, a large KG claim
verbalisation dataset built from Wikidata, with a tight coupling between
triples and text, covering a wide variety of entities and predicates. We also
evaluate the quality of our verbalisations through a reusable workflow for
measuring human-centred fluency and adequacy scores. Our data and code are
openly available in the hopes of furthering research towards KG verbalisation.


  We discuss the way non-perturbative quantization of cosmological spacetimes
in loop quantum cosmology provides insights on the physics of Planck scale and
the resolution of big bang singularity. In recent years, rigorous examination
of mathematical and physical aspects of the quantum theory has led to a
consistent quantization which is consistent and physically viable and some
early ideas have been ruled out. The latter include so called `physical
effects' originating from modifications to inverse scale factors in the flat
models. The singularity resolution is understood to originate from the
non-local nature of curvature in the quantum theory and the underlying polymer
representation. Using an exactly solvable model various insights have been
gained. The model predicts a generic occurrence of bounce for states in the
physical Hilbert space and a supremum for the spectrum of the energy density
operator. It also provides answers to the growth of fluctuations, showing that
semi-classicality is preserved to an amazing degree across the bounce.


  We calculate the effect of the electron-phonon interaction on the electronic
density of states (DOS), the quasiparticle properties and on the optical
conductivity of graphene. In metals with DOS constant on the scale of phonon
energies, the electron-phonon renormalizations drop out of the dressed DOS,
however, due to the Dirac nature of the electron dynamics in graphene, the band
DOS is linear in energy and phonon structures remain, which can be emphasized
by taking an energy derivative. There is a shift in the chemical potential and
in the position in energy of the Dirac point. Also, the DOS can be changed from
a linear dependence out of value zero at the Dirac point to quadratic out of a
finite value. The optical scattering rate $1/\tau$ sets the energy scale for
the rise of the optical conductivity from its universal DC value $4e^2/\pi h$
(expected in the simplest theory when chemical potential and temperature are
both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi
e^2/2h)$. As in ordinary metals the DC conductivity remains unrenormalized
while its AC value is changed. The optical spectral weight under the intraband
Drude is reduced by a mass renormalization factor as is the effective
scattering rate. Optical weight is transferred to an Holstein phonon-assisted
side band. Due to Pauli blocking the interband transitions are sharply
suppressed, but also nearly constant, below twice the value of renormalized
chemical potential and also exhibit a phonon-assisted contribution. The
universal background conductivity is reduced below $\sigma_0$ at large
energies.


  Using prompts to explore the knowledge contained within pre-trained language
models for downstream tasks has now become an active topic. Current prompt
tuning methods mostly convert the downstream tasks to masked language modeling
problems by adding cloze-style phrases and mapping all labels to verbalizations
with fixed length, which has proven effective for tasks with simple label
spaces. However, when applied to relation classification exhibiting complex
label spaces, vanilla prompt tuning methods may struggle with label
verbalizations with arbitrary lengths due to rigid prompt restrictions.
Inspired by the text infilling task for pre-training generative models that can
flexibly predict missing spans, we propose a novel generative prompt tuning
method to reformulate relation classification as an infilling problem, which
frees our approach from limitations of current prompt based approaches and thus
fully exploits rich semantics of entity and relation types. In addition, we
design entity-guided decoding and discriminative relation scoring to generate
and align relations effectively and efficiently during inference. Extensive
experiments under fully supervised settings and low-resource settings
demonstrate the effectiveness of our approach.


  The complete one-loop electroweak corrections to charged Higgs boson pair
production in $\gamma\gamma$ collision mode at linear colliders in the minimal
supersymmetric standard model (MSSM), are calculated in this paper. We discuss
the dependence of the corrections to the subprocess $\gamma\gamma \to
H^{+}H^{-}$ on the related parameters, such as the colliding energy, charged
Higgs boson mass $M_{H^{\pm}}$ and some supersymmetric parameters $\tan \beta$,
$M_{SUSY}$ and gaugino mass parameter $M_2$. We find that the corrections
generally reduce the Born cross sections and the relative one-loop corrections
to both the subprocess typically in the range of -10% to -30%. We also present
the numerical results at the SPS1a' point from the SPA project. We conclude
that the full one-loop electroweak corrections to subprocess $\gamma \gamma \to
H^{+}H^{-}$ and the parent process $e^+e^- \to \gamma \gamma \to H^{+}H^{-}$
are significant and therefore should be considered in precise analysis of
charged Higgs boson pair productions via $\gamma\gamma$ collision at future
linear colliders.


  We show that determining the rank of a tensor over a field has the same
complexity as deciding the existential theory of that field. This implies
earlier NP-hardness results by H{\aa}stad~\cite{H90}. The hardness proof also
implies an algebraic universality result.


  A microscopic kinetic theory is developed which allows to investigate
non-Abelian SU(2) systems interacting with meanfields and spin-orbit coupling
under magnetic fields in one, two, and three dimensions. The coupled kinetic
equations for the scalar and spin components are presented and linearized with
respect to an external electric field. The dynamical classical and quantum Hall
effect are described in this way as well as the anomalous Hall effect where a
new symmetric dynamical contribution to the conductivity is presented. The
coupled density and spin response functions to an electric field are derived
including arbitrary magnetic fields. The magnetic field induces a staircase
structure at frequencies of the Landau levels. It is found that for linear
Dresselhaus and Rashba spin-orbit coupling a dynamical out-of-plane spin
response appears at these Landau level frequencies establishing terahertz
resonances.


  Interpreting gradient methods as fixed-point iterations, we provide a
detailed analysis of those methods for minimizing convex objective functions.
Due to their conceptual and algorithmic simplicity, gradient methods are widely
used in machine learning for massive data sets (big data). In particular,
stochastic gradient methods are considered the de- facto standard for training
deep neural networks. Studying gradient methods within the realm of fixed-point
theory provides us with powerful tools to analyze their convergence properties.
In particular, gradient methods using inexact or noisy gradients, such as
stochastic gradient descent, can be studied conveniently using well-known
results on inexact fixed-point iterations. Moreover, as we demonstrate in this
paper, the fixed-point approach allows an elegant derivation of accelerations
for basic gradient methods. In particular, we will show how gradient descent
can be accelerated by a fixed-point preserving transformation of an operator
associated with the objective function.


  As a supplement of our previous work, we consider the localized region of the
random Schroedinger operators on $l^2({\bf Z}^d)$ and study the point process
composed of their eigenvalues and corresponding localization centers. For the
Anderson model, we show that, this point process in the natural scaling limit
converges in distribution to the Poisson process on the product space of energy
and space. In other models with suitable Wegner-type bounds, we can at least
show that any limiting point processes are infinitely divisible.


  The success of deep learning in visual recognition tasks has driven
advancements in multiple fields of research. Particularly, increasing attention
has been drawn towards its application in agriculture. Nevertheless, while
visual pattern recognition on farmlands carries enormous economic values,
little progress has been made to merge computer vision and crop sciences due to
the lack of suitable agricultural image datasets. Meanwhile, problems in
agriculture also pose new challenges in computer vision. For example, semantic
segmentation of aerial farmland images requires inference over extremely
large-size images with extreme annotation sparsity. These challenges are not
present in most of the common object datasets, and we show that they are more
challenging than many other aerial image datasets. To encourage research in
computer vision for agriculture, we present Agriculture-Vision: a large-scale
aerial farmland image dataset for semantic segmentation of agricultural
patterns. We collected 94,986 high-quality aerial images from 3,432 farmlands
across the US, where each image consists of RGB and Near-infrared (NIR)
channels with resolution as high as 10 cm per pixel. We annotate nine types of
field anomaly patterns that are most important to farmers. As a pilot study of
aerial agricultural semantic segmentation, we perform comprehensive experiments
using popular semantic segmentation models; we also propose an effective model
designed for aerial agricultural pattern recognition. Our experiments
demonstrate several challenges Agriculture-Vision poses to both the computer
vision and agriculture communities. Future versions of this dataset will
include even more aerial images, anomaly patterns and image channels. More
information at https://www.agriculture-vision.com.


  In wireless networks, many problems can be formulated as subset selection
problems where the goal is to select a subset from the ground set with the
objective of maximizing some objective function. These problems are typically
NP-hard and hence solved through carefully constructed heuristics, which are
themselves mostly NP-complete and thus not easily applicable to large networks.
On the other hand, subset selection problems occur in slightly different
context in machine learning (ML) where the goal is to select a subset of high
quality yet diverse items from a ground set. In this paper, we introduce a
novel DPP-based learning (DPPL) framework for efficiently solving subset
selection problems in wireless networks. The DPPL is intended to replace the
traditional optimization algorithms for subset selection by learning the
quality-diversity trade-off in the optimal subsets selected by an optimization
routine. As a case study, we apply DPPL to the wireless link scheduling
problem, where the goal is to determine the subset of simultaneously active
links which maximizes the network-wide sum-rate. We demonstrate that the
proposed DPPL approaches the optimal solution with significantly lower
computational complexity than the popular optimization algorithms used for this
problem in the literature.


  Radiative corrections in quantum field theories with small departures from
Lorentz symmetry alter structural aspects of the theory, in particular the
definition of asymptotic single-particle states. Specifically, the mass-shell
condition, the standard renormalization procedure as well as the
Lehmann-Symanzik-Zimmermann reduction formalism are affected.


  The observables useful for the model independent search for signals of the
abelian Z' in the processes e^+ e^- \to {\bar f}f are introduced. They are
based on the renormalization group relations between the Z' couplings to the
Standard Model particles developed recently and extend the variables suggested
by Osland, Pankov and Paver. The bounds on the values of the observables at the
center-of-mass energy \sqrt{s} = 500GeV are derived.


  HadV98 = CoD-22 12017 = GSC 6825.253 is a variable star discovered by Katsumi
Haseda. This object has been recently confirmed to be a new R CrB star
(Hasselbach et al. 2002), as had been originally proposed by us at the time of
the discovery alert in VSNET. We studied the light curve based on Haseda's
photographic material and ASAS-3 V-band data. There was only major fading
episode in the past decade. The fading started in 2001 May was composed of at
least two minima, and followed by a slow recovery.


  The paper surveys automated scientific discovery, from equation discovery and
symbolic regression to autonomous discovery systems and agents. It discusses
the individual approaches from a "big picture" perspective and in context, but
also discusses open issues and recent topics like the various roles of deep
neural networks in this area, aiding in the discovery of human-interpretable
knowledge. Further, we will present closed-loop scientific discovery systems,
starting with the pioneering work on the Adam system up to current efforts in
fields from material science to astronomy. Finally, we will elaborate on
autonomy from a machine learning perspective, but also in analogy to the
autonomy levels in autonomous driving. The maximal level, level five, is
defined to require no human intervention at all in the production of scientific
knowledge. Achieving this is one step towards solving the Nobel Turing Grand
Challenge to develop AI Scientists: AI systems capable of making Nobel-quality
scientific discoveries highly autonomously at a level comparable, and possibly
superior, to the best human scientists by 2050.


  We present the most recent results from XENON100, the current phase of the
XENON dark matter search program. XENON100 is a dual phase time-projection
chamber operated at the Laboratori Nazionali del Gran Sasso (LNGS) whose
ultra-low electromagnetic background, about 5 x 10^-3 events/(kg x day x keV),
allowed to set the most stringent limit to date, excluding WIMP-nucleon
spin-independent interaction down to cross-sections of 2 x 10^-45 cm^2 for a 55
GeV/c^2 mass at 90% confidence level and 3.5 x10^-40 for 45 GeV/c^2 in the
spin-dependent interaction with neutrons. We also introduce the status and
physics goal of XENON1T, the next phase of the program, which will be able to
achieve sensitivity down to 2 x 10^-47 cm^2 for a WIMP of 50 GeV/c^2.


  The Cauchy-Szeg\"o singular integral is a fundamental tool in the study of
holomorphic $H^p$ Hardy space. But for a kind of Siegel domains, the
Cauchy-Szeg\"o kernels are neither product ones nor flag ones on the Shilov
boundaries, which have the structure of nilpotent Lie groups $\mathscr N $ of
step two. We use the lifting method to investigate flag-like singular integrals
on $\mathscr N $, which includes these Cauchy-Szeg\"o ones as a special case.
The lifting group is the product $\tilde {\mathscr N }$ of three Heisenberg
groups, and naturally geometric or analytical objects on $\mathscr N $ are the
projection of those on $\tilde {\mathscr N } $. As in the flag case, we
introduce various notions on $\mathscr N $ adapted to geometric feature of
these kernels, such as tubes, nontangential regions, tube maximal functions,
Littlewood-Paley functions, tents, shards and atoms etc. They have the feature
of tri-parameters, although the second step of the group $\mathscr N$ is only
$2$-dimensional, i.e. there exists a hidden parameter as in the flag case. We
also establish the corresponding Calder\'on reproducing formula,
characterization of $ L ^p (\mathscr N)$ by Littlewood-Paley functions, $ L ^p
$-boundedness of tube maximal functions and flag-like singular integrals and
atomic decomposition of $H^1$ Hardy space on $ {\mathscr N } $.


  The matter content of the Universe is generally regarded as a perfect fluid
on sufficiently large scales, for all epochs. But the recent cosmological
matter distribution, consisting of an (ideally) random distribution of
gravitationally collapsed structures, is more accurately described as a
collection of discrete grains, than as a fluid. It is well known that granular
materials may have very different macroscopic properties than fluids;
analogously, we investigate the possibility that pervasive small-scale
inhomogeneities in the recent Universe may lead to perturbations of the
cosmological expansion on intermediate and/or large scales.


  We discuss the geometry of homogeneous Ricci solitons. After showing the
nonexistence of compact homogeneous and noncompact steady homogeneous solitons,
we concentrate on the study of left invariant Ricci solitons. We show that, in
the unimodular case, the Ricci soliton equation does not admit solutions in the
set of left invariant vector fields. We prove that a left invariant soliton of
gradient type must be a Riemannian product with a nontrivial Euclidean de Rham
factor. As an application of our results we prove that any generalized metric
Heisenberg Lie group is a nongradient left invariant Ricci soliton of expanding
type.


  In low-light conditions, a conventional camera imaging pipeline produces
sub-optimal images that are usually dark and noisy due to a low photon count
and low signal-to-noise ratio (SNR). We present a data-driven approach that
learns the desired properties of well-exposed images and reflects them in
images that are captured in extremely low ambient light environments, thereby
significantly improving the visual quality of these low-light images. We
propose a new loss function that exploits the characteristics of both
pixel-wise and perceptual metrics, enabling our deep neural network to learn
the camera processing pipeline to transform the short-exposure, low-light RAW
sensor data to well-exposed sRGB images. The results show that our method
outperforms the state-of-the-art according to psychophysical tests as well as
pixel-wise standard metrics and recent learning-based perceptual image quality
measures.


  Physical considerations strongly indicate that spacetime at Planck scales is
noncommutative. A popular model for such a spacetime is the Moyal plane. The
Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the
latter is not appropriate for more complicated spacetimes such as those
containing the Friedman-Sorkin (topological) geons. They have rich
diffeomorphism groups and in particular mapping class groups, so that the
statistics groups for N identical geons is strikingly different from the
permutation group $S_N$. We generalise the Drinfel'd twist to (essentially)
generic groups including to finite and discrete ones and use it to modify the
commutative spacetime algebras of geons as well to noncommutative algebras. The
latter support twisted actions of diffeos of geon spacetimes and associated
twisted statistics. The notion of covariant fields for geons is formulated and
their twisted versions are constructed from their untwisted versions.
Non-associative spacetime algebras arise naturally in our analysis. Physical
consequences, such as the violation of Pauli principle, seem to be the outcomes
of such nonassociativity.
  The richness of the statistics groups of identical geons comes from the
nontrivial fundamental groups of their spatial slices. As discussed long ago,
extended objects like rings and D-branes also have similar rich fundamental
groups. This work is recalled and its relevance to the present quantum geon
context is pointed out.


  We study self-regulating processes modeling biological transportation
networks as presented in \cite{portaro2023}. In particular, we focus on the 1D
setting for Dirichlet and Neumann boundary conditions. We prove an existence
and uniqueness result under the assumption of positivity of the diffusivity
$D$. We explore systematically various scenarios and gain insights into the
behavior of $D$ and its impact on the studied system. This involves analyzing
the system with a signed measure distribution of sources and sinks. Finally, we
perform several numerical tests in which the solution $D$ touches zero,
confirming the previous hints of local existence in particular cases.


  We demonstrate electron cooling in silicon using platinum silicide as a
superconductor contact to selectively remove the highest energy electrons. The
superconducting critical temperature of bulk PtSi is reduced from around 1 K to
0.79 K using a thin film (10 nm) of PtSi, which enhances cooling performance at
lower temperatures and enables electron cooling to be demonstrated from 100 mK
to 50 mK.


  Within the likes of any highly contagious and unpredictable disease, lies a
predictable and attainable growth rate that researchers can find in order to
make logistical conclusions about that particular disease and its affected
regions' counterparts. The foundation that researchers pull from when studying
a particular disease and looking for its growth rate is the
Susceptible-Infected-Removed (SIR) model, presented by a series of differential
equations. The issue with the SIR model lies not in its complexity, but
actually its simplicity and lack of a potentially high-finite amount of
factors; the limit being bounded by the amount of data available for that
particular factor. Our research involves the application of multiple
regressions to pinpoint and identify our Covid lockdown periods, followed by
the modification of the SIR model. This involved creating new model
approximations such as the time-delayed SIR model and the reinfected SIR model
in order to take into account factors such as incubation and reinfection, and
get the lowest error discrepancy as possible for our infection rate. We were
able to conclude that the more factors that we took into account, our error
rate became lower and our results became more accurate. We could also identify
outlier Metros and draw certain conclusions on performance level and the
reasons behind them. We then moved on to find correlations, if any, between the
infection rates and outside factors. We looked at demographic and weather data
to demonstrate whether correlations appeared. We found that there are a few
factors with high correlations, including graduate education and low
temperatures.


  The large value of non-minimal coupling constant $\xi$ required to satisfy
CMB observations in Higgs inflation violates unitarity. In this work we study
Higgs-inflation with non-canonical kinetic term of DBI form to find whether
$\xi$ can be reduced. To study the inflationary dynamics, we transform the
action to the Einstein frame, in which the Higgs is minimally coupled to
gravity with a non-canonical kinetic term and modified potential. We choose the
Higgs self coupling constant $\lambda=0.14$ for our analysis. We find that the
value of $\xi$ can be reduced from $10^{3}-10^{4}$ to $\mathcal{O}(10)$ to
satisfy Planck constraints on amplitude of scalar power spectrum. However, this
model produces a larger tensor-to-scalar ratio $r$, in comparison to the Higgs
inflation with canonical kinetic term. We also find that, to satisfy joint
constraints on scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from
Planck-2018 and bounds on $r$ from Planck and BICEP3, the value of $\xi$ should
be of the order of $10^4$. Thus, the issue of unitarity violation remains even
after considering Higgs inflation with non-canonical kinetic term


  Predicting intraday trading volume plays an important role in trading alpha
research. Existing methods such as rolling means(RM) and a two-states based
Kalman Filtering method have been presented in this topic. We extend two states
into various states in Kalman Filter framework to improve the accuracy of
prediction. Specifically, for different stocks we utilize cross validation and
determine best states number by minimizing mean squared error of the trading
volume. We demonstrate the effectivity of our method through a series of
comparison experiments and numerical analysis.


  It is pointed out that certain CP-odd momentum correlations in the production
and subsequent decay of tau pairs in $e^+e^-$ collisions get enhanced when the
$e^-$ is longitudinally polarized. Analytic expressions for these correlations
are obtained for the single-pion decay mode of $\tau$ when $\tau^+\tau^-$ have
a ``weak" dipole form factor (WDFF) coupling to $Z$ . For $e^+e^-$ collisions
at the $Z$ peak, a sensitivity of about 1-5$\times 10^{-17}$\mbox{$e$ cm} for
the $\tau$ WDFF can be reached using a {\em single} $\tau^+\tau^-$ decay
channel, with $10^6\, Z$'s likely to be available at the SLC at Stanford with
$e^-$ polarization of 62\%-75\%.


  Age-structured models with nonlocal diffusion arise naturally in describing
the population dynamics of biological species and the transmission dynamics of
infectious diseases in which individuals disperse nonlocally and interact each
other and the age structure of individuals matters. In the first part of our
series papers, we study the principal spectral theory of age-structured models
with nonlocal diffusion of Dirichlet type. First, we provide two criteria on
the existence of principal eigenvalues by using the theory of resolvent
positive operators with their perturbations. Then we define the generalized
principal eigenvalue and use it to investigate the influence of diffusion rate
on the principal eigenvalue. In addition, we establish the strong maximum
principle for age-structured nonlocal diffusion operators. In the second part
\cite{Ducrot2022Age-structuredII} we will investigate the effects of principal
eigenvalues on the global dynamics of the model with monotone nonlinearity in
the birth rate and show that the principal eigenvalue being zero is critical.


  As more and more personal photos are shared online, being able to obfuscate
identities in such photos is becoming a necessity for privacy protection.
People have largely resorted to blacking out or blurring head regions, but they
result in poor user experience while being surprisingly ineffective against
state of the art person recognizers. In this work, we propose a novel head
inpainting obfuscation technique. Generating a realistic head inpainting in
social media photos is challenging because subjects appear in diverse
activities and head orientations. We thus split the task into two sub-tasks:
(1) facial landmark generation from image context (e.g. body pose) for seamless
hypothesis of sensible head pose, and (2) facial landmark conditioned head
inpainting. We verify that our inpainting method generates realistic person
images, while achieving superior obfuscation performance against automatic
person recognizers.


  We consider a version of the fractional Sobolev inequality in domains and
study whether the best constant in this inequality is attained. For the
half-space and a large class of bounded domains we show that a minimizer
exists, which is in contrast to the classical Sobolev inequalities in domains.


  The Laser Interferometer Space Antenna (LISA) of the European Space Agency
(ESA) will be the first low-frequency gravitational-wave observatory orbiting
the Sun at 1 AU. The LISA Pathfinder (LPF) mission, aiming at testing of the
instruments to be located on board the LISA spacecraft (S/C), hosted, among the
others, fluxgate magnetometers and a particle detector as parts of a
diagnostics subsystem. These instruments allowed us for the estimate of the
magnetic and Coulomb spurious forces acting on the test masses that constitute
the mirrors of the interferometer. With these instruments we also had the
possibility to study the galactic cosmic-ray short term-term variations as a
function of the particle energy and the associated interplanetary disturbances.
Platform magnetometers and particle detectors will be also placed on board each
LISA S/C. This work reports about an empirical method that allowed us to
disentangle the interplanetary and onboard-generated components of the magnetic
field by using the LPF magnetometer measurements. Moreover, we estimate the
number and fluence of solar energetic particle events expected to be observed
with the ESA Next Generation Radiation Monitor during the mission lifetime. An
additional cosmic-ray detector, similar to that designed for LPF, in
combination with magnetometers, would permit to observe the evolution of
recurrent and non-recurrent galactic cosmic-ray variations and associated
increases of the interplanetary magnetic field at the transit of high-speed
solar wind streams and interplanetary counterparts of coronal mass ejections.
The diagnostics subsystem of LISA makes this mission also a natural multi-point
observatory for space weather science investigations.


  We study GPT-3, a recent large language model, using tools from cognitive
psychology. More specifically, we assess GPT-3's decision-making, information
search, deliberation, and causal reasoning abilities on a battery of canonical
experiments from the literature. We find that much of GPT-3's behavior is
impressive: it solves vignette-based tasks similarly or better than human
subjects, is able to make decent decisions from descriptions, outperforms
humans in a multi-armed bandit task, and shows signatures of model-based
reinforcement learning. Yet we also find that small perturbations to
vignette-based tasks can lead GPT-3 vastly astray, that it shows no signatures
of directed exploration, and that it fails miserably in a causal reasoning
task. These results enrich our understanding of current large language models
and pave the way for future investigations using tools from cognitive
psychology to study increasingly capable and opaque artificial agents.


  As a new model for signing quantum message, arbitrated quantum signature
(AQS) has recently received a lot of attention. In this paper we study the
cryptanalysis of previous AQS protocols from the aspects of forgery and
disavowal. We show that in these protocols the receiver Bob can realize
existential forgery of the sender's signature under known message attack. Bob
can even achieve universal forgery when the protocols are used to sign a
classical message. Furthermore, the sender Alice can successfully disavow any
of her signatures by simple attack. The attack strategies are described in
detail and some discussions about the potential improvements of the protocols
are given. Finally we also present several interesting topics in future study
on AQS protocols.


  The population growth of a Staphylococcus aureus culture was followed by
rheological measurements, under steady-state and dynamic shear flows. We
observed a rich viscoelastic behaviour as a consequence of the bacteria
activity. First, the viscosity increased ~10 times due to cell multiplication
and aggregation. This viscosity increase presented several drops and full
recoveries, which are reproducible, allowing us to evoke the existence of a
percolation phenomenon. Eventually, as the bacteria population reached a final
stage of development, fulfilling the sample volume, the viscosity returned to
its initial value, most probably caused by a change in the bacteria
physiological activity, in particular the decrease of their adhesion
properties. Finally, the viscous and the elastic moduli presented power law
behaviours compatible with the "soft glassy materials" model, which exponents
are dependent on the bacteria growth stage.


  We use the Markov Chain Monte Carlo method to investigate a global
constraints on the generalized Chaplygin gas (GCG) model as the unification of
dark matter and dark energy from the latest observational data: the
Constitution dataset of type supernovae Ia (SNIa), the observational Hubble
data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic
oscillation (BAO), and the cosmic microwave background (CMB) data. In a
non-flat universe, the constraint results for GCG model are,
$\Omega_{b}h^{2}=0.0235^{+0.0021}_{-0.0018}$ ($1\sigma$) $^{+0.0028}_{-0.0022}$
$(2\sigma)$, $\Omega_{k}=0.0035^{+0.0172}_{-0.0182}$ ($1\sigma$)
$^{+0.0226}_{-0.0204}$ $(2\sigma)$, $A_{s}=0.753^{+0.037}_{-0.035}$ ($1\sigma$)
$^{+0.045}_{-0.044}$ $(2\sigma)$, $\alpha=0.043^{+0.102}_{-0.106}$ ($1\sigma$)
$^{+0.134}_{-0.117}$ $(2\sigma)$, and $H_{0}=70.00^{+3.25}_{-2.92}$ ($1\sigma$)
$^{+3.77}_{-3.67}$ $(2\sigma)$, which is more stringent than the previous
results for constraint on GCG model parameters. Furthermore, according to the
information criterion, it seems that the current observations much support
$\Lambda$CDM model relative to the GCG model.


  Neutrino with magnetic moment can experience a chirality flip while
scattering off charged particles. This effect may lead to important
consequences for the dynamics and the neutrino signal of the core-collapse
supernova. It is known that if neutrino is a Dirac fermion, then nu_L->nu_R
transition induced by the chirality flip leads to the emission of sterile
right-handed neutrinos. The typical energies of these neutrinos are rather
high, E ~ (100-200)MeV. Neutrino spin precession in the magnetic field either
inside the collapsing star or in the interstellar space may lead to the
backward transition, nu_R->nu_L. Both possibilities are known to be
interesting. In the former case high-energy neutrinos can deliver additional
energy to the supernova envelope, which can help the supernova to explode. In
the latter case high-energy neutrinos may be detected simultaneously with the
"normal" supernova neutrino signal, which would be a smoking gun for the Dirac
neutrino magnetic moment. We report the results of the calculation of the
supernova right-handed neutrino luminosity up to 250 ms after bounce. They
allow to refine the estimates of the energy emitted in right-handed neutrinos.
Also the sensitivity of water Cherenkov detectors to the Dirac neutrino
magnetic moment is estimated. For mu_Dirac=10^{-13}mu_B Super-Kamiokande is
expected to detect at least few high-energy events from a galactic supernova
explosion.
  Also we briefly discuss the case of Majorana neutrino magnetic moment. It is
pointed out that spin flips may quickly equilibrate electron neutrinos with
non-electron antineutrinos if mu_Majorana~10^{-12}mu_B. This may lead to
various consequences for supernova physics.


  We investigate inflation in closed Friedmann-Robertson-Walker universe filled
with the scalar field with power-law potential. For a wide range of powers and
parameters of the potential we numerically calculated the slow-roll parameters
and scalar spectral index at the epoch when present Hubble scale leaves the
horizon and at the end of inflation. Also we compare results of our numerical
calculations with recent observation data. This allows us to set a constraint
on the power of the potential: alpha < (3.5 - 4.5).


  Based on the scaling relation for the dynamics at the early time, a new
method is proposed to measure both the static and dynamic critical exponents.
The method is applied to the two dimensional Ising model. The results are in
good agreement with the existing results. Since the measurement is carried out
in the initial stage of the relaxation process starting from independent
initial configurations, our method is efficient.


  We study in detail the role of covariant Lyapunov vectors and their
respective angles for detecting transitions between metastable states in
dynamical systems, as recently discussed in several atmospheric science
applications. The underlying models are built from data by the dynamical
clustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximated
based on these models. We test this data-based numerical approach at the hand
of three well-understood example systems with increasing dynamical complexity,
identifying crucial properties that allow for a successful application of the
method: in particular, it turns out that the method requires a clear multiple
time scale structure with fast transitions between slow subsystems which can be
dynamically characterized by invariant neutral directions of the linear
approximation model.


  In his celebrated article, Aronson established Gaussian bounds for the
fundamental solution to the Cauchy problem governed by a second order
divergence form operator with uniformly elliptic coefficients. We extend
Aronson's proof of upper heat kernel estimates to nonlocal operators whose
jumping kernel satisfies a pointwise upper bound and whose energy form is
coercive. A detailed proof is given in the Euclidean space and extensions to
doubling metric measure spaces are discussed.


  Deep learning-based image fusion approaches have obtained wide attention in
recent years, achieving promising performance in terms of visual perception.
However, the fusion module in the current deep learning-based methods suffers
from two limitations, \textit{i.e.}, manually designed fusion function, and
input-independent network learning. In this paper, we propose an unsupervised
adaptive image fusion method to address the above issues. We propose a feature
mutual mapping fusion module and dual-branch multi-scale autoencoder. More
specifically, we construct a global map to measure the connections of pixels
between the input source images. % The found mapping relationship guides the
image fusion. Besides, we design a dual-branch multi-scale network through
sampling transformation to extract discriminative image features. We further
enrich feature representations of different scales through feature aggregation
in the decoding process. Finally, we propose a modified loss function to train
the network with efficient convergence property. Through sufficient training on
infrared and visible image data sets, our method also shows excellent
generalized performance in multi-focus and medical image fusion. Our method
achieves superior performance in both visual perception and objective
evaluation. Experiments prove that the performance of our proposed method on a
variety of image fusion tasks surpasses other state-of-the-art methods, proving
the effectiveness and versatility of our approach.


  Based on the effective four-band model we analyze the spin response in the
normal and superconducting states of the Fe-pnictide superconductors. While the
normal state spin excitations are dominated by the continuum of the
interorbital antiferromagnetic fluctuations and the intraband spin density wave
fluctuations, the unconventional superconductivity yields different feedback.
The resonance peak in form of the well-defined spin exciton occurs {\it only}
for the interband scattering at the antiferromagnetic momentum ${\bf Q}_{AFM}$
for the $s_\pm$ (extended s-wave) superconducting order parameter and it
disappears rapidly for ${\bf q} < {\bf Q}_{AFM}$. The resonance feature is
extremely weak for the $d_{x^2 -y^2}$-wave order parameter due to specific
Fermi surface topology of these compounds. The essential difference between
$s_\pm$-wave and $d_{x^2 -y^2}$-wave symmetries for the magnetic excitations
can be used for experimental determination of the superconducting wave function
symmetry.


This paper collects many results on galoisian ideals and Galois theory.


  We study the suppression of reflections in the numerical simulation of the
time-dependent Schr\"odinger equation for strong-field problems on a grid using
exterior complex scaling (ECS) as absorbing boundary condition. It is shown
that the ECS method can be applied in both the length and the velocity gauge as
long as appropriate restrictions are applied in the ECS transformation of the
electron-field coupling. It is found that the ECS method improves the
suppression of reflection as compared to the conventional masking technique in
typical simulations of atoms exposed to an intense laser pulse. Finally, we
demonstrate the advantage of the ECS technique to avoid unphysical artifacts in
the evaluation of high harmonic spectra.


  Using data drawn from the Sloan Digital Sky Survey (SDSS) and the SDSS-II
Supernova Survey, we study the local environments of confirmed type Ia
supernovae (SNe Ia) in the nearby Universe. At 0.05 < z < 0.15, we find that SN
Ia events in blue, star-forming galaxies occur preferentially in regions of
lower galaxy density relative to galaxies of like stellar mass and
star-formation rate, while SNe Ia in nearby red galaxies show no significant
environment dependence within the measurement uncertainties. Even though our
samples of SNe in red hosts are relatively small in number, tests on simulated
galaxy samples suggest that the observed distribution of environments for red
SN Ia hosts is in poor agreement with a cluster type Ia rate strongly elevated
relative to the field rate. Finally, after considering the impact of galaxy
morphology, stellar age, stellar metallicity, and other relevant galaxy
properties, we conclude that the observed correlation between the SN Ia rate
and environment in the star-forming galaxy population is likely driven by a
gas-phase metallicity effect, such that prompt type Ia supernovae occur more
often or are more luminous in metal-poor systems.


  In this paper we demonstrate that the Riesz representation of excessive
functions is a useful and enlightening tool to study optimal stopping problems.
After a short general discussion of the Riesz representation we concretize,
firstly, on a d-dimensional and, secondly, a space-time one-dimensional
geometric Brownian motion. After this, two classical optimal stopping problems
are discussed: 1) the optimal investment problem and 2) the valuation of the
American put option. It is seen in both of these problems that the boundary of
the stopping region can be characterized as a unique solution of an integral
equation arising immediately from the Riesz representation of the value
function. In Problem 2 the derived equation coincides with the standard
well-known equation found in the literature.


  Constrained KP and super-KP hierarchies of integrable equations (generalized
NLS hierarchies) are systematically produced through a Lie algebraic AKS-matrix
framework associated to the homogeneous grading. The role played by different
regular elements to define the corresponding hierarchies is analyzed as well as
the symmetry properties under the Weyl group transformations. The coset
structure of higher order hamiltonian densities is proven.\par For a generic
Lie algebra the hierarchies here considered are integrable and essentially
dependent on continuous free parameters. The bosonic hierarchies studied in
\cite{{FK},{AGZ}} are obtained as special limit restrictions on hermitian
symmetric-spaces.\par In the supersymmetric case the homogeneous grading is
introduced consistently by using alternating sums of bosons and fermions in the
spectral parameter power series.\par The bosonic hierarchies obtained from
${\hat {sl(3)}}$ and the supersymmetric ones derived from the $N=1$
affinization of $sl(2)$, $sl(3)$ and $osp(1|2)$ are explicitly constructed.
\par An unexpected result is found: only a restricted subclass of the $sl(3)$
bosonic hierarchies can be supersymmetrically extended while preserving
integrability.


  This dissertation is devoted to provide advanced nonconvex nonsmooth
variational models of (Magnetic Resonance Image) MRI reconstruction, efficient
learnable image reconstruction algorithms and parameter training algorithms
that improve the accuracy and robustness of the optimization-based deep
learning methods for compressed sensing MRI reconstruction and synthesis. The
first part introduces a novel optimization based deep neural network whose
architecture is inspired by proximal gradient descent for solving a variational
model. The second part is a substantial extension of the preliminary work in
the first part by solving the calibration-free fast pMRI reconstruction problem
in a discrete-time optimal control framework. The third part aims at developing
a generalizable Magnetic Resonance Imaging (MRI) reconstruction method in the
meta-learning framework. The last part aims to synthesize target modality of
MRI by using partially scanned k-space data from source modalities instead of
fully scanned data that is used in the state-of-the-art multimodal synthesis.


  Image classification models often demonstrate unstable performance in
real-world applications due to variations in image information, driven by
differing visual perspectives of subject objects and lighting discrepancies. To
mitigate these challenges, existing studies commonly incorporate additional
modal information matching the visual data to regularize the model's learning
process, enabling the extraction of high-quality visual features from complex
image regions. Specifically, in the realm of multimodal learning, cross-modal
alignment is recognized as an effective strategy, harmonizing different modal
information by learning a domain-consistent latent feature space for visual and
semantic features. However, this approach may face limitations due to the
heterogeneity between multimodal information, such as differences in feature
distribution and structure. To address this issue, we introduce a Multimodal
Alignment and Reconstruction Network (MARNet), designed to enhance the model's
resistance to visual noise. Importantly, MARNet includes a cross-modal
diffusion reconstruction module for smoothly and stably blending information
across different domains. Experiments conducted on two benchmark datasets,
Vireo-Food172 and Ingredient-101, demonstrate that MARNet effectively improves
the quality of image information extracted by the model. It is a plug-and-play
framework that can be rapidly integrated into various image classification
frameworks, boosting model performance.


  We propose a machine learning approach based on artificial neural network to
gain faster insights on the role of geometric contributions to the
nonequilibrium fluctuations of an adiabatically temperature-driven quantum heat
engine coupled to a cavity. Using the artificial neural network we have
explored the interplay between bunched and antibunched photon exchange
statistics for different engine parameters. We report that beyond a pivotal
cavity temperature, the Fano factor oscillates between giant and low values as
a function of phase difference between the driving protocols. We further
observe that the standard thermodynamic uncertainty relation is not valid when
there are finite geometric contributions to the fluctuations, but holds true
for zero phase difference even in presence of coherences.


  We propose a new method for automatically detecting monotonic input-output
relationships from data using Gaussian Process (GP) models with virtual
derivative observations. Our results on synthetic and real datasets show that
the proposed method detects monotonic directions from input spaces with high
accuracy. We expect the method to be useful especially for improving
explainability of the models and improving the accuracy of regression and
classification tasks, especially near the edges of the data or when
extrapolating.


  State-of-the-art transmon qubits rely on large capacitors which
systematically improves their coherence due to reduced surface loss
participation. However, this approach increases both the footprint and the
parasitic cross-coupling and is ultimately limited by radiation losses - a
potential roadblock for scaling up quantum processors to millions of qubits. In
this work we present transmon qubits with sizes as low as 36$ \times $39$
\mu$m$^2$ with $\gtrsim$100 nm wide vacuum gap capacitors that are
micro-machined from commercial silicon-on-insulator wafers and shadow
evaporated with aluminum. After the release in HF vapor we achieve a vacuum
participation ratio up to 99.6\% in an in-plane design that is compatible with
standard coplanar circuits. Qubit relaxation time measurements for small gaps
with high vacuum electric fields of up to 22 V/m reveal a double exponential
decay indicating comparably strong coupling to long-lived two-level-systems
(TLS). The exceptionally high selectivity of $>$20 dB to the
superconductor-vacuum surface allows to precisely back out the
sub-single-photon dielectric loss tangent of aluminum oxide exposed to ambient
conditions. In terms of future scaling potential we achieve a qubit quality
factor by footprint area of $20 \mu \mathrm{s}^{-2}$, which is on par with the
highest $T_1$ devices relying on larger geometries and expected to improve
substantially for lower loss superconductors like NbTiN, TiN or Ta.


  This paper presents a general description of a parameter estimation inverse
problem for systems governed by nonlinear differential equations. The inverse
problem is presented using optimal control tools with state constraints, where
the minimization process is based on a first-order optimization technique such
as adaptive monotony-backtracking steepest descent technique and nonlinear
conjugate gradient methods satisfying strong Wolfe conditions. Global
convergence theory of both methods is rigorously established where new linear
convergence rates have been reported. Indeed, for the nonlinear non-convex
optimization we show that under the Lipschitz-continuous condition of the
gradient of the objective function we have a linear convergence rate toward a
stationary point. Furthermore, nonlinear conjugate gradient method has also
been shown to be linearly convergent toward stationary points where the second
derivative of the objective function is bounded. The convergence analysis in
this work has been established in a general nonlinear non-convex optimization
under constraints framework where the considered time-dependent model could
whether be a system of coupled ordinary differential equations or partial
differential equations. Numerical evidence on a selection of popular nonlinear
models is presented to support the theoretical results. Nonlinear Conjugate
gradient methods, Nonlinear Optimal control and Convergence analysis and
Dynamical systems and Parameter estimation and Inverse problem


  Human motion stylization aims to revise the style of an input motion while
keeping its content unaltered. Unlike existing works that operate directly in
pose space, we leverage the latent space of pretrained autoencoders as a more
expressive and robust representation for motion extraction and infusion.
Building upon this, we present a novel generative model that produces diverse
stylization results of a single motion (latent) code. During training, a motion
code is decomposed into two coding components: a deterministic content code,
and a probabilistic style code adhering to a prior distribution; then a
generator massages the random combination of content and style codes to
reconstruct the corresponding motion codes. Our approach is versatile, allowing
the learning of probabilistic style space from either style labeled or
unlabeled motions, providing notable flexibility in stylization as well. In
inference, users can opt to stylize a motion using style cues from a reference
motion or a label. Even in the absence of explicit style input, our model
facilitates novel re-stylization by sampling from the unconditional style prior
distribution. Experimental results show that our proposed stylization models,
despite their lightweight design, outperform the state-of-the-art in style
reenactment, content preservation, and generalization across various
applications and settings. Project Page: https://murrol.github.io/GenMoStyle


  In this paper we study a shallow water equation derivable using the
Boussinesq approximation, which includes as two special cases, one equation
discussed by Ablowitz et. al. [Stud. Appl. Math., 53 (1974) 249--315] and one
by Hirota and Satsuma [J. Phys. Soc. Japan}, 40 (1976) 611--612]. A catalogue
of classical and nonclassical symmetry reductions, and a Painleve analysis, are
given. Of particular interest are families of solutions found containing a rich
variety of qualitative behaviours. Indeed we exhibit and plot a wide variety of
solutions all of which look like a two-soliton for t>0 but differ radically for
t<0. These families arise as nonclassical symmetry reduction solutions and
solutions found using the singular manifold method. This example shows that
nonclassical symmetries and the singular manifold method do not, in general,
yield the same solution set. We also obtain symmetry reductions of the shallow
water equation solvable in terms of solutions of the first, third and fifth
Painleve equations. We give evidence that the variety of solutions found which
exhibit ``nonlinear superposition'' is not an artefact of the equation being
linearisable since the equation is solvable by inverse scattering. These
solutions have important implications with regard to the numerical analysis for
the shallow water equation we study, which would not be able to distinguish the
solutions in an initial value problem since an exponentially small change in
the initial conditions can result in completely different qualitative
behaviours.