  We report theoretical investigations on the role of interfacial bonding
mechanism and its resulting structures to quantum transport in molecular wires.
Two bonding mechanisms for the Au-S bond in an
Au(111)/1,4-benzenedithiol(BDT)/Au(111) junction were identified by ab initio
calculation, confirmed by a recent experiment, which, we showed, critically
control charge conduction. It was found, for Au/ BDT/Au junctions, the hydrogen
atom, bound by a dative bond to the Sulfur, is energetically non-dissociative
after the interface formation. The calculated conductance and junction
breakdown forces of H-non-dissociative Au/BDT/Au devices are consistent with
the experimental values, while the H-dissociated devices, with the interface
governed by typical covalent bonding, give conductance more than an order of
magnitude larger. By examining the scattering states that traverse the
junctions, we have revealed that mechanical and electric properties of a
junction have strong correlation with the bonding configuration. This work
clearly demonstrates that the interfacial details, rather than previously
believed many-body effects, is of vital importance for correctly predicting
equilibrium conductance of molecular junctions; and manifests that the
interfacial contact must be carefully understood for investigating quantum
transport properties of molecular nanoelectronics.


  The presence of methanol among the common ice components in interstellar
clouds and protostellar envelopes has been confirmed by the James Webb Space
Telescope. Methanol is often detected in the gas phase toward lines of sight
shielded from UV radiation. We measured the volumetric density of methanol ice,
grown under simulated interstellar conditions, and the infrared spectroscopy at
different deposition temperatures and during the warm-up. The IR band strengths
are provided and the experimental spectra are compared to those computed with a
model. The transition from amorphous to crystalline methanol ice was also
explored. Finally, we propose new observations of methanol ice at high
resolution to probe the methanol ice structure.


  We study the rate of energy decay for solutions of a coupled wave-heat system
on a rectangular domain. Using techniques from the theory of $C_0$-semigroups,
and in particular a well-known result due to Borichev and Tomilov, we prove
that the energy of classical solutions decays like $t^{-2/3}$ as $t\to\infty$.
This rate is moreover shown to be sharp. Our result implies in particular that
a general estimate in the literature, which predicts at least logarithmic decay
and is known to be best possible in general, is suboptimal in the special case
under consideration here. Our strategy of proof involves direct estimates based
on separation of variables and a refined version of the technique developed in
our earlier paper for a one-dimensional wave-heat system.


  Rapid localization of gravitational-wave events is important for the success
of the multi-messenger observations. The forthcoming improvements and
constructions of gravitational-wave detectors will enable detecting and
localizing compact-binary coalescence events even before mergers, which is
called early warning. The performance of early warning can be improved by
considering modulation of gravitational wave signal amplitude due to the Earth
rotation and the precession of a binary orbital plane caused by the misaligned
spins of compact objects. In this paper, for the first time we estimate
localization precision in the early warning quantitatively, taking into account
an orbital precession. We find that a neutron star-black hole binary at $z=0.1$
can typically be localized to $100\,\mathrm{deg}^2$ and $10\,\mathrm{deg^2}$ at
the time of $12$ -- $15 \,\mathrm{minutes}$ and $50$ -- $300\,\mathrm{seconds}$
before merger, respectively, which cannot be achieved without the precession
effect.


  In this survey paper we give an overview over constructions of geometries
associated to Jordan structures (algebras, triple systems and pairs), featuring
analogs of these constructions with the Lie functor on the one hand and with
the approach of non-commutative geometry on the other hand.


  The amplitude mode of a fermionic superfluid, analogous to the Higgs Boson,
becomes undamped in the strong coupling regime when its frequency is pushed
inside the BCS energy gap. We argue that this is the case in cold gases due to
the energy dispersion and nonlocality of the pairing interaction, and propose
to use the Feshbach resonance regime for parametric excitation of this mode.
The results presented for the BCS pairing dynamics indicate that even weak
dispersion suppresses dephasing and gives rise to persistent oscillations. The
frequency of oscillations extracted from our simulation of the BCS dynamics
agrees with the prediction of the many-body theory.


  A star completely destroyed in a tidal disruption event (TDE) ignites a
luminous flare that is powered by the fallback of tidally stripped debris to a
supermassive black hole (SMBH) of mass $M_{\bullet}$. We analyze two estimates
for the peak fallback rate in a TDE, one being the "frozen-in" model, which
predicts a strong dependence of the time to peak fallback rate, $t_{\rm peak}$,
on both stellar mass and age, with $15\textrm{ days} \lesssim t_{\rm peak}
\lesssim 10$ yr for main sequence stars with masses $0.2\le M_{\star}/M_{\odot}
\le 5$ and $M_{\bullet} = 10^6M_{\odot}$. The second estimate, which postulates
that the star is completely destroyed when tides dominate the maximum stellar
self-gravity, predicts that $t_{\rm peak}$ is very weakly dependent on stellar
type, with $t_{\rm peak} = \left(23.2\pm4.0\textrm{
days}\right)\left(M_{\bullet}/10^6M_{\odot}\right)^{1/2}$ for $0.2\le
M_{\star}/M_{\odot} \le 5$, while $t_{\rm peak} = \left(29.8\pm3.6\textrm{
days}\right)\left(M_{\bullet}/10^6M_{\odot}\right)^{1/2}$ for a Kroupa initial
mass function truncated at $1.5 M_{\odot}$. This second estimate also agrees
closely with hydrodynamical simulations, while the frozen-in model is
discrepant by orders of magnitude. We conclude that (1) the time to peak
luminosity in complete TDEs is almost exclusively determined by SMBH mass, and
(2) massive-star TDEs power the largest accretion luminosities. Consequently,
(a) decades-long extra-galactic outbursts cannot be powered by complete TDEs,
including massive-star disruptions, and (b) the most highly super-Eddington
TDEs are powered by the complete disruption of massive stars, which -- if
responsible for producing jetted TDEs -- would explain the rarity of jetted
TDEs and their preference for young and star-forming host galaxies.


  The early Universe was characterized by the presence of heavy particles that
decoupled at different temperatures leading to different phases of the
Universe. This had a consequences on the time evolution of the thermodynamic
and the cosmological parameters characterizing each phase of the early
Universe. In this study, we derive the analytic expressions of the equations
governing the time evolution of these parameters in the early eras of the
Universe namely, the radiation era, the quark-gluon plasma era, the hadron era
and the mixed era. The parameters under concern include the energy density, the
entropy density, the temperature, the pressure in addition to Hubble parameter
and the scale factor. Having these expressions allows us to give estimations of
the times corresponding to the beginning and ending of each era of the Universe
as will be presented in this work.


  This paper presents a 2D/3D Free Surface Lattice Boltzmann Method simulation
package called LBfoam for the simulation of foaming processes. The model
incorporates the essential physics of foaming phenomena: gas diffusion into
nucleated bubbles, bubble dynamics and coalescence, surface tension, the
stabilizing disjoining pressure between bubbles, and Newtonian and
non-Newtonian rheological models. The software can simulate the growth and
interaction of bubbles, and predict final foam structures. The implementation
is based on the Palabos library (in C++), which enables large-scale parallel
simulations. The software is freely available under the GNU Affero General
Public License version 3 at: https://github.com/mehdiataei/LBfoam


  In this paper, we investigate the controllability of a class of formation
control systems. Given a directed graph, we assign an agent to each of its
vertices and let the edges of the graph describe the information flow in the
system. We relate the strongly connected components of this graph to the
reachable set of the formation control system. Moreover, we show that the
formation control model is approximately path-controllable over a
path-connected, open dense subset as long as the graph is weakly connected and
satisfies some mild assumption on the numbers of vertices of the strongly
connected components.


  Due to the development of graph neural networks, graph-based representation
learning methods have made great progress in recommender systems. However, data
sparsity is still a challenging problem that most graph-based recommendation
methods are confronted with. Recent works try to address this problem by
utilizing side information. In this paper, we exploit the relevant and easily
accessible textual information by advanced natural language processing (NLP)
models and propose a light RGCN-based (RGCN, relational graph convolutional
network) collaborative filtering method on heterogeneous graphs. Specifically,
to incorporate rich textual knowledge, we utilize a pre-trained NLP model to
initialize the embeddings of text nodes. Afterward, by performing a simplified
RGCN-based node information propagation on the constructed heterogeneous graph,
the embeddings of users and items can be adjusted with textual knowledge, which
effectively alleviates the negative effects of data sparsity. Moreover, the
matching function used by most graph-based representation learning methods is
the inner product, which is not appropriate for the obtained embeddings that
contain complex semantics. We design a predictive network that combines
graph-based representation learning with neural matching function learning, and
demonstrate that this architecture can bring a significant performance
improvement. Extensive experiments are conducted on three publicly available
datasets, and the results verify the superior performance of our method over
several baselines.


  We report on the results of the first measurement of exclusive $f_0(980)$
meson photoproduction on protons for $E_\gamma=3.0 - 3.8$ GeV and $-t =
0.4-1.0$ GeV$^2$. Data were collected with the CLAS detector at the Thomas
Jefferson National Accelerator Facility. The resonance was detected via its
decay in the $\pi^+ \pi^-$ channel by performing a partial wave analysis of the
reaction $\gamma p \to p \pi^+ \pi^-$. Clear evidence of the $f_0(980)$ meson
was found in the interference between $P$ and $S$ waves at $M_{\pi^+ \pi^-}\sim
1$ GeV. The $S$-wave differential cross section integrated in the mass range of
the $f_0(980)$ was found to be a factor of 50 smaller than the cross section
for the $\rho$ meson. This is the first time the $f_0(980)$ meson has been
measured in a photoproduction experiment.


  We present first results from a number of experiments conducted on a 0.53 kg
cylindrical dumbbell-shaped sapphire crystal. This is the first reported
optomechanical experiment of this nature utilising a novel modification to the
typical cylindrical architecture. Mechanical motion of the crystal structure
alters the dimensions of the crystal, and the induced strain changes the
permittivity. These two effects result in parametric frequency modulation of
resonant microwave whispering gallery modes that are simultaneously excited
within the crystal. A novel low-noise microwave readout system is implemented
allowing extremely low noise measurements of this frequency modulation near our
modes of interest, having a phase noise floor of -165 dBc/Hz at 100 kHz.
Fine-tuning of the crystal's suspension has allowed for the optimisation of
mechanical quality factors in preparation for cryogenic experiments, with a
value of Q=8 x 10^7 achieved at 127 kHz. This results in a Q x f product of
10^13, equivalent to the best measured values in a macroscopic sapphire
mechanical system. Results are presented that demonstrate the excitation of
mechanical modes via radiation pressure force, allowing an experimental method
of determining the transducer's displacement sensitivity df/dx, and calibrating
the system. Finally, we demonstrate parametric back-action phenomenon within
the system. These are all important steps towards the overall goal of the
experiment; to cool a macroscopic device to the quantum ground state at
millikelvin temperatures.


  Galactic halos are of great importance for our understanding of both the dark
matter nature and primordial non-Gaussianity in the perturbation spectrum, a
powerful discriminant of the physical mechanisms that generated the
cosmological fluctuations observed today. In this paper we analyze {\it Planck}
data towards the galaxy M104 (Sombrero) and find an asymmetry in the microwave
temperature which extends up to about $1 \degr$ from the galactic center. This
frequency-independent asymmetry is consistent with that induced by the Doppler
effect due to the galactic rotation and we find a probability of less than
about $0.2\%$ that it is due to a random fluctuation of the microwave
background. In addition, {\it Planck} data indicate the relatively complex
dynamics of the M104 galactic halo, and this appears to be in agreement with
previous studies. In view of our previous analysis of the dark halos of nearby
galaxies, this finding confirms the efficiency of the method used in revealing
and mapping the dark halos around relatively nearby edge-on galaxies.


  Sorting quantum fields into different modes according to their Fock-space
quantum numbers is a highly desirable quantum operation. In this Letter, we
show that a pair of two-level emitters, chirally coupled to a waveguide, may
scatter single- and two-photon components of an input pulse into orthogonal
temporal modes with a fidelity $\gtrsim 0.9997$. We develop a general theory to
characterize and optimize this process and observe an interesting dynamics in
the two-photon scattering regime: while the first emitter gives rise to a
complex multimode field, the second emitter recombines the field amplitudes and
the net two-photon scattering induces a self-time reversal of the pulse mode.
The presented scheme can be employed to construct logic elements for
propagating photons, such as a deterministic nonlinear-sign gate with a
fidelity $\gtrsim 0.9995$


  This article is concerned with the infinite depth water wave equation in two
space dimensions. We consider this problem expressed in position-velocity
potential holomorphic coordinates,and prove that small localized data leads to
global solutions. This article is a continuation of authors' earlier paper
arXiv:1401.1252.


  Asymptotic symmetries at future null infinity (I+) of Minkowski space for
electrodynamics with massless charged fields, as well as non-Abelian gauge
theories with gauge group G, are considered at the semiclassical level. The
possibility of charge/color flux through I+ suggests the symmetry group is
infinite-dimensional. It is conjectured that the symmetries include a G
Kac-Moody symmetry whose generators are "large" gauge transformations which
approach locally holomorphic functions on the conformal two-sphere at I+ and
are invariant under null translations. The Kac-Moody currents are constructed
from the gauge field at the future boundary of I+. The current Ward identities
include Weinberg's soft photon theorem and its colored extension.


  In this paper we consider the problem \begin{equation*} \left \{
\begin{array}{l} -\Delta u \pm \phi u + W'(x,u) = 0\hbox{ in }
\mathbb{R}^2,\newline \Delta \phi = u^2 \hbox{ in } \mathbb{R}^2, \end{array}
\right. \end{equation*} where $W$ is assumed positive. In dimension three, the
problem with the sign + (we call it $(\mathcal P_+)$) was considered and solved
in \cite{M}, whereas in the same paper it was showed that no nontrivial
solution exists if we consider the sign -- (say it $(\mathcal P_-)$). We
provide a general existence result for $(\mathcal P_+)$ and two examples
falling in the case $(\mathcal P_-)$ for which there exists at least a
nontrivial solution.


  Let k(B_0) and l(B_0) respectively denote the number of ordinary and p-Brauer
irreducible characters in the principal block B_0 of a finite group G. We prove
that, if k(B_0)-l(B_0)=1, then l(B_0)\geq p-1 or else p=11 and l(B_0)=9. This
follows from a more general result that for every finite group G in which all
non-trivial p-elements are conjugate, l(B_0)\geq p-1 or else p = 11 and
G/O_{p'}(G) =11^2:SL(2,5). These results are useful in the study of principal
blocks with a few characters.
  We propose that, in every finite group G of order divisible by p, the number
of irreducible Brauer characters in the principal p-block of G is always at
least 2\sqrt{p-1}+1-k_p(G), where k_p(G) is the number of conjugacy classes of
p-elements of G. This indeed is a consequence of the celebrated Alperin weight
conjecture and known results on bounding the number of p-regular classes in
finite groups.


  We introduce C*-algebras over C_{\infty}(Q,C) as Banach-Kantorovich
*-algebras over the algebra C_{\infty}(Q,C) of extended continuous
complex-valued functions, defined on comeager subsets of Stonean compact Q,
whose norm satisfies conditions similar to the axioms of C*-algebras, and show
that such algebras can be uniquely up to a Q-C*-isomorphism represented by
means of a continuous complete fiber bundle of C*-algebras over Q.


  We consider the finite volume mean values of current operators in integrable
spin chains with local interactions, and provide an alternative derivation of
the exact result found recently by the author and two collaborators. We use a
certain type of long range deformation of the local spin chains, which was
discovered and explored earlier in the context of the AdS/CFT correspondence.
This method is immediately applicable also to higher rank models: as a concrete
example we derive the current mean values in the SU(3)-symmetric fundamental
model, solvable by the nested Bethe Ansatz. The exact results take the same
form as in the Heisenberg spin chains: they involve the one-particle
eigenvalues of the conserved charges and the inverse of the Gaudin matrix.


  We present a new mechanism of fluctuation-induced Nambu-Goldstone bosons in a
scalar field theory of Higgs-Josephson systems. We consider a simple scalar
field model with $U(1)^n$ rotational symmetry. When there is an interaction
which violates the rotational symmetry, the Nambu-Goldstone bosons become
massive and massless bosons are concealed. We present a model where the massive
boson becomes a massless boson as a result of the perturbative fluctuation. In
our model the ${\bf Z}_2$-symmetry associated with the chirality is also
broken. The transition occurs as a (weak) first-order transition at the
critical point. The ground state at absolute zero will flow into the state with
more massless bosons due to fluctuation effects at finite temperature.


  For precision studies with QCD observables at colliders, higher order
perturbative corrections are often mandatory. For exclusive observables, like
jet cross sections or differential distributions, these corrections were until
recently only known to next-to-leading order (NLO) in perturbation theory.
Owing to many new technical developments, first next-to-next-to-leading order
(NNLO) QCD calculations are now becoming available. We review the recent
progress in this field.


  In a recent preprint arXiv:2203.15521 G. X. Chan, P. Huang, and X. Wang claim
that triple-quantum dot superexchange in a (1, 0, 1) charge configuration
exhibits a change of sign (going from positive to negative) as a function of
middle dot detuning. Furthermore, their claim is that charge sweet-spots exist
for specific values of the inter-dot detuning. Their analysis is based on the
Hubbard model and something to what they refer to as the full
Configuration-Interaction method. All of this findings were already reported by
M. J. Ran\v{c}i\'{c} and G. Burkard in Ref. Phys. Rev. B 96, 201304(R) (2017)
based on the Hubbard model. No reference to this manuscript was made in Ref.
arXiv:2203.15521. I have asked the authors to urgently modify the pre-print and
position their work with respect to the previously conducted study - which they
rejected to do at the current moment, quoting that pp. it is not their style to
modify preprints before they were accepted. This alongside with a very similar
style of some figures lead me to the conclusion that they are deliberately
misleading the scientific community and trying to adopt other peoples work and
ideas as their own.


  Let $\Omega$ be a $m$-hyperconvex domain of $\mathbb{C}^n$ and $\beta$ be the
standard K\"{a}hler form in $\mathbb{C}^n$. We introduce finite energy classes
of $m$-subharmonic functions of Cegrell type, $\mathcal{E}_m^p, p>0$ and
$\mathcal{F}_m$. Using a variational method we show that the degenerate complex
Hessian equation $(dd^c\varphi)^m\wedge \beta^{n-m}=\mu$ has a unique solution
in $\mathcal{E}_m^1$ if and only if every function in $\mathcal{E}_m^1$ is
integrable with respect to $\mu$. If $\mu$ has finite total mass and does not
charge $m$-polar sets, then the equation has a unique solution in
$\mathcal{F}_m$.


  The problem of matching a query string to a directed graph, whose vertices
are labeled by strings, has application in different fields, from data mining
to computational biology. Several variants of the problem have been considered,
depending on the fact that the match is exact or approximate and, in this
latter case, which edit operations are considered and where are allowed. In
this paper we present results on the complexity of the approximate matching
problem, where edit operations are symbol substitutions and are allowed only on
the graph labels or both on the graph labels and the query string. We introduce
a variant of the problem that asks whether there exists a path in a graph that
represents a query string with any number of edit operations and we show that
is is NP-complete, even when labels have length one and in the case the
alphabet is binary. Moreover, when it is parameterized by the length of the
input string and graph labels have length one, we show that the problem is
fixed-parameter tractable and it is unlikely to admit a polynomial kernel. The
NP-completeness of this problem leads to the inapproximability (within any
factor) of the approximate matching when edit operations are allowed only on
the graph labels. Moreover, we show that the variants of approximate string
matching to graph we consider are not fixed-parameter tractable, when the
parameter is the number of edit operations, even for graphs that have distance
one from a DAG. The reduction for this latter result allows us to prove the
inapproximability of the variant where edit operations can be applied both on
the query string and on graph labels.


  We propose an extension of the Dubrovin-Zhang perturbative approach to the
study of normal forms for non-Hamiltonian integrable scalar conservation laws.
The explicit computation of the first few corrections leads to the conjecture
that such normal forms are parameterized by one single functional parameter,
named viscous central invariant. A constant valued viscous central invariant
corresponds to the well-known Burgers hierarchy. The case of a linear viscous
central invariant provides a viscous analog of the Camassa-Holm equation, that
formerly appeared as a reduction of a two-component Hamiltonian integrable
systems. We write explicitly the negative and positive hierarchy associated
with this equation and prove the integrability showing that they can be mapped
respectively into the heat hierarchy and its negative counterpart, named the
Klein-Gordon hierarchy. A local well-posedness theorem for periodic initial
data is also proven. We show how transport equations can be used to effectively
construct asymptotic solutions via an extension of the quasi-Miura map that
preserves the initial datum. The method is alternative to the method of the
string equation for Hamiltonian conservation laws and naturally extends to the
viscous case. Using these tools we derive the viscous analog of the Painlev\'e
I2 equation that describes the universal behaviour of the solution at the
critical point of gradient catastrophe.


  Intense recent discussions have focused on how to provide individuals with
control over when their data can and cannot be used --- the EU's Right To Be
Forgotten regulation is an example of this effort. In this paper we initiate a
framework studying what to do when it is no longer permissible to deploy models
derivative from specific user data. In particular, we formulate the problem of
efficiently deleting individual data points from trained machine learning
models. For many standard ML models, the only way to completely remove an
individual's data is to retrain the whole model from scratch on the remaining
data, which is often not computationally practical. We investigate algorithmic
principles that enable efficient data deletion in ML. For the specific setting
of k-means clustering, we propose two provably efficient deletion algorithms
which achieve an average of over 100X improvement in deletion efficiency across
6 datasets, while producing clusters of comparable statistical quality to a
canonical k-means++ baseline.


  We show that the optimal trial wave function of a fractional Chern insulator
depends on the form of its electron-electron interaction. The gauge of single
particle Bloch bases for constructing the optimal trail wave function is
obtained by applying the variational principle proposed by Zhang et al. [Phys.
Rev. B 93, 165129 (2016)]. We consider a short-range interaction, the Coulomb
interaction, and an interpolation between them, and determine the evolution of
the optimal gauge with the different interactions. We compare the optimal gauge
with those proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] and Wu et al.
[Phys. Rev. B 86, 085129 (2012)], and find that Wu et al.'s gauge is close to
the optimal gauge when the interaction is a certain mixture of the Coulomb
interaction and the short-range interaction, while Qi's gauge is qualitatively
different from the optimal gauge in all the cases. Both the gauges deviate
significantly from the optimal gauge when the short-range component of the
interaction becomes more prominent.


  Gaussian curvature is an important geometric property of surfaces, which has
been used broadly in mathematical modeling. Due to the full nonlinearity of the
Gaussian curvature, efficient numerical methods for models based on it are
uncommon in literature. In this article, we propose an operator-splitting
method for a general Gaussian curvature model. In our method, we decouple the
full nonlinearity of Gaussian curvature from differential operators by
introducing two matrix- and vector-valued functions. The optimization problem
is then converted into the search for the steady state solution of a time
dependent PDE system. The above PDE system is well-suited to time
discretization by operator splitting, the sub-problems encountered at each
fractional step having either a closed form solution or being solvable by
efficient algorithms. The proposed method is not sensitive to the choice of
parameters, its efficiency and performances being demonstrated via systematic
experiments on surface smoothing and image denoising.


  The COHERENT collaboration is deploying a suite of low-energy detectors in a
low-background corridor of the ORNL Spallation Neutron Source (SNS) to measure
coherent elastic neutrino-nucleus scattering (CEvNS) on an array of nuclear
targets employing different detector technologies. A measurement of CEvNS on
different nuclei will test the $N^2$-dependence of the CEvNS cross section and
further the physics reach of the COHERENT effort. The first step of this
program has been realized recently with the observation of CEvNS in a 14.6 kg
CsI detector. Operation and deployment of Ge and NaI detectors are also
underway. A 22 kg, single-phase, liquid argon detector (CENNS-10) started
data-taking in Dec. 2016 and will provide results on CEvNS from a lighter
nucleus. Initial results indicate that light output, pulse-shape
discrimination, and background suppression are sufficient for a measurement of
CEvNS on argon.


  Recursive max-linear vectors model causal dependence between its components
by expressing each node variable as a max-linear function of its parental nodes
in a directed acyclic graph and some exogenous innovation. Motivated by extreme
value theory, innovations are assumed to have regularly varying distribution
tails. We propose a scaling technique in order to determine a causal order of
the node variables. All dependence parameters are then estimated from the
estimated scalings. Furthermore, we prove asymptotic normality of the estimated
scalings and dependence parameters based on asymptotic normality of the
empirical spectral measure. Finally, we apply our structure learning and
estimation algorithm to financial data and food dietary interview data.


  Objective: In the framework of the Cometary Physics Laboratory (CoPhyLab) and
its sublimation experiments of cometary surface analogues under simulated space
conditions, we characterize the properties of intimate mixtures of juniper
charcoal and SiO$_2$ chosen as a dust analogue \citep{Lethuillier_2022}. We
present the details of these investigations for the spectrophotometric
properties of the samples.
  Methods: We measured these properties using a hyperspectral imager and a
radio-goniometer. From the samples' spectra, we evaluated reflectance ratios
and spectral slopes. From the measured phase curves, we inverted a photometric
model for all samples. Complementary characterizations were obtained using a
pycnometer, a scanning electron microscope and an organic elemental analyser.
  Results: We report the first values for the apparent porosity, elemental
composition, and VIS-NIR spectrophotometric properties for juniper charcoal, as
well as for intimate mixtures of this charcoal with the SiO$_2$. We find that
the juniper charcoal drives the spectrophotometric properties of the intimate
mixtures and that its strong absorbance is consistent with its elemental
composition. We find that SiO$_2$ particles form large and compact agglomerates
in every mixture imaged with the electron microscope, and its
spectrophotometric properties are affected by such features and their
particle-size distribution. We compare our results to the current literature on
comets and other small Solar System bodies and find that most of the
characterized properties of the dust analogue are comparable to some extent
with the spacecraft-visited cometary nucleii, as well as to Centaurs, Trojans
and the bluest TNOs.


  This paper provides a variational analysis of the unconstrained formulation
of the LASSO problem, ubiquitous in statistical learning, signal processing,
and inverse problems. In particular, we establish smoothness results for the
optimal value as well as Lipschitz properties of the optimal solution as
functions of the right-hand side (or measurement vector) and the regularization
parameter. Moreover, we show how to apply the proposed variational analysis to
study the sensitivity of the optimal solution to the tuning parameter in the
context of compressed sensing with subgaussian measurements. Our theoretical
findings are validated by numerical experiments.


  There are a multitude of emerging imaging technologies that could benefit
robotics. However the need for bespoke models, calibration and low-level
processing represents a key barrier to their adoption. In this work we present
NOCaL, Neural odometry and Calibration using Light fields, a semi-supervised
learning architecture capable of interpreting previously unseen cameras without
calibration. NOCaL learns to estimate camera parameters, relative pose, and
scene appearance. It employs a scene-rendering hypernetwork pretrained on a
large number of existing cameras and scenes, and adapts to previously unseen
cameras using a small supervised training set to enforce metric scale. We
demonstrate NOCaL on rendered and captured imagery using conventional cameras,
demonstrating calibration-free odometry and novel view synthesis. This work
represents a key step toward automating the interpretation of general camera
geometries and emerging imaging technologies.


  Laser irradiation, as a versatile tool to tune topological properties of
electronic systems, is under intensive studies. Experimentally, laser
irradiation induced anomalous Hall effect in graphene has been observed (McIver
et al., Nat. Phys. 16, 38 (2020)). Disorder is ubiquitous in real materials,
and it has been shown that diagonal disorders, i.e., onsite disorder, can
enhance topological properties of time-periodically driven quantum materials
(Titum et al., Phys. Rev. Lett. 114, 056801 (2015)). Here, we investigate
circularly polarized laser irradiated graphene with non-diagonal disorders,
i.e., disordered tunneling, and find that disorder can induce nontrivial
topological properties, characterized by Bott index and the real-space Chern
number. Moreover, we show that one can turn on the laser irradiation
non-adiabatically to drive the disordered graphene into non-trivial topological
phase. It is a scheme which is especially interesting for experimental
implementations.


  We have conducted a kinematic study of 165 young M dwarfs with ages of <300
Myr. Our sample is composed of stars and brown dwarfs with spectral types
ranging from K7 to L0, detected by ROSAT and with photometric distances of <25
pc assuming the stars are single and on the main-sequence. In order to find
stars kinematically linked to known young moving groups (YMGs), we measured
radial velocities for the complete sample with Keck and CFHT optical
spectroscopy and trigonometric parallaxes for 75 of the M dwarfs with the
CAPSCam instrument on the du Pont 2.5-m Telescope. Due to their youthful
overluminosity and unresolved binarity, the original photometric distances for
our sample underestimated the distances by 70% on average, excluding two
extremely young (<3 Myr) objects found to have distances beyond a few hundred
parsecs. We searched for kinematic matches to 14 reported YMGs and identified 9
new members of the AB Dor YMG and 2 of the Ursa Majoris group. Additional
possible candidates include 6 Castor, 4 Ursa Majoris, 2 AB Dor members, and 1
member each of the Her-Lyr and beta Pic groups. Our sample also contains 27
young low-mass stars and 4 brown dwarfs with ages <150 Myr which are not
associated with any known YMG. We identified an additional 15 stars which are
kinematic matches to one of the YMGs, but the ages from spectroscopic
diagnostics and/or the positions on the sky do not match. These warn against
grouping stars together based only on kinematics and that a confluence of
evidence is required to claim that a group of stars originated from the same
star-forming event.


  We present results about the Cantor-Bendixson index of some subspaces of a
uniform family F of finite subsets of natural numbers with respect to the
lexicographic order topology. As a corollary of our results we get that for any
omega-uniform family F the restriction F|M is homeomorphic to F iff M contains
intervals of arbitrary length of consecutive integers. We show the connection
of these results with a topological partition problem of uniform families.


  We propose a strategy to measure the dark matter power spectrum using minimal
assumptions about the galaxy distribution and the galaxy-dark matter
cross-correlations. We argue that on large scales the central limit theorem
generically assures Gaussianity of each smoothed density field, but not
coherence. Asymptotically, the only surviving parameters on a given scale are
galaxy variance $\sigma$, bias $b=\Omega^{.6}/\beta$ and the galaxy-dark matter
correlation coefficient $r$. These can all be determined by measuring the
quadrupole and octupole velocity distortions in the power spectrum. Measuring
them simultaneously may restore consistency between all $\beta$ determinations
independent of galaxy type.
  The leading deviations from Gaussianity are conveniently parameterized by an
Edgeworth expansion. In the mildly non-linear regime, two additional parameters
describe the full picture: the skewness parameter $s$ and non-linear bias
$b_2$. They can both be determined from the measured skewness combined with
second order perturbation theory or from an N-body simulation. By measuring the
redshift distortion of the skewness, one can measure the density parameter
$\Omega$ with minimal assumptions about the galaxy formation process. This
formalism also provides a convenient parametrization to quantify statistical
galaxy formation properties.


  A recently published article by Klapdor-Kleingrothaus et al. critiques the
limit on the stability of the electron obtained by the Borexino collaboration.
We respond here to the criticisms raised by Klapdor-Kleingrothaus and his
colleagues, and re-establish that our result is based on very conservative
premises and that the "indication of a signal of 1.4 $\sigma$" for the decay of
the electron in the $\gamma+\nu$ channel, reported by Klapdor-Kleingrothaus and
colleagues, is excluded by the Borexino result.


  Current top performing Pascal VOC object detectors employ detection proposals
to guide the search for objects thereby avoiding exhaustive sliding window
search across images. Despite the popularity of detection proposals, it is
unclear which trade-offs are made when using them during object detection. We
provide an in depth analysis of ten object proposal methods along with four
baselines regarding ground truth annotation recall (on Pascal VOC 2007 and
ImageNet 2013), repeatability, and impact on DPM detector performance. Our
findings show common weaknesses of existing methods, and provide insights to
choose the most adequate method for different settings.


  A numerical method is developed to solve linear semi-infinite programming
problem (LSIP) in which the iterates produced by the algorithm are feasible for
the original problem. This is achieved by constructing a sequence of standard
linear programming problems with respect to the successive discretization of
the index set such that the approximate regions are included in the original
feasible region. The convergence of the approximate solutions to the solution
of the original problem is proved and the associated optimal objective function
values of the approximate problems are monotonically decreasing and converge to
the optimal value of LSIP. An adaptive refinement procedure is designed to
discretize the index set and update the constraints for the approximate
problem. Numerical experiments demonstrate the performance of the proposed
algorithm.


  We give a skein theoretic proof the Reshetikhin hook length formula for
quantum dimension for the quantum group U_q(sl(N)).


  ISO spectral observations of the supernova remnant RCW103 are presented. This
object is the prototype of relatively young remnants with fast shocks
interacting with dense interstellar medium. The spectrum is dominated by
prominent lines of [NeII], [SiII], [FeII] and other low excitation species
which provide, for the first time, a simple and reliable estimate of the gas
abundances of refractory (Si, Fe, Ni) and non-refractory (Ne, P, S, Cl, Ar)
species. Apart from nickel, all the derived abundances are close to solar,
confirming that the shock has destroyed all dust grains. Like the optical
nickel lines, [NiII] 6.64micron yields Ni abundances a factor ~10 solar which
we propose results from a large underestimation of the computed Ni+ collision
strengths. The observed intensities and velocity widths of ionic lines are
compatible with emission from the post-shock region alone with only a very
small (if any) contribution from the photoionized precursor. This result does
not agree with shock models which predict that the precursor should emit
powerful line emission, especially from highly ionized species. The possible
consequence of this on the modelling of Seyfert spectra is briefly discussed.


  We show how to extend a classic Morita Equivalence Result of Green's to the
\cs-algebras of Fell bundles over transitive groupoids. Specifically, we show
that if $p:\B\to G$ is a saturated Fell bundle over a transitive groupoid $G$
with stability group $H=G(u)$ at $u\in \go$, then $\cs(G,\B)$ is Morita
equivalent to $\cs(H,\CC)$, where $\CC=\B\restr H$. As an application, we show
that if $p:\B\to G$ is a Fell bundle over a group $G$ and if there is a
continuous $G$-equivariant map $\sigma:\Prim A\to G/H$, where $A=B(e)$ is the
\cs-algebra of $\B$ and $H$ is a closed subgroup, then $\cs(G,\B)$ is Morita
equivalent to $\cs(H,\CC^{I})$ where $\CC^{I}$ is a Fell bundle over $H$ whose
fibres are $A/I\sme A/I$-\ib s and $I=\bigcap\set{P:\sigma(P)=eH}$. Green's
result is a special case of our application to bundles over groups.


  Feedback in creativity support tools can help crowdworkers to improve their
ideations. However, current feedback methods require human assessment from
facilitators or peers. This is not scalable to large crowds. We propose
Interpretable Directed Diversity to automatically predict ideation quality and
diversity scores, and provide AI explanations - Attribution, Contrastive
Attribution, and Counterfactual Suggestions - to feedback on why ideations were
scored (low), and how to get higher scores. These explanations provide
multi-faceted feedback as users iteratively improve their ideations. We
conducted formative and controlled user studies to understand the usage and
usefulness of explanations to improve ideation diversity and quality. Users
appreciated that explanation feedback helped focus their efforts and provided
directions for improvement. This resulted in explanations improving diversity
compared to no feedback or feedback with scores only. Hence, our approach opens
opportunities for explainable AI towards scalable and rich feedback for
iterative crowd ideation and creativity support tools.


  A condition of supersymmetric cosmological solutions of simple (N=1)
supergravity is formulated in the classical case. As an application we prove
that supersymmetry is spontaneously broken in Friedmann-Robertson-Walker type
cosmologies as well as in the Kasner universe, except for the Minkowski space.


  In this paper we derive the infinite summation formulas of Srivastava's
general triple hypergeometric function. Certain particular cases leading to
infinite summation formulas for fourteen Lauricella and three Srivastava\'s
triple hypergeometric functions are also presented.


  We generalize the theory of thermoelectrics to include coherent electron
systems under adiabatic ac driving, accounting for quantum pumping of charge
and heat as well as the associated work exchange between electron system and
driving potentials. We derive the relevant response coefficients in the
adiabatic regime and show that they obey Onsager reciprocity relations. We
analyze the consequences of our generalized thermoelectric framework for
quantum motors, generators, heat engines, and heat pumps, characterizing them
in terms of efficiencies and figures of merit.


  In this article we introduce a new class of weighted sequence spaces of
Sobolev type and prove several compact embedding theorems for them. In all
cases our proofs are based on the existence of a Schauder basis that spans all
of the spaces under consideration. Our choice of spaces is primarily motivated
by earlier work on infinite-dimensional dynamical systems of hyperbolic type
arising in non-equilibrium statistical mechanics. We also prove a theorem of
Pitt's type asserting that under some conditions every linear bounded
transformation from one weighted sequence space into another is compact.


  We present a unified description of zitterbewegung-like phenomena for
electron and hole systems showing Rashba spin splitting as well as for
electrons in single-layer and bilayer graphene. The former class of systems can
be interpreted as "nonrelativistic" whereas the latter are often called
"ultrarelativistic" so that our unified description indicates an interesting
connection between these two opposite limits.


  We show that the cross section of at least one of the s-channel processes
e-e- (mu-mu-) --> l_i^- l_i^-, i=e,mu,tau, mediated by a doubly-charged scalar
triplet bilepton is bounded from below and observable at a linear or muon
collider if one of the light neutrinos has a mass in the range where it is
required to be unstable by cosmological considerations. The result is model
independent. We therefore stress the importance of the e-e- and mu-mu-
collision modes of the future colliders for discovering new physics.


  We present a flavour-covariant formalism for scalar triplet leptogenesis,
which takes into account the effects of the different lepton flavours in a
consistent way. Our main finding is that flavour effects can never be neglected
in scalar triplet leptogenesis, even in the temperature regime where all
charged lepton Yukawa interactions are out of equilibrium. This is at variance
with the standard leptogenesis scenario with heavy Majorana neutrinos. In
particular, the so-called single flavour approximation leads to predictions for
the baryon asymmetry of the universe that can differ by a large amount from the
flavour-covariant computation in all temperature regimes. We investigate
numerically the impact of flavour effects and spectator processes on the
generated baryon asymmetry, and find that the region of triplet parameter space
allowed by successsful leptogenesis is significantly enlarged.


  This paper as technology report is focusing on evaluation and performance
about depth estimations based on lidar data and stereo images(front left and
front right). The lidar 3d cloud data and stereo images are provided by ford.
In addition, this paper also will explain some details about optimization for
depth estimation performance. And some reasons why not use machine learning to
do depth estimation, replaced by pure mathmatics to do stereo depth estimation.
The structure of this paper is made of by following:(1) Performance: to discuss
and evaluate about depth maps created from stereo images and 3D cloud points,
and relationships analysis for alignment and errors;(2) Depth estimation by
stereo images: to explain the methods about how to use stereo images to
estimate depth;(3)Depth estimation by lidar: to explain the methods about how
to use 3d cloud datas to estimate depth;In summary, this report is mainly to
show the performance of depth maps and their approaches, analysis for them.


  Many plants become limp or droop through heat, loss of water, or disease.
This is also known as wilting. In this paper, we examine plant wilting caused
by bacterial infection. In particular, we want to design a metric for wilting
based on images acquired of the plant. A quantifiable wilting metric will be
useful in studying bacterial wilt and identifying resistance genes. Since there
is no standard way to estimate wilting, it is common to use ad hoc visual
scores. This is very subjective and requires expert knowledge of the plants and
the disease mechanism. Our solution consists of using various wilting metrics
acquired from RGB images of the plants. We also designed several experiments to
demonstrate that our metrics are effective at estimating wilting in plants.


  We consider the problem of navigating a nonlinear dynamical system from some
initial set to some target set while avoiding collision with an unsafe set. We
extend the concept of density function to control density function (CDF) for
solving navigation problems with safety constraints. The occupancy-based
interpretation of the measure associated with the density function is
instrumental in imposing the safety constraints. The navigation problem with
safety constraints is formulated as a quadratic program (QP) using CDF. The
existing approach using the control barrier function (CBF) also formulates the
navigation problem with safety constraints as QP. One of the main advantages of
the proposed QP using CDF compared to QP formulated using CBF is that both the
convergence/stability and safety can be combined and imposed using the CDF.
Simulation results involving the Duffing oscillator and safe navigation of
Dubin car models are provided to verify the main findings of the paper.


  In each of the last five years, a few dozen empirical studies appeared in
visualization journals and conferences. The existing empirical studies have
already featured a large number of variables. There are many more variables yet
to be studied. While empirical studies enable us to obtain knowledge and
insight about visualization processes through observation and analysis of user
experience, it seems to be a stupendous challenge for exploring such a huge
variable space at the current pace. In this position paper, we discuss the
implication of not being able to explore this space effectively and
efficiently, and propose means for addressing this challenge.


  Neural networks have demonstrated significant accuracy across various
domains, yet their vulnerability to subtle input alterations remains a
persistent challenge. Conventional methods like data augmentation, while
effective to some extent, fall short in addressing unforeseen corruptions,
limiting the adaptability of neural networks in real-world scenarios. In
response, this paper introduces a novel paradigm known as the Mixture of
Class-Specific Expert Architecture. The approach involves disentangling feature
learning for individual classes, offering a nuanced enhancement in scalability
and overall performance. By training dedicated network segments for each class
and subsequently aggregating their outputs, the proposed architecture aims to
mitigate vulnerabilities associated with common neural network structures. The
study underscores the importance of comprehensive evaluation methodologies,
advocating for the incorporation of benchmarks like the common corruptions
benchmark. This inclusion provides nuanced insights into the vulnerabilities of
neural networks, especially concerning their generalization capabilities and
robustness to unforeseen distortions. The research aligns with the broader
objective of advancing the development of highly robust learning systems
capable of nuanced reasoning across diverse and challenging real-world
scenarios. Through this contribution, the paper aims to foster a deeper
understanding of neural network limitations and proposes a practical approach
to enhance their resilience in the face of evolving and unpredictable
conditions.


  We introduce an efficient approach for optimization over orthogonal groups on
highly parallel computation units such as GPUs or TPUs. As in earlier work, we
parametrize an orthogonal matrix as a product of Householder reflections.
However, to overcome low parallelization capabilities of computing Householder
reflections sequentially, we propose employing an accumulation scheme called
the compact WY (or CWY) transform -- a compact parallelization-friendly matrix
representation for the series of Householder reflections. We further develop a
novel Truncated CWY (or T-CWY) approach for Stiefel manifold parametrization
which has a competitive complexity and, again, yields benefits when computed on
GPUs and TPUs. We prove that our CWY and T-CWY methods lead to convergence to a
stationary point of the training objective when coupled with stochastic
gradient descent. We apply our methods to train recurrent neural network
architectures in the tasks of neural machine translation and video prediction.


  Knowledge of the state of plastic deformation in metallic structures is vital
to prevent failure. This is why non-destructive acoustic tests based on the
measurement of first order elastic constants have been developed and
intensively used. However, plastic deformations, which are usually
heterogeneous in space, may be invisible to these methods if the variation of
the elastic constants is too small. In recent years, digital image correlation
techniques, based on measurements carried out at the surface of a sample, have
been successfully used in conjunction with finite element modeling to gain
information about plastic deformation in the sample interior. Acoustic waves
can penetrate deep into a sample and offer the possibility of probing into the
bulk of a plastically deformed material. Previously, we have demonstrated that
nonlinear acoustic methods are far more sensitive to changes in dislocation
density than linear ones. Here, we show that the nonlinear Second Harmonic
Generation method (SHG) is sensitive enough to detect different zones of von
Mises stress as well as effective plastic strain in centimeter-size aluminium
pieces. This is achieved by way of ultrasonic measurements on a sample that has
undergone a three-point bending test. Because of the relatively low stress and
small deformations, the sample undergoes plastic deformation by dislocation
proliferation. Thus, we conclude that the nonlinear parameter measured by SHG
is also sensitive to dislocation density. Our experimental results agree with
numerical results obtained by Finite Element Method (FEM) modeling. We also
support the acoustic results by X-Ray Diffraction measurements (XRD). Although
intrusive and less accurate, they also agree with the acoustic measurements and
plastic deformations in finite element simulations.


  State-of-the-art rest-frame UV and FIR photometric and spectroscopic
observations are now pushing the redshift frontiers of galaxy formation studies
up to $z\sim9-11$ and beyond. Recent HST observations unveiled the presence of
a star-forming galaxy exhibiting the Lyman break at $\lambda_{\rm
obs}=1.47\pm0.01$ $\mu$m, i.e., a $z=11.09^{+0.08}_{-0.12}$ galaxy with a
stellar mass of $\sim10^9 M_\odot$, demonstrating that galaxy build-up was well
underway early in the epoch of reionization (EoR) at $z>10$. Targeted
spectroscopy of a lensed Lyman break galaxy uncovers the earliest metals known
to date up to $z=9.1096\pm0.0006$ by detecting the bright [OIII] 88~$\mu$m
nebular line, indicating the onset of star formation 250 million years after
the Big Bang, i.e., corresponding to a redshift of $z\sim15$. These latest
findings lead us to a number of key questions: How and when metal enrichment
happened in the EoR? What was the nature of the earliest-epoch star-forming
galaxies at $z=10-15$? What was the spatial distribution of such galaxies, and
what was the relation to the putative large-scale ionization bubbles during the
EoR? What were the dark-halo masses of such earliest-epoch star-forming
galaxies? To address all these questions, we need to uncover a statistically
large number of $z=10-15$ galaxies in the pre-reionization era. Here we argue
two possible pathways: (1) a wide-area, sensitive blind spectroscopic survey of
[OIII] 88 $\mu$m line-emitting galaxies at submillimeter wavelengths, and (2)
an ultra-wide-area, high-cadence photometric survey of transient sources at
radio-to-(sub)millimeter wavelengths, together with the immediate follow-up
spectroscopy with an ultra-wide-band spectrograph, to catch the pop-III
$\gamma$-ray bursts.


  Let $I$ be a monomial ideal of a polynomial ring $R$. In this paper we
determine a number $B$ such that $\Ass (I^n/I^{n+1}) = \Ass (I^{B}/I^{B+1})$
for all $n\geq B$.


  We present an improved model for the absorption of X-rays in the ISM intended
for use with data from future X-ray missions with larger effective areas and
increased energy resolution such as Chandra and XMM, in the energy range above
100eV. Compared to previous work, our formalism includes recent updates to the
photoionization cross section and revised abundances of the interstellar
medium, as well as a treatment of interstellar grains and the H2molecule. We
review the theoretical and observational motivations behind these updates and
provide a subroutine for the X-ray spectral analysis program XSPEC that
incorporates our model.


  In this paper, we describe a new active-set algorithmic framework for
minimizing a non-convex function over the unit simplex. At each iteration, the
method makes use of a rule for identifying active variables (i.e., variables
that are zero at a stationary point) and specific directions (that we name
active-set gradient related directions) satisfying a new "nonorthogonality"
type of condition. We prove global convergence to stationary points when using
an Armijo line search in the given framework. We further describe three
different examples of active-set gradient related directions that guarantee
linear convergence rate (under suitable assumptions). Finally, we report
numerical experiments showing the effectiveness of the approach.


  The Sanathanan-Koerner iteration developed in 1963 is classical approach for
rational approximation. This approach multiplies both sides of the
approximation by the denominator polynomial yielding a linear problem and then
introduces a weight at each iteration to correct for this linearization.
Unfortunately this weight introduces a numerical instability. We correct this
instability by constructing Vandermonde matrices for both the numerator and
denominator polynomials using the Arnoldi iteration with an initial vector that
enforces this weighting. This Stabilized Sanathanan-Koerner iteration corrects
the instability and yields accurate rational approximations of arbitrary
degree. Using a multivariate extension of Vandermonde with Arnoldi, we can
apply the Stabilized Sanathanan-Koerner iteration to multivariate rational
approximation problems. The resulting multivariate approximations are often
significantly better than existing techniques and display a more uniform
accuracy throughout the domain.


  Science teaching in secondary schools is often abstract for students. Even if
some experiments can be conducted in classrooms, mainly for chemistry or some
physics fields, mathematics is not an experimental science. Teachers have to
convince students that theorems have practical implications. We present
teachers an original and easy-to-use pedagogical tool: a cable-driven robot
with a Web-based remote control interface. The robot implements several
scientific concepts such as 3D-geometry and kinematics. The remote control
enables the teacher to move freely in the classroom.


  This paper introduces the united monocular-stereo features into a
visual-inertial tightly coupled odometry (UMS-VINS) for robust pose estimation.
UMS-VINS requires two cameras and a low-cost inertial measurement unit (IMU).
The UMS-VINS is an evolution of VINS-FUSION, which modifies the VINS-FUSION
from the following three perspectives. 1) UMS-VINS extracts and tracks features
from the sub-pixel plane to achieve better positions of the features. 2)
UMS-VINS introduces additional 2-dimensional features from the left and/or
right cameras. 3) If the visual initialization fails, the IMU propagation is
directly used for pose estimation, and if the visual-IMU alignment fails,
UMS-VINS estimates the pose via the visual odometry. The performances on both
public datasets and new real-world experiments indicate that the proposed
UMS-VINS outperforms the VINS-FUSION from the perspective of localization
accuracy, localization robustness, and environmental adaptability.


  In this work, we have established the relations between the T-even proton
transverse momentum-dependent parton distributions (TMDs) at all twist levels
up to twist-4 using the light-front quark diquark model (LFQDM). From the
parameterization equations of TMDs, we have found that there are multiple ways
by which a particular TMD can be expressed in terms of the helicities of the
proton in the initial and final states. For the first time, we have presented a
parameterization table that can be applied to the derivation and recognition of
proton TMDs based on their helicity. We have constructed the linear and
quadratic relationships of TMDs at the intra-twist and inter-twist levels
within the same model. We have also looked at the inequality relations that
TMDs follow. Additionally, to provide an easy access to the calculations,
amplitude matrices have been expressed in the form of TMDs over all the
possible helicities of the diquark.


  In this paper we construct a global, continuous flow of solutions to the
Camassa-Holm equation on the space H^1(R). In a previous paper [2], A. Bressan
and the author constructed spatially periodic solutions, whereas in this paper
the solutions are defined in all the real line. We introduce a distance
functional, defined in terms of an optimal transportation problem, which allows
us to study the continuous dependance w.r.t. the inital data with a certain
decay at infinity.


  In very young clusters, stellar age distribution is the empirical proof of
the duration of star formation (SF) and of the physical mechanisms involved in
the process. We derived accurate stellar ages for the cluster NGC6530,
associated with the Lagoon Nebula to infer its SF history. We use the Gaia-ESO
survey observations and Gaia DR2 data, to derive cluster membership and
fundamental stellar parameters. We identified 652 confirmed and 9 probable
members. The reddening inferred for members and non-members allows us to
distinguish MS stars and giants, in agreement with the distances inferred from
Gaia DR2 data. The foreground and background stars show a spatial pattern that
traces the 3D structure of the nebular dust component. We derive stellar ages
for 382 confirmed cluster members and we find that the gravity-sensitive gamma
index distribution for M stars is correlated with stellar age. For all members
with Teff<5500 K, the mean logarithmic age is 5.84 (units of years) with a
dispersion of 0.36 dex. The age distribution of stars with accretion and/or
disk (CTTSe) is similar to that of stars without accretion and without disk
(WTTSp). We interpret this dispersion as evidence of a real age spread since
the total uncertainties on age determinations, derived from Monte Carlo
simulations, are significantly smaller than the observed spread. This
conclusion is supported by the evidence of a decreasing of the
gravity-sensitive gamma index as a function of stellar ages. The presence of
the age spread is also supported by the spatial distribution and the kinematics
of old and young members. In particular, members with accretion and/or disk,
formed in the last 1 Myr, show evidence of subclustering around the cluster
center, in the Hourglass Nebula and in the M8-E region, suggesting a possible
triggering of star formation events by the O-type star ionization fronts.


  We investigate the intrinsic continuum linear polarization from axisymmetric
density distributions of gas surrounding classical Be stars during the
formation and dissipation of their circumstellar disks. We implement a Monte
Carlo calculation of the Stokes parameters with the use of the non-LTE
radiative transfer code of Sigut & Jones (2007) to reproduce the continuous
polarimetric spectra of classical Be stars. The scattering of light in the
nonspherical circumstellar envelopes of classical Be stars produces a distinct
polarization signature that can be used to study the physical nature of the
scattering environment. In this paper, we highlight the utility of polarimetric
measurements as important diagnostics in the modeling of these systems. We
illustrate the effects of using self-consistent calculation of the thermal
structure of the circumstellar gas on the characteristic wavelength-dependence
of the polarization spectrum. In showing that the principal features of the
polarization spectrum originate from different parts of the disk, we emphasize
the capability of polarimetric observations to trace the evolution of the disk
on critical scales. We produce models that approximate the disk formation and
dissipation periods and illustrate how the polarimetric properties of these
systems can have a pivotal role in determining the mechanism for mass decretion
from the central star.


  When particle dark matter is bound gravitationally around a massive black
hole in sufficiently high densities, the dark matter will affect the rate of
inspiral of a secondary compact object that forms a binary with the massive
black hole. In this paper, we revisit previous estimates of the impact of
dark-matter accretion by black-hole secondaries on the emitted gravitational
waves. We identify a region of parameter space of binaries for which estimates
of the accretion were too large (specifically, because the dark-matter
distribution was assumed to be unchanging throughout the process, and the
secondary black hole accreted more mass in dark matter than that enclosed
within the orbit of the secondary). To restore consistency in these scenarios,
we propose and implement a method to remove dark-matter particles from the
distribution function when they are accreted by the secondary. This new
feedback procedure then satisfies mass conservation, and when evolved with
physically reasonable initial data, the mass accreted by the secondary no
longer exceeds the mass enclosed within its orbital radius. Comparing the
simulations with accretion feedback to those without this feedback, including
feedback leads to a smaller gravitational-wave dephasing from binaries in which
only the effects of dynamical friction are being modeled. Nevertheless, the
dephasing can be hundreds to almost a thousand gravitational-wave cycles, an
amount that should allow the effects of accretion to be inferred from
gravitational-wave measurements of these systems.


  The standard eleven-dimensional supergravity action depends on a three-form
gauge field and does not allow direct coupling to five-branes. Using previously
developed methods, we construct a covariant eleven-dimensional supergravity
action depending on a three-form and six-form gauge field in a
duality-symmetric manner. This action is coupled to both the M-theory two-brane
and five-brane, and corresponding equations of motion are obtained. Consistent
coupling relates D=11 duality properties with self-duality properties of the
M-5-brane. From this duality-symmetric formulation, one can derive an action
describing coupling of the M-branes to standard D=11 supergravity.


  In the present contribution, we propose a quantum computational algorithm for
the Lattice Boltzmann Method (LBM) to solve fluid flow equations in the low
Reynolds number ($Re$) regime. Firstly, we express the LBM collision and
streaming operators in matrix form. Since quantum logic gates are typically
expressed as unitary matrices, we first decompose LBM operations as a product
of unitaries. The particle distribution functions (PDFs) of LBM are encoded as
probability amplitudes of the quantum state. We have observed that the
amplitudes in the state vector (SV) can be affected: (i) by the choice of
encoding the PDFs during the quantum state preparation or (ii) when collision
is followed by streaming, as in classical LBM implementation. In the first
case, we show that the ancilla qubit must be in superposition with the compute
qubits during the quantum state preparation. The superposition allows the SV to
utilize the increased Hilbert space offered by the ancilla qubit rather than
placing the ancilla in a separate register, which restricts the space of
possible outcomes. Next, we show that the second issue can be resolved by
having an intermediate Hadamard gate before the streaming operation. The
proposed algorithm has been tested through typical benchmark problems like
advection-diffusion of a Gaussian hill, Poiseuille flow, Couette flow, and the
lid-driven cavity problem. The results are validated with the respective
analytic or reference solutions. Translating the unitaries into quantum gates
(circuit synthesis) presents a primary challenge, as a unitary matrix can be
decomposed in multiple ways. We report on the CNOT and U gate counts obtained
for the test cases with the range of qubits from 9 to 12. Although the gate
count closely agrees with the theoretical limit, the number of two qubit gates
is in the $O(10^7)$ prompts special attention to circuit synthesis.


  Recently the CERN ALICE experiment, in its dedicated cosmic ray run, observed
muon bundles of very high multiplicities, thereby confirming similar findings
from the LEP era at CERN (in the CosmoLEP project). Originally it was argued
that they apparently stem from the primary cosmic rays with a heavy masses. We
propose an alternative possibility arguing that muonic bundles of highest
multiplicity are produced by strangelets, hypothetical stable lumps of strange
quark matter infiltrating our Universe. We also address the possibility of
additionally deducing their directionality which could be of astrophysical
interest. Significant evidence for anisotropy of arrival directions of the
observed high multiplicity muonic bundles is found. Estimated directionality
suggests their possible extragalactic provenance.


  We revisit Wigner's question about the admissible commutation relations for
coordinate and velocity operators given their equations of motion (EOM). In
more general terms we want to consider the question of how to quantize
dynamically equivalent Hamiltonian structures. A unique answer can presumably
be given in those cases, where we have a dynamical symmetry. In this case
arbitrary deformations of the symmetry algebra should be dynamically
equivalent. We illustrate this for the linear as well as the singular
1d-oscillator. In the case of nonlinear EOM quantum corrections have to be
taken into account. We present some examples thereof New phenomena arise in
case of more then one degree of freedom, where sometimes the interaction can be
described either by the Hamiltonian or by nonstandard commutation relations.
This may induce a noncommutative geometry (for example the 2d-oscillator in a
constant magnetic field). Also some related results from nonrelativistic
quantum field theory applied to solid state physics are briefly discussed
within this framework


  We study a model of diffusion in a brownian potential. This model was firstly
introduced by T. Brox (1986) as a continuous time analogue of random walk in
random environment. We estimate the deviations of this process above or under
its typical behavior. Our results rely on different tools such as a
representation introduced by Y. Hu, Z. Shi and M. Yor, Kotani's lemma,
introduced at first by K. Kawazu and H. Tanaka (1997), and a decomposition of
hitting times developed in a recent article by A. Fribergh, N. Gantert and S.
Popov (2008). Our results are in agreement with their results in the discrete
case.


  We report a correlation between the presence of a Gaia-Sausage-Enceladus
(GSE) analogue and dark matter halo spin in the ARTEMIS simulations of Milky
Way-like galaxies. The haloes which contain a large population of accreted
stars on highly radial orbits (like the GSE) have lower spin on average than
their counterparts with more isotropic stellar velocity distributions. The
median modified spin parameters $\lambda^\prime$ differ by a factor of
$\sim1.7$ at the present-day, with a similar value when the haloes far from
virial equilibrium are removed. We also show that accreted stars make up a
smaller proportion of the stellar populations in haloes containing a GSE
analogue, and are stripped from satellites with stellar masses typically
$\sim4$ times smaller. Our findings suggest that the higher spin of DM haloes
without a GSE-like feature is due to mergers with large satellites of stellar
mass $\sim10^{10}M_\odot$, which do not result in prominent radially
anisotropic features like the GSE.


  The sequential sampling of populations with unequal probabilities and with
replacement in a closed population is a recurrent problem in ecology and
evolution. Many of these questions can be reformulated as urn problems, often
as special cases of the coupon collector problem, most simply expressed as the
number of coupons that must be collected to have a complete set. We aimed to
apply the coupon collector model in a comprehensive manner to one example
-hosts (balls) being searched (draws) and parasitized (ball color change) by
parasitic wasps- to evaluate the influence of differences in sampling
probabilities between items on collection speed.
  Based on the model of a complete multinomial process over time, we define the
distribution, distribution function, expectation and variance of the number of
hosts parasitized after a given time, as well as the inverse problem,
estimating the sampling effort. We develop the relationship between the risk
distribution on the set of hosts and the speed of parasitization and propose a
more elegant proof of the weak stochastic dominance among speed of
parasitization, using the concept of Schur convexity and the "Robin Hood
transfer" numerical operation.
  Numerical examples are provided and a conjecture about strong dominance is
proposed. The speed at which new items are discovered is a function of the
entire shape of the sampling probability distribution. The sole comparison of
values of variances is not sufficient to compare speeds associated to two
different distributions, as generally assumed in ecological studies.


  Recent work on nearby AGNs has shown that X-ray variability is correlated
with the mass and accretion rate onto the central SMBH. Here we present the
application of the variability-luminosity relation to high redshift AGNs in the
CDFS, making use of XMM-Newton observations. We use Monte Carlo simulations in
order to properly account for bias and uncertainties introduced by the sparse
sampling and the very low statistics. Our preliminary results indicate that BH
masses span over the range from 10^5 to 10^9 solar mass while accretion rates
range from 10^-3 up to values greater than 1, in unit of Eddington accretion
rate.


  We study the problem of controlling multi-agent systems under a set of signal
temporal logic tasks. Signal temporal logic is a formalism that is used to
express time and space constraints for dynamical systems. Recent methods to
solve the control synthesis problem for single-agent systems under signal
temporal logic tasks are, however, subject to a high computational complexity.
Methods for multi-agent systems scale at least linearly with the number of
agents and induce even higher computational burdens. We propose a
computationally-efficient control strategy to solve the multi-agent control
synthesis problem that results in a robust satisfaction of a set of signal
temporal logic tasks. In particular, a decentralized feedback control law is
proposed that is based on time-varying control barrier functions. The obtained
control law is discontinuous and formal guarantees are provided by nonsmooth
analysis. Simulations show the efficacy of the presented method.


  We present the derivation of an ab-initio and parameter free effective
electron-electron interaction that goes beyond the screened RPA and accounts
for superconducting pairing driven by spin-fluctuations. The construction is
based on many body perturbation theory and relies on the approximation of the
exchange-correlation part of the electronic self-energy within time dependent
density functional theory. This effective interaction is included in an
exchange correlation kernel for superconducting density functional theory, in
order to achieve a completely parameter free superconducting gap equation.
First results from applying the new functional to a simplified two-band
electron gas model are consistent with experiments.


  Graph Neural Networks (GNNs) are deep learning models that take graph data as
inputs, and they are applied to various tasks such as traffic prediction and
molecular property prediction. However, owing to the complexity of the GNNs, it
has been difficult to analyze which parts of inputs affect the GNN model's
outputs. In this study, we extend explainability methods for Convolutional
Neural Networks (CNNs), such as Local Interpretable Model-Agnostic Explanations
(LIME), Gradient-Based Saliency Maps, and Gradient-Weighted Class Activation
Mapping (Grad-CAM) to GNNs, and predict which edges in the input graphs are
important for GNN decisions. The experimental results indicate that the
LIME-based approach is the most efficient explainability method for multiple
tasks in the real-world situation, outperforming even the state-of-the-art
method in GNN explainability.


  We investigate the application of inconsistency measures to the problem of
analysing business rule bases. Due to some intricacies of the domain of
business rule bases, a straightforward application is not feasible. We
therefore develop some new rationality postulates for this setting as well as
adapt and modify existing inconsistency measures. We further adapt the notion
of inconsistency values (or culpability measures) for this setting and give a
comprehensive feasibility study.


  We study the collapse of a self-gravitating thick shell of bosons coupled to
a scalar radiation field. Due to the non-adiabaticity of the collapse, the
shell (quantum) internal degrees of freedom absorb energy from the (classical)
gravitational field and are excited. The excitation energy is then emitted in
the form of bursts of (thermal) radiation and the corresponding backreaction on
the trajectory is estimated.


  CsCa$_2$Fe$_4$As$_4$F$_2$ is a newly discovered iron-based superconductor
with $T_\mathrm{c}\sim$ 30 K containing double Fe$_2$As$_2$ layers that are
separated by insulating Ca$_2$F$_2$ spacer layers. Here we report the transport
and magnetization measurements on CsCa$_2$Fe$_4$As$_4$F$_2$ single crystals
grown for the first time using the self flux of CsAs. We observed a huge
resistivity anisotropy $\rho_c(T)/\rho_{ab}(T)$, which increases with
decreasing temperature, from 750 at 300 K to 3150 at 32 K. The $\rho_c(T)$ data
exhibit a non-metallic behavior above $\sim$140 K, suggesting an incoherent
electronic state at high temperatures due to the dimension crossover. The
superconducting onset transition temperature in $\rho_{ab}$ is 0.7 K higher
than that in $\rho_c$, suggesting two-dimensional (2D) superconducting
fluctuations. The lower and upper critical fields also show an exceptional
anisotropy among iron-based superconductors. The $H_{c1}^\bot(T)$ data are well
fitted using the model with two $s$-wave-like superconducting gaps,
$\Delta_1(0)=6.75$ meV and $\Delta_2(0)=2.32$ meV. The inter-plane coherence
length $\xi_c(0)$ is $3.6$ \AA, remarkably smaller than the distance between
conducting layers (8.6 \AA), consolidating the 2D nature in the title material.


  The algebra $\mathcal H:= H_{1,\nu}(I_2(2m+1))$ of observables of the
Calogero model based on the root system $I_2(2m+1)$ has an $m$-dimensional
space of traces and an $(m+1)$-dimensional space of supertraces. In the
preceding paper we found all values of the parameter $\nu$ for which either the
space of traces contains a~degenerate nonzero trace $tr_{\nu}$ or the space of
supertraces contains a~degenerate nonzero supertrace $str_{\nu}$ and, as
a~consequence, the algebra $\mathcal H$ has two-sided ideals: one consisting of
all vectors in the kernel of the form $B_{tr_{\nu}}(x,y)=tr_{\nu}(xy)$ or
another consisting of all vectors in the kernel of the form
$B_{str_{\nu}}(x,y)=str_{\nu}(xy)$. We noticed that if $\nu=\frac z {2m+1}$,
where $z\in \mathbb Z \setminus (2m+1) \mathbb Z$, then there exist both a
degenerate trace and a~degenerate supertrace on $\mathcal H$.
  Here we prove that the ideals determined by these degenerate forms coincide.


  Connes' distance formula is applied to endow linear metric to three 1D
lattices of different topology, with a generalization of lattice Dirac operator
written down by Dimakis et al to contain a non-unitary link-variable. Geometric
interpretation of this link-variable is lattice spacing and parallel transport.


  Let $A$ be an operator on {a separable } Hilbert space $\cH$, and let $G
\subset \cH$. It is known that - under appropriate conditions on $A$ and $G$ -
the set of iterations $F_G(A)= \{A^j \gbf \; | \; \gbf \in G, \; 0 \leq j \leq
L(\gbf) \} $ is a frame for $\cH$. We call $F_G(A)$ a dynamical frame for
$\cH$, and explore further its properties; in particular, we show that the
canonical dual frame of $F_G(A)$ also has an iterative set structure.
  We explore the relations between the operator $A$, the set $G$ and the number
of iterations $L$ which ensure that the system $F_G(A)$ is a scalable frame. We
give a general statement on frame scalability, We and study in detail the case
when $A$ is a normal operator, utilizing the unitary diagonalization in finite
dimensions. In addition, we answer the question of when $F_G(A)$ is a scalable
frame in several special cases involving block-diagonal and companion
operators.


  We introduce an optimal transport-based model for learning a metric tensor
from cross-sectional samples of evolving probability measures on a common
Riemannian manifold. We neurally parametrize the metric as a spatially-varying
matrix field and efficiently optimize our model's objective using a simple
alternating scheme. Using this learned metric, we can nonlinearly interpolate
between probability measures and compute geodesics on the manifold. We show
that metrics learned using our method improve the quality of trajectory
inference on scRNA and bird migration data at the cost of little additional
cross-sectional data.


  BurstCube will detect long GRBs, attributed to the collapse of massive stars,
short GRBs (sGRBs), resulting from binary neutron star mergers, as well as
other gamma-ray transients in the energy range 10-1000 keV. sGRBs are of
particular interest because they are predicted to be the counterparts of
gravitational wave (GW) sources soon to be detectable by LIGO/Virgo. BurstCube
contains 4 CsI scintillators coupled with arrays of compact low-power Silicon
photomultipliers (SiPMs) on a 6U Dellingr bus, a flagship modular platform that
is easily modifiable for a variety of 6U CubeSat architectures. BurstCube will
complement existing facilities such as Swift and Fermi in the short term, and
provide a means for GRB detection, localization, and characterization in the
interim time before the next generation future gamma-ray mission flies, as well
as space-qualify SiPMs and test technologies for future use on larger gamma-ray
missions. The ultimate configuration of BurstCube is to have a set of $\sim10$
BurstCubes to provide all-sky coverage to GRBs for substantially lower cost
than a full-scale mission.


  Deep Learning (DL) has transformed the automation of a wide range of
industries and finds increasing ubiquity in society. The high complexity of DL
models and its widespread adoption has led to global energy consumption
doubling every 3-4 months. Currently, the relationship between the DL model
configuration and energy consumption is not well established. At a general
computational energy model level, there is both strong dependency to both the
hardware architecture (e.g. generic processors with different configuration of
inner components- CPU and GPU, programmable integrated circuits - FPGA), as
well as different interacting energy consumption aspects (e.g., data movement,
calculation, control). At the DL model level, we need to translate non-linear
activation functions and its interaction with data into calculation tasks.
Current methods mainly linearize nonlinear DL models to approximate its
theoretical FLOPs and MACs as a proxy for energy consumption. Yet, this is
inaccurate (est. 93\% accuracy) due to the highly nonlinear nature of many
convolutional neural networks (CNNs) for example.
  In this paper, we develop a bottom-level Transistor Operations (TOs) method
to expose the role of non-linear activation functions and neural network
structure in energy consumption. We translate a range of feedforward and CNN
models into ALU calculation tasks and then TO steps. This is then statistically
linked to real energy consumption values via a regression model for different
hardware configurations and data sets. We show that our proposed TOs method can
achieve a 93.61% - 99.51% precision in predicting its energy consumption.


  We investigate a model of inflationary cosmology where the minimally coupled
scalar field theory is modified by additional correction terms. Among the most
general ten correction terms remarked by Weinberg in context of effective field
theory, we consider only two terms, $f_1(\phi) R^2$ and $f_2(\phi)
R^{ab}R_{ab}$, following the work by Noh and Hwang where $f_1$ and $f_2$ are
constant. The fourth order differential equations for the background universe
and the tensor-type perturbation are derived out of this model. We show that
these equations can be reduced to second order equations, supposing that $f_n$
are small. From these approximated equations, we find that the propagation
speed of gravitational wave is slightly less than the speed of light due to
$f_2$ term, and that the evolution of the tensor-type perturbation is conserved
in the large scale limit.


  Murchikova et al 2019 discovered a disk of cool ionized gas within 20,000
Schwarzschild radii of the Milky Way's Galactic Center black hole Sagittarius
A*. They further demonstrated that the ionizing photon flux in the region is
enough to keep the disk ionized, but there is not ample excess of this
radiation. This raised the possibility that some neutral gas could also be in
the region shielded within the cool ionized clumps. Here we present ALMA
observations of a broad 1.3 millimeter hydrogen recombination line H30alpha: n
= 31 -> 30, conducted during the flyby of the S0-2 star by Sgr A*. We report
that the velocity-integrated H30alpha line flux two month prior to the S0-2
pericenter passage is about 20% larger than it was one month prior to the
passage. The S0-2 is a strong source of ionizing radiation moving at several
thousand kilometers per second during the approach. Such a source is capable of
ionising parcels of neural gas along its trajectory, resulting in variation of
the recombination line spectra from epoch to epoch. We conclude that there are
at least (6.6 +- 3.3) x 10^{-6} Msun of neutral gas within 20,000 Schwarzschild
radii of Sgr A*.


  We present an updated determination of nuclear parton distributions (nPDFs)
from a global NLO QCD analysis of hard processes in fixed-target lepton-nucleus
and proton-nucleus together with collider proton-nucleus experiments. In
addition to neutral- and charged-current deep-inelastic and Drell-Yan
measurements on nuclear targets, we consider the information provided by the
production of electroweak gauge bosons, isolated photons, jet pairs, and
charmed mesons in proton-lead collisions at the LHC across centre-of-mass
energies of 5.02 TeV (Run I) and 8.16 TeV (Run II). For the first time in a
global nPDF analysis, the constraints from these various processes are
accounted for both in the nuclear PDFs and in the free-proton PDF baseline. The
extensive dataset underlying the nNNPDF3.0 determination, combined with its
model-independent parametrisation, reveals strong evidence for nuclear-induced
modifications of the partonic structure of heavy nuclei, specifically for the
small-$x$ shadowing of gluons and sea quarks, as well as the large-$x$
anti-shadowing of gluons. As a representative phenomenological application, we
provide predictions for ultra-high-energy neutrino-nucleon cross-sections,
relevant for data interpretation at neutrino observatories. Our results provide
key input for ongoing and future experimental programs, from that of heavy-ion
collisions in controlled collider environments to the study of high-energy
astrophysical processes.


  We present a rotational study of Post-T Tauri stars (PTTSs) in Lindroos
systems, defined as binaries with early type primaries on the main-sequence
(MS) and late-type secondaries on the pre-main-sequence (PMS) phase. The
importance of this study in comparison with previous ones is that the Lindroos
sample is not X-ray selected so we avoid a possible bias towards fast rotators.
In this preliminary study we have monitored eleven stars in the UBVRI bands
during two campaigns of ten consecutive nights each. Eight of the observed
PTTSs show periodic modulations in their lightcurves and the derived periods
range from 1.9d to 8.0d. The comparison of these results with theoretical
rotational tracks based on disk-star locking theory shows that star-disk
decoupling times of 1-20 Myr could reproduce the rotational properties of the
targets, assuming an initial rotation period of ~8d and a mass of 1 Mo. We have
studied the rotation-activity relations of Lindroos PTTSs and compared them
with those found in other groups of PMS and zero-age main-sequence (ZAMS) ~1 Mo
stars. The Lindroos sample displays activity-rotation relations very similar to
those found in TTSs. It contains a mixture of very active stars, with Lx/Lbol
ratios close to the saturation level of -3, and less active (unsaturated)
stars. This could be the result of different star-disk decoupling times. Future
monitoring of a larger and unbiased sample of PTTS will be important to confirm
the significance of these results.


  This thesis serves three primary purposes, first of which is to forecast two
stocks, i.e. Goldman Sachs (GS) and General Electric (GE). In order to forecast
stock prices, we used a long short-term memory (LSTM) model in which we
inputted the prices of two other stocks that lie in rather close correlation
with GS. Other models such as ARIMA were used as benchmark. Empirical results
manifest the practical challenges when using LSTM for forecasting stocks. One
of the main upheavals was a recurring lag which we called "forecasting lag".
  The second purpose is to develop a more general and objective perspective on
the task of time series forecasting so that it could be applied to assist in an
arbitrary that of forecasting by ANNs. Thus, attempts are made for
distinguishing previous works by certain criteria (introduced by a review paper
written by Ahmed Tealab) so as to summarise those including effective
information. The summarised information is then unified and expressed through a
common terminology that can be applied to different steps of a time series
forecasting task.
  The last but not least purpose of this thesis is to elaborate on a
mathematical framework on which ANNs are based. We are going to use the
framework introduced in the book "Neural Networks in Mathematical Framework" by
Anthony L. Caterini in which the structure of a generic neural network is
introduced and the gradient descent algorithm (which incorporates
backpropagation) is introduced in terms of their described framework. In the
end, we use this framework for a specific architecture, which is recurrent
neural networks on which we concentrated and our implementations are based. The
book proves its theorems mostly for classification case. Instead, we proved
theorems for regression case, which is the case of our problem.


  The shell-type supernova remnant RX J0852.0-4622 was observed with the High
Energy Stereoscopic System (H.E.S.S.) of Atmospheric Cherenkov Telescopes
between December 2004 and May 2005 for a total observation time of 33 hours,
above an average gamma-ray energy threshold of 250 GeV. The angular resolution
of ~0.06 degree (for events triggering 3 or 4 telescopes) and the large field
of view of H.E.S.S. ($5^{\circ}$ diameter) are well adapted to studying the
morphology of the object in very high energy gamma-rays, which exhibits a
remarkably thin shell very similar to the features observed in the radio range
and in X-rays. The spectral analysis of the source from 300 GeV to 20 TeV is
also presented. Finally, the possible origins of the very high energy gamma-ray
emission (Inverse Compton scattering by electrons or the decay of neutral pions
produced by proton interactions) are discussed, on the basis of morphological
and spectral features obtained at different wavelengths.


  The theory of modular forms and spherical harmonic analysis are applied to
establish new best bounds towards the counting and equidistribution of rational
points on spheres and other higher dimensional ellipsoids, in what may be
viewed as a textbook display of the 'unreasonable effectiveness' of modular
forms.


  We have calculated the frictional drag between spatially separated quantum
wells with parallel two-dimensional electron gases due to interlayer
electron-electron interaction mediated by virtual exchange of acoustic phonons
due to piezoelectric and deformation potential interaction. It is shown that
the frictional drag is dominated by the piezoelectric coupling. According to
our calculations temperature dependence of the drag scattering rate divided by
squared temperature T exhibits a pronounced peak which for the experimental
situation and in agreement with the finding of T. J. Gramila, et al., Phys.
Rev. B 47, (1993) 12957 is obtained at about T=2.1 K. We ascribe the appearance
of this peak to a change from small to large angle scattering in the virtual
phonon exchange.


  As the number of fine tuning of pretrained models increased, understanding
the bias of pretrained model is essential. However, there is little tool to
analyse transformer architecture and the interpretation of the attention maps
is still challenging. To tackle the interpretability, we propose
Input-Attribution and Attention Score Vector (IAV) which measures the
similarity between attention map and input-attribution and shows the general
trend of interpretable attention patterns. We empirically explain the
pretraining bias of supervised and unsupervised pretrained ViT models, and show
that each head in ViT has a specific range of agreement on the decision of the
classification. We show that generalization, robustness and entropy of
attention maps are not property of pretraining types. On the other hand, IAV
trend can separate the pretraining types.


  We present the first statistically meaningful results from two-K0s
interferometry in heavy-ion collisions. A model that takes the effect of the
strong interaction into account has been used to fit the measured correlation
function. The effects of single and coupled channel were explored. At the mean
transverse mass m_T = 1.07 GeV, we obtain the values R = 4.09 +/- 0.46 (stat.)
+/- 0.31 (sys) fm and lambda = 0.92 +/- 0.23 (stat) +/- 0.13 (sys), where R and
lambda are the invariant radius and chaoticity parameters respectively. The
results are qualitatively consistent with m_T systematics established with
pions in a scenario characterized by a strong collective flow.


  The demonstration of a quantum link between microwave and optical frequencies
would be an important step towards the realization of a quantum network of
superconducting processors. A major impediment to quantum electro-optic
transduction in all platforms explored to date is noise added by thermal
occupation of modes involved in the transduction process, and it has proved
difficult to realize low thermal occupancy concurrently with other desirable
features like high duty cycle and high efficiency. In this work, we present an
efficient and continuously operating electro-optomechanical transducer whose
mechanical mode has been optically sideband-cooled to its quantum ground state.
The transducer achieves a maximum efficiency of 47% and minimum input-referred
added noise of 3.2 photons in upconversion. Moreover, the thermal occupancy of
the transducer's microwave mode is minimally affected by continuous laser
illumination with power more than two orders of magnitude greater than that
required for optomechanical ground-state cooling.


  We have realized a two-dimensional hole system (2DHS), in which the 2DHS is
induced at an atomically flat hydrogen-terminated Si(111) surface by a negative
gate voltage applied across a vacuum cavity. Hole densities up to
$7.5\times10^{11}$ cm$^{-2}$ are obtained, and the peak hole mobility is about
$10^4$ cm$^2$/Vs at 70 mK. The quantum Hall effect is observed. Shubnikov-de
Haas oscillations show a beating pattern due to the spin-orbit effects, and the
inferred zero-field spin splitting can be tuned by the gate voltage.


  Artificial intelligence is considered as a key technology. It has a huge
impact on our society. Besides many positive effects, there are also some
negative effects or threats. Some of these threats to society are well-known,
e.g., weapons or killer robots. But there are also threats that are ignored.
These unknown-knowns or blind spots affect privacy, and facilitate manipulation
and mistaken identities. We cannot trust data, audio, video, and identities any
more. Democracies are able to cope with known threats, the known-knowns.
Transforming unknown-knowns to known-knowns is one important cornerstone of
resilient societies. An AI-resilient society is able to transform threats
caused by new AI tecchnologies such as generative adversarial networks.
Resilience can be seen as a positive adaptation of these threats. We propose
three strategies how this adaptation can be achieved: awareness, agreements,
and red flags. This article accompanies the TEDx talk "Why we urgently need an
AI-resilient society", see https://youtu.be/f6c2ngp7rqY.


  We propose an extended Nambu--Jona-Lasinio model to include the heavy mesons
with the heavy quark symmetry. The quark current-current interaction is
generalized to include the heavy quark currents. In order to comply with the
heavy quark spin symmetry at the heavy quark limit, the quark mass dependence
of the interaction strength is introduced. The light and heavy pseudo-scalar
and vector meson, their masses and the weak decay constants, are calculated in
the unified frame.


  In this note we show that there exists a new set of operators {Q} (this set
is different from the operators which satisfy the Lie algebra of the Poincare
group P(1,3) with respect to which the Dirac and Maxwell equations are
invariant. We shall give the detailed proof of our assertions only for the
Dirac equation, since for the Maxwell equations all the assertions are proved
analogously.


  In this paper we introduce the notion of $\Delta$-weak character amenable
Banach algebras and investigate $\Delta$-weak character amenability of certain
Banach algebras such as projective tensor product $A\widehat{\otimes}B$, Lau
product $A\times_TB$ for every Banach algebra $ A$ and $B$, where $T$ be a
homomorphism from $B$ into $A$, abstract Segal algebras and module extension
Banach algebras.