  The outcoupling of a Bose-Einstein condensate through an optical lattice
provides an interesting scenario to study quantum transport phenomena or the
analog Hawking effect as the system can reach a quasi-stationary black-hole
configuration. We devote this work to characterize the quantum transport
properties of quasi-particles on top of this black-hole configuration by
computing the corresponding scattering matrix. We find that most of the
features can be understood in terms of the usual Schr\"odinger scattering. In
particular, a transmission band appears in the spectrum, with the normal-normal
transmission dominating over the anomalous-normal one. We show that this
picture still holds in a realistic experimental situation where the actual
Gaussian envelope of the optical lattice is considered. A peaked resonant
structure is displayed near the upper end of the transmission band, which
suggests that the proposed setup is a good candidate to provide a clear signal
of spontaneous Hawking radiation.


  The inner crust of neutron stars, formed of a crystal lattice of uclear
clusters immersed in a sea of unbound neutrons, may be the nique example of
periodic nuclear systems. We have calculated the neutron specific heat in the
shallow part of the crust using the band theory of solids with Skyrme
nucleon-nucleon interactions. We have also tested the validity of various
approximations. We have found that the neutron specific heat is well described
by that of a Fermi gas, while the motion of the unbound neutrons is strongly
affected by the nuclear lattice. These apparently contradictory results are
explained by the particular properties of the neutron Fermi surface.


  We report experimental and theoretical studies of MoTe$_2$-MoSe$_2$
heterobilayers with rigid moir\'e superlattices controlled by the twist angle.
Using an effective continuum model that combines resonant interlayer electron
tunneling with stacking-dependent moir\'e potentials, we identify the nature of
moir\'e excitons and the dependence of their energies, oscillator strengths and
Land\'e $g$-factors on the twist angle. Within the same framework, we interpret
distinct signatures of bound complexes among electrons and moir\'e excitons in
nearly collinear heterostacks. Our work provides fundamental understanding of
hybrid moir\'e excitons and trions in MoTe$_2$-MoSe$_2$ heterobilayers, and
establishes the material system as a prime candidate for optical studies of
correlated phenomena in moir\'e lattices.


  We discuss the role of dilaton, which is supposed to be representing a
special feature of scale symmetry of QCD, trace anomaly, in dense baryonic
matter. The idea that the scale symmetry breaking of QCD is responsible for the
spontaneous breaking of chiral symmetry is presented along the similar spirit
of Freund-Nambu model. The incorporation of dilaton field in the hidden local
symmetric parity doublet model is briefly sketched with the possible role of
dilaton at high density baryonic matter, the emergence of linear sigma model in
dilaton limit.


  The postulate that coordinate and momentum representations are related to
each other by the Fourier transform has been accepted from the beginning of
quantum theory. As a consequence, coordinate wave functions of photons emitted
by stars have cosmic sizes. This results in a paradox because predictions of
the theory contradict observations. The reason of the paradox and its
resolution are discussed.


  We investigate theoretically the conditions under which a multi-mode
nanomechanical resonator, operated as a purely mechanical parametric
oscillator, can be driven into highly nonclassical states. We find that when
the device can be cooled to near its ground state, and certain mode matching
conditions are satisfied, it is possible to prepare distinct resonator modes in
quantum entangled states that violate Bell inequalities with homodyne
quadrature measurements. We analyze the parameter regimes for such Bell
inequality violations, and while experimentally challenging, we believe that
the realization of such states lies within reach. This is a re-imagining of a
quintessential quantum optics experiment by using phonons that represent
tangible mechanical vibrations.


  Using simulated redshift surveys generated from a high resolution N-body
cosmological structure simulation, we study algorithms used to identify groups
of galaxies in redshift space. Two algorithms are investigated; both are
friends-of-friends schemes with variable linking lengths in the radial and
transverse dimensions. The chief difference between the algorithms is in the
redshift linking length. The algorithm proposed by Huchra \& Geller (1982) uses
a generous linking length designed to find ``fingers of god'' while that of
Nolthenius \& White (1987) uses a smaller linking length to minimize
contamination by projection.
  We find that neither of the algorithms studied is intrinsically superior to
the other; rather, the ideal algorithm as well as the ideal algorithm
parameters depend on the purpose for which groups are to be studied. The
Huchra/Geller algorithm misses few real groups, at the cost of including some
spurious groups and members, while the Nolthenius/White algorithm misses high
velocity dispersion groups and members but is less likely to include
interlopers in its group assignments.
  In a companion paper we investigate the accuracy of virial mass estimates and
clustering properties of groups identified using these algorithms.


  The cell structure of clusters in the inner crust of a cold \beta-equilibrium
neutron star is studied within a Thomas Fermi approach and compared with other
approaches which include shell effects. Relativistic nuclear models are
considered. We conclude that the symmetry energy slope L may have quite
dramatic effects on the cell structure if it is very large or small. Rod-like
and slab-like pasta clusters have been obtained in all models except one with a
large slope L.


  We obtain compact formulae for tree super-amplitudes for 10 and
11-dimensional supergravity and 10-dimensional supersymmetric Yang-Mills and
Born-Infeld. These are based on the \emph{polarised scattering equations}.
These incorporate polarization data into a spinor field on the Riemann sphere
and arise from a twistorial representation of ambitwistor strings in 10 and 11
dimensions. They naturally extend amplitude formulae to manifest maximal
supersymmetry. The framework is the natural generalization of twistorial
ambitwistor string formulae found previously in four and six dimensions and is
informally motivated from a vertex operator prescription for a family of
supersymmetric worldsheet ambitwistor string models.


  This study experimentally validated the possibility of angle of departure
(AoD) estimation using multiple signal classification (MUSIC) with only WiFi
control frames for beamforming feedback (BFF), defined in IEEE 802.11ac/ax. The
examined BFF-based MUSIC is a model-driven algorithm, which does not require a
pre-obtained database. This contrasts with most existing BFF-based sensing
techniques, which are data-driven and require a pre-obtained database.
Moreover, the BFF-based MUSIC affords an alternative AoD estimation method
without access to channel state information (CSI). Specifically, the extensive
experimental and numerical evaluations demonstrated that the BFF-based MUSIC
successfully estimates the AoDs for multiple propagation paths. Moreover, the
evaluations performed in this study revealed that the BFF-based MUSIC achieved
a comparable error of AoD estimation to the CSI-based MUSIC, while BFF is a
highly compressed version of CSI in IEEE 802.11ac/ax.


  Recent papers by Kievsky, Viviani, and Rosati are commented. It is pointed
out that the techniques for treatment few-body reactions and bound states in
the framework of the hyperspherical approach presented in those papers as
original ones were in fact known and have been applied previously.


  The real-axis direct solution of the Eliashberg equations for the retarded
electron-boson interaction in the half-filling case and in the presence of
impurities is obtained for six different symmetries of the order parameter:
$s$, $s+\mathrm{i}d$, $s+d$, $d$, anisotropic-$s$ and extended-$s$. The
spectral function is assumed to contain an isotropic part
$\alpha_{is}^{2}F(\Omega) $ and an anisotropic one $\alpha_{an}^{2}F(\Omega)$
such that $\alpha_{is}^{2}F(\Omega)=g\cdot\alpha_{an}^{2}F(\Omega)$, where $g$
is a constant, and the Coulomb pseudopotential $\mu^{\ast}$ is set to zero for
simplicity. The density of states is calculated for each symmetry at $T= 2, 4,
40$ and 80 K. The resulting curves are compared to those obtained by analytical
continuation of the imaginary-axis solution of the Eliashberg equations and to
the experimental tunneling curves of optimally-doped Bi 2212 crystals.


  Cd(Se,Te) Quantum Dots (QD) in ZnSe barrier typically exhibit a very high
spectral density, which precludes investigation of single dot
photoluminescence. We design, grow and study individual Cd(Se,Te)/ZnSe QDs of
low spectral density of emission lines achieved by implementation of a
Mn-assisted epitaxial growth. We find an unusually large variation of
exciton-biexciton energy difference (3 meV $\leq$ $\Delta \mathrm{E_{X-XX}}$
$\leq$ 26 meV) and of exciton radiative recombination rate in the statistics of
QDs. We observe a strong correlation between the exciton-biexciton energy
difference, exciton recombination rate, splitting between dark and bright
exciton, and additionally the exciton fine structure splitting $\delta_1$ and
Land\'e factor. Above results indicate that values of the $\delta_1$ and of the
Land\'e factor in the studied QDs are dictated primarily by the electron and
hole respective spatial shift and wavefunctions overlap, which vary from dot to
dot due to a different degree of localization of electrons and holes in,
respectively, CdSe and CdTe rich QD regions.


  A new approach to quantum gravity is described which joins the loop
representation formulation of the canonical theory to the causal set
formulation of the path integral. The theory assigns quantum amplitudes to
special classes of causal sets, which consist of spin networks representing
quantum states of the gravitational field joined together by labeled null
edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also
be interepreted as a theory of labeled timelike surfaces. The dynamics is
specified by a choice of functions of the labelings of d+1 dimensional
simplices,which represent elementary future light cones of events in these
discrete spacetimes. The quantum dynamics thus respects the discrete causal
structure of the causal sets. In the 1+1 dimensional case the theory is closely
related to directed percolation models. In this case, at least, the theory may
have critical behavior associated with percolation, leading to the existence of
a classical limit.


  We analyze the lepton-universality violating $B\to K^{(*)}\ell^+\ell^-$
puzzle $R(K^{(*)})$ in a model-independent way. The branching ratio ${\rm
Br}(B_s\to\mu^+\mu^-)$ is also considered as a main constraint. We show how the
branching ratio restricts the allowed region of the parameter space, and
investigate new physics effects on the electronic as well as muonic sector in
$R(K^{(*)})$. Within a reasonable range of parameters we find that the new
physics scale goes up to $\sim 5$ TeV, and the new physics effects on the
Wilson coefficient is $-1\lesssim C_{9NP}^\mu\lesssim 0$.


  Kondo correlations are responsible for the emergence of a zero-bias peak in
the low temperature differential conductance of Coulomb blockaded quantum dots.
In the presence of a global SU(2)$\otimes$SU(2) symmetry, which can be realized
in carbon nanotubes, they also inhibit inelastic transitions which preserve the
Kramers pseudospins associated to the symmetry. We report on magnetotransport
experiments on a Kondo correlated carbon nanotube where resonant features at
the bias corresponding to the pseudospin-preserving transitions are observed.
We attribute this effect to a simultaneous enhancement of
pseudospin-non-preserving transitions occurring at that bias. This process is
boosted by asymmetric tunneling couplings of the two Kramers doublets to the
leads and by asymmetries in the potential drops at the leads. Hence, the
present work discloses a fundamental microscopic mechanisms ruling transport in
Kondo systems far from equilibrium.


  We propose a method for predicting the 3D shape of a deformable surface from
a single view. By contrast with previous approaches, we do not need a
pre-registered template of the surface, and our method is robust to the lack of
texture and partial occlusions. At the core of our approach is a {\it
geometry-aware} deep architecture that tackles the problem as usually done in
analytic solutions: first perform 2D detection of the mesh and then estimate a
3D shape that is geometrically consistent with the image. We train this
architecture in an end-to-end manner using a large dataset of synthetic
renderings of shapes under different levels of deformation, material
properties, textures and lighting conditions. We evaluate our approach on a
test split of this dataset and available real benchmarks, consistently
improving state-of-the-art solutions with a significantly lower computational
time.


  We investigate predicative aspects of order theory in constructive univalent
foundations. By predicative and constructive, we respectively mean that we do
not assume Voevodsky's propositional resizing axioms or excluded middle. Our
work complements existing work on predicative mathematics by exploring what
cannot be done predicatively in univalent foundations. Our first main result is
that nontrivial (directed or bounded) complete posets are necessarily large.
That is, if such a nontrivial poset is small, then weak propositional resizing
holds. It is possible to derive full propositional resizing if we strengthen
nontriviality to positivity. The distinction between nontriviality and
positivity is analogous to the distinction between nonemptiness and
inhabitedness. We prove our results for a general class of posets, which
includes directed complete posets, bounded complete posets and sup-lattices,
using a technical notion of a $\delta_{\mathcal V}$-complete poset. We also
show that nontrivial locally small $\delta_{\mathcal V}$-complete posets
necessarily lack decidable equality. Specifically, we derive weak excluded
middle from assuming a nontrivial locally small $\delta_{\mathcal V}$-complete
poset with decidable equality. Moreover, if we assume positivity instead of
nontriviality, then we can derive full excluded middle. Secondly, we show that
each of Zorn's lemma, Tarski's greatest fixed point theorem and Pataraia's
lemma implies propositional resizing. Hence, these principles are inherently
impredicative and a predicative development of order theory must therefore do
without them. Finally, we clarify, in our predicative setting, the relation
between the traditional definition of sup-lattice that requires suprema for all
subsets and our definition that asks for suprema of all small families.


  Using both fractional derivatives, defined in the Riemann-Liouville and
Caputo senses, and classical derivatives of the integer order we examine
different numerical approaches to ordinary differential equations. Generally we
formulate some algorithms where four discrete forms of the Caputo derivative
and three different numerical techniques of solving ordinary differential
equations are proposed. We then illustrate how to introduce classical initial
conditions into equations where the Riemann-Liouville derivative is included.


  We report the first low temperature magnetotransport measurements on
electrochemically fabricated atomic scale gold nanojunctions. As $T \to 0$, the
junctions exhibit nonperturbatively large zero bias anomalies (ZBAs) in their
differential conductance. We consider several explanations and find that the
ZBAs are consistent with a reduced local density of states (LDOS) in the
disordered metal. We suggest that this is a result of Coulomb interactions in a
granular metal with moderate intergrain coupling. Magnetoconductance of atomic
scale junctions also differs significantly from that of less geometrically
constrained devices, and supports this explanation.


  General relativity predicts the existence of black holes, compact objects
whose spacetimes depend on only their mass, spin, and charge in vacuum (the "no
hair" theorem). As various observations probe deeper into the strong fields of
black hole candidates, it is becoming possible to test this prediction.
Previous work suggested that such tests can be performed by measuring whether
the multipolar structure of black hole candidates has the form that general
relativity demands, and introduced a family of "bumpy black hole" spacetimes to
be used for making these measurements. These spacetimes have generalized
multipoles, where the deviation from the Kerr metric depends on the spacetime's
"bumpiness." In this paper, we show how to compute the Geroch-Hansen moments of
a bumpy black hole, demonstrating that there is a clean mapping between the
deviations used in the bumpy black hole formalism and the Geroch-Hansen
moments. We also extend our previous results to define bumpy black holes whose
{\it current} moments, analogous to magnetic moments of electrodynamics,
deviate from the canonical Kerr value.


  This article explores the constraints of perception and cognition in
relativistic physics. Describing reality as a cognitive representation of our
sensory inputs, the article shows how the limitations in perception translate
to the properties of space and time in physics. This framework of looking at
the visual reality as our brain's representation limited by the speed of light
unifies and explains a wide array of seemingly unrelated astrophysical and
cosmological phenomena. Understanding the constraints on our space and time due
to the limitations in perception and cognitive representation opens the
possibility of understanding astrophysics and cosmology from a whole new
viewpoint.


  We extend a well-known D-brane construction of the AdS/dCFT correspondence to
non-abelian defects. We focus on the bulk side of the correspondence and show
that there exists a regime of parameters in which the low-energy description
consists of two approximately decoupled sectors. The two sectors are gravity in
the ambient spacetime, and a six-dimensional supersymmetric Yang-Mills theory.
The Yang-Mills theory is defined on a rigid AdS_4 x S^2 background and admits
sixteen supersymmetries. We also consider a one-parameter deformation that
gives rise to a family of Yang-Mills theories on asymptotically AdS_4 x S^2
spacetimes, which are invariant under eight supersymmetries. With future
holographic applications in mind, we analyze the vacuum structure and
perturbative spectrum of the Yang-Mills theory on AdS_4 x S^2, as well as
systems of BPS equations for finite-energy solitons. Finally, we demonstrate
that the classical Yang-Mills theory has a consistent truncation on the
two-sphere, resulting in maximally supersymmetric Yang-Mills on AdS_4.


  This work investigates the detection of instabilities that may occur when
utilizing deep learning models for image reconstruction tasks. Although neural
networks often empirically outperform traditional reconstruction methods, their
usage for sensitive medical applications remains controversial. Indeed, in a
recent series of works, it has been demonstrated that deep learning approaches
are susceptible to various types of instabilities, caused for instance by
adversarial noise or out-of-distribution features. It is argued that this
phenomenon can be observed regardless of the underlying architecture and that
there is no easy remedy. Based on this insight, the present work demonstrates
on two use cases how uncertainty quantification methods can be employed as
instability detectors. In particular, it is shown that the recently proposed
Interval Neural Networks are highly effective in revealing instabilities of
reconstructions. Such an ability is crucial to ensure a safe use of deep
learning-based methods for medical image reconstruction.


  Let $(X,L)$ be a polarized complex abelian variety of dimension $g$ where $L$
is a polarization of type $(1,...,1,d)$. For $(X,L)$ genberic we prove the
following:
  (1) If $d \ge g+2$, then $\phi_L\colon X \to {\bf P}^{d-1}$ defines a
birational morphism onto its image.
  (2) If $d > 2^g$, then $L$ is very ample.
  We show the latter by checking it on a suitable rank-$(g-1)$-degeneration.


  Using high spatial resolution HST WFC3 and ACS imaging of resolved stellar
populations, we constrain the contribution of thermally-pulsing asymptotic
giant branch (TP-AGB) stars and red helium burning (RHeB) stars to the 1.6 um
near-infrared (NIR) luminosities of 23 nearby galaxies. The TP-AGB phase
contributes as much as 17% of the integrated F160W flux, even when the red
giant branch is well populated. The RHeB population contribution can match or
even exceed the TP-AGB contribution, providing as much as 21% of the integrated
F160W light. The NIR mass-to-light (M/L) ratio should therefore be expected to
vary significantly due to fluctuations in the star formation rate over
timescales from 25 Myr to several Gyr. We compare our observational results to
predictions based on optically derived star formation histories and stellar
population synthesis (SPS) models, including models based on the Padova
isochrones (used in popular SPS programs). The SPS models generally reproduce
the expected numbers of TP-AGB stars in the sample. The same SPS models,
however, give a larger discrepancy in the F160W flux contribution from the
TP-AGB stars, over-predicting the flux by a weighted mean factor of 2.3 +/-0.8.
This larger offset is driven by the prediction of modest numbers of high
luminosity TP-AGB stars at young (<300 Myrs) ages. The best-fit SPS models
simultaneously tend to under-predict the numbers and fluxes of stars on the
RHeB sequence, typically by a factor of 2.0+/-0.6 for galaxies with significant
numbers of RHeBs. Coincidentally, over-prediction of the TP-AGB and
under-prediction of the RHeBs result in a NIR M/L ratio largely unchanged for a
rapid star formation rate. However, the NIR-to-optical flux ratio of galaxies
could be significantly smaller than AGB-rich models would predict, an outcome
that has been observed in some intermediate redshift post-starburst galaxies.
(Abridged)


  Let $\xi$ be a Dawson--Watanabe superprocess in $\mathbb{R}^d$ such that
$\xi_t$ is a.s. locally finite for every $t\geq 0$. Then for $d\geq2$ and fixed
$t>0$, the singular random measure $\xi_t$ can be a.s. approximated by suitably
normalized restrictions of Lebesgue measure to the $\varepsilon$-neighborhoods
of $\operatorname {supp}\xi_t$. When $d\geq3$, the local distributions of
$\xi_t$ near a hitting point can be approximated in total variation by those of
a stationary and self-similar pseudo-random measure $\tilde{\xi}$. By contrast,
the corresponding distributions for $d=2$ are locally invariant. Further
results include improvements of some classical extinction criteria and some
limiting properties of hitting probabilities. Our main proofs are based on a
detailed analysis of the historical structure of $\xi$.


  We study the classifying space of a twisted loop group $L_{\sigma}G$ where
$G$ is a compact Lie group and $\sigma$ is an automorphism of $G$ of finite
order modulo inner automorphisms. Equivalently, we study the $\sigma$-twisted
adjoint action of $G$ on itself. We derive a formula for the cohomology ring
$H^*(BL_{\sigma}G)$ and explicitly carry out the calculation for all
automorphisms of simple Lie groups. More generally, we derive a formula for the
equivariant cohomology of compact Lie group actions with constant rank
stabilizers.


  We present a functional programming language for specifying constraints over
tree-shaped data. The language allows for Haskell-like algebraic data types and
pattern matching. Our constraint compiler CO4 translates these programs into
satisfiability problems in propositional logic. We present an application from
the area of automated analysis of (non-)termination of rewrite systems.


  Given a large real symmetric, positive semidefinite m-by-m matrix, the goal
of this paper is to show how a numerical approximation of the entropy, given by
the sum of the entropies of the individual eigenvalues, can be computed in an
efficient way. An application from quantum-optics illustrates the new
algorithm.


  We propose an original application of screening methods using machine
learning to detect collusive groups of firms in procurement auctions. As a
methodical innovation, we calculate coalition-based screens by forming
coalitions of bidders in tenders to flag bid-rigging cartels. Using Swiss,
Japanese and Italian procurement data, we investigate the effectiveness of our
method in different countries and auction settings, in our cases first-price
sealed-bid and mean-price sealed-bid auctions. We correctly classify 90\% of
the collusive and competitive coalitions when applying four machine learning
algorithms: lasso, support vector machine, random forest, and super learner
ensemble method. Finally, we find that coalition-based screens for the variance
and the uniformity of bids are in all the cases the most important predictors
according the random forest.


  Unconditionally secure physical key distribution schemes are very slow, and
it is practically impossible to use a one-time-pad based cipher to guarantee
unconditional security for the encryption of data because using the key bits
more than once gives out statistical information, for example via the
known-plain-text-attack or by utilizing known components of the protocol and
language statistics. Here we outline a protocol that reduces this speed problem
and allows almost-one-time-pad based communication with an unconditionally
secure physical key of finite length. The physical, unconditionally secure key
is not used for data encryption but is employed in order to generate and share
a new software-based key without any known-plain-text component. The
software-only-based key distribution is then changed from computationally
secure to unconditionally secure, because the communicated key-exchange data
(algorithm parameters, one-way functions of random numbers, etc.) are encrypted
in an unconditionally secure way with a one-time-pad. For practical
applications, this combined physical/software key distribution based
communication looks favorable compared to the software-only and physical-only
key distribution based communication whenever the speed of the physical key
distribution is much lower than that of the software-based key distribution. A
mathematical security proof of this new scheme remains an open problem.


  In 1917, G.H.Hardy and S.Ramanujan proved that the `typical' number of prime
factors of a positive integer $n$ is approximately $\ln\ln n$. In this
technical paper we proffer a complete exposition of this proof, and further
provide novel approaches based on probabalistic techniques in order to extract
number theoretic results. Using elementary methods in probability theory, we
expand on current methods to prove a substantially sharper distributional
result than in current literature. We conclude the paper with an original proof
of the Hardy-Ramanujan theorem.


  New metallic glasses containing La or Ce have been introduced that have
dynamic properties bordering on extremes of conventional metallic glasses. This
provides opportunity to test trends or correlations established before in
molecular and polymeric glass-formers if exist the same exist in the broader
family of metallic glasses. Due to the drastically different chemical and
physical structure of metallic glass-formers than soft matter, there is no
guarantee that any correlation found in the latter will hold in the former. If
found, the result brings metallic glasses closer to the much wider classes of
glass-formers by the similarity in properties, and possibly have the same
explanation. In non-metallic glass-formers, a general and fundamental
connection has been established between the non-exponentiality parameter of the
structural alpha-relaxation and the separation between its relaxation time and
the beta-relaxation time. In this paper we explore the experimental data of
metallic glass-formers and show the correlation applies. An explanation of this
correlation is given. The establishment of the correlation may facilitate the
understanding of the roles played by the beta-relaxation observed in
macroscopic properties of metallic glasses including the relations to shear
transformation zone, ductile-brittle transition in deformation,
crystallization, and diffusion.


  In this work, the operator-sum representation of a quantum process is
extended to the probability representation of quantum mechanics. It is shown
that each process admitting the operator-sum representation is assigned a
kernel, convolving of which with the initial tomogram set characterizing the
system state gives the tomographic state of the transformed system. This
kernel, in turn, is broken into the kernels of partial operations, each of them
incorporating the symbol of the evolution operator related to the joint
evolution of the system and an ancillary environment. Such a kernel
decomposition for the projection to a certain basis state and a Gaussian-type
projection is demonstrated as well as qubit flipping and amplitude damping
processes.


  We characterize the finite codimension sub-K-algebras of K[[t]] as the
solutions of a computable finite family of higher differential operators. For
this end, we establish a duality between such a sub-algebras and the finite
codimension K-vector spaces of K[u], this ring acts on K[[t]] by
differentiation.


  The enhanced distributed channel access (EDCA) mechanism enables IEEE 802.11p
to accommodate differential quality of service (QoS) levels in
vehicle-to-vehicle (V2V) communications, through four access categories (ACs).
This paper presents multi-dimensional discrete-time Markov chain (DTMC) based
model to study the effect of parallel operation of the ACs on the medium access
control (MAC) layer performance of ITS-G5 IEEE 802.11p. The overall model
consists of four queue models with their respective traffic generators, which
are appropriately linked with the DTMCs modeling the operation of each AC.
Closed-form solutions for the steady-state probabilities of the models are
obtained, which are then utilized to derive expressions for key performance
indicators at the MAC layer. An application for a highway scenario is presented
to draw insights on the performance. The results show how the performance
measures vary among ACs according to their priority levels, and emphasize the
importance of analytical modeling of the parallel operation of all four ACs.


  We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier
multipiers with multiple weights. We also give weighted estimates for their
commutators with vector $BMO$ functions.


  Radiation-pressure-induced optomechanical coupling permits exquisite control
of micro- and mesoscopic mechanical oscillators. This ability to manipulate and
even damp mechanical motion with light---a process known as dynamical
backaction cooling---has become the basis for a range of novel phenomena within
the burgeoning field of cavity optomechanics, spanning from dissipation
engineering to quantum state preparation. As this field moves toward more
complex systems and dynamics, there has been growing interest in the prospect
of cooling traveling-wave phonons in continuous optomechanical waveguides.
Here, we demonstrate optomechanical cooling in a continuous system for the
first time. By leveraging the dispersive symmetry breaking produced by
inter-modal Brillouin scattering, we achieve continuous mode optomechanical
cooling in an extended 2.3-cm silicon waveguide, reducing the temperature of a
band of traveling-wave phonons by more than 30 K from room temperature. This
work reveals that optomechanical cooling is possible in macroscopic linear
waveguide systems without an optical cavity or discrete acoustic modes.
Moreover, through an intriguing type of wavevector-resolved phonon
spectroscopy, we show that this system permits optomechanical control over
continuously accessible groups of phonons and produces a new form of
nonreciprocal reservoir engineering. Beyond this study, this work represents a
first step towards a range of novel classical and quantum traveling-wave
operations in continuous optomechanical systems.


  Relative and absolute emission line shifts have been previously found for
symbiotic binaries, but their cause was not clear. This work aims to better
understand the emission line shifts. Positions of strong emission lines were
measured on archival UV spectra of Z And, AG Dra, RW Hya, SY Mus and AX Per and
relative shifts between the lines of different ions compared. Profiles of lines
of RW Hya and Z And were also examined. The reality of the relative shift
between resonance and intercombination lines of several times ionised atoms was
clearly shown except for AG Dra. This redshift shows a well defined variation
with orbital phase for Z And and RW Hya. In addition the intercombination lines
from more ionised atoms and especially OIV are redshifted with respect to those
from less ionised atoms. Other effects are seen in the profiles. The
resonance-intercombination line shift variation can be explained in quiescence
by P Cygni shorter wavelength component absorption, due to the wind of the cool
component, which is specially strong in inferior conjunction of this cool
giant. The velocity stratification permits absorption of line emission. The
relative intercombination line shifts may be connected with varying occultation
of line emission near an accretion disk, which is optically thick in the
continuum.


  We investigate limits on the extinction values of Type Ia supernovae to
statistically determine the most probable color excess, E(B-V), with
galactocentric distance, and use these statistics to determine the
absorption-to-reddening ratio, $R_V$, for dust in the host galaxies. We
determined pixel-based dust mass surface density maps for 59 galaxies from the
Key Insight on Nearby Galaxies: a Far-Infrared Survey with \textit{Herschel}
(KINGFISH, Kennicutt et al. (2011)). We use Type Ia supernova spectral
templates (Hsiao et al. 2007) to develop a Monte Carlo simulation of color
excess E(B-V) with $R_V$ = 3.1 and investigate the color excess probabilities
E(B-V) with projected radial galaxy center distance. Additionally, we tested
our model using observed spectra of SN 1989B, SN 2002bo and SN 2006X, which
occurred in three KINGFISH galaxies. Finally, we determined the most probable
reddening for Sa-Sap, Sab-Sbp, Sbc-Scp, Scd-Sdm, S0 and Irregular galaxy
classes as a function of $R/R_{25}$. We find that the largest expected
reddening probability are in Sab-Sb and Sbc-Sc galaxies, while S0 and
Irregulars are very dust poor. We present a new approach for determining the
absorption-to-reddening ratio $R_V$ using color excess probability functions,
and find for a sample of 21 SNe Ia observed in Sab-Sbp galaxies, and 34 SNe in
Sbc-Scp, an $R_V$ of 2.71 $\pm$ 1.58 and $R_V$ = 1.70 $\pm$ 0.38 respectively.


  In this paper, we provide a compositional framework for synthesizing hybrid
controllers for interconnected discrete-time control systems enforcing
specifications expressed by co-Buchi automata. In particular, we first
decompose the given specification to simpler reachability tasks based on
automata representing the complements of original co-Buchi automata. Then, we
provide a systematic approach to solve those simpler reachability tasks by
computing corresponding control barrier functions. We show that such control
barrier functions can be constructed compositionally by assuming some
small-gain type conditions and composing so-called local control barrier
functions computed for subsystems. We provide two systematic techniques to
search for local control barrier functions for subsystems based on the
sum-of-squares optimization program and counter-example guided inductive
synthesis approach. Finally, we illustrate the effectiveness of our results
through two large-scale case studies.


  We consider the hypothesis that Evolution promotes population-wide genome
patterns that, under randomization, ensures the External Validity of
adaptations across population members. An adaptation is Externally Valid (EV)
if its effect holds under a wide range of population genetic variations. A
prediction following the hypothesis is that pairwise base substitutions in
segregating regions must be 'random' as in Erdos-Renyi-Gilbert random graphs,
but with edge probabilities derived from Experimental-Design concepts. We
demonstrate these probabilities, and consequent mutation rates, in the
full-genomes of 2504 humans, 1135 flowering plants, 1170 flies, 453 domestic
sheep and 1223 brown rats.


  In a recent article [Phys. Rev. A 86, 024302 (2012)], the authors have
derived some hierarchy relations between geometric discord and entanglement
(measured by negativity and its square). We point out that these results are
incorrect and give analytic counterexamples. We also discuss briefly the reason
for such violations.


  Transitions between different inflationary slow-roll scenarios are known to
provide short non-slow-roll periods with non-trivial consequences. We consider
the effect of quantum diffusion on the inflationary dynamics in a transition
process. Using the stochastic {\delta}N formalism, we follow the detailed
evolution of noises through a sharp transition modeled by the Starobinsky
potential, although some of our results apply to any sharp transition. We find
how the stochastic noise induced by the transition affects the coarse-grained
fields. We then consider the special case that the potential is flat after the
transition. It is found that the particular noise we obtain cannot drive the
inflaton past the classically unreachable field values. By deriving the
characteristic function, we also study the tail behavior for the distribution
of curvature perturbations {\zeta}, which we find to decay faster than
e^(-3{\zeta}).


  The aim of this article is to solve the system $XA=Y$ where $A=(a_{ij})\in
M_{m\times n}(S)$, $Y\in S^{m}$ and $X$ is an unknown vector of size $n$, being
$S$ an additively idempotent semiring. If the system has solutions then we
completely characterize its maximal one, and in the particular case where $S$
is a generalized tropical semiring a complete characterization of its solutions
is provided as well as an explicit bound of the computational cost associated
to its computation. Finally, when $S$ is finite, we give a cryptographic
application by presenting an attack to the key exchange protocol proposed by
Maze, Monico and Rosenthal.


  We experimentally probe the distribution of kink pairs resulting from driving
a one-dimensional quantum Ising chain through the paramagnet-ferromagnet
quantum phase transition, using a single trapped ion as a quantum simulator in
momentum space. The number of kink pairs after the transition follows a Poisson
binomial distribution, in which all cumulants scale with a universal power-law
as a function of the quench time in which the transition is crossed. We
experimentally verified this scaling for the first cumulants and report
deviations due to noise-induced dephasing of the trapped ion. Our results
establish that the universal character of the critical dynamics can be extended
beyond the paradigmatic Kibble-Zurek mechanism, which accounts for the mean
kink number, to characterize the full probability distribution of topological
defects.


  People convey their intention and attitude through linguistic styles of the
text that they write. In this study, we investigate lexicon usages across
styles throughout two lenses: human perception and machine word importance,
since words differ in the strength of the stylistic cues that they provide. To
collect labels of human perception, we curate a new dataset, Hummingbird, on
top of benchmarking style datasets. We have crowd workers highlight the
representative words in the text that makes them think the text has the
following styles: politeness, sentiment, offensiveness, and five emotion types.
We then compare these human word labels with word importance derived from a
popular fine-tuned style classifier like BERT. Our results show that the BERT
often finds content words not relevant to the target style as important words
used in style prediction, but humans do not perceive the same way even though
for some styles (e.g., positive sentiment and joy) human- and
machine-identified words share significant overlap for some styles.


  The present work studies and analyzes general defaultable OTC contract in
presence of a contingent CSA, which is a theoretical counterparty risk
mitigation mechanism of switching type that allows the counterparty of a
general OTC contract to switch from zero to full/perfect collateralization and
switch back whenever she wants until contract maturity paying some switching
costs and taking into account the running costs that emerge over time. The
motivation and the underlying economic idea is to show that the current
full/partial collateralization mechanisms defined within contracts' CSA - and
now imposed by the banking supervision authorities - are "suboptimal" and less
economic than the contingent one that allows to optimally take in account all
the relevant driver namely the expected costs of counterparty default losses -
represented by the (bilateral) CVA - and the expected collateral and funding
costs. In this perspective, we tackle the problem from the risk management and
optimal design point of view solving - under some working assumptions - the
derived stochastic switching control model via Snell envelope technique and
important results of the theory of the backward stochastic differential
equations with reflection (RBSDE). We have also studied the numerical solution
providing an algorithm procedure for the value function computation based on an
iterative optimal stopping approach.


  In this study, we develop an innovative data-driven optimization approach to
solve the drone delivery service planning problem with online demand.
Drone-based logistics are expected to improve operations by enhancing
flexibility and reducing congestion effects induced by last-mile deliveries.
With rising digitalization and urbanization, however, logistics service
providers are constantly grappling with the challenge of uncertain real-time
demand. This study investigates the problem of planning drone delivery service
through an urban air traffic network to fulfil online and stochastic demand.
Customer requests, if accepted, generate profit and are serviced by individual
drone flights as per request origins, destinations and time windows. We cast
this stochastic optimization problem as a Markov decision process. We present a
novel data-driven optimization approach which generates predictive
prescriptions of parameters of a surrogate optimization formulation. Our
solution method consists of synthesizing training data via lookahead
simulations to train a supervised machine learning model for predicting
relative link priority based on the state of the network. This knowledge is
then leveraged to selectively create weighted reserve capacity in the network
and via a surrogate objective function that controls the trade-off between
reserve capacity and profit maximization to maximize the cumulative profit
earned. Using numerical experiments based on benchmarking transportation
networks, the resulting data-driven optimization policy is shown to outperform
a myopic policy. Sensitivity analyses on learning parameters reveal insights
into the design of efficient policies for drone delivery service planning with
online demand.


  The strong-property-fluctuation theory (SPFT) provides a sophisticated means
of estimating the effective constitutive parameters of a homogenized composite
material (HCM), which takes account of the statistical distribution of the
component particles. We present an extended version of the third-order SPFT in
which the component particles are represented as depolarization regions of
nonzero volume. Numerical results are provided for a bianisotropic
homogenization scenario wherein the HCM is a Faraday chiral medium. Thereby,
convergence of the extended SPFT at the second-order level of approximation is
demonstrated within the long-wavelength regime.


  In contrast to their empirical counterparts, machine-learning interatomic
potentials (MLIAPs) promise to deliver near-quantum accuracy over broad regions
of configuration space. However, due to their generic functional forms and
extreme flexibility, they can catastrophically fail to capture the properties
of novel, out-of-sample configurations, making the quality of the training set
a determining factor, especially when investigating materials under extreme
conditions. In the present study, we propose a novel automated dataset
generation method based on the maximization of the information entropy of the
feature distribution, aiming at an extremely broad coverage of the
configuration space in a way that is agnostic to the properties of specific
target materials. The ability of the dataset to capture unique material
properties is demonstrated on a range of unary materials, including elements
with the fcc (Al), bcc (W), hcp (Be, Re and Os), and graphite (C) ground
states. MLIAPs trained to this dataset are shown to be accurate over a broad
range of application-relevant metrics, as well as extremely robust over very
broad swaths of configurations space, even without dataset fine-tuning or
hyper-parameter optimization, making the approach extremely attractive to
rapidly and autonomously develop general-purpose MLIAPs suitable for
simulations in extreme conditions.


  We consider the problem of path inference: given a path prefix, i.e., a
partially observed sequence of nodes in a graph, we want to predict which nodes
are in the missing suffix. In particular, we focus on natural paths occurring
as a by-product of the interaction of an agent with a network---a driver on the
transportation network, an information seeker in Wikipedia, or a client in an
online shop. Our interest is sparked by the realization that, in contrast to
shortest-path problems, natural paths are usually not optimal in any
graph-theoretic sense, but might still follow predictable patterns.
  Our main contribution is a graph neural network called Gretel. Conditioned on
a path prefix, this network can efficiently extrapolate path suffixes, evaluate
path likelihood, and sample from the future path distribution. Our experiments
with GPS traces on a road network and user-navigation paths in Wikipedia
confirm that Gretel is able to adapt to graphs with very different properties,
while also comparing favorably to previous solutions.


  In this work we describe the thermodynamics and mechanism of CO$_2$
polymorphic transitions under pressure from form I to form III combining
standard molecular dynamics, well-tempered metadynamics and committor analysis.
We find that the phase transformation takes place through a concerted
rearrangement of CO$_2$ molecules, which unfolds via an anisotropic expansion
of the CO$_2$ supercell. Furthermore, at high pressures we find that defected
form I configurations are thermodynamically more stable with respect to form I
without structural defects. Our computational approach shows the capability of
simultaneously providing an extensive sampling of the configurational space,
estimates of the thermodynamic stability and a suitable description of a
complex, collective polymorphic transition mechanism.


  The oldest stars in the Milky Way (born in the first few billion years) are
expected to have a high density in the inner few kpc, spatially overlapping
with the Galactic bulge. We use spectroscopic data from the Pristine Inner
Galaxy Survey (PIGS) to study the dynamical properties of ancient, metal-poor
inner Galaxy stars. We compute distances using StarHorse, and orbital
properties in a barred Galactic potential. With this paper, we release the
spectroscopic AAT/PIGS catalogue (13 235 stars). We find that most PIGS stars
have orbits typical for a pressure-supported population. The fraction of stars
confined to the inner Galaxy decreases with decreasing metallicity, but many
very metal-poor stars (VMP, [Fe/H] < -2.0) stay confined (~ 60% stay within 5
kpc). The azimuthal velocity v$_\phi$ also decreases between [Fe/H] = -1.0 and
-2.0, but is constant for VMP stars (at ~ 40 km/s). The carbon-enhanced
metal-poor (CEMP) stars in PIGS appear to have similar orbital properties
compared to normal VMP stars. Our results suggest a possible transition between
two spheroidal components - a more metal-rich, more concentrated, faster
rotating component, and a more metal-poor, more extended and
slower/non-rotating component. We propose that the former may be connected to
pre-disc in-situ stars (or those born in large building blocks), whereas the
latter may be dominated by contributions from smaller galaxies. This is an
exciting era where large metal-poor samples, such as in this work (as well as
upcoming surveys, e.g., 4MOST), shed light on the earliest evolution of our
Galaxy.


  The paper focuses on numerical simulation of the phase-field (PF) equations
for modeling martensitic transformations in shape memory alloys (SMAs), their
complex microstructures and thermo-mechanical behavior. The PF model is based
on the Landau-Ginzburg potential for the 3D cubic-to-tetragonal phase
transformations in SMAs. The treatment of domain walls as diffuse interfaces,
leads to a fourth-order differential equation in a strain-based order parameter
PF model. The fourth-order equations introduce a number of unexplored numerical
challenges because traditional numerical schemes have been primarily applied to
second-order problems. We propose isogeometric analysis (IGA) as a numerical
formulation for a straightforward solution to the fourth-order differential PF
equations using continuously differentiable non-uniform rational B-splines
(NURBS). We present microstructure evolution in different geometries of SMA
nanostructures under temperature-induced phase transformations to illustrate
the geometrical flexibility, accuracy and robustness of our approach. The
simulations successfully capture the dynamic thermo-mechanical behavior of SMAs
observed experimentally.


  The mixing of the photon with a hypothetical sterile paraphotonic state would
have consequences on the cosmological propagation of photons. Observations of
gamma-rays from active galactic nuclei in GLAST and MAGIC will open a new
domain in the search for such a phenomenon.


  The motion of test particles in the gravitational fields generated by the
first four members of the infinite family of generalized Kalnajs discs, is
studied. In first instance, we analyze the stability of circular orbits under
radial and vertical perturbations and describe the behavior of general
equatorial orbits and so we find that radial stability and vertical instability
dominate such disc models. Then we study bounded axially symmetric orbits by
using the Poincare surfaces of section and Lyapunov characteristic numbers and
find chaos in the case of disc-crossing orbits and completely regular motion in
other cases.


  The projection construction has been used to construct semifields of odd
characteristic using a field and a twisted semifield [Commutative semifields
from projection mappings, Designs, Codes and Cryptography, 61 (2011),
187--196]. We generalize this idea to a projection construction using two
twisted semifields to construct semifields of odd characteristic. Planar
functions and semifields have a strong connection so this also constructs new
planar functions.


  Let $G$ be a semisimple Lie group. We describe the irreducible
representations of $G$ by linear isometries on $L_p$-spaces for $p\in
(1,+\infty)$ with $p\neq 2.$ More precisely, we show that, for every such
representation $\pi,$ there exists a parabolic subgroup $Q$ of $G$ such that
$\pi$ is equivalent to the natural representation of $G$ on $L_p(G/Q)$ twisted
by a unitary character of $Q.$ When $G$ is of real rank one, we give a complete
classification of the possible irreducible representations of $G$ on an
$L_p$-space for $p\neq 2,$ up to equivalence.


  In a node-labeled graph, keyword search finds subtrees of the graph whose
nodes contain all of the query keywords. This provides a way to query graph
databases that neither requires mastery of a query language such as SPARQL, nor
a deep knowledge of the database schema. Previous work ranks answer trees using
combinations of structural and content-based metrics, such as path lengths
between keywords or relevance of the labels in the answer tree to the query
keywords. We propose two new ways to rank keyword search results over graphs.
The first takes node importance into account while the second is a bi-objective
optimization of edge weights and node importance. Since both of these problems
are NP-hard, we propose greedy algorithms to solve them, and experimentally
verify their effectiveness and efficiency on a real dataset.


  The step-scaling function, the lattice analog of the renormalization group
$\beta$ function, is presented for the SU(3) gauge system with eight flavors in
the fundamental representation. Our investigation is based on generating
dynamical eight flavor gauge field configurations using stout-smeared M\"obius
domain wall fermions and Symanzik gauge action. On these gauge field
configurations we perform gradient flow measurements using the Zeuthen, Wilson,
or Symanzik kernel and consider the Symanzik, Wilson plaquette, or clover
operators to determine step-scaling functions for a scale change $s=2$
including large, up to $48^4$, volumes. Considering different flows and
operators as well as the optional use of tree-level improvement allows us to
check for possible systematic effects. Our result covers the range of
renormalized coupling up to $g_c^2 \lesssim 10$. In the case of $N_f=8$ we
observe that the reach in $g_c^2$ is limited due to an unphysical first order
bulk phase transition caused by large ultra-violet fluctuations.
  We compare our findings to $N_f=4$, 6, 10 or 12 flavors results that are
obtained using the same lattice action and analysis. In addition we investigate
the phase structure for simulations with different number of flavors using
stout-smeared M\"obius domain wall fermions and Symanzik gauge actions to shed
some light on the limited reach in $g_c^2$.


  We describe a nuclear spin gyroscope based on an alkali-metal-noble-gas
co-magnetometer. An optically pumped alkali-metal vapor is used to polarize the
noble gas atoms and detect their gyroscopic precession. Spin precession due to
magnetic fields as well as their gradients and transients can be cancelled in
this arrangement. The sensitivity is enhanced by using a high-density
alkali-metal vapor in a spin-exchange relaxation free (SERF) regime. With a
K-3He co-magnetometer we demonstrate rotation sensitivity of 5 10^(-7)
rad/sec/Hz^(1/2). The rotation signal can be increased by a factor of 10 using
21Ne due to its smaller magnetic moment and the fundamental rotation
sensitivity limit for a 21Ne gyroscope with a 10 cm^3 measurement volume is
about 2 10^(-10) rad/sec/Hz^(1/2).


  While recent methods for motion and stereo estimation recover an
unprecedented amount of details, such highly detailed structures are neither
adequately reflected in the data of existing benchmarks nor their evaluation
methodology. Hence, we introduce Spring $-$ a large, high-resolution,
high-detail, computer-generated benchmark for scene flow, optical flow, and
stereo. Based on rendered scenes from the open-source Blender movie "Spring",
it provides photo-realistic HD datasets with state-of-the-art visual effects
and ground truth training data. Furthermore, we provide a website to upload,
analyze and compare results. Using a novel evaluation methodology based on a
super-resolved UHD ground truth, our Spring benchmark can assess the quality of
fine structures and provides further detailed performance statistics on
different image regions. Regarding the number of ground truth frames, Spring is
60$\times$ larger than the only scene flow benchmark, KITTI 2015, and
15$\times$ larger than the well-established MPI Sintel optical flow benchmark.
Initial results for recent methods on our benchmark show that estimating fine
details is indeed challenging, as their accuracy leaves significant room for
improvement. The Spring benchmark and the corresponding datasets are available
at http://spring-benchmark.org.


  Automated attack discovery techniques, such as attacker synthesis or
model-based fuzzing, provide powerful ways to ensure network protocols operate
correctly and securely. Such techniques, in general, require a formal
representation of the protocol, often in the form of a finite state machine
(FSM). Unfortunately, many protocols are only described in English prose, and
implementing even a simple network protocol as an FSM is time-consuming and
prone to subtle logical errors. Automatically extracting protocol FSMs from
documentation can significantly contribute to increased use of these techniques
and result in more robust and secure protocol implementations.
  In this work we focus on attacker synthesis as a representative technique for
protocol security, and on RFCs as a representative format for protocol prose
description. Unlike other works that rely on rule-based approaches or use
off-the-shelf NLP tools directly, we suggest a data-driven approach for
extracting FSMs from RFC documents. Specifically, we use a hybrid approach
consisting of three key steps: (1) large-scale word-representation learning for
technical language, (2) focused zero-shot learning for mapping protocol text to
a protocol-independent information language, and (3) rule-based mapping from
protocol-independent information to a specific protocol FSM. We show the
generalizability of our FSM extraction by using the RFCs for six different
protocols: BGPv4, DCCP, LTP, PPTP, SCTP and TCP. We demonstrate how automated
extraction of an FSM from an RFC can be applied to the synthesis of attacks,
with TCP and DCCP as case-studies. Our approach shows that it is possible to
automate attacker synthesis against protocols by using textual specifications
such as RFCs.


  Problem for the first order differential equation with an unbounded operator
coefficient in Banach space and integral nonlocal condition is considered. An
exponentially convergent algorithm is proposed and justified for the numerical
solution of this problem in assumption that an operator coefficient $A$ is
strongly positive and some existence and uniqueness conditions are fulfilled.
This algorithm is based on the representations of operator functions by a
Dunford-Cauchy integral along a hyperbola, enveloping the spectrum of $A$, and
on the proper quadratures involving short sums of resolvents. The efficiency of
the proposed algorithms is demonstrated by several numerical examples.


  In this paper, we introduce two new methods of mitigating decoder error
propagation for low-latency sliding window decoding (SWD) of spatially coupled
low density parity check (SC-LDPC) codes. Building on the recently introduced
idea of \emph{check node (CN) doping} of regular SC-LDPC codes, here we employ
variable node (VN) doping to fix (set to a known value) a subset of variable
nodes in the coupling chain. Both of these doping methods have the effect of
allowing SWD to recover from error propagation, at a cost of a slight rate
loss. Experimental results show that, similar to CN doping, VN doping improves
performance by up to two orders of magnitude compared to undoped SC-LDPC codes
in the typical signal-to-noise ratio operating range. Further, compared to CN
doping, VN doping has the advantage of not requiring any changes to the
decoding process.In addition, a log-likelihood-ratio based window extension
algorithm is proposed to reduce the effect of error propagation. Using this
approach, we show that decoding latency can be reduced by up to a significant
fraction without suffering any loss in performance.


  Reinforcement Learning has been able to solve many complicated robotics tasks
without any need for feature engineering in an end-to-end fashion. However,
learning the optimal policy directly from the sensory inputs, i.e the
observations, often requires processing and storage of a huge amount of data.
In the context of robotics, the cost of data from real robotics hardware is
usually very high, thus solutions that achieve high sample-efficiency are
needed. We propose a method that aims at learning a mapping from the
observations into a lower-dimensional state space. This mapping is learned with
unsupervised learning using loss functions shaped to incorporate prior
knowledge of the environment and the task. Using the samples from the state
space, the optimal policy is quickly and efficiently learned. We test the
method on several mobile robot navigation tasks in a simulation environment and
also on a real robot.


  Many networks can be usefully decomposed into a dense core plus an outlying,
loosely-connected periphery. Here we propose an algorithm for performing such a
decomposition on empirical network data using methods of statistical inference.
Our method fits a generative model of core-periphery structure to observed data
using a combination of an expectation--maximization algorithm for calculating
the parameters of the model and a belief propagation algorithm for calculating
the decomposition itself. We find the method to be efficient, scaling easily to
networks with a million or more nodes and we test it on a range of networks,
including real-world examples as well as computer-generated benchmarks, for
which it successfully identifies known core-periphery structure with low error
rate. We also demonstrate that the method is immune from the detectability
transition observed in the related community detection problem, which prevents
the detection of community structure when that structure is too weak. There is
no such transition for core-periphery structure, which is detectable, albeit
with some statistical error, no matter how weak it is.


  The potential of using hydrogen as a sustainable energy carrier is attributed
to its high energy density and its utilization without CO$_2$ emissions.
Existing technologies mainly produce hydrogen thermochemically via natural gas
reforming or electrochemically through water splitting. Organic solid
feedstocks rich in hydrogen, such as biomass and plastic waste, are
under-utilized for this purpose. Approaches based on low-temperature
atmospheric pressure plasma powered by renewable electricity could lead to the
production of green hydrogen more viably than current approaches, leading to
sustainable alternatives for upcycling plastic and biomass waste. This doctoral
research dissertation focuses on the production of hydrogen from solids via
atmospheric nonthermal plasma. First, two low-temperature atmospheric pressure
plasma reactors, based on transferred arc (transarc) and gliding arc (glidarc)
discharges and depicting complementary operational characteristics, are
designed, built, and characterized to produce hydrogen from low-density
polyethylene (LDPE) as a model plastic waste. Experimental results show that
hydrogen production rate and efficiency increase monotonically with increasing
voltage level in both reactors. Despite the reactors' markedly different modes
of operation, their hydrogen production performance metrics are comparable.


  This paper investigates the hybrid precoding design for millimeter wave
(mmWave) multiple-input multiple-output (MIMO) systems with finite-alphabet
inputs. The precoding problem is a joint optimization of analog and digital
precoders, and we treat it as a matrix factorization problem with power and
constant modulus constraints. Our work presents three main contributions:
First, we present a sufficient condition and a necessary condition for hybrid
precoding schemes to realize unconstrained optimal precoders exactly when the
number of data streams Ns satisfies Ns = minfrank(H);Nrfg, where H represents
the channel matrix and Nrf is the number of radio frequency (RF) chains.
Second, we show that the coupled power constraint in our matrix factorization
problem can be removed without loss of optimality. Third, we propose a
Broyden-Fletcher-Goldfarb-Shanno (BFGS)-based algorithm to solve our matrix
factorization problem using gradient and Hessian information. Several numerical
results are provided to show that our proposed algorithm outperforms existing
hybrid precoding algorithms.


  Indistinguishable laser pulse is important in realization of qubits in
quantum cryptography. Implementation of such cryptography in automotive
framework needs to be compact and cheap. However, modern implementation of
quantum cryptography is bulky and expensive. Significant effort has been put
into to reduce the form factor of quantum cryptography implementation. We
report a compact, low cost, indistinguishable, sub-nanosecond pulse generator
with adjusted delay and amplitude using a Fabry-Perot laser diode. The approach
was derived based on algebraic topology formulation of electrical network, and
the implementation is time dependent perturbation of a constant current node,
generating tun-able, sub-nanosecond excitation with constant pre-bias.
Parameters for simulation model for the laser diode was obtained considering
effect of spontaneous emission and relaxation oscillation. The shortest pulse
was measured to have FWHM of 496ps.


  The Transient Fluctuation Theorem is used to calibrate an Atomic Force
Microscope by measuring the fluctuations of the work performed by a time
dependent force applied between a collo{\"i}dal probe and the surface. From
this measure one can easily extract the value of the interaction force and the
relevant parameters of the cantilever. The results of this analysis are
compared with those obtained by standard calibration methods. a) present
adress: ISIS, Univ.


  Despite observed strong correlations between central supermassive black holes
(SMBHs) and star-formation in galactic nuclei, uncertainties exist in our
understanding of their coupling. We present observations of the ratio of
heavily-obscured to unobscured quasars as a function of cosmic epoch up to z~3,
and show that a simple physical model describing mergers of massive, gas-rich
galaxies matches these observations. In the context of this model, every
obscured and unobscured quasar represent two distinct phases that result from a
massive galaxy merger event. Much of the mass growth of the SMBH occurs during
the heavily-obscured phase. These observations provide additional evidence for
a causal link between gas-rich galaxy mergers, accretion onto the nuclear SMBH
and coeval star formation.


  We prove a discrete version of the Lusternik-Schnirelmann theorem for
discrete Morse functions and the recently introduced simplicial
Lusternik-Schnirelmann category of a simplicial complex. To accomplish this, a
new notion of critical object of a discrete Morse function is presented, which
generalizes the usual concept of critical simplex (in the sense of R. Forman).
We show that the non-existence of such critical objects guarantees the strong
homotopy equivalence (in the Barmak and Minian's sense) between the
corresponding sublevel complexes. Finally, we establish that the number of
critical objects of a discrete Morse function defined on $K$ is an upper bound
for the non-normalized simplicial Lusternik-Schnirelmann category of $K$.


  We propose an effective lattice model for the moir\'e structure of the
twisted bilayer dice lattice. In the chiral limit, we find that there are flat
bands at the zero-energy level at any twist angle besides the magic ones and
these flat bands are broadened by small perturbation away from the chiral
limit. The flat bands contain both bands with zero Chern number which originate
from the destructive interference of the states on the dice lattice and the
topological nontrivial bands at the magic angle. The existence of the flat
bands can be detected from the peak-splitting structure of the optical
conductance at all angles, while the transition peaks do not split and only
occur at magic angles in twisted bilayer graphene.


  We examine the mean first passage time for a particle driven by highly
correlated Gaussian fluctuations to reach one or more predetermined boundaries.
We discuss a numerical algorithm to generate power-law correlated fluctuations
and apply these to three physical examples. One is the arrival of a free
particle at either end of an interval. The second is the decay of a particle
from an unstable state. The third is the time for a particle to cross a barrier
separating one well from another in a double well potential. In each case a
comparison with the first passage time for a particle driven by Gaussian white
noise is presented, as is an analysis of the dependence of the first passage
time properties on the correlated noise parameters.


  We investigate the capabilities of the ESA Gaia mission for detecting and
character- izing short timescale variability, from tens of seconds to a dozen
hours. We assess the efficiency of the variogram analysis, for both detecting
short timescale variability and estimating the underlying characteristic
timescales from Gaia photometry, through extensive light-curve simulations for
various periodic and transient short timescale variable types. We show that,
with this approach, we can detect fast periodic variabil- ity, with amplitudes
down to a few millimagnitudes, as well as some M dwarf flares and supernovae
explosions, with limited contamination from longer timescale variables or
constant sources. Timescale estimates from the variogram give valuable informa-
tion on the rapidity of the underlying variation, which could complement
timescale estimates from other methods, like Fourier-based periodograms, and be
reinvested in preparation of ground-based photometric follow-up of short
timescale candidates evi- denced by Gaia. The next step will be to find new
short timescale variable candidates from real Gaia data, and to further
characterize them using all the Gaia information, including color and spectrum.


  We propose a natural realization of linear seesaw model with hidden gauge
symmetry in which $SU(2)_L$ triplet fermions, one extra Higgs singlet, doublet
and quartet scalar are introduced. Small neutrino mass can be realized by two
suppression factors that are small vacuum expectation value of quartet scalar
and inverse of Dirac mass for triplet. After formulating neutrino mass matrix,
we discuss collider phenomenology of the model focusing on signals from exotic
charged particles production at the LHC.


  In this paper, we propose a fully decentralized and smart contract-based
insurance protocol. We identify various issues in the Decentralized Finance
(DeFi) insurance context and propose a solution to overcome these shortcomings.
We introduce an economic model that allows for risk transfer without any
external dependencies or centralized intermediaries. In particular, our
proposal does not need any sort of subjective claim assessment, community
voting or external data providers (oracles). Moreover, it solves the problem of
over-insurance and proposes various ways to mitigate the capital inefficiencies
usually seen with DeFi collateral. The work takes inspiration from peer-to-peer
(P2P) insurance and collateralized debt obligations (CDO). We formally describe
the protocol, assess its efficiency and key properties and present a reference
implementation. Finally, we address limitations, extensions and ideas for
further research.


  Deep convolutional neural networks have achieved great success in various
applications. However, training an effective DNN model for a specific task is
rather challenging because it requires a prior knowledge or experience to
design the network architecture, repeated trial-and-error process to tune the
parameters, and a large set of labeled data to train the model. In this paper,
we propose to overcome these challenges by actively adapting a pre-trained
model to a new task with less labeled examples. Specifically, the pre-trained
model is iteratively fine tuned based on the most useful examples. The examples
are actively selected based on a novel criterion, which jointly estimates the
potential contribution of an instance on optimizing the feature representation
as well as improving the classification model for the target task. On one hand,
the pre-trained model brings plentiful information from its original task,
avoiding redesign of the network architecture or training from scratch; and on
the other hand, the labeling cost can be significantly reduced by active label
querying. Experiments on multiple datasets and different pre-trained models
demonstrate that the proposed approach can achieve cost-effective training of
DNNs.


  We combine two non-perturbative approaches, one based on the
two-particle-irreducible (2PI) action, the other on the functional
renormalization group (fRG), in an effort to develop new non-perturbative
approximations for the field theoretical description of strongly coupled
systems. In particular, we exploit the exact 2PI relations between the
two-point and four-point functions in order to truncate the infinite hierarchy
of equations of the functional renormalization group. The truncation is "exact"
in two ways. First, the solution of the resulting flow equation is independent
of the choice of the regulator. Second, this solution coincides with that of
the 2PI equations for the two-point and the four-point functions, for any
selection of two-skeleton diagrams characterizing a so-called $\Phi$-derivable
approximation. The transformation of the equations of the 2PI formalism into
flow equations offers new ways to solve these equations in practice, and
provides new insight on certain aspects of their renormalization. It also opens
the possibility to develop approximation schemes going beyond the strict
$\Phi$-derivable ones, as well as new truncation schemes for the fRG hierarchy.


  This paper presents an energy management framework for building climate
comfort (BCC) systems interconnected in a grid via aquifer thermal energy
storage (ATES) systems in the presence of two types of uncertainty (private and
common). ATES can be used either as a heat source (hot well) or sink (cold
well) depending on the season. We consider the uncertain thermal energy demand
of individual buildings as a private uncertainty source and the uncertain
common resource pool (ATES) between neighbors as a common uncertainty source.
We develop a large-scale stochastic hybrid dynamical model to predict the
thermal energy imbalance in a network of interconnected BCC systems together
with mutual interactions between their local ATES. We formulate a
finite-horizon mixed-integer quadratic optimization problem with multiple
chance constraints at each sampling time, which is in general a non-convex
problem and difficult to solve. We then provide a computationally tractable
framework by extending the so-called robust randomized approach and offering a
less conservative solution for a problem with multiple chance constraints. A
simulation study is provided to compare completely decoupled, centralized and
move-blocking centralized solutions. We also present a numerical study using a
geohydrological simulation environment (MODFLOW) to illustrate the advantages
of our proposed framework.


  We investigate the multicritical behavior of the three-dimensional Z_2 gauge
Higgs model, at the multicritical point (MCP) of its phase diagram, where one
first-order transition line and two continuous Ising-like transition lines
meet. The duality properties of the model determine some features of the
multicritical behavior at the MCP located along the self-dual line. Moreover,
we argue that the system develops a multicritical XY behavior at the MCP, which
is controlled by the stable XY fixed point of the three-dimensional
multicritical Landau-Ginzburg-Wilson field theory with two competing scalar
fields associated with the continuous Z_2 transition lines meeting at the MCP.
This implies an effective enlargement of the symmetry of the multicritical
modes at the MCP, to the continuous group O(2). We also provide some numerical
results to support the multicritical XY scenario.


  Known for their ability to identify hidden patterns in data, artificial
neural networks are among the most powerful machine learning tools. Most
notably, neural networks have played a central role in identifying states of
matter and phase transitions across condensed matter physics. To date, most
studies have focused on systems where different phases of matter and their
phase transitions are known, and thus the performance of neural networks is
well controlled. While neural networks present an exciting new tool to detect
new phases of matter, here we demonstrate that when the training sets are
poisoned (i.e., poor training data or mislabeled data) it is easy for neural
networks to make misleading predictions.


  The flow models of complex network system are developed and main flow
characteristics of its elements are defined. Those characteristics are applied
for determining actual structure of the system, analyzing its development on
all lifecycle stages and finding alternative flow directions that bypass
isolated areas of network. Influence and betweenness parameters of components
of network systems are defined. Using those parameters, the conditions were
studied under which system is resistant to negative internal and external
influence. The notion of flow core of complex network systems is defined, that
allows to distinguish the most important components of system structure in
terms of operation to solve the problem of finding communities within the
network. The notions of p-core and kernel of mono flow partially overlapped
multilayered network are defined that allow to determine components of system
structure that play the most important role in implementation of interactions
between systems. The methodology is developed for complex evaluation of quality
of complex hierarchical network systems. This methodology combines the
interconnected methods of local, forecasting, interactive and aggregated
analysis of system components behavior on all hierarchy levels. It is
demonstrated that application of proposed complex evaluation methodology is
efficient for solving problem of defining practically possible criteria of
network system element quality, novelty detection, determining critical and
optimal system operation modes and selecting optimal system of given class of
systems.


  We show that, under certain general assumptions, any sensible lattice Dirac
operator satisfies a generalized form of the Ginsparg-Wilson relation (GWR).
Those assumptions, on the other hand, are mostly dictated by large momentum
behaviour considerations. We also show that all the desirable properties often
deduced from the standard GWR hold true of the general case as well; hence one
has, in fact, more freedom to modify the form of the lattice Dirac operator,
without spoiling its nice properties. Our construction, a generalized
Ginsparg-Wilson relation (GGWR), is satisfied by some known proposals for the
lattice Dirac operator. We discuss some of these examples, and also present a
derivation of the GGWR in terms of a renormalization group transformation with
a blocking which is not diagonal in momentum space, but nevertheless commutes
with the Dirac operator.


  We study the convex-hull problem in a probabilistic setting, motivated by the
need to handle data uncertainty inherent in many applications, including sensor
databases, location-based services and computer vision. In our framework, the
uncertainty of each input site is described by a probability distribution over
a finite number of possible locations including a \emph{null} location to
account for non-existence of the point. Our results include both exact and
approximation algorithms for computing the probability of a query point lying
inside the convex hull of the input, time-space tradeoffs for the membership
queries, a connection between Tukey depth and membership queries, as well as a
new notion of $\some$-hull that may be a useful representation of uncertain
hulls.


  Reverse derivative categories (RDCs) have recently been shown to be a
suitable semantic framework for studying machine learning algorithms. Whereas
emphasis has been put on training methodologies, less attention has been
devoted to particular \emph{model classes}: the concrete categories whose
morphisms represent machine learning models. In this paper we study
presentations by generators and equations of classes of RDCs. In particular, we
propose \emph{polynomial circuits} as a suitable machine learning model. We
give an axiomatisation for these circuits and prove a functional completeness
result. Finally, we discuss the use of polynomial circuits over specific
semirings to perform machine learning with discrete values.


  Perivascular Spaces (PVS) are a recently recognised feature of Small Vessel
Disease (SVD), also indicating neuroinflammation, and are an important part of
the brain's circulation and glymphatic drainage system. Quantitative analysis
of PVS on Magnetic Resonance Images (MRI) is important for understanding their
relationship with neurological diseases. In this work, we propose a
segmentation technique based on the 3D Frangi filtering for extraction of PVS
from MRI. Based on prior knowledge from neuroradiological ratings of PVS, we
used ordered logit models to optimise Frangi filter parameters in response to
the variability in the scanner's parameters and study protocols. We optimized
and validated our proposed models on two independent cohorts, a dementia sample
(N=20) and patients who previously had mild to moderate stroke (N=48). Results
demonstrate the robustness and generalisability of our segmentation method.
Segmentation-based PVS burden estimates correlated with neuroradiological
assessments (Spearman's $\rho$ = 0.74, p $<$ 0.001), suggesting the great
potential of our proposed method


  As the second wave in India mitigates, COVID-19 has now infected about 29
million patients countrywide, leading to more than 350 thousand people dead. As
the infections surged, the strain on the medical infrastructure in the country
became apparent. While the country vaccinates its population, opening up the
economy may lead to an increase in infection rates. In this scenario, it is
essential to effectively utilize the limited hospital resources by an informed
patient triaging system based on clinical parameters. Here, we present two
interpretable machine learning models predicting the clinical outcomes,
severity, and mortality, of the patients based on routine non-invasive
surveillance of blood parameters from one of the largest cohorts of Indian
patients at the day of admission. Patient severity and mortality prediction
models achieved 86.3% and 88.06% accuracy, respectively, with an AUC-ROC of
0.91 and 0.92. We have integrated both the models in a user-friendly web app
calculator, https://triage-COVID-19.herokuapp.com/, to showcase the potential
deployment of such efforts at scale.


  The coherent interaction between a laser-driven single trapped atom and an
optical high-finesse resonator allows to produce entangled multi-photon light
pulses on demand. The mechanism is based on the mechanical effect of light. The
degree of entanglement can be controlled through the parameters of the laser
excitation. Experimental realization of the scheme is within reach of current
technology. A variation of the technique allows for controlled generation of
entangled subsequent pulses, with the atomic motion serving as intermediate
memory of the quantum state.


  We show that for any permutation $\omega$, the increasing flip graph on
acyclic pipe dreams with exiting permutation $\omega$ is a lattice quotient of
the interval $[e,\omega]$ of the weak order. We then discuss conjectural
generalizations of this result to acyclic facets of subword complexes on
arbitrary finite Coxeter groups.


  Using an approach of Bergh, we give an alternate proof of Bennett's result on
lower bounds for non-negative matrices acting on non-increasing non-negative
sequences in $l^p$ when $p \geq 1$ and its dual version, the upper bounds when
$0<p \leq 1$. We also determine such bounds explicitly for some families of
matrices.


  The proton spectrum in the kinetic energy range 0.1 to 200 GeV was measured
by the Alpha Magnetic Spectrometer (AMS) during space shuttle flight STS-91 at
an altitude of 380 km. Above the geomagnetic cutoff the observed spectrum is
parameterized by a power law. Below the geomagnetic cutoff a substantial second
spectrum was observed concentrated at equatorial latitudes with a flux ~ 70
m^-2 sec^-1 sr^-1. Most of these second spectrum protons follow a complicated
trajectory and originate from a restricted geographic region.


  We address some key conditions under which many-body lattice models, intended
mainly as simulated condensed matter systems, can be investigated via immersed,
fully controllable quantum objects, namely quantum probes. First, we present a
protocol that, for a certain class of many-body systems, allows for full
momentum resolved spectroscopy using one single probe. Furthermore, we
demonstrate how one can extract the two-point correlations using two entangled
probes. We apply our theoretical proposal to two well-known exactly solvable
lattice models, a 1D Kitaev chain and 2D superfluid Bose-Hubbard model, and
show its accuracy as well as its robustness against external noise.


  During the third all-sky survey (eRASS3), eROSITA, the soft X-ray instrument
aboard Spectrum-Roentgen-Gamma, detected a new hard X-ray transient, eRASSt
J040515.6-745202, in the direction of the Magellanic Bridge. We arranged
follow-up observations and searched for archival data to reveal the nature of
the transient. Using X-ray observations with XMM-Newton, NICER, and Swift, we
investigated the temporal and spectral behaviour of the source for over about
10 days. The X-ray light curve obtained from the XMM-Newton observation with an
28 ks exposure revealed a type-I X-ray burst with a peak bolometric luminosity
of at least 1.4e37 erg/s. The burst energetics are consistent with a location
of the burster at the distance of the Magellanic Bridge. The relatively long
exponential decay time of the burst of 70 s indicates that it ignited in a
H-rich environment. The non-detection of the source during the other eROSITA
surveys, twelve and six months before and six months after eRASS3, suggests
that the burst was discovered during a moderate outburst which reached 2.6e36
erg/s in persistent emission. During the NICER observations, the source showed
alternating flux states with the high level at a similar brightness as during
the XMM-Newton observation. This behaviour is likely caused by dips as also
seen during the last hour of the XMM-Newton observation. Evidence for a
recurrence of the dips with a period of 21.8 hr suggests eRASSt
J040515.6-745202 is a low-mass X-ray binary (LMXB) system with an accretion
disk seen nearly edge on. We identify a multi-wavelength counterpart to the
X-ray source in UVW1 and g, r, i, and z images obtained by the optical/UV
monitor on XMM-Newton and the Dark Energy Camera at the Cerro Tololo
Inter-American Observatory. (abbreviated)


  The Lehmann-Newton-Wu mass matrix, which was recently applied to neutrinos,
is further investigated. The analytic results presented earlier are confirmed
numerically for the solar density profile of the Standard Solar Model. The
combined analysis of atmospheric and solar neutrino data favors the MSW
solution over the vacuum-oscillation solution. The total rates from the solar
neutrino detectors and spectrum distortion reported by the Super-Kamiokande
collaboration for solar neutrinos favors one heavy (m3\sim 0.05 eV) and two
light (m1, m2\lsim 0.003 eV) neutrinos.


  In this note we generalize several well known results concerning invariants
of finite groups from characteristic zero to positive characteristic not
dividing the group order. The first is Schmid's relative version of Noether's
theorem. That theorem compares the degrees of generators of a group with those
of a subgroup. Then we prove a suitable positive characteristic version of
Weyl's theorem on vector invariants: polarization works in small degrees. Using
that we show that the regular representation has the "most general" ring of
invariants, thereby generalizing theorems of Schmid and Smith.


  This paper investigates the controller optimization for a helicopter system
with three degrees of freedom (3-DOF). To control the system, we combined fuzzy
logic with adaptive control theory. The system is extensively nonlinear and
highly sensitive to the controller's parameters, making it a real challenge to
study these parameters' effect on the controller's performance. Using
metaheuristic algorithms for determining these parameters is a promising
solution. This paper proposes using a modified particle swarm optimization
(MPSO) algorithm to optimize the controller. The algorithm shows a high ability
to perform the global search and find a reasonable search space. The algorithm
modifies the search space of each particle based on its fitness function value
and substitutes weak particles for new ones. These modifications have led to
better accuracy and convergence rate. We prove the efficiency of the MPSO
algorithm by comparing it with the standard PSO and six other well-known
metaheuristic algorithms when optimizing the adaptive fuzzy logic controller of
the 3-DOF helicopter. The proposed method's effectiveness is shown through
computer simulations while the system is subject to uncertainties and
disturbance. We demonstrate the method's superiority by comparing the results
when the MPSO and the standard PSO optimize the controller.


  We investigate the limiting cases of Tsallis statistics. The viewpoint
adopted is not the standard information-theoretic one, where one derives the
distribution from a given measure of information. Instead the mechanical
approach recently proposed in [M. Campisi, G.B. Bagci, Phys. Lett. A (2006),
doi:10.1016/j.physleta.2006.09.081], is adopted, where the distribution is
given and one looks for the associated physical entropy. We show that, not only
the canonical ensemble is recovered in the limit of $q$ tending to one, as one
expects, but also the microcanonical ensemble is recovered in the limit of $q$
tending to minus infinity. The physical entropy associated with Tsallis
ensemble recovers the microcanonical entropy as well and we note that the
microcanonical equipartition theorem is recovered too. We are so led to
interpret the extensivity parameter q as a measure of the thermal bath heat
capacity: $q=1$ (i.e. canonical) corresponds to an infinite bath (thermalised
case, temperature is fixed), $q=-\infty$ (microcanonical) corresponds to a bath
with null heat capacity (isolated case, energy is fixed), intermediate $q's$
(i.e. Tsallis) correspond to the realistic cases of finite heat capacity (both
temperature and energy fluctuate).


  We study Markowitz's mean-variance portfolio selection problem in a
continuous-time Black-Scholes market with different borrowing and saving rates.
The associated Hamilton-Jacobi-Bellman equation is fully nonlinear. Using a
delicate partial differential equation and verification argument, the value
function is proven to be $C^{3,2}$ smooth. It is also shown that there are a
borrowing boundary and a saving barrier which divide the entire trading area
into a borrowing-money region, an all-in-stock region, and a saving-money
region in ascending order. The optimal trading strategy is a mixture of
continuous-time strategy (as suggested by most continuous-time models) and
discontinuous-time strategy (as suggested by models with transaction costs):
one should put all her wealth in the stock in the middle all-in-stock region,
and continuously trade it in the other two regions in a feedback form of wealth
and time. It is never optimal to short sale the stock. Numerical examples are
also presented to verify the theoretical results and to give more financial
insights beyond them.


  Incremental learning enables the learner to accommodate new knowledge without
retraining the existing model. It is a challenging task which requires learning
from new data as well as preserving the knowledge extracted from the previously
accessed data. This challenge is known as the stability-plasticity dilemma. We
propose AILearn, a generic model for incremental learning which overcomes the
stability-plasticity dilemma by carefully integrating the ensemble of base
classifiers trained on new data with the current ensemble without retraining
the model from scratch using entire data. We demonstrate the efficacy of the
proposed AILearn model on spoof fingerprint detection application. One of the
significant challenges associated with spoof fingerprint detection is the
performance drop on spoofs generated using new fabrication materials. AILearn
is an adaptive incremental learning model which adapts to the features of the
``live'' and ``spoof'' fingerprint images and efficiently recognizes the new
spoof fingerprints as well as the known spoof fingerprints when the new data is
available. To the best of our knowledge, AILearn is the first attempt in
incremental learning algorithms that adapts to the properties of data for
generating a diverse ensemble of base classifiers. From the experiments
conducted on standard high-dimensional datasets LivDet 2011, LivDet 2013 and
LivDet 2015, we show that the performance gain on new fake materials is
significantly high. On an average, we achieve $49.57\%$ improvement in accuracy
between the consecutive learning phases.


  I investigate useful shape quantities for the classical and quantum mechanics
of the relational quadrilateral in 2-d. This is relational in the sense that
only relative times, relative ratios of separations and relative angles are
significant. Relational particle mechanics models such as this paper's have
many analogies with the geometrodynamical formulation of general relativity.
This renders them suitable as toy models for 1) studying Problem of Time in
Quantum Gravity strategies, in particular timeless, semiclassical and histories
theory approaches and combinations of these. 2) For consideration of various
other quantum-cosmological issues, such as structure formation/inhomogeneity
and notions of uniform states and their significance. The relational
quadrilateral is more useful in these respects than previously investigated
simpler RPM's due to simultaneously possessing linear constraints, nontrivial
subsystems and nontrivial complex-projective mathematics. Such shape have been
found to be useful in simpler relational models such as the relational triangle
and in 1-d.


  The data available in literature, concerning the binding energy of double
hypernuclei and their production techniques are briefly reviewed. Then, a new
technique for producing double hypernuclei with antiprotons in flight and
measuring their binding energy, proposed for the PANDA experiment at GSI, is
investigated. Furthermore, preliminary results of the calculations for
evaluating the double hypernuclei production and detection rates at the
antiproton beam intensity foreseen at HESR are reported.


  The idea that spacetime has to be replaced by Clifford space (C-space) is
explored. Quantum field theory (QFT) and string theory are generalized to
C-space. It is shown how one can solve the cosmological constant problem and
formulate string theory without central terms in the Virasoro algebra by
exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw
definition of the vacuum state. As an introduction into the subject, a toy
model of the harmonic oscillator in pseudo-Euclidean space is studied.


  Quantum algorithm is constructed which verifies the formulas of predicate
calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the
time required for classical algorithms. This algorithm uses the polynomial
number of simultaneous oracle queries. This is a modification of the result of
Buhrman, Cleve and Wigderson quant-ph/9802040.


  We have used a single-particle detector system, based on secondary electron
emission, for counting low-energetic (~keV/u) massive products originating from
atomic and molecular ion reactions in the electrostatic Cryogenic Storage Ring
(CSR). The detector is movable within the cryogenic vacuum chamber of CSR, and
was used to measure production rates of a variety of charged and neutral
daughter particles. In operation at a temperature of ~6 K, the detector is
characterised by a high dynamic range, combining a low dark event rate with
good high-rate particle counting capability. On-line measurement of the pulse
height distributions proved to be an important monitor of the detector response
at low temperature. Statistical pulse-height analysis allows to infer the
particle detection efficiency of the detector, which has been found to be close
to unity also in cryogenic operation at 6 K.


  The low-temperature thermoelectric power of the repulsive-interaction
one-dimensional Hubbard model is calculated using an asymptotic Bethe ansatz
for holons and spinons. The competition between the entropy carried by the
holons and that carried by the backflow of the spinons gives rise to an unusual
temperature and doping dependence of the thermopower which is qualitatively
similar to that observed in the normal state of high-$T_{c}$ superconductors.