  Emitters of indistinguishable single photons are crucial for the growing
field of quantum technologies. To realize scalability and increase the
complexity of quantum optics technologies, multiple independent yet identical
single photon emitters are also required. However typical solid-state single
photon sources are inherently dissimilar, necessitating the use of electrical
feedback or optical cavities to improve spectral overlap between distinct
emitters. Here, we demonstrate bright silicon-vacancy (SiV-) centres in
low-strain bulk diamond which intrinsically show spectral overlap of up to 91%
and near transform-limited excitation linewidths. Our results have impact upon
the application of single photon sources for quantum optics and cryptography,
and the production of next generation fluorophores for bio-imaging.


  We present an inflationary model in which the Standard Model Higgs doublet
field with non-minimal coupling to gravity drives inflation, and the effective
Higgs potential is stabilized by new physics which includes a dark matter
particle and right-handed neutrinos for the seesaw mechanism. All of the new
particles are fermions, so that the Higgs doublet is the unique inflaton
candidate. With central values for the masses of the top quark and the Higgs
boson, the renormalization group improved Higgs potential is employed to yield
the scalar spectral index $n_s \simeq 0.968$, the tensor-to-scalar ratio $r
\simeq 0.003$, and the running of the spectral index $\alpha=dn_s/d \ln k
\simeq -5.2 \times 10^{-4}$ for the number of e-folds $N_0=60$ ($n_s \simeq
0.962$, $r \simeq 0.004$, and $\alpha \simeq -7.5 \times 10^{-4}$ for
$N_0=50$). The fairly low value of $r \simeq 0.003$ predicted in this class of
models means that the ongoing space and land based experiments are not expected
to observe gravity waves generated during inflation.
  [Dedicated to the memory of Dr. Paul Weber (1947 - 2015). Paul was an
exceptional human being and a very special friend who will be sorely missed.]


  We consider training-based channel estimation for a cloud radio access
network (CRAN), in which a large amount of remote radio heads (RRHs) and users
are randomly scattered over the service area. In this model, assigning
orthogonal training sequences to all users will incur a substantial overhead to
the overall network, and is even impossible when the number of users is large.
Therefore, in this paper, we introduce the notion of local orthogonality, under
which the training sequence of a user is orthogonal to those of the other users
in its neighborhood. We model the design of locally orthogonal training
sequences as a graph coloring problem. Then, based on the theory of random
geometric graph, we show that the minimum training length scales in the order
of $\ln K$, where $K$ is the number of users covered by a CRAN. This indicates
that the proposed training design yields a scalable solution to sustain the
need of large-scale cooperation in CRANs. Numerical results show that the
proposed scheme outperforms other reference schemes.


  Neural scene representations, both continuous and discrete, have recently
emerged as a powerful new paradigm for 3D scene understanding. Recent efforts
have tackled unsupervised discovery of object-centric neural scene
representations. However, the high cost of ray-marching, exacerbated by the
fact that each object representation has to be ray-marched separately, leads to
insufficiently sampled radiance fields and thus, noisy renderings, poor
framerates, and high memory and time complexity during training and rendering.
Here, we propose to represent objects in an object-centric, compositional scene
representation as light fields. We propose a novel light field compositor
module that enables reconstructing the global light field from a set of
object-centric light fields. Dubbed Compositional Object Light Fields (COLF),
our method enables unsupervised learning of object-centric neural scene
representations, state-of-the-art reconstruction and novel view synthesis
performance on standard datasets, and rendering and training speeds at orders
of magnitude faster than existing 3D approaches.


  The Fon-Der-Flaass action partitions the order ideals of a poset into
disjoint orbits. For a product of two chains, Propp and Roby observed ---
across orbits --- the mean cardinality of the order ideals within an orbit to
be invariant. That this phenomenon, which they christened homomesy, extends to
all minuscule posets is shown herein.
  Given a minuscule poset $P$, there exists a complex simple Lie algebra
$\mathfrak{g}$ and a representation $V$ of $\mathfrak{g}$ such that the lattice
of order ideals of $P$ coincides with the weight lattice of $V$. For a weight
$\mu$ with corresponding order ideal $I$, it is demonstrated that the behavior
of the Weyl group simple reflections on $\mu$ not only uniquely determines
$\mu$, but also encodes the cardinality of $I$. After recourse to work of Rush
and Shi mapping the anatomy of the lattice isomorphism, the upshot is a uniform
proof that the cardinality statistic exhibits homomesy.
  A further application of these ideas shows that the statistic tracking the
number of maximal elements in an order ideal is also homomesic, extending
another result of Propp and Roby.


  The magnetic structure of antiferromagnetically ordered phases of
quasi-one-dimensional organic conductors is studied theoretically at absolute
zero based on the mean field approximation to the quarter-filled band with
on-site and nearest-neighbor Coulomb interaction. The differences in magnetic
properties between the antiferromagnetic phase of (TMTTF)$_2$X and the spin
density wave phase in (TMTSF)$_2$X are seen to be due to a varying degrees of
roles played by the on-site Coulomb interaction. The nearest-neighbor Coulomb
interaction introduces charge disproportionation, which has the same spatial
periodicity as the Wigner crystal, accompanied by a modified antiferromagnetic
phase. This is in accordance with the results of experiments on (TMTTF)$_2$Br
and (TMTTF)$_2$SCN. Moreover, the antiferromagnetic phase of (DI-DCNQI)$_2$Ag
is predicted to have a similar antiferromagnetic spin structure.


  The Berger-Wang formula establishes equality between the joint and
generalized spectral radii of a set of matrices. For matrix products whose
multipliers are applied not arbitrarily but in accordance with some Markovian
law, there are also known analogs of the joint and generalized spectral radii.
However, the known proofs of the Berger-Wang formula hardly can be directly
applied in the case of Markovian products of matrices since they essentially
rely on the arbitrariness of appearance of different matrices in the related
matrix products. Nevertheless, as has been shown by X. Dai the Berger-Wang
formula is valid for the case of Markovian analogs of the joint and the
generalized spectral radii too, although the proof in this case heavily
exploits the more involved techniques of multiplicative ergodic theory. In the
paper we propose a matrix theory construction allowing to deduce the Markovian
analog of the Berger-Wang formula from the classical Berger-Wang formula.


  The millimeter wave (mmWave) frequency band is seen as a key enabler of
multi-gigabit wireless access in future cellular networks. In order to overcome
the propagation challenges, mmWave systems use a large number of antenna
elements both at the base station and at the user equipment, which lead to high
directivity gains, fully-directional communications, and possible noise-limited
operations. The fundamental differences between mmWave networks and traditional
ones challenge the classical design constraints, objectives, and available
degrees of freedom. This paper addresses the implications that highly
directional communication has on the design of an efficient medium access
control (MAC) layer. The paper discusses key MAC layer issues, such as
synchronization, random access, handover, channelization, interference
management, scheduling, and association. The paper provides an integrated view
on MAC layer issues for cellular networks, identifies new challenges and
tradeoffs, and provides novel insights and solution approaches.


  We present a method for estimating the edge of a two-dimensional bounded set,
given a finite random set of points drawn from the interior. The estimator is
based both on projections on C^1 bases and on extreme points of the point
process. We give conditions on the Dirichlet's kernel associated to the C^1
bases for various kinds of convergence and asymptotic normality. We propose a
method for reducing the negative bias and illustrate it by a simulation.


  Among the various candidates for dark matter (DM), ultralight vector DM can
be probed by laser interferometric gravitational wave detectors through the
measurement of oscillating length changes in the arm cavities. In this context,
KAGRA has a unique feature due to differing compositions of its mirrors,
enhancing the signal of vector DM in the length change in the auxiliary
channels. Here we present the result of a search for $U(1)_{B-L}$ gauge boson
DM using the KAGRA data from auxiliary length channels during the first joint
observation run together with GEO600. By applying our search pipeline, which
takes into account the stochastic nature of ultralight DM, upper bounds on the
coupling strength between the $U(1)_{B-L}$ gauge boson and ordinary matter are
obtained for a range of DM masses. While our constraints are less stringent
than those derived from previous experiments, this study demonstrates the
applicability of our method to the lower-mass vector DM search, which is made
difficult in this measurement by the short observation time compared to the
auto-correlation time scale of DM.


  A new approach to problem of glueball search is presented. It refers to early
J. Rosner's attempts to detect the tensor glueball. In the present description
the glueball state is treated on equal footing with singlet $q\bar{q}$ one.
Mixing glueball with $q\bar{q}$ nonet creates decuplet. Glueball can be
detected as its component. Our approach is based on hypothesis of vanishing
exotic commutators described as VEC model. The model describes all multiplets
of light mesons. This makes possible to compare the mass patterns of different
multiplets. According to VEC description some abnormal nonets can be
interpreted as incomplete decuplets. This makes possible to relate the anomaly
of the nonet to a glueball component of decuplet. The model reflects rich
diversity of strong interaction properties. The treatment presented is quite
elementary: only masses of physical states are required to be known.


  We describe how the Mordell-Weil group of rational points on a certain family
of elliptic curves give rise to solutions to a conjecture of Erd\"{o}s on
$3$-powerful numbers, and state a related conjecture which can be viewed as an
elliptic curve analogue of the Ankeny-Artin-Chowla conjecture.


  This is a short note on how a particular graph construction on a subset of
edges that lead to a subalgebra construction, provided a tool in proving some
ring theoretical properties of Leavitt path algebras.


  An irreversible thermodynamical theory of solids is presented where the
kinematic quantities are defined in an automatically objective way. Namely,
auxiliary elements like reference frame, reference time and reference
configuration are avoided by formulating the motion of the continuum on
spacetime directly. Solids are distinguished from fluids by possessing not only
an instantaneous metric tensor but also a relaxed metric. The elastic state
variable is defined through comparing these two metrics. Thermal expansion is
conceived as temperature dependence of the relaxed metric and plasticity, an
irreversible change in the relaxed metric, is described via a plastic change
rate tensor. Thermomechanics is built around these -- finite deformation --
kinematic quantities by starting from mechanics and adding thermodynamical
requirements gradually. The obtained theory is not restricted to isotropic
media.


  We couple two-dimensional hydrodynamics to realistic one-dimensional
multigroup flux-limited diffusion neutrino transport to investigate
protoneutron star convection in core collapse supernovae, and more
specifically, the interplay between its development and neutrino transport, for
both 15 and 25 solar mass models. In the presence of neutrino transport,
protoneutron star convection velocities are too small relative to bulk inflow
velocities to result in any significant convective transport of entropy and
leptons. A simple analytical model supports our numerical results, indicating
that the inclusion of neutrino transport reduces the entropy-driven
(lepton-driven) convection growth rates and asymptotic velocities by a factor
of 3 (50) at the neutrinosphere and a factor 250 (1000) at a density of 10^{12}
g/cm^{3}, for both our 15 and 25 solar mass models. Moreover, when transport is
included, the initial postbounce entropy gradient is smoothed out by neutrino
diffusion, whereas the initial lepton gradient is maintained by electron
capture and neutrino escape near the neutrinosphere. Despite the maintenance of
the lepton gradient, protoneutron star convection does not develop over the 100
ms duration typical of all our simulations, except in the instance where
``low-test'' initial conditions are used, which are generated by core collapse
and bounce simulations that neglect neutrino-electron scattering and ion-ion
screening corrections to neutrino- nucleus elastic scattering.


  In the generalized-tJ model the effect of the large local Coulomb repulsion
is accounted for by restricting the Hilbert space to states with at most one
electron per site. In this case the electronic system can be viewed in terms of
holes hopping in a lattice of correlated spins, where holes are the carriers
doped into the half-filled Mott insulator. To explicitly capture the interplay
between the hole dynamics and local spin correlations we derive a new
formulation of the generalized-tJ model where doped carrier operators are used
instead of the original electron operators. This ``doped carrier'' formulation
provides a new starting point to address doped spin systems and we use it to
develop a new, fully fermionic, mean-field description of doped Mott insulators
This mean-field approach reveals a new mechanism for superconductivity, namely
spinon-dopon mixing, and we apply it to the tt't''J model as of interest to
high-temperature superconductors. In particular, we use model parameters
borrowed from band calculations and from fitting ARPES data to obtain a
mean-field phase diagram that reproduces semi-quantitatively that of hole and
electron doped cuprates. The mean-field approach hereby presented accounts for
the local antiferromagnetic and d-wave superconducting correlations which, we
show, provide a rational for the role of t' and t'' in strengthening
superconductivity as expected by experiments and other theoretical approaches.
As we discuss how t, t' and t'' affect the phase diagram, we also comment on
possible scenarios to understand the differences between as-grown and oxygen
reduced electron doped samples.


  We propose new methodologies for stabilizing all-metal antiaromatic clusters
like: Al$_{4}$Li$_{4}$. We demonstrate that these all-metal species can be
stabilized by complexation with 3d-transition metals very similar to its
organic counterpart, C$_4$H$_4$. Complexation to transition metal ions reduce
the frontier orbital energies and introduces aromaticity. We consider a series
of such complexes [$\eta$$^4$(Al$_4$Li$_4$)-Fe(CO)$_3$,
$\eta$$^2$$\sigma$$^2$(Al$_4$Li$_4$)-Ni and (Al$_{4}$Li$_{4}$)$_{2}$Ni] and
make a comparison between the all-metal species and the organometallic
compounds to prove conclusively our theory. Fragmentation energy analysis as
well as NICS support similar mechanism of complexation induced stability in
these all-metal molecules.


  The clover coefficient $\csw$ is computed at one loop order of perturbation
theory for improved gluon actions including six-link loops. The O(a)
improvement coefficients for the dimension three isovector composite operators
bilinear in the quark fields are also calculated.


  The relations between the effective Majorana mass of the electron neutrino,
$m_{ee}$, responsible for neutrinoless double beta decay, and the neutrino
oscillation parameters are considered. We show that for any specific
oscillation pattern $m_{ee}$ can take any value (from zero to the existing
upper bound) for normal mass hierarchy and it can have a minimum for inverse
hierarchy. This means that oscillation experiments cannot fix in general
$m_{ee}$. Mass ranges for $m_{ee}$ can be predicted in terms of oscillation
parameters with additional assumptions about the level of degeneracy and the
type of hierarchy of the neutrino mass spectrum. These predictions for $m_{ee}$
are systematically studied in the specific schemes of neutrino mass and flavor
which explain the solar and atmospheric neutrino data. The contributions from
individual mass eigenstates in terms of oscillation parameters have been
quantified. We study the dependence of $m_{ee}$ on the non-oscillation
parameters: the overall scale of the neutrino mass and the relative mass
phases. We analyze how forthcoming oscillation experiments will improve the
predictions for $m_{ee}$. On the basis of these studies we evaluate the
discovery potential of future \znbb decay searches. The role \znbb decay
searches will play in the reconstruction of the neutrino mass spectrum is
clarified. The key scales of $m_{ee}$, which will lead to the discrimination
among various schemes are: $m_{ee} \sim 0.1$ eV and $m_{ee} \sim 0.005$ eV.


  The SCUBA instrument on the James Clerk Maxwell Telescope has already had an
impact on cosmology by detecting relatively large numbers of dusty galaxies at
high redshift. Apart from identifying well-detected sources, such data can also
be mined for information about fainter sources and their correlations, as
revealed through low level fluctuations in SCUBA maps. As a first step in this
direction we analyse a small SCUBA data-set as if it were obtained from a
Cosmic Microwave Background (CMB) differencing experiment. This enables us to
place limits on CMB anisotropy at 850 microns. Expressed as Q_{flat}, the
quadrupole expectation value for a flat power spectrum, the limit is 152
microKelvin at 95 per cent confidence, corresponding to C_0^{1/2} < 355
microKelvin for a Gaussian autocorrelation function, with a coherence angle of
about 20--25 arcsec; These results could easily be reinterpretted in terms of
any other fluctuating sky signal. This is currently the best limit for these
scales at high frequency, and comparable to limits at similar angular scales in
the radio. Even with such a modest data-set, it is possible to put a constraint
on the slope of the SCUBA counts at the faint end, since even randomly
distributed sources would lead to fluctuations. Future analysis of sky
correlations in more extensive data-sets ought to yield detections, and hence
additional information on source counts and clustering.


  This work provides an elementary introduction to the Higgs sector
renormalisation within the Minimal Suppersymmetric Standard Model (MSSM)
framework. The MSSM tree-level relation $m_h^2+m_H^2=m_A^2+m_Z^2$ is
renormalised using the standard technique of direct computation of the relevant
one-loop Feynman diagrams. The expected cancellation of ultraviolet divergences
is explicitly checked and the well-known leading-log term is recovered.


  3D Human motion style transfer is a fundamental problem in computer graphic
and animation processing. Existing AdaIN- based methods necessitate datasets
with balanced style distribution and content/style labels to train the
clustered latent space. However, we may encounter a single unseen style example
in practical scenarios, but not in sufficient quantity to constitute a style
cluster for AdaIN-based methods. Therefore, in this paper, we propose a novel
two-stage framework for few-shot style transfer learning based on the diffusion
model. Specifically, in the first stage, we pre-train a diffusion-based
text-to-motion model as a generative prior so that it can cope with various
content motion inputs. In the second stage, based on the single style example,
we fine-tune the pre-trained diffusion model in a few-shot manner to make it
capable of style transfer. The key idea is regarding the reverse process of
diffusion as a motion-style translation process since the motion styles can be
viewed as special motion variations. During the fine-tuning for style transfer,
a simple yet effective semantic-guided style transfer loss coordinated with
style example reconstruction loss is introduced to supervise the style transfer
in CLIP semantic space. The qualitative and quantitative evaluations
demonstrate that our method can achieve state-of-the-art performance and has
practical applications.


  Stable lumps of quark matter may be present in cosmic rays at a flux level,
which can be detected by high precision cosmic ray experiments sensitive to
anomalous "nuclei" with high mass-to-charge ratio. The properties of these
lumps, called strangelets, are described, and so is the production and
propagation of strangelets in cosmic rays. Two experiments underway which are
sensitive to a strangelet flux in the predicted range are briefly described.
Finally it is summarized how strangelets circumvent the acceleration problem
encountered by conventional candidates for ultra-high energy cosmic rays and
move the Greisen-Zatsepin-Kuzmin cutoff to energies well above the observed
maximum energies.


  A plethora of static and dynamic models exist to forecast Value-at-Risk and
other quantile-related metrics used in financial risk management. Industry
practice tends to favour simpler, static models such as historical simulation
or its variants whereas most academic research centres on dynamic models in the
GARCH family. While numerous studies examine the accuracy of multivariate
models for forecasting risk metrics, there is little research on accurately
predicting the entire multivariate distribution. Yet this is an essential
element of asset pricing or portfolio optimization problems having non-analytic
solutions. We approach this highly complex problem using a variety of proper
multivariate scoring rules to evaluate over 100,000 forecasts of
eight-dimensional multivariate distributions: of exchange rates, interest rates
and commodity futures. This way we test the performance of static models, viz.
empirical distribution functions and a new factor-quantile model, with commonly
used dynamic models in the asymmetric multivariate GARCH class.


  Connes' noncommutative Riemannian distance formula is constructed in two
steps, the first one being the construction of a path-independent geometrical
functional using a global constraint on continuous functions. This paper
generalizes this first step to Lorentzian geometry. We show that, in a globally
hyperbolic spacetime, a single global timelike eikonal condition is sufficient
to construct a path-independent Lorentzian distance function.


  We introduce a notion of holomorphic stability for pairs of function spaces
on a planar domain $\Omega$. In the case of the open unit disk $\Omega =
\mathbb{D}$ equipped with a radial measure $\mu$, by establishing
Bourgain-Brezis type inequalities, we show that the pair \[(B^2(\mathbb{D},
\mu), h^1(\mathbb{D}))\] of weighted harmonic Bergman space and harmonic Hardy
space is holomorphically stable if and only if $\mu$ is a $(1,2)$-Carleson
measure. With some extra efforts, we also obtain an analogous result for the
upper half plane equipped with horizontal-translation invariant measures.


  We analyze the valley composition of one electron bound to a shallow donor
close to a Si/barrier interface as a function of an applied electric field. A
full six-valley effective mass model Hamiltonian is adopted. For low fields,
the electron ground state is essentially confined at the donor. At high fields
the ground state is such that the electron is drawn to the interface, leaving
the donor practically ionized. Valley splitting at the interface occurs due to
the valley-orbit coupling, V_vo^I = |V_vo^I| e^{i theta}. At intermediate
electric fields, close to a characteristic shuttling field, the electron states
may constitute hybridized states with valley compositions different from the
donor and the interface ground states. The full spectrum of energy levels shows
crossings and anti-crossings as the field varies. The degree of level
repulsion, thus the width of the anti-crossing gap, depends on the relative
valley compositions, which vary with |V_vo^I|, theta and the interface-donor
distance. We focus on the valley configurations of the states involved in the
donor-interface tunneling process, given by the anti-crossing of the three
lowest eigenstates. A sequence of two anti-crossings takes place and the
complex phase theta affects the symmetries of the eigenstates and level
anti-crossing gaps. We discuss the implications of our results on the practical
manipulation of donor electrons in Si nanostructures.


  We propose a new dark matter candidate, {\it light decoupled techni-dilaton},
which arises from the almost scale-invariant/conformal (walking) technicolor.
We investigate its characteristic nature and discuss several cosmological and
astrophysical constraints. It turns out that techni-dilatons are extremely
weakly interacting and produced dominantly by the non-thermal mechanism to be
the main component of dark matter with mass range between around 0.01 eV and
500 eV for typical walking technicolor scenarios.


  Using Monte Carlo simulations, we study the assembly of colloidal particles
interacting via isotropic core-corona potentials in two dimensions and confined
in a circular box. We explore the structural variety at low temperatures as
function of the number of particles (N) and the size of the confining box and
find a rich variety of patterns that are not observed in unconfined flat space.
For a small number of particles (N<=6), we identify the zero-temperature
minimal energy configurations at a given box size and we construct the phase
diagram as function of temperature and box radius for the specific case of N=4.
When the number of particles is large (N>=100), we distinguish different
regimes that appear in route towards close packing configurations as the box
size decreases. These regimes are characterized by the increase in the number
of branching points and their coordination number. In contrast to the case of
confined hard disks, we obtain open structures with unexpected highly
anisotropic character in spite of the isotropy of the interactions and of the
confinement. Our findings show that confined core-corona particles can be a
suitable system to engineer particles with highly complex internal structure
that may serve as building blocks in hierarchical assembly.


  We present a new algorithmic framework which utilizes tropical geometry and
homotopy continuation for solving systems of polynomial equations where some of
the polynomials are generic elements in linear subspaces of the polynomial
ring. This approach generalizes the polyhedral homotopies by Huber and
Sturmfels.


  Given a quasi-split reductive group $G$ and a symmetric variety $X$, we
introduce a notion of endoscopic varieties for $(G,X)$, and establish the
foundational properties of these varieties such as matching of stable
semi-simple orbits. To do this, we introduce certain automorphism groups of
homogeneous spherical varieties, which encode the fine rational structure
needed to work over non-algebraically closed fields. In particular, we
establish the existence and uniqueness of the corresponding symmetric varieties
under a mild restriction of the characteristic of the field of definition. We
conjecture that this construction plays a role analogous to endoscopic groups
in the context of the relative trace formula. As evidence, we show how our
construction gives a pre-stabilization of regular elliptic terms of relative
trace formulae for many pairs $(G,X)$.
  When the cotangent bundle of the symmetric variety is hyperspherical, we
relate our theory to the Hamiltonian variety of the Langlands dual group
introduced by Ben-Zvi, Sakellaridis, and Venkatesh, proving some structural
conjectures for this variety in the symmetric setting.


  Speculative decoding is a widely used method that accelerates the generation
process of large language models (LLMs) with no compromise in model
performance. It achieves this goal by using an existing smaller model for
drafting and then employing the target LLM to verify the draft in a low-cost
parallel manner. Under such a drafting-verification framework, drafting
efficiency has become a bottleneck in the final speedup of speculative
decoding. Therefore, generating longer drafts at less cost can lead to better
decoding speedup. To achieve this, we introduce Ouroboros, which can generate
draft phrases to parallelize the drafting process and meanwhile lengthen drafts
in a training-free manner. The experimental results on various typical text
generation tasks show that Ouroboros can achieve speedups of up to $2.4\times$
over speculative decoding and $3.9\times$ over vanilla decoding, without
fine-tuning draft and target models.


  We provide a framework to estimate the systematic uncertainties in chemical
freeze-out parameters extracted from $\chi^2$ analysis of thermal model, using
hadron multiplicity ratios in relativistic heavy-ion collision experiments.
Using a well known technique of graph theory, we construct all possible sets of
independent ratios from available hadron yields and perform $\chi^2$
minimization on each set. We show that even for ten hadron yields, one obtains
a large number ($10^8$) of independent sets which results in a distribution of
extracted freeze-out parameters. We analyze these distributions and compare our
results for chemical freeze-out parameters and associated systematic
uncertainties with previous results available in the literature.


  Secular evolution and fueling is driven by bars in spiral galaxies, and the
related dynamical processes are reviewed. It is shown that gravity torques
dominate over viscous torques, and produce gas infall to the center. In this
infall, the bar wave accepts the angular momentum, which produces its
destruction. In the end, a central mass concentration is build, which also
contributes to this destruction. While gas can be stalled at ILR for a while,
secondary bars then take over the fueling. In a galaxy life-time, several bar
episodes can successively develop. Through external gas accretion, disks are
replenished by intermittence, between two bar phases. While the general trend
for a galaxy is to evolve towards early-types, its morphology can oscillate,
and turn back transiently to later-types.


  Target encoding plays a central role when learning Convolutional Neural
Networks. In this realm, One-hot encoding is the most prevalent strategy due to
its simplicity. However, this so widespread encoding schema assumes a flat
label space, thus ignoring rich relationships existing among labels that can be
exploited during training. In large-scale datasets, data does not span the full
label space, but instead lies in a low-dimensional output manifold. Following
this observation, we embed the targets into a low-dimensional space,
drastically improving convergence speed while preserving accuracy. Our
contribution is two fold: (i) We show that random projections of the label
space are a valid tool to find such lower dimensional embeddings, boosting
dramatically convergence rates at zero computational cost; and (ii) we propose
a normalized eigenrepresentation of the class manifold that encodes the targets
with minimal information loss, improving the accuracy of random projections
encoding while enjoying the same convergence rates. Experiments on CIFAR-100,
CUB200-2011, Imagenet, and MIT Places demonstrate that the proposed approach
drastically improves convergence speed while reaching very competitive accuracy
rates.


  Using methods from math-ph/9907010, we study families of Hopf algebra
structures on coloured trees.


  With the evolution of mobile devices, and smart-phones in particular, comes
the ability to create new experiences that enhance the way we see, interact,
and manipulate objects, within the world that surrounds us. It is now possible
to blend data from our senses and our devices in numerous ways that simply were
not possible before using Augmented Reality technology. In a near future, when
all of the office devices as well as your personal electronic gadgets are on a
common wireless network, operating them using a universal remote controller
would be possible. This paper presents an off-the-shelf, low-cost prototype
that leverages the Augmented Reality technology to deliver a novel and
interactive way of operating office network devices around using a mobile
device. We believe this type of system may provide benefits to controlling
multiple integrated devices and visualizing interconnectivity or utilizing
visual elements to pass information from one device to another, or may be
especially beneficial to control devices when interacting with them physically
may be difficult or pose danger or harm.


  The main aim of this work - to calculate 2- and 4-point connected
contributions to the $S$-matrix and correlation functions for the euclidean
scalar field on the lattice with self-action $|\phi|^{n}$ for $n>2$ with
coupling constant renormalised in a special way for arbitrary dimension. It is
shown that the considered theory has a nontrivial continuous limit. A new
method is proposed without the use of perturbation theory and diagrams. We have
used the explored duality between different lattice field theories. After its
application, it turns out that it is possible to apply the saddle-point method
to the generating functional, where the concentration of nodes of the initial
lattice approximation acts as a large parameter. In addition to the connected
contributions to the $S$-matrix, the beta function is calculated. We have found
a critical point for the theory of $\phi^{4k}$ in arbitrary dimension and a
nontrivial mass gap of the interacting massless theory. We have received the
masses of bound and single-particle states of the interacting theory. The
proposed method can be extend for application to QED and gauge theories, as
well as generalized to the arbitrary geometry of space. Though the way of
coupling rescaling is specific, it gives nontrivial theory with the majority of
perturbatively expected effects.


  Given a non-quasianalytic subadditive weight function $\omega$ we consider
the weighted Schwartz space $\mathcal{S}_\omega$ and the short-time Fourier
transform on $\mathcal{S}_\omega$, $\mathcal{S}'_\omega$ and on the related
modulation spaces with exponential weights. In this setting we define the
$\omega$-wave front set $WF'_\omega(u)$ and the Gabor $\omega$-wave front set
$WF^G_\omega(u)$ of $u\in\mathcal{S}'_{\omega}$, and we prove that they
coincide. Finally we look at applications of this wave front set for operators
of differential and pseudo-differential type.


  We present analysis using a citizen science campaign to improve the
cosmological measures from the Hobby-Eberly Telescope Dark Energy Experiment
(HETDEX). The goal of HETDEX is to measure the Hubble expansion rate, $H(z)$,
and angular diameter distance, $D_A(z)$, at $z =$ 2.4, each to percent-level
accuracy. This accuracy is determined primarily from the total number of
detected Lyman-$\alpha$ emitters (LAEs), the false positive rate due to noise,
and the contamination due to [O II] emitting galaxies. This paper presents the
citizen science project, Dark Energy Explorers, with the goal of increasing the
number of LAEs, decreasing the number of false positives due to noise and the
[O II] galaxies. Initial analysis shows that citizen science is an efficient
and effective tool for classification most accurately done by the human eye,
especially in combination with unsupervised machine learning. Three aspects
from the citizen science campaign that have the most impact are 1) identifying
individual problems with detections, 2) providing a clean sample with 100%
visual identification above a signal-to-noise cut, and 3) providing labels for
machine learning efforts. Since the end of 2022, Dark Energy Explorers has
collected over three and a half million classifications by 11,000 volunteers in
over 85 different countries around the world. By incorporating the results of
the Dark Energy Explorers we expect to improve the accuracy on the $D_A(z)$ and
$H(z)$ parameters at $z =$ 2.4 by 10 - 30%. While the primary goal is to
improve on HETDEX, Dark Energy Explorers has already proven to be a uniquely
powerful tool for science advancement and increasing accessibility to science
worldwide.


  Some effects of surface tension on fully-nonlinear, long, surface water waves
are studied by numerical means. The differences between various solitary waves
and their interactions in subcritical and supercritical surface tension regimes
are presented. Analytical expressions for new peaked travelling wave solutions
are presented in the case of critical surface tension. The numerical
experiments were performed using a high-accurate finite element method based on
smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method
of order four.


  Using the criteria of simplicity, positivity, smoothness and process-
independence of construction, we find a non-polynomial model for the quark
distribution amplitude of the nucleon that is in agreement with QCD sum-rule
constraints. This simpler ("haplousterotic") model solves some of the problems
connected with the longitudinal momentum dependence of the wave function,
whereas the k_T-dependence of the wave function, which is also important, is
still left undetermined. The expansion pro- perties of the model into a
polynomial series are examined.


  Assuming $\rm PFA$, we shall use internally club $\omega_1$-guessing models
as side conditions to show that for every tree $T$ of height $\omega_2$ without
cofinal branches, there is a proper and $\aleph_2$-preserving forcing notion
with finite conditions which specialises $T$. Moreover, the forcing has the
$\omega_1$-approximation property.


  In the typical multiagent formation tracking problem centered on consensus,
the prevailing assumption in the literature is that the agents' nonlinear
models can be approximated by integrator systems, by their feedback-linearized
equivalents, or by dynamics composed of deterministic linear and nonlinear
terms. The resulting approaches associated with such assumptions, however, are
hardly applicable to general nonlinear systems. To this end, we present
consensus-based control laws for multiagent formation tracking in
finite-dimensional state space, with the agents represented by a more general
class of dynamics: control-affine nonlinear systems. The agents also exchange
information via a leader-follower communication topology modeled as an
undirected and connected graph with a single leader node. By leveraging
standard tools from algebraic graph theory and Lyapunov analysis, we first
derive a locally asymptotically stabilizing formation tracking law. Next, to
demonstrate the effectiveness of our approach, we present results from
numerical simulations of an example in robotics. These results -- together with
a comparison of the formation errors obtained with our approach and those
realized via an optimization-based method -- further validate our theoretical
propositions.


  We consider equation $-\Delta u+f(x,u)=0$ in smooth bounded domain
$\Omega\in\mathbb{R}^N$, $N\geqslant2$, with $f(x,r)>0$ in
$\Omega\times\mathbb{R}^1_+$ and $f(x,r)=0$ on $\partial\Omega$. We find the
condition on the order of degeneracy of $f(x,r)$ near $\partial\Omega$, which
is a criterion of the existence-nonexistence of a very singular solution with a
strong point singularity on $\partial\Omega$. Moreover, we prove that the
mentioned condition is a sufficient condition for the uniqueness of a large
solution and conjecture that this condition is also a necessary condition of
the uniqueness.


  This is an introduction to the quantum groups, or rather to the simplest
quantum groups. The idea is that the unitary group $U_N$ has a free analogue
$U_N^+$, whose standard coordinates $u_{ij}\in C(U_N^+)$ are allowed to be
free, and the closed subgroups $G\subset U_N^+$ can be thought of as being the
compact quantum Lie groups. There are many interesting examples of such quantum
groups, for the most designed in order to help with questions in quantum
mechanics and statistical mechanics, and some general theory available as well,
including Peter-Weyl theory, Tannakian duality, Brauer theorems and Weingarten
integration. We discuss here the basic aspects of all this.


  We prove that Runge-Kutta (RK) methods for numerical integration of
arbitrarily large systems of Ordinary Differential Equations are linearly
stable. Standard stability arguments -- based on spectral analysis, resolvent
condition or strong stability, fail to secure the stability of arbitrarily
large RK systems. We explain the failure of different approaches, offer a new
stability theory and demonstrate a few examples.


  We discuss the phase diagram and phase transitions in $U(1)\times \groupZ{2}$
three-band superconductors with broken time reversal symmetry. We find that
beyond mean field approximation and for sufficiently strong frustration of
interband interactions there appears an unusual metallic state precursory to a
superconducting phase transition. In that state, the system is not
superconducting. Nonetheless, it features a spontaneously broken $\groupZ{2}$
time reversal symmetry. By contrast, for weak frustration of interband coupling
the energy of a domain wall between different $\groupZ{2}$ states is low and
thus fluctuations restore broken time reversal symmetry in the superconducting
state at low temperatures.


  We determine the first homology group of the mapping class group M(N) of a
nonorientable surface N with coefficients in H_1(N;Z).


  The Nahm pole boundary condition for certain gauge theory equations in four
and five dimensions is defined by requiring that a solution should have a
specified singularity along the boundary. In the present paper, we show that
this boundary condition is elliptic and has regularity properties analogous to
more standard elliptic boundary conditions. We also establish a uniqueness
theorem for the solution of the relevant equations on a half-space with Nahm
pole boundary conditions. These results are expected to have a generalization
involving knots, with applications to the Jones polynomial and Khovanov
homology.


  Reaction-diffusion systems which include processes of the form A+A->A or
A+A->0 are characterised by the appearance of `imaginary' multiplicative noise
terms in an effective Langevin-type description. However, if `real' as well as
`imaginary' noise is present, then competition between the two could
potentially lead to novel behaviour. We thus investigate the asymptotic
properties of the following two `mixed noise' reaction-diffusion systems. The
first is a combination of the annihilation and scattering processes 2A->0,
2A->2B, 2B->2A, and 2B->0. We demonstrate (to all orders in perturbation
theory) that this system belongs to the same universality class as the single
species annihilation reaction 2A->0. Our second system consists of competing
annihilation and fission processes, 2A->0 and 2A->(n+2)A, a model which
exhibits a transition between active and absorbing phases. However, this
transition and the active phase are not accessible to perturbative methods, as
the field theory describing these reactions is shown to be non-renormalisable.
This corresponds to the fact that there is no stationary state in the active
phase, where the particle density diverges at finite times. We discuss the
implications of our analysis for a recent study of another active / absorbing
transition in a system with multiplicative noise.


  In this paper, we describe a stable finite element formulation for
advection-diffusion-reaction problems that allows for robust automatic adaptive
strategies to be easily implemented. We consider locally vanishing,
heterogeneous, and anisotropic diffusivities, as well as advection-dominated
diffusion problems. The general stabilized finite element framework was
described and analyzed in arXiv:1907.12605v3 for linear problems in general,
and tested for pure advection problems. The method seeks for the discrete
solution through a residual minimization process on a proper stable
discontinuous Galerkin (dG) dual norm. This technique leads to a saddle-point
problem that delivers a stable discrete solution and a robust error estimate
that can drive mesh adaptivity. In this work, we demonstrate the efficiency of
the method in extreme scenarios, delivering stable solutions. The quality and
performance of the solutions are comparable to classical discontinuous Galerkin
formulations in the respective discrete space norm on each mesh. Meanwhile,
this technique allows us to solve on coarse meshes and adapt the solution to
achieve a user-specified solution quality.


  Pancreas segmentation has been traditionally challenging due to its small
size in computed tomography abdominal volumes, high variability of shape and
positions among patients, and blurred boundaries due to low contrast between
the pancreas and surrounding organs. Many deep learning models for pancreas
segmentation have been proposed in the past few years. We present a thorough
systematic review based on the Preferred Reporting Items for Systematic Reviews
and Meta-analyses (PRISMA) statement. The literature search was conducted on
PubMed, Web of Science, Scopus, and IEEE Xplore on original studies published
in peer-reviewed journals from 2013 to 2023. Overall, 130 studies were
retrieved. We initially provided an overview of the technical background of the
most common network architectures and publicly available datasets. Then, the
analysis of the studies combining visual presentation in tabular form and text
description was reported. The tables grouped the studies specifying the
application, dataset size, design (model architecture, learning strategy, and
loss function), results, and main contributions. We first analyzed the studies
focusing on parenchyma segmentation using coarse-to-fine approaches,
multi-organ segmentation, semi-supervised learning, and unsupervised learning,
followed by those studies on generalization to other datasets and those
concerning the design of new loss functions. Then, we analyzed the studies on
segmentation of tumors, cysts, and inflammation reporting multi-stage methods,
semi-supervised learning, generalization to other datasets, and design of new
loss functions. Finally, we provided a critical discussion on the subject based
on the published evidence underlining current issues that need to be addressed
before clinical translation.


  We systematically study a Kitaev chain with imbalanced pair creation and
annihilation, which is introduced by non-Hermitian pairing terms. Exact phase
diagram shows that the topological phase is still robust under the influence of
the conditional imbalance. The gapped phases are characterized by a topological
invariant, the extended Zak phase, which is defined by the biorthonormal inner
product. Such phases are destroyed at the points where the coalescence of
groundstates occur, associating with the time-reversal symmetry breaking. We
find that the Majorana edge modes also exist for the open chain within unbroken
time-reversal symmetric region, demonstrating the bulk-edge correspondence in
such a non-Hermitian system.


  This paper is a comment to M Wilkinson, EPL 106 (2014) 40001, arXiv:1401.4620
[physics.ao-ph,cond-mat.soft], which draws conclusion from our data that are at
variance with our observations.


  A new mechanism of Bragg reflection is identified, one that, remarkably,
occurs in a uniform medium and relies on resonant tuning of the medium's
parameters. Due to uniformity, reflection ensues over a broad wavelength range,
much like a metal, but it is polarization dependent: one circular state is
reflected, whilst the other is transmitted. Such a medium can thus provide a
broadband, low-loss polarization divider/combiner. Assessment of the required
parameters suggests that manufacturing is within range of current metamaterials
technology. By externally regulating the medium's parameters, a highly
efficient optical modulator is possible with potential applications across
optics, optoelectronics, and photonics.


  The 2-dimensional Hamming graph H(2,n) consists of the $n^2$ vertices
$(i,j)$, $1\leq i,j\leq n$, two vertices being adjacent when they share a
common coordinate. We examine random subgraphs of H(2,n) in percolation with
edge probability $p$, so that the average degree $2(n-1)p=1+\epsilon$. Previous
work by van der Hofstad and Luczak had shown that in the barely supercritical
region $n^{-2/3}\ln^{1/3}n\ll \epsilon \ll 1$ the largest component has size
$\sim 2\epsilon n$. Here we show that the second largest component has size
close to $\epsilon^{-2}$, so that the dominant component has emerged. This
result also suggests that a {\it discrete duality principle} might hold,
whereby, after removing the largest connected component in the supercritical
regime, the remaining random subgraphs behave as in the subcritical regime.


  Realizing topological superconductivity and Majorana zero modes in the
laboratory is one of the major goals in condensed matter physics. We review the
current status of this rapidly-developing field, focusing on
semiconductor-superconductor proposals for topological superconductivity.
Material science progress and robust signatures of Majorana zero modes in
recent experiments are discussed. After a brief introduction to the subject, we
outline several next-generation experiments probing exotic properties of
Majorana zero modes, including fusion rules and non-Abelian exchange
statistics. Finally, we discuss prospects for implementing Majorana-based
topological quantum computation in these systems.


  The time-dependent Ginzburg-Landau formalism is applied to analyze the vortex
states and vortex dynamics in superconducting spherical nanoshells, subjected
to mutually perpendicular strong dc and weak ac magnetic fields. We demonstrate
that nonuniformity of the shell thickness can dramatically affect the ac
magnetic response of a 3D array of superconducting nanoshells. Remarkably, this
response is strongly influenced not only by the relevant geometric and material
parameters and the ac-field frequency but also by the magnitude of the applied
dc field: by changing this field the real part of the effective ac magnetic
permeability can be tuned from positive values significantly larger than one
down to negative values.


  Laser-induced breakdown has shown many potential applications in the various
field of science and engineering. As the breakdown occurs in gas or aerosol, a
rapid hydrodynamic expansion as shock (blast) wave initiated from the
deposition location. The nature of the shock wave is one of the controlling
factors in many physical processes; unfortunately, its nature has still not
been clearly understood. In this study, an error was found during the
calculation of shock wave properties with the classical non-relativistic
approach. The error in calculation was due to the initial relativistic
propagation of high-temperature plasma. Initially, the plasma and shock wave
travel together with higher acceleration up to the point of inflation, and in
later time shockwave dissociate itself from the plasma. However, this
accelerating effect is neglected in the earlier studies. To address the
spontaneous accelerating and deaccelerating nature of the shock wave, the
theoretical details of the relativistic approach of shock wave propagation is
presented.


  A reliable locoregional recurrence (LRR) prediction model is important for
the personalized management of head and neck cancers (HNC) patients. This work
aims to develop a delta-radiomics feature-based multi-classifier,
multi-objective, and multi-modality (Delta-mCOM) model for post-treatment HNC
LRR prediction and adopting a learning with rejection option (LRO) strategy to
boost the prediction reliability by rejecting samples with high prediction
uncertainties. In this retrospective study, we collected PET/CT image and
clinical data from 224 HNC patients. We calculated the differences between
radiomics features extracted from PET/CT images acquired before and after
radiotherapy as the input features. Using clinical parameters, PET and CT
radiomics features, we built and optimized three separate single-modality
models. We used multiple classifiers for model construction and employed
sensitivity and specificity simultaneously as the training objectives. For
testing samples, we fused the output probabilities from all these
single-modality models to obtain the final output probabilities of the
Delta-mCOM model. In the LRO strategy, we estimated the epistemic and aleatoric
uncertainties when predicting with Delta-mCOM model and identified patients
associated with prediction of higher reliability. Predictions with higher
epistemic uncertainty or higher aleatoric uncertainty than given thresholds
were deemed unreliable, and they were rejected before providing a final
prediction. Different thresholds corresponding to different low-reliability
prediction rejection ratios were applied. The inclusion of the delta-radiomics
feature improved the accuracy of HNC LRR prediction, and the proposed
Delta-mCOM model can give more reliable predictions by rejecting predictions
for samples of high uncertainty using the LRO strategy.


  The three-body problem (3BP) poses a longstanding challenge in physics and
celestial mechanics. Despite the impossibility of obtaining general analytical
solutions, statistical theories have been developed based on the ergodic
principle. This assumption is justified by chaos, which is expected to fully
mix the accessible phase space of the 3BP. This study probes the presence of
regular (i.e. non chaotic) trajectories within the 3BP and assesses their
impact on statistical escape theories. Using numerical simulations, we
establish criteria for identifying regular trajectories and analyse their
impact on statistical outcomes. Our analysis reveals that regular trajectories
occupy up to 32% of the phase space, and their outcomes defy the predictions of
statistical escape theories. The coexistence of regular and chaotic regions at
all scales is characterized by a multi-fractal behaviour. Integration errors
manifest as numerical chaos, artificially enhancing the mixing of the phase
space and affecting the reliability of individual simulations, yet preserving
the statistical correctness of an ensemble of realizations. Our findings
underscore the challenges in applying statistical escape theories to
astrophysical problems, as they may bias results by excluding the outcome of
regular trajectories. This is particularly important in the context of
formation scenarios of gravitational wave mergers, where biased estimates of
binary eccentricity can significantly impact estimates of coalescence
efficiency and detectable eccentricity.


  Attacks targeting several millions of non-internet based application users
are on the rise. These applications such as SMS and USSD typically do not
benefit from existing multi-factor authentication methods due to the nature of
their interaction interfaces and mode of operations. To address this problem,
we propose an approach that augments blockchain with multi-factor
authentication based on evidence from blockchain transactions combined with
risk analysis. A profile of how a user performs transactions is built overtime
and is used to analyse the risk level of each new transaction. If a transaction
is flagged as high risk, we generate n-factor layers of authentication using
past endorsed blockchain transactions. A demonstration of how we used the
proposed approach to authenticate critical financial transactions in a
blockchain-based asset financing platform is also discussed.


  We introduce the concept of {\em maximal lineability cardinal number},
$\mL(M)$, of a subset $M$ of a topological vector space and study its relation
to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability
$\HL(M)$, and lineability $\LL(M)$ of $M$. In particular, we will describe, in
terms of $\LL$, the lineability and spaceability of the families of the
following Darboux-like functions on $\real^n$, $n\ge 1$: extendable, Jones, and
almost continuous functions.


  We consider the problem of determining the optimal aggregate power
consumption of a population of thermostatically controlled loads. This is
motivated by the problem of synthesizing the demand response for a load serving
entity (LSE) serving a population of such customers. We show how the LSE can
opportunistically design the aggregate reference consumption to minimize its
energy procurement cost, given day-ahead price, load and ambient temperature
forecasts, while respecting each individual load's comfort range constraints.
The resulting synthesis problem is shown to be amenable to optimal control
techniques, but computationally difficult otherwise. Numerical simulations
elucidate how the LSE can use the optimal aggregate power consumption
trajectory thus computed, for the purpose of demand response.


  We investigate the effect of a strong large scale magnetic field on the
reflection of high frequency acoustic modes in rapidly oscillating Ap stars. To
that end we consider a toy model composed of an isothermal atmosphere matched
onto a polytropic interior and determine the numerical solution to the set of
ideal magneto-hydrodynamic equations in a local plane-parallel approximation
with constant gravity. Using the numerical solution in combination with
approximate analytical solutions that are valid in the limits where the
magnetic and acoustic components are decoupled, we calculate the relative
fraction of energy flux that is carried away in each oscillation cycle by
running acoustic waves in the atmosphere and running magnetic waves in the
interior. For oscillation frequencies above the acoustic cutoff we show that
most energy losses associated with the presence of running waves occur in
regions where the magnetic field is close to vertical. Moreover, by considering
the depth dependence of the energy associated with the magnetic component of
the wave in the atmosphere we show that a fraction of the wave energy is kept
in the oscillation every cycle. For frequencies above the acoustic cutoff
frequency such energy is concentrated in regions where the magnetic field is
significantly inclined in relation to the local vertical. Even though our
calculations were aimed at studying oscillations with frequencies above the
acoustic cutoff frequency, based on our results we discuss what results may be
expected for oscillations of lower frequency.


  We show, in the case of a U(1)L spontaneously broken gauge theory, how
introducing a composite Wess-Zumino field, with a derivative coupling to the
fermionic current, and a composite scalar sector leads to infinitely massive
quarks and Higgs boson, making them unobservable as asymptotic states. This
results from the constraints that need to be introduced in the Feynman path
integral to take into account the non-independent scalar degrees of freedom,
and from the breaking of the symmetry by the non-vanishing vacuum expectation
value of the Higgs boson. Unitarity and gauge invariance are achieved; the
former can be made explicit by "gauging" the Wess-Zumino field into the third
component of the massive gauge boson; the latter is recovered at the level of
Green functions through the cancellation of the non-invariance of the action
with that of the fermionic measure. The compensation of the anomaly can also be
seen as a consequence of the infinite mass of the fermions. The pseudoscalar
partner of the Higgs is shown to behave like an abelian pion, specially as far
are its leptonic decays are concerned; in particular, no extra scale of
interaction is needed, unlike in "technicolour" theories. The correct decay of
the pion into two photons is recovered despite the abscence of anomaly.
Arguments are given in favour of renormalizability. The leptonic sector is the
object of a subsequent work.


  A series of asymmetric dimers with an odd number of atoms in the spacer were
found to form different types of twisted structures despite being achiral. The
formation of a variety of helical structures is accompanied by a gradual
freezing of molecular rotation. The tight pitch heliconical nematic (NTB) phase
and heliconical tilted smectic C (SmCTB) phase are formed. In the lowest
temperature smectic phase, HexI, the twist is expressed through the formation
of hierarchical structure: nano-scale helices and mesoscopic helical filaments.
The short pitch helical structure in smectic phases is confirmed by resonant
x-ray measurements.


  Let $(X,T)$ be a topological dynamical system. A pair of points $(x,y)\in
X^2$ is called Banach proximal if for any $\epsilon>0$, the set
$\{n\in\mathbb{Z}:\ d(T^nx,T^ny)<\epsilon\}$ has Banach density one. We study
the structure of the Banach proximal relation. An useful tool is the notion of
the support of a topological dynamical system. We show that a dynamical system
is strongly proximal if and only if every pair in $X^2$ is Banach proximal. A
subset $S$ of $X$ is Banach scrambled if every two distinct points in $S$ form
a Banach proximal pair but not asymptotic. We construct a dynamical system with
the whole space being a Banach scrambled set. Even though the Banach proximal
relation of the full shift is of first category, it has a dense Mycielski
invariant Banach scrambled set. We also show that for an interval map it is
Li-Yorke chaotic if and only if it has a Cantor Banach scrambled set.


  Large scale correlations in the orientations of galaxies can result from
alignments in their angular momentum vectors. These alignments arise from the
tidal torques exerted on neighboring proto-galaxies by the smoothly varying
shear field. We compute the predicted amplitude of such ellipticity
correlations using the Zel'dovich approximation for a realistic distribution of
galaxy shapes. Weak gravitational lensing can also induce ellipticity
correlations since the images of neighboring galaxies will be distorted
coherently. On comparing these two effects that induce shape correlations, we
find that for current weak lensing surveys with a median redshift of z_m = 1,
the intrinsic signal is of order 1 - 10 percent of the measured signal.
However, for shallower surveys with z_m < 0.3, the intrinsic correlations
dominate over the lensing signal. The distortions induced by lensing are
curl-free, whereas those resulting from intrinsic alignments are not. This
difference can be used to disentangle these two sources of ellipticity
correlations.


  In this paper, we prove the asymptotic multipartite version of the
Alon-Yuster theorem, which is a generalization of the Hajnal-Szemer\'edi
theorem: If $k\geq 3$ is an integer, $H$ is a $k$-colorable graph and
$\gamma>0$ is fixed, then, for every sufficiently large $n$, where $|V(H)|$
divides $n$, and for every balanced $k$-partite graph $G$ on $kn$ vertices with
each of its corresponding $\binom{k}{2}$ bipartite subgraphs having minimum
degree at least $(k-1)n/k+\gamma n$, $G$ has a subgraph consisting of
$kn/|V(H)|$ vertex-disjoint copies of $H$.
  The proof uses the Regularity method together with linear programming.


  We present a general unified approach for the study of quantum thermal
machines, including both heat engines and refrigerators, operating under
periodic adiabatic driving and in contact with thermal reservoirs kept at
different temperatures. We show that many observables characterizing this
operating mode and the performance of the machine are of geometric nature.
Heat-work conversion mechanisms and dissipation of energy can be described,
respectively, by the antisymmetric and symmetric components of a thermal
geometric tensor defined in the space of time-dependent parameters generalized
to include the temperature bias. The antisymmetric component can be identified
as a Berry curvature, while the symmetric component defines the metric of the
manifold. We show that the operation of adiabatic thermal machines, and
consequently also their efficiency, are intimately related to these geometric
aspects. We illustrate these ideas by discussing two specific cases: a slowly
driven qubit asymmetrically coupled to two bosonic reservoirs kept at different
temperatures, and a quantum dot driven by a rotating magnetic field and
strongly coupled to electron reservoirs with different polarizations. Both
examples are already amenable for an experimental verification.


  We describe a solid state implementation of a quantum computer using
ballistic single electrons as flying qubits in 1D nanowires. We show how to
implement all the steps required for universal quantum computation: preparation
of the initial state, measurement of the final state and a universal set of
quantum gates. An important advantage of this model is the fact that we do not
need ultrafast optoelectronics for gate operations. We use cold programming (or
pre-programming), i.e., the gates are set before launching the electrons; all
programming can be done using static electric fields only.


  World Wide Web consists of more than 50 billion pages online. It is highly
dynamic i.e. the web continuously introduces new capabilities and attracts many
people. Due to this explosion in size, the effective information retrieval
system or search engine can be used to access the information. In this paper we
have proposed the EPOW (Effective Performance of WebCrawler) architecture. It
is a software agent whose main objective is to minimize the overload of a user
locating needed information. We have designed the web crawler by considering
the parallelization policy. Since our EPOW crawler has a highly optimized
system it can download a large number of pages per second while being robust
against crashes. We have also proposed to use the data structure concepts for
implementation of scheduler & circular Queue to improve the performance of our
web crawler.


  Optimal control (OC) algorithms such as Differential Dynamic Programming
(DDP) take advantage of the derivatives of the dynamics to efficiently control
physical systems. Yet, in the presence of nonsmooth dynamical systems, such
class of algorithms are likely to fail due, for instance, to the presence of
discontinuities in the dynamics derivatives or because of non-informative
gradient. On the contrary, reinforcement learning (RL) algorithms have shown
better empirical results in scenarios exhibiting non-smooth effects (contacts,
frictions, etc). Our approach leverages recent works on randomized smoothing
(RS) to tackle non-smoothness issues commonly encountered in optimal control,
and provides key insights on the interplay between RL and OC through the prism
of RS methods. This naturally leads us to introduce the randomized Differential
Dynamic Programming (R-DDP) algorithm accounting for deterministic but
non-smooth dynamics in a very sample-efficient way. The experiments demonstrate
that our method is able to solve classic robotic problems with dry friction and
frictional contacts, where classical OC algorithms are likely to fail and RL
algorithms require in practice a prohibitive number of samples to find an
optimal solution.


  We derive asymptotic information on the iterates of a Volterra convolution
operator acting on L^p(0,1), subject to a mild smoothness condition on the
kernel. In particular, an asymptotically equal sequence of rank 1 operators is
obtained, leading to a simple asymptotic formula for the operator norms of the
iterates.


  In this short note, we are concerned with the fairness condition "A and B
hold almost equally often", which is important for specifying and verifying the
correctness of non-terminating processes and protocols. We introduce the logic
of temporal domination, in which the above condition can be expressed. We
present syntax and semantics of our logic and show that it is a proper
extension of linear time temporal logic. In order to obtain this result, we
rely on the corresponding result for k-counting automata.


  Optimization of thin-walled structures like an aircraft wing, aircraft
fuselage or submarine hull often involves dividing the shell surface into
numerous localized panels, each characterized by its own set of design
variables. The process of extracting information about a localized panel (nodal
coordinates, mesh connectivity) from a finite element model, input file is
usually a problem-specific task. In this work, a generalized process to extract
localized panels from the two-dimensional (2D) mesh is discussed. The process
employs set operations on elemental connectivity information and is independent
of nodal coordinates. Thus, it is capable of extracting panel of any shape
given the boundary and thus can be used during optimization of a wide range of
structures. A method to create stiffeners on the resulting local panels is also
presented, and the effect of stiffener element size on buckling is studied. The
local panel extraction process is demonstrated by integrating it into a
distributed MDO framework for optimization of an aircraft wing having
curvilinear spars and ribs (SpaRibs). A range of examples is included wherein
the process is used to create panels on the wing-skin, bounded by adjacent
SpaRibs.


  To draw scientifically meaningful conclusions and build reliable models of
quantitative phenomena, cause and effect must be taken into consideration
(either implicitly or explicitly). This is particularly challenging when the
measurements are not from controlled experimental (interventional) settings,
since cause and effect can be obscured by spurious, indirect influences. Modern
predictive techniques from machine learning are capable of capturing
high-dimensional, nonlinear relationships between variables while relying on
few parametric or probabilistic model assumptions. However, since these
techniques are associational, applied to observational data they are prone to
picking up spurious influences from non-experimental (observational) data,
making their predictions unreliable. Techniques from causal inference, such as
probabilistic causal diagrams and do-calculus, provide powerful (nonparametric)
tools for drawing causal inferences from such observational data. However,
these techniques are often incompatible with modern, nonparametric machine
learning algorithms since they typically require explicit probabilistic models.
Here, we develop causal bootstrapping for augmenting classical nonparametric
bootstrap resampling with information on the causal relationship between
variables. This makes it possible to resample observational data such that, if
it is possible to identify an interventional relationship from that data, new
data representing that relationship can be simulated from the original
observational data. In this way, we can use modern machine learning algorithms
unaltered to make statistically powerful, yet causally-robust, predictions. We
develop several causal bootstrapping algorithms for drawing interventional
inferences from observational data, for classification and regression problems,
and demonstrate, using synthetic and real-world examples, the value of this
approach.


  As large language models (LLMs) become increasingly prevalent in critical
applications, the need for interpretable AI has grown. We introduce TokenSHAP,
a novel method for interpreting LLMs by attributing importance to individual
tokens or substrings within input prompts. This approach adapts Shapley values
from cooperative game theory to natural language processing, offering a
rigorous framework for understanding how different parts of an input contribute
to a model's response. TokenSHAP leverages Monte Carlo sampling for
computational efficiency, providing interpretable, quantitative measures of
token importance. We demonstrate its efficacy across diverse prompts and LLM
architectures, showing consistent improvements over existing baselines in
alignment with human judgments, faithfulness to model behavior, and
consistency.
  Our method's ability to capture nuanced interactions between tokens provides
valuable insights into LLM behavior, enhancing model transparency, improving
prompt engineering, and aiding in the development of more reliable AI systems.
TokenSHAP represents a significant step towards the necessary interpretability
for responsible AI deployment, contributing to the broader goal of creating
more transparent, accountable, and trustworthy AI systems.


  Over the last two decades, the hierarchical equations of motion (HEOM) of
Tanimura and Kubo have become the equation of motion-based tool for numerically
exact calculations of system-bath problems. The HEOM is today generalized to
many cases of dissipation and transfer processes through an external bath. In
spatially extended photonic systems, the propagation of photons through the
bath leads to retardation/delays in the coupling of quantum emitters. Here, the
idea behind the HEOM derivation is generalized to the case of photon
retardation and applied to the simple example of two dielectric slabs. The
derived equations provide a simple reliable framework for describing
retardation and may provide an alternative to path integral treatments.


  We present a new technique to determine distances to major star-forming
regions across the Perseus Molecular Cloud, using a combination of stellar
photometry, astrometric data, and $\rm ^{12} CO$ spectral-line maps.
Incorporating the Gaia DR2 parallax measurements when available, we start by
inferring the distance and reddening to stars from their Pan-STARRS1 and 2MASS
photometry, based on a technique presented in Green et al. 2014; Green et al.
2015 and implemented in their 3D "Bayestar" dust map of three-quarters of the
sky. We then refine the Green et al. technique by using the velocity slices of
a CO spectral cube as dust templates and modeling the cumulative distribution
of dust along the line of sight towards these stars as a linear combination of
the emission in the slices. Using a nested sampling algorithm, we fit these
per-star distance-reddening measurements to find the distances to the CO
velocity slices towards each star-forming region. This results in distance
estimates explicitly tied to the velocity structure of the molecular gas. We
determine distances to the B5, IC348, B1, NGC1333, L1448, and L1451
star-forming regions and find that individual clouds are located between
$\approx 275-300$ pc, with typical combined uncertainties of $\approx 5\%$. We
find that the velocity gradient across Perseus corresponds to a distance
gradient of about 25 pc, with the eastern portion of the cloud farther away
than the western portion. We determine an average distance to the complex of
$294\pm 17$ pc, about 60 pc higher than the distance derived to the western
portion of the cloud using parallax measurements of water masers associated
with young stellar objects. The method we present is not limited to the Perseus
Complex, but may be applied anywhere on the sky with adequate CO data in the
pursuit of more accurate 3D maps of molecular clouds in the solar neighborhood
and beyond.


  In mathematical logic there are two seemingly distinct kinds of principles
called "reflection principles." Semantic reflection principles assert that if a
formula holds in the whole universe, then it holds in a set-sized model.
Syntactic reflection principles assert that every provable sentence from some
complexity class is true. In this paper we study connections between these two
kinds of reflection principles in the setting of second-order arithmetic. We
prove that, for a large swathe of theories, $\omega$-model reflection is
equivalent to the claim that arbitrary iterations of uniform $\Pi^1_1$
reflection along countable well-orderings are $\Pi^1_1$-sound. This result
yields uniform ordinal analyses of theories with strength between
$\mathsf{ACA}_0$ and $\mathsf{ATR}$. The main technical novelty of our analysis
is the introduction of the notion of the proof-theoretic dilator of a theory
$T$, which is the operator on countable ordinals that maps the order-type of
$\prec$ to the proof-theoretic ordinal of $T+\mathsf{WO}(\prec)$. We obtain
precise results about the growth of proof-theoretic dilators as a function of
provable $\omega$-model reflection. This approach enables us to simultaneously
obtain not only $\Pi^0_1$, $\Pi^0_2$, and $\Pi^1_1$ ordinals but also
reverse-mathematical theorems for well-ordering principles.


  Higher-order networks encode the many-body interactions existing in complex
systems, such as the brain, protein complexes, and social interactions.
Simplicial complexes are higher-order networks that allow a comprehensive
investigation of the interplay between topology and dynamics. However,
simplicial complexes have the limitation that they only capture undirected
higher-order interactions while in real-world scenarios, often there is a need
to introduce the direction of simplices, extending the popular notion of
direction of edges. On graphs and networks the Magnetic Laplacian, a special
case of Connection Laplacian, is becoming a popular operator to treat edge
directionality. Here we tackle the challenge of treating directional simplicial
complexes by formulating Higher-order Connection Laplacians taking into account
the configurations induced by the simplices' directions. Specifically, we
define all the Connection Laplacians of directed simplicial complexes of
dimension two and we discuss the induced higher-order diffusion dynamics by
considering instructive synthetic examples of simplicial complexes. The
proposed higher-order diffusion processes can be adopted in real scenarios when
we want to consider higher-order diffusion displaying non-trivial frustration
effects due to conflicting directionalities of the incident simplices.


  We report the first uniform and systematic study of dust and molecular gas in
nearby molecular clouds. We use surveys of dust extinction and emission to
determine the opacity and map the distribution of the dust within a dozen local
clouds in order to derive a uniform set of basic cloud properties. We find: 1)
the average dust opacity $\langle\kappa_{d,353}\rangle = 0.8\ {\rm cm^{2}\,
g^{-1}}$ with variations of a factor of $\sim$ 2 between clouds, 2) cloud PDFs
are exquisitely described by steeply falling power-laws with a narrow range of
slope, and 3) a tight $M_{\rm GMC} \sim R_{\rm GMC}^2$ scaling relation for the
cloud sample, indicative of a cloud population with an exactingly constant
average surface density above a common fixed boundary. We compare these results
to uniformly analyzed CO surveys. We measure the CO mass conversion factors and
assess the efficacy of CO for tracing the physical properties of molecular
clouds. We find $\langle \alpha_{\rm CO}\rangle = 4.31 \pm 0.67$ M$_\odot$ (K
km s$^{-1}$ pc$^2$)$^{-1}$ (corresponding to $X_{\rm CO}$ = 1.97 $\times$
10$^{20}$ cm$^{-2}$(K km s$^{-1}$)$^{-1}$). We demonstrate that CO observations
are a poor tracer of column density and structure on sub-cloud spatial scales.
On cloud scales, CO observations can provide measurements consistent with those
of the dust, provided data are analyzed in a similar, self-consistent fashion.
Measurements of average GMC surface density are sensitive to choice of cloud
boundary. Care must be exercised to adopt common fixed boundaries when
comparing surface densities for cloud populations within and between galaxies.


  There has been concern about ideological basis and possible discrimination in
text generated by Large Language Models (LLMs). We test possible value biases
in ChatGPT using a psychological value theory. We designed a simple experiment
in which we used a number of different probes derived from the Schwartz basic
value theory (items from the revised Portrait Value Questionnaire, the value
type definitions, value names). We prompted ChatGPT via the OpenAI API
repeatedly to generate text and then analyzed the generated corpus for value
content with a theory-driven value dictionary using a bag of words approach.
Overall, we found little evidence of explicit value bias. The results showed
sufficient construct and discriminant validity for the generated text in line
with the theoretical predictions of the psychological model, which suggests
that the value content was carried through into the outputs with high fidelity.
We saw some merging of socially oriented values, which may suggest that these
values are less clearly differentiated at a linguistic level or alternatively,
this mixing may reflect underlying universal human motivations. We outline some
possible applications of our findings for both applications of ChatGPT for
corporate usage and policy making as well as future research avenues. We also
highlight possible implications of this relatively high-fidelity replication of
motivational content using a linguistic model for the theorizing about human
values.


  The ASTRI Mini-Array is an international collaboration led by the Italian
National Institute for Astrophysics (INAF), aiming to construct and operate an
array of nine Imaging Atmospheric Cherenkov Telescopes (IACTs) to study
gamma-ray sources at very high energy (TeV) and to perform stellar intensity
interferometry observations. This contribution describes the design and the
technologies used by the ASTRI team to implement the Online Observation Quality
System (OOQS). The main objective of the OOQS is to perform data quality
analyses in real-time during Cherenkov and intensity interferometry
observations to provide feedback to both the Central Control System and the
Operator. The OOQS performs the analysis of key data quality parameters and can
generate alarms to other sub-systems for a fast reaction to solve critical
conditions. The results from the data quality analyses are saved into the
Quality Archive for further investigations. The Operator can visualise the OOQS
results through the Operator Human Machine Interface as soon as they are
produced. The main challenge addressed by the OOQS design is to perform online
data quality checks on the data streams produced by nine telescopes, acquired
by the Array Data Acquisition System and forwarded to the OOQS. In the current
OOQS design, the Redis in-memory database manages the data throughput generated
by the telescopes, and the Slurm workload scheduler executes in parallel the
high number of data quality analyses.


  The linearization method builds a bridge from mature methods for linear
systems to nonlinear systems and has been widely used in various areas. There
are currently two main linearization methods: Jacobian linearization and
feedback linearization. However, the Jacobian linearization method has
approximate and local properties, and the feedback linearization method has a
singularity problem and loses the physical meaning of the obtained states.
Thus, as a kind of complementation, a new linearization method named state
compensation linearization is proposed in the paper. Their differences,
advantages, and disadvantages are discussed in detail. Based on the state
compensation linearization, a state-compensation-linearization-based control
framework is proposed for a class of nonlinear systems. Under the new
framework, the original problem can be simplified. The framework also allows
different control methods, especially those only applicable to linear systems,
to be incorporated. Three illustrative examples are also given to show the
process and effectiveness of the proposed linearization method and control
framework.


  Protecting the dynamics of coupled quantum systems from decoherence by the
environment is a key challenge for solid-state quantum information processing.
An idle qubit can be efficiently insulated from the outside world via dynamical
decoupling, as has recently been demonstrated for individual solid-state
qubits. However, protection of qubit coherence during a multi-qubit gate poses
a non-trivial problem: in general the decoupling disrupts the inter-qubit
dynamics, and hence conflicts with gate operation. This problem is particularly
salient for hybrid systems, wherein different types of qubits evolve and
decohere at vastly different rates. Here we present the integration of
dynamical decoupling into quantum gates for a paradigmatic hybrid system, the
electron-nuclear spin register. Our design harnesses the internal resonance in
the coupled-spin system to resolve the conflict between gate operation and
decoupling. We experimentally demonstrate these gates on a two-qubit register
in diamond operating at room temperature. Quantum tomography reveals that the
qubits involved in the gate operation are protected as accurately as idle
qubits. We further illustrate the power of our design by executing Grover's
quantum search algorithm, achieving fidelities above 90% even though the
execution time exceeds the electron spin dephasing time by two orders of
magnitude. Our results directly enable decoherence-protected interface gates
between different types of promising solid-state qubits. Ultimately, quantum
gates with integrated decoupling may enable reaching the accuracy threshold for
fault-tolerant quantum information processing with solid-state devices.


  Due to increasing numbers of product piracy worldwide, a cost-effective
method for verifying the origin of a product is to be developed. For this
purpose, a certificate of authenticity can be created using precisely
measurable, unique properties of special physical objects that are difficult to
reconstruct. In the context of the present work, this is a counterfeit-proof
label composed of randomly distributed gold nanospheres or rods in a
semi-transparent material. The characteristic positioning of the label's
elements can be precisely measured using a smartphone's camera and additional
technologies. This can create an offline usable verification method for the
general public without the need for an existing network connection. The present
work provides a first part of the proof of concept that such a system and
especially the associated algorithmic computation method can be implemented and
efficiently used in a mobile application. In addition, a method suitable in
practice for transmitting and securing the required information is determined
in each case. Furthermore, the results of the validation of counterfeit-proof
product labels are analyzed in detail and existing weaknesses are pointed out.
  -- Auf Grund weltweit steigender Zahlen der Produktpiraterie soll ein
kosteng\"unstiges Verfahren zur Verifizierung der Herkunft eines Produktes
entwickelt werden. Daf\"ur l\"asst sich durch exakt messbare, einzigartige,
jedoch schwer rekonstruierbare Eigenschaften spezieller physischer Objekte ein
Echtheitszertifikat kreieren. Dieses ist im Kontext der vorliegenden Arbeit ein
f\"alschungssicheres Label, das sich in einem semi-transparenten Material aus
zuf\"allig verteilten Goldnanok\"ugelchen oder -st\"abchen zusammensetzt. Die
charakteristischen Positionierungen der Elemente des Labels lassen sich mit der
Kamera eines Smartphones und zus\"atzlichen Technologien pr\"azise messen.
Dadurch kann f\"ur die breite Bev\"olkerung ohne die Notwendigkeit einer
bestehenden Netzwerkverbindung ein offline verwendbares Verifikationsverfahren
erschaffen werden. Die vorliegende Arbeit liefert einen ersten Teil des
Machbarkeitsnachweises, dass ein derartiges System und insbesondere das damit
einhergehende algorithmische Berechnungsverfahren in einer mobilen Applikation
implementier -- und effizient einsetzbar ist. Zudem wird je eine in der Praxis
geeignete Methode zur \"Ubermittlung und Sicherung der ben\"otigten
Informationen eruiert. Des Weiteren werden die Resultate der Validierung von
f\"alschungssicheren Produktlabeln ausf\"uhrlich analysiert und vorhandene
Schw\"achen aufgezeigt.


  In order for coreference resolution systems to be useful in practice, they
must be able to generalize to new text. In this work, we demonstrate that the
performance of the state-of-the-art system decreases when the names of PER and
GPE named entities in the CoNLL dataset are changed to names that do not occur
in the training set. We use the technique of adversarial gradient-based
training to retrain the state-of-the-art system and demonstrate that the
retrained system achieves higher performance on the CoNLL dataset (both with
and without the change of named entities) and the GAP dataset.


  In this paper, the time dynamics of the daily means of wind speed measured in
complex mountainous regions are investigated. For 293 measuring stations
distributed over all Switzerland, the Fisher information measure and the
Shannon entropy power are calculated. The results reveal a clear relationship
between the computed measures and both the elevation of the wind stations and
the slope of the measuring sites. In particular, the Shannon entropy power and
the Fisher information measure have their highest (respectively lowest) values
in the Alps, where the time dynamics of wind speed follows a more disordered
pattern. The spatial mapping of the calculated quantities allows the
identification of two regions, which is in agreement with the topography of the
Swiss territory. The present study could contribute to a better
characterization of the temporal dynamics of wind speed in complex mountainous
terrain.


  We explore the phenomenology of the minimal supersymmetric flipped SU(5) GUT
model (CFSU(5)), whose soft supersymmetry-breaking (SSB) mass parameters are
constrained to be universal at some input scale, $M_{in}$, above the GUT scale,
$M_{GUT}$. We analyze the parameter space of CFSU(5) assuming that the lightest
supersymmetric particle (LSP) provides the cosmological cold dark matter,
paying careful attention to the matching of parameters at the GUT scale. We
first display some specific examples of the evolutions of the SSB parameters
that exhibit some generic features. Specifically, we note that the relationship
between the masses of the lightest neutralino and the lighter stau is sensitive
to $M_{in}$, as is the relationship between the neutralino mass and the masses
of the heavier Higgs bosons. For these reasons, prominent features in generic
$(m_{1/2}, m_0)$ planes such as coannihilation strips and rapid-annihilation
funnels are also sensitive to $M_{in}$, as we illustrate for several cases with
tan(beta)=10 and 55. However, these features do not necessarily disappear at
large $M_{in}$, unlike the case in the minimal conventional SU(5) GUT. Our
results are relatively insensitive to neutrino masses.


  We study modulational instability of two-component Bose-Einstein condensates
in an optical lattice, which is modelled as a coupled discrete nonlinear Schr
\"{o}dinger equation. The excitation spectrum and the modulational instability
condition of the total system are presented analytically. In the
long-wavelength limit, our results agree with the homogeneous two-component
Bose-Einstein condensates case. The discreteness effects result in the
appearance of the modulational instability for the condensates in miscible
region. The numerical calculations confirm our analytical results and show that
the interspecies coupling can transfer the instability from one component to
another.


  We present the analysis of photometric and spectroscopic data on eight
candidates for post-nova systems. Five post-novae, V528 Aql, HS Sge, BS Sgr, GR
Sgr and V999 Sgr, are successfully recovered. We furthermore identify likely
candidates for the fields of V1301 Aql, V1151 Sgr and V3964 Sgr. The
spectroscopic properties of the confirmed post-novae are briefly discussed. We
find that two of the oldest post-novae in our sample, GR Sgr and V999 Sgr,
contain an optically thick accretion disc, and thus can be suspected to have a
high mass-transfer rate, contrary to what one would expect from most models. HS
Sge and V528 Aql show evidence for a (comparatively) high system inclination,
which makes them attractive targets for time-series observations. Finally, the
presence of particularly strong He II emission together with a small eruption
amplitude suggests that BS Sgr is a good candidate for an intermediate polar.


  We present a detailed study of cardinality-aware top-$k$ classification, a
novel approach that aims to learn an accurate top-$k$ set predictor while
maintaining a low cardinality. We introduce a new target loss function tailored
to this setting that accounts for both the classification error and the
cardinality of the set predicted. To optimize this loss function, we propose
two families of surrogate losses: cost-sensitive comp-sum losses and
cost-sensitive constrained losses. Minimizing these loss functions leads to new
cardinality-aware algorithms that we describe in detail in the case of both
top-$k$ and threshold-based classifiers. We establish $H$-consistency bounds
for our cardinality-aware surrogate loss functions, thereby providing a strong
theoretical foundation for our algorithms. We report the results of extensive
experiments on CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets demonstrating
the effectiveness and benefits of our cardinality-aware algorithms.


  We derive an observational constraint on a spherical inhomogeneity of the
void centered at our position from the angular power spectrum of the cosmic
microwave background(CMB) and local measurements of the Hubble parameter. The
late time behaviour of the void is assumed to be well described by the
so-called $\Lambda$-Lema\^itre-Tolman-Bondi~($\Lambda$LTB) solution. Then, we
restrict the models to the asymptotically homogeneous models each of which is
approximated by a flat Friedmann-Lema\^itre-Robertson-Walker model. The late
time $\Lambda$LTB models are parametrized by four parameters including the
value of the cosmological constant and the local Hubble parameter. The other
two parameters are used to parametrize the observed distance-redshift relation.
Then, the $\Lambda$LTB models are constructed so that they are compatible with
the given distance-redshift relation. Including conventional parameters for the
CMB analysis, we characterize our models by seven parameters in total. The
local Hubble measurements are reflected in the prior distribution of the local
Hubble parameter. As a result of a Markov-Chains-Monte-Carlo analysis for the
CMB temperature and polarization anisotropies, we found that the inhomogeneous
universe models with vanishing cosmological constant are ruled out as is
expected. However, a significant under-density around us is still compatible
with the angular power spectrum of CMB and the local Hubble parameter.


  The sensitivity of the lightest supersymmetric particle relic density
calculation to different cosmological scenarios is discussed. In particular, we
investigate the effects of modifications of the expansion rate and of the
entropy content in the Early Universe. These effects, even with no
observational consequences, can still drastically modify the relic density
constraints on the SUSY parameter space. We suggest general parametrizations to
evaluate such effects, and derive also constraints from Big-Bang
nucleosynthesis. We show that using the relic density in the context of
supersymmetric constraints requires a clear statement of the underlying
cosmological model assumptions to avoid misinterpretations. On the other hand,
we note that combining the relic density calculation with the eventual future
discoveries at the LHC will hopefully shed light on the Very Early Universe
properties.


  A matrix inverse free method to solve time-dependent Schrodinger equation is
presented. The method is not subject to form of Hamiltonian and adopting real
space grid system such as structured and unstructured grid, and achieves the
order N algorithm even if we adopt unstructured grid systems to adjust complex
regions. We have demonstrated some error evaluation problems that have exact
solution and application in which it has non-Schrodinger type Hamiltonian, and
we have successfully simulated the time-evolution of wave function for all of
the case.


  We consider coupled models for particulate flows, where the disperse phase is
made of particles with distinct sizes. We are thus led to a system coupling the
incompressible Navier-Stokes equations to the multi-component
Vlasov-Fokker-Planck equations. We design an asymptotic-preserving numerical
scheme to approximate the system. The scheme is based on suitable implicit
treatment of the stiff drag force term as well as the Fokker-Planck operator,
and can be formally shown to capture the hydrodynamic limit with time step and
mesh size independent of the Stokes number. Numerical examples illustrate the
accuracy and asymptotic behavior of the scheme, with several interesting
applications.


  We propose a discontinuous Galerkin(DG) method to approximate the elliptic
interface problem on unfitted mesh using a new approximation space. The
approximation space is constructed by patch reconstruction with one degree of
freedom per element. The optimal error estimates in both L2 norm and DG energy
norm are obtained, without the typical constraints for DG method on how the
interface intersects to the elements in the mesh. Other than enjoying the
advantages of DG method, our method may achieve even better efficiency than the
conforming finite element method, as illustrated by numerical examples.


  We show that introducing an exponential cut-off on a suitable Sobolev norm
facilitates the proof of quasi-invariance of Gaussian measures with respect to
Hamiltonian PDE flows and allows us to establish the exact Jacobi formula for
the density. We exploit this idea in two different contexts, namely the
periodic fractional Benjamin-Bona-Mahony (BBM) equation with dispersion~$\gamma
>1$ and the periodic one dimensional quintic defocussing nonlinear
Schr\"odinger equation (NLS). For the BBM equation we study the transport of
the cut-off Gaussian measures on fractional Sobolev spaces, while for the NLS
equation we study the measures based on the modified energies introduced by
Planchon-Visciglia and the third author. Moreover for the BBM equation we also
show almost sure global well-posedness for data in~$C^\a(\T)$ for arbitrarily
small~$\a>0$ and invariance of the Gaussian measure associated with the
$H^{\gamma/2}(\T)$ norm.