  Developing equivariant neural networks for the E(3) group plays an important
role in modeling 3D data across real-world applications. Enforcing this
equivariance primarily involves the tensor products of irreducible
representations (irreps). However, the computational complexity of such
operations increases significantly as higher-order tensors are used. In this
work, we propose a systematic approach to substantially accelerate the
computation of the tensor products of irreps. We mathematically connect the
commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are
integrals of products of three spherical harmonics. Through Gaunt coefficients,
the tensor product of irreps becomes equivalent to the multiplication between
spherical functions represented by spherical harmonics. This perspective
further allows us to change the basis for the equivariant operations from
spherical harmonics to a 2D Fourier basis. Consequently, the multiplication
between spherical functions represented by a 2D Fourier basis can be
efficiently computed via the convolution theorem and Fast Fourier Transforms.
This transformation reduces the complexity of full tensor products of irreps
from $\mathcal{O}(L^6)$ to $\mathcal{O}(L^3)$, where $L$ is the max degree of
irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which
serves as a new method to construct efficient equivariant operations across
different model architectures. Our experiments on the Open Catalyst Project and
3BPA datasets demonstrate both the increased efficiency and improved
performance of our approach.


  We prove that if a subgroup $H$ of the automorphism group
$\mathrm{Aut}(\Sigma^{\mathbb{Z}})$ of a non-trivial full shift acts on points
of finite support with a free orbit, then for every finitely-generated abelian
group $A$, the abstract group $A \wr H$ also embeds in
$\mathrm{Aut}(\Sigma^{\mathbb{Z}})$. The groups admitting an action with such a
free orbit include $A \wr {\mathbb{Z}}$ for $A$ a finite abelian group, and
finitely-generated free groups. The class of such groups is also closed under
commensurability and direct products. We obtain for example that ${\mathbb{Z}}
\wr {\mathbb{Z}}$, ${\mathbb{Z}}_2 \wr ({\mathbb{Z}}_2 \wr {\mathbb{Z}})$ and
${\mathbb{Z}} \wr ({\mathbb{Z}}_2 \wr {\mathbb{Z}})$ embed in
$\mathrm{Aut}(\Sigma^{\mathbb{Z}})$. To our knowledge, the group ${\mathbb{Z}}
\wr {\mathbb{Z}}$ is the first example of a finitely-generated torsion-free
subgroup of $\mathrm{Aut}(\Sigma^{\mathbb{Z}})$ with infinite cohomological
dimension. It answers an implicit question of Kim and Roush and an explicit
question of the author. We also explore a simpler variant of the construction
that gives some near-misses to iterated permutational wreath products, as well
as some Neumann groups.


  A standard form of analysis for linguistic typology is the universal
implication. These implications state facts about the range of extant
languages, such as ``if objects come after verbs, then adjectives come after
nouns.'' Such implications are typically discovered by painstaking hand
analysis over a small sample of languages. We propose a computational model for
assisting at this process. Our model is able to discover both well-known
implications as well as some novel implications that deserve further study.
Moreover, through a careful application of hierarchical analysis, we are able
to cope with the well-known sampling problem: languages are not independent.


  The integration of various power sources, including renewables and electric
vehicles, into smart grids is expanding, introducing uncertainties that can
result in issues like voltage imbalances, load fluctuations, and power losses.
These challenges negatively impact the reliability and stability of online
scheduling in smart grids. Existing research often addresses uncertainties
affecting current states but overlooks those that impact future states, such as
the unpredictable charging patterns of electric vehicles. To distinguish
between these, we term them static uncertainties and dynamic uncertainties,
respectively. This paper introduces WDR-MPC, a novel approach that stands for
two-stage Wasserstein-based Distributionally Robust (WDR) optimization within a
Model Predictive Control (MPC) framework, aimed at effectively managing both
types of uncertainties in smart grids. The dynamic uncertainties are first
reformulated into ambiguity tubes and then the distributionally robust bounds
of both dynamic and static uncertainties can be established using WDR
optimization. By employing ambiguity tubes and WDR optimization, the stochastic
MPC system is converted into a nominal one. Moreover, we develop a convex
reformulation method to speed up WDR computation during the two-stage
optimization. The distinctive contribution of this paper lies in its holistic
approach to both static and dynamic uncertainties in smart grids. Comprehensive
experiment results on IEEE 38-bus and 94-bus systems reveal the method's
superior performance and the potential to enhance grid stability and
reliability.


  We investigate the influence of environmental noise on polarization entangled
light generated by parametric emission in a cavity. By adopting a recently
developed separability criterion, we show that: i) self-stimulation may
suppress the detrimental influence of noise on entanglement; ii) when
self-stimulation becomes effective, a classical model of parametric emission
incorporating noise provides the same results of quantum theory for the
expectation values involved in the separability criterion. Moreover we show
that, in the macroscopic limit, it is impossible to observe violations of local
realism with measurements of $n$-particle correlations, whatever n but finite.
These results provide an interesting example of the emergence of macroscopic
local realism in the presence of strong entanglement even in the absence of
decoherence.


  We use bosonization to derive the effective field theory that properly
describes ferromagnetic transition in one-dimensional itinerant electron
systems. The resultant theory is shown to have dynamical exponent z=2 at tree
leve and upper critical dimension d_c=2. Thus one dimension is below the upper
critical dimension of the theory, and the critical behavior of the transition
is controlled by an interacting fixed point, which we study via epsilon
expansion. Comparisons will be made with the Hertz-Millis theory, which
describes the ferromagnetic transition in higher dimensions.


  Deep cascaded architectures for magnetic resonance imaging (MRI) acceleration
have shown remarkable success in providing high-quality reconstruction.
However, as the number of cascades increases, the improvements in
reconstruction tend to become marginal, indicating possible excess model
capacity. Knowledge distillation (KD) is an emerging technique to compress
these models, in which a trained deep teacher network is used to distill
knowledge to a smaller student network such that the student learns to mimic
the behavior of the teacher. Most KD methods focus on effectively training the
student with a pre-trained teacher unaware of the student model. We propose
SFT-KD-Recon, a student-friendly teacher training approach along with the
student as a prior step to KD to make the teacher aware of the structure and
capacity of the student and enable aligning the representations of the teacher
with the student. In SFT, the teacher is jointly trained with the unfolded
branch configurations of the student blocks using three loss terms -
teacher-reconstruction loss, student-reconstruction loss, and teacher-student
imitation loss, followed by KD of the student. We perform extensive experiments
for MRI acceleration in 4x and 5x under-sampling on the brain and cardiac
datasets on five KD methods using the proposed approach as a prior step. We
consider the DC-CNN architecture and setup teacher as D5C5 (141765 parameters),
and student as D3C5 (49285 parameters), denoting a compression of 2.87:1.
Results show that (i) our approach consistently improves the KD methods with
improved reconstruction performance and image quality, and (ii) the student
distilled using our approach is competitive with the teacher, with the
performance gap reduced from 0.53 dB to 0.03 dB.


  I discuss the estimate of the CP-violating parameter eps'/eps based on
hadronic matrix elements computed in the chiral quark model. This estimate
suggested, before the current experimental results, that the favored value of
eps'/eps in the standard model is of the order of 10^{-3}. I briefly review the
physical effects on which this result is based and summarize current estimates.


  This paper describes a simple method for estimating lower bounds on the
number of classes of equivalence for a special kind of integer sequences,
called division sequences. The method is based on adding group structure to
classes of equivalence and studying properties of resulting groups as
presentations of free group.


  We describe briefly a new approach to some problems related to Teichm\"uller
spaces, invariant metrics, and extremal quasiconformal maps. This approach is
based on the properties of plurisubharmonic functions, especially of the
plurisubharmonic Green function. The main theorem gives an explicit
representation of the Green function for Teichm\"uller spaces by the
Kobayashi-Teichm\"uller metric of these spaces. This leads to various
applications. In particular, this gives a new characterization of extremal
quasiconformal maps.


  Using molecular dynamics computer simulations we investigate how the glass
transition and the properties of the resulting glass depend on the cooling rate
with which the sample has been quenched. This is done by studying a two
component Lennard-Jones system which is coupled to a heat bath whose
temperature is decreased from a high temperature, where the system is a liquid,
to zero temperature, where the system is a glass. The temperature $T_b$ of the
heat bath is decreased linearly in time, i.e. $T_b=T_0-\gamma t$, where
$\gamma$ is the cooling rate. In accordance with simple theoretical arguments
and with experimental observations we find that the glass transition, as
observed in the specific heat and the thermal expansion coefficient, becomes
sharper when $\gamma$ is decreased. A decrease of the cooling rate also leads
to a decrease of the glass transition temperature $T_g$ and we show that the
dependence of $T_g$ on $\gamma$ can be rationalized by assuming that the
temperature dependence of the relaxation times of the system is given by either
a Vogel-Fulcher law or a power-law. By investigating the structural properties
of the glass, such as the radial distribution functions, the coordination
numbers and the angles between three neighbor-sharing particles, we show how
the local order of the glass increases with decreasing cooling rate. The
enthalpy and the density of the glass decrease and increase, respectively, with
decreasing $\gamma$. By investigating the $\gamma$ dependence of clusters of
nearest neighbors, we show how these observations can be understood from a
microscopic point of view. We also show that the spectrum of the glass, as
computed from the dynamical matrix, shows a shift towards higher frequencies
when $\gamma$ is decreased. All these effects show that there is a significant


  One of the main sources of a background in underground physics experiments
(such as the investigation of solar neutrino flux, neutrino oscillations,
neutrinoless double beta decay, and the search for annual and daily Cold Dark
Matter particle flux modulation) are fast neutrons originating from the
surrounding rocks. The measurements of fast neutron flux in the new DULB
Laboratory situated at a depth of 4900 m w.e. in the Baksan Neutrino
Observatory have been performed. The relative neutron shielding properties of
several commonly available natural materials were investigated too. The
preliminary results obtained with a high-sensitive fast neutron spectrometer at
the level of sensitivity of about 10^(-7) neutron/ (cm^2 sec) are presented and
discussed.


  The behavior of an interior test particle in the secular 3-body problem has
been studied extensively. A well-known feature is the Lidov-Kozai resonance in
which the test particle's argument of periapse librates about $\pm 90^\circ$
and large oscillations in eccentricity and inclination are possible. Less
explored is the inverse problem: the dynamics of an exterior test particle and
an interior perturber. We survey numerically the inverse secular problem,
expanding the potential to hexadecapolar order and correcting an error in the
published expansion. Four secular resonances are uncovered that persist in full
$N$-body treatments (in what follows, $\varpi$ and $\Omega$ are the longitudes
of periapse and of ascending node, $\omega$ is the argument of periapse, and
subscripts 1 and 2 refer to the inner perturber and outer test particle): (i)
an orbit-flipping quadrupole resonance requiring a non-zero perturber
eccentricity $e_1$, in which $\Omega_2-\varpi_1$ librates about $\pm 90^\circ$;
(ii) a hexadecapolar resonance (the "inverse Kozai" resonance) for perturbers
that are circular or nearly so and inclined by $I \simeq 63^\circ/117^\circ$,
in which $\omega_2$ librates about $\pm 90^\circ$ and which can vary the
particle eccentricity by $\Delta e_2 \simeq 0.2$ and lead to orbit crossing;
(iii) an octopole "apse-aligned" resonance at $I \simeq 46^\circ/107^\circ$
wherein $\varpi_2 - \varpi_1$ librates about $0^\circ$ and $\Delta e_2$ grows
with $e_1$; and (iv) an octopole resonance at $I \simeq 73^\circ/134^\circ$
wherein $\varpi_2 + \varpi_1 - 2 \Omega_2$ librates about $0^\circ$ and $\Delta
e_2$ can be as large as 0.3 for small $e_1 \neq 0$. The more eccentric the
perturber, the more the particle's eccentricity and inclination vary; also,
more polar orbits are more chaotic. Our inverse solutions may be applied to the
Kuiper belt and debris disks, circumbinary planets, and stellar systems.


  The gravitational collapse of a massless scalar field enclosed with a
perfectly reflecting wall in a spacetime with a cosmological constant $\Lambda$
is investigated. The mass scaling for the gapped collapse $ M_{AH}-M_g \propto
(\epsilon_c-\epsilon)^\xi$ is confirmed and a new time scaling for the gapped
collapse $T_{AH}-T_g\propto(\epsilon_c-\epsilon)^\zeta$ is found. We find that
both of these two critical exponents depend on the combination $\Lambda R^2$,
where $R$ is the radial position of the reflecting wall. Especially, we find an
evolution of the critical exponent $\xi$ from $0.37$ in the confined asymptotic
dS case with $\Lambda R^2=1.5$ to $0.7$ in asymptotic AdS case ($\Lambda
R^2\rightarrow-\infty$), while the critical exponent $\zeta$ varies from $0.10$
to $0.26$, which shows the new critical behavior for the gapped collapse is
essentially different from the one in the Choptuik's case.


  In the control system of the JAERI-KEK joint project (High Intensity Proton
Accelerator Facility), it is planned to employ network-based controllers such
as PLC's and measurement stations instead of using other field control
networks, since the network hardware and software can be standardized and they
have been successfully utilized in other accelerator control systems in KEK.
  EPICS software support for those controllers was designed paying special
attention to robustness and has been implemented and applied for the
accelerator test stand. Basic functionalities were confirmed and miscellaneous
functions such as diagnosis of the software itself would be added.
  Since many kinds of network-based equipment such as oscilloscopes have become
available recently, they are considered to be integrated as well. They may
enable more manageable controllers.


  Nanoscale magnetic skyrmions are considered as potential information carriers
for future spintronics memory and logic devices. Such applications will require
the control of their local creation and annihilation, which involves so far
solutions that are either energy consuming or difficult to integrate. Here we
demonstrate the control of skyrmion bubbles nucleation and annihilation using
electric field gating, an easily integrable and potentially energetically
efficient solution. We present a detailed stability diagram of the skyrmion
bubbles in a Pt/Co/oxide trilayer and show that their stability can be
controlled via an applied electric field. An analytical bubble model, with the
Dzyaloshinskii-Moriya interaction imbedded in the domain wall energy, account
for the observed electrical skyrmion switching effect. This allows us to unveil
the origin of the electrical control of skyrmions stability and to show that
both magnetic dipolar interaction and the Dzyaloshinskii-Moriya interaction
play an important role in the skyrmion bubble stabilization.


  In this paper we calculate the entanglement entropy for topological
interfaces in rational conformal field theories for the case where the
interface lies at the boundary of the entangling interval and for the case
where it is located in the center of the entangling interval. We compare the
results to each other and also to the recently calculated left/right entropy of
a related BCFT. We also comment of the entanglement entropies for topological
interfaces for a free compactified boson and Liouville theory.


  We carry out a Painlev\'e analysis to find the cases where the cohomogeneity
one steady Ricci soliton equation can be integrable. We concentrate on two
classes of solitons: warped products and complex line bundles over a Fano
K\"ahler Einstein base. For warped products, the analysis singles out the case
with one factor where the dimension of the hypersurface is a perfect square,
with the $n=4$ particularly distinguished. The case with two factors each of
dimension $2$ is also singled out by the analysis. In the case of complex line
bundles, a 1-parameter family is singled out for every even dimension.


  While deep learning succeeds in a wide range of tasks, it highly depends on
the massive collection of annotated data which is expensive and time-consuming.
To lower the cost of data annotation, active learning has been proposed to
interactively query an oracle to annotate a small proportion of informative
samples in an unlabeled dataset. Inspired by the fact that the samples with
higher loss are usually more informative to the model than the samples with
lower loss, in this paper we present a novel deep active learning approach that
queries the oracle for data annotation when the unlabeled sample is believed to
incorporate high loss. The core of our approach is a measurement Temporal
Output Discrepancy (TOD) that estimates the sample loss by evaluating the
discrepancy of outputs given by models at different optimization steps. Our
theoretical investigation shows that TOD lower-bounds the accumulated sample
loss thus it can be used to select informative unlabeled samples. On basis of
TOD, we further develop an effective unlabeled data sampling strategy as well
as an unsupervised learning criterion that enhances model performance by
incorporating the unlabeled data. Due to the simplicity of TOD, our active
learning approach is efficient, flexible, and task-agnostic. Extensive
experimental results demonstrate that our approach achieves superior
performances than the state-of-the-art active learning methods on image
classification and semantic segmentation tasks.


  The representation theory of finite groups began with Frobenius's
factorization of Dedekind's group determinant. In this paper, we consider the
case of the semigroup determinant. The semigroup determinant is nonzero if and
only if the complex semigroup algebra is Frobenius, and so our results include
applications to the study of Frobenius semigroup algebras. We explicitly factor
the semigroup determinant for commutative semigroups and inverse semigroups. We
recover the Wilf-Lindstr\"om factorization of the semigroup determinant of a
meet semilattice and Wood's factorization for a finite commutative chain ring.
The former was motivated by combinatorics and the latter by coding theory over
finite rings. We prove that the algebra of the multiplicative semigroup of a
finite Frobenius ring is Frobenius over any field whose characteristic doesn't
divide that of the ring. As a consequence we obtain an easier proof of
Kov\'acs's theorem that the algebra of the monoid of matrices over a finite
field is a direct product of matrix algebras over group algebras of general
linear groups (outside of the characteristic of the finite field).


  We present the analysis of publicly available NuSTAR, Suzaku and XMM-Newton
observations of the symbiotic recurrent nova T CrB covering the 2006.77-2022.66
yr period. The X-ray spectra are analysed by adopting a model that includes a
reflection component produced by the presence of a disk that mimics the
accretion disk and the immediate surrounding medium. Our best-fit model
requires this disk to have a radius of 1 AU, effective thickness of 0.1 AU,
averaged column density 10$^{25}$ cm$^{-2}$ and orientation of 50$^{\circ}$
with respect to the line of sight. This disk is about a factor of two larger
than recent estimations for the accretion disk and its presence contributes
significantly via reflection to the total X-ray flux detected from T CrB, which
naturally produces the emission of the 6.4 keV Fe line. Our analysis suggests
that the temperature of the boundary layer evolved from 14.8 keV in the
steady-state phase (before 2016), to 2.8 keV in the 2017.24 epoch, to finally
stabilise to about $\sim$8 keV in the subsequent epochs. These variations in
the plasma temperature of the boundary layer are attributed to the evolution of
the mass accretion rate ($\dot{M}_\mathrm{acc}$), which is estimated to have an
averaged value of $\dot{M}_\mathrm{acc}$=2.6$\times10^{-8}$ M$_\odot$ yr$^{-1}$
for the current active phase. The presence of emission lines in the XMM-Newton
RGS spectrum of 2017.24 prevents from adopting a black body emission model to
fit the soft X-ray range. Instead, we use plasma emission models that suggest
the presence of adiabatically-shocked gas produced by gas velocities of 110-200
km s$^{-1}$, very likely tracing jet-like ejections similar to what is found in
other symbiotic systems. The analysis of X-ray and optical data together show
that T CrB has a similar evolution as black hole binaries, accreting neutron
stars and AGN in the hardness-intensity diagram.


  The purpose of this study was to find the most accurate model for
radiochromic film dosimetry by comparing different channel independent
perturbation models. A model selection approach based on (algorithmic)
information theory was followed, and the results were validated using
gamma-index analysis on a set of benchmark test cases. Several questions were
addressed: (a) whether incorporating the information of the non-irradiated
film, by scanning prior to irradiation, improves the results; (b) whether
lateral corrections are necessary when using multichannel models; (c) whether
multichannel dosimetry produces better results than single-channel dosimetry;
(d) which multichannel perturbation model provides more accurate film doses. It
was found that scanning prior to irradiation and applying lateral corrections
improved the accuracy of the results. For some perturbation models, increasing
the number of color channels did not result in more accurate film doses.
Employing Truncated Normal perturbations was found to provide better results
than using Micke-Mayer perturbation models.} Among the models being compared,
the triple-channel model with Truncated Normal perturbations, net optical
density as the response and subject to the application of lateral corrections
was found to be the most accurate model. The scope of this study was
circumscribed by the limits under which the models were tested. In this study,
the films were irradiated with megavoltage radiotherapy beams, with doses from
about 20 cGy to 600 cGy, entire (8 ${\rm inch}$ $\times$ 10 ${\rm inch}$) films
were scanned, the functional form of the sensitometric curves was a polynomial
and the different lots were calibrated using the plane-based method.


  Assurance of information flow security by formal methods is mandated in
security certification of separation kernels. As an industrial standard for
separation kernels, ARINC 653 has been complied with by mainstream separation
kernels. Security of functionalities defined in ARINC 653 is thus very
important for the development and certification of separation kernels. This
paper presents the first effort to formally specify and verify separation
kernels with ARINC 653 channel-based communication. We provide a reusable
formal specification and security proofs for separation kernels in
Isabelle/HOL. During reasoning about information flow security, we find some
security flaws in the ARINC 653 standard, which can cause information leakage,
and fix them in our specification. We also validate the existence of the
security flaws in two open-source ARINC 653 compliant separation kernels.


  Patterns in complex systems store hidden information of the system which is
needed to be explored. We present a simple model of cytokine and T-cells
interaction and studied the model within stochastic framework by constructing
Master equation of the system and solving it. The solved probability
distribution function of the model show classical Poisson pattern in the large
population limit $M,Z\rightarrow large$ indicating the system has the tendency
to attract a large number small-scale random processes of the cytokine
population towards the basin of attraction of the system by segregating from
nonrandom processes. Further, in the large $\langle Z\rangle$ limit, the
pattern transform to classical Normal pattern, where, uncorrelated small-scale
fluctuations are wiped out to form a regular but memoryless spatiotemporal
aggregated pattern. The estimated noise using Fano factor shows clearly that
the cytokine dynamics is noise induced process driving the system far away from
equilibrium.


  High-angular-resolution imaging is crucial for many applications in modern
astronomy and astrophysics. The fundamental diffraction limit constrains the
resolving power of both ground-based and spaceborne telescopes. The recent idea
of a quantum telescope based on the optical parametric amplification (OPA) of
light aims to bypass this limit for the imaging of extended sources by an order
of magnitude or more. We present an updated scheme of an OPA-based device and a
more accurate model of the signal amplification by such a device. The
semiclassical model that we present predicts that the noise in such a system
will form so-called light speckles as a result of light interference in the
optical path. Based on this model, we analysed the efficiency of OPA in
increasing the angular resolution of the imaging of extended targets and the
precise localization of a distant point source. According to our new model, OPA
offers a gain in resolved imaging in comparison to classical optics. For a
given time-span, we found that OPA can be more efficient in localizing a single
distant point source than classical telescopes.


  In this thesis, we study performance analysis and resource allocation designs
for non-orthogonal multiple access (NOMA) in wireless communication systems. In
contrast to conventional orthogonal multiple access (OMA) schemes, NOMA allows
multiple users to share the same degree of freedom via superposition coding and
the successive interference cancelation (SIC) decoding. Inspired by the solid
foundations from the information theory perspective, NOMA has rekindled the
interests of researchers as a benefit of the recent advancement in signal
processing and silicon technologies. However, comprehensive performance
analysis on NOMA and practical resource allocation designs to exploit potential
gains of NOMA in terms of spectral and energy efficiency have not been fully
studied and investigated in the literature. This thesis attempts to address
these problems by providing a unified performance analysis and a systematic
resource allocation design for NOMA in wireless communication systems.


  Attitude estimation is the process of computing the orientation angles of an
object with respect to a fixed frame of reference. Gyroscope, accelerometer,
and magnetometer are some of the fundamental sensors used in attitude
estimation. The orientation angles computed from these sensors are combined
using the sensor fusion methodologies to obtain accurate estimates. The
complementary filter is one of the widely adopted techniques whose performance
is highly dependent on the appropriate selection of its gain parameters. This
paper presents a novel cascaded architecture of the complementary filter that
employs a nonlinear and linear version of the complementary filter within one
framework. The nonlinear version is used to correct the gyroscope bias, while
the linear version estimates the attitude angle. The significant advantage of
the proposed architecture is its independence of the filter parameters, thereby
avoiding tuning the filters gain parameters. The proposed architecture does not
require any mathematical modeling of the system and is computationally
inexpensive. The proposed methodology is applied to the real-world datasets,
and the estimation results were found to be promising compared to the other
state-of-the-art algorithms.


  Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag
(or clique) complexes, which can in particular speed up the computation of its
persistent homology. They used so-called edge collapse to reduce the input flag
filtration and their reduction method required only the 1-skeleton of the
filtration. In this paper we revisit the usage of edge collapse for efficient
computation of persistence homology. We first give a simple and intuitive
explanation of the principles underlying that algorithm. This in turn allows us
to propose various extensions including a zigzag filtration simplification
algorithm. We finally show some experiments to better understand how it
behaves.


  The very rare Bd0 --> mu+ mu- decay may be the last chance for New Physics in
flavor sector at the LHC, before the 13 TeV run in 2015. Partially motivated by
the known tension in sin(2beta/phi_1), enhancement beyond (3-4) x 10^-10 would
likely imply the effect of a fourth generation of quarks. If observed at this
level, the 126 GeV boson may not be the actual Higgs boson, while the b --> d
quadrangle (modulo m_t') would jump out. The 2011-2012 data is likely not
sensitive to values below 3 x 10^-10, and the mode should continue to be
pursued with the 13 TeV run.


  Given a large edge-weighted network $G$ with $k$ terminal vertices, we wish
to compress it and store, using little memory, the value of the minimum cut (or
equivalently, maximum flow) between every bipartition of terminals. One
appealing methodology to implement a compression of $G$ is to construct a
\emph{mimicking network}: a small network $G'$ with the same $k$ terminals, in
which the minimum cut value between every bipartition of terminals is the same
as in $G$. This notion was introduced by Hagerup, Katajainen, Nishimura, and
Ragde [JCSS '98], who proved that such $G'$ of size at most $2^{2^k}$ always
exists. Obviously, by having access to the smaller network $G'$, certain
computations involving cuts can be carried out much more efficiently.
  We provide several new bounds, which together narrow the previously known gap
from doubly-exponential to only singly-exponential, both for planar and for
general graphs. Our first and main result is that every $k$-terminal planar
network admits a mimicking network $G'$ of size $O(k^2 2^{2k})$, which is
moreover a minor of $G$. On the other hand, some planar networks $G$ require
$|E(G')| \ge \Omega(k^2)$. For general networks, we show that certain bipartite
graphs only admit mimicking networks of size $|V(G')| \geq 2^{\Omega(k)}$, and
moreover, every data structure that stores the minimum cut value between all
bipartitions of the terminals must use $2^{\Omega(k)}$ machine words.


  We prove new upper bounds on homotopy and homology groups of o-minimal sets
in terms of their approximations by compact o-minimal sets. In particular, we
improve the known upper bounds on Betti numbers of semialgebraic sets defined
by quantifier-free formulae, and obtain for the first time a singly exponential
bound on Betti numbers of sub-Pfaffian sets.


  We consider the problem of describing the asymptotic behaviour of
\textsc{FRW} universes near their spacetime singularities in general
relativity. We find that the Bel-Robinson energy of these universes in
conjunction with the Hubble expansion rate and the scale factor proves to be an
appropriate measure leading to a complete classification of the possible
singularities. We show how our scheme covers all known cases of cosmological
asymptotics possible in these universes and also predicts new and distinct
types of singularities. We further prove that various asymptotic forms met in
flat cosmologies continue to hold true in their curved counterparts. These
include phantom universes with their recently discovered big rips, sudden
singularities as well as others belonging to graduated inflationary models.


  Over-the-air computation (AirComp), which leverages the superposition
property of wireless multiple-access channel (MAC) and the mathematical tool of
function representation, has been considered as a promising technique for
effective collection and computation of massive sensor data in wireless Big
Data applications. In most of the existing work on AirComp, optimal
system-parameter design is commonly considered under the peak-power constraint
of each sensor. In this paper, we propose an optimal transmitter-receiver
(Tx-Rx) parameter design problem to minimize the computation mean-squared error
(MSE) of an AirComp system under the sum-power constraint of the sensors. We
solve the non-convex problem and obtain a closed-form solution. Also, we
investigate another problem that minimizes the sum power of the sensors under
the constraint of computation MSE. Our results show that in both of the
problems, the sensors with poor and good channel conditions should use less
power than the ones with moderate channel conditions.


  Context is important for accurate visual recognition. In this work we propose
an object detection algorithm that not only considers object visual appearance,
but also makes use of two kinds of context including scene contextual
information and object relationships within a single image. Therefore, object
detection is regarded as both a cognition problem and a reasoning problem when
leveraging these structured information. Specifically, this paper formulates
object detection as a problem of graph structure inference, where given an
image the objects are treated as nodes in a graph and relationships between the
objects are modeled as edges in such graph. To this end, we present a so-called
Structure Inference Network (SIN), a detector that incorporates into a typical
detection framework (e.g. Faster R-CNN) with a graphical model which aims to
infer object state. Comprehensive experiments on PASCAL VOC and MS COCO
datasets indicate that scene context and object relationships truly improve the
performance of object detection with more desirable and reasonable outputs.


  Finding families that admit a linear $\chi$-binding function is a problem
that has interested researchers for a long time. Recently, the question of
finding linear subfamilies of $2K_2$-free graphs has garnered much attention.
In this paper, we are interested in finding a linear subfamily of a specific
superclass of $2K_2$-free graphs, namely $(P_3\cup P_2)$-free graphs. We show
that the class of $\{P_3\cup P_2,gem\}$-free graphs admits $f=2\omega$ as a
linear $\chi$-binding function. Furthermore, we give examples to show that the
optimal $\chi$-binding function $f^*\geq
\left\lceil\frac{5\omega(G)}{4}\right\rceil$ for the class of $\{P_3\cup P_2,
gem\}$-free graphs and that the $\chi$-binding function $f=2\omega$ is tight
when $\omega=2$ and $3$.


  Given a sequence of integers b = (b_0,b_1,b_2,...) one gives a Dyck path P of
length 2n the weight
  wt(P) = b_{h_1} b_{h_2} ... b_{h_n},
  where h_i is the height of the ith ascent of P. The corresponding weighted
Catalan number is
  C_n^b = sum_P wt(P),
  where the sum is over all Dyck paths of length 2n. So, in particular, the
ordinary Catalan numbers C_n correspond to b_i = 1 for all i >= 0. Let xi(n)
stand for the base two exponent of n, i.e., the largest power of 2 dividing n.
We give a condition on b which implies that
  xi(C_n^b) = xi(C_n).
  In the special case b_i=(2i+1)^2, this settles a conjecture of Postnikov
about the number of plane Morse links. Our proof generalizes the recent
combinatorial proof of Deutsch and Sagan of the classical formula for xi(C_n).


  We have successfully synthesized four Mo$_3$O$_8$-type cluster Mott
insulators (CMI) by intercalating lithium into nonmagnetic precursors to
regulate the Mo$_3$ cluster valence. The resulting materials are
Li$_{1+x}$$R$Mo$_3$O$_8$ ($R$ = Sc, Y, Lu) and Li$_x$Zn$_2$Mo$_3$O$_8$. Our
magnetic susceptibility measurements revealed that these materials display
characteristics akin to a valence bond glass state and suggest the presence of
short-range ordering when the Mo$_3$ cluster valence approximates its ideal
value. These findings challenge the prevailing belief that the plaquette charge
ordering state is an inherent feature of Mo$_3$O$_8$-type CMI. Instead, they
underscore the importance of Mo$_3$ cluster valence in determining the physical
properties of these systems. These insights furnish a fresh understanding of
the Mo$_3$O$_8$-type CMI and open new research opportunities in highly
frustrated magnetism.


  In this paper, we investigate the verification and enforcement of strong
state-based opacity (SBO) in discrete-event systems modeled as
partially-observed (nondeterministic) finite-state automata, including strong
K-step opacity (K-SSO), strong current-state opacity (SCSO), strong
initial-state opacity (SISO), and strong infinite-step opacity (Inf-SSO). They
are stronger versions of four widely-studied standard opacity notions,
respectively. We firstly propose a new notion of K-SSO, and then we construct a
concurrent-composition structure that is a variant of our previously-proposed
one to verify it. Based on this structure, a verification algorithm for the
proposed notion of K-SSO is designed. Also, an upper bound on K in the proposed
K-SSO is derived. Secondly, we propose a distinctive opacity-enforcement
mechanism that has better scalability than the existing ones (such as
supervisory control). The basic philosophy of this new mechanism is choosing a
subset of controllable transitions to disable before an original system starts
to run in order to cut off all its runs that violate a notion of strong SBO of
interest. Accordingly, the algorithms for enforcing the above-mentioned four
notions of strong SBO are designed using the proposed two
concurrent-composition structures. In particular, the designed algorithm for
enforcing Inf-SSO has lower time complexity than the existing one in the
literature, and does not depend on any assumption. Finally, we illustrate the
applications of the designed algorithms using examples.


  Using a sample of four million hadronic Z events collected in ALEPH from 1991
to 1995, the decays D*+ -> D0pi^+_s, with D0 decaying to K-pi+ or to K+pi-, are
studied. The relative branching ratio B(D0 -> K+pi-)/B(D0 -> K-pi+) is measured
to be (1.84+-0.59(stat.)+-0.34(syst.))%. The two possible contributions to the
D0 -> K+pi- decay, doubly cabibbo-suppressed decays and D0-Dbar0 mixing, are
disentangled by measuring the proper-time ditribution of the reconstructed
D0's. Assuming no interference between the two processes, the upper limit
obtained on the mixing rate is 0.92% at 95% CL. The possible effect of
interference between the two amplitudes is also assessed.


  We briefly review our work on the cascading renormalization group flows for
gauge theories on D-branes probing Calabi-Yau singularities. Such RG flows are
sometimes chaotic and exhibit duality walls. We construct supergravity
solutions dual to logarithmic flows for these theories. We make new
observations about a surface of conformal theories and more complicated
supergravity solutions.


  We study the bulk deformation properties of the Skyrme nuclear energy density
functionals. Following simple arguments based on the leptodermous expansion and
liquid drop model, we apply the nuclear density functional theory to assess the
role of the surface symmetry energy in nuclei. To this end, we validate the
commonly used functional parametrizations against the data on excitation
energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers
in actinide nuclei. After subtracting shell effects, the results of our
self-consistent calculations are consistent with macroscopic arguments and
indicate that experimental data on strongly deformed configurations in
neutron-rich nuclei are essential for optimizing future nuclear energy density
functionals. The resulting survey provides a useful benchmark for further
theoretical improvements. Unlike in nuclei close to the stability valley, whose
macroscopic deformability hangs on the balance of surface and Coulomb terms,
the deformability of neutron-rich nuclei strongly depends on the
surface-symmetry energy; hence, its proper determination is crucial for the
stability of deformed phases of the neutron- rich matter and description of
fission rates for r-process nucleosynthesis.


  We explore various facets of the cosmology of the Randall-Sundrum scenario
with two branes by considering the dynamics of the branes moving in a bulk
AdS/Schwarzschild geometry. This approach allows us both to understand in more
detail and from a different perspective the role of the stabilization of the
hierarchy in the brane cosmology, as well as to extend to the situation where
the metric contains a horizon. In particular, we explicitly determine how the
Goldberger-Wise stabilization mechanism perturbs the background bulk geometry
to produce a realistic cosmology.


  We have developed a new ISOCAM data reduction technique based on wavelet
analysis, especially designed for the detection of faint sources in
mid-infrared surveys. This method, the Pattern REcognition Technique for Isocam
data (PRETI) has been used to reduce the observations of the Hubble Deep Field
(HDF) and flanking fields with ISOCAM at 6.75 (LW2) and 15 microns (LW3).
Simulations of ISOCAM data allow us to test the photometric accuracy and
completeness of the reduction. We detect 49 objects in the ISO-HDF at high
confidence level, 42 in the LW3 filter, 3 in the LW2 filter, and 4 in both
filters. An additional, less secure, list of 100 sources is presented, of which
89 are detected at 15 microns only, 7 at 6.75 microns only and 4 in both
filters. Number counts derived from our results show an excess by a factor of
10 with respect to the prediction of a no evolution model (Franceschini 1998)
in the LW3 band. On the contrary, the number of sources in the LW2 band is
compatible with the prediction of such a model, but with greater uncertainties,
given the small number of detections.


  This paper reviews the first-ever image demoireing challenge that was part of
the Advances in Image Manipulation (AIM) workshop, held in conjunction with
ICCV 2019. This paper describes the challenge, and focuses on the proposed
solutions and their results. Demoireing is a difficult task of removing moire
patterns from an image to reveal an underlying clean image. A new dataset,
called LCDMoire was created for this challenge, and consists of 10,200
synthetically generated image pairs (moire and clean ground truth). The
challenge was divided into 2 tracks. Track 1 targeted fidelity, measuring the
ability of demoire methods to obtain a moire-free image compared with the
ground truth, while Track 2 examined the perceptual quality of demoire methods.
The tracks had 60 and 39 registered participants, respectively. A total of
eight teams competed in the final testing phase. The entries span the current
the state-of-the-art in the image demoireing problem.


  Given a set of points $P \subset \mathbb{R}^d$, the $k$-means clustering
problem is to find a set of $k$ {\em centers} $C = \{c_1,...,c_k\}, c_i \in
\mathbb{R}^d,$ such that the objective function $\sum_{x \in P} d(x,C)^2$,
where $d(x,C)$ denotes the distance between $x$ and the closest center in $C$,
is minimized. This is one of the most prominent objective functions that have
been studied with respect to clustering.
  $D^2$-sampling \cite{ArthurV07} is a simple non-uniform sampling technique
for choosing points from a set of points. It works as follows: given a set of
points $P \subseteq \mathbb{R}^d$, the first point is chosen uniformly at
random from $P$. Subsequently, a point from $P$ is chosen as the next sample
with probability proportional to the square of the distance of this point to
the nearest previously sampled points.
  $D^2$-sampling has been shown to have nice properties with respect to the
$k$-means clustering problem. Arthur and Vassilvitskii \cite{ArthurV07} show
that $k$ points chosen as centers from $P$ using $D^2$-sampling gives an
$O(\log{k})$ approximation in expectation. Ailon et. al. \cite{AJMonteleoni09}
and Aggarwal et. al. \cite{AggarwalDK09} extended results of \cite{ArthurV07}
to show that $O(k)$ points chosen as centers using $D^2$-sampling give $O(1)$
approximation to the $k$-means objective function with high probability. In
this paper, we further demonstrate the power of $D^2$-sampling by giving a
simple randomized $(1 + \epsilon)$-approximation algorithm that uses the
$D^2$-sampling in its core.


  Machine learning models have demonstrated remarkable success across diverse
domains but remain vulnerable to adversarial attacks. Empirical defence
mechanisms often fall short, as new attacks constantly emerge, rendering
existing defences obsolete. A paradigm shift from empirical defences to
certification-based defences has been observed in response. Randomized
smoothing has emerged as a promising technique among notable advancements. This
study reviews the theoretical foundations, empirical effectiveness, and
applications of randomized smoothing in verifying machine learning classifiers.
We provide an in-depth exploration of the fundamental concepts underlying
randomized smoothing, highlighting its theoretical guarantees in certifying
robustness against adversarial perturbations. Additionally, we discuss the
challenges of existing methodologies and offer insightful perspectives on
potential solutions. This paper is novel in its attempt to systemise the
existing knowledge in the context of randomized smoothing.


  Advances in AI invite the misuse of language models as stand-ins for human
minds or participants, which fundamentally mischaracterizes these statistical
algorithms. We argue that language models should be embraced as flexible
simulation tools, able to mimic a wide range of behaviors, perspectives, and
psychological attributes evident in human language data, but the models
themselves should not be equated to or anthropomorphized as human minds.


  This study focuses on the single depot electric vehicle scheduling problem
(SDEVSP) within the broader context of the vehicle scheduling problem (VSP). By
developing an effective scheduling model using mixed-integer linear
programming, we generate bus blocks that accommodate electric vehicles (EVs),
ensuring successful completion of each block while considering recharging
requirements between blocks and during off-hours. Next day operability
constraints are also incorporated, allowing for seamless repetition of blocks
on subsequent days. The SDEVSP is known to be computationally complex, deriving
optimal solutions unattainable for large-scale problems within reasonable
timeframes. To address this, we propose a two-step solution approach: first
solving the single depot VSP, and then addressing the block chaining problem
(BCP) using the blocks generated in the first step. The BCP focuses on
optimizing block combinations to facilitate recharging between consecutive
blocks, considering operational constraints. A case study conducted reveals
that nearly 100% electrification for Chicago, IL and Austin, TX transit buses
is viable yet requires 1.6 EVs at 150-mile range per diesel vehicle.


  Supergiant Fast X-ray Transients (SFXTs) are one of the most intriguing (and
unexpected) results of the INTEGRAL mission. They are a new class of High Mass
X-ray Binaries involving about 20 sources to date, with 8 firmly identified
SFXTs and many candidates. They are composed by a massive OB supergiant star as
companion donor and a compact object. At least four SFXTs host a neutron star,
because X-ray pulsations have been discovered, while for the others a black
hole cannot be excluded. SFXTs display short X-ray outbursts (compared with
Be/X-ray transients) characterized by fast flares on brief timescales of hours
and large flux variability typically in the range 1,000-100,000. The
INTEGRAL/IBIS sensitivity allowed to catch only the bright flares (peaking at
1E36-1E37erg/s), without persistent or quiescent emission. The investigation of
their properties, in particular the rapid variability time scales of their
flaring activity, will greatly benefit from observations with the Energetic
X-ray Imaging Survey Telescope (EXIST), with the possibility to perform a long
term and continuous as possible monitoring of the hard X-ray sky.


  We introduce a simple scenario involving fermionic dark matter ($\chi$) and
singlet scalar mediators that may account for the Galactic Center GeV
$\gamma$-ray excess while satisfying present direct detection constraints.
CP-violation in the scalar potential leads to mixing between the Standard Model
Higgs boson and the scalar singlet, resulting in three scalars $h_{1,2,3}$ of
indefinite CP-transformation properties. This mixing enables s-wave
$\chi{\bar\chi}$ annihilation into di-scalar states, followed by decays into
four fermion final states. The observed $\gamma$-ray spectrum can be fitted
while respecting present direct detection bounds and Higgs boson properties for
$m_{\chi} = 60 \sim 80 $ GeV, and $m_{h_3} \sim m_{\chi}$. Searches for the
Higgs exotic decay channel $h_1 \to h_3 h_3$ at the 14 TeV LHC should be able
to further probe the parameter region favored by the $\gamma$-ray excess.


  In optical imaging, light propagation is affected by the inhomogeneities of
the medium. Sample-induced aberrations and multiple scattering can strongly
degrade the image resolution and contrast. Based on a dynamic correction of the
incident and/or reflected wave-fronts, adaptive optics has been employed to
compensate for those aberrations. However, it only applies to
spatially-invariant aberrations or to thin aberrating layers. Here, we propose
a global and non-invasive approach based on the distortion matrix concept. This
matrix basically connects any focusing point of the image with the distorted
part of its wave-front in reflection. A singular value decomposition of the
distortion matrix allows to correct for high-order aberrations and forward
multiple scattering over multiple isoplanatic modes. Proof-of-concept
experiments are performed through biological tissues including a turbid cornea.
We demonstrate a Strehl ratio enhancement up to 2500 and recover a
diffraction-limited resolution until a depth of ten scattering mean free paths.


  The purpose of this paper is to make a further contribution to the Mackey
bijection for a complex reductive group G, between the tempered dual of G and
the unitary dual of the associated Cartan motion group. We shall construct an
embedding of the C*-algebra of the motion group into the reduced C*-algebra of
G, and use it to characterize the continuous field of reduced group C*-algebras
that is associated to the Mackey bijection. We shall also obtain a new
characterization of the Mackey bijection using the same embedding.


  A novel radio guided surgery (RGS) technique for cerebral tumors using
$\beta^{-}$ radiation is being developed. Checking the availability of a
radio-tracer that can deliver a $\beta^{-}$ emitter to the tumor is a
fundamental step in the deployment of such technique. This paper reports a
study of the uptake of 90Y labeled (DOTATOC) in the meningioma and the high
grade glioma (HGG) and a feasibility study of the RGS technique in these cases.


  Since the PAMELA results on the "anomalously" high positron fraction and the
lack of antiproton excess in our Galaxy, there has been a tremendous number of
studies advocating new types of dark matter, with larger couplings to electrons
than to quarks.
  This raises the question of the production of dark matter particles (and
heavy associated coloured states) at LHC. Here, we explore a very simple
benchmark dark matter model and show that, in spite of the agreement between
the PAMELA antiproton measurements and the expected astrophysical secondary
background, there is room for large couplings of a WIMP candidate to heavy
quarks. Contrary to what could have been naively anticipated, the PAMELA pbar/p
measurements do not challenge dark matter model building, as far as the quark
sector is concerned. A quarkophillic species is therefore not forbidden.Owing
to these large couplings, one would expect that a new production channel opens
up at the LHC, through quark--quark and quark--gluon interactions. Alas, when
the PDF of the quark is taken into account, prospects for a copious production
fade away.


  Spiking neural networks (SNNs) take inspiration from the brain to enable
energy-efficient computations. Since the advent of Transformers, SNNs have
struggled to compete with artificial networks on modern sequential tasks, as
they inherit limitations from recurrent neural networks (RNNs), with the added
challenge of training with non-differentiable binary spiking activations.
However, a recent renewed interest in efficient alternatives to Transformers
has given rise to state-of-the-art recurrent architectures named state space
models (SSMs). This work systematically investigates, for the first time, the
intersection of state-of-the-art SSMs with SNNs for long-range sequence
modelling. Results suggest that SSM-based SNNs can outperform the Transformer
on all tasks of a well-established long-range sequence modelling benchmark. It
is also shown that SSM-based SNNs can outperform current state-of-the-art SNNs
with fewer parameters on sequential image classification. Finally, a novel
feature mixing layer is introduced, improving SNN accuracy while challenging
assumptions about the role of binary activations in SNNs. This work paves the
way for deploying powerful SSM-based architectures, such as large language
models, to neuromorphic hardware for energy-efficient long-range sequence
modelling.


  In this paper we consider inhomogeneous cubic-quintic NLS in space dimension
$d = 3$: $$ iu_t = -\Delta u + K_1(x)|u|^2u + K_2(x)|u|^4u. $$ We study local
well-posedness, finite time blowup, and small data scattering and
non-scattering for the ICQNLS when $K_1, K_2 \in C^4(\mathbb R^3 \setminus
\{0\})$ satisfy growth condition $|\partial^j K_i(x)| \lesssim |x|^{b_i-j}\, (j
= 0, 1, 2, 3, 4)$ for some $b_i \ge 0$ and for $x \neq 0$. To this end we use
the Sobolev inequality for the functions $f \in H^n \,(n = 1, 2)$ such that
$\||\mathbf L|^\ell f\|_{H^n} < \infty \,(\ell = 1, 2)$, where $\mathbf L$ is
the angular momentum operator defined by $\mathbf L = x \times (-i\nabla)$.


  Icy grains in the interstellar medium and star-formation regions consist of a
variety of materials. Such composite grains interact differently with
cosmic-ray (CR) particles compared to simple single-material grains. We aim to
calculate the spectra of energies and temperatures of mixed-composition grains
undergoing whole-grain heating by CRs. The grains were assumed to consist of a
mixture of carbon and olivine, covered by ices consisting of carbon oxides and
water. The energy and temperature spectra for grains with radii 0.05; 0.1, and
0.2 microns impacted by CRs were calculated for eight values of column density,
relevant to molecular clouds and star-forming cores. The approach takes into
account changes in ice thickness and composition with increasing column
density. These detailed data for CR interaction with interstellar grains are
intended for applications in astrochemical models. The main finding is that the
a more accurate approach on grain heat capacity and other factors prevent a
frequent heating of 0.1 micron or larger icy grains to high temperatures.


  Inspiraling massive black-hole binaries (MBHBs) forming in the aftermath of
galaxy mergers are expected to be the loudest gravitational-wave (GW) sources
relevant for pulsar-timing arrays (PTAs) at nHz frequencies. The incoherent
overlap of signals from a cosmic population of MBHBs gives rise to a stochastic
GW background (GWB) with characteristic strain around $h_c\sim10^{-15}$ at a
reference frequency of 1 yr$^{-1}$, although uncertainties around this value
are large. Current PTAs are piercing into the GW amplitude range predicted by
MBHB-population models, but no detection has been reported so far. To assess
the future success prospects of PTA experiments, it is therefore important to
estimate the minimum GWB level consistent with our current understanding of the
formation and evolution of galaxies and massive black holes (MBHs). To this
purpose, we couple a semianalytic model of galaxy evolution and an extensive
study of the statistical outcome of triple MBH interactions. We show that even
in the most pessimistic scenario where all MBHBs stall before entering the
GW-dominated regime, triple interactions resulting from subsequent galaxy
mergers inevitably drive a considerable fraction of the MBHB population to
coalescence. At frequencies relevant for PTA, the resulting GWB is only a
factor of 2-to-3 suppressed compared to a fiducial model where binaries are
allowed to merge over Gyr timescales. Coupled with current estimates of the
expected GWB amplitude range, our findings suggest that the minimum GWB from
cosmic MBHBs is unlikely to be lower than $h_c\sim 10^{-16}$ (at $f = 1$
yr$^{-1}$), well within the expected sensitivity of projected PTAs based on
future observations with FAST, MeerKAT and SKA.


  Massive galaxies with a half-mass radius <~ 1kpc are observed in the early
universe (z~>2), but not in the local universe. In the local universe
similar-mass (within a factor of two) galaxies tend to be a factor of 4 to 5
larger. Dry minor mergers are known to drive the evolution of the size of a
galaxy without much increasing the mass, but it is unclear if the growth in
size is sufficient to explain the observations. We test the hypothesis that
galaxies grow through dry minor mergers by simulating merging galaxies with
mass ratios of q=1:1 (equal mass) to q=1:160. In our N-body simulations the
total mass of the parent galaxy doubles. We confirm that major mergers do not
cause a sufficient growth in size. The observation can be explained with
mergers with a mass ratio of q=1:5--1:10. Smaller mass ratios cause a more
dramatic growth in size, up to a factor of ~17 for mergers with a mass ratio of
1:80. For relatively massive minor mergers q ~> 1:20 the mass of the incoming
child galaxies tend to settle in the halo of the parent galaxy. This is caused
by the tidal stripping of the child galaxies by the time they enter the central
portion of the parent. When the accretion of minor galaxies becomes more
continuous, when q <~ 1:40, the foreign mass tends to concentrate more in the
central region of the parent galaxy. We speculate that this is caused by
dynamic interactions between the child galaxies inside the merger remnant and
the longer merging times when the difference in mass is larger. These
interactions cause dynamical heating which results in accretion of mass inside
the galaxy core and a reduction of the parent's circular velocity and density.


  Self-training is a classical approach in semi-supervised learning which is
successfully applied to a variety of machine learning problems. Self-training
algorithm generates pseudo-labels for the unlabeled examples and progressively
refines these pseudo-labels which hopefully coincides with the actual labels.
This work provides theoretical insights into self-training algorithm with a
focus on linear classifiers. We first investigate Gaussian mixture models and
provide a sharp non-asymptotic finite-sample characterization of the
self-training iterations. Our analysis reveals the provable benefits of
rejecting samples with low confidence and demonstrates that self-training
iterations gracefully improve the model accuracy even if they do get stuck in
sub-optimal fixed points. We then demonstrate that regularization and class
margin (i.e. separation) is provably important for the success and lack of
regularization may prevent self-training from identifying the core features in
the data. Finally, we discuss statistical aspects of empirical risk
minimization with self-training for general distributions. We show how a purely
unsupervised notion of generalization based on self-training based clustering
can be formalized based on cluster margin. We then establish a connection
between self-training based semi-supervision and the more general problem of
learning with heterogenous data and weak supervision.


  We show that it is possible to introduce the confining hidden sector gauge
group SU(5)' with the chiral matter 10 plus 5-bar, which are neutral under the
standard model gauge group, toward a gauge mediated supersymmetry breaking
(GMSB) in a Z_{12-I} orbifold compactification of E_8xE_8 heterotic string.
Three families of MSSM result without exotics. We also find a desirable matter
parity P (or R-parity) assignment. We note that this model contains the
spectrum of the Lee-Weinberg model which has a nice solution of the mu problem.


  We present Herschel-PACS spectroscopy of four main-sequence star-forming
galaxies at z~1.5. We detect [OI]63micron line emission in BzK-21000 at
z=1.5213, and measure a line luminosity, L([OI]63micron) = (3.9+/-0.7)x1.E+9
Lsun. Our PDR modelling of the interstellar medium in BzK-21000 suggests a UV
radiation field strength, G~320 G0, and gas density, n~1800 cm-3, consistent
with previous LVG modelling of the molecular CO line excitation. The other
three targets in our sample are individually undetected in these data, and we
perform a spectral stacking analysis which yields a detection of their average
emission and an [OI]63micron line luminosity, L([OI]63micron) =(1.1+/-0.2)x1E+9
Lsun. We find that the implied luminosity ratio, L([OI]63micron)/L(IR), of the
undetected BzK-selected star-forming galaxies broadly agrees with that of
low-redshift star-forming galaxies, while BzK-21000 has a similar ratio to that
of a dusty star-forming galaxy at z~6. The high [OI]63micron line luminosities
observed in BzK-21000 and the $z \sim 1 -3$ dusty and submm luminous
star-forming galaxies may be associated with extended reservoirs of low
density, cool neutral gas.


  Sparse optimization problems are ubiquitous in many fields such as
statistics, signal/image processing and machine learning. This has led to the
birth of many iterative algorithms to solve them. A powerful strategy to boost
the performance of these algorithms is known as safe screening: it allows the
early identification of zero coordinates in the solution, which can then be
eliminated to reduce the problem's size and accelerate convergence. In this
work, we extend the existing Gap Safe screening framework by relaxing the
global strong-concavity assumption on the dual cost function. Instead, we
exploit local regularity properties, that is, strong concavity on well-chosen
subsets of the domain. The non-negativity constraint is also integrated to the
existing framework. Besides making safe screening possible to a broader class
of functions that includes beta-divergences (e.g., the Kullback-Leibler
divergence), the proposed approach also improves upon the existing Gap Safe
screening rules on previously applicable cases (e.g., logistic regression). The
proposed general framework is exemplified by some notable particular cases:
logistic function, beta = 1.5 and Kullback-Leibler divergences. Finally, we
showcase the effectiveness of the proposed screening rules with different
solvers (coordinate descent, multiplicative-update and proximal gradient
algorithms) and different data sets (binary classification, hyperspectral and
count data).


  To appear in Encyclopedia of Mathematical Physics, published by Elsevier in
early 2006. Comments/corrections welcome. The article surveys topological
aspects in gauge theories.


  A vortex in a quasi two-dimensional Bose-Einstein condensate is subject to
the Magnus force and can be effectively described as a planar particle in a
uniform magnetic field. Quantization of this effective particle leads to the
lowest Landau level where the most localized wave function is a gaussian. In
this gaussian state vortex position seems to fluctuate with an average
magnitude set by the magnetic width of the gaussian. We readdress this problem
using the number-conserving version of the Bogoliubov theory. We find that the
Bogoliubov mode that might be interpreted as a fluctuation of vortex position
actually does not contribute to position fluctuation at all. The only non-zero
contribution comes from phonons but it is an order of magnitude less than the
simple estimate, based on the magnetic width of the effective gaussian wave
packet.


  We consider a model of nonlinear wave equations with periodically varying
wave speed and periodic external forcing. By imposing non-resonance conditions
on the frequency, we establish the existence of the response solutions (i.e.,
periodic solutions with the same frequency as the forcing) for such a model in
a Cantor set of asymptotically full measure. The proof relies on a
Lyapunov--Schmidt reduction together with the Nash--Moser iteration.


  We describe our preliminary results on a search for high-redshift ($z >$ 0.5)
galaxy clusters using near-infrared photometry obtained with the Omega camera
at the 3.5m telescope at Calar Alto.


  A. Huber and B. Kahn construct a relative slice filtration on the motive M(X)
associated to a principal T-bundle X over a smooth scheme Y. As a consequence
of their result, one can observe that the mixed Tateness of the motive M(Y)
implies that the motive M(X) is mixed Tate. In this note we prove the inverse
implication for a principal G-bundle, for a split reductive group G.


  Charged particles are continually generated in atmospheric air, and the
interaction between natural ionisation and atmospheric particles is
complicated. It is of some climatic importance to establish if ions are
implicated in particle formation. Atmospheric ion concentrations have been
investigated here at high temporal resolution, using Gerdien ion analysers at a
site where synchronous meteorological measurements were also made. The
background ionisation rate was also monitored with a Geiger counter, enabling
ion production from natural radioactivity to be distinguished from other
effects. Measurements at 1Hz offer some promise in establishing the atmospheric
electrical influences in ionic nucleation bursts, although combinations of
other meteorological factors are also known to be significant. High time
resolution meteorological and ion measurements are therefore clearly necessary
in advancing basic understanding in the behaviour of atmospheric aerosol.


  In order to solve the problem that current convolutional neural networks can
not capture the correlation features between the time domain signals of rolling
bearings effectively, and the model accuracy is limited by the number and
quality of samples, a rolling bearing fault diagnosis method based on
generative adversarial enhanced multi-scale convolutional neural network model
is proposed. Firstly, Gram angular field coding technique is used to encode the
time domain signal of the rolling bearing and generate the feature map to
retain the complete information of the vibration signal. Then, the re-sulting
data is divided into a training set, a validation set, and a test set. Among
them, the training set is input into the gradient penalty Wasserstein distance
generation adversarial network to complete the training, and a new sample with
similar features to the training sample is obtained, and then the original
training set is expanded. Next, multi-scale convolution is used to extract the
fault features of the extended training set, and the feature graph is
normalized by example to overcome the influence of the difference in feature
distribution. Finally, the attention mechanism is applied to the adaptive
weighting of normalized features and the extraction of deep features, and the
fault diagnosis is completed by the softmax classifier. Compared with ResNet
method, the experimental results show that the proposed method has better
generalization performance and anti-noise performance.


  This paper devotes to studying abstract stochastic evolution equations in
M-type 2 Banach spaces. First, we handle nonlinear evolution equations with
multiplicative noise. The existence and uniqueness of local and global mild
solutions under linear growth and Lipschitz conditions on coefficients are
presented. The regular dependence of solutions on initial data is also studied.
Second, we investigate linear evolution equations with additive noise. The
existence and uniqueness of strict and mild solutions and their regularity are
shown. Finally, we explore semilinear evolution equations with additive noise.
We concentrate on the existence, uniqueness and regular dependence of solutions
on initial data.


  If deconfined quark matter exists inside compact stars, the primary cooling
mechanism is neutrino radiation via the direct Urca processes d->u+e+antinu_e
and u+e->d+nu_e. Below a critical temperature, T_c, quark matter forms a colour
superconductor, one possible manifestation of which is a condensate of <ud>
quark Cooper pairs in an electric-charge neutralising background of electrons.
We compute the neutrino emission rate from such a phase, including charged
pair-breaking and recombination effects, and find that on a material
temperature domain below T_c the pairing-induced suppression of the neutrino
emission rate is not uniformly exponential. If gapless modes are present in the
condensed phase, the emissivity at low temperatures is moderately enhanced
above that of completely unpaired matter. The importance of charged current
pair-breaking processes for neutrino emission both in the fully gapped and
partially gapped regimes is emphasised.


  Quantum groups were invented largely to provide solutions of the Yang-Baxter
equation and hence solvable models in 2-dimensional statistical mechanics and
one-dimensional quantum mechanics. They have been hugely successful. But not
all Yang-Baxter solutions fit into the framework of quantum groups. We shall
explain how other mathematical structures, especially subfactors, provide a
language and examples for solvable models. The prevalence of the Connes tensor
product of Hilbert spaces over von Neumann algebras leads us to speculate
concerning its potential role in describing entangled or interacting quantum
systems.


  Anomaly detection in data analysis is an interesting but still challenging
research topic in real world applications. As the complexity of data dimension
increases, it requires to understand the semantic contexts in its description
for effective anomaly characterization. However, existing anomaly detection
methods show limited performances with high dimensional data such as ImageNet.
Existing studies have evaluated their performance on low dimensional, clean and
well separated data set such as MNIST and CIFAR-10. In this paper, we study
anomaly detection with high dimensional and complex normal data. Our
observation is that, in general, anomaly data is defined by semantically
explainable features which are able to be used in defining semantic
sub-clusters of normal data as well. We hypothesize that if there exists
reasonably good feature space semantically separating sub-clusters of given
normal data, unseen anomaly also can be well distinguished in the space from
the normal data. We propose to perform semantic clustering on given normal data
and train a classifier to learn the discriminative feature space where anomaly
detection is finally performed. Based on our careful and extensive experimental
evaluations with MNIST, CIFAR-10, and ImageNet with various combinations of
normal and anomaly data, we show that our anomaly detection scheme outperforms
state of the art methods especially with high dimensional real world images.


  We present pumping lemmas for five classes of functions definable by
fragments of weighted automata over the min-plus semiring, the max-plus
semiring and the semiring of natural numbers. As a corollary we show that the
hierarchy of functions definable by unambiguous, finitely-ambiguous,
polynomially-ambiguous weighted automata, and the full class of weighted
automata is strict for the min-plus and max-plus semirings.


  Fairness is a concept of justice. Various definitions exist, some of them
conflicting with each other. In the absence of an uniformly accepted notion of
fairness, choosing the right kind for a specific situation has always been a
central issue in human history. When it comes to implementing sustainable
fairness in artificial intelligence systems, this old question plays a key role
once again: How to identify the most appropriate fairness metric for a
particular application? The answer is often a matter of context, and the best
choice depends on ethical standards and legal requirements. Since ethics
guidelines on this topic are kept rather general for now, we aim to provide
more hands-on guidance with this document. Therefore, we first structure the
complex landscape of existing fairness metrics and explain the different
options by example. Furthermore, we propose the "Fairness Compass", a tool
which formalises the selection process and makes identifying the most
appropriate fairness definition for a given system a simple, straightforward
procedure. Because this process also allows to document the reasoning behind
the respective decisions, we argue that this approach can help to build trust
from the user through explaining and justifying the implemented fairness.


  The assumption of separability is a simplifying and very popular assumption
in the analysis of spatio-temporal or hypersurface data structures. It is often
made in situations where the covariance structure cannot be easily estimated,
for example because of a small sample size or because of computational storage
problems. In this paper we propose a new and very simple test to validate this
assumption. Our approach is based on a measure of separability which is zero in
the case of separability and positive otherwise. The measure can be estimated
without calculating the full non-separable covariance operator. We prove
asymptotic normality of the corresponding statistic with a limiting variance,
which can easily be estimated from the available data. As a consequence
quantiles of the standard normal distribution can be used to obtain critical
values and the new test of separability is very easy to implement. In
particular, our approach does neither require projections on subspaces
generated by the eigenfunctions of the covariance operator, nor resampling
procedures to obtain critical values nor distributional assumptions as used by
other available methods of constructing tests for separability. We investigate
the finite sample performance by means of a simulation study and also provide a
comparison with the currently available methodology. Finally, the new procedure
is illustrated analyzing wind speed and temperature data.


  In this paper, we compute Gram determinants associated to all cell modules of
quantized walled Brauer algebras $\mathscr B_{r, t}(\rho, q)$ over an arbitrary
field $\kappa$. Suppose $e$ is the quantum characteristic of $q^2$. We classify
the blocks of $\mathscr B_{r, t}(\rho, q)$ when $e>\max\{r,t\}$ and
$\rho^2=q^{2n}$, $n\in\mathbb Z$. As an application, we give a criterion for a
cell module of $\mathscr B_{r, t}(\rho, q)$ being equal to its simple head over
$\kappa$.


  We define tensors, corresponding to cubic polynomials, which have the same
exponent $\omega$ as the matrix multiplication tensor. In particular, we study
the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$
matrix $A$ by $sM_n(A)=trace(A^3)$. The use of polynomials enables the
introduction of additional techniques from algebraic geometry in the study of
the matrix multiplication exponent $\omega$.


  Manually tracking nutritional intake via food diaries is error-prone and
burdensome. Automated computer vision techniques show promise for dietary
monitoring but require large and diverse food image datasets. To address this
need, we introduce NutritionVerse-Synth (NV-Synth), a large-scale synthetic
food image dataset. NV-Synth contains 84,984 photorealistic meal images
rendered from 7,082 dynamically plated 3D scenes. Each scene is captured from
12 viewpoints and includes perfect ground truth annotations such as RGB, depth,
semantic, instance, and amodal segmentation masks, bounding boxes, and detailed
nutritional information per food item. We demonstrate the diversity of NV-Synth
across foods, compositions, viewpoints, and lighting. As the largest
open-source synthetic food dataset, NV-Synth highlights the value of
physics-based simulations for enabling scalable and controllable generation of
diverse photorealistic meal images to overcome data limitations and drive
advancements in automated dietary assessment using computer vision. In addition
to the dataset, the source code for our data generation framework is also made
publicly available at https://saeejithnair.github.io/nvsynth.


  We present a path algorithm for the generalized lasso problem. This problem
penalizes the $\ell_1$ norm of a matrix D times the coefficient vector, and has
a wide range of applications, dictated by the choice of D. Our algorithm is
based on solving the dual of the generalized lasso, which greatly facilitates
computation of the path. For $D=I$ (the usual lasso), we draw a connection
between our approach and the well-known LARS algorithm. For an arbitrary D, we
derive an unbiased estimate of the degrees of freedom of the generalized lasso
fit. This estimate turns out to be quite intuitive in many applications.


  Quantum projection synthesis can be used for phase-probability-distribution
measurement, optical-state truncation and preparation. The method relies on
interfering optical lights, which is a major challenge in experiments performed
by pulsed light sources. In the pulsed regime, the time frequency overlap of
the interfering lights plays a crucial role on the efficiency of the method
when they have different mode structures. In this paper, the pulsed mode
projection synthesis is developed, the mode structure of interfering lights are
characterized and the effect of this overlap (or mode match) on the fidelity of
optical-state truncation and preparation is investigated. By introducing the
positive-operator-valued measure (POVM) for the detection events in the scheme,
the effect of mode mismatch between the photon-counting detectors and the
incident lights are also presented.


  Session contracts is a formalism enabling to investigate client/server
interaction protocols and to interpret session types. We extend session
contracts in order to represent outputs whose actual sending in an interaction
depends on a third party or on a mutual agreement between the partners. Such
contracts are hence adaptable, or as we say "affectible". In client/server
systems, in general, compliance stands for the satisfaction of all client's
requests by the server. We define an abstract notion of "affectible compliance"
and show it to have a precise three-party game-theoretic interpretation. This
in turn is shown to be equivalent to a compliance based on interactions that
can undergo a sequence of failures and rollbacks, as well as to a compliance
based on interactions which can be mediated by an orchestrator. Besides, there
is a one-to-one effective correspondence between winning strategies and
orchestrators. The relation of subcontract for affectible contracts is also
investigated.


  I review our understanding of the structure and kinematics of the Large
Magellanic Cloud (LMC), with a particular focus on recent results. This is an
important topic, given the status of the LMC as a benchmark for studies of
microlensing, tidal interactions, stellar populations, and the extragalactic
distance scale. I address the observed morphology and kinematics of the LMC;
the angles under which we view the LMC disk; its in-plane and vertical
structure; the LMC self-lensing contribution to the total microlensing optical
depth; the LMC orbit around the Milky Way; and the origin and interpretation of
the Magellanic Stream. Our understanding of these topics is evolving rapidly,
in particular due to the many large photometric and kinematic datasets that
have become available in the last few years. It has now been established that:
the LMC is considerably elongated in its disk plane; the LMC disk is thicker
than previously believed; the LMC disk may have warps and twists; the LMC may
have a pressure-supported halo; the inner regions of the LMC show unexpected
complexities in their vertical structure; and precession and nutation of the
LMC disk plane contribute measurably to the observed line-of-sight velocity
field. However, many open questions remain and more work is needed before we
can expect to converge on a fully coherent structural, dynamical and
evolutionary picture that explains all observed features of the LMC.


  Contrary to the conviction expressed by J. Kijowski [Phys. Rev. A 59, 897
(1999)] and shared in some other papers, the reasons to look for the 'time
operator' in the context of the standard quantum doctrine of orthogonal
projectors and self-adjoint observables are highly questionable. Some improved
solutions in terms of POV measures invite critical discussions as well.


  We study, analytically and numerically, a simple $\mathcal{PT}$-symmetric
tight-binding ring with an onsite energy $a$ at the gain and loss sites. We
show that if $a\neq 0$, the system generically exhibits an unbroken
$\mathcal{PT}$-symmetric phase. We study the nature of the spectrum in terms of
the singularities in the complex parameter space as well as the behavior of the
eigenstates at large values of the gain and loss strength. We find that in
addition to the usual exceptional points, there are "diabolical points", and
inverse exceptional points at which complex eigenvalues reconvert into real
eigenvalues. We also study the transport through the system. We calculate the
total flux from the source to the drain, and how it splits along the branches
of the ring. We find that while usually the density flows from the source to
the drain, for certain eigenstates a stationary "backflow" of density from the
drain to the source along one of the branches can occur. We also identify two
types of singular eigenstates, i.e. states that do not depend on the strength
of the gain and loss, and classify them in terms of their transport properties.


  We propose the exact S-matrix for the planar limit of the N=6 super
Chern-Simons theory recently proposed by Aharony, Bergman, Jafferis, and
Maldacena for the AdS_4/CFT_3 correspondence. Assuming SU(2|2) symmetry,
factorizability and certain crossing-unitarity relations, we find the S-matrix
including the dressing phase. We use this S-matrix to formulate the asymptotic
Bethe ansatz. Our result for the Bethe-Yang equations and corresponding Bethe
ansatz equations confirms the all-loop Bethe ansatz equations recently
conjectured by Gromov and Vieira.


  For a periodic structure sandwiched between two homogeneous media, a bound
state in the continuum (BIC) is a guided Bloch mode with a frequency in the
radiation continuum. Optical BICs have found many applications, mainly because
they give rise to resonances with ultra-high quality factors. If the periodic
structure has a relevant symmetry, a BIC may have a symmetry mismatch with
incoming and outgoing propagating waves of the same frequency and compatible
wavevectors, and is considered as protected by symmetry. Propagating BICs with
nonzero Bloch wavevectors have been found on many highly symmetric periodic
structures. They are not protected by symmetry in the usual sense (i.e., there
is no symmetry mismatch), but some of them seem to depend on symmetry for their
existence and robustness. In this paper, we show that the low-frequency
propagating BICs (with only one radiation channel) on biperiodic structures
with an inversion symmetry in the plane of periodicity and a reflection
symmetry in the perpendicular direction are robust to symmetry-preserving
structural perturbations. In other words, a propagating BIC continues its
existence with a slightly different frequency and a slightly different Bloch
wavevector, when the biperiodic structure is perturbed slightly preserving the
inversion and reflection symmetries. Our study enhances theoretical
understanding for BICs on periodic structures and provides useful guidelines
for their applications.


  The breaking of detailed balance, the symmetry between forward and backward
probability transition between two states, is crucial to understand
irreversible systems. In hydrodynamic turbulence, a far-from equilibrium
system, we observe a strong manifestation of the breaking of detailed balance
by following the evolution of the kinetic energy of individual fluid elements.
We found in all the flows that we have investigated that fluid elements
decelerate faster than they accelerate, giving rise to negative third moment of
energy increments, independently of space dimensionality. The exchange of
energy between fluid elements however is fundamentally different in two and
three dimensions. While pressure forces do not provide net energy change to
slow or fast particles in two dimensions, they tend to transfer energy from
{\it slow} to {\it fast} particles in three dimensions, possibly implying a
runaway of energy.


  A device based on Polarization sensitive optical coherence tomography is
developed to monitor blood glucose levels in human subjects. The device was
initially tested with tissue phantom. The measurements with human subjects for
various glucose concentration levels are found to be linearly dependent on the
degree of circular polarization obtainable from the PS-OCT.


  We have obtained high-resolution data of the z 2 ring-like, clumpy
star-forming galaxy (SFG) ZC406690 using the VLT/SINFONI with AO (in K-band)
and in seeing-limited mode (in H- and J-band). Our data includes all of the
main strong optical emission lines: [OII], [OIII], Ha, Hb, [NII] and [SII]. We
find broad, blueshifted Ha and [OIII] emission line wings in the spectra of the
galaxy's massive, star-forming clumps (sigma \sim 85 km s^-1) and even broader
wings (up to 70% of the total Ha flux, with sigma \sim 290 km s^-1) in regions
spatially offset from the clumps by \sim 2 kpc. The broad emission likely
originates from large-scale outflows with mass outflow rates from individual
clumps that are 1-8x the SFR of the clumps. Based on emission line ratio
diagnostics ([NII]/Ha and [SII]/Ha) and photoionization and shock models, we
find that the emission from the clumps is due to a combination of
photoionization from the star-forming regions and shocks generated in the
outflowing component, with 5-30% of the emission deriving from shocks. In terms
of the ionization parameter (6x10^7-10^8 cm/s, based on both the SFR and the
O32 ratio), density (local electron densities of 300-1800 cm^-3 in and around
the clumps, and ionized gas column densities of 1200-8000 Msol/pc^2), and SFR
(10-40 Msol/yr), these clumps more closely resemble nuclear starburst regions
of local ULIRGs and dwarf irregulars than HII regions in local galaxies.
However, the star-forming clumps are not located in the nucleus as in local
starburst galaxies but instead are situated in a ring several kpc from the
center of their high-redshift host galaxy, and have an overall disk-like
morphology. The two brightest clumps are quite different in terms of their
internal properties, energetics and relative ages, and thus we are given a
glimpse at two different stages in the formation and evolution of rapidly
star-forming giant clumps at high-z.


  Algebraic relations are established that determine the invariance of the
transformed number after several transformations. The restrictions that
determine the group structure of these relationships are analyzed, as is the
case of the Klein group. Parametric Kr functions associated with the existence
of cycles are presented, as well as the role of the number of their links in
the grouping of numbers in higher order equivalence classes. For this we have
developed a methodology based on binary equivalence relations and the complete
parameterization of the Kaprekar routine using Ki functions of parametric
transformation.


  We discuss a scalar Dark Matter candidate from the Inert Doublet Model in
light of discovery of a 125 GeV SM-like Higgs boson at the LHC. We explore the
possibility of using the recent and future data from LHC experiments, namely
the Higgs diphoton decay measurements, to constrain the properties of Dark
Matter particles.


  Bilevel optimization is one of the fundamental problems in machine learning
and optimization. Recent theoretical developments in bilevel optimization focus
on finding the first-order stationary points for nonconvex-strongly-convex
cases. In this paper, we analyze algorithms that can escape saddle points in
nonconvex-strongly-convex bilevel optimization. Specifically, we show that the
perturbed approximate implicit differentiation (AID) with a warm start strategy
finds $\epsilon$-approximate local minimum of bilevel optimization in
$\tilde{O}(\epsilon^{-2})$ iterations with high probability. Moreover, we
propose an inexact NEgative-curvature-Originated-from-Noise Algorithm (iNEON),
a pure first-order algorithm that can escape saddle point and find local
minimum of stochastic bilevel optimization. As a by-product, we provide the
first nonasymptotic analysis of perturbed multi-step gradient descent ascent
(GDmax) algorithm that converges to local minimax point for minimax problems.


  In the coming years and decades, autonomous vehicles (AVs) will become
increasingly prevalent, offering new opportunities for safer and more
convenient travel and potentially smarter traffic control methods exploiting
automation and connectivity. Car following is a prime function in autonomous
driving. Car following based on reinforcement learning has received attention
in recent years with the goal of learning and achieving performance levels
comparable to humans. However, most existing RL methods model car following as
a unilateral problem, sensing only the vehicle ahead. Recent literature,
however, Wang and Horn [16] has shown that bilateral car following that
considers the vehicle ahead and the vehicle behind exhibits better system
stability. In this paper we hypothesize that this bilateral car following can
be learned using RL, while learning other goals such as efficiency
maximisation, jerk minimization, and safety rewards leading to a learned model
that outperforms human driving.
  We propose and introduce a Deep Reinforcement Learning (DRL) framework for
car following control by integrating bilateral information into both state and
reward function based on the bilateral control model (BCM) for car following
control. Furthermore, we use a decentralized multi-agent reinforcement learning
framework to generate the corresponding control action for each agent. Our
simulation results demonstrate that our learned policy is better than the human
driving policy in terms of (a) inter-vehicle headways, (b) average speed, (c)
jerk, (d) Time to Collision (TTC) and (e) string stability.


  The main result of this paper is, that if we suppose that a function is
absolutely continuous and uniformly H\"older continuous and that it's finite
difference function does not oscillate infinitely often on a bounded interval,
then the decay rate of its Fourier coefficients can be estimated exactly. This
rate of decay predicts the same uniform H\"older continuity but the two other
conditions are not necessary. Several examples from literature and by the
author show that none of the assumptions can be relaxed without weakening the
decay for some functions. The uniform H\"older continuity of chirps and the
decay of their Fourier coefficients are studied. The main result is then
applied in the estimation of the error of numerical Weyl fractional derivatives
calculated using the discrete Fourier transform. The main result is also
extended to Fourier transforms.


  We study the cascading dynamics immediately before and immediately after 219
market shocks. We define the time of a market shock T_{c} to be the time for
which the market volatility V(T_{c}) has a peak that exceeds a predetermined
threshold. The cascade of high volatility "aftershocks" triggered by the "main
shock" is quantitatively similar to earthquakes and solar flares, which have
been described by three empirical laws --- the Omori law, the productivity law,
and the Bath law. We analyze the most traded 531 stocks in U.S. markets during
the two-year period 2001-2002 at the 1-minute time resolution. We find
quantitative relations between (i) the "main shock" magnitude M \equiv \log
V(T_{c}) occurring at the time T_{c} of each of the 219 "volatility quakes"
analyzed, and (ii) the parameters quantifying the decay of volatility
aftershocks as well as the volatility preshocks. We also find that stocks with
larger trading activity react more strongly and more quickly to market shocks
than stocks with smaller trading activity. Our findings characterize the
typical volatility response conditional on M, both at the market and the
individual stock scale. We argue that there is potential utility in these three
statistical quantitative relations with applications in option pricing and
volatility trading.


  Despite being invented in 1951 by R. Kikuchi, the 2-D Cluster Variation
Method (CVM), has not yet received attention. Nevertheless, this method can
usefully characterize 2-D topographies using just two parameters; the
activation enthalpy and the interaction enthalpy. This Technical Report
presents 2-D CVM details, including the dependence of the various configuration
variables on the enthalpy parameters, as well as illustrations of various
topographies (ranging from scale-free-like to rich club-like) that result from
different parameter selection. The complete derivation for the analytic
solution, originally presented simply as a result in Kikuchi and Brush (1967)
is given here, along with careful comparison of the analytically-predicted
configuration variables versus those obtained when performing computational
free energy minimization on a 2-D grid. The 2-D CVM can potentially function as
a secondary free energy minimization within the hidden layer of a neural
network, providing a basis for extending node activations over time and
allowing temporal correlation of patterns.


  Frequentist-style large-sample properties of Bayesian posterior
distributions, such as consistency and convergence rates, are important
considerations in nonparametric problems. In this paper we give an analysis of
Bayesian asymptotics based primarily on predictive densities. Our analysis is
unified in the sense that essentially the same approach can be taken to develop
convergence rate results in iid, mis-specified iid, independent non-iid, and
dependent data cases.


  JPEG-XS offers low complexity image compression for applications with
constrained but reasonable bit-rate, and low latency. Our paper explores the
deployment of JPEG-XS on lossy packet networks. To preserve low latency,
Forward Error Correction (FEC) is envisioned as the protection mechanism of
interest. Despite the JPEG-XS codestream is not scalable in essence, we observe
that the loss of a codestream fraction impacts the decoded image quality
differently, depending on whether this codestream fraction corresponds to
codestream headers, to coefficients significance information, or to low/high
frequency data, respectively. Hence, we propose a rate-distortion optimal
unequal error protection scheme that adapts the redundancy level of
Reed-Solomon codes according to the rate of channel losses and the type of
information protected by the code. Our experiments demonstrate that, at 5% loss
rates, it reduces the Mean Squared Error by up to 92% and 65%, compared to a
transmission without and with optimal but equal protection, respectively.


  The observation of single-photon optomechanical effects is a desired task in
cavity optomechanics. However, the realization of ultrastrong optomechanical
interaction remains a big challenge. Here, we present an all-optical scheme to
simulate ultrastrong optomechanical coupling based on a Fredkin-type
interaction, which consists of two exchange-coupled modes with the coupling
strength depending on the photon number in another controller mode. This
coupling enhancement is assisted by the displacement amplification according to
the physical idea of the Bogoliubov approximation, which is realized by
utilizing a strong driving to pump one of the two exchanging modes. Our
numerical simulations demonstrate that the enhanced optomechanical coupling can
enter the single-photon strong-coupling and even ultrastrong-coupling regimes.
We also show the creation of macroscopic quantum superposed states and the
implementation of a weak-to-strong transition for quantum measurement in this
system. This work will pave the way to quantum simulation of single-photon
optomechanical effects with current experimental platforms.