  Let $X$ be a smooth hypersurface of dimension $n\geq 1$ and degree $d\geq 3$
in the projective space given as the zero set of a homogeneous form $F$. If
$(n,d)\neq (1,3), (2,4)$ it is well known that every automorphism of $X$
extends to an automorphism of the projective space, i.e.,
$\operatorname{Aut}(X)\subseteq \operatorname{PGL}(n+2,\mathbb{C})$. We say
that the automorphism group $\operatorname{Aut}(X)$ is $F$-liftable if there
exists a subgroup of $\operatorname{GL}(n+2,\mathbb{C})$ projecting
isomorphically onto $\operatorname{Aut}(X)$ and leaving $F$ invariant. Our main
result in this paper shows that the automorphism group of every smooth
hypersurface of dimension $n$ and degree $d$ is $F$-liftable if and only if $d$
and $n+2$ are relatively prime. We also provide an effective criterion to
compute all the integers which are a power of a prime number and that appear as
the order of an automorphism of a smooth hypersurface of dimension $n$ and
degree $d$. As an application, we give a sufficient condition under which some
Sylow $p$-subgroups of $\operatorname{Aut}(X)$ are trivial or cyclic of order
$p$.


  Trusted Computing is a security base technology that will perhaps be
ubiquitous in a few years in personal computers and mobile devices alike.
Despite its neutrality with respect to applications, it has raised some privacy
concerns. We show that trusted computing can be applied for service access
control in a manner protecting users' privacy. We construct a ticket system --
a concept which is at the heart of Identity Management -- relying solely on the
capabilities of the trusted platform module and the standards specified by the
Trusted Computing Group. Two examples show how it can be used for pseudonymous
and protected service access.


  This paper demonstrates the application of Bayesian Artificial Neural
Networks to Ordinary Differential Equation (ODE) inverse problems. We consider
the case of estimating an unknown chaotic dynamical system transition model
from state observation data. Inverse problems for chaotic systems are
numerically challenging as small perturbations in model parameters can cause
very large changes in estimated forward trajectories. Bayesian Artificial
Neural Networks can be used to simultaneously fit a model and estimate model
parameter uncertainty. Knowledge of model parameter uncertainty can then be
incorporated into the probabilistic estimates of the inferred system's forward
time evolution. The method is demonstrated numerically by analysing the chaotic
Sprott B system. Observations of the system are used to estimate a posterior
predictive distribution over the weights of a parametric polynomial kernel
Artificial Neural Network. It is shown that the proposed method is able to
perform accurate time predictions. Further, the proposed method is able to
correctly account for model uncertainties and provide useful prediction
uncertainty bounds.


  The key to achieve high-quality van der Waals heterostructure devices made of
stacking various two-dimensional (2D) layered materials lies in the clean
interface without bubbles and wrinkles. Although polymethylmethacrylate (PMMA)
is generally used as a sacrificial transfer film due to its strong adhesion
property, it is always dissolved in the solvent after the transfer, resulting
in the unavoidable PMMA residue on the top surface. This makes it difficult to
locate clean interface areas. In this work, we present a fully dry PMMA
transfer of graphene onto h-BN using a heating/cooling system which allows
identification of clean interface area for high quality graphene/h-BN
heterostructure fabrication. The mechanism lies in the utilization of the large
difference in thermal expansion coefficients between polymers (PMMA/PDMS) and
inorganic materials (graphene/h-BN substrate) to mechanically peel off PMMA
from graphene by the thermal shrinkage of polymers, leaving no PMMA residue on
the graphene surface. This method can be applied to all types of 2D layered
materials.


  Markov cohort state-transition models have been the standard approach for
simulating the prognosis of patients or, more generally, the life trajectories
of individuals over a time period. Current approaches for estimating the
variance of a Markov model using a Monte Carlo sampling or a master equation
representation are computationally expensive and analytically difficult to
express and solve. We introduce an alternative representation of a Markov model
in the form of a multinomial distribution. We derive this representation from
principles and then verify its veracity in a simulation exercise. This
representation provides an exact and fast approach to compute the variance and
a way to estimate transition probabilities in a Bayesian setting.


  We present a Rayleigh-Schroedinger-Goldstone perturbation formalism for many
fermion systems. Based on this formalism, variational perturbation scheme which
goes beyond the Gaussian approximation is developed. In order to go beyond the
Gaussian approximation, we identify a parent Hamiltonian which has an effective
Gaussian vacuum as a variational solution and carry out further perturbation
with respect to the renormalized interaction using Goldstone's expansion.
Perturbation rules for the ground state wavefunctional and energy are found.
Useful commuting relations between operators and the Gaussian wavefunctional
are also found, which could reduce the calculational efforts substantially. As
examples, we calculate the first order correction to the Gaussian
wavefunctional and the second order correction to the ground state of an
electron gas system with the Yukawa-type interaction.


  We report the discovery of transient radio emission from the nearby
optically-discovered TDE ASASSN-14li (distance of 90 Mpc), making it the first
typical TDE detected in the radio, and unambiguously pointing to the formation
of a non-relativistic outflow with a kinetic energy of $\approx
(4-10)\times10^{47}$ erg, a velocity of $\approx 12,000-36,000$ km s$^{-1}$,
and a mass of $\approx 3\times10^{-5}-7\times10^{-4}$ M$_{\odot}$. We show that
the outflow was ejected on 2014 August 11--25, in agreement with an independent
estimate of the timing of super-Eddington accretion based on the optical, UV,
and X-ray observations, and that the ejected mass corresponds to about $1-10\%$
of the mass accreted in the super-Eddington phase. The temporal evolution of
the radio emission also uncovers the circumnuclear density profile,
$\rho(R)\propto R^{-2.5}$ on a scale of about 0.01 pc, a scale that cannot be
probed via direct measurements even in the nearest SMBHs. Our discovery of
radio emission from the nearest well-studied TDE to date, with a radio
luminosity lower than all previous limits, indicates that non-relativistic
outflows are ubiquitous in TDEs, and that future, more sensitive, radio surveys
will uncover similar events.


  For a long time, it has been widely assumed that if the underlying laws of
nature are supersymmetric, supersymmetry is broken at a scale intermediate
between the weak scale and the Planck mass. The construction of realistic
models of dynamical supersymmetry breaking in which supersymmetry is broken at
a much lower scale, as well as a growing appreciation of the supersymmetric
flavor problem has reopened this question. After reviewing some ideas for
understanding the microscopic origin of the soft breaking parameters in the
context of string theory, I turn to low energy breaking. Independent of the
details of the underlying theory, events with photons and missing energy, like
the CDF $e^+e^-\gamma \gamma \not{E}_T$ event, are likely signals of low energy
breaking. I briefly review the predictions of the simplest model of low energy
supersymmetry breaking for the soft breaking parameters (MGM), and then ask
what sorts of generalizations are possible. It turns out that if all couplings
are weak, there are only a limited number of ways to modify the model.


  Every 4d $\mathcal{N} = 2$ SCFT $\mathcal{T}$ corresponds to an associated
VOA $\mathbb{V}(\mathcal{T})$, which is in general non-rational with a more
involved representation theory. Null states in $\mathbb{V}(\mathcal{T})$ can
give rise to non-trivial flavored modular differential equations, which must be
satisfied by the refined/flavored character of all the
$\mathbb{V}(\mathcal{T})$-modules. Taking some $A_1$ theories
$\mathcal{T}_{g,n}$ of class-$\mathcal{S}$ as examples, we construct the
flavored modular differential equations satisfied by the Schur index. We show
that three types of surface defect indices give rise to common solutions to
these differential equations, and therefore are sources of
$\mathbb{V}(\mathcal{T})$-module characters. These equations transform almost
covariantly under modular transformations, ensuring the presence of logarithmic
solutions which may correspond to characters of logarithmic modules.


  We establish the existence of static, classically-stable, winding solitons in
renormalizable three-dimensional gauge models, with topologically trivial
target space and vacuum manifold. They are prototypes for possible analogous
particle-like excitations in the higgs sector of the standard electroweak
theory.


  We investigate the well-known Loday-Quillen-Tsygan theorem, which calculates
the Lie algebra homology of the general linear algebra $\mathfrak{gl}(A)$ for
an associative algebra $A$ in terms of cyclic homology, and extend the proof to
bornological Lie algebra homology of Fr\'echet and LF-algebras. For Fr\'echet
spaces, this equals continuous Lie algebra homology. To this end we prepare
several statements about homological algebra of topological vector spaces, and
discuss when the differential of the bornological Hochschild and cyclic complex
are topological homomorphisms in the setting of Fr\'echet algebras. We apply
the results to the algebras of smooth functions on a smooth manifold and
compactly supported smooth functions on Euclidean space, and construct from a
local-to-global principle a Gelfand-Fuks-like spectral sequence which
calculates the stable part of bornological Lie algebra homology of nontrivial
gauge algebras. This complements results by Maier, Janssens and Wockel.


  The energy-momentum tensor coming from one-parameter effective Yang- Mills
theory is here used to describe the matter-energy content of the homogeneous
and isotropic Friedmann cosmology in its early stages. The behavior of all
solutions is examined. Particularly, it is shown that only solutions
corresponding to an open model allow the universe to evolve into an accelerated
expansion. This result appears as a possible mechanism for an inflationary
phase produced by a vector field. Further, depending on the value of some
parameters characterizing the system, the resulting models are classified as
singular or nonsingular.


  The stellar spectra from LAMOST Medium Resolution Survey can be used to
search for compact objects in binaries. The LAMOST DR10 catalog includes > 980,
000 targets with multiple medium resolution spectra. We select the targets with
large or rapid radial velocity variation, and obtained an input-sample of 1822
sources. We use light curves and spectra to identify and exclude eclipsing
binaries and double-lined spectroscopic binaries in the input-sample. We
finally derive a catalog of 89 candidates with well-folded radial velocity,
which are all single-lined spectroscopic binaries, indicating an unseen
companion residing in each system. The mass function of each system can be well
constrained based on the radial velocity curve. In our sample, 26 sources have
mass function higher than 0.1 $M_{\odot}$, among which 18 sources have
ellipsoidal type light curves. In our opinion, compact objects are likely
existent in all these 26 binaries, which are worth follow-up identification.


  We survey the theory of Muchnik (weak) and Medvedev (strong) degrees of
subsets of ${}^\omega\omega$ with particular attention to the degrees of
$\Pi^0_1$ subsets of ${}^\omega2$. Later sections present proofs, some more
complete than others, of the major results of the subject.


  Consider the optimal stopping problem of a one-dimensional diffusion with
positive discount. Based on Dynkin's characterization of the value as the
minimal excessive majorant of the reward and considering its Riesz
representation, we give an explicit equation to find the optimal stopping
threshold for problems with one-sided stopping regions, and an explicit formula
for the value function of the problem. This representation also gives light on
the validity of the smooth fit principle. The results are illustrated by
solving some classical problems, and also through the solution of: optimal
stopping of the skew Brownian motion, and optimal stopping of the sticky
Brownian motion, including cases in which the smooth fit principle fails.


  Driving behavior monitoring plays a crucial role in managing road safety and
decreasing the risk of traffic accidents. Driving behavior is affected by
multiple factors like vehicle characteristics, types of roads, traffic, but,
most importantly, the pattern of driving of individuals. Current work performs
a robust driving pattern analysis by capturing variations in driving patterns.
It forms consistent groups by learning compressed representation of time series
(Auto Encoded Compact Sequence) using a multi-layer seq-2-seq autoencoder and
exploiting hierarchical clustering along with recommending the choice of best
distance measure. Consistent groups aid in identifying variations in driving
patterns of individuals captured in the dataset. These groups are generated for
both train and hidden test data. The consistent groups formed using train data,
are exploited for training multiple instances of the classifier. Obtained
choice of best distance measure is used to select the best train-test pair of
consistent groups. We have experimented on the publicly available UAH-DriveSet
dataset considering the signals captured from IMU sensors (accelerometer and
gyroscope) for classifying driving behavior. We observe proposed method,
significantly outperforms the benchmark performance.


  In this paper, we first propose a single-species system with impulsive
effects on time scales and by establishing some new comparison theorems of
impulsive dynamic equations on time scales, we obtain sufficient conditions to
guarantee the permanence of the system. Then we prove a Massera type theorem
for impulsive dynamic equations on time scales and based on this theorem, we
establish a criterion for the existence and uniformly asymptotic stability of
unique positive almost periodic solution of the system. Finally, we give an
example to show the feasibility of our main results. Our example also shows
that the continuous time system and its corresponding discrete time system have
the same dynamics. Our results of this paper are completely new.


  We investigate the widths of the recently observed charmonium like resonances
X(3872), Z(4430) and Z_2(4250) using QCD sum rules. Extending previous analyses
regarding these states as diquark-antiquark states or molecules of D mesons, we
introduce the Breit-Wigner function in the pole term. We find that introducing
the width increases the mass at small Borel window region. Using the OPE up to
dimension eight, we find that the sum rules based on interpolating current with
molecular components give a stable Borel curve from which both the masses and
widths of these resonances can be well obtained. Thus the QCD sum rule approach
strongly favors the molecular description of these states.


  A tropical polynomial in nr variables divided into blocks of r variables
each, is r-symmetric, if it is invariant under the action of Sn that permutes
the blocks. For r=1 we call these tropical polynomials symmetric. We can define
r-symmetric and symmetric rational functions in a similar manner. In this paper
we identify generators for the sets of symmetric tropical polynomials and
rational functions. While r-symmetric tropical polynomials are not finitely
generated, we show that r-symmetric rational functions are and provide a list
of generators.


  A new covariant generalization of Einstein's general relativity is developed
which allows the existence of a term proportional to
$T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory
($T_{\alpha\beta}$ is the energy-momentum tensor). Consequently the relevant
field equations are different from general relativity only in the presence of
matter sources. In the case of a charged black hole, we find exact solutions
for the field equations. Applying this theory to a homogeneous and isotropic
space-time, we find that there is a maximum energy density $\rho_{\text{max}}$,
and correspondingly a minimum length $a_{\text{min}}$, at early universe. This
means that there is a bounce at early times and this theory avoids the
existence of an early time singularity. Moreover we show that this theory
possesses a true sequence of cosmological eras. Also, we argue that although in
the context of the standard cosmological model the cosmological constant
$\Lambda$ does not play any important role in the early times and becomes
important only after the matter dominated era, in this theory the "repulsive"
nature of the cosmological constant plays a crucial role at early times for
resolving the singularity.


  In 1962 E. H. Rauch established the existence of points in the moduli space
of Riemann surfaces not having a neighbourhood homeomorphic to a ball. These
points are called here topologically singular. We give a different proof of the
results of Rauch and also determine the topologically singular and non-singular
points in the branch locus of some equisymmetric families of Riemann surfaces.


  Material and product life cycles are based on complex value chains of
technology-specific elements. Resource strategy aspects of essential and
strategic raw materials have a direct impact on applications of new
functionalized materials or the development of novel products. Thus, an urgent
challenge of modern materials science is to obtain information about the supply
risk and environmental aspects of resource utilization, especially at an early
stage of basic research. Combining the fields of materials science, industrial
engineering and resource strategy enables a multidisciplinary research approach
to identify specific risks within the value chain, aggregated as the so-called
resource criticality. Here, we demonstrate a step-by-step criticality
assessment in the sector of basic materials research for multifunctional
hexagonal manganite YMnO3, which can be a candidate for future electronic
systems. Raw material restrictions can be quantitatively identified, even at
such an early stage of materials research, from eleven long-term indicators
including our new developed Sector Competition Index. This approach for
resource strategy for modern material science integrates two objective targets:
reduced supply risk and enhanced environmental sustainability of new
functionalized materials, showing drawbacks but also benefits towards a
sustainable materials research and development.


  Transporting objects using quadrotors with cables has been widely studied in
the literature. However, most of those approaches assume that the cables are
previously attached to the load by human intervention. In tasks where multiple
objects need to be moved, the efficiency of the robotic system is constrained
by the requirement of manual labor. Our approach uses a non-stretchable cable
connected to two quadrotors, which we call the catenary robot, that fully
automates the transportation task. Using the cable, we can roll and drag the
cuboid object (box) on planar surfaces. Depending on the surface type, we
choose the proper action, dragging for low friction, and rolling for high
friction. Therefore, the transportation process does not require any human
intervention as we use the cable to interact with the box without requiring
fastening. We validate our control design in simulation and with actual robots,
where we show them rolling and dragging boxes to track desired trajectories.


  Fermi arcs, i.e., surface states connecting topologically-distinct Weyl
points, represent a paradigmatic manifestation of the topological aspects of
Weyl physics. Here, we investigate a light-matter interface based on the
photonic counterpart of these states and we prove that it can lead to phenomena
with no analogue in other setups. First, we show how to image the Fermi arcs by
studying the spontaneous decay of one or many emitters coupled to the system's
border. Second, we demonstrate that the Fermi arc surface states can act as a
robust quantum link. To do that we exploit the negative refraction experienced
by these modes at the hinges of the system. Thanks to this mechanism a
circulatory photonic current is created which, depending on the occurrence of
revivals, yields two distinct regimes. In the absence of revivals, the surface
states behave as a dissipative chiral quantum channel enabling, e.g., perfect
quantum state transfer. In the presence of revivals, an effective off-resonant
cavity is induced, which leads to coherent emitter couplings that can entangle
them maximally. In addition to their fundamental interest, our findings
evidence the potential offered by the photonic Fermi arc light-matter
interfaces for the design of more robust quantum technologies.


  We propose a new type of leaf node for use in Symbolic Regression (SR) that
performs linear combinations of feature variables (LCF). These nodes can be
handled in three different modes -- an unsynchronized mode, where all LCFs are
free to change on their own, a synchronized mode, where LCFs are sorted into
groups in which they are forced to be identical throughout the whole
individual, and a globally synchronized mode, which is similar to the previous
mode but the grouping is done across the whole population. We also present two
methods of evolving the weights of the LCFs -- a purely stochastic way via
mutation and a gradient-based way based on the backpropagation algorithm known
from neural networks -- and also a combination of both. We experimentally
evaluate all configurations of LCFs in Multi-Gene Genetic Programming (MGGP),
which was chosen as baseline, on a number of benchmarks. According to the
results, we identified two configurations which increase the performance of the
algorithm.


  Several applications such as nuclear forensics, nuclear fuel cycle
simulations and sensitivity analysis require methods to quickly compute spent
fuel nuclide compositions for various irradiation histories. Traditionally,
this has been done by interpolating between one-group cross-sections that have
been pre-computed from nuclear reactor simulations for a grid of input
parameters, using fits such as Cubic Spline. We propose the use of Gaussian
Processes (GP) to create surrogate models, which not only provide nuclide
compositions, but also the gradient and estimates of their prediction
uncertainty. The former is useful for applications such as forward and inverse
optimization problems, the latter for uncertainty quantification applications.
For this purpose, we compare GP-based surrogate model performance with Cubic-
Spline-based interpolators based on infinite lattice simulations of a CANDU 6
nuclear reactor using the SERPENT 2 code, considering burnup and temperature as
input parameters. Additionally, we compare the performance of various grid
sampling schemes to quasirandom sampling based on the Sobol sequence. We find
that GP-based models perform significantly better in predicting spent fuel
compositions than Cubic-Spline-based models, though requiring longer
computational runtime. Furthermore, we show that the predicted nuclide
uncertainties are reasonably accurate. While in the studied two-dimensional
case, grid- and quasirandom sampling provide similar results, quasirandom
sampling will be a more effective strategy in higher dimensional cases.


  Deep near-IR images from the VISTA Variables in the V\'ia L\'actea (VVV)
Survey were used to search for RR Lyrae stars in the Southern Galactic plane. A
sizable sample of 404 RR Lyrae of type ab stars was identified across a thin
slice of the 4$^{\rm th}$ Galactic quadrant ($295\deg < l < 350\deg$,
$-2.24\deg < b < -1.05\deg$). The sample's distance distribution exhibits a
maximum density that occurs at the bulge tangent point, which implies that this
primarily Oosterhoff type I population of RRab stars does not trace the bar
delineated by their red clump counterparts. The bulge RR Lyrae population does
not extend beyond $l \sim340 \deg$, and the sample's spatial distribution
presents evidence of density enhancements and substructure that warrants
further investigation. Indeed, the sample may be employed to evaluate Galactic
evolution models, and is particularly lucrative since half of the discovered RR
Lyrae are within reach of Gaia astrometric observations.


  We investigate the wave packet dynamics and eigenstate localization in
recently proposed generalized lattice models whose low-energy dynamics mimics a
quantum field theory in (1+1)D curved spacetime with the aim of creating
systems analogous to black holes. We identify a critical slowdown of
zero-energy wave packets in a family of 1D tight-binding models with power-law
variation of the hopping parameter, indicating the presence of a horizon.
Remarkably, wave packets with non-zero energies bounce back and reverse
direction before reaching the horizon. We additionally observe a power-law
localization of all eigenstates, each bordering a region of exponential
suppression. These forbidden regions dictate the closest possible approach to
the horizon of states with any given energy. These numerical findings are
supported by a semiclassical description of the wave packet trajectories, which
are shown to coincide with the geodesics expected for the effective metric
emerging from the considered lattice models in the continuum limit.


  We investigate the distribution of the gas (ionized, neutral atomic and
molecular), and interstellar dust in the complex star forming region NGC6357
with the goal of studying the interplay between the massive stars in the open
cluster Pis24 and the surrounding interstellar matter. Our study of the
distribution of the ionized gas is based on narrow-band Hhalfa, [SII], and
[OIII] images obtained with the Curtis-Schmidt Camera at CTIO, Chile, and on
radio continuum observations at 1465 MHz taken with the VLA with a synthesized
beam of 40 arcsec. The distribution of the molecular gas is analyzed using
12CO(1-0) data obtained with the Nanten radiotelescope, Chile (angular
resolution = 2.7 arcmin). The interstellar dust distribution was studied using
mid-infrared data from the GLIMPSE survey and far-infrared observations from
IRAS. NGC6357 consists of a large ionized shell and a number of smaller optical
nebulosities. The optical, radio continuum, and near- and mid-IR images
delineate the distributions of the ionized gas and interstellar dust in the HII
regions and in previously unknown wind blown bubbles linked to the massive
stars in Pis24 revealing surrounding photodissociation regions. The CO line
observations allowed us to identify the molecular counterparts of the ionized
structures in the complex and to confirm the presence of photodissociation
regions. The action of the WR star HD157504 on the surrounding gas was also
investigated. The molecular mass in the complex is estimated to be (4+/-2)X10^5
Mo. Mean electron densities derived from the radio data suggest electron
densities > 200 cm^-3, indicating that NGC6357 is a complex formed in a region
of high ambient density. The known massive stars in Pis24 and a number of newly
inferred massive stars are mainly responsible for the excitation and
photodissociation of the parental molecular cloud.


  We discuss the problems of dark matter, quantum gravity, and vacuum energy
within the context of a theory for which Lorentz invariance is not postulated,
but instead emerges as a natural consequence in the physical regimes where it
has been tested.


  We investigate when a skew polynomial extension T = R[x; {\sigma}, {\delta}]
of a Hopf algebra R admits a Hopf algebra structure, substantially generalising
a theorem of Panov. When this construction is applied iteratively in
characteristic 0 one obtains a large family of connected noetherian Hopf
algebras of finite Gelfand-Kirillov dimension, including for example all
enveloping algebras of finite dimensional solvable Lie algebras and all
coordinate rings of unipotent groups. The properties of these Hopf algebras are
investigated.


  A wide variety of approaches to estimate the degree of synchrony between two
or more spike trains have been proposed. One of the most recent methods is the
ISI-distance which extracts information from the interspike intervals (ISIs) by
evaluating the ratio of the instantaneous firing rates. In contrast to most
previously proposed measures it is parameter free and time-scale independent.
However, it is not well suited to track changes in synchrony that are based on
spike coincidences. Here we propose the SPIKE-distance, a complementary measure
which is sensitive to spike coincidences but still shares the fundamental
advantages of the ISI-distance. In particular, it is easy to visualize in a
time-resolved manner and can be extended to a method that is also applicable to
larger sets of spike trains. We show the merit of the SPIKE-distance using both
simulated and real data.


  We suggest two new scenarios of high-energy particle collisions in the
background of a wormhole. In scenario 1 the novelty consists in that the effect
does not require two particles coming from different mouths. Instead, all such
scenarios of high energy collisions develop, when an experimenter sends
particles towards a wormhole from the same side of the throat. For static
wormholes, this approach leads to indefinitely large energy in the center of
mass. For rotating wormholes, it makes possible the super-Penrose process
(unbounded energies measured at infinity). In scenario 2, one of colliding
particles oscillates near the wormhole throat from the very beginning. In this
sense, scenario 2 is intermediate between the standard one and scenario 1 since
the particle under discussion does not come from infinity at all.


  Bayesian inference is a principled framework for dealing with uncertainty.
The practitioner can perform an initial assumption for the physical phenomenon
they want to model (prior belief), collect some data and then adjust the
initial assumption in the light of the new evidence (posterior belief).
Approximate Bayesian Computation (ABC) methods, also known as likelihood-free
inference techniques, are a class of models used for performing inference when
the likelihood is intractable. The unique requirement of these models is a
black-box sampling machine. Due to the modelling-freedom they provide these
approaches are particularly captivating. Robust Optimisation Monte Carlo (ROMC)
is one of the most recent techniques of the specific domain. It approximates
the posterior distribution by solving independent optimisation problems. This
dissertation focuses on the implementation of the ROMC method in the software
package Engine for Likelihood-Free Inference (ELFI). In the first chapters, we
provide the mathematical formulation and the algorithmic description of the
ROMC approach. In the following chapters, we describe our implementation; (a)
we present all the functionalities provided to the user and (b) we demonstrate
how to perform inference on some real examples. Our implementation provides a
robust and efficient solution to a practitioner who wants to perform inference
on a simulator-based model. Furthermore, it exploits parallel processing for
accelerating the inference wherever it is possible. Finally, it has been
designed to serve extensibility; the user can easily replace specific subparts
of the method without significant overhead on the development side. Therefore,
it can be used by a researcher for further experimentation.


  We study the influence of a perpendicular magnetic field with the asymptotics
$B(r\to \infty)= B_0$ in a electrons in graphene. It is shown that the
zero-energy solutions can exist only for one pseudospin direction, depending on
the sign of the magnetic field in the infinite boundary. This, shows that
zero-energy level is robust with respect to possible inhomogeneities of the
magnetic field. In addition, we show that the number of the states with zero
energy for one pseudospin projection is infinity. These results should be
useful in the study of ripples which cause a scattering of Dirac particles in
slowly decreasing magnetic fields where the asymptotic states is easy to
define.


  Yuan's theorem of the alternative is an important theoretical tool in
optimization, which provides a checkable certificate for the infeasibility of a
strict inequality system involving two homogeneous quadratic functions. In this
paper, we provide a tractable extension of Yuan's theorem of the alternative to
the symmetric tensor setting. As an application, we establish that the optimal
value of a class of nonconvex polynomial optimization problems with suitable
sign structure (or more explicitly, with essentially non-positive coefficients)
can be computed by a related convex conic programming problem, and the optimal
solution of these nonconvex polynomial optimization problems can be recovered
from the corresponding solution of the convex conic programming problem.
Moreover, we obtain that this class of nonconvex polynomial optimization
problems enjoy exact sum-of-squares relaxation, and so, can be solved via a
single semidefinite programming problem.


  We present a new algebraic description of the dual $K$-theoretic $P$-function
$gq_\lambda$ and the dual $K$-theoretic $Q$-function $gp_\lambda$. Using a
``$\beta$-deformed version'' of the boson-fermion correspondence, these
functions are realized as the bosonic counterparts to certain bases of the
neutral fermion Fock space. This result generalizes Date-Jimbo-Miwa's
neutral-fermionic presentation of the Schur $P$-function and the $Q$-function,
developed in their study of the BKP-equation. As a corollary, we derive a
generating function of $gq_\lambda$, which was previously conjectured by
Nakagawa-Naruse. Additionally, we provide a generating function of
$gp_\lambda$.


  To protect themselves from attacks, networks need to enforce ingress
filtering, i.e., block inbound packets sent from spoofed IP addresses. Although
this is a widely known best practice, it is still not clear how many networks
do not block spoofed packets. Inferring the extent of spoofability at Internet
scale is challenging and despite multiple efforts the existing studies
currently cover only a limited set of the Internet networks: they can either
measure networks that operate servers with faulty network-stack
implementations, or require installation of the measurement software on
volunteer networks, or assume specific properties, like traceroute loops.
Improving coverage of the spoofing measurements is critical.
  In this work we present the Spoofing Mapper (SMap): the first scanner for
performing Internet-wide studies of ingress filtering. SMap evaluates
spoofability of networks utilising standard protocols that are present in
almost any Internet network. We applied SMap for Internet-wide measurements of
ingress filtering: we found that 69.8% of all the Autonomous Systems (ASes) in
the Internet do not filter spoofed packets and found 46880 new spoofable ASes
which were not identified in prior studies. Our measurements with SMap provide
the first comprehensive view of ingress filtering deployment in the Internet as
well as remediation in filtering spoofed packets over a period of two years
until May 2021.
  We set up a web service at https://smap.cad.sit.fraunhofer.de to perform
continual Internet-wide data collection with SMap and display statistics from
spoofing evaluation. We make our datasets as well as the SMap (implementation
and the source code) publicly available to enable researchers to reproduce and
validate our results, as well as to continually keep track of changes in
filtering spoofed packets in the Internet.


  To overcome the sim-to-real gap in reinforcement learning (RL), learned
policies must maintain robustness against environmental uncertainties. While
robust RL has been widely studied in single-agent regimes, in multi-agent
environments, the problem remains understudied -- despite the fact that the
problems posed by environmental uncertainties are often exacerbated by
strategic interactions. This work focuses on learning in distributionally
robust Markov games (RMGs), a robust variant of standard Markov games, wherein
each agent aims to learn a policy that maximizes its own worst-case performance
when the deployed environment deviates within its own prescribed uncertainty
set. This results in a set of robust equilibrium strategies for all agents that
align with classic notions of game-theoretic equilibria. Assuming a
non-adaptive sampling mechanism from a generative model, we propose a
sample-efficient model-based algorithm (DRNVI) with finite-sample complexity
guarantees for learning robust variants of various notions of game-theoretic
equilibria. We also establish an information-theoretic lower bound for solving
RMGs, which confirms the near-optimal sample complexity of DRNVI with respect
to problem-dependent factors such as the size of the state space, the target
accuracy, and the horizon length.


  This work presents the design, hardware realization, autonomous exploration
and object detection capabilities of RMF-Owl, a new collision-tolerant aerial
robot tailored for resilient autonomous subterranean exploration. The system is
custom built for underground exploration with focus on collision tolerance,
resilient autonomy with robust localization and mapping, alongside
high-performance exploration path planning in confined, obstacle-filled and
topologically complex underground environments. Moreover, RMF-Owl offers the
ability to search, detect and locate objects of interest which can be
particularly useful in search and rescue missions. A series of results from
field experiments are presented in order to demonstrate the system's ability to
autonomously explore challenging unknown underground environments.


  Under Gromov--Hausdorff convergence, and equivariant Gromov--Hausdorff
convergence, we prove stability results of Wasserstein spaces over certain
classes of singular and non-singular spaces. For example, we obtain an analogue
of Perelman's stability theorem on Wasserstein spaces.


  In Part I, we defined a LASSO condition number and developed an algorithm --
for computing support sets (feature selection) of the LASSO minimisation
problem -- that runs in polynomial time in the number of variables and the
logarithm of the condition number. The algorithm is trustworthy in the sense
that if the condition number is infinite, the algorithm will run forever and
never produce an incorrect output. In this Part II article, we demonstrate how
finite precision algorithms (for example algorithms running floating point
arithmetic) will fail on open sets when the condition number is large -- but
still finite. This augments Part I's result: If an algorithm takes inputs from
an open set that includes at least one point with an infinite condition number,
it fails to compute the correct support set for all inputs within that set.
Hence, for any finite precision algorithm working on open sets for the LASSO
problem with random inputs, our LASSO condition number -- as a random variable
-- will estimate the probability of success/failure of the algorithm. We show
that a finite precision version of our algorithm works on traditional Gaussian
data for LASSO with high probability. The algorithm is trustworthy,
specifically, in the random cases where the algorithm fails, it will not
produce an output. Finally, we demonstrate classical random ensembles for which
the condition number will be large with high probability, and hence where any
finite precision algorithm on open sets will fail. We show numerically how
commercial software fails on these cases.


  Steric effect in the threshold dissociative ionizations of serine conformers
[CH2OH-C\alphaH(NH2)-C\betaOOH] is revealed by high-level ab initio
calculations combined with our newly developed infrared laser desorption /
tunable VUV photoionization mass spectrometry. We find that near the ionization
thresholds the C\alpha-C\beta and C\alpha-C bonds are selectively broken for
the respective cationic conformers, yielding the different fragments. Novel
dynamic processes, proton transfer and reorientation between the
predissociative fragments, are involved in the threshold photoionization
dissociations.


  The ground state of the $S=1/2$ $J_{1}-J_{1}$ Heisenberg model on the 2D
square lattice with arbitrary signs of exchange constants is considered. States
with different spin long-range order types (antiferromagnetic checkerboard,
stripe, collinear ferromagnetic) as well as disordered spin-liquid states are
described in the frames of one and the same analytical approach. It is shown
inter alia, that the phase transition between ferromagnetic spin liquid and
long-range order ferromagnet is a second-order one. On the ordered side of the
transition the ferromagnetic state with rapidly varying condensate function is
detected.


  We prove that for every bounded linear operator $T:X\to X$, where $X$ is a
non-reflexive quotient of a von Neumann algebra, the point spectrum of $T^*$ is
non-empty (i.e. for some $\lambda\in\mathbb C$ the operator $\lambda I-T$ fails
to have dense range.) In particular, and as an application, we obtain that such
a space cannot support a topologically transitive operator.


  Numba is a game-changing compiler for high-performance computing with Python.
It produces machine code that runs outside of the single-threaded Python
interpreter and that fully utilizes the resources of modern CPUs. This means
support for parallel multithreading and auto vectorization if available, as
with compiled languages such as C++ or Fortran. In this article we document our
experience developing PyExaFMM, a multithreaded Numba implementation of the
Fast Multipole Method, an algorithm with a non-linear data structure and a
large amount of data organization. We find that designing performant Numba code
for complex algorithms can be as challenging as writing in a compiled language.


  Deploying Large Language Models (LLMs) on edge or mobile devices offers
significant benefits, such as enhanced data privacy and real-time processing
capabilities. However, it also faces critical challenges due to the substantial
memory requirement of LLMs. Quantization is an effective way of reducing the
model size while maintaining good performance. However, even after
quantization, LLMs may still be too big to fit entirely into the limited memory
of edge or mobile devices and have to be partially loaded from the storage to
complete the inference. In this case, the I/O latency of model loading becomes
the bottleneck of the LLM inference latency. In this work, we take a
preliminary step of studying applying data compression techniques to reduce
data movement and thus speed up the inference of quantized LLM on
memory-constrained devices. In particular, we discussed the compressibility of
quantized LLMs, the trade-off between the compressibility and performance of
quantized LLMs, and opportunities to optimize both of them jointly.


  In this paper we derive the bi-orthogonality relations, diagonal term
evaluations and evaluation formulas for the non-symmetric Koornwinder
polynomials. For the derivation we use certain representations of the (double)
affine Hecke algebra which were originally defined by Noumi and Sahi. The
structure of the diagonal terms is clarified by expressing them as residues of
the bi-orthogonality weight function. We furthermore give the explicit
connection between the non-symmetric and the (anti-)symmetric theory.


  Deep learning-solutions for hand-object 3D pose and shape estimation are now
very effective when an annotated dataset is available to train them to handle
the scenarios and lighting conditions they will encounter at test time.
Unfortunately, this is not always the case, and one often has to resort to
training them on synthetic data, which does not guarantee that they will work
well in real situations. In this paper, we introduce an effective approach to
addressing this challenge by exploiting 3D geometric constraints within a cycle
generative adversarial network (CycleGAN) to perform domain adaptation.
Furthermore, in contrast to most existing works, which fail to leverage the
rich temporal information available in unlabeled real videos as a source of
supervision, we propose to enforce short- and long-term temporal consistency to
fine-tune the domain-adapted model in a self-supervised fashion. We will
demonstrate that our approach outperforms state-of-the-art 3D hand-object joint
reconstruction methods on three widely-used benchmarks and will make our code
publicly available.


  This note makes an observation that significantly simplifies a number of
previous parallel, two-way merge algorithms based on binary search and
sequential merge in parallel. First, it is shown that the additional merge step
of distinguished elements as found in previous algorithms is not necessary,
thus simplifying the implementation and reducing constant factors. Second, by
fixating the requirements to the binary search, the merge algorithm becomes
stable, provided that the sequential merge subroutine is stable. The stable,
parallel merge algorithm can easily be used to implement a stable, parallel
merge sort.
  For ordered sequences with $n$ and $m$ elements, $m\leq n$, the simplified
merge algorithm runs in $O(n/p+\log n)$ operations using $p$ processing
elements. It can be implemented on an EREW PRAM, but since it requires only a
single synchronization step, it is also a candidate for implementation on other
parallel, shared-memory computers.


  We present the science case and observations plan of the MeerKAT Fornax
Survey, an HI and radio continuum survey of the Fornax galaxy cluster to be
carried out with the SKA precursor MeerKAT. Fornax is the second most massive
cluster within 20 Mpc and the largest nearby cluster in the southern
hemisphere. Its low X-ray luminosity makes it representative of the environment
where most galaxies live and where substantial galaxy evolution takes place.
Fornax's ongoing growth makes it an excellent laboratory for studying the
assembly of clusters, the physics of gas accretion and stripping in galaxies
falling in the cluster, and the connection between these processes and the
neutral medium in the cosmic web.
  We will observe a region of 12 deg$^2$ reaching a projected distance of 1.5
Mpc from the cluster centre. This will cover a wide range of environment
density out to the outskirts of the cluster, where gas-rich in-falling groups
are found. We will: study the HI morphology of resolved galaxies down to a
column density of a few times 1e+19 cm$^{-2}$ at a resolution of 1 kpc; measure
the slope of the HI mass function down to M(HI) 5e+5 M(sun); and attempt to
detect HI in the cosmic web reaching a column density of 1e+18 cm$^{-2}$ at a
resolution of 10 kpc.


  Language models (LMs) are trained on collections of documents, written by
individual human agents to achieve specific goals in an outside world. During
training, LMs have access only to text of these documents, with no direct
evidence of the internal states of the agents that produced them -- a fact
often used to argue that LMs are incapable of modeling goal-directed aspects of
human language production and comprehension. Can LMs trained on text learn
anything at all about the relationship between language and use? I argue that
LMs are models of intentional communication in a specific, narrow sense. When
performing next word prediction given a textual context, an LM can infer and
represent properties of an agent likely to have produced that context. These
representations can in turn influence subsequent LM generation in the same way
that agents' communicative intentions influence their language. I survey
findings from the recent literature showing that -- even in today's non-robust
and error-prone models -- LMs infer and use representations of fine-grained
communicative intentions and more abstract beliefs and goals. Despite the
limited nature of their training data, they can thus serve as building blocks
for systems that communicate and act intentionally.


  This paper presents efficient algorithms for testing the finite, polynomial,
and exponential ambiguity of finite automata with $\epsilon$-transitions. It
gives an algorithm for testing the exponential ambiguity of an automaton $A$ in
time $O(|A|_E^2)$, and finite or polynomial ambiguity in time $O(|A|_E^3)$.
These complexities significantly improve over the previous best complexities
given for the same problem. Furthermore, the algorithms presented are simple
and are based on a general algorithm for the composition or intersection of
automata. We also give an algorithm to determine the degree of polynomial
ambiguity of a finite automaton $A$ that is polynomially ambiguous in time
$O(|A|_E^3)$. Finally, we present an application of our algorithms to an
approximate computation of the entropy of a probabilistic automaton.


  The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.


  The nonlinear photon-photon interaction mediated by a single two-level atom
is studied theoretically based on a one-dimensional model of the field-atom
interaction. This model allows us to determine the effects of an atomic
nonlinearity on the spatiotemporal coherence of a two photon state.
Specifically, the complete two photon output wave function can be obtained for
any two photon input wave function. It is shown that the quantum interference
between the components of the output state associated with different
interaction processes causes bunching and anti-bunching in the two photon
statistics. This theory may be useful for various applications in photon
manipulation, e.g. quantum information processing using photonic qubits,
quantum nondemolition measurements, and the generation of entangled photons.


  We present an open-source differentiable acoustic simulator, j-Wave, which
can solve time-varying and time-harmonic acoustic problems. It supports
automatic differentiation, which is a program transformation technique that has
many applications, especially in machine learning and scientific computing.
j-Wave is composed of modular components that can be easily customized and
reused. At the same time, it is compatible with some of the most popular
machine learning libraries, such as JAX and TensorFlow. The accuracy of the
simulation results for known configurations is evaluated against the widely
used k-Wave toolbox and a cohort of acoustic simulation software. j-Wave is
available from https://github.com/ucl-bug/jwave.


  In the thirty years since the end of real socialism, Bulgaria's went from
having a rather radically 'different' tax system to adopting flat-rate taxation
with marginal tax rates that fell from figures as high as 40% to 10% for both
the corporate-income tax and the personal-income tax. Crucially, the
econometric forecasting models in use at the Bulgarian Ministry of Finance
hinted at an increase in tax revenue compatible with the so-called 'Laffer
curve'. Similarly, many economists held the view that revenues would have
increased. However, reality fell short of those expectations based on
forecasting models and rooted in mainstream economic theory. Thus, this paper
asks whether there are betterperforming forecasting models for personal-and
corporate-income tax-revenues in Bulgaria that are readily implementable and
overperform the ones currently in use. After articulating a constructive
critique of the current forecasting models, the paper offers readily
implementable, transparent alternatives and proves their superiority.


  The class of self-nested trees presents remarkable compression properties
because of the systematic repetition of subtrees in their structure. In this
paper, we provide a better combinatorial characterization of this specific
family of trees. In particular, we show from both theoretical and practical
viewpoints that complex queries can be quickly answered in self-nested trees
compared to general trees. We also present an approximation algorithm of a tree
by a self-nested one that can be used in fast prediction of edit distance
between two trees.


  The challenge of communication-efficient distributed optimization has
attracted attention in recent years. In this paper, a communication efficient
algorithm, called ordering-based alternating direction method of multipliers
(OADMM) is devised in a general fully decentralized network setting where a
worker can only exchange messages with neighbors. Compared to the classical
ADMM, a key feature of OADMM is that transmissions are ordered among workers at
each iteration such that a worker with the most informative data broadcasts its
local variable to neighbors first, and neighbors who have not transmitted yet
can update their local variables based on that received transmission. In OADMM,
we prohibit workers from transmitting if their current local variables are not
sufficiently different from their previously transmitted value. A variant of
OADMM, called SOADMM, is proposed where transmissions are ordered but
transmissions are never stopped for each node at each iteration. Numerical
results demonstrate that given a targeted accuracy, OADMM can significantly
reduce the number of communications compared to existing algorithms including
ADMM. We also show numerically that SOADMM can accelerate convergence,
resulting in communication savings compared to the classical ADMM.


  We study Hecke algebras for pairs $({\mathfrak g},K)$ over arbitrary fields
$E$ of characteristic $0$, define the Bernstein functor and give another
definition of the Zuckerman functor over $E$. Building on this and the author's
previous work on rational structures on automorphic representations, we show
that hard duality remains valid over $E$ and apply this result to the study of
rationality properties of Sun's cohomologically induced functionals. Our main
application are period relations for the special values of standard
$L$-functions of automorphic representations of $\mathrm{GL}(2n)$ admitting
Shalika models.


  In line with a recent proposal for the study of asymptotic gravitational
charges, we investigate higher derivative asymptotic charges. We show that the
higher derivative BMS charges are related to the two-derivative BMS charges.
Significantly, we find that internal Lorentz transformations are relevant in
the higher derivative case in contrast to the two-derivative case. We give a
prescription for their precise definition and derive the associated charges,
finding, again, a relation with two-derivative BMS charges.


  Brown Dwarf atmosphere are a chemically extremely rich, one example being the
formation of clouds driven by the phase-non-equilibrium of the atmospheric gas.
Cloud formation modelling is an integral part of any atmosphere simulation used
to interpret spectral observations of ultra-cool objects and to determine
fundamental parameters like log(g) and Teff. This proceeding to the workshop
'GAIA and the Unseen: The Brown Dwarf Question' first summarizes what a model
atmosphere simulation is, and then advocates two ideas: A) The use of a
multitude of model families to determine fundamental parameters with realistic
confidence interval. B) To keep an eye on the unexpected, like for example,
ionisation signatures resulting plasma processes


  Magnetic field-induced giant modification of the probabilities of five
transitions of $5S_{1/2}, F_g=2 \rightarrow 5P_{3/2}, F_e=4$ of $^{85}$Rb and
three transitions of $5S_{1/2}, F_g=1 \rightarrow 5P_{3/2}, F_e=3$ of $^{87}$Rb
forbidden by selection rules for zero magnetic field has been observed
experimentally and described theoretically for the first time. For the case of
excitation with circularly-polarized ($\sigma^+$) laser radiation, the
probability of $F_g=2, ~m_F=-2 \rightarrow F_e=4, ~m_F=-1$ transition becomes
the largest among the seventeen transitions of $^{85}$Rb $F_g=2 \rightarrow
F_e=1,2,3,4$ group, and the probability of $F_g=1,~m_F=-1 \rightarrow
F_e=3,~m_F=0$ transition becomes the largest among the nine transitions of
$^{87}$Rb $F_g=1 \rightarrow F_e=0,1,2,3$ group, in a wide range of magnetic
field 200 -- 1000 G. Complete frequency separation of individual Zeeman
components was obtained by implementation of derivative selective reflection
technique with a 300 nm-thick nanocell filled with Rb, allowing formation of
narrow optical resonances. Possible applications are addressed. The theoretical
model is perfectly consistent with the experimental results.


  We propose a scheme for entangling two photons via the quantum Zeno effect,
which describes the inhibition of quantum evolution by frequent measurements
and is based on the difference between summing amplitudes and probabilities.
For a given error probability $P_{\rm error}$, our scheme requires that the
one-photon loss rate $\xi_{1\gamma}$ and the two-photon absorption rate
$\xi_{2\gamma}$ in some medium satisfy $\xi_{1\gamma}/\xi_{2\gamma}=2P_{\rm
error}^2/\pi^2$, which is significantly improved in comparison to previous
approaches. Again based on the quantum Zeno effect, as well as coherent
excitations, we present a possibility to fulfill this requirement in an
otherwise linear optics set-up.


  Developing deep learning models for resource-constrained Internet-of-Things
(IoT) devices is challenging, as it is difficult to achieve both good quality
of results (QoR), such as DNN model inference accuracy, and quality of service
(QoS), such as inference latency, throughput, and power consumption. Existing
approaches typically separate the DNN model development step from its
deployment on IoT devices, resulting in suboptimal solutions. In this paper, we
first introduce a few interesting but counterintuitive observations about such
a separate design approach, and empirically show why it may lead to suboptimal
designs. Motivated by these observations, we then propose a novel and practical
bi-directional co-design approach: a bottom-up DNN model design strategy
together with a top-down flow for DNN accelerator design. It enables a joint
optimization of both DNN models and their deployment configurations on IoT
devices as represented as FPGAs. We demonstrate the effectiveness of the
proposed co-design approach on a real-life object detection application using
Pynq-Z1 embedded FPGA. Our method obtains the state-of-the-art results on both
QoR with high accuracy (IoU) and QoS with high throughput (FPS) and high energy
efficiency.


  Recent Transformer-based diffusion models have shown remarkable performance,
largely attributed to the ability of the self-attention mechanism to accurately
capture both global and local contexts by computing all-pair interactions among
input tokens. However, their quadratic complexity poses significant
computational challenges for long-sequence inputs. Conversely, a recent state
space model called Mamba offers linear complexity by compressing a filtered
global context into a hidden state. Despite its efficiency, compression
inevitably leads to information loss of fine-grained local dependencies among
tokens, which are crucial for effective visual generative modeling. Motivated
by these observations, we introduce Local Attentional Mamba (LaMamba) blocks
that combine the strengths of self-attention and Mamba, capturing both global
contexts and local details with linear complexity. Leveraging the efficient
U-Net architecture, our model exhibits exceptional scalability and surpasses
the performance of DiT across various model scales on ImageNet at 256x256
resolution, all while utilizing substantially fewer GFLOPs and a comparable
number of parameters. Compared to state-of-the-art diffusion models on ImageNet
256x256 and 512x512, our largest model presents notable advantages, such as a
reduction of up to 62\% GFLOPs compared to DiT-XL/2, while achieving superior
performance with comparable or fewer parameters.


  Information sharing among organizations has been gaining attention as a
method for improving cybersecurity. However, the associated disclosure costs
act as deterrents for firms' voluntary cooperation. In this work, we take a
game-theoretic approach to understanding firms' incentives in these agreements.
We propose the design of inter-temporal incentives (i.e. conditioning future
cooperation on past interactions). Specifically, we show that incentives for
full cooperation can be designed if firms share their private assessments of
other firms' disclosure decisions through a common communication platform. We
further show that similar incentives can be designed based on outcomes of a
public rating/assessment system.


  We find exact solitons in a large class of noncommutative gauge theories
using a simple solution generating technique. The solitons in the effective
field theory description of open string field theory are interpreted as
D-branes for any value of the noncommutativity. We discuss the vacuum structure
of open string field theory in view of our results.


  We demonstrate experimentally an air-slot mode-gap photonic crystal cavity
with quality factor of 15,000 and modal volume of 0.02 cubic wavelengths, based
on the design of an air-slot in a width-modulated line-defect in a photonic
crystal slab. The origin of the high Q air-slot cavity mode is the mode-gap
effect from the slotted photonic crystal waveguide mode with negative
dispersion. The high Q cavities with ultrasmall mode volume are important for
applications such as cavity quantum electrodynamics, nonlinear optics and
optical sensing.


  By adding generalizations involving translations, the machinery of the
quantum theory of free fields leads to the semiclassical equations of motion
for a charged massive particle in electromagnetic and gravitational fields.
With the particle field translated along one displacement, particle states are
translated along a possibly different displacement. Arbitrary phase results.
And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when
field and states are translated. It is shown that a path of extreme phase obeys
a semiclassical equation for force with derived terms that can describe
electromagnetism and gravitation.


  We analyze the onset and initial expansion of the 2018 Martian Global Dust
Storm (GDS 2018) using ground-based images in the visual range. This is the
first case of a confirmed GDS initiating in the Northern Hemisphere. A dusty
area extending about 1.4x10e5 km^2 and centered at latitude +31.7{\deg} $\pm$
1.8{\deg} and west longitude 18{\deg} $\pm$ 5{\deg}W in Acidalia Planitia was
captured on 30 and 31 May 2018 (Ls = 184.9{\deg}). From 1 to 8 June, daily
image series showed the storm expanding southwards along the Acidalia corridor
with velocities of 5 m/s, and simultaneously progressing eastwards and
westwards with horizontal velocities ranging from 5 to 40 m/s. By 8 June the
dust reached latitude -55{\deg} and later penetrated in the South polar region,
whereas in the North the dust progression stopped at latitude +46{\deg}. We
compare the onset and expansion stage of this GDS with the previous confirmed
storms.


  We demonstrate a two-pulse Ramsey-type interferometer for non-classical
motional states of a Bose-Einstein condensate in an anharmonic trap. The
control pulses used to manipulate the condensate wavefunction are obtained from
Optimal Control Theory and directly optimised to maximise the interferometric
contrast. They permit a fast manipulation of the atomic ensemble compared to
the intrinsic decay and many-body dephasing effects, and thus to reach an
interferometric contrast of 92% in the experimental implementation.


  Data-driven approaches to assist operating room (OR) workflow analysis depend
on large curated datasets that are time consuming and expensive to collect. On
the other hand, we see a recent paradigm shift from supervised learning to
self-supervised and/or unsupervised learning approaches that can learn
representations from unlabeled datasets. In this paper, we leverage the
unlabeled data captured in robotic surgery ORs and propose a novel way to fuse
the multi-modal data for a single video frame or image. Instead of producing
different augmentations (or 'views') of the same image or video frame which is
a common practice in self-supervised learning, we treat the multi-modal data as
different views to train the model in an unsupervised manner via clustering. We
compared our method with other state of the art methods and results show the
superior performance of our approach on surgical video activity recognition and
semantic segmentation.


  For a class of manifolds that includes quotients of real hyperbolic space by
a convex co-compact discrete group, we show that the resonances of the
meromorphically continued resolvent kernel for the Laplacian coincide, with
multiplicities, with the poles of the meromorphically continued scattering
operator. In order to carry out the proof, we use Shmuel Agmon's perturbation
theory of resonances to show that both resolvent resonances and scattering
poles are simple for generic potential perturbations.


  Mixing theoretical topological structures with cutting-edge simulation
methods, a recent study in Nature Communications has finally confirmed the
existence of topological defects in glasses and their crucial role for
plasticity.


  The structure and thermodynamic state of a system changes under the influence
of external electric fields. Neutral systems are characterized by their
dielectric constant epsilon, while charged ones also by their charge
distribution. In this Colloquium several phenomena occurring in soft-matter
systems in spatially uniform and nonuniform fields are surveyed and the role of
the conductivity sigma and the linear or nonlinear dependency of epsilon on
composition are identified. Uniform electric fields are responsible for
elongation of droplets, for destabilization of interfaces between two liquids,
and for mixing effects in liquid mixtures. Electric fields, when acting on
phases with mesoscopic order, also give rise to block copolymer orientation, to
destabilization of polymer-polymer interfaces, and to order-order phase
transitions. The role of linear and nonlinear dependences of epsilon on
composition will be elucidated in these systems. In addition to the dielectric
anisotropy, existence of a finite conductivity leads to appearance of large
stresses when these systems are subject to external fields and usually to a
reduction in the voltages required for the instabilities or phase transitions
to occur. Finally, phase transitions which occur in nonuniform fields are
described and emphasis on the importance of epsilon and sigma is given.


  Social learning algorithms provide models for the formation of opinions over
social networks resulting from local reasoning and peer-to-peer exchanges.
Interactions occur over an underlying graph topology, which describes the flow
of information and relative influence between pairs of agents. For a given
graph topology, these algorithms allow for the prediction of formed opinions.
In this work, we study the inverse problem. Given a social learning model and
observations of the evolution of beliefs over time, we aim at identifying the
underlying graph topology. The learned graph allows for the inference of
pairwise influence between agents, the overall influence agents have over the
behavior of the network, as well as the flow of information through the social
network. The proposed algorithm is online in nature and can adapt dynamically
to changes in the graph topology or the true hypothesis.


  We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator
on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a
(suitably weighted) graph Laplace operator of a proximity graph on an
epsilon-net.


  Joint replacement is the most common inpatient surgical treatment in the US.
We investigate the clinical pathway optimization for knee replacement, which is
a sequential decision process from onset to recovery. Based on episodic claims
from previous cases, we view the pathway optimization as an intelligence
crowdsourcing problem and learn the optimal decision policy from data by
imitating the best expert at every intermediate state. We develop a
reinforcement learning-based pipeline that uses value iteration, state
compression and aggregation learning, kernel representation and cross
validation to predict the best treatment policy. It also provides forecast of
the clinical pathway under the optimized policy. Empirical validation shows
that the optimized policy reduces the overall cost by 7 percent and reduces the
excessive cost premium by 33 percent.


  We have studied ultraviolet images of 40 Green Pea galaxies and 15 local
Lyman Break Galaxy Analogs to understand the relation between Ly$\alpha$ photon
escape and central UV photometric properties. We measured star formation
intensity (SFI, star formation rate per unit area) from the central 250 pc
region ($S_{\rm 250pc}$) using COS/NUV images from the \textit{Hubble Space
Telescope}. The measured $S_{\rm 250pc}$ of our sample Green Peas ranges from
2.3--46 $M_{\odot} \ \rm{year}^{-1} \ \rm{kpc^{-2}}$, with a geometric mean of
$15 M_{\odot} \ \rm{year}^{-1} \ \rm{kpc^{-2}}$ and a standard deviation of
0.266 dex, forming a relatively narrow distribution. The Lyman Break Galaxy
Analogs show a similarly narrow distribution of $S_{\rm 250pc}$ (0.271 dex),
though with a larger mean of 28 $M_{\odot} \ \rm{year}^{-1} \ \rm{kpc^{-2}}$.
We show that while the Ly$\alpha$ equivalent width (EW(Ly$\alpha$)) and the
Ly$\alpha$ escape fraction ($f^{Ly\alpha}_{esc}$) are not significantly
correlated with the central SFI ($S_{\rm 250pc}$), both are positively
correlated with the ratio of surface brightness to galaxy stellar mass ($S_{\rm
250pc}/M_{\rm star}$), with correlation coefficients ($p$-values) of 0.702
($1\times 10^{-8}$) and 0.529 ($5\times 10^{-4}$) with EW(Ly$\alpha$) and
$f^{Ly\alpha}_{esc}$, respectively. These correlations suggest a scenario where
intense central star formation can drive a galactic wind in galaxies with
relatively shallow gravitational potential wells, thus clearing channels for
the escape of Ly$\alpha$ photons.


  Segal's Gamma-rings provide a natural framework for absolute algebraic
geometry. We use Almkvist's global Witt construction to explore the relation
with J. Borger F1-geometry and compute the Witt functor-ring of Almkvist for
the simplest Gamma-ring S. We prove that it is isomorphic to the Galois
invariant part of the BC-system, and exhibit the close relation between
Lambda-rings and the Arithmetic site. Then, we concentrate on the Arakelov
compactification of Z which acquires a structure sheaf of S-algebras. After
supplying a probabilistic interpretation of the classical theta invariant of a
divisor D, we show how to associate to D a Gamma-space that encodes, in
homotopical terms, the Riemann-Roch problem for D.


  Temperature maps are presented of the 9 largest clusters in the mock
catalogues of Muanwong et al. for both the Preheating and Radiative models. The
maps show that clusters are not smooth, featureless systems, but contain a
variety of substructure which should be observable. The surface brightness
contours are generally elliptical and features that are seen include cold
clumps, hot spiral features, and cold fronts. Profiles of emission-weighted
temperature, surface brightness and emission-weighted pressure across the
surface brightness discontinuities seen in one of the bimodal clusters are
consistent with the cold front in Abell 2142 observed by Markevitch et al.


  One of the most successful theories of a non-Fermi liquid metallic state is
the composite Fermi liquid (CFL) theory of the half-filled Landau level. In
this paper, we study continuous quantum phase transitions out of the CFL state
and into a Landau Fermi liquid, in the limit of no disorder and fixed particle
number. This transition can be induced by tuning the bandwidth of the Landau
level relative to the interaction energy, for instance through an externally
applied periodic potential. We find a transition to the Landau Fermi liquid
through a gapless Mott insulator with a Fermi surface of neutral fermionic
excitations. In the presence of spatial symmetries, we also find a direct
continuous transition between the CFL and the Landau Fermi liquid. The
transitions have a number of characteristic observable signatures, including
the presence of two crossover temperature scales, resistivity jumps, and
vanishing compressibility. When the composite fermions are paired instead, our
results imply quantum critical points between various non-Abelian topological
states, including the \nu = 1/2 Moore-Read Pfaffian (Ising x U(1) topological
order), a version of the Kitaev B phase (Ising topological order), and paired
electronic superconductors. To study such transitions, we use a projective
construction of the CFL, which goes beyond the conventional framework of flux
attachment to include a broader set of quantum fluctuations. These
considerations suggest a possible route to fractionalized Mott insulators by
starting with FQH states and tuning the Landau level bandwidth.


  Hybrid systems, which take advantage of low material dimensionality, have
great potential for designing nanoscale devices. Quantum dots (QDs) -- a 0D
nanostructure -- can be combined with 2D monolayers to achieve success in
photovoltaics and photocatalytic water splitting. In such colloidal systems,
ligand molecules such as cysteine play an important role in device performance.
The role of the ligand molecule in these QD heterostructures is poorly
understood. In this study, time-dependent density functional theory (TD-DFT) is
employed in order to explore how the ligand affect the charge transfer at the
ultra-fast timescale. We study the charge transfer dynamics in CdS-MoS2
heterostructures both with and without an organic linker molecule. We find that
the ligand molecule enhances the ultrafast charge transfer, and that electrons
are preferentially transferred from CdS to MoS2 as band alignment would
predict. The electronic dynamics and time-evolved projection character are
sensitive to the ionic temperature and excitation density.


  In recent years, the technology in visual-inertial odometry (VIO) has matured
considerably and has been widely used in many applications. However, we still
encounter challenges when applying VIO to a micro air vehicle (MAV) equipped
with a downward-looking camera. Specifically, VIO cannot compute the correct
initialization results during take-off and the cumulative drift is large when
the MAV is flying in the air. To overcome these problems, we propose a
homographybased initialization method, which utilizes the fact that the
features detected by the downward-looking camera during take-off are
approximately on the same plane. Then we introduce the prior normal vector and
motion field to make states more accurate. In addition, to deal with the
cumulative drift, a strategy for dynamically weighting visual residuals is
proposed. Finally, we evaluate our method on the collected real-world datasets.
The results demonstrate that our system can be successfully initialized no
matter how the MAV takes off and the positioning errors are also greatly
improved.


  Traditional Bayesian random partition models assume that the size of each
cluster grows linearly with the number of data points. While this is appealing
for some applications, this assumption is not appropriate for other tasks such
as entity resolution, modeling of sparse networks, and DNA sequencing tasks.
Such applications require models that yield clusters whose sizes grow
sublinearly with the total number of data points -- the microclustering
property. Motivated by these issues, we propose a general class of random
partition models that satisfy the microclustering property with
well-characterized theoretical properties. Our proposed models overcome major
limitations in the existing literature on microclustering models, namely a lack
of interpretability, identifiability, and full characterization of model
asymptotic properties. Crucially, we drop the classical assumption of having an
exchangeable sequence of data points, and instead assume an exchangeable
sequence of clusters. In addition, our framework provides flexibility in terms
of the prior distribution of cluster sizes, computational tractability, and
applicability to a large number of microclustering tasks. We establish
theoretical properties of the resulting class of priors, where we characterize
the asymptotic behavior of the number of clusters and of the proportion of
clusters of a given size. Our framework allows a simple and efficient Markov
chain Monte Carlo algorithm to perform statistical inference. We illustrate our
proposed methodology on the microclustering task of entity resolution, where we
provide a simulation study and real experiments on survey panel data.


  We provide a parameterized polynomial algorithm for the propositional model
counting problem #SAT, the runtime of which is single-exponential in the
rank-width of a formula. Previously, analogous algorithms have been known --
e.g.~[Fischer, Makowsky, and Ravve] -- with a single-exponential dependency on
the clique-width of a formula. Our algorithm thus presents an exponential
runtime improvement (since clique-width reaches up to exponentially higher
values than rank-width), and can be of practical interest for small values of
rank-width. We also provide an algorithm for the MAX-SAT problem along the same
lines.


  Random vacancies in a graphene monolayer induce defect states that are known
to form a narrow impurity band centered around zero energy at half-filling. We
use a space-resolved formulation of the quantum metric and establish a strong
enhancement of the electronic correlations in this impurity band. The
enhancement is primarily due to strong correlations between pairs of vacancies
situated on different sublattices at anomalously large spatial distances. We
trace the strong enhancement to both the multifractal vacancy wave functions,
which ties the system exactly at the Anderson insulator transition for all
defect concentrations, and preserving the chiral symmetry.


  We obtain limit theorems (Stable Laws and Central Limit Theorems, both
Gaussian and non-Gaussian) and thermodynamic properties for a class of
non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The
proofs of the limit theorems for these flows are applications of corresponding
theorems in an abstract functional analytic framework, which may be applicable
to other classes of non-uniformly hyperbolic flows.


  Trace monoids and heaps of pieces appear in various contexts in
combinatorics. They also constitute a model used in computer science to
describe the executions of asynchronous systems. The design of a natural
probabilistic layer on top of the model has been a long standing challenge. The
difficulty comes from the presence of commuting pieces and from the absence of
a global clock. In this paper, we introduce and study the class of Bernoulli
probability measures that we claim to be the simplest adequate probability
measures on infinite traces. For this, we strongly rely on the theory of trace
combinatorics with the M\"obius polynomial in the key role. These new measures
provide a theoretical foundation for the probabilistic study of concurrent
systems.


  Within the framework of transverse-momentum-dependent factorization, we
investigate for the first time the impact of a flavor-dependent intrinsic
transverse momentum of quarks on the production of $W^{\pm}$ bosons in
proton-proton collisions at $\sqrt{s}$ = 7 TeV. We estimate the shift in the
extracted value of the $W$ boson mass $M_W$ induced by different choices of
flavor-dependent parameters for the intrinsic quark transverse momentum by
means of a template fit to the transverse-mass and the lepton
transverse-momentum distributions of the $W$-decay products. We obtain $-6\leq
\Delta M_{W^+} \leq 9$ MeV and $-4\leq \Delta M_{W^-} \leq 3$ MeV with a
statistical uncertainty of $\pm 2.5$ MeV. Our findings call for more detailed
investigations of flavor-dependent nonperturbative effects linked to the proton
structure at hadron colliders.


  This note places primary emphasis on improving the asymptotic behavior of a
multi-dimensional delayed wave equation in the absence of any displacement
term. In the first instance, the delay is assumed to occur in the boundary.
Then, invoking a geometric condition BLR on the domain, the exponential
convergence of solutions to their equilibrium state is proved. The strategy
adopted of the proof is based on an interpolation inequality combined with a
resolvent method. In turn, an internal delayed wave equation is considered in
the second case, where the domain possesses trapped ray and hence (BLR)
geometric condition does not hold. In such a situation polynomial convergence
results are established. These finding improve earlier results of
Ammari-Chentouf and Phung.


  This is an expository paper about a $\mathcal{C}_2$-equivariant analog of the
bar construction. We will explain its construction and prove how it acts as a
$\sigma$-fold delooping machine on twisted monoids, where $\sigma$ denotes the
sign representation.


  Both theoretical and experimental evidence are presented in this work in
order to validate the existence of an Energy/Frequency Convexity Rule, which
relates energy consumption and microprocessor frequency for nanometer-scale
microprocessors. Data gathered during several month-long experimental
acquisition campaigns, supported by several independent publications, suggest
that energy consumed is indeed depending on the microprocessor's clock
frequency, and, more interestingly, the curve exhibits a clear minimum over the
processor's frequency range. An analytical model for this behavior is presented
and motivated, which fits well with the experimental data. A parameter
sensitivity analysis shows how parameters affect the energy minimum in the
clock frequency space. The conditions are discussed under which this convexity
rule can be exploited, and when other methods are more effective, with the aim
of improving the computer system's energy management efficiency. We show that
the power requirements of the computer system, besides the microprocessor, and
the overhead affect the location of the energy minimum the most. The
sensitivity analysis of the Energy/Frequency Convexity Rule puts forward a
number of simple guidelines especially for by low-power systems, such as
battery-powered and embedded systems, and less likely by high-performance
computer systems.


  Aspects of a generalized representation theory of current algebras in $3+1$
dimensions are discussed in terms of the Fock bundle method, the sesquilinear
form approach (of Langmann and Ruijsenaars), and Hilbert space cocycles.


  The NKCS model was introduced to explore coevolutionary systems, that is,
systems in which multiple species are closely interconnected. The fitness
landscapes of the species are coupled to a controllable amount, where the
underlying properties of the individual landscapes are also controllable. No
previous work has explored the use of hierarchical control within the model.
This paper explores the effects of using a confederation, based on Bookchins
communalism, and a single point of global control. Significant changes in
behaviour from the traditional model are seen across the parameter space.


  Simulational studies of spin glasses in the last decade have focussed on the
so-called replicon exponent $\alpha$ as a means of determining whether the
low-temperature phase of spin glasses is described by the replica symmetry
breaking picture of Parisi or by the droplet-scaling picture. On the latter
picture, it should be zero, but we shall argue that it will only be zero for
systems of linear dimension $L > L^*$. The crossover length $L^*$ may be of the
order of hundreds of lattice spacings in three dimensions and approach infinity
in 6 dimensions. We use the droplet-scaling picture to show that the apparent
non-zero value of $\alpha$ when $L < L^*$ should be $2 \theta$, where $\theta$
is the domain wall energy scaling exponent, This formula is in reasonable
agreement with the reported values of $\alpha$.


  We derive basic analytical results for the timing and decay of the
GRB-counterpart and delayed-afterglow light-curves for a brief emission episode
from a relativistic surface endowed with angular structure, consisting of a
uniform Core of size theta_c (Lorentz factor Gamma_c and surface emissivity
i_nu are angle-independent) and an axially-symmetric power-law Envelope (Gamma
~ theta^{-g}).
  In this Large-Angle Emission (LAE) model, radiation produced during the
prompt emission phase (GRB) at angles theta > theta_c arrives at observer well
after the burst (delayed emission). The dynamical time-range of the very
fast-decaying GRB "tail" and of the flat afterglow "plateau", and the
morphology of GRB counterpart/afterglow, are all determined by two parameters:
the Core's parameter Gamma_c*theta_c and the Envelope's Lorentz factor index g,
leading to three types of light-curves that display three post-GRB phases (type
1: tail, plateau/slow-decay, post-plateau/normal-decay), two post-GRB phases
(type 2: tail and fast-decay), or just one (type 3: normal decay).
  We show how X-ray light-curve features can be used to determine Core and
Envelope dynamical and spectral parameters.
  Testing of the LAE model is done using the Swift/XRT X-ray emission of two
afterglows of type 1 (060607A, 061121), one of type 2 (061110A), and one of
type 3 (061007). We find that the X-ray afterglows with plateaus require an
Envelope Lorentz factor Gamma ~ theta^{-2} and a comoving-frame emissivity i_nu
~ theta^2, thus, for a typical afterglow spectrum F_nu ~ nu^{-1}, the lab-frame
energy release is uniform over the emitting surface.


  We propose an unsupervised method for reference resolution in instructional
videos, where the goal is to temporally link an entity (e.g., "dressing") to
the action (e.g., "mix yogurt") that produced it. The key challenge is the
inevitable visual-linguistic ambiguities arising from the changes in both
visual appearance and referring expression of an entity in the video. This
challenge is amplified by the fact that we aim to resolve references with no
supervision. We address these challenges by learning a joint visual-linguistic
model, where linguistic cues can help resolve visual ambiguities and vice
versa. We verify our approach by learning our model unsupervisedly using more
than two thousand unstructured cooking videos from YouTube, and show that our
visual-linguistic model can substantially improve upon state-of-the-art
linguistic only model on reference resolution in instructional videos.


  For a given data set the problem of selecting either Lindley or xgamma
distribution with unknown parameter is investigated in this article. Both these
distributions can be used quite effectively for analyzing skewed non-negative
data and in modeling time-to-event data sets. We have used the ratio of the
maximized likelihoods in choosing between the Lindley and xgamma distributions.
Asymptotic distributions of the ratio of the maximized likelihoods are obtained
and those are utilized to determine the minimum sample size required to
discriminate between these two distributions for user specified probability of
correct selection and tolerance limit.


  Optics is a core field in the curricula of secondary physics education. In
this study, we present the development and validation of a test instrument in
the field of optics, the Converging Lenses Concept Inventory (CLCI). It can be
used as a formative or a summative assessment of middle school students'
conceptual understanding of image formation by converging lenses. The CLCI
assesses: (1) the overall understanding of fundamental concepts related to
converging lenses, (2) the understanding of specific concepts, and (3)
students' propensity for difficulties within this topic. The initial CLCI
consists of 16 multiple-choice items; however, one item was removed based on
various quality checks. We validated the CLCI thoroughly with distractor
analyses, classical test theory, item response theory, structural analyses, and
analyses of students' total scores at different measurement points as
quantitative approaches, as well as student interviews and an expert survey as
qualitative approaches. The quantitative analyses are mostly based on a dataset
of N = 318 middle school students who took the CLCI as a posttest. The student
interviews were conducted with seven middle school students after they were
taught the concepts of converging lenses. The expert survey included five
experts who evaluated both individual items and the test as a whole. The
analyses showed good to excellent results for the test instrument,
corroborating the 15-item CLCI's validity and its compliance with the three
foci outlined above.


  The global properties of elliptical galaxies are connected through the
so-called fundamental plane of ellipticals, which is an empirical relation
between their parameters: effective radius, central velocity dispersion and
mean surface brightness within the effective radius. We investigated the
relation between the parameters of the fundamental plane equation and the
parameters of modified gravity potential $f(R)$. With that aim, we compared
theoretical predictions for circular velocity in $f(R)$ gravity with the
corresponding values from a large sample of observed elliptical galaxies.
Besides, we consistently reproduced the values of coefficients of the
fundamental plane equation as deduced from observations, showing that the
photometric quantities like mean surface brightness are related to
gravitational parameters. We show that this type of modified gravity,
especially its power-law version - $R^n$, is able to reproduce the stellar
dynamics in elliptical galaxies. Also, it is shown that $R^n$ gravity fits the
observations very well, without need for a dark matter.


  The research documents the impact of a teaching experiment designed in order
to make students consider not only the spectral composition of light but also
its intensity when they interpret colour phenomena. The analysis of eight
recorded and transcribed teaching interviews conducted with third-year
university students indicates that the comprehension of the colour vision
process benefits from a "more or less" approach. Such an approach is likely to
facilitate students' understanding of everyday observed phenomena.


  It is demonstrated how dynamic storage allocation algorithms can be analyzed
in terms of finite size scaling. The method is illustrated in the three simple
cases of the it first-fit, next-fit and it best-fit algorithms, and the system
works at full capacity. The analysis is done from two different points of view
- running speed and employed memory. In both cases, and for all algorithms, it
is shown that a simple scaling function exists and the relevant exponents are
calculated. The method can be applied on similar problems as well.


  It has recently been argued that steady-state vorticity bands cannot arise in
shear thickening suspensions, because the normal stress imbalance across the
interface between the bands will set up particle migrations. In this Letter, we
develop a simple continuum model that couples shear thickening to particle
migration. We show by linear stability analysis that homogeneous flow is
unstable towards vorticity banding, as expected, in the regime of negative
constitutive slope. In full nonlinear computations, we show however that the
resulting vorticity bands are unsteady, with spatiotemporal patterns governed
by stress-concentration coupling. We furthermore show that these dynamical
bands also arise in direct particle simulations, in good agreement with the
continuum model.


  In this paper the group structure of the $p$-adic ball and sphere are
studied. The dynamical system of isometry defined on invariant sphere is
investigated. We define the binary operations $\oplus$ and $\odot$ on a ball
and sphere respectively, and prove that this sets are compact topological
abelian group with respect to the operations. Then we show that any two balls
(spheres) with positive radius are isomorphic as groups. We prove that the Haar
measure introduced in $\mathbb Z_p$ is also a Haar measure on an arbitrary
balls and spheres. We study the dynamical system generated by the isometry
defined on a sphere, and show that the trajectory of any initial point that is
not a fixed point isn't convergent. We study ergodicity of this $p$-adic
dynamical system with respect to normalized Haar measure reduced on the sphere.
For $p\geq 3$ we prove that the dynamical systems are not ergodic. But for
$p=2$ under some conditions the dynamical system may be ergodic.


  We investigate the time evolution of dust properties, molecular hydrogen
(H_2) contents, and star formation histories in galaxies by using our original
chemodynamical simulations. The simulations include the formation of dust in
the stellar winds of supernovae (SNe) and asymptotic giant branch (AGB) stars,
the growth and destruction processes of dust in the interstellar medium (ISM),
the formation of polycyclic aromatic hydrocarbon (PAH) dust in carbon-rich AGB
stars, the H_2 formation on dust grains, and the H_2 photo-dissociation due to
far ultra-violet (FUV) light in a self-consistent manner. We focus mainly on
disk galaxies with different total masses in this preliminary study. The
principle results are as follows: The star formation histories of disk galaxies
can be regulated by the time evolution of interstellar dust, mainly because the
formation rates of H_2 can be controlled by dust properties. The observed
correlation between dust-to-gas-ratios (D) and gas-phase oxygen abundances (A_O
= 12+log(O/H)) can be reproduced reasonably well in the present models. The
disks show negative radial gradients (i.e., larger in inner regions) of H_2
fraction (f_H2), PAH-to-dust mass ratio (f_PAH), D, and A_O and these gradients
evolve with time. The surface-mass densities of dust (Sigma_dust) are
correlated more strongly with the total surface gas densities than with those
of H_2. Local gaseous regions with higher D are more likely to have higher f_H2
in individual disks and total H_2 masses correlate well with total dust masses.
More massive disk galaxies are more likely to have higher D, f_PAH, and f_H2
and smaller dust-to-stellar mass ratios. We also compare between galactic star
formation histories in the metallicity-dependent and dust-dependent star
formation models and find no major differences.


  We study the optimal scaling of the expected total queue size in an $n\times
n$ input-queued switch, as a function of the number of ports $n$ and the load
factor $\rho$, which has been conjectured to be $\Theta (n/(1-\rho))$. In a
recent work, the validity of this conjecture has been established for the
regime where $1-\rho = O(1/n^2)$. In this paper, we make further progress in
the direction of this conjecture. We provide a new class of scheduling policies
under which the expected total queue size scales as
$O(n^{1.5}(1-\rho)^{-1}\log(1/(1-\rho)))$ when $1-\rho = O(1/n)$. This is an
improvement over the state of the art; for example, for $\rho = 1 - 1/n$ the
best known bound was $O(n^3)$, while ours is $O(n^{2.5}\log n)$.


  In this paper we explicitly attach to a geometric classical r-matrix $r$ (not
necessarily unitary), a geometric (i.e., set-theoretical) quantum R-matrix $R$,
which is a quantization of $r$. To accomplish this, we use the language of
bijective cocycle 7-tuples, developed by A. Soloviev in the study of
set-theoretical quantum R-matrices. Namely, we define a classical version of
bijective cocycle 7-tuples, and show that there is a bijection between them and
geometric classical r-matrices. Then we show how any classical bijective
cocycle 7-tuple can be quantized, and finally use Soloviev's construction,
which turns a (quantum) bijective cocycle 7-tuple into a geometric quantum
R-matrix.