  I prove the existence, and describe the structure, of moduli space of pairs
$(p,\Theta)$ consisting of a projective variety $P$ with semiabelian group
action and an ample Cartier divisor on it satisfying a few simple conditions.
Every connected component of this moduli space is proper. A component
containing a projective toric variety is described by a configuration of
several polytopes, the main one of which is the secondary polytope. On the
other hand, the component containing a principally polarized abelian variety
provides a moduli compactification of $A_g$. The main irreducible component of
this compactification is described by an "infinite periodic" analog of the
secondary polytope and coincides with the toroidal compactification of $A_g$
for the second Voronoi decomposition.


  This paper is concerned with the Floating Body Problem of S. Ulam: the
existence of objects other than the sphere, which can float in a liquid in any
orientation. Despite recent results of F. Wegner pointing towards an
affirmative answer, a full proof of their existence is still unavailable. For
objects with cylindrical symmetry and density 1/2, the conditions of neutral
floating are formulated as an initial value problem, for which a unique
solution is predicted in certain cases by a suitable generalization of the
Picard-Lindel\"of theorem. Numerical integration of the initial value problem
provides a rich variety of neutrally floating shapes.


  We investigate the impact of electronic correlations and quantum
delocalization onto the static structure factor and static density response
function of the strongly coupled electron liquid. In contrast to a classical
system, the density response of the electron liquid vanishes on small length
scales due to quantum delocalization effects, which we rigorously quantify in
terms of imaginary-time correlation functions and dynamic Matsubara response
functions. This allows us to analyze the interplay of structural order and
dynamic quantum effects as it manifests in the dynamic Matsubara local field
correction. Finally, we identify an effective electronic attraction in the
spin-offdiagonal static density response when the wavelength of the
perturbation is commensurate with the average interparticle distance.


  As electronic data becomes the lifeline of modern society, privacy concerns
increase. These concerns are reflected by the European Union's enactment of the
General Data Protection Regulation (GDPR), one of the most comprehensive and
robust privacy regulations globally. This project aims to evaluate and
highlight associations between eHealth systems' policies and personal data
privacy regulations. Using bias-corrected Cramer's V and Thiel's U tests, we
found weak and zero associations between e-health systems' rules and
protections for data privacy. A simple decision tree model is trained, which
validates the association scores obtained


  This paper derives confidence intervals (CI) and time-uniform confidence
sequences (CS) for the classical problem of estimating an unknown mean from
bounded observations. We present a general approach for deriving concentration
bounds, that can be seen as a generalization and improvement of the celebrated
Chernoff method. At its heart, it is based on a class of composite nonnegative
martingales, with strong connections to testing by betting and the method of
mixtures. We show how to extend these ideas to sampling without replacement,
another heavily studied problem. In all cases, our bounds are adaptive to the
unknown variance, and empirically vastly outperform existing approaches based
on Hoeffding or empirical Bernstein inequalities and their recent
supermartingale generalizations. In short, we establish a new state-of-the-art
for four fundamental problems: CSs and CIs for bounded means, when sampling
with and without replacement.


  The problem of computing saddle points is important in certain problems in
numerical partial differential equations and computational chemistry, and is
often solved numerically by a minimization problem over a set of mountain
passes. We point out that a good global mountain pass algorithm should have
good local and global properties. Next, we define the parallel distance, and
show that the square of the parallel distance has a quadratic property. We show
how to design algorithms for the mountain pass problem based on perturbing
parameters of the parallel distance, and that methods based on the parallel
distance have midrange local and global properties.


  Two-dimensional transitional metal dichalcogenide (TMD) field-effect
transistors (FETs) are promising candidates for future electronic applications,
owing to their excellent transport properties and potential for ultimate device
scaling. However, it is widely acknowledged that substantial contact resistance
associated with the contact-TMD interface has impeded device performance to a
large extent. It has been discovered that O2 plasma treatment can convert WSe2
into WO3-x and substantially improve contact resistances of p-type WSe2 devices
by strong doping induced thinner depletion width. In this paper, we carefully
study the temperature dependence of this conversion, demonstrating an oxidation
process with a precise monolayer control at room temperature and multilayer
conversion at elevated temperatures. Furthermore, the lateral oxidation of WSe2
under the contact revealed by HR-STEM leads to potential unpinning of the metal
Fermi level and Schottky barrier lowering, resulting in lower contact
resistances. The p-doping effect is attributed to the high electron affinity of
the formed WO3-x layer on top of the remaining WSe2 channel, and the doping
level is found to be dependent on the WO3-x thickness that is controlled by the
temperature. Comprehensive materials and electrical characterizations are
presented, with a low contact resistance of ~528 ohm-um and record high
on-state current of 320 uA/um at -1V bias being reported.


  The Swift-Hohenberg fluid convection system with both local and nonlocal
nonlinearities under the influence of white noise is studied. The objective is
to understand the difference in the dynamical behavior in both local and
nonlocal cases. It is proved that when sufficiently many of its Fourier modes
are forced, the system has a unique invariant measure, or equivalently, the
dynamics is ergodic. Moreover, it is found that the number of modes to be
stochastically excited for ensuring the ergodicity in the local Swift-Hohenberg
system depends {\em only} on the Rayleigh number (i.e., it does not even depend
on the random term itself), while this number for the nonlocal Swift-Hohenberg
system relies additionally on the bound of the kernel in the nonlocal
interaction (integral) term, and on the random term itself


  Geometry is a fundamental part of robotics and there have been various
frameworks of representation over the years. Recently, geometric algebra has
gained attention for its property of unifying many of those previous ideas into
one algebra. While there are already efficient open-source implementations of
geometric algebra available, none of them is targeted at robotics applications.
We want to address this shortcoming with our library gafro. This article
presents an overview of the implementation details as well as a tutorial of
gafro, an efficient c++ library targeting robotics applications using geometric
algebra. The library focuses on using conformal geometric algebra. Hence,
various geometric primitives are available for computation as well as rigid
body transformations. The modeling of robotic systems is also an important
aspect of the library. It implements various algorithms for calculating the
kinematics and dynamics of such systems as well as objectives for optimisation
problems. The software stack is completed by python bindings in pygafro and a
ROS interface in gafro_ros.


  We study the asymptotic convergence of AA($m$), i.e., Anderson acceleration
with window size $m$ for accelerating fixed-point methods $x_{k+1}=q(x_{k})$,
$x_k \in R^n$. Convergence acceleration by AA($m$) has been widely observed but
is not well understood. We consider the case where the fixed-point iteration
function $q(x)$ is differentiable and the convergence of the fixed-point method
itself is root-linear. We identify numerically several conspicuous properties
of AA($m$) convergence: First, AA($m$) sequences $\{x_k\}$ converge
root-linearly but the root-linear convergence factor depends strongly on the
initial condition. Second, the AA($m$) acceleration coefficients $\beta^{(k)}$
do not converge but oscillate as $\{x_k\}$ converges to $x^*$. To shed light on
these observations, we write the AA($m$) iteration as an augmented fixed-point
iteration $z_{k+1} =\Psi(z_k)$, $z_k \in R^{n(m+1)}$ and analyze the continuity
and differentiability properties of $\Psi(z)$ and $\beta(z)$. We find that the
vector of acceleration coefficients $\beta(z)$ is not continuous at the fixed
point $z^*$. However, we show that, despite the discontinuity of $\beta(z)$,
the iteration function $\Psi(z)$ is Lipschitz continuous and directionally
differentiable at $z^*$ for AA(1), and we generalize this to AA($m$) with $m>1$
for most cases. Furthermore, we find that $\Psi(z)$ is not differentiable at
$z^*$. We then discuss how these theoretical findings relate to the observed
convergence behaviour of AA($m$). The discontinuity of $\beta(z)$ at $z^*$
allows $\beta^{(k)}$ to oscillate as $\{x_k\}$ converges to $x^*$, and the
non-differentiability of $\Psi(z)$ allows AA($m$) sequences to converge with
root-linear convergence factors that strongly depend on the initial condition.
Additional numerical results illustrate our findings.


  This paper generalizes earlier work on Hamiltonian boundary terms by omitting
the requirement that the spacelike hypersurfaces $\Sigma_t$ intersect the
timelike boundary $\cal B$ orthogonally. The expressions for the action and
Hamiltonian are calculated and the required subtraction of a background
contribution is discussed. The new features of a Hamiltonian formulation with
non-orthogonal boundaries are then illustrated in two examples.


  Zipf's law is the most common statistical distribution displaying scaling
behavior. Cities, populations or firms are just examples of this seemingly
universal law. Although many different models have been proposed, no general
theoretical explanation has been shown to exist for its universality. Here we
show that Zipf's law is, in fact, an inevitable outcome of a very general class
of stochastic systems. Borrowing concepts from Algorithmic Information Theory,
our derivation is based on the properties of the symbolic sequence obtained
through successive observations over a system with an unbounded number of
possible states. Specifically, we assume that the complexity of the description
of the system provided by the sequence of observations is the one expected for
a system evolving to a stable state between order and disorder. This result is
obtained from a small set of mild, physically relevant assumptions. The general
nature of our derivation and its model-free basis would explain the ubiquity of
such a law in real systems.


  A Bayesian inference analysis is performed to quantify the pion excess in the
low transverse momentum ($p_{\rm T}$) regime in heavy-ion collisions. This
quantification is conducted across centrality classes and collision systems at
the LHC and top RHIC energy. The analysis is based on the relativistic fluid
dynamics description of $p_{\rm T}$ spectra of identified charged hadrons. A
$p_{\rm T}$ range scan investigation to determine the optimal range for the
pion $p_{\rm T}$ spectra with respect to a fluid dynamic description is
performed, finding 0.5~$< p_{\rm T} < $~2.0~GeV$/c$. A significant low-$p_{\rm
T}$ pion excess is computed across all centrality classes and collision systems
investigated, indicating that a clear low-$p_{\rm T}$ component arises from
different physics mechanisms, rather than thermal production. Further
comparison with measurements by the PHOBOS Collaboration confirms the
persistence of the pion excess into very low-$p_{\rm T}$, with no enhancement
observed in kaons and protons within the current experimental precision.


  Animal hair examination at a criminal scene may provide valuable information
in forensic investigations. However, local reference databases for animal hair
identification are rare. In the present study, we provide differential
histological analysis of hair of some domestic animals in Upper Egypt. For this
purpose, guard hair of large ruminants (buffalo, camel and cow), small
ruminants (sheep and goat), equine (horse and donkey) and canine (dog and cat)
were collected and comparative analysis was performed by light microscopy.
Based on the hair cuticle scale pattern, type and diameter of the medulla, and
the pigmentation, characteristic differential features of each animal species
were identified. The cuticle scale pattern was imbricate in all tested animals
except in donkey, in which coronal scales were identified. The cuticle scale
margin type, shape and the distance in between were characteristic for each
animal species. The hair medulla was continuous in most of the tested animal
species with the exception of sheep, in which fragmental medulla was detected.
The diameter of the hair medulla and the margins differ according to the animal
species. Hair shaft pigmentation were not detected in all tested animals with
the exception of camel and buffalo, in which granules and streak-like
pigmentation were detected. In conclusion, the present study provides a
first-step towards preparation of a complete local reference database for
animal hair identification that can be used in forensic investigations.


  We show that families of action graphs, with initial graphs which are linear
of varying length, give rise to self-convolutions of the Catalan sequence. We
prove this result via a comparison with planar rooted forests with a fixed
number of trees.


  Wireless Sensor Networks (WSNs) are increasing to handle complex situations
and functions. In these networks some of the nodes become Cluster Heads (CHs)
which are responsible to aggregate data of from cluster members and transmit it
to Base Stations (BS). Those clustering techniques which are designed for
homogenous network are not enough efficient for consuming energy. Stable
Election Protocol (SEP) introduces heterogeneity in WSNs, consisting of two
type of nodes. SEP is based on weighted election probabilities of each node to
become CH according to remaining energy of nodes. We propose
Heterogeneity-aware Hierarchal Stable Election Protocol (HSEP) having two level
of energies. Simulation results show that HSEP prolongs stability period and
network lifetime, as compared to conventional routing protocols and having
higher average throughput than selected clustering protocols in WSNs.


  Traditional member-based two-step design approaches included in current
structural codes for steel structures, as well as more recent system-based
direct-design alternatives, require building rigorous structural reliability
frameworks for the calibration of partial coefficients (resistance factors) to
achieve specified target reliability requirements. Key design parameters
affecting the strength of structures and their random variations are generally
modelled by nominal or characteristic values in design standards, which are
combined with partial coefficients that need to be calibrated from measurements
on real samples. While the statistical characterization of material and
geometric properties of structural steels has been consolidated over the last
decades, information about the characterization of structural stainless steels
is virtually non-existent due to the limited pool of available data. Thus, this
paper presents the basic ingredient for developing reliability frameworks for
stainless steel structures and components by statistically characterizing the
main random parameters affecting their strength through a comprehensive
database collected from the literature. Based on the collected data,
appropriate probabilistic models are proposed for geometric properties,
material properties, imperfections and residual stresses of different stainless
steel alloys and cross-section or product types. The data is equally applicable
to member-based reliability analyses as described in existing codes and
system-based analyses targeted at the direct-design of stainless steel
structures by advanced analysis.


  In this Master's project, the X-ray nuclear properties of a sample of bright
nearby galaxies are explored. This is done by matching their comprehensive
optical spectroscopic classification to the latest available XMM-Newton
catalogue - 3XMM-DR4. The good coverage (approx. 38 per cent) ensures that a
statistically representative sample is investigated. All nuclear and
morphological subsets found within the original sample of 486 galaxies are
encompassed, but early-type galaxies and galaxies with optical features
characteristic for active galactic nuclei (AGN) are favoured. The results from
the investigation of the properties of our cross-matched sample are overall
consistent with the presence of a large fraction of X-ray - detected
low-luminosity AGN (LLAGN). The X-ray - detected galaxies within our HII and
transition-LINER subsets are of particular interest, as they could harbour
LLAGN missed by optical spectroscopic selection. The properties of these nuclei
are explored by X-ray spectral fitting of available XMM-Newton observations.
The majority of the examined spectra are found to be consistent with a thermal
plasma model and an underlying power-law continuum, and the relative
contributions of a potential LLAGN and of thermal emission to the source
luminosity are presented. In the case that these spectra are not highly
contaminated, as confirmed for some of the nuclei by examining available
higher-resolution Chandra images, we classify approx. 43 per cent of the HII
nuclei and 40 per cent of the transition-LINER nuclei as optically undetected
LLAGN-candidates. This classification is found to be reasonably successful,
given the project limitations, when compared to X-ray and multi-wavelength
results found in literature for many of the nuclei.


  In this work, methods for the evaluation of LES-quality and LES-accuracy are
presented, which include the Lyapunov exponent for the analysis of short-time
predictability of LES-calculation and the Wasserstein metric for the
quantitative assessment of simulation results. Both methods are derived and
evaluated in application to the Volvo test case. Both the non-reacting and
reacting cases are calculated. For the non- reacting cases, good agreement with
the experimental data is achieved by solvers at high numerical resolution. The
reacting cases are more challenging due to the small length scale of the flame
and the suppression of sinuous mode of absolute instability by the density
ratio. The analysis of the turbulent simulation data using the concept of the
Lyapunov exponent and the Wasserstein metric provides a more quantitative
approach to assess the mesh dependency of the simulation results. The
convergence of the Lyapunov exponent is shown to be a more sensitive and
stronger indication of mesh-independence. Though grid convergence for the
reacting cases cannot be reached with the chosen resolutions, the Lyapunov
exponents and the Wasserstein metric are shown to be capable of identifying
quantity-specific sensitivities with respect to the numerical resolution, while
requiring significantly less computational resources than acquiring profiles of
conventional turbulent statistics.


  The topological terms of the bulk effective action for the integer quantum
Hall effect, capturing the dynamics of gauge and gravitational fluctuations,
reveal a curiosity, namely, the Abelian potential for the magnetic field
appears in a particular combination with the Abelian spin connection. This
seems to hold for quantum Hall effect on complex projective spaces of arbitrary
dimensions. An interpretation of this in terms of the algebra of symplectic
transformations is given. This can also be viewed in terms of the metaplectic
correction in geometric quantization.


  Vibrating membranes are the cornerstone of acoustic technology, forming the
backbone of modern loudspeakers and microphones. Acoustic performance of
condenser microphone is derived mainly from the membrane's size and achievable
static tension. The widely studied and available nickel has been the one of
dominant membrane material for several decades. In this paper we introduce
multilayer graphene as membrane material for a condenser microphone. The
graphene device outperforms a high end commercial nickel-based microphone over
a significant part of the acoustic spectrum, with a larger than 10 dB
enhancement of sensitivity. Our experimental results are supported with
numerical simulations, which show that a 300 layer thick graphene membrane
under maximum tension would offer excellent extension of the frequency range,
up to 1 MHz, with similar sensitivity as commercial condenser microphones.


  Non-Terrestrial Networks (NTNs) are widely recognized as a potential solution
to achieve ubiquitous connections of Narrow Bandwidth Internet of Things
(NB-IoT). In order to adopt NTNs in NB-IoT, one of the main challenges is the
uplink synchronization of Narrowband Physical Random Access procedure which
refers to the estimation of time of arrival (ToA) and carrier frequency offset
(CFO). Due to the large propagation delay and Doppler shift in NTNs,
traditional estimation methods for Terrestrial Networks (TNs) can not be
applied in NTNs directly. In this context, we design a two stage ToA and CFO
estimation scheme including coarse estimation and fine estimation based on
abrupt change point detection (CPD) of phase series with machine learning. Our
method achieves high estimation accuracy of ToA and CFO under the low
signal-noise ratio (SNR) and large Doppler shift conditions and extends the
estimation range without enhancing Random Access preambles.


  Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem
asks to compute the minimum number of unit disks required to cover the points,
along with a placement of the disks. The problem is NP-hard and several
approximation algorithms have been designed over the last three decades. In
this paper, we have engineered and experimentally compared practical
performances of some of these algorithms on massive pointsets. The goal is to
investigate which algorithms run fast and give good approximation in practice.
  We present a simple $7$-approximation algorithm for UDC that runs in $O(n)$
expected time and uses $O(s)$ extra space, where $s$ denotes the size of the
generated cover. In our experiments, it turned out to be the speediest of all.
We also present two heuristics to reduce the sizes of covers generated by it
without slowing it down by much.
  To our knowledge, this is the first work that experimentally compares
geometric covering algorithms. Experiments with them using massive pointsets
(in the order of millions) throw light on their practical uses. We share the
engineered algorithms via GitHub -
https://github.com/ghoshanirban/UnitDiskCoverAlgorithms for broader uses and
future research in the domain of geometric optimization.


  A system defined by two coupled Ising models, with a bimodal random field
acting in one of them, is investigated. The interactions among variables of
each Ising system are infinite-ranged, a limit where mean field becomes exact.
This model is studied at zero temperature, as well as for finite temperatures,
representing physical situations which are appropriate for describing real
systems, such as plastic crystals. A very rich critical behavior is found,
depending directly on the particular choices of the temperature, couplings, and
random-field strengths. Phase diagrams exhibiting ordered, partially-ordered,
and disordered phases are analyzed, showing the sequence of transitions through
all these phases, similarly to what occurs in plastic crystals. Due to the wide
variety of critical phenomena presented by the model, its usefulness for
describing critical behavior in other substances is also expected.


  We have made the first observation of a charged particle beam by means of its
electro-optical effect on the polarization of laser light in a birefringent
crystal. The modulation of the laser light during the passage of a pulsed
electron beam was observed using a fast photodiode and a digital oscilloscope.
The fastest rise time measured in a single shot, 120 ps, was limited by the
bandwidth of the oscilloscope and the associated electronics. This technology
holds promise for detectors of greatly improved spatial and temporal resolution
for single relativistic charged particles as well as particle beams.


  A completely positive master equation describing quantum dissipation for a
Brownian particle is derived starting from microphysical collisions, exploiting
a recently introduced approach to subdynamics of a macrosystem. The obtained
equation can be cast into Lindblad form with a single generator for each
Cartesian direction. Temperature dependent friction and diffusion coefficients
for both position and momentum are expressed in terms of the collision
cross-section.


  Let $X$ be a compact Riemann surface $X$ of genus at--least two. Fix a
holomorphic line bundle $L$ over $X$. Let $\mathcal M$ be the moduli space of
Hitchin pairs $(E ,\phi\in H^0(End(E)\otimes L))$ over $X$ of rank $r$ and
fixed determinant of degree $d$. We prove that, for some numerical conditions,
$\mathcal M$ is irreducible, and that the isomorphism class of the variety
$\mathcal M$ uniquely determines the isomorphism class of the Riemann surface
$X$.


  A cornerstone of the theory of phase transitions is the observation that
many-body systems exhibiting a spontaneous symmetry breaking in the
thermodynamic limit generally show extensive fluctuations of an order parameter
in large but finite systems. In this work, we introduce the dynamical analogue
of such a theory. Specifically, we consider local dissipative dynamics
preparing a steady-state of quantum spins on a lattice exhibiting a discrete or
continuous symmetry but with extensive fluctuations in a local order parameter.
We show that for all such processes satisfying detailed balance, there exist
metastable symmetry-breaking states, i.e., states that become stationary in the
thermodynamic limit and give a finite value to the order parameter. We give
results both for discrete and continuous symmetries and explicitly show how to
construct the symmetry-breaking states. Our results show in a simple way that,
in large systems, local dissipative dynamics satisfying detailed balance cannot
uniquely and efficiently prepare states with extensive fluctuations with
respect to local operators. We discuss the implications of our results for
quantum simulators and dissipative state preparation.


  In a society, a proportion of the individuals can benefit from creativity
without being creative themselves by copying the creators. This paper uses an
agent-based model of cultural evolution to investigate how society is affected
by different levels of individual creativity. We performed a time series
analysis of the mean fitness of ideas across the artificial society varying
both the percentage of creators, C, and how creative they are, p using two
discounting methods. Both analyses revealed a valley in the adaptive landscape,
indicating a tradeoff between C and p. The results suggest that excess
creativity at the individual level can be detrimental at the level of the
society because creators invest in unproven ideas at the expense of propagating
proven ideas.


  We study a four-dimensional effective theory of the five-dimensional (5D)
gauged supergravity with a universal hypermultiplet and perturbative
superpotential terms at the orbifold fixed points. Among eight independent
isometries of the scalar manifold, we focus on three directions for gauging by
the graviphoton. The class of models we consider includes the 5D heterotic
M-theory and the supersymmetric Randall-Sundrum model as special limits of the
gauging parameters. We analyze the vacuum structure of such models, especially
the nature of moduli stabilization, from the viewpoint of the effective theory.
We also discuss the uplifting of supersymmetric anti-de Sitter vacua.


  We extend the notion of graph homomorphism to cellularly embedded graphs
(maps) by designing operations on vertices and edges that respect the surface
topology; we thus obtain the first definition of map homomorphism that
preserves both the combinatorial structure (as a graph homomorphism) and the
topological structure of the surface (in particular, orientability and genus).
Notions such as the core of a graph and the homomorphism order on cores are
then extended to maps. We also develop a purely combinatorial framework for
various topological features of a map such as the contractibility of closed
walks, which in particular allows us to characterize map cores. We then show
that the poset of map cores ordered by the existence of a homomorphism is
connected and, in contrast to graph homomorphisms, does not contain any dense
interval (so it is not universal for countable posets). Finally, we give
examples of a pair of cores with an infinite number of cores between them, an
infinite chain of gaps, and arbitrarily large antichains with a common
homomorphic image.


  An acceptable response time of a server is an important aspect in many
client-server applications; this is evident in situations in which the server
is overloaded by many computationally intensive requests. In this work, we
consider that the requests, or in this case tasks, generated by the clients are
instances of optimization problems solved by anytime algorithms, i.e. the
quality of the solution increases with the processing time of a task. These
tasks are submitted to the server which schedules them to the available
computational resources where the tasks are processed. To tackle the overload
problem, we propose a scheduling algorithm which combines traditional
scheduling approaches with a quality control heuristic which adjusts the
requested quality of the solutions and thus changes the processing time of the
tasks. Two efficient quality control heuristics are introduced: the first
heuristic sets a global quality for all tasks, whereas the second heuristic
sets the quality for each task independently. Moreover, in practice, the
relationship between the processing time and the quality is not known a priori.
Because it is crucial for scheduling algorithms to know at least the estimation
of these relationships, we propose a general procedure for estimating these
relationships using information obtained from the already executed tasks.
Finally, the performance of the proposed scheduling algorithm is demonstrated
on a real-world problem from the domain of personnel rostering with very good
results.


  We consider how to optimally allocate investments in a portfolio of competing
technologies using the standard mean-variance framework of portfolio theory. We
assume that technologies follow the empirically observed relationship known as
Wright's law, also called a "learning curve" or "experience curve", which
postulates that costs drop as cumulative production increases. This introduces
a positive feedback between cost and investment that complicates the portfolio
problem, leading to multiple local optima, and causing a trade-off between
concentrating investments in one project to spur rapid progress vs.
diversifying over many projects to hedge against failure. We study the
two-technology case and characterize the optimal diversification in terms of
progress rates, variability, initial costs, initial experience, risk aversion,
discount rate and total demand. The efficient frontier framework is used to
visualize technology portfolios and show how feedback results in nonlinear
distortions of the feasible set. For the two-period case, in which learning and
uncertainty interact with discounting, we compare different scenarios and find
that the discount rate plays a critical role.


  In this paper we propose a new approach to quantum neural networks. Our
multi-layer architecture avoids the use of measurements that usually emulate
the non-linear activation functions which are characteristic of the classical
neural networks. Despite this, our proposed architecture is still able to learn
any Boolean function. This ability arises from the correspondence that exists
between a Boolean function and a particular quantum circuit made out of
multi-controlled NOT gates. This correspondence is built via a polynomial
representation of the function called the algebraic normal form. We use this
construction to introduce the idea of a generic quantum circuit whose gates can
be tuned to learn any Boolean functions. In order to perform the learning task,
we have devised an algorithm that leverages the absence of measurements. When
presented with a superposition of all the binary inputs of length $n$, the
network can learn the target function in at most $n+1$ updates.


  We present the first public data release of the GOGREEN and GCLASS surveys of
galaxies in dense environments, spanning a redshift range $0.8<z<1.5$. The
surveys consist of deep, multiwavelength photometry and extensive Gemini GMOS
spectroscopy of galaxies in 26 overdense systems ranging in halo mass from
small groups to the most massive clusters. The objective of both projects was
primarily to understand how the evolution of galaxies is affected by their
environment, and to determine the physical processes that lead to the quenching
of star formation. There was an emphasis on obtaining unbiased spectroscopy
over a wide stellar mass range ($M\gtrsim 2\times 10^{10}~\mathrm{M}_\odot$),
throughout and beyond the cluster virialized regions. The final spectroscopic
sample includes 2771 unique objects, of which 2257 have reliable spectroscopic
redshifts. Of these, 1704 have redshifts in the range $0.8<z<1.5$, and nearly
800 are confirmed cluster members. Imaging spans the full optical and
near-infrared wavelength range, at depths comparable to the UltraVISTA survey,
and includes \textit{HST}/WFC3 F160W (GOGREEN) and F140W (GCLASS). This data
release includes fully reduced images and spectra, with catalogues of advanced
data products including redshifts, line strengths, star formation rates,
stellar masses and rest-frame colours. Here we present an overview of the data,
including an analysis of the spectroscopic completeness and redshift quality.


  There is increasing interest in applying verification tools to programs that
have bitvector operations (eg., binaries). SMT solvers, which serve as a
foundation for these tools, have thus increased support for bitvector reasoning
through bit-blasting and linear arithmetic approximations. In this paper we
show that similar linear arithmetic approximation of bitvector operations can
be done at the source level through transformations. Specifically, we introduce
new paths that over-approximate bitvector operations with linear
conditions/constraints, increasing branching but allowing us to better exploit
the well-developed integer reasoning and interpolation of verification tools.
We show that, for reachability of bitvector programs, increased branching
incurs negligible overhead yet, when combined with integer interpolation
optimizations, enables more programs to be verified. We further show this
exploitation of integer interpolation in the common case also enables
competitive termination verification of bitvector programs and leads to the
first effective technique for LTL verification of bitvector programs. Finally,
we provide an in-depth case study of decompiled ("lifted") binary programs,
which emulate X86 execution through frequent use of bitvector operations. We
present a new tool DarkSea, the first tool capable of verifying reachability,
termination, and LTL of lifted binaries.


  In this paper we completely solve the problem of finding the (upper)
approximation order with respect to the Kolmogorov, Gel'fand, and linear widths
for the embedding of the Sobolev spaces $W^{\alpha,p}$ and $W_{0}^{\alpha,p}$
in the euclidian measure spaces $L_{\nu}^{q}$ for an arbitrary Borel
probability measure $\nu$ with support contained in the open $m$-dimensional
unit cube and for all possible choices of $1\leq p,q\leq\infty$. We will
determine the exact values for the various upper approximation orders in terms
of the $L^{q}$-spectrum of $\nu$ only and finally give sufficient conditions
imposed on the regularity of the $L^{q}$-spectrum for the approximation orders
to exist. We also elucidate some intrinsic connections between the concept of
approximation order and the fractal geometric notion of the upper and lower
Minkowski dimension of the support of $\nu$.


  Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a
collection of edges of $G$ such that no two edges from $M$ share a vertex. A
matching $M$ is maximal if it cannot be extended to a larger matching in $G$.
The cardinality of any smallest maximal matching in $G$ is the saturation
number of $G$ and is denoted by $s(G)$. In this paper we study the saturation
number of the corona product of two specific graphs. We also consider some
graphs with certain constructions that are of importance in chemistry and study
their saturation number.


  This work deals with the computation of electron pair correction to small
angle Bhabha scattering, in order to contribute to the improvement of
luminometry precision at LEP/SLC below 0.1% theoretical accuracy. The exact QED
four-fermion matrix element for $e^+e^-\to e^+e^-e^+e^-$, including all
diagrams and mass terms, is computed and different Feynman graph topologies are
studied to quantify the error of approximate calculations present in the
literature. Several numerical results, obtained by a Monte Carlo program with
full matrix element, initial-state radiation via collinear structure functions,
and realistic event selections, are shown and critically compared with the
existing ones. The present calculation, together with recent progress in the
sector of $O(\alpha^2)$ purely photonic corrections, contributes to achieve a
total theoretical error in luminometry at the 0.05% level, close to the current
experimental precision and important in view of the final analysis of the
electroweak precision data.


  This paper presents a command-line tool, called Entropia, that implements a
family of conformance checking measures for process mining founded on the
notion of entropy from information theory. The measures allow quantifying
classical non-deterministic and stochastic precision and recall quality
criteria for process models automatically discovered from traces executed by
IT-systems and recorded in their event logs. A process model has "good"
precision with respect to the log it was discovered from if it does not encode
many traces that are not part of the log, and has "good" recall if it encodes
most of the traces from the log. By definition, the measures possess useful
properties and can often be computed quickly.


  This paper proposes a deep learning-based method to identify the segments of
a clinical note corresponding to ICD-9 broad categories which are further
color-coded with respect to 17 ICD-9 categories. The proposed Medical Segment
Colorer (MSC) architecture is a pipeline framework that works in three stages:
(1) word categorization, (2) phrase allocation, and (3) document
classification. MSC uses gated recurrent unit neural networks (GRUs) to map
from an input document to word multi-labels to phrase allocations, and uses
statistical median to map phrase allocation to document multi-label. We compute
variable length segment coloring from overlapping phrase allocation
probabilities. These cross-level bidirectional contextual links identify
adaptive context and then produce segment coloring. We train and evaluate MSC
using the document labeled MIMIC-III clinical notes. Training is conducted
solely using document multi-labels without any information on phrases,
segments, or words. In addition to coloring a clinical note, MSC generates as
byproducts document multi-labeling and word tagging -- creation of ICD9
category keyword lists based on segment coloring. Performance comparison of MSC
byproduct document multi-labels versus methods whose purpose is to produce
justifiable document multi-labels is 64% vs 52.4% micro-average F1-score
against the CAML (CNN attention multi label) method. For evaluation of MSC
segment coloring results, medical practitioners independently assigned the
colors to broad ICD9 categories given a sample of 40 colored notes and a sample
of 50 words related to each category based on the word tags. Binary scoring of
this evaluation has a median value of 83.3% and mean of 63.7%.


  Gravitational wave signals from compact astrophysical sources such as those
observed by LIGO and Virgo require a high-accuracy, theory-based waveform model
for the analysis of the recorded signal. Current inspiral-merger-ringdown
models are calibrated only up to moderate mass ratios, thereby limiting their
applicability to signals from high-mass ratio binary systems. We present
EMRISur1dq1e4, a reduced-order surrogate model for gravitational waveforms of
13,500M in duration and including several harmonic modes for non-spinning black
hole binary systems with mass-ratios varying from 3 to 10,000 thus vastly
expanding the parameter range beyond the current models. This surrogate model
is trained on waveform data generated by point-particle black hole perturbation
theory (ppBHPT) both for large mass-ratio and comparable mass-ratio binaries.
We observe that the gravitational waveforms generated through a simple
application of ppBHPT to the comparable mass-ratio cases agree remarkably (and
surprisingly) well with those from full numerical relativity after a rescaling
of the ppBHPT's total mass parameter. This observation and the EMRISur1dq1e4
surrogate model will enable data analysis studies in the high-mass ratio
regime, including potential intermediate mass-ratio signals from LIGO/Virgo and
extreme-mass ratio events of interest to the future space-based observatory
LISA.


  To tackle Named Entity Recognition (NER) tasks, supervised methods need to
obtain sufficient cleanly annotated data, which is labor and time consuming. On
the contrary, distantly supervised methods acquire automatically annotated data
using dictionaries to alleviate this requirement. Unfortunately, dictionaries
hinder the effectiveness of distantly supervised methods for NER due to its
limited coverage, especially in specific domains. In this paper, we aim at the
limitations of the dictionary usage and mention boundary detection. We
generalize the distant supervision by extending the dictionary with headword
based non-exact matching. We apply a function to better weight the matched
entity mentions. We propose a span-level model, which classifies all the
possible spans then infers the selected spans with a proposed dynamic
programming algorithm. Experiments on all three benchmark datasets demonstrate
that our method outperforms previous state-of-the-art distantly supervised
methods.


  We derive a universal formula for the one-loop renormalization of the
effective K\"ahler potential that applies to general supersymmetric effective
field theories of chiral multiplets, with arbitrary interactions respecting N=1
supersymmetry in four dimensions. The resulting expression depends only on the
tree-level mass spectrum and the form of the regulator. This formula simplifies
and generalizes existing results in the literature. We include two examples to
illustrate its use.


  We investigate the finite-time behavior of pair production from the vacuum by
a time-dependent Sauter pulsed electric field using the spinor quantum
electrodynamics (QED). In the adiabatic basis, the one-particle distribution
function in momentum space is determined by utilizing the exact analytical
solution of the Dirac equation. By examining the temporal behavior of the
one-particle distribution function and the momentum spectrum of created pairs
in the sub-critical field limit $(E_0 = 0.2E_c)$, we observe oscillatory
patterns in the longitudinal momentum spectrum(LMS) of particles at finite
times. These oscillations arise due to quantum interference effects resulting
from the dynamical tunneling. Furthermore, we derive an approximate and
simplified analytical expression for the distribution function at finite times,
which allows us to explain the origin and behavior of these oscillations.
Additionally, we discuss the role of the vacuum polarization function and its
counter term to the oscillations in LMS vacuum excitation. We also analyse the
transverse momentum spectrum (TMS).


  Thought to be responsible for memory, synaptic plasticity has been widely
studied in the past few decades. One example of plasticity models is the
popular Spike Timing Dependent Plasticity (STDP). The huge litterature of STDP
models are mainly based deterministic rules whereas the biological mechanisms
involved are mainly stochastic ones. Moreover, there exist only few
mathematical studies on plasticity taking into account the precise spikes
timings. In this article, we aim at proposing a new stochastic STDP rule with
discrete synaptic weights which allows a mathematical analysis of the full
network dynamics under the hypothesis of separation of timescales. This model
attempts to answer the need for understanding the interplay between the weights
dynamics and the neurons ones.


  In iron-based superconductors, a unique tri-layer Fe-As (Se, Te, P) plays an
essential role in controlling the electronic properties, especially the Cooper
pairing interaction. Here we use scanning tunneling microscopy/spectroscopy
(STM/S) to investigate the role of arsenic atom in superconducting
Ba0.4K0.6Fe2As2 by directly breaking and restoring the Fe-As structure at
atomic scale. After the up-As-layer peeled away, the tunneling spectrum of the
exposed iron surface reveals a shallow incoherent gap, indicating a severe
suppression of superconductivity without arsenic covering. When a pair of
arsenic atoms is placed on such iron surface, a localized topographic feature
is formed due to Fe-As orbital hybridization, and the superconducting coherent
peaks recover locally with the gap magnitude the same as that on the iron-layer
fully covered by arsenic. These observations unravel the Fe-As interactions on
an atomic scale and imply its essential roles in the iron-based
superconductivity.


  Rough terrain locomotion has remained one of the most challenging mobility
questions. In 2022, NASA's Innovative Advanced Concepts (NIAC) Program invited
US academic institutions to participate NASA's Breakthrough, Innovative \&
Game-changing (BIG) Idea competition by proposing novel mobility systems that
can negotiate extremely rough terrain, lunar bumpy craters. In this
competition, Northeastern University won NASA's top Artemis Award award by
proposing an articulated robot tumbler called COBRA (Crater Observing
Bio-inspired Rolling Articulator). This report briefly explains the underlying
principles that made COBRA successful in competing with other concepts ranging
from cable-driven to multi-legged designs from six other participating US
institutions.


  We present a best-response based algorithm for computing verifiable
$\varepsilon$-perfect Bayesian equilibria for sequential auctions with
combinatorial bidding spaces and incomplete information. Previous work has
focused only on computing Bayes-Nash equilibria for static single-round
auctions, which our work captures as a special case. Additionally, we prove an
upper bound $\varepsilon$ on the utility loss of our approximate equilibria and
present an algorithm to efficiently compute $\varepsilon$ based on the
immediate loss at each subgame. We evaluate the performance of our algorithm by
reproducing known results from several auctions previously introduced in the
literature, including a model of combinatorial split-award auctions used in
procurement.


  The quantum image segmentation algorithm is to divide a quantum image into
several parts, but most of the existing algorithms use more quantum
resource(qubit) or cannot process the complex image. In this paper, an improved
two-threshold quantum segmentation algorithm for NEQR image is proposed, which
can segment the complex gray-scale image into a clear ternary image by using
fewer qubits and can be scaled to use n thresholds for n + 1 segmentations. In
addition, a feasible quantum comparator is designed to distinguish the
gray-scale values with two thresholds, and then a scalable quantum circuit is
designed to segment the NEQR image. For a 2^(n)*2^(n) image with q gray-scale
levels, the quantum cost of our algorithm can be reduced to 60q-6, which is
lower than other existing quantum algorithms and does not increase with the
image's size increases. The experiment on IBM Q demonstrates that our algorithm
can effectively segment the image.


  In this manuscript we study the cosmological constant of a
$(p+1)$-dimensional world, which lives in the higher dimensional bulk space. We
assume the extra dimensions are compact on tori. We consider two cases:
positive and negative bulk cosmological constant. It is pointed out that the
tiny cosmological constant of our world can be obtained by the dynamics of a
scalar field and adjusting the parameters of the model. The cosmological
constant of the dual world also will be discussed. We obtain the Dirac
quantization of these cosmological constants.


  Let $\alpha_X^{\underline d}$ be the Abel map of multidegree $\underline d$
of a singular curve $X$ of genus $g$. We describe the closure of ${\rm
Im}\alpha_X^{\underline d}$ inside Caporaso's compactified Jacobian
$\bar{P_X^d}$ for irreducible curves, curves of compact type and binary curves.


  A new approach to generalised Casimir type of problems is derived within the
context of renormalisable quantum field theory (QFT). We study the simplest
case of a massive fluctuating boson field coupled to a time-independent
background potential. We use analytic properties of scattering data to compute
the relevant Green's functions at imaginary momenta, which in turn yields a
simple and efficient method to compute (one-loop) vacuum energy densities in
QFT. Renormalisation is easily performed in the perturbative sector by
identifying low order Feynman diagrams with the first few Born approximation to
the Green's function. Numerical examples illustrate the efficiency of our
approach.


  We study quantization of a minimally gauged massless Rarita-Schwinger field,
by both Dirac bracket and functional integral methods. The Dirac bracket
approach in covariant radiation gauge leads to an anticommutator that has a
non-singular limit as gauge fields approach zero, is manifestly positive
semidefinite, and is Lorentz invariant. The constraints also have the form
needed to apply the Faddeev-Popov method for deriving a functional integral,
using the same constrained Hamiltonian and inverse constraint matrix that
appear in the Dirac bracket approach.


  We report on the development of an GRPCs (Glass Resistive Plate chambers)
Semi- Digital hadron calorimeter for the future International Linear Collider
(ILC).Two types of GRPCs (small and 1m2) were tested in PS beam at CERN.
Detector performances are presented here in terms of efficiency, pad
multiplicity, homogeneity and stability in time.


  In this paper, the problem of stability analysis of a large-scale
interconnection of nonlinear systems for which the small-gain condition does
not hold globally is considered. A combination of the small-gain and density
propagation inequalities is employed to prove almost input-to-state stability
of the network.


  The fine-structure constant, $\alpha$, controls the strength of the
electromagnetic interaction. There are extensions of the standard model in
which $\alpha$ is dynamical on cosmological length and time-scales. The physics
of the cosmic microwave background (CMB) depends on the value of $\alpha$. The
effects of spatial variation in $\alpha$ on the CMB are similar to those
produced by weak lensing: smoothing of the power spectrum, and generation of
non-Gaussian features. These would induce a bias to estimates of the
weak-lensing potential power spectrum of the CMB. Using this effect, Planck
measurements of the temperature and polarization power spectrum, as well as
estimates of CMB lensing, are used to place limits (95% C. L.) on the amplitude
of a scale-invariant angular power spectrum of $\alpha$ fluctuations relative
to the mean value ($C_L^{\alpha}=A^\alpha_{\rm SI}/[L(L+1)]$) of $A^\alpha_{\rm
SI}\leq 1.6 \times 10^{-5}$. The limits depend on the assumed shape of the
$\alpha$-fluctuation power spectrum. For example, for a white noise angular
power spectrum ($C_L^{\alpha}=A^\alpha_{\rm WN}$), the limit is $A^\alpha_{\rm
WN}\leq 2.3 \times 10^{-8}$. It is found that the response of the CMB to
$\alpha$ fluctuations depends on a separate-universe approximation, such that
theoretical predictions are only reliable for $\alpha$ multipoles with
$L\lesssim 100$ . An optimal trispectrum estimator can be constructed and it is
found that it is only marginally more sensitive than lensing techniques for
Planck but significantly more sensitive when considering the next generation of
experiments. For a future CMB experiment with cosmic-variance limited
polarization sensitivity (e.g., CMB-S4), the optimal estimator could detect
$\alpha$ fluctuations with $A^\alpha_{\rm SI}>1.9 \times 10^{-6}$ and
$A^\alpha_{\rm WN} > 1.4 \times 10^{-9}$.


  X-ray astronomy needs to set bold, science driven goals for the next decade.
Only with defined science goals can we know what to work on, and a funding
agency appreciate the need for significant technology developments. To be a
forefront science the scale of advance must be 2 decades of sensitivity per
decade of time. To be stable to new discoveries these should be general,
discovery space, goals.
  A detailed consideration of science goals leads us to propose that a mirror
collecting area of 10 sq.meters with arcsecond resolution, good field of view
(>10 arcmin), and with high spectral resolution spectroscopy (R=1000-10,000)
defines the proper goal. This is about 100 times AXAF, or 30 times XMM. This
workshop has shown that this goal is only a reasonable stretch from existing
concepts, and may be insufficiently bold.
  An investment of roughly $10M/year for 5 years in X-ray optics technologies,
comparable to NASA's investment in ASTRO-E or a SMEX, is needed, and would pay
off hugely more than any small X-ray mission.


  We present quantum algorithms for the following graph problems: finding a
maximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal
non-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a
maximal flow in an integer network in time O(min(n^{7/6} sqrt m * U^{1/3},
sqrt{n U} m) log n), where n is the number of vertices, m is the number of
edges, and U <= n^{1/4} is an upper bound on the capacity of an edge.


  We study the symmetry reduction of nonlinear partial differential equations
which are used for describing diffusion processes in nonhomogeneous medium. We
find ansatzes reducing partial differential equations to systems of ordinary
differential equations. The ansatzes are constructed by using operators of
Lie-B\"acklund symmetry of third order ordinary differential equation. The
method gives the possibility to find solutions which cannot be obtained by
virtue of classical Lie method. Such solutions have been constructed for
nonlinear diffusion equations which are invariant with respect to
one-parameter, two-parameter and three-parameter Lie groups of point
transformations.


  Smart speakers and voice-based virtual assistants are core components for the
success of the IoT paradigm. Unfortunately, they are vulnerable to various
privacy threats exploiting machine learning to analyze the generated encrypted
traffic. To cope with that, deep adversarial learning approaches can be used to
build black-box countermeasures altering the network traffic (e.g., via packet
padding) and its statistical information. This letter showcases the inadequacy
of such countermeasures against machine learning attacks with a dedicated
experimental campaign on a real network dataset. Results indicate the need for
a major re-engineering to guarantee the suitable protection of commercially
available smart speakers.


  We introduce a new numerical method to compute resonances induced by
localized defects in crystals. This method solves an integral equation in the
defect region to compute analytic continuations of resolvents. Such an approach
enables one to express the resonance in terms of a "resonance source", a
function that is strictly localized within the defect region. The kernel of the
integral equation, to be applied on such a source term, is the Green function
of the perfect crystal, which we show can be computed efficiently by a complex
deformation of the Brillouin zone, named Brillouin Complex Deformation (BCD),
thereby extending to reciprocal space the concept of complex coordinate
transformations.


  We report jet substructure measurements in $\mathrm{p\kern-0.05em p}$ and
$\mbox{Pb-Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ALICE
detector. Charged-particle jets were reconstructed at midrapidity with the
ALICE tracking detectors using the anti-$k_{\mathrm{T}}$ algorithm with
resolution parameters $R=0.2$ and $R=0.4$. In $\mathrm{p\kern-0.05em p}$
collisions, the groomed jet momentum fraction, $z_{\mathrm{g}}$, and the
groomed jet radius, $\theta_{\mathrm{g}} \equiv R_{\mathrm{g}}/R$, are measured
for the first time using the Dynamical Grooming method. Additionally, new
systematic measurements of the infrared and collinear (IRC) safe ungroomed jet
angularities are presented. In heavy-ion collisions, we measure
$z_{\mathrm{g}}$ and $\theta_{\mathrm{g}}$ with the Soft Drop grooming
algorithm. The large underlying event in heavy-ion collisions poses a challenge
for the reconstruction of groomed jet observables, since fluctuations in the
background can cause groomed splittings to be misidentified. By using strong
grooming conditions to reduce this background, we report these observables
fully corrected for detector effects and background fluctuations for the first
time, and compare them to several theoretical models.


  We study the gauge and gravitational interactions of the stable non-BPS
D-particles of the type I string theory. The gravitational interactions are
obtained using the boundary state formalism while the SO(32) gauge interactions
are determined by evaluating disk diagrams with suitable insertions of boundary
changing (or twist) operators. In particular the gauge coupling of a D-particle
is obtained from a disk with two boundary components produced by the insertion
of two twist operators. We also compare our results with the amplitudes among
the non-BPS states of the heterotic string which are dual to the D-particles.
After taking into account the known duality and renormalization effects, we
find perfect agreement, thus confirming at a non-BPS level the expectations
based on the heterotic/type I duality.


  This paper aims to solve two fundamental problems on finite or infinite
horizon dynamic games with perfect or almost perfect information. Under some
mild conditions, we prove (1) the existence of subgame-perfect equilibria in
general dynamic games with almost perfect information, and (2) the existence of
pure-strategy subgame-perfect equilibria in perfect-information dynamic games
with uncertainty. Our results go beyond previous works on continuous dynamic
games in the sense that public randomization and the continuity requirement on
the state variables are not needed. As an illustrative application, a dynamic
stochastic oligopoly market with intertemporally dependent payoffs is
considered.


  This paper reports on the methods and results of a theoretical analysis to
design an insulator which must provide a thermally quiet environment to test on
ground delicate temperature sensors and associated electronics. These will fly
on board ESA's LISA PathFinder (LPF) mission as part of the thermal diagnostics
subsystem of the LISA Test-flight Package (LTP). We evaluate the heat transfer
function (in frequency domain) of a central body of good thermal conductivity
surrounded by a layer of a very poorly conducting substrate. This is applied to
assess the materials and dimensions necessary to meet temperature stability
requirements in the metal core, where sensors will be implanted for test. The
analysis is extended to evaluate the losses caused by heat leakage through
connecting wires, linking the sensors with the electronics in a box outside the
insulator. The results indicate that, in spite of the very demanding stability
conditions, a sphere of outer diameter of the order one metre is sufficient.


  In this paper, we construct a sequence $(c_k)_{k\in\mathbb{N}}$ of symplectic
capacities based on the Chiu-Tamarkin complex $C_{T,\ell}$, a
$\mathbb{Z}/\ell$-equivariant invariant coming from the microlocal theory of
sheaves. We compute $(c_k)_{k\in\mathbb{N}}$ for convex toric domains, which
are the same as the Gutt-Hutchings capacities. Our method also works for the
prequantized contact manifold $T^*X\times S^1$. We define a sequence of
"contact capacities" $([c]_k)_{k\in\mathbb{N}}$ on the prequantized contact
manifold $T^*X\times S^1$, and we compute them for prequantized convex toric
domains.


  The superconducting pairing instability---as determined by a divergence of
the two-particle susceptibility---is obtained in the mean field (BCS)
approximation in the thermodynamic limit. The usual practice is to examine this
property for a finite lattice. We illustrate that, while the conclusions remain
unchanged, the technical features are very different in the thermodynamic limit
and conform more closely with the usual treatment of phase transitions
encountered in, for example, the mean-field paramagnetic-ferromagnetic
transition. Furthermore, by going to the extreme dilute limit, one can
distinguish three dimensions from one and two dimensions, in which a pairing
instability occurs even for two particles.


  This article deals with the numerical modeling of the pulsating heat pipe
(PHP) and is based on the film evaporation/condensation model recently applied
to the single-bubble PHP (Das et al., 2010, "Thermally Induced Two-Phase
Oscillating Flow Inside a Capillary Tube," Int. J. Heat Mass Transfer,
53(19--20), pp. 3905--3913). The described numerical code can treat the PHP of
an arbitrary number of bubbles and branches. Several phenomena that occur
inside the PHP are taken into account: coalescence of liquid plugs, film
junction or rupture, etc. The model reproduces some of the experimentally
observed regimes of functioning of the PHP such as chaotic or intermittent
oscillations of large amplitudes. Some results on the PHP heat transfer are
discussed.


  We calculate numerically the fidelity and its susceptibility for the ground
state of the Dicke model. A minimum in the fidelity identifies the critical
value of the interaction where a quantum phase crossover, the precursor of a
phase transition for finite number of atoms N, takes place. The evolution of
these observables is studied as a function of N, and their critical exponents
evaluated. Using the critical exponents the universal curve for the specific
susceptibility is recovered. An estimate to the precision to which the ground
state wave function is numerically calculated is given, and found to have its
lowest value, for a fixed truncation, in a vicinity of the critical coupling.


  We determine the 6-dimensional solvmanifolds admitting an invariant complex
structure with holomorphically trivial canonical bundle. Such complex
structures are classified up to isomorphism, and the existence of strong
K\"ahler with torsion (SKT), generalized Gauduchon, balanced and strongly
Gauduchon metrics is studied. As an application we construct a holomorphic
family $(M,J_a)$ of compact complex manifolds such that $(M,J_a)$ satisfies the
$\partial\bar\partial$-Lemma and admits a balanced metric for any $a\not=0$,
but the central limit neither satisfies the $\partial\bar\partial$-Lemma nor
admits balanced metrics.


  The paper continues a series of publications devoted to the 3D nonlinear
localized coherent structures on the surface of vertically falling liquid
films. The work is primarily focussed on experimental investigations. We study:
(i) instabilities and transitions leading to 3D coherent structures; (ii)
characteristics of these structures. Some nonstationary effects are also
studied numerically. Our experimental results, as well as the results of other
investigators, are in a good agreement with our theoretical and numerical
predictions.


  We develop an incremental-tableau-based decision procedure for the
multi-agent epistemic logic MAEL(CD) (aka S5_n (CD)), whose language contains
operators of individual knowledge for a finite set Ag of agents, as well as
operators of distributed and common knowledge among all agents in Ag. Our
tableau procedure works in (deterministic) exponential time, thus establishing
an upper bound for MAEL(CD)-satisfiability that matches the (implicit)
lower-bound known from earlier results, which implies ExpTime-completeness of
MAEL(CD)-satisfiability. Therefore, our procedure provides a complexity-optimal
algorithm for checking MAEL(CD)-satisfiability, which, however, in most cases
is much more efficient. We prove soundness and completeness of the procedure,
and illustrate it with an example.


  When technology enters applications and processes with a long tradition of
controversial societal debate, multi-faceted new ethical and legal questions
arise. This paper focusses on the process of whistleblowing, an activity with
large impacts on democracy and business. Computer science can, for the first
time in history, provide for truly anonymous communication. We investigate this
in relation to the values and rights of accountability, fairness and data
protection, focusing on opportunities and limitations of the anonymity that can
be provided computationally; possible consequences of outsourcing
whistleblowing support; and challenges for the interpretation and use of some
relevant laws. We conclude that to address these questions, whistleblowing and
anonymous whistleblowing must rest on three pillars, forming a 'triangle of
whistleblowing protection and incentivisation' that combines anonymity in a
formal and technical sense; whistleblower protection through laws; and other
norms and practices including organisational error culture.


  Magnetic excitations are investigated for a hexagonal polar magnet Fe2Mo3O8
by terahertz spectroscopy. We observed magnon modes including an electric-field
active magnon, electromagnon, in the collinear antiferromagnetic phase with
spins parallel to the c axis. We unravel the nature of these excitations by
investigating the correlation between the evolution of the mode profile and the
magnetic transition from antiferromagnetic to ferrimagnetic order induced by
magnetic field or Zn-doping. We propose that the observed electromagnon mode
involves the collective precession of the spins with oscillating in-plane
electric polarization through the mechanism of the linear magnetoelectric
effect.


  Rabi nutations of a single electron spin in a single defect center have been
detected. The coherent evolution of the spin quantum state is followed via
optical detection of the spin state. Coherence times up to several microseconds
at room temperature have been measured. Optical readout of the spin states
leads to decoherence, equivalent to the so-called Zeno effect. Quantum beats
between electron spin transitions in a single spin Hahn echo experiment are
observed. A closer analysis reveals that beats also result from the hyperfine
coupling of the electron spin to a single 14N nuclear spin. The results are
analysed in terms of a density matrix approach of an electron spin interacting
with two oscillating fields.


  Let $FI(X,K)$ be the finitary incidence algebra of a poset $X$ over a field
$K$. In this short note we establish when $FI(X,K)$ satisfies a polynomial
identity and when its group of units $\mathcal{U}(FI(X,K))$ satisfies a group
identity. The Lie derived length of $FI(X,K)$ and the derived length of
$\mathcal{U}(FI(X,K))$ are also determined.


  The orthogonal derivative is defined as a limit of an integral whose kernel
contains an orthogonal polynomial with its measure. When in practice no limit
is taken, it means that the accuracy of the derivative depends on the second
derivative of the given function. Liptaj shows that it is possible to define a
kernel in such a way that the accuracy depends on a higher derivative at your
own choice. The accuracy is therefore much greater than with the orthogonal
derivative. However Diekema and Koornwinder find a similar extension starting
directly from of the orthogonal derivative. The new kernel is not orthogonal
for order greater then one. The transfer function for this new derivative is
given.


  This study proposes a novel precoding scheme for multiuser multiple-input
multiple-output (MIMO) relay systems in the presence of imperfect channel state
information (CSI). The base station (BS) and the MIMO relay station (RS) are
both equipped with the same codebook of unitary matrices. According to each
element of the codebook, we create a latent precoding matrix pair, namely a BS
precoding matrix and an RS precoding matrix. The RS precoding matrix is formed
by multiplying the appropriate unitary matrix from the codebook by a power
scaling factor. Based on the given CSI and a block of transmit symbols, the
optimum precoding matrix pair, within the class of all possible latent
precoding matrix pairs derived from the various unitary matrices, is selected
by a suitable selection mechanism for transmission, which is designed to
minimize the squared Euclidean distance between the pre-estimated received
vector and the true transmit symbol vector. We develop a minimum mean square
error (MMSE) design algorithm for the construction of the latent precoding
matrix pairs. In the proposed scheme, rather than sending the complete
processing matrix, only the index of the unitary matrix and its power scaling
factor are sent by the BS to the RS. This significantly reduces the overhead.
Simulation results show that compared to other recently reported precoding
algorithms the proposed precoding scheme is capable of providing improved
robustness against the effects of CSI estimation errors and multiuser
interference.


  We present BVR polarimetric study of the cool active star LO Peg for the
first time. LO Peg was found to be highly polarized among the cool active
stars. Our observations yield average values of polarization in LO Peg: $P_B
=0.387\pm 0.004%$, $\theta_B = 88\deg\pm1\deg$; $P_V=0.351\pm0.004%$,
$\theta_V=91\deg\pm1\deg$; and $P_R= 0.335\pm0.003%$, $\theta_R =
91\deg\pm1\deg$. Both the degree of polarization and the position angle are
found to be variable. The semi-amplitude of the polarization variability in B,
V and R bands are found to be $0.18\pm0.02$%, $0.13\pm0.01$% and
$0.10\pm0.02$%, respectively. We suggest that the levels of polarization
observed in LO Peg could be the result of scattering of an anisotropic stellar
radiation field by an optically thin circumstellar envelope or scattering of
the stellar radiation by prominence-like structures.


  We study numerical methods of tomography in domains with a reflecting
obstacle. It will be shown that tomography with sets containing both broken
rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a
smaller error between the original and reconstructed image compared to
classical tomography methods.


  We present a three player Bayesian game for which there is no epsilon
equilibria in Borel measurable strategies for small enough epsilon, however
there are non-measurable equilibria.


  The classical problem of construction of Gardner's deformations for
infinite-dimensional completely integrable systems of evolutionary partial
differential equations (PDE) amounts essentially to finding the recurrence
relations between the integrals of motion. Using the correspondence between the
zero-curvature representations and Gardner deformations for PDE, we construct a
Gardner's deformation for the Krasil'shchik-Kersten system. For this, we
introduce the new nonlocal variables in such a way that the rules to
differentiate them are consistent by virtue of the equations at hand and
second, the full system of Krasil'shchik-Kersten's equations and the new rules
contains the Korteweg-de Vries equation and classical Gardner's deformation for
it.
  PACS: 02.30.Ik, 02.30,Jr, 02.40.-k, 11.30.-j


  We introduce an operational rewriting-based semantics for strictly positive
nested higher-order (co)inductive types. The semantics takes into account the
"limits" of infinite reduction sequences. This may be seen as a refinement and
generalization of the notion of productivity in term rewriting to a setting
with higher-order functions and with data specified by nested higher-order
inductive and coinductive definitions. Intuitively, we interpret lazy data
structures in a higher-order functional language by potentially infinite terms
corresponding to their complete unfoldings.
  We prove an approximation theorem which essentially states that if a term
reduces to an arbitrarily large finite approximation of an infinite object in
the interpretation of a coinductive type, then it infinitarily (i.e. in the
"limit") reduces to an infinite object in the interpretation of this type. We
introduce a sufficient syntactic correctness criterion, in the form of a type
system, for finite terms decorated with type information. Using the
approximation theorem, we show that each well-typed term has a well-defined
interpretation in our semantics.


  Large Language Models (LLMs) have shown impressive capabilities across a wide
variety of tasks. However, they still face challenges with long-horizon
planning. To study this, we propose path planning tasks as a platform to
evaluate LLMs' ability to navigate long trajectories under geometric
constraints. Our proposed benchmark systematically tests path-planning skills
in complex settings. Using this, we examined GPT-4's planning abilities using
various task representations and prompting approaches. We found that framing
prompts as Python code and decomposing long trajectory tasks improve GPT-4's
path planning effectiveness. However, while these approaches show some promise
toward improving the planning ability of the model, they do not obtain optimal
paths and fail at generalizing over extended horizons.


  This study shows that the dielectric function of crystalline Si quantum wells
(c-Si QW) is influenced by both carrier confinement and electron-phonon
interactions. The energy shifts and lifetime broadening of the excitonic E1
direct gap transition of c-Si QWs from 2 to 10 nm are found to have a
significant dimensional and temperature dependence that can be traced to
changes in the phonon dispersion of nanoscale films. The influence of
electron-phonon interactions on the dielectric function was verified by
altering the phonon dispersion using different dielectric layers above a 5 nm
c-Si QW.


  In a recent landmark paper, Khoa L\^e (2020) established a stochastic sewing
lemma which since has found many applications in stochastic analysis. He
further conjectured that a similar result may hold in the context of the
reconstruction theorem within Hairer's regularity structures. The purpose of
this article is to provide such a stochastic reconstruction theorem. We also
discuss two variations of this theorem, motivated by different constructions of
stochastic integration against white noise. Our formulation makes use of the
distributional viewpoint of Caravenna--Zambotti (2021).


  We demonstrate quantum computation of two-point correlation functions for a
Heisenberg spin chain. Using the IBM Q 20 quantum machines, we find that for
two sites the correlation functions produce the exact results reliably. For
four sites, results from the IBM Q 20 Tokyo quantum computer are noisy due to
read out errors and decoherence. Nevertheless, the correlation functions retain
the correct spectral information. This is illustrated in the frequency domain
by accurately extracting the magnon energies from peaks in the spectral
function.


  When a quantum system is divided into two local subsystems, measurements on
the two subsystems can exhibit correlations beyond those possible in a
classical joint probability distribution; these are partially explained by
entanglement, and more generally by a wider class of measures such as the
quantum discord. In this work, I introduce a simple thought experiment defining
a new measure of quantum correlations, which I call the accord, and write the
result as a minimax optimization over unitary matrices. I find the exact result
for pure states as a simple function of the Schmidt coefficients and provide a
complete proof, and I likewise provide and prove the result for several classes
of mixed states, notably including all states of two qubits and the
experimentally relevant case of a pure state mixed with colorless noise. I
demonstrate that for two qubit states the accord provides a tight lower bound
on the discord; for Bell diagonal states it is also an upper bound on
entanglement.


  The development of algorithms for unsupervised pattern recognition by
nonlinear clustering is a notable problem in data science. Markov clustering
(MCL) is a renowned algorithm that simulates stochastic flows on a network of
sample similarities to detect the structural organization of clusters in the
data, but it has never been generalized to deal with data nonlinearity. Minimum
Curvilinearity (MC) is a principle that approximates nonlinear sample distances
in the high-dimensional feature space by curvilinear distances, which are
computed as transversal paths over their minimum spanning tree, and then stored
in a kernel. Here we propose MC-MCL, which is the first nonlinear kernel
extension of MCL and exploits Minimum Curvilinearity to enhance the performance
of MCL in real and synthetic data with underlying nonlinear patterns. MC-MCL is
compared with baseline clustering methods, including DBSCAN, K-means and
affinity propagation. We find that Minimum Curvilinearity provides a valuable
framework to estimate nonlinear distances also when its kernel is applied in
combination with MCL. Indeed, MC-MCL overcomes classical MCL and even baseline
clustering algorithms in different nonlinear datasets.


  Previous research has studied the task of segmenting cinematic videos into
scenes and into narrative acts. However, these studies have overlooked the
essential task of multimodal alignment and fusion for effectively and
efficiently processing long-form videos (>60min). In this paper, we introduce
Multimodal alignmEnt aGgregation and distillAtion (MEGA) for cinematic
long-video segmentation. MEGA tackles the challenge by leveraging multiple
media modalities. The method coarsely aligns inputs of variable lengths and
different modalities with alignment positional encoding. To maintain temporal
synchronization while reducing computation, we further introduce an enhanced
bottleneck fusion layer which uses temporal alignment. Additionally, MEGA
employs a novel contrastive loss to synchronize and transfer labels across
modalities, enabling act segmentation from labeled synopsis sentences on video
shots. Our experimental results show that MEGA outperforms state-of-the-art
methods on MovieNet dataset for scene segmentation (with an Average Precision
improvement of +1.19%) and on TRIPOD dataset for act segmentation (with a Total
Agreement improvement of +5.51%)


  In this paper we present low-complexity blind multi-input multi-output (MIMO)
adaptive linear multiuser receivers for direct sequence code division multiple
access (DS-CDMA) systems using multiple transmit antennas and space-time block
codes (STBC) in multipath channels. A space-time code-constrained constant
modulus (CCM) design criterion based on constrained optimization techniques and
low-complexity stochastic gradient (SG) adaptive algorithms are developed for
estimating the parameters of the space-time linear receivers. The receivers are
designed by exploiting the unique structure imposed by both spreading codes and
STBC. A blind space-time channel estimation scheme for STBC systems based on a
subspace approach is also proposed along with an efficient SG algorithm.
Simulation results for a downlink scenario assess the receiver structures and
algorithms and show that the proposed schemes achieve excellent performance,
outperforming existing methods.


  Consider the problem of a Multiple-Input Multiple-Output (MIMO)
Multiple-Access Channel (MAC) at the limit of large number of users. Clearly,
in practical scenarios, only a small subset of the users can be scheduled to
utilize the channel simultaneously. Thus, a problem of user selection arises.
However, since solutions which collect Channel State Information (CSI) from all
users and decide on the best subset to transmit in each slot do not scale when
the number of users is large, distributed algorithms for user selection are
advantageous.
  In this paper, we analyse a distributed user selection algorithm, which
selects a group of users to transmit without coordinating between users and
without all users sending CSI to the base station. This threshold-based
algorithm is analysed for both Zero-Forcing (ZF) and Minimum Mean Square Error
(MMSE) receivers, and its expected sum-rate in the limit of large number of
users is investigated. It is shown that for large number of users it achieves
the same scaling laws as the optimal centralized scheme.


  All attempts to directly detect particle dark matter (DM) scattering on
nuclei suffer from the partial or total loss of sensitivity for DM masses in
the GeV range or below. We derive novel constraints from the inevitable
existence of a subdominant, but highly energetic, component of DM generated
through collisions with cosmic rays. Subsequent scattering inside conventional
DM detectors, as well as neutrino detectors sensitive to nuclear recoils,
limits the DM-nucleon scattering cross section to be below $10^{-31}$ cm$^2$
for both spin-independent and spin-dependent scattering of light DM.


  We study the approximation of fixed points of nonexpansive mappings in CAT(k)
spaces. We show that the iterative sequence generated by the Moudafi's
viscosity type algorithm converges to one of the fixed points of the
nonexpansive mapping depending on the contraction applied in the algorithm.


  We give infinite series of groups Gamma and of compact complex surfaces of
general type S with fundamental group Gamma such that 1) Any surface S' with
the same Euler number as S, and fundamental group Gamma, is diffeomorphic to S.
2) The moduli space of S consists of exactly two connected components,
exchanged by complex conjugation.
  Whence, i) On the one hand we give simple counterexamples to the DEF = DIFF
question whether deformation type and diffeomorphism type coincide for
algebraic surfaces. ii) On the other hand we get examples of moduli spaces
without real points. iii) Another interesting corollary is the existence of
complex surfaces S whose fundamental group Gamma cannot be the fundamental
group of a real surface. Our surfaces are surfaces isogenous to a product;
i.e., they are quotients (C_1 X C_2)/G of a product of curves by the free
action of a finite group G. They resemble the classical hyperelliptic surfaces,
in that G operates freely on C_1, while the second curve is a triangle curve,
meaning that $C_2 / G \equiv \PP ^1 and the covering is branched in exactly
three points.


  We propose an invariant see-saw (ISS) approach to model building, based on
the observation that see-saw models of neutrino mass and mixing fall into basis
invariant classes labelled by the Casas-Ibarra $R$-matrix, which we prove to be
invariant not only under basis transformations but also non-unitary
right-handed neutrino transformations $S$. According to the ISS approach, given
any see-saw model in some particular basis one may determine the invariant $R$
matrix and hence the invariant class to which that model belongs. The
formulation of see-saw models in terms of invariant classes puts them on a
firmer theoretical footing, and allows different see-saw models in the same
class to be related more easily, while their relation to the $R$-matrix makes
them more easily identifiable in phenomenological studies. We also present an
ISS mass formula which may be useful in model building. To illustrate the ISS
approach we show that sequential dominance (SD) models form basis invariant
classes in which the $R$-matrix is approximately related to a permutation of
the unit matrix, and quite accurately so in the case of constrained sequential
dominance (CSD) and tri-bimaximal mixing. Using the ISS approach we discuss
examples of models in which the mixing naturally arises (at least in part) from
the charged lepton or right-handed neutrino sectors and show that they are in
the same invariant class as SD models. We also discuss the application of our
results to flavour-dependent leptogenesis where we show that the case of a real
$R$ matrix is approximately realized in SD, and accurately realized in CSD.


  This paper presents the analysis of an efficient alternative interface
circuit for MEMS electrostatic energy harvesters. It is entirely composed by
diodes and capacitors. Based on modeling and simulation, the anti-phase
gap-closing structure is investigated. We find that when configured as a
voltage multiplier, it can operate at very low acceleration amplitudes. In
addition, the allowed maximum voltage between electrodes is barely limited by
the pull-in effect. The parasitic capacitance of the harvester and non-ideal
characteristics of electronic components are taken into account. A lumped-model
of the harvesting system has been implemented in a circuit simulator.
Simulation results show that an output voltage of 22 V is obtained with 0.15 g
input acceleration. The minimum necessary ratio between the maximum and minimum
capacitances of the generators which allows operation of the circuit, can be
lower than 2. This overcomes a crucial obstacle in low-power energy harvesting
devices. A comparison between the voltage multiplier against other current
topologies is highlighted. An advantage of the former over the latter is to
generate much higher saturation voltage, while the minimum required initial
bias and the minimum capacitance ratio in both cases are in the similar levels.


  The paper considers a general concept of dichotomy with different growth
rates for linear discrete-time systems in Banach spaces. Characterizations in
terms of Lyapunov type sequences of norms are given. The approach is
illustrated by various examples.


  A necessary and sufficient condition is given for semi-ampleness of a
numerically effective (nef) and big line bundle in positive characteristic. One
application is to the geometry of the universal stable curve over M_g,
specifically, the semi-ampleness of the relative dualizing sheaf, in positive
characteristic. An example is given which shows this and the semi-ampleness
criterion fail in characteristic zero. A second application is to Mori's
program for minimal models of 3-folds in positive characteristic, namely, to
the existence of birational extremal contractions.


  The universality of deep neural networks across different modalities and
their generalization capabilities to unseen domains play an essential role in
medical image segmentation. The recent Segment Anything Model (SAM) has
demonstrated its potential in both settings. However, the huge computational
costs, demand for manual annotations as prompts and conflict-prone decoding
process of SAM degrade its generalizability and applicability in clinical
scenarios. To address these issues, we propose an efficient self-prompting SAM
for universal domain-generalized medical image segmentation, named ESP-MedSAM.
Specifically, we first devise the Multi-Modal Decoupled Knowledge Distillation
(MMDKD) strategy to construct a lightweight semi-parameter sharing image
encoder that produces discriminative visual features for diverse modalities.
Further, we introduce the Self-Patch Prompt Generator (SPPG) to automatically
generate high-quality dense prompt embeddings for guiding segmentation
decoding. Finally, we design the Query-Decoupled Modality Decoder (QDMD) that
leverages a one-to-one strategy to provide an independent decoding channel for
every modality. Extensive experiments indicate that ESP-MedSAM outperforms
state-of-the-arts in diverse medical imaging segmentation tasks, displaying
superior modality universality and generalization capabilities. Especially,
ESP-MedSAM uses only 4.5\% parameters compared to SAM-H. The source code is
available at https://github.com/xq141839/ESP-MedSAM.


  Using the cluster Gutzwiller mean-field method, we numerically study the
ground-state phase diagram of the non-hard-core two-component interacting
bosons trapped in a two-leg ladder with and without an artificial magnetic
field. There are three quantum phases namely Mott insulator (MI),
supercounterfluid (SCF), and superfluid (SF) are found in the phase diagram.
Interestingly, several loophole SCF phases are observed at a sufficiently small
intra- to inter-leg hopping ratio when the magnetic flux is absent. While if
the ratio is not so small, the loophole SCF phase would disappear, but it can
still be induced by applying a sufficiently large magnetic flux. Additionally,
we also find that the presence of the magnetic flux leads to an enlargement of
the MI lobe and the conventional SCF lobe. Moreover, the SF-MI phase boundary
is quantitatively consistent with the strong-couping expansion at a weak
hopping amplitude.


  We introduce an odd double affine Hecke algebra (DaHa) generated by a
classical Weyl group W and two skew-polynomial subalgebras of anticommuting
generators. This algebra is shown to be Morita equivalent to another new DaHa
which are generated by W and two polynomial-Clifford subalgebras. There is yet
a third algebra containing a spin Weyl group algebra which is Morita
(super)equivalent to the above two algebras. We establish the PBW properties
and construct Verma-type representations via Dunkl operators for these
algebras.


  Experiments with $\Omega^{\pm}$ baryons moving in a crystal at LHC in
addition to EDM measurement open possibility to study electric quadrupole
moment, to observe birefringence effect (spin oscillations and spin dichroism)
for $\Omega^{\pm}$ baryons and to get information about constants describing
P-odd, T-odd effects at $\Omega^{\pm}$ baryon interactions with electrons and
nuclei


  If r(s, t) = p, we shall call Kp a Ramsey Minimal Example. We prove that if
r{s,t) = p, and one edge is deleted from the Ramsey Minimal Example, Kp, the
resulting graph no longer has the Ramsey property, that is, its edges can be
colored red or blue so that the "red" subgraph does not contain Ks and the
"blue" subgraph does not contain Kt. The paper is written in an accessible
style explaining the process that led us to make the conjecture and then prove
this result.


  In this paper, we study the extinction time of logistic branching processes
which are perturbed by an independent random environment driven by a Brownian
motion. Our arguments use a Lamperti-type representation which is interesting
on its own right and provides a one to one correspondence between the latter
family of processes and the family of Feller diffusions which are perturbed by
an independent spectrally positive L\'evy process. When the independent random
perturbation (of the Feller diffusion) is driven by a subordinator then the
logistic branching processes in a Brownian environment converges to a specified
distribution; otherwise, it becomes extinct a.s. In the latter scenario, and
following a similar approach to Lambert (Lambert, Ann. Appl. Probab., 2005), we
provide the expectation and the Laplace transform of the absorption time, as a
functional of the solution to a Ricatti differential equation. In particular,
the latter characterises the law of the process coming down from infinity.


  This note aims at presenting several new theoretical results for the compound
Poisson point process, which follows the work of Zhang \emph{et al.}
[Insurance~Math.~Econom.~59(2014), 325-336]. The first part provides a new
characterization for a discrete compound Poisson point process (proposed by
{Acz{\'e}l} [Acta~Math.~Hungar.~3(3)(1952), 219-224]), it extends the
characterization of the Poisson point process given by Copeland and Regan
[Ann.~Math.~(1936): 357-362]. Next, we derive some concentration inequalities
for discrete compound Poisson point process (negative binomial random variable
with unknown dispersion is a significant example). These concentration
inequalities are potentially useful in count data regressions. We give an
application in the weighted Lasso penalized negative binomial regression whose
KKT conditions of penalized likelihood hold with high probability and then we
derive non-asymptotic oracle inequalities for a weighted Lasso estimator.


  We characterize the $2$-Killing vector fields on a multiply twisted product
manifold, with a special view towards generalized spacetimes. More precisely,
we determine the nonlinear differential equations that completely describe them
and the twisted functions, give particular solutions, and construct examples.


  A new interpretation offers a consistent conceptual basis for nonrelativistic
quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the
violation of Bell's inequality is explained by maintaining realism, inductive
inference and Einstein separability.


  We employ a master equation approach to study the second-order quantum
autocorrelation functions for up to two independent quantum dot excitons,
coupled to an off-resonant cavity in a photonic crystal - single quantum dot
system. For a single coupled off-resonant exciton, we observe novel oscillatory
behaviour in the early-time dynamics of the cavity autocorrelation function,
which leads to decreased antibunching relative to the exciton mode. With a
second coupled exciton in the system, we find that the magnitude and the
lifetime of these oscillations greatly increases, since the cavity is then able
to exchange photons with multiple excitonic resonances. We unambiguously show
that this spoils the antibunching characteristics of the cavity quasi-mode,
while the autocorrelation of the first exciton is unaffected. We also examine
the effects of detector time resolution and make a direct connection to a
series of recent experiments.


  A review of the distribution of dark matter on sub-parsec scales at the
centers of galaxies.


  We have analytically determined the refractive index for the mechanical
refraction of a relativistic particle for its all possible speeds. We have
critically analysed the importance of Descartes' metaphysical theory and
extended it in this regard. We have considered the conservation of the
tangential component of the relativistic momentum and the relativistic energy
of the particle in the process of the mechanical refraction within the
optical-mechanical analogy. Our result for the mechanical refractive index
exactly matches with the forms of both the Fermat's result on Snell's law of
optical refraction at the ultra-relativistic limit and the Descartes'
metaphysical result on the pseudo-Snell law of optical refraction at the
non-relativistic limit.


  Dark matter (DM) with masses of order an electronvolt or below can have a
non-zero coupling to electromagnetism. In these models, the ambient DM behaves
as a new classical source in Maxwell's equations, which can excite potentially
detectable electromagnetic (EM) fields in the laboratory. We describe a new
proposal for using integrated photonics to search for such DM candidates with
masses in the 0.1 eV - few eV range. This approach offers a wide range of
wavelength-scale devices like resonators and waveguides that can enable a novel
and exciting experimental program. In particular, we show how refractive
index-modulated resonators, such as grooved or periodically-poled microrings,
or patterned slabs, support EM modes with efficient coupling to DM. When
excited by the DM, these modes can be read out by coupling the resonators to a
waveguide that terminates on a micron-scale-sized single photon detector, such
as a single pixel of an ultra-quiet charge-coupled device or a superconducting
nanowire. We then estimate the sensitivity of this experimental concept in the
context of axion-like particle and dark photon models of DM, showing that the
scaling and confinement advantages of nanophotonics may enable exploration of
new DM parameter space.


  In this paper we present a method to design paraunitary polyphase matrices of
critically sampled rational filter banks. The method is based on (P,Q)
shift-invariant systems, and so any kind of rational splitting of the frequency
spectrum can be achieved using this method. Ideal (P,Q) shift-invariant system
with smallest P and Q that map of a band of input spectrum to the output
spectrum are obtained. A new set of filters is obtained that characterize a
(P,Q) shift-invariant system. Ideal frequency spectrum of these filters are
obtained using ideal $(P,Q)$ shift-invariant systems. Actual paraunitary
polyphase matrices are then obtained by minimizing the stopband energies of
these filters against the parameters of the paraunitary polyphase matrices.


  We consider the problem of estimating the roughness of the volatility in a
stochastic volatility model that arises as a nonlinear function of fractional
Brownian motion with drift. To this end, we introduce a new estimator that
measures the so-called roughness exponent of a continuous trajectory, based on
discrete observations of its antiderivative. We provide conditions on the
underlying trajectory under which our estimator converges in a strictly
pathwise sense. Then we verify that these conditions are satisfied by almost
every sample path of fractional Brownian motion (with drift). As a consequence,
we obtain strong consistency theorems in the context of a large class of rough
volatility models. Numerical simulations show that our estimation procedure
performs well after passing to a scale-invariant modification of our estimator.