  In many human brain network studies, we do not have sufficient number (n) of
images relative to the number (p) of voxels due to the prohibitively expensive
cost of scanning enough subjects. Thus, brain network models usually suffer the
small-n large-p problem. Such a problem is often remedied by sparse network
models, which are usually solved numerically by optimizing L1-penalties.
Unfortunately, due to the computational bottleneck associated with optimizing
L1-penalties, it is not practical to apply such methods to construct
large-scale brain networks at the voxel-level. In this paper, we propose a new
scalable sparse network model using cross-correlations that bypass the
computational bottleneck. Our model can build sparse brain networks at the
voxel level with p > 25000. Instead of using a single sparse parameter that may
not be optimal in other studies and datasets, the computational speed gain
enables us to analyze the collection of networks at every possible sparse
parameter in a coherent mathematical framework via persistent homology. The
method is subsequently applied in determining the extent of heritability on a
functional brain network at the voxel-level for the first time using twin fMRI.


  This paper derives fundamental limits on the performance of compressive
classification when the source is a mixture of Gaussians. It provides an
asymptotic analysis of a Bhattacharya based upper bound on the
misclassification probability for the optimal Maximum-A-Posteriori (MAP)
classifier that depends on quantities that are dual to the concepts of
diversity-order and coding gain in multi-antenna communications. The
diversity-order of the measurement system determines the rate at which the
probability of misclassification decays with signal-to-noise ratio (SNR) in the
low-noise regime. The counterpart of coding gain is the measurement gain which
determines the power offset of the probability of misclassification in the
low-noise regime. These two quantities make it possible to quantify differences
in misclassification probability between random measurement and
(diversity-order) optimized measurement. Results are presented for two-class
classification problems first with zero-mean Gaussians then with nonzero-mean
Gaussians, and finally for multiple-class Gaussian classification problems. The
behavior of misclassification probability is revealed to be intimately related
to certain fundamental geometric quantities determined by the measurement
system, the source and their interplay. Numerical results, representative of
compressive classification of a mixture of Gaussians, demonstrate alignment of
the actual misclassification probability with the Bhattacharya based upper
bound. The connection between the misclassification performance and the
alignment between source and measurement geometry may be used to guide the
design of dictionaries for compressive classification.


  We prove that, for every graph $F$ with at least one edge, there is a
constant $c_F$ such that there are graphs of arbitrarily large chromatic number
and the same clique number as $F$ in which every $F$-free induced subgraph has
chromatic number at most $c_F$. This generalises recent theorems of
Bria\'{n}ski, Davies and Walczak, and Carbonero, Hompe, Moore and Spirkl. Our
results imply that for every $r\geq 3$ the class of $K_r$-free graphs has a
very strong vertex Ramsey-type property, giving a vast generalisation of a
result of Folkman from 1970. We also prove related results for tournaments,
hypergraphs and infinite families of graphs, and show an analogous statement
for graphs where clique number is replaced by odd girth.


  For the origin of heavy r-process elements, different sources have been
proposed, e.g., core-collapse supernovae or neutron star mergers. Old
metal-poor stars carry the signature of the astrophysical source(s). Among the
elements dominantly made by the r-process, europium (Eu) is relatively easy to
observe. In this work we simulate the evolution of europium in our galaxy with
the inhomogeneous chemical evolution model 'ICE', and compare our results with
spectroscopic observations. We test the most important parameters affecting the
chemical evolution of Eu: (a) for neutron star mergers the coalescence time
scale of the merger ($t_{\mathrm{coal}}$) and the probability to experience a
neutron star merger event after two supernova explosions occurred and formed a
double neutron star system ($P_{\mathrm{NSM}}$) and (b) for the sub-class of
magneto-rotationally driven supernovae ("Jet-SNe"), their occurrence rate
compared to standard supernovae ($P_{\mathrm{Jet-SN}}$). We find that the
observed [Eu/Fe] pattern in the galaxy can be reproduced by a combination of
neutron star mergers and magneto-rotationally driven supernovae as r-process
sources. While neutron star mergers alone seem to set in at too high
metallicities, Jet-SNe provide a cure for this deficiency at low metallicities.
Furthermore, we confirm that local inhomogeneities can explain the observed
large spread in the europium abundances at low metallicities. We also predict
the evolution of [O/Fe] to test whether the spread in $\alpha$-elements for
inhomogeneous models agrees with observations and whether this provides
constraints on supernova explosion models and their nucleosynthesis.


  We consider a functional calculus for compact operators, acting on the
singular values rather than the spectrum, which appears frequently in applied
mathematics. Necessary and sufficient conditions for this singular value
functional calculus to be Lipschitz-continuous with respect to the
Hilbert-Schmidt norm are given. We also provide sharp constants.


  Metals are highly opaque, yet we show that densely packed arrays of metallic
nanoparticles can be more transparent to infrared radiation than dielectrics
such as germanium, even for arrays that are over 75% metal by volume. Despite
strong interactions between the metallic particles, these arrays form effective
dielectrics that are virtually dispersion-free, making possible the design of
optical components that are achromatic over ultra-broadband ranges of
wavelengths from a few microns up to millimetres or more. Furthermore, the
local refractive indices may be tuned by altering the size, shape, and spacing
of the nanoparticles, allowing the design of gradient-index lenses that guide
and focus light on the microscale. The electric field is also strongly
concentrated in the gaps between the metallic nanoparticles, and the
simultaneous focusing and squeezing of the electric field produces strong
`doubly-enhanced' hotspots which could boost measurements made using infrared
spectroscopy and other non-linear processes over a broad range of frequencies,
with minimal heat production.


  Prices of commodities or assets produce what is called time-series. Different
kinds of financial time-series have been recorded and studied for decades.
Nowadays, all transactions on a financial market are recorded, leading to a
huge amount of data available, either for free in the Internet or commercially.
Financial time-series analysis is of great interest to practitioners as well as
to theoreticians, for making inferences and predictions. Furthermore, the
stochastic uncertainties inherent in financial time-series and the theory
needed to deal with them make the subject especially interesting not only to
economists, but also to statisticians and physicists. While it would be a
formidable task to make an exhaustive review on the topic, with this review we
try to give a flavor of some of its aspects.


  We employ physics-informed neural networks (PINNs) to infer properties of
biological materials using synthetic data. In particular, we successfully apply
PINNs on inferring the thrombus permeability and visco-elastic modulus from
thrombus deformation data, which can be described by the fourth-order
Cahn-Hilliard and Navier-Stokes Equations. In PINNs, the partial differential
equations are encoded into the loss function, where partial derivatives can be
obtained through automatic differentiation (AD). In addition, to tackling the
challenge of calculating the fourth-order derivative in the Cahn-Hilliard
equation with AD, we introduce an auxiliary network along with the main neural
network to approximate the second-derivative of the energy potential term. Our
model can predict simultaneously unknown parameters and velocity, pressure, and
deformation gradient fields by merely training with partial information among
all data, i.e., phase-field and pressure measurements, and is also highly
flexible in sampling within the spatio-temporal domain for data acquisition. We
validate our model by numerical solutions from the spectral/\textit{hp} element
method (SEM) and demonstrate its robustness by training it with noisy
measurements. Our results show that PINNs can accurately infer the material
properties with noisy synthetic data, and thus they have great potential for
inferring these properties from experimental multi-modality and multi-fidelity
data.


  In this paper we estimate the Lusternik-Schnirelmann category of the
connected sum of two manifolds through their categories. We achieve a more
general result regarding the category of a quotient space X/A where A is a
suitable subspace of X.


  The antiproton-to-proton ratio in the cosmic-ray spectrum is a sensitive
probe of new physics. Using recent measurements of the cosmic-ray antiproton
and proton fluxes in the energy range of 1-1000 GeV, we study the contribution
to the $\bar{p}/p$ ratio from secondary antiprotons that are produced and
subsequently accelerated within individual supernova remnants. We consider
several well-motivated models for cosmic-ray propagation in the interstellar
medium and marginalize our results over the uncertainties related to the
antiproton production cross section and the time-, charge-, and
energy-dependent effects of solar modulation. We find that the increase in the
$\bar{p}/p$ ratio observed at rigidities above $\sim$ 100 GV cannot be
accounted for within the context of conventional cosmic-ray propagation models,
but is consistent with scenarios in which cosmic-ray antiprotons are produced
and subsequently accelerated by shocks within a given supernova remnant. In
light of this, the acceleration of secondary cosmic rays in supernova remnants
is predicted to substantially contribute to the cosmic-ray positron spectrum,
accounting for a significant fraction of the observed positron excess.


  A recently developed method, introduced in Phys. Rev. Lett. 94 (2005) 180403,
Phys. Rev. B 72 (2005) 064302, Phys. Lett. A 344 (2005) 84, systematically
improved the convergence of generic path integrals for transition amplitudes.
This was achieved by analytically constructing a hierarchy of $N$-fold
discretized effective actions $S^{(p)}_N$ labeled by a whole number $p$ and
starting at $p=1$ from the naively discretized action in the mid-point
prescription. The derivation guaranteed that the level $p$ effective actions
lead to discretized transition amplitudes differing from the continuum limit by
a term of order $1/N^p$. Here we extend the applicability of the above method
to the calculation of energy expectation values. This is done by constructing
analytical expressions for energy estimators of a general theory for each level
$p$. As a result of this energy expectation values converge to the continuum as
$1/N^p$. Finally, we perform a series of Monte Carlo simulations of several
models, show explicitly the derived increase in convergence, and the ensuing
speedup in numerical calculation of energy expectation values of many orders of
magnitude.


  We describe some recent approaches to likelihood based inference in the
presence of nuisance parameters. Our approach is based on plotting the
likelihood function and the $p$-value function, using recently developed third
order approximations. Orthogonal parameters and adjustments to profile
likelihood are also discussed. Connections to classical approaches of
conditional and marginal inference are outlined.


  In this work, an analytic expression is derived for the optical field
generated by an off-axis Gaussian beam diffracted by a Discrete
Vortex-Producing Lens. With this system, a multifocal arrangement of asymmetric
optical vortices is obtained whose topological charge values change with the
position along the optical axis. This scheme allows obtaining a principal
asymmetric vortex corresponding with the topological charge value of the phase
mask and secondary ones with different charges. With the analytical expression,
the effects induced by the discretization and misalignment on the irradiance
and phase of each vortex can be simultaneously studied. A signal-to-noise ratio
expression is derived to verify if the noise of the multifocal system might
affect importantly the optical vortices of interest. Finally, we proposed new
metrics to measure the off-axis displacement using the phase of the vortex. We
concluded that noise is not a problem, then a Discrete Vortex-Producing Lens
can be used as a continuous Spiral Phase Plate with the bonus that secondary
optical vortices can be used in the same way as principal optical vortices.


  Inspection of the CM diagrams of globular clusters having similar heavy
element content shows that the luminosity of the red giant bump relative to the
turnoff (Delta V_{TO}^{bump}) differs by more than 0.1 mag between clusters
with different horizontal branch morphology. Unfortunately, careful
consideration of the data leaves us with only one pair (M3 and M13) of clusters
good for a quantitative discussion. For this pair we consider differences in
age and helium content as possible causes for the difference in Delta
V_{TO}^{bump}, and find more convincing support for the latter. A larger helium
content in M13 stars (Y~0.28 vs. Y~0.24) accounts for various CM diagram
features, such as the difference in the luminosity level of RR Lyr variables
and of the red giant bump with respect to the turnoff luminosity, and the
horizontal branch morphology. This enhanced helium can be tentatively
understood in the framework of self--enrichment by massive asymptotic giant
branch stars in the first ~100 Myr of the cluster life. A modest
self--enrichment can be present also in M3 and can be the reason for the still
unexplained presence of a not negligible number of luminous, Oosterhoff II type
RR Lyr variables. The hypothesis that a larger helium content is the second
parameter for clusters with very blue horizontal branch morphology could be
checked by an accurate set of data for more clusters giving turnoff, RR Lyrs
and bump magnitudes within a unique photometry.


  We study a Jupiter-mass planet formation for the first time in radiative
magneto-hydrodynamics (MHD) simulations and compare it with pure hydrodynamical
simulations, as well as to different isothermal configurations. We found that
the meridional circulation is the same in every setup. The planetary spiral
wakes drive a vertical stirring inside the protoplanetary disc and the
encounter with these shock fronts also helps in delivering gas vertically onto
the Hill-sphere. The accretion dynamics are unchanged: the planet accretes
vertically, and there is outflow in the midplane regions inside the
Hill-sphere. We determined the effective $\alpha$-viscosity generated in the
disc by the various angular momentum loss mechanisms, which showed that
magnetic fields produce high turbulence in the ideal MHD limit, that grows from
$\alpha \sim 10^{-2.5}$ up to $\sim 10^{-1.5}$ after the planet spirals
develop. In the HD simulations, the planetary spirals contribute to $\alpha
\sim 10^{-3}$, making this a very important angular momentum transport
mechanism. Due to the various $\alpha$ values in the different setups, the gap
opening is different in each case. In the radiative MHD setups, the high
turbulent viscosity prevents gap opening, leading to a higher Hill mass, and no
clear dust trapping regions. While the Hill accretion rate is $10^{-6}
\rm{M_{Jup}/yr}$ in all setups, the accretion variability is orders of
magnitude higher in radiative runs than in isothermal ones. Finally, with
higher-resolution runs, the magneto-rotational instability started to be
resolved, changing the effective viscosity and increasing the heating in the
disc.


  We report novel design for thermoelectric device which can control
thermoelectric properties of p-type and n-type materials simultaneously by
electric double-layer gating. Here, p-type Cu2O and n-type ZnO were used as
positive and negative electrodes of the electric double-layer capacitor
structure. When the gate voltage was applied between two electrodes, the holes
and electrons were accumulated on the surface of Cu2O and ZnO, respectively.
The thermopower was measured by applying thermal gradient along the accumulated
layer on the electrodes. We demonstrate here that the accumulated layers are
worked as a p-n pair of the thermoelectric device.


  We consider boundary integral equations (BIEs) met in the scattering by
dielectric cylinders and compare numerical algorithms based on elementary and
Muller's BIEs near the "numerical resonances". A procedure of partial removal
of well-known defect of elementary BIEs related to the loss of their unique
solvability is discussed.


  We propose a mathematical framework for natural selection in finite
populations. Traditionally, many of the selection-based processes used to
describe cultural and genetic evolution (such as imitation and birth-death
models) have been studied on a case-by-case basis. Over time, these models have
grown in sophistication to include population structure, differing phenotypes,
and various forms of interaction asymmetry, among other features. Furthermore,
many processes inspired by natural selection, such as evolutionary algorithms
in computer science, possess characteristics that should fall within the realm
of a "selection process," but so far there is no overarching theory
encompassing these evolutionary processes. The framework of $\textit{stochastic
selection processes}$ we present here provides such a theory and consists of
three main components: a $\textit{population state space}$, an
$\textit{aggregate payoff function}$, and an $\textit{update rule}$. A
population state space is a generalization of the notion of population
structure, and it can include non-spatial information such as strategy-mutation
rates and phenotypes. An aggregate payoff function allows one to generically
talk about the fitness of traits without explicitly specifying a method of
payoff accounting or even the nature of the interactions that determine
payoff/fitness. An update rule is a fitness-based function that updates a
population based on its current state, and it includes as special cases the
classical update mechanisms (Moran, Wright-Fisher, etc.) as well as more
complicated mechanisms involving chromosomal crossover, mutation, and even
complex cultural syntheses of strategies of neighboring individuals. Our
framework covers models with variable population size as well as with
arbitrary, measurable trait spaces.


  The electromagnetic pion form-factor is calculated in a Bethe-Salpeter
approach which accounts for pion rescattering. In the scattering kernel the
pion-pion contact interaction from lowest-order chiral perturbation theory is
considered together with an optional vector meson in the s-channel.
Correspondingly the virtual photon couples to a two-pion state and optionally
to the vector meson. It is shown that for reasonable ranges of input parameters
the experimentally observed pion form-factor cannot be described by the
iterated pion-pion contact interaction alone, i.e. without an elementary vector
meson. The inclusion of an elementary vector meson allows for an excellent
description. This completes a recent study (``Information on the structure of
the a_1 from tau decay'') where it has been shown that the a_1 meson can be
well understood as a rescattering process of rho meson and pion. Here it is
demonstrated that within the same formalism the rho meson cannot be understood
as a pion-pion rescattering process. This suggests that the chiral partners a_1
and rho are not only different in mass, but also different in nature.


  Most existing topic models rely on bag-of-words (BOW) representation, which
limits their ability to capture word order information and leads to challenges
with out-of-vocabulary (OOV) words in new documents. Contextualized word
embeddings, however, show superiority in word sense disambiguation and
effectively address the OOV issue. In this work, we introduce a novel neural
topic model called the Contextlized Word Topic Model (CWTM), which integrates
contextualized word embeddings from BERT. The model is capable of learning the
topic vector of a document without BOW information. In addition, it can also
derive the topic vectors for individual words within a document based on their
contextualized word embeddings. Experiments across various datasets show that
CWTM generates more coherent and meaningful topics compared to existing topic
models, while also accommodating unseen words in newly encountered documents.


  We propose a system that estimates people's body and head orientations using
low-resolution point cloud data from two LiDAR sensors. Our models make
accurate estimations in real-world conversation settings where the subject
moves naturally with varying head and body poses. The body orientation
estimation model uses ellipse fitting while the head orientation estimation
model is a pipeline of geometric feature extraction and an ensemble of neural
network regressors. Compared with other body and head orientation estimation
systems using RGB cameras, our proposed system uses LiDAR sensors to preserve
user privacy, while achieving comparable accuracy. Unlike other body/head
orientation estimation systems, our sensors do not require a specified
placement in front of the subject. Our models achieve a mean absolute
estimation error of 5.2 degrees for body orientation and 13.7 degrees for head
orientation. We use our models to quantify behavioral differences between
neurotypical and autistic individuals in triadic conversations. Tests of
significance show that people with autism spectrum disorder display
significantly different behavior compared to neurotypical individuals in terms
of distributing attention between participants in a conversation, suggesting
that the approach could be a component of a behavioral analysis or coaching
system.


  Session types provide a flexible programming style for structuring
interaction, and are used to guarantee a safe and consistent composition of
distributed processes. Traditional session types include only one-directional
input (external) and output (internal) guarded choices. This prevents the
session-processes to explore the full expressive power of the pi-calculus where
the mixed choices are proved more expressive than the (non-mixed) guarded
choices. To account this issue, recently Casal, Mordido, and Vasconcelos
proposed the binary session types with mixed choices (CMV+). This paper carries
a surprising, unfortunate result on CMV+: in spite of an inclusion of
unrestricted channels with mixed choice, CMV+'s mixed choice is rather separate
and not mixed. We prove this negative result using two methodologies (using
either the leader election problem or a synchronisation pattern as
distinguishing feature), showing that there exists no good encoding from the
pi-calculus into CMV+, preserving distribution. We then close their open
problem on the encoding from CMV+ into CMV (without mixed choice), proving its
soundness and thereby that the encoding is good up to coupled similarity. This
technical report extends a paper presented at the workshop EXPRESS/SOS'22.


  We study finitely additive extensions of the asymptotic density to all the
subsets of natural numbers. Such measures are called density measures. We
consider a class of density measures constructed from free ultrafilters on
$\mathbb{N}$ and investigate absolute continuity and singularity for those
density measures. In particular, for any pair of such density measures we prove
necessary and sufficient conditions that one is absolutely continuous with
respect to the other and that they are singular. Also we prove the same results
for weak absolute continuity and strong singularity.


  Using the language of coarse homology theories, we provide an axiomatic
account of vanishing results for the fibres of forget-control maps associated
to spaces with equivariant finite decomposition complexity.


  The notion of compliance in Multiset Rewriting Models (MSR) has been
introduced for untimed models and for models with discrete time. In this paper
we revisit the notion of compliance and adapt it to fit with additional
nondeterminism specific for dense time domains. Existing MSR with dense time
are extended with critical configurations and non-critical traces, that is,
traces involving no critical configurations. Complexity of related {\em
non-critical reachability problem} is investigated. Although this problem is
undecidable in general, we prove that for balanced MSR with dense time the
non-critical reachability problem is PSPACE-complete.


  We propose an analog implementation of the transcendental activation function
leveraging two spin-orbit torque magnetoresistive random-access memory
(SOT-MRAM) devices and a CMOS inverter. The proposed analog neuron circuit
consumes 1.8-27x less power, and occupies 2.5-4931x smaller area, compared to
the state-of-the-art analog and digital implementations. Moreover, the
developed neuron can be readily integrated with memristive crossbars without
requiring any intermediate signal conversion units. The architecture-level
analyses show that a fully-analog in-memory computing (IMC) circuit that use
our SOT-MRAM neuron along with an SOT-MRAM based crossbar can achieve more than
1.1x, 12x, and 13.3x reduction in power, latency, and energy, respectively,
compared to a mixed-signal implementation with analog memristive crossbars and
digital neurons. Finally, through cross-layer analyses, we provide a guide on
how varying the device-level parameters in our neuron can affect the accuracy
of multilayer perceptron (MLP) for MNIST classification.


  Denote by $\| \cdot \|$ the euclidean norm in $\RR^k$. We prove that the
local pair correlation density of the sequence $\| \vecm -\vecalf \|^k$,
$\vecm\in\ZZ^k$, is that of a Poisson process, under diophantine conditions on
the fixed vector $\vecalf\in\RR^k$: in dimension two, vectors $\vecalf$ of any
diophantine type are admissible; in higher dimensions ($k>2$), Poisson
statistics are only observed for diophantine vectors of type
$\kappa<(k-1)/(k-2)$. Our findings support a conjecture of Berry and Tabor on
the Poisson nature of spectral correlations in quantized integrable systems.


  The rigidity theorem of Witten-Bott-Taubes-Hirzebruch tells us that, if the
circle group acts on a closed almost complex (or more generally unitary)
manifold whose first Chern class is divisible by a positive integer N greater
than 1, then its equivariant elliptic genus of level N is rigid. Applying this
to a non-singular compact toric variety, we see that its elliptic genus of
level N is rigid if its first Chern class is divisible by N. But, using a
vanishing theorem of Hirzebruch, we can show moreover that the genus actually
vanishes. In this note we shall extend this result to torus manifolds. In fact,
a non-singular complete multi-fan is associated with a torus manifold, and
rigidity and vanishing of elliptic genus of level N can be formulated and
proved for non-singular complete multi-fans. Some applications on compact
non-singular toric varieties with the first Chern class divisible by a large
positive integer are given.


  We investigate the response of harmonically confined bosons with contact
interactions (trapped Lieb-Liniger gas) to modulations of the trapping
strength. We explain the structure of resonances at a series of driving
frequencies, where size oscillations and energy grow exponentially. For strong
interactions (Tonks-Girardeau gas), we show the effect of resonant driving on
the bosonic momentum distribution. The treatment is `exact' for zero and
infinite interactions, where the dynamics is captured by a single-variable
ordinary differential equation. For finite interactions the system is no longer
exactly solvable. For weak interactions, we show how interactions modify the
resonant behavior for weak and strong driving, using a variational
approximation which adds interactions to the single-variable description in a
controlled way.


  A dynamic sieve method is designed according to the basic sieve method. It
mainly refers to the symbolic dynamics theory. By this method, we could connect
the prime system with familiar 'Logistic Mapping'. An interesting discovery is
that the pattern of primes could be depicted by a series of orbits of this
mapping. Some heuristic proofs for open problems like twin primes are obtained
through this relation. This research gives a new viewpoint for the distribution
of prime numbers.


  The CP tensor decomposition is a low-rank approximation of a tensor. We
present a distributed-memory parallel algorithm and implementation of an
alternating optimization method for computing a CP decomposition of dense
tensor data that can enforce nonnegativity of the computed low-rank factors.
The principal task is to parallelize the matricized-tensor times Khatri-Rao
product (MTTKRP) bottleneck subcomputation. The algorithm is computation
efficient, using dimension trees to avoid redundant computation across MTTKRPs
within the alternating method. Our approach is also communication efficient,
using a data distribution and parallel algorithm across a multidimensional
processor grid that can be tuned to minimize communication. We benchmark our
software on synthetic as well as hyperspectral image and neuroscience dynamic
functional connectivity data, demonstrating that our algorithm scales well to
100s of nodes (up to 4096 cores) and is faster and more general than the
currently available parallel software.


  One-dimensional systems have unusual properties such as fractionalization of
degrees of freedom. Possible extensions to higher dimensional systems have been
considered in the literature. In this work we construct a mean field theory of
the Hubbard model taking into account a separation of the degrees of freedom
inspired by the one-dimensional case and study the finite-temperature phase
diagram for the Hubbard chain and square lattice. The mean field variables are
defined along the links of the underlying lattice. We obtain the spectral
function and identify the regions of higher spectral weight with the
fractionalized fermionic (spin) and bosonic (charge) excitations.


  Linear Temporal Logic (LTL) offers a precise means for constraining the
behavior of reinforcement learning agents. However, in many tasks, LTL is
insufficient for task specification; LTL-constrained policy optimization, where
the goal is to optimize a scalar reward under LTL constraints, is needed. Prior
methods for this constrained problem are restricted to finite state spaces. In
this work, we present Cycle Experience Replay (CyclER), a reward-shaping
approach to this problem that allows continuous state and action spaces and the
use of function approximations. CyclER guides a policy towards satisfaction by
encouraging partial behaviors compliant with the LTL constraint, using the
structure of the constraint. In doing so, it addresses the optimization
challenges stemming from the sparse nature of LTL satisfaction. We evaluate
CyclER in three continuous control domains. On these tasks, CyclER outperforms
existing reward-shaping methods at finding performant and LTL-satisfying
policies.


  We study dynamical self-localization of gauge theories in higher dimensions.
Specifically, we consider a 5D $U(1)$ gauge theory in the linear dilaton
(clockwork) background, with anisotropic gauge couplings along the transverse
(fifth) direction and the longitudinal (four-dimensional) directions. By using
lattice techniques, we calculate the space plaquettes and the helicity moduli
and we determine the phase diagram of the model. We find strong evidence that
the model exhibits a new phase, a layer phase, where the four-dimensional
physics decouples from the five-dimensional dynamics. The layer phase
corresponds to a strong force along the fifth direction and a Coulomb phase
along the four-dimensional longitudinal directions. This is in accordance with
the clockwork mechanism where light particles with exponentially suppressed
interactions are generated in theories with no fundamental small parameters.


  The basic workings of inflationary models are summarized, along with the
arguments that strongly suggest that our universe is the product of inflation.
I describe the quantum origin of density perturbations, giving a heuristic
derivation of the scale invariance of the spectrum and the leading corrections
to scale invariance. The mechanisms that lead to eternal inflation in both new
and chaotic models are described. Although the infinity of pocket universes
produced by eternal inflation are unobservable, it is argued that eternal
inflation has real consequences in terms of the way that predictions are
extracted from theoretical models. Although inflation is generically eternal
into the future, it is not eternal into the past: it can be proven under
reasonable assumptions that the inflating region must be incomplete in past
directions, so some physics other than inflation is needed to describe the past
boundary of the inflating region. The ambiguities in defining probabilities in
eternally inflating spacetimes are reviewed, with emphasis on the youngness
paradox that results from a synchronous gauge regularization technique.


  Telementoring surgeons as they perform surgery can be essential in the
treatment of patients when in situ expertise is not available. Nonetheless,
expert mentors are often unavailable to provide trainees with real-time medical
guidance. When mentors are unavailable, a fallback autonomous mechanism should
provide medical practitioners with the required guidance. However,
AI/autonomous mentoring in medicine has been limited by the availability of
generalizable prediction models, and surgical procedures datasets to train
those models with. This work presents the initial steps towards the development
of an intelligent artificial system for autonomous medical mentoring.
Specifically, we present the first Database for AI Surgical Instruction
(DAISI). DAISI leverages on images and instructions to provide step-by-step
demonstrations of how to perform procedures from various medical disciplines.
The dataset was acquired from real surgical procedures and data from academic
textbooks. We used DAISI to train an encoder-decoder neural network capable of
predicting medical instructions given a current view of the surgery.
Afterwards, the instructions predicted by the network were evaluated using
cumulative BLEU scores and input from expert physicians. According to the BLEU
scores, the predicted and ground truth instructions were as high as 67%
similar. Additionally, expert physicians subjectively assessed the algorithm
using Likert scale, and considered that the predicted descriptions were related
to the images. This work provides a baseline for AI algorithms to assist in
autonomous medical mentoring.


  Nonlinear Schr\"odinger (NLS) equations with focusing power nonlinearities
have solitary wave solutions. The spectra of the linearized operators around
these solitary waves are intimately connected to stability properties of the
solitary waves, and to the long-time dynamics of solutions of (NLS). We study
these spectra in detail, both analytically and numerically.


  By measuring the Hall coefficient R_H up to 1000 K in La_2CuO_4,
Pr_{1.3}La_{0.7}CuO_4, and La_{2-x}Sr_xCuO_4 (LSCO), we found that the
temperature (T) dependence of R_H in LSCO for x = 0 - 0.05 at high temperature
undoubtedly signifies a gap over which the charge carriers are thermally
activated, which in turn indicates that in lightly-doped cuprates strong charge
fluctuations are present at high temperature and the carrier number is not a
constant. At higher doping (x = 0.08 - 0.21), the high-temperature R_H(T)
behavior is found to be qualitatively the same, albeit with a weakened
temperature dependence, and we attempt to understand its behavior in terms of a
phenomenological two-carrier model where the thermal activation is considered
for one of the two species. Despite the crude nature of the model, our analysis
gives a reasonable account of R_H both at high temperature and at 0 K for a
wide range of doping, suggesting that charge fluctuations over a gap remain
important at high temperature in LSCO deep into the superconducting doping
regime. Moreover, our model gives a perspective to understand the seemingly
contradicting high-temperature behavior of R_H and the in-plane resistivity
near optimum doping in a consistent manner. Finally, we discuss possible
implications of our results on such issues as the scattering-time separation
and the large pseudogap.


  Graph Neural Networks (GNNs) excel in various graph learning tasks but face
computational challenges when applied to large-scale graphs. A promising
solution is to remove non-essential edges to reduce the computational overheads
in GNN. Previous literature generally falls into two categories:
topology-guided and semantic-guided. The former maintains certain graph
topological properties yet often underperforms on GNNs due to low integration
with neural network training. The latter performs well at lower sparsity on
GNNs but faces performance collapse at higher sparsity levels. With this in
mind, we take the first step to propose a new research line and concept termed
Graph Sparse Training (GST), which dynamically manipulates sparsity at the data
level. Specifically, GST initially constructs a topology & semantic anchor at a
low training cost, followed by performing dynamic sparse training to align the
sparse graph with the anchor. We introduce the Equilibria Sparsification
Principle to guide this process, effectively balancing the preservation of both
topological and semantic information. Ultimately, GST produces a sparse graph
with maximum topological integrity and no performance degradation. Extensive
experiments on 6 datasets and 5 backbones showcase that GST (I) identifies
subgraphs at higher graph sparsity levels (1.67%~15.85% $\uparrow$) than
state-of-the-art sparsification methods, (II) preserves more key spectral
properties, (III) achieves 1.27-3.42$\times$ speedup in GNN inference and (IV)
successfully helps graph adversarial defense and graph lottery tickets.


  By definition, reciprocal matrices are tridiagonal $n$-by-$n$ matrices $A$
with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for
$i=1,\ldots,n-1$. For $n\leq 6$, we establish criteria under which the
numerical range generating curves (also called Kippenhahn curves) of such
matrices consist of elliptical components only. As a corollary, we also provide
a complete description of higher-rank numerical ranges when the criteria are
met.


  We determine the thermal evolution of the intergalactic medium (IGM) over
$3\, \mathrm{Gyr}$ of cosmic time $1.8<z<5.4$ by comparing measurements of the
Ly{\alpha} forest power spectrum to a suite of $\sim70$ hydrodynamical
simulations. We conduct Bayesian inference of IGM thermal parameters using an
end-to-end forward modeling framework whereby mock spectra generated from our
simulation grid are used to build a custom emulator which interpolates the
power spectrum between thermal grid points. The temperature at mean density
$T_0$ rises steadily from $T_0\sim 6000\, \mathrm{K}$ at $z=5.4$, peaks at
$14000\, \mathrm{K}$ for $z\sim 3.4$, and decreases at lower redshift reaching
$T_0\sim 7000\, \mathrm{K}$ by $z\sim1.8$. This evolution provides conclusive
evidence for photoionization heating resulting from the reionization of He II,
as well as the subsequent cooling of the IGM due to the expansion of the
Universe after all reionization events are complete. Our results are broadly
consistent with previous measurements of thermal evolution based on a variety
of approaches, but the sensitivity of the power spectrum, the combination of
high precision BOSS measurements of large-scale modes ($k\lesssim 0.02\,
\mathrm{s/km}$) with our recent determination of the small-scale power, our
large grid of models, and our careful statistical analysis allow us to break
the well known degeneracy between the temperature at mean density $T_0$ and the
slope of the temperature density relation $\gamma$ that has plagued previous
analyses. At the highest redshifts $z\geq5$ we infer lower temperatures than
expected from the standard picture of IGM thermal evolution leaving little room
for additional smoothing of the Ly{\alpha} forest by free streaming of warm
dark matter.


  Stochastic (sub)gradient methods require step size schedule tuning to perform
well in practice. Classical tuning strategies decay the step size polynomially
and lead to optimal sublinear rates on (strongly) convex problems. An
alternative schedule, popular in nonconvex optimization, is called
\emph{geometric step decay} and proceeds by halving the step size after every
few epochs. In recent work, geometric step decay was shown to improve
exponentially upon classical sublinear rates for the class of \emph{sharp}
convex functions. In this work, we ask whether geometric step decay similarly
improves stochastic algorithms for the class of sharp nonconvex problems. Such
losses feature in modern statistical recovery problems and lead to a new
challenge not present in the convex setting: the region of convergence is
local, so one must bound the probability of escape. Our main result shows that
for a large class of stochastic, sharp, nonsmooth, and nonconvex problems a
geometric step decay schedule endows well-known algorithms with a local linear
rate of convergence to global minimizers. This guarantee applies to the
stochastic projected subgradient, proximal point, and prox-linear algorithms.
As an application of our main result, we analyze two statistical recovery
tasks---phase retrieval and blind deconvolution---and match the best known
guarantees under Gaussian measurement models and establish new guarantees under
heavy-tailed distributions.


  The current response of a d-wave superconductor containing a single impurity
is calculated and shown to be singular in the low-temperature limit, leading in
the case of strong scattering to a 1/T term in the penetration depth
$\lambda(T)$ similar to that induced by Andreev surface bound states. For a
small number of such impurities, we argue this low-$T$ upturn could be
observable in cuprate superconductors.


  Several attacks have been proposed on quantum key distribution systems with
gated single-photon detectors. The attacks involve triggering the detectors
outside the center of the detector gate, and/or using bright illumination to
exploit classical photodiode mode of the detectors. Hence a secure detection
scheme requires two features: The detection events must take place in the
middle of the gate, and the detector must be single-photon sensitive. Here we
present a technique called bit-mapped gating, which is an elegant way to force
the detections in the middle of the detector gate by coupling detection time
and quantum bit error rate. We also discuss how to guarantee single-photon
sensitivity by directly measuring detector parameters. Bit-mapped gating also
provides a simple way to measure the detector blinding parameter in security
proofs for quantum key distribution systems with detector efficiency mismatch,
which up until now has remained a theoretical, unmeasurable quantity. Thus if
single-photon sensitivity can be guaranteed within the gates, a detection
scheme with bit-mapped gating satisfies the assumptions of the current security
proofs.


  Under the sublinear expectation $\mathbb{E}[\cdot]:=\sup_{\theta\in \Theta}
E_\theta[\cdot]$ for a given set of linear expectations $\{E_\theta: \theta\in
\Theta\}$, we establish a new law of large numbers and a new central limit
theorem with rate of convergence. We present some interesting special cases and
discuss a related statistical inference problem. We also give an approximation
and a representation of the $G$-normal distribution, which was used as the
limit in Peng (2007)'s central limit theorem, in a probability space.


  Temporal Point Processes (TPP) with partial likelihoods involving a latent
structure often entail an intractable marginalization, thus making inference
hard. We propose a novel approach to Maximum Likelihood Estimation (MLE)
involving approximate inference over the latent variables by minimizing a tight
upper bound on the approximation gap. Given a discrete latent variable $Z$, the
proposed approximation reduces inference complexity from $O(|Z|^c)$ to
$O(|Z|)$. We use convex conjugates to determine this upper bound in a closed
form and show that its addition to the optimization objective results in
improved results for models assuming proportional hazards as in Survival
Analysis.


  In this paper, we establish that FFLV polytopes, which describe monomial
bases compatible with the PBW filtration on finite-dimensional simple modules
for $\lie{sl}_n$ and $\lie{sp}_n$, are actually string polytopes as described
by Littelmann and Berenstein-Zelevinsky for Demazure modules of higher-rank Lie
algebras.


  A competition process is a continuous time Markov chain that can be
interpreted as a system of interacting birth-and-death processes, the
components of which evolve subject to a competitive interaction. This paper is
devoted to the study of the long-term behaviour of such a competition process,
where a component of the process increases with a linear birth rate and
decreases with a rate given by a linear function of other components. A zero is
an absorbing state for each component, that is, when a component becomes zero,
it stays zero forever (and we say that this component becomes extinct). We show
that, with probability one, eventually only a random subset of non-interacting
components of the process survives. A similar result also holds for the
relevant generalized Polya urn model with removals.


  We report high resolution spectral observations of the yellow symbiotic star
V417 Cen obtained in 2004. We find that the equivalent widths of the emission
lines decreased, while the brightness increased. The FWHMs and wavelengths of
the emission lines do not change. We estimated the interstellar extinction
towards V417 Cen as $E_{B-V}$ = 0.95 $\pm$0.10, using the KI interstellar line.
Using the [O III] lines, we obtain a rough estimation of the density and the
temperature in the forbidden lines region $\log N_e \approx 4.5 \pm$ 0.5 and
$T_e=100000 \pm 25000$~K. Tidal interaction in this binary is also discussed.


  Randich and Schmitt [1995, A&A 298, 115] found that the coronal activity of
solar-type and low mass stars in Praesepe is significantly lower than that of
stars in the Hyades cluster. We have carried out several tests in order to find
a possible explanation for this result. We have measured radial velocities of
two groups of Praesepe stars (a dF-dK sample and a dM sample) and have measured
H$\alpha$ as a chromospheric activity index for the dM sample. We conclude that
the Praesepe catalog used in the X-ray analysis does not contain a significant
number of non-members. The comparison of the H$\alpha$ equivalent widths for
the M dwarfs in Praesepe with those in the Hyades indicates that, at least for
stars in this mass range, the Praesepe stars are as active or more active than
their Hyades counterparts. We have also analyzed a few ROSAT PSPC pointings of
Praesepe in order to obtain a new and independent estimate of the X-ray
luminosities and upper limits for a small sample of Praesepe members concluding
that the small differences between the old and new upper limits are not large
enough to explain the dichotomy in the X-ray properties of Praesepe and the
Hyades. Therefore, our examination of the available data does not provide a
clear reason to explain why the X-ray luminosity functions of the two clusters
are different. Part of the explanation could be found in the binaries.
Speculatively, these clusters could have different orbital period
distributions, with more short period binaries among the Hyades, which would
show larger coronal activity.


  We study the dynamics of an optoelectronic circuit composed of an excitable
nanoscale resonant-tunneling diode (RTD) driving a nanolaser diode (LD) coupled
via time-delayed feedback. Using a combination of numerical path-continuation
methods and time simulations, we demonstrate that this RTD-LD system can serve
as an artificial neuron, generating pulses in the form of temporal localized
states (TLSs) that can be employed as memory for neuromorphic computing. In
particular, our findings reveal that the prototypical delayed FitzHugh-Nagumo
model previously employed to model the RTD-LD resembles our more realistic
model only in the limit of a slow RTD. We show that the RTD time scale plays a
critical role in memory capacity as it governs a shift in pulse interaction
from repulsive to attractive, leading to a transition from stable to unstable
multi-pulse TLSs. Our theoretical analysis uncovers novel features and
challenges, including the multistability of TLSs and attractive interaction
forces, stemming from the previously neglected intrinsic dynamics of the laser.
These effects are crucial to consider since they define the memory properties
of the RTD-LD.


  We calculate the elementary excitations and pairing of a trapped atomic Fermi
gas in the superfluid phase. The level spectra and pairing gaps undergo several
transitions as the strength of the interactions between and the number of atoms
are varied. For weak interactions, the Cooper pairs are formed between
particles residing in the same harmonic oscillator shell. In this regime, the
nature of the paired state is shown to depend critically on the position of the
chemical potential relative to the harmonic oscillator shells and on the size
of the mean field. For stronger interactions, we find a region where pairing
occur between time-reversed harmonic oscillator states in different shells
also.


  In this paper, we investigate complete Riemannian manifolds satisfying the
lower weighted Ricci curvature bound $\mathrm{Ric}_{N} \geq K$ with $K>0$ for
the negative effective dimension $N<0$. We analyze two $1$-dimensional examples
of constant curvature $\mathrm{Ric}_N \equiv K$ with finite and infinite total
volumes. We also discuss when the first nonzero eigenvalue of the Laplacian
takes its minimum under the same condition $\mathrm{Ric}_N \ge K>0$, as a
counterpart to the classical Obata rigidity theorem. Our main theorem shows
that, if $N<-1$ and the minimum is attained, then the manifold splits off the
real line as a warped product of hyperbolic nature.


  In the cuprate superconductors, the spatial coherence of the charge density
wave (CDW) state grows rapidly below a characteristic temperature
$T_\mathrm{CDW}$, the nature of which is debated. We have combined a set of
x-ray scattering techniques to study La$_{1.88}$Sr$_{0.12}$CuO$_{4}$
($T_\mathrm{CDW}$~$\approx$~80\,K) to shed light on this discussion. We observe
the emergence of a crystal structure, which is consistent with the CDW
modulation in symmetry, well above $T_\mathrm{CDW}$. This global structural
change also induces strong fluctuations of local atomic disorder in the
intermediate temperature region. At $T_\mathrm{CDW}$, the temperature
dependence of this structure develops a kink, while the atomic disorder is
minimized. We find that the atomic relaxation dynamics cross over from a
cooperative to an incoherent response at $T_\mathrm{CDW}$. These results reveal
a rich interplay between the CDWs and atomic fluctuations of distinct
spatio-temporal scales. For example, the CDW coherence is enhanced on
quasi-elastic timescales by incoherent atomic relaxation.


  We show how energy flow lines answer the question about diffraction phenomena
presented in 1818 by the French Academy: "deduce by mathematical induction, the
movements of the rays during their crossing near the bodies". This provides a
complementary answer to Fresnel's wave theory of light. A numerical simulation
of these energy flow lines proves that they can reach the bright spot of
Poisson-Arago in the shadow center of a circular opaque disc. For a
monochromatic wave in vacuum, these energy flow lines correspond to the
diffracted rays of Newton's Opticks.


  Molecular oxygen, nitrogen, and ozone have been detected in the Solar System.
They are also expected to be present in ice-grain mantles within star-forming
regions. Laboratory experiments that simulate energetic processing (ions,
photons, and electrons) of ices are essential for interpreting and directing
future astronomical observations. We provide VUV photoabsorption spectroscopic
data of energetically processed nitrogen- and oxygen-rich ices that will help
to identify absorption bands and/or spectral slopes observed on icy objects in
the Solar System and on ice-grain mantles of the interstellar medium. We
present VUV photoabsorption spectra of frozen O2 and N2, a 1:1 mixture of both,
and a new systematic set of pure and mixed nitrogen oxide ices. Spectra were
obtained at 22 K before and after 1 keV electron bombardment of the ice sample.
Ices were then annealed to higher temperatures to study their thermal
evolution. In addition, Fourier-transform infrared spectroscopy was used as a
secondary probe of molecular synthesis to better identify the physical and
chemical processes at play. Our VUV data show that ozone and the azide radical
(N3) are observed in our experiments after electron irradiation of pure O2 and
N2 ices, respectively. Energetic processing of an O2:N2 = 1:1 ice mixture leads
to the formation of ozone along with a series of nitrogen oxides. The electron
irradiation of solid nitrogen oxides, pure and in mixtures, induces the
formation of new species such as O2, N2 , and other nitrogen oxides not present
in the initial ice. Results are discussed here in light of their relevance to
various astrophysical environments. Finally, we show that VUV spectra of solid
NO2 and water can reproduce the observational VUV profile of the cold surface
of Enceladus, Dione, and Rhea, strongly suggesting the presence of nitrogen
oxides on the surface of the icy Saturn moons.


  Weak interactions of solitary waves in the generalized nonlinear
Schr\"{o}dinger equations are studied. It is first shown that these
interactions exhibit similar fractal dependence on initial conditions for
different nonlinearities. Then by using the Karpman-Solov'ev method, a
universal system of dynamical equations is derived for the velocities,
amplitudes, positions and phases of interacting solitary waves. These dynamical
equations contain a single parameter, which accounts for the different forms of
nonlinearity. When this parameter is zero, these dynamical equations are
integrable, and the exact analytical solutions are derived. When this parameter
is non-zero, the dynamical equations exhibit fractal structures which match
those in the original wave equations both qualitatively and quantitatively.
Thus the universal nature of fractal structures in the weak interaction of
solitary waves is analytically established. The origin of these fractal
structures is also explored. It is shown that these structures bifurcate from
the initial conditions where the solutions of the integrable dynamical
equations develop finite-time singularities. Based on this observation, an
analytical criterion for the existence and locations of fractal structures is
obtained. Lastly, these analytical results are applied to the generalized
nonlinear Schr\"{o}dinger equations with various nonlinearities such as the
saturable nonlinearity, and predictions on their weak interactions of solitary
waves are made.


  We construct a family of $q$-series with rational coefficients satisfying a
variant of the extended double shuffle equations, which are a lift of a given
$\mathbb{Q}$-valued solution of the extended double shuffle equations. These
$q$-series will be called combinatorial (bi-)multiple Eisenstein series, and in
depth one they are given by Eisenstein series. The combinatorial multiple
Eisenstein series can be seen as an interpolation between the given
$\mathbb{Q}$-valued solution of the extended double shuffle equations (as
$q\rightarrow 0$) and multiple zeta values (as $q\rightarrow 1$). In
particular, they are $q$-analogues of multiple zeta values closely related to
modular forms. Their definition is inspired by the Fourier expansion of
multiple Eisenstein series introduced by Gangl-Kaneko-Zagier. Our explicit
construction is done on the level of their generating series, which we show to
be a so-called symmetril and swap invariant bimould.


  Incompatibility of quantum devices is a useful resource in various quantum
information theoretical tasks, and it is at the heart of some fundamental
features of quantum theory. While the incompatibility of measurements and
quantum channels is well-studied, the incompatibility of quantum instruments
has not been explored in much detail. In this work, we revise a notion of
instrument compatibility introduced in the literature that we call traditional
compatibility. Then, we introduce the new notion of parallel compatibility, and
show that these two notions are inequivalent. Then, we argue that the notion of
traditional compatibility is incomplete, and prove that while parallel
compatibility captures measurement and channel compatibility, traditional
compatibility does not. Hence, we propose parallel compatibility as the
conceptually complete definition of compatibility of quantum instruments.


  Dialogue systems have been widely applied in many scenarios and are now more
powerful and ubiquitous than ever before. With large neural models and massive
available data, current dialogue systems have access to more knowledge than any
people in their life. However, current dialogue systems still do not perform at
a human level. One major gap between conversational agents and humans lies in
their abilities to be aware of social norms. The development of socially-aware
dialogue systems is impeded due to the lack of resources. In this paper, we
present the first socially-aware dialogue corpus - SocialDial, based on Chinese
social culture. SocialDial consists of two parts: 1,563 multi-turn dialogues
between two human speakers with fine-grained labels, and 4,870 synthetic
conversations generated by ChatGPT. The human corpus covers five categories of
social norms, which have 14 sub-categories in total. Specifically, it contains
social factor annotations including social relation, context, social distance,
and social norms. However, collecting sufficient socially-aware dialogues is
costly. Thus, we harness the power of ChatGPT and devise an ontology-based
synthetic data generation framework. This framework is able to generate
synthetic data at scale. To ensure the quality of synthetic dialogues, we
design several mechanisms for quality control during data collection. Finally,
we evaluate our dataset using several pre-trained models, such as BERT and
RoBERTa. Comprehensive empirical results based on state-of-the-art neural
models demonstrate that modeling of social norms for dialogue systems is a
promising research direction. To the best of our knowledge, SocialDial is the
first socially-aware dialogue dataset that covers multiple social factors and
has fine-grained labels.


  Transparent topology is common in many mobile ad hoc networks (MANETs) such
as vehicle ad hoc networks (VANETs), unmanned aerial vehicle (UAV) ad hoc
networks, and wireless sensor networks due to their decentralization and
mobility nature. There are many existing works on distributed scheduling scheme
design for topology-transparent MANETs. Most of them focus on
delay-unconstrained settings. However, with the proliferation of real-time
applications over wireless communications, it becomes more and more important
to support delay-constrained traffic in MANETs. In such applications, each
packet has a given hard deadline: if it is not delivered before its deadline,
its validity will expire and it will be removed from the system. This feature
is fundamentally different from the traditional delay-unconstrained one. In
this paper, we for the first time investigate distributed scheduling schemes
for a topology-transparent MANET to support delay-constrained traffic. We
analyze and compare probabilistic ALOHA scheme and deterministic sequence
schemes, including the conventional time division multiple access (TDMA), the
Galois field (GF) sequence scheme proposed in \cite{chlamtac1994making}, and
the combination sequence scheme that we propose for a special type of sparse
network topology.We use both theoretical analysis and empirical simulations to
compare all these schemes and summarize the conditions under which different
individual schemes perform best.


  Two groundbreaking new facilities will commence operations early in the 2020s
and thereafter define much of the broad landscape of US optical-infrared
astronomy in the remaining decade. The Large Synoptic Survey Telescope (LSST),
perched atop Cerro Pachon in the Chilean Andes, will revolutionize the young
field of Time Domain Astronomy through its wide-field, multi-band optical
imaging survey. At the same time, the James Webb Space Telescope (JWST),
orbiting at the Sun-Earth L2 Lagrange point, will provide stunningly
high-resolution views of selected targets from the red end of the optical
spectrum to the mid-infrared. However, the spatial resolution of the LSST
observations will be limited by atmospheric seeing, while JWST will be limited
in its time-domain capabilities. This paper highlights the scientific
opportunities lying between these two landmark missions, i.e., science enabled
by systems capable of astronomical observations with both high cadence in the
time domain and high resolution in the spatial domain. The opportunities range
from constraining the late phases of stellar evolution in nearby resolved
populations to constraining dark matter distributions and cosmology using
lensed transient sources. We describe a system that can deliver the required
capabilities.


  The present paper introduces a quantum weak measurement (WM) scheme for the
measurement of the complex magneto-optical Kerr effect (MOKE). We achieve the
simultaneous measurement of the Kerr rotation angle and the ellipticity in a
single WM process by utilizing two auxiliary pointers derived from the same
meter state. The experimental measurement precision for both the Kerr rotation
angle and the ellipticity is capable of reaching $10^{-4}$ deg. This technique
is also employed for the determination of the complex magneto-optical constant
$Q$. The proposed method overcomes the limitation of acquiring the complex
magneto-optical Kerr parameters through a multi-step measurement process, which
was previously encountered. This breakthrough holds immense significance for
efficiently measuring and applying the complex MOKE with high precision and
cost-effectiveness.


  We carefully rederive the Schiff theorem and prove that the usual expression
of the Schiff moment operator is correct and should be applied for calculations
of atomic electric dipole moments. The recently discussed corrections to the
definition of the Schiff moment are absent.


  We adapt the Coupled Cluster Method to solid state strongly correlated
lattice Hamiltonians extending the Coupled Cluster linear response method to
the calculation of electronic spectra and obtaining the space-time Fourier
transforms of generic Green's functions. We apply our method to the $MnO_2$
plane with orbital and magnetic ordering, to interpret electron energy loss
experimental data, and to the Hubbard model, where we get insight into a
possible pairing mechanism.


  The effect of explicit chiral-symmetry breaking on inhomogeneous chiral
phases is studied within a Nambu-Jona-Lasinio model with nonzero current quark
mass. Generalizing an earlier result obtained in the chiral limit, we show
within a Ginzburg-Landau analysis that the critical endpoint of the first-order
chiral phase boundary between two homogeneous phases gets replaced by a
"pseudo-Lifshitz point" when the possibility of inhomogeneous order parameters
is considered. Performing a stability analysis we also show that the unstable
mode along the phase boundary is in the scalar but not in the pseudoscalar
channel, suggesting that modulations which contain pseudoscalar condensates,
like a generalized dual chiral density wave, are disfavored against purely
scalar ones. Numerically we find that the inhomogeneous phase shrinks as one
moves away from the chiral limit, but survives even at significantly large
values of the current quark mass.


  We study a classification problem where each feature can be acquired for a
cost and the goal is to optimize a trade-off between the expected
classification error and the feature cost. We revisit a former approach that
has framed the problem as a sequential decision-making problem and solved it by
Q-learning with a linear approximation, where individual actions are either
requests for feature values or terminate the episode by providing a
classification decision. On a set of eight problems, we demonstrate that by
replacing the linear approximation with neural networks the approach becomes
comparable to the state-of-the-art algorithms developed specifically for this
problem. The approach is flexible, as it can be improved with any new
reinforcement learning enhancement, it allows inclusion of pre-trained
high-performance classifier, and unlike prior art, its performance is robust
across all evaluated datasets.


  We propose a replica-exchange method (REM) which does not use pseudo random
numbers. For this purpose, we first give a conditional probability for Gibbs
sampling replica-exchange method (GSREM) based on the heat bath method. In
GSREM, replica exchange is performed by conditional probability based on the
weight of states using pseudo random numbers. From the conditional probability,
we propose a new method called deterministic replica-exchange method (DETREM)
that produces thermal equilibrium distribution based on a differential equation
instead of using pseudo random numbers. This method satisfies the detailed
balance condition using a conditional probability of Gibbs heat bath method and
thus results can reproduce the Boltzmann distribution within the condition of
the probability. We confirmed that the equivalent results were obtained by REM
and DETREM with two-dimensional Ising model. DETREM can avoid problems of
choice of seeds in pseudo random numbers for REM using a differential equation.


  Group equivariant convolutional neural networks (G-CNNs) have been
successfully applied in geometric deep learning. Typically, G-CNNs have the
advantage over CNNs that they do not waste network capacity on training
symmetries that should have been hard-coded in the network. The recently
introduced framework of PDE-based G-CNNs (PDE-G-CNNs) generalises G-CNNs.
PDE-G-CNNs have the core advantages that they simultaneously 1) reduce network
complexity, 2) increase classification performance, and 3) provide geometric
interpretability. Their implementations primarily consist of linear and
morphological convolutions with kernels.
  In this paper we show that the previously suggested approximative
morphological kernels do not always accurately approximate the exact kernels
accurately. More specifically, depending on the spatial anisotropy of the
Riemannian metric, we argue that one must resort to sub-Riemannian
approximations. We solve this problem by providing a new approximative kernel
that works regardless of the anisotropy. We provide new theorems with better
error estimates of the approximative kernels, and prove that they all carry the
same reflectional symmetries as the exact ones.
  We test the effectiveness of multiple approximative kernels within the
PDE-G-CNN framework on two datasets, and observe an improvement with the new
approximative kernels. We report that the PDE-G-CNNs again allow for a
considerable reduction of network complexity while having comparable or better
performance than G-CNNs and CNNs on the two datasets. Moreover, PDE-G-CNNs have
the advantage of better geometric interpretability over G-CNNs, as the
morphological kernels are related to association fields from neurogeometry.


  We consider a version of generalised $q$-oscillators and some of their
applications. The generalisation includes also "quons" of infinite statistics
and deformed oscillators of parastatistics. The statistical distributions for
different $q$-oscillators are derived for their corresponding Fock space
representations. The deformed Virasoro algebra and SU(2) algebra are also
treated.


  In the presence of strong disorder, the statistics of quasiparticle levels in
the core of a vortex in a two-dimensional p-wave superconductor belongs to the
universality class B corresponding to the ensemble of orthogonal matrices in
odd dimensions. This novel universality class appears as a consequence of the
O(2) spin symmetry of p-wave pairing. It is preserved in the presence of random
disorder, of electromagnetic vector potential, and of an admixture of the
pairing of opposite chirality in the vortex core, but may be destroyed by
spin-orbit coupling and by Zeeman splitting.


  COVID-19 presence classification and severity prediction via (3D) thorax
computed tomography scans have become important tasks in recent times.
Especially for capacity planning of intensive care units, predicting the future
severity of a COVID-19 patient is crucial. The presented approach follows
state-of-theart techniques to aid medical professionals in these situations. It
comprises an ensemble learning strategy via 5-fold cross-validation that
includes transfer learning and combines pre-trained 3D-versions of ResNet34 and
DenseNet121 for COVID19 classification and severity prediction respectively.
Further, domain-specific preprocessing was applied to optimize model
performance. In addition, medical information like the infection-lung-ratio,
patient age, and sex were included. The presented model achieves an AUC of
79.0% to predict COVID-19 severity, and 83.7% AUC to classify the presence of
an infection, which is comparable with other currently popular methods. This
approach is implemented using the AUCMEDI framework and relies on well-known
network architectures to ensure robustness and reproducibility.


  We extend our finite difference time domain method for numerical solution of
the Schrodinger equation to cases where eigenfunctions are complex-valued.
Illustrative numerical results for an electron in two dimensions, subject to a
confining potential V(x,y), in a constant perpendicular magnetic field
demonstrate the accuracy of the method.


  We show that many hyperbolic monopoles can be distinguished from each other
via their asymptotic values in contrast to the case of Euclidean monopoles.


  We present a detailed analysis of the use of heavy quark fragmentation into
heavy hadrons for testing the heavy quark effective theory through comparison
of the measured fragmentation parameters of the $c$ and $b$ quarks. Our
analysis is entirely model independent. We interpret the known perturbative
evolution in a way useful for exploiting heavy quark symmetry at low energy. We
first show consistency with perturbative QCD scaling for measurements done
solely with $c$ quarks. We then apply the perturbative analysis and the heavy
quark expansion to relate measurements from ARGUS and LEP. We place bounds on a
nonperturbative quark mass suppressed parameter, and compare the values for the
$b$ and $c$ quarks. We find consistency with the heavy quark expansion but
fairly sizable QCD uncertainties. We also suggest that one might reduce the
systematic uncertainty in the result by not extrapolating to low $z$.


  The Schwarzschild metric is derived in a manner that does not require
familiarity with the formalism of differential geometry beyond the ability to
interpret a general spacetime metric. As such, the derivation is suitable for
an undergraduate course on general relativity. The derivation uses infalling
coordinates that are particularly well adapted to the situation, as well as
Einstein's equation in the simple form introduced by Baez and Bunn. That
version of the vacuum Einstein equations corresponds to requiring a particular
local Newtonian limit: that, to first order, the deformation of a "test ball"
of freely falling, initially-at-rest test particles is governed by the tidal
forces of Newtonian gravity.


  Human Activity Recognition has witnessed a significant progress in the last
decade. Although a great deal of work in this field goes in recognizing normal
human activities, few studies focused on identifying motion in sports.
Recognizing human movements in different sports has high impact on
understanding the different styles of humans in the play and on improving their
performance. As deep learning models proved to have good results in many
classification problems, this paper will utilize deep learning to classify
cross-country skiing movements, known as gears, collected using a 3D
accelerometer. It will also provide a comparison between different deep
learning models such as convolutional and recurrent neural networks versus
standard multi-layer perceptron. Results show that deep learning is more
effective and has the highest classification accuracy.


  In the framework of the density functional theory a new electronegativity
formulation via the Feynman-Kleinert path integral formalism in the markovian
limit is proposed. The computation of the electronic density follows, in terms
of partition function, the same procedure of the Levy constrained-search for
the wave function. The obtained electronegativity scale seems to respect the
main criteria largely used for its acceptability.


  This is a tutorial for using ETA, a MAPLE package for calculating with
Dedekind's eta function. The ETA package is designed for proving eta-product
identities using the valence formula for modular functions.


  We propose a new method for linear second-order cone programs. It is based on
the sequential quadratic programming framework for nonlinear programming. In
contrast to interior point methods, it can capitalize on the warm-start
capabilities of active-set quadratic programming subproblem solvers and achieve
a local quadratic rate of convergence.
  In order to overcome the non-differentiability or singularity observed in
nonlinear formulations of the conic constraints, the subproblems approximate
the cones with polyhedral outer approximations that are refined throughout the
iterations. For nondegenerate instances, the algorithm implicitly identifies
the set of cones for which the optimal solution lies at the extreme points. As
a consequence, the final steps are identical to regular sequential quadratic
programming steps for a differentiable nonlinear optimization problem, yielding
local quadratic convergence.
  We prove the global and local convergence guarantees of the method and
present numerical experiments that confirm that the method can take advantage
of good starting points and can achieve higher accuracy compared to a
state-of-the-art interior point solver.


  We review the application of non-Abelian discrete groups to Tri-Bimaximal
(TB) neutrino mixing, which is supported by experiment as a possible good first
approximation to the data. After summarizing the motivation and the formalism,
we discuss specific models, mainly those based on A4 but also on other finite
groups, and their phenomenological implications, including the extension to
quarks. The recent measurements of \theta_13 favour versions of these models
where a suitable mechanism leads to corrections to \theta_13 that can naturally
be larger than those to \theta_12 and \theta_23. The virtues and the problems
of TB mixing models are discussed, also in connection with lepton flavour
violating processes, and the different approaches are compared.


  Trust is the basis of any distributed, fault-tolerant, or secure system. A
trust assumption specifies the failures that a system, such as a blockchain
network, can tolerate and determines the conditions under which it operates
correctly. In systems subject to Byzantine faults, the trust assumption is
usually specified through sets of processes that may fail together. Trust has
traditionally been symmetric, such that all processes in the system adhere to
the same, global assumption about potential faults. Recently, asymmetric trust
models have also been considered, especially in the context of blockchains,
where every participant is free to choose who to trust.
  In both cases, it is an open question how to compose trust assumptions.
Consider two or more systems, run by different and possibly disjoint sets of
participants, with different assumptions about faults: how can they work
together? This work answers this question for the first time and offers
composition rules for symmetric and for asymmetric quorum systems. These rules
are static and do not require interaction or agreement on the new trust
assumption among the participants. Moreover, they ensure that if the original
systems allow for running a particular protocol (guaranteeing consistency and
availability), then so will the joint system. At the same time, the composed
system tolerates as many faults as possible, subject to the underlying
consistency and availability properties.
  Reaching consensus with asymmetric trust in the model of personal Byzantine
quorum systems (Losa et al., DISC 2019) was shown to be impossible, if the
trust assumptions of the processes diverge from each other. With asymmetric
quorum systems, and by applying our composition rule, we show how consensus is
actually possible, even with the combination of disjoint sets of processes.


  The CSR External-target Experiment (CEE) will be the first large-scale
nuclear physics experiment device at the Cooling Storage Ring (CSR) of the
Heavy-Ion Research Facility in Lanzhou (HIRFL) in China. A new T0 detector has
been proposed to measure the multiplicity, angular distribution and timing
information of charged particles produced in heavy-ion collisions at the target
region. Multi-gap resistive plate chamber (MRPC) technology was chosen as part
of the construction of the T0 detector, which provides precision event
collision times (T0) and collision geometry information. The prototype was
tested with hadron and heavy-ion beams to study its performance. By comparing
the experimental results with a Monte Carlo simulation, the time resolution of
the MRPCs are found to be $\sim$ 50 ps or better. The timing performance of the
T0 detector, including both detector and readout electronics, we found to
fulfil the requirements of the CEE.


  The $G$-strand equations for a map $\mathbb{R}\times \mathbb{R}$ into a Lie
group $G$ are associated to a $G$-invariant Lagrangian. The Lie group manifold
is also the configuration space for the Lagrangian. The $G$-strand itself is
the map $g(t,s): \mathbb{R}\times \mathbb{R}\to G$, where $t$ and $s$ are the
independent variables of the $G$-strand equations. The Euler-Poincar\'e
reduction of the variational principle leads to a formulation where the
dependent variables of the $G$-strand equations take values in the
corresponding Lie algebra $\mathfrak{g}$ and its co-algebra, $\mathfrak{g}^*$
with respect to the pairing provided by the variational derivatives of the
Lagrangian.
  We review examples of different $G$-strand constructions, including matrix
Lie groups and diffeomorphism group. In some cases the $G$-strand equations are
completely integrable 1+1 Hamiltonian systems that admit soliton solutions.


  Single crystals of the Sr$_2$RuO$_4$-Ru eutectic system are known to exhibit
enhanced superconductivity at 3~K, in addition to the bulk superconductivity of
Sr$_2$RuO$_4$ at 1.5~K. The 1.5-K phase is believed to be a spin-triplet,
chiral $p$-wave state with the multi-component order parameter, giving rise to
chiral domain structure. In contrast, the 3-K phase is attributable to enhanced
superconductivity of Sr$_2$RuO$_4$ in the strained interface region between Ru
inclusion of a few to tens of micrometers in size and the surrounding
Sr$_2$RuO$_4$. We investigate the dynamic behavior of a topological junction,
where a superconductor is surrounded by another superconductor. Specifically,
we fabricated Nb/Ru/Sr$_2$RuO$_4$ topological superconducting junctions, in
which the difference in phase winding between the $s$-wave superconductivity in
Ru micro-islands induced from Nb and the superconductivity of Sr$_2$RuO$_4$
mainly governs the junction behavior. Comparative results of the asymmetry,
hysteresis and noise in junctions with different sizes, shapes, and
configurations of Ru inclusions are explained by the chiral domain-wall motion
in these topological junctions. Furthermore, a striking difference between the
1.5-K and 3-K phases is clearly revealed: the large noise in the 1.5-K phase
sharply disappears in the 3-K phase. These results confirm the multi-component
order-parameter superconductivity of the bulk Sr$_2$RuO$_4$, consistent with
the chiral $p$-wave state, and the proposed non-chiral single-component
superconductivity of the 3-K phase.


  The paper addresses two variants of the stochastic shortest path problem
('optimize the accumulated weight until reaching a goal state') in Markov
decision processes (MDPs) with integer weights. The first variant optimizes
partial expected accumulated weights, where paths not leading to a goal state
are assigned weight 0, while the second variant considers conditional expected
accumulated weights, where the probability mass is redistributed to paths
reaching the goal. Both variants constitute useful approaches to the analysis
of systems without guarantees on the occurrence of an event of interest
(reaching a goal state), but have only been studied in structures with
non-negative weights. Our main results are as follows. There are
polynomial-time algorithms to check the finiteness of the supremum of the
partial or conditional expectations in MDPs with arbitrary integer weights. If
finite, then optimal weight-based deterministic schedulers exist. In contrast
to the setting of non-negative weights, optimal schedulers can need infinite
memory and their value can be irrational. However, the optimal value can be
approximated up to an absolute error of $\epsilon$ in time exponential in the
size of the MDP and polynomial in $\log(1/\epsilon)$.


  Age-related Macular Degeneration (AMD) and Diabetic Macular Edema (DME) are
the major causes of vision loss in developed countries. Alteration of retinal
layer structure and appearance of exudate are the most significant signs of
these diseases. With the aim of automatic classification of DME, AMD and normal
subjects from Optical Coherence Tomography (OCT) images, we proposed a
classification algorithm. The two important issues intended in this approach
are, not utilizing retinal layer segmentation which by itself is a challenging
task and attempting to identify diseases in their early stages, where the signs
of diseases appear in a small fraction of B-Scans. We used a histogram of
oriented gradients (HOG) feature descriptor to well characterize the
distribution of local intensity gradients and edge directions. In order to
capture the structure of extracted features, we employed different dictionary
learning-based classifiers. Our dataset consists of 45 subjects: 15 patients
with AMD, 15 patients with DME and 15 normal subjects. The proposed classifier
leads to an accuracy of 95.13%, 100.00%, and 100.00% for DME, AMD, and normal
OCT images, respectively, only by considering the 4% of all B-Scans of a volume
which outperforms the state of the art methods.


  Highly localized kernels based on orthogonal polynomials have been studied
and utilized over several regular domains. Much of the results deduced via
these kernels can be treated uniformly in the framework of localizable spaces
of homogeneous type. We clarify the concept of localness and provide a list of
such localizable spaces.


  William Thomson proved Carnot's theorem basing on postulate: "It is
impossible, by means of inanimate material agency, to derive mechanical effect
from any portion of matter by cooling it below the temperature of the coldest
of the surrounding objects". The present paper demonstrates that Carnot's
theorem can be proved based on the contrary Thomson's postulate: "It is
impossible to use the mechanical effect to the heating the coldest of
surrounding objects". A conclusion that Carnot's theorem does not follow from
the Thomson's postulate has been drawn.


  The exchange of diffusive metabolites is known to control the spatial
patterns formed by microbial populations, as revealed by recent studies in the
laboratory. However, the matrices used, such as agarose pads, lack the
structured geometry of many natural microbial habitats, including in the soil
or on the surfaces of plants or animals. Here we address the important question
of how such geometry may control diffusive exchanges and microbial interaction.
We model mathematically mutualistic interactions within a minimal unit of
structure: two growing reservoirs linked by a diffusive channel through which
metabolites are exchanged. The model is applied to study a synthetic mutualism,
experimentally parameterised on a model algal-bacterial co-culture. Analytical
and numerical solutions of the model predict conditions for the successful
establishment of remote mutualisms, and how this depends, often
counterintutively, on diffusion geometry. We connect our findings to
understanding complex behaviour in synthetic and naturally occurring microbial
communities.


  The scientific community has witnessed tremendous expansion of research on
layered (i.e. two-dimensional, 2D) materials, with increasing recent focus on
applications to photonics. Layered materials are particularly exciting for
manipulating light in the confined geometry of photonic integrated circuits,
where key material properties include strong and controllable light-matter
interaction, and limited optical loss. Layered materials feature tunable
optical properties, phases that are promising for electro-optics, and a panoply
of polymorphs that suggest a rich design space for highly-nonperturbative
photonic integrated devices based on phase-change functionality. All of these
features are manifest in materials with band gap above the photonics-relevant
near-infrared (NIR) spectral band ($\sim$ 0.5 - 1 eV), meaning that they can be
harnessed in refractive (i.e. non-absorptive) applications.


  Large Language Models such as GPTs (Generative Pre-trained Transformers)
exhibit remarkable capabilities across a broad spectrum of applications.
Nevertheless, due to their intrinsic complexity, these models present
substantial challenges in interpreting their internal decision-making
processes. This lack of transparency poses critical challenges when it comes to
their adaptation by financial institutions, where concerns and accountability
regarding bias, fairness, and reliability are of paramount importance.
Mechanistic interpretability aims at reverse engineering complex AI models such
as transformers. In this paper, we are pioneering the use of mechanistic
interpretability to shed some light on the inner workings of large language
models for use in financial services applications. We offer several examples of
how algorithmic tasks can be designed for compliance monitoring purposes. In
particular, we investigate GPT-2 Small's attention pattern when prompted to
identify potential violation of Fair Lending laws. Using direct logit
attribution, we study the contributions of each layer and its corresponding
attention heads to the logit difference in the residual stream. Finally, we
design clean and corrupted prompts and use activation patching as a causal
intervention method to localize our task completion components further. We
observe that the (positive) heads $10.2$ (head $2$, layer $10$), $10.7$, and
$11.3$, as well as the (negative) heads $9.6$ and $10.6$ play a significant
role in the task completion.


  We have carried out long-term (14 years) V and R photometric monitoring of 12
carbon-rich proto-planetary nebulae. The light and color curves display
variability in all of them. The light curves are complex and suggest multiple
periods, changing periods, and/or changing amplitudes, which are attributed to
pulsation. A dominant period has been determined for each and found to be in
the range of ~150 d for the coolest (G8) to 35-40 d for the warmest (F3). A
clear, linear inverse relationship has been found in the sample between the
pulsation period and the effective temperature and also an inverse linear
relationship between the amplitude of light variation and the effective
temperature. These are consistent with the expectation for a pulsating post-AGB
star evolving toward higher temperature at constant luminosity. The published
spectral energy distributions and mid-infrared images show these objects to
have cool (200 K), detached dust shells and published models imply that
intensive mass loss ended a few thousand years ago. The detection of periods as
long as 150 d in these requires a revision in the published post-AGB evolution
models that couple the pulsation period to the mass loss rate and that assume
that intensive mass loss ended when the pulsation period had decreased to 100
d. This revision will have the effect of extending the time scale for the early
phases of post-AGB evolution. It appears that real time evolution in the
pulsation periods of individual objects may be detectable on the time scale of
two decades.


  We compute the two-loop QCD corrections to the heavy quark form factors in
case of the vector, axial-vector, scalar and pseudo-scalar currents up to
second order in the dimensional parameter $\epsilon = (4-D)/2$. These terms are
required in the renormalization of the higher order corrections to these form
factors.


  We investigate the ability of current CMB data to reliably constrain the form
of the primordial power spectrum generated during inflation. We attempt to
identify more exotic power spectra that yield equally good fits to the data as
simple power-law spectra. In order to test a wide variety of spectral shapes,
we combine the flow formalism, which is a method of stochastic model
generation, with a numerical integration of the mode equations of quantum
fluctuations. This allows us to handle inflation models that yield spectra that
are not well described by the standard spectral parameterization. Using the
latest WMAP data-set, we find a high degree of variation in possible spectral
shapes. In particular, we find strongly running spectra arising from
fast-rolling inflaton fields providing equally good fits to the data as
power-law spectra arising from slowly-rolling fields. Current data poorly
constrains the spectrum on scales (k < 0.01 h{\rm Mpc}^{-1}), where the error
due to cosmic variance is large. Among the statistically degenerate models, we
identify spectra with strong running on these larger scales, but with reduced
running at smaller scales. These models predict values for the tensor-to-scalar
ratio, (r), that lie outside the 2-(\sigma) confidence interval obtained from
SDSS+WMAP data for spectra that are parametrized as power-laws or spectra with
constant running. By considering more generalized power spectra, we therefore
open up regions of parameter space excluded for simpler models.


  Let $K\ < x_i\ >$ be the free associative algebra generated by a finite or
countable number of variables $x_i$. The notion of "letterplace correspondence"
introduced in [1,2] for the graded (two-sided) ideals of $K\ < x_i\ >$ is
extended in this paper also to the nongraded case. This amounts to the
possibility of modelizing nongraded noncommutative presented algebras by means
of a class of graded commutative algebras that are invariant under the action
of the monoid $\mathbb N$ of natural numbers. For such purpose we develop the
notion of saturation for the graded ideals of $K\ < x_i,t\ >$, where $t$ is an
extra variable and for their letterplace analogues in the commutative
polynomial algebra $K[x_{ij},t_j]$, where $j$ ranges in $\mathbb N$. In
particular, one obtains an alternative algorithm for computing inhomogeneous
noncommutative Gr\"obner bases using just homogeneous commutative polynomials.
The feasibility of the proposed methods is shown by an experimental
implementation developed in the computer algebra system Maple and by using
standard routines for the Buchberger algorithm contained in Singular.
  References
  [1] La Scala, R.; Levandovskyy, V., Letterplace ideals and non-commutative
Gr\"obner bases. J. Symbolic Comput., 44 (2009), 1374--1393.
  [2] La Scala, R.; Levandovskyy, V., Skew polynomial rings, Gr\"obner bases
and the letterplace embedding of the free associative algebra. J. Symbolic
Comput., 48 (2013), 110--131


  Nonlinear simulations of neutron star mergers are complicated by the need to
represent turbulent dynamics. As we cannot (yet) perform simulations that
resolve accurately both the gravitational-wave scale and the smallest scales at
which magneto/hydrodynamic turbulence plays a role, we need to rely on
approximations. Addressing this problem in the context of large-eddy models, we
outline a coherent Lagrangian filtering framework that allows us to explore the
many issues that arise, linking conceptual problems to practical
implementations and the interpretation of the results. We develop understanding
crucial for quantifying unavoidable uncertainties in current and future
numerical relativity simulations and consider the implications for neutron-star
parameter estimation and constraints on the equation of state of matter under
extreme conditions.


  We present an overview of the "KIFF" project, which provides ultra-deep
Ks-band imaging of all six of the Hubble Frontier Fields clusters Abell 2744,
MACS-0416, Abell S1063, Abell 370, MACS-0717 and MACS-1149. All of these fields
have recently been observed with large allocations of Directors' Discretionary
Time with the HST and Spitzer telescopes covering 0.4 < lambda < 1.6 microns
and 3.6--4.5 microns, respectively. VLT/HAWK-I integrations of the first four
fields reach 5-sigma limiting depths of Ks~26.0 (AB, point sources) and have
excellent image quality (FWHM ~ 0."4). Shorter Keck/MOSFIRE integrations of the
MACS-0717 (MACS-1149) field better observable in the north reach limiting
depths Ks=25.5 (25.1) with seeing FWHM ~0."4 (0."5). In all cases the Ks-band
mosaics cover the primary cluster and parallel HST/ACS+WFC3 fields. The total
area of the Ks-band coverage is 490 arcmin^2. The Ks-band at 2.2 microns
crucially fills the gap between the reddest HST filter (1.6 micron ~ H-band)
and the IRAC 3.6 micron passband. While reaching the full depths of the
space-based imaging is not currently feasible from the ground, the deep Ks-band
images provide important constraints on both the redshifts and the stellar
population properties of galaxies extending well below the characteristic
stellar mass across most of the age of the universe, down to, and including,
the redshifts of the targeted galaxy clusters (z < 0.5).


  Deviations from unitarity in the three-neutrino mixing canonical picture are
expected in many physics scenarios beyond the Standard Model. The mixing of new
heavy neutral leptons with the three light neutrinos would in principle modify
the strength and flavour structure of charged-current and neutral-current
interactions with matter. Non-unitarity effects would therefore have an impact
on the neutrino decoupling processes in the early Universe and on the value of
the effective number of neutrinos, $N_{\rm eff}$. We calculate the cosmological
energy density in the form of radiation with a non-unitary neutrino mixing
matrix, addressing the possible interplay between parameters. Highly accurate
measurements of $N_{\rm eff}$ from forthcoming cosmological observations can
provide independent and complementary limits on the departures from unitarity.
For completeness, we relate the scenario of small deviations from unitarity to
non-standard neutrino interactions and compare the forecasted constraints to
other existing limits in the literature.


  We present new observations of the cataclysmic variable DW Cancri, after the
system recovered from a low state. We performed a power spectrum analysis that
reveals a clear signal of the 38 min spin period in our photometric data. Our
spectroscopic power spectrum search was consistent with studies performed
before the low state, showing the orbital and spin modulations. We also
conducted a Doppler Tomography study which exhibits a disc structure and an
enhanced emission region, possibly related to a hot spot component. Through a
wavelet transform analysis we also found evidence of the 70 min spin-orbit beat
period. We interpret these results as indication of a partial recovery of the
system. Nonetheless, DW Cnc does not yet show all the original photometric
modulations reported in 2004, before experiencing the low state. Namely, these
signals are a 38 min spin period, an 86 min orbital period, a 70 min beat
period between the latter modulations, and an unresolved 110 min period. Even
though our photometry shows a spin cycle modulation and a long 108 min period,
it lacks the beat and orbital period signals. Thus, we propose further
observations of DW Cancri, to elucidate if the mechanisms giving rise to the
signatures observed prior to the low state, require more time to reactivate.


  We introduce the $L_p$ Traveling Salesman Problem ($L_p$-TSP), given by an
origin, a set of destinations, and underlying distances. The objective is to
schedule a destination visit sequence for a traveler of unit speed to minimize
the Minkowski $p$-norm of the resulting vector of visit/service times. For $p =
\infty$ the problem becomes a path variant of the TSP, and for $p = 1$ it
defines the Traveling Repairman Problem (TRP), both at the center of classical
combinatorial optimization. We provide an approximation preserving
polynomial-time reduction of $L_p$-TSP to the segmented-TSP Problem [Sitters
'14] and further study the case of $p = 2$, which we term the Traveling
Firefighter Problem (TFP), when the cost due to a delay in service is quadratic
in time.
  We also study the all-norm-TSP problem [Golovin et al. '08], in which the
objective is to find a route that is (approximately) optimal with respect to
the minimization of any norm of the visit times, and improve corresponding
(in)approximability bounds on metric spaces.