  The asymptotic behaviour of the commonly used bootstrap percentile confidence
interval is investigated when the parameters are subject to linear inequality
constraints. We concentrate on the important one- and two-sample problems with
data generated from general parametric distributions in the natural exponential
family. The focus of this paper is on quantifying the coverage probabilities of
the parametric bootstrap percentile confidence intervals, in particular their
limiting behaviour near boundaries. We propose a local asymptotic framework to
study this subtle coverage behaviour. Under this framework, we discover that
when the true parameters are on, or close to, the restriction boundary, the
asymptotic coverage probabilities can always exceed the nominal level in the
one-sample case; however, they can be, remarkably, both under and over the
nominal level in the two-sample case. Using illustrative examples, we show that
the results provide theoretical justification and guidance on applying the
bootstrap percentile method to constrained inference problems.


  The ability to classify spoken speech based on the style of speaking is an
important problem. With the advent of BPO's in recent times, specifically those
that cater to a population other than the local population, it has become
necessary for BPO's to identify people with certain style of speaking
(American, British etc). Today BPO's employ accent analysts to identify people
having the required style of speaking. This process while involving human bias,
it is becoming increasingly infeasible because of the high attrition rate in
the BPO industry. In this paper, we propose a new metric, which robustly and
accurately helps classify spoken speech based on the style of speaking. The
role of the proposed metric is substantiated by using it to classify real
speech data collected from over seventy different people working in a BPO. We
compare the performance of the metric against human experts who independently
carried out the classification process. Experimental results show that the
performance of the system using the novel metric performs better than two
different human expert.


  We study the nonlinear Schr\"odinger equation with $\delta'_s$ coupling of
intensity $\beta\in\mathbb{R}\setminus\{0\}$ on the star graph $\Gamma$
consisting of $N$ half-lines. The nonlinearity has the form $g(u)=|u|^{p-1}u,
p>1.$ In the first part of the paper, under certain restriction on $\beta$, we
prove the existence of the ground state solution as a minimizer of the action
functional $S_\omega$ on the Nehari manifold. It appears that the family of
critical points which contains a ground state consists of $N$ profiles (one
symmetric and $N-1$ asymmetric). In particular, for the attractive $\delta'_s$
coupling ($\beta<0$) and the frequency $\omega$ above a certain threshold, we
managed to specify the ground state.
  The second part is devoted to the study of orbital instability of the
critical points. We prove spectral instability of the critical points using
Grillakis/Jones Instability Theorem. Then orbital instability for $p>2$ follows
from the fact that data-solution mapping associated with the equation is of
class $C^2$ in $H^1(\Gamma)$. Moreover, for $p>5$ we complete and concertize
instability results showing strong instability (by blow up in finite time) for
the particular critical points.


  The ever-increasing amount of multimedia content on modern social media
platforms are valuable in many applications. While the openness and convenience
features of social media also foster many rumors online. Without verification,
these rumors would reach thousands of users immediately and cause serious
damages. Many efforts have been taken to defeat online rumors automatically by
mining the rich content provided on the open network with machine learning
techniques. Most rumor detection methods can be categorized in three paradigms:
the hand-crafted features based classification approaches, the
propagation-based approaches and the neural networks approaches. In this
survey, we introduce a formal definition of rumor in comparison with other
definitions used in literatures. We summary the studies of automatic rumor
detection so far and present details in three paradigms of rumor detection. We
also give an introduction on existing datasets for rumor detection which would
benefit following researches in this area. We give our suggestions for future
rumors detection on microblogs as a conclusion.


  It has been observed that the composite fermion (CF) approach tends to
overcount the number of linearly independent candidate states for fixed sets of
quantum numbers [number of particles, total angular momentum, and (pseudo)spin
if applicable]. That is, CF Slater determinants that are orthogonal before
projection, may lead to wave functions that are identical, or possess linear
dependencies, after projection. This has been pointed out both in the context
of rotating bosons in the lowest Landau level, and for excited bands of the
(fermionic) fractional quantum Hall effect. We present a systematic approach
that enables us to reveal all linear dependencies between bosonic compact
states in the lowest CF "cyclotron energy" sub-band, and almost all
dependencies in higher sub-bands, at the level of the CF Slater determinants,
i.e. before projection, which implies a major computational simplification. Our
approach is introduced for so-called simple states of two-species rotating
bosons, and then generalised to generic compact bosonic states, both one- and
two-species. Some perspectives also apply to fermionic systems. The identities
and linear dependencies we find, are analytically exact for "brute force"
projection in the disk geometry.


  The history of neutrino mixing and oscillations is briefly presented. Basics
of neutrino mixing and oscillations and convenient formalism of neutrino
oscillations in vacuum is given. The role of neutrino in the Standard Model and
the Weinberg mechanism of the generation of the Majorana neutrino masses are
discussed.


  Generating realistic time series data is important for many engineering and
scientific applications. Existing work tackles this problem using generative
adversarial networks (GANs). However, GANs are unstable during training, and
they can suffer from mode collapse. While variational autoencoders (VAEs) are
known to be more robust to the these issues, they are (surprisingly) less
considered for time series generation. In this work, we introduce Koopman VAE
(KoVAE), a new generative framework that is based on a novel design for the
model prior, and that can be optimized for either regular and irregular
training data. Inspired by Koopman theory, we represent the latent conditional
prior dynamics using a linear map. Our approach enhances generative modeling
with two desired features: (i) incorporating domain knowledge can be achieved
by leveraging spectral tools that prescribe constraints on the eigenvalues of
the linear map; and (ii) studying the qualitative behavior and stability of the
system can be performed using tools from dynamical systems theory. Our results
show that KoVAE outperforms state-of-the-art GAN and VAE methods across several
challenging synthetic and real-world time series generation benchmarks. Whether
trained on regular or irregular data, KoVAE generates time series that improve
both discriminative and predictive metrics. We also present visual evidence
suggesting that KoVAE learns probability density functions that better
approximate the empirical ground truth distribution.


  When limited by their own morphologies, humans and some species of animals
have the remarkable ability to use objects from the environment toward
accomplishing otherwise impossible tasks. Robots might similarly unlock a range
of additional capabilities through tool use. Recent techniques for jointly
optimizing morphology and control via deep learning are effective at designing
locomotion agents. But while outputting a single morphology makes sense for
locomotion, manipulation involves a variety of strategies depending on the task
goals at hand. A manipulation agent must be capable of rapidly prototyping
specialized tools for different goals. Therefore, we propose learning a
designer policy, rather than a single design. A designer policy is conditioned
on task information and outputs a tool design that helps solve the task. A
design-conditioned controller policy can then perform manipulation using these
tools. In this work, we take a step towards this goal by introducing a
reinforcement learning framework for jointly learning these policies. Through
simulated manipulation tasks, we show that this framework is more sample
efficient than prior methods in multi-goal or multi-variant settings, can
perform zero-shot interpolation or fine-tuning to tackle previously unseen
goals, and allows tradeoffs between the complexity of design and control
policies under practical constraints. Finally, we deploy our learned policies
onto a real robot. Please see our supplementary video and website at
https://robotic-tool-design.github.io/ for visualizations.


  We present and study C*-algebras generated by "periodic weighted creation
operators" on the Fock space associated with an automorphism $\alpha$ on a
C*-algebra $A$. These algebras can be viewed as generalized Bunce-Deddens
algebras associated with the automorphism and can be written as a certain
direct limit. We prove a crossed product presentation for such an algebra and
find a necessary and sufficient condition for it to be simple. In the case
where the automorphism is induced by an irrational rotation (on
$C(\mathbb{T})$) we compute the K-theory groups and obtain a complete
classification of these algebras.


  To expedite the commissioning process of the proton therapy system at Samsung
Medical Center (SMC), we have developed a Monte Carlo simulation model of the
proton therapy nozzles using TOPAS. At SMC proton therapy center, we have two
gantry rooms with different types of nozzles; a multi-purpose nozzle and a
dedicated scanning nozzle. Each nozzle has been modeled in detail following the
geometry information provided by the manufacturer, Sumitomo Heavy Industries,
Ltd. For this purpose, novel features of TOPAS, such as the time feature or the
ridge filter class, have been used. And the appropriate physics models for
proton nozzle simulation were defined. Dosimetric properties, like percent
depth dose curve, spread-out Bragg peak (SOBP), beam spot size, have been
simulated and verified against measured beam data. Beyond the Monte Carlo
nozzle modeling, we have developed an interface between TOPAS and the treatment
planning system (TPS), RayStation. An exported RT plan data from the TPS has
been interpreted by the interface and then translated into the TOPAS input
text. The developed Monte Carlo nozzle model can be used to estimate non-beam
performance of the nozzles such as the neutron background. Furthermore, the
nozzle model can be used to study mechanical optimization in the design of the
nozzle.


  Among the four fundamental forces, only gravity does not couple to particle
spins according to the general theory of relativity. We test this principle by
searching for an anomalous scalar coupling between the neutron spin and the
Earth gravity on the ground. We develop an atomic gas comagnetometer to measure
the ratio of nuclear spin-precession frequencies between $^{129}$Xe and
$^{131}$Xe, and search for a change of this ratio to the precision of 10$^{-9}$
as the sensor is flipped in the Earth gravitational field. The null results of
this search set an upper limit on the coupling energy between the neutron spin
and the gravity on the ground at 5.3$\times$10$^{-22}$~eV (95\% confidence
level), resulting in a 17-fold improvement over the previous limit. The results
can also be used to constrain several other anomalous interactions. In
particular, the limit on the coupling strength of axion-mediated
monopole-dipole interactions at the range of the Earth radius is improved by a
factor of 17.


  Fine-tuning pre-trained language models has become the prevalent paradigm for
building downstream NLP models. Oftentimes fine-tuned models are readily
available but their training data is not, due to data privacy or intellectual
property concerns. This creates a barrier to fusing knowledge across individual
models to yield a better single model. In this paper, we study the problem of
merging individual models built on different training data sets to obtain a
single model that performs well both across all data set domains and can
generalize on out-of-domain data. We propose a dataless knowledge fusion method
that merges models in their parameter space, guided by weights that minimize
prediction differences between the merged model and the individual models. Over
a battery of evaluation settings, we show that the proposed method
significantly outperforms baselines such as Fisher-weighted averaging or model
ensembling. Further, we find that our method is a promising alternative to
multi-task learning that can preserve or sometimes improve over the individual
models without access to the training data. Finally, model merging is more
efficient than training a multi-task model, thus making it applicable to a
wider set of scenarios.


  Multiplex networks are collections of networks with identical nodes but
distinct layers of edges. They are genuine representations for a large variety
of real systems whose elements interact in multiple fashions or flavors.
However, multiplex networks are not always simple to observe in the real world;
often, only partial information on the layer structure of the networks is
available, whereas the remaining information is in the form of aggregated,
single-layer networks. Recent works have proposed solutions to the problem of
reconstructing the hidden multiplexity of single-layer networks using tools
proper of network science. Here, we develop a machine learning framework that
takes advantage of graph embeddings, i.e., representations of networks in
geometric space. We validate the framework in systematic experiments aimed at
the reconstruction of synthetic and real-world multiplex networks, providing
evidence that our proposed framework not only accomplishes its intended task,
but often outperforms existing reconstruction techniques.


  Emerging intelligent embedded devices rely on Deep Neural Networks (DNNs) to
be able to interact with the real-world environment. This interaction comes
with the ability to retrain DNNs, since environmental conditions change
continuously in time. Stochastic Gradient Descent (SGD) is a widely used
algorithm to train DNNs by optimizing the parameters over the training data
iteratively. In this work, first we present a novel approach to add the
training ability to a baseline DNN accelerator (inference only) by splitting
the SGD algorithm into simple computational elements. Then, based on this
heuristic approach we propose TaxoNN, a light-weight accelerator for DNN
training. TaxoNN can easily tune the DNN weights by reusing the hardware
resources used in the inference process using a time-multiplexing approach and
low-bitwidth units. Our experimental results show that TaxoNN delivers, on
average, 0.97% higher misclassification rate compared to a full-precision
implementation. Moreover, TaxoNN provides 2.1$\times$ power saving and
1.65$\times$ area reduction over the state-of-the-art DNN training accelerator.


  The commuting variety of a reductive Lie algebra ${\goth g}$ is the
underlying variety of a well defined subscheme of $\gg g{}$. In this note, it
is proved that this scheme is normal. In particular, its ideal of definition is
a prime ideal.


  The problem of using observed correlations to infer causal relations is
relevant to a wide variety of scientific disciplines. Yet given correlations
between just two classical variables, it is impossible to determine whether
they arose from a causal influence of one on the other or a common cause
influencing both, unless one can implement a randomized intervention. We here
consider the problem of causal inference for quantum variables. We introduce
causal tomography, which unifies and generalizes conventional quantum
tomography schemes to provide a complete solution to the causal inference
problem using a quantum analogue of a randomized trial. We furthermore show
that, in contrast to the classical case, observed quantum correlations alone
can sometimes provide a solution. We implement a quantum-optical experiment
that allows us to control the causal relation between two optical modes, and
two measurement schemes -- one with and one without randomization -- that
extract this relation from the observed correlations. Our results show that
entanglement and coherence, known to be central to quantum information
processing, also provide a quantum advantage for causal inference.


  In this work we study the time evolutions of (Renyi) entanglement entropy of
locally excited states in two dimensional conformal field theories (CFTs) at
finite temperature. We consider excited states created by acting with local
operators on thermal states and give both field theoretic and holographic
calculations. In free field CFTs, we find that the growth of Renyi entanglement
entropy at finite temperature is reduced compared to the zero temperature
result by a small quantity proportional to the width of the localized
excitations. On the other hand, in finite temperature CFTs with classical
gravity duals, we find that the entanglement entropy approaches a
characteristic value at late time. This behaviour does not occur at zero
temperature. We also study the mutual information between the two CFTs in the
thermofield double (TFD) formulation and give physical interpretations of our
results.


  The pioneering experiments of Karl H. Drexhage explained the classical
interaction of light with matter and the modification of the decay rates of an
emitter.1 Here, we tried to mimic these experiments in a slightly different
configuration and measured the electron mobility of a thin film semiconductor
from weak to strong coupling regime. Perylene diimide (organic semiconductor
dye) molecules are deposited on a MOSFET device. The refractive index mismatch
between the silicon/silicon dioxide layer and the dye molecules forms an
interference pattern. The frequency of the interference lines is tuned by
changing the thickness of the organic semiconductor. Interestingly, we observed
an increase in the electron mobility of the active layer once the system slowly
entered into strong coupling condition in a {\lambda} cavity. Whereas resonance
tuning of a {\lambda}/2 cavity does not affect the electron transport,
suggesting the system is still in the weak coupling regime. These results are
further correlated by optical measurements and transfer matrix simulations. The
increase in electron mobility is not large due to high dissipation or
low-quality factors of the cavity modes. However, the mirrorless configuration
presented here may offer a simpler way of studying the properties of the
polaritonic states.


  In this paper, considering the geometric equivalence for algebras of a
variety $_{S}A$ of S-acts over a monoid S, we obtain representation theorems
describing all types of the equivalence classes of geometrically equivalent
S-acts of varieties $_{S}A$ over groups S.


  We present the results of a CO line survey of 30 galaxies at moderate
redshift (z \sim 0.2-0.6), with the IRAM 30m telescope, with the goal to follow
galaxy evolution and in particular the star formation efficiency (SFE) as
defined by the ratio between far-infrared luminosity and molecular gas mass
(LFIR/M(H2)). The sources are selected to be ultra-luminous infrared galaxies
(ULIRGs), with LFIR larger than 2.8 10^{12} Lsol, experiencing starbursts;
adopting a low ULIRG CO-to-H2 conversion factor, their gas consumption
time-scale is lower than 10^8 yr. To date only very few CO observations exist
in this redshift range that spans nearly 25% of the universe's age.
Considerable evolution of the star formation rate is already observed during
this period. 18 galaxies out of our sample of 30 are detected (of which 16 are
new detections), corresponding to a detection rate of 60%. The average CO
luminosity for the 18 galaxies detected is L'CO = 2 10^{10} K km/s pc^2,
corresponding to an average H2 mass of 1.6 10^{10} Msol. The FIR luminosity
correlates well with the CO luminosity, in agreement with the correlation found
for low and high redshift ULIRGs. Although the conversion factor between CO
luminosity and H2 mass is uncertain, we find that the maximum amount of gas
available for a single galaxy is quickly increasing as a function of redshift.
Using the same conversion factor, the SFEs for z\sim 0.2-0.6 ULIRGs are found
to be significantly higher, by a factor 3, than for local ULIRGs, and are
comparable to high redshift ones. We compare this evolution to the expected
cosmic H2 abundance and the cosmic star formation history.


  We analyze the existence and stability of two kinds of self-trapped spatially
localized gap modes, gap solitons and truncated nonlinear Bloch waves, in
one-and two-dimensional optical or matter-wave media with self-focusing
nonlinearity, supported by a combination of linear and nonlinear periodic
lattice potentials. The former is found to be stable once placed inside a
single well of the nonlinear lattice, it is unstable otherwise. Contrary to the
case with constant self-focusing nonlinearity, where the latter solution is
always unstable, here, we demonstrate that it nevertheless can be stabilized by
the nonlinear lattice since the model under consideration combines the unique
properties of both the linear and nonlinear lattices. The practical
possibilities for experimental realization of the predicted solutions are also
discussed.


  In this paper we construct two groupoids from morphisms of groupoids, with
one from a categorical viewpoint and the other from a geometric viewpoint. We
show that for each pair of groupoids, the two kinds of groupoids of morphisms
are equivalent. Then we study the automorphism groupoid of a groupoid.


  Polarized upconversion luminescence (PUCL) of lanthanide (Ln3+) ions has been
widely used in single particle tracking, microfluidics detection,
three-dimensional displays, and so on. However, no effective strategy has been
developed for modulating PUCL. Here, we report a strategy to regulate PUCL in
Ho3+-doped NaYF4 single nanorods based on the number of upconversion photons.
By constructing a multiphoton upconversion system for Ho3+, we regulate the
degree of polarization (DOP) of PUCL from 0.6 for two-photon luminescence to
0.929 for three-photon upconversion luminescence (UCL). Furthermore, our
strategy is verified by cross-relaxation between Ho3+ and Yb3+, excitation
wavelength, excitation power density, and local site symmetry. And this
regulation strategy of PUCL has also been achieved in Tm3+, where DOP is ranged
from 0.233 for two-photon luminescence to 0.925 for four-photon UCL. Besides,
multi-dimensional anti-counterfeiting display has been explored with PUCL. This
work provides an effective strategy for the regulation of PUCL and also
provides more opportunities for the development of polarization display,
optical encoding, anti-counterfeiting, and integrated optical devices.


  The crystal lattice of Sr$_2$IrO$_4$ is investigated with synchrotron X-ray
powder diffraction under hydrostatic pressures up to $P=43$ GPa and
temperatures down to $20$ K. The tetragonal unit cell is maintained over the
whole investigated pressure range, within our resolution and sensitivity. The
$c$-axis compressibility $\kappa_c(P,T) \equiv -({1} / {c}) ({d c} / {d P})$
presents an anomaly with pressure at $P_1=17$ GPa at fixed $T=20$ K that is not
observed at $T=300$ K, whereas $\kappa_a(P,T)$ is nearly
temperature-independent and shows a linear behavior with $P$. The anomaly in
$\kappa_c(P,T)$ is associated with the onset of long-range magnetic order, as
evidenced by an analysis of the temperature-dependence of the lattice
parameters at fixed $P=13.7 \pm 0.5$ GPa. At fixed $T=20$ K, the tetragonal
elongation $c/a(P,T)$ shows a gradual increment with pressure and a depletion
above $P_2=30$ GPa that indicates an orbital transition and possibly marks the
collapse of the $J_{eff}=1/2$ spin-orbit-entangled state. Our results support
pressure-induced phase transitions or crossovers between electronic ground
states that are sensed, and therefore can be probed, by the crystal lattice at
low temperatures in this prototype spin-orbit Mott insulator.


  Many bacterial species produce toxins that inhibit their competitors. We
model this phenomenon by extending classic two-species Lotka-Volterra
competition in one spatial dimension to incorporate toxin production by one
species. Considering solutions comprising two adjacent single-species colonies,
we show how the toxin inhibits the susceptible species near the interface
between the two colonies. Moreover, a sufficiently effective toxin inhibits the
susceptible species to such a degree that an `inhibition zone' is formed
separating the two colonies. In the special case of truly non-motile bacteria,
i.e. with zero bacterial diffusivity, we derive analytical expressions
describing the bacterial distributions and size of the inhibition zone. In the
more general case of weakly motile bacteria, i.e. small bacterial diffusivity,
these two-colony solutions become travelling waves. We employ numerical methods
to show that the wavespeed is dependent upon both interspecific competition and
toxin strength; precisely which colony expands at the expense of the other
depends upon the choice of parameter values. In particular, a sufficiently
effective toxin allows the producer to expand at the expense of the
susceptible, with a wavespeed magnitude that is bounded above as the toxin
strength increases. This asymptotic wavespeed is independent of interspecific
competition and due to the formation of the inhibition zone; when the colonies
are thus separated, there is no longer direct competition between the two
species and the producer can invade effectively unimpeded by its competitor. We
note that the minimum toxin strength required to produce an inhibition zone
increases rapidly with increasing bacterial diffusivity, suggesting that even
moderately motile bacteria must produce very strong toxins if they are to
benefit in this way.


  A java-based graphical tool for drawing Feynman diagrams is presented. It
differs from similar existing tools in various respects. For example, it is
based on models, consisting of particles (lines) and (optionally) vertices,
each of which can be given their individual properties (line style, color,
arrows, label, etc.). The diagrams can be exported in any standard image
format, or as PDF. Aside from its plain graphical aspect, the goal of FeynGame
is also educative, as it can check a Feynman diagrams validity. This provides
the basis to play games with diagrams, for example. Here we describe on such
game where a given set of initial and final states must be connected through a
Feynman diagram within a given interaction model.


  We study the bulk-boundary correspondence for topological crystalline phases,
where the crystalline symmetry is an order-two (anti)symmetry, unitary or
antiunitary. We obtain a formulation of the bulk-boundary correspondence in
terms of a subgroup sequence of the bulk classifying groups, which uniquely
determines the topological classification of the boundary states. This
formulation naturally includes higher-order topological phases as well as
topologically nontrivial bulk systems without topologically protected boundary
states. The complete bulk and boundary classification of higher-order
topological phases with an additional order-two symmetry or antisymmetry is
contained in this work.


  We study the BPS equations in ABJM theory furthermore. Besides the known
funnel solutions which are proposed to describe M2-M5 systems we find a new
kind solution. We analyze the properties therein and see that it can describe
M2-KK6 (2D membranes with 6D Kaluza-Klein monopole) systems. Our solutions also
reveal new vacua in the mass deformed ABJM theory. Contrast to the previous
investigation in which the vacua are reducible, ours may be irreducible. We
also discuss a possible interpretation of the new BPS solutions as a M2-2M5
system.


  Discerning the exact nature of the sub-mJy radio population has been
historically difficult due to the low luminosity of these sources at most
wavelengths. Using deep ground based optical follow-up and observations from
the Spitzer Space Telescope we are able to disentangle the radio-selected
Active Galactic Nuclei (AGN) and Star Forming Galaxy (SFG) populations for the
first time in a deep multi-frequency VLA/MERLIN Survey of the 13^H
XMM-Newton/Chandra Deep Field. The discrimination diagnostics include radio
morphology, radio spectral index, radio/near-IR and mid-IR/radio flux density
ratios. We are now able to calculate the extragalactic Euclidean normalised
source counts separately for AGN and SFGs. We find that while SFGs dominate at
the faintest flux densities and account for the majority of the up-turn in the
counts, AGN still make up around one quarter of the counts at ~5 uJy (1.4 GHz).
Using radio luminosity as an unobscured star formation rate (SFR) measure we
are then able to examine the comoving SFR density of the Universe up to z=3
which agrees well with measures at other wavelengths. We find a rough
correlation of SFR with stellar mass for both the sample presented here and a
sample of local radio-selected SFGs from the 6df-NVSS survey. This work also
confirms the existence of, and provides alternative evidence for, the evolution
of distribution of star formation by galaxy mass: ``downsizing''. As both these
samples are SFR-selected, this result suggests that there is a maximum SFR for
a given galaxy that depends linearly on its stellar mass. The low
``characteristic times'' (inverse specific SFR) of the SFGs in our sample are
similar to those of the 6dF-NVSS sample, implying that most of these sources
are in a current phase of enhanced star formation.


  Brief lecture notes for a course about random matrices given at the
University of Cambridge.


  In the present work we investigate a subgroup $I_n$ of the McCool group
$M_n$. We show that $I_n$ has solvable conjugacy problem. Next, we investigate
its Lie Algebra gr($I_n$) and we find a presentation for it. Finally we show
that gr($I_n$) is naturally embedded into the Andreadakis-Johnson Lie Algebra
of the IA automorphisms of the free group $F_n$.


  We show that if two singular points $x' \in X'$ and $x \in X$ on schemes over
a field $k$ of characteristic $p > 0$ are contact equivalent then the rigid
cohomology spaces $H^{\bullet}_{rig, \{x\}}(X)$ and $H^{\bullet}_{rig,
\{x'\}}(X')$ are isomorphic. The isomorphism that we construct is moreover
compatible with the Frobenius structure on rigid cohomology.


  We study tachyon inflation within the large-$N$ formalism, which takes a
prescription for the small Hubble flow slow--roll parameter $\epsilon_1$ as a
function of the large number of $e$-folds $N$. This leads to a classification
of models through their behaviour at large $N$. In addition to the perturbative
$N$ class, we introduce the polynomial and exponential classes for the
$\epsilon_1$ parameter. With this formalism we reconstruct a large number of
potentials used previously in the literature for Tachyon Inflation. We also
obtain new families of potentials form the polynomial class. We characterize
the realizations of Tachyon Inflation by computing the usual cosmological
observables up to second order in the Hubble flow slow--roll parameters. This
allows us to look at observable differences between tachyon and canonical
single field inflation. The analysis of observables in light of the Planck 2015
data shows the viability of some of these models, mostly for certain
realization of the polynomial and exponential classes.


  Fault-tolerant spin-based quantum computers will require fast and accurate
qubit readout. This can be achieved using radio-frequency reflectometry given
sufficient sensitivity to the change in quantum capacitance associated with the
qubit states. Here, we demonstrate a 23-fold improvement in capacitance
sensitivity by supplementing a cryogenic semiconductor amplifier with a SQUID
preamplifier. The SQUID amplifier operates at a frequency near 200 MHz and
achieves a noise temperature below 600 mK when integrated into a reflectometry
circuit, which is within a factor 120 of the quantum limit. It enables a record
sensitivity to capacitance of 0.07 aF/\sqrt{Hz}. The setup is used to acquire
charge stability diagrams of a gate-defined double quantum dot in a short time
with a signal-to-noise ration of about 38 in 1 microsecond of integration time.


  We present two reduced-rank channel estimators for large-scale
multiple-input, multiple-output (MIMO) systems and analyze their mean square
error (MSE) performance. Taking advantage of the channel's transform domain
sparseness, the estimators yield outstanding performance and may offer
additional mean angle-of-arrival (AoA) information. It is shown that, for the
estimators to be effective, one has to select a proper predetermined unitary
basis (transform) and be able to determine the dominant channel rank and the
associated subspace. Further MSE analysis reveals the relations among the array
size, channel rank, signal-to-noise ratio (SNR), and the estimators'
performance. It provides rationales for the proposed rank determination and
mean AoA estimation algorithms as well.
  An angle alignment operation included in one of our channel models is proved
to be effective in further reducing the required rank, shifting the dominant
basis vectors' range (channel spectrum) and improving the estimator's
performance when a suitable basis is used. We also draw insightful analogies
among MIMO channel modeling, transform coding, parallel spatial search, and
receive beamforming. Computer experiment results are provided to examine the
numerical effects of various estimator parameters and the advantages of the
proposed channel estimators and rank determination method.


  This paper concerns the single machine total weighted tardiness scheduling
with sequence-dependent setup times, usually referred as $1|s_{ij}|\sum
w_jT_j$. In this $\mathcal{NP}$-hard problem, each job has an associated
processing time, due date and a weight. For each pair of jobs $i$ and $j$,
there may be a setup time before starting to process $j$ in case this job is
scheduled immediately after $i$. The objective is to determine a schedule that
minimizes the total weighted tardiness, where the tardiness of a job is equal
to its completion time minus its due date, in case the job is completely
processed only after its due date, and is equal to zero otherwise. Due to its
complexity, this problem is most commonly solved by heuristics. The aim of this
work is to develop a simple yet effective limitation strategy that speeds up
the local search procedure without a significant loss in the solution quality.
Such strategy consists of a filtering mechanism that prevents unpromising moves
to be evaluated. The proposed strategy has been embedded in a local search
based metaheuristic from the literature and tested in classical benchmark
instances. Computational experiments revealed that the limitation strategy
enabled the metaheuristic to be extremely competitive when compared to other
algorithms from the literature, since it allowed the use of a large number of
neighborhood structures without a significant increase in the CPU time and,
consequently, high quality solutions could be achieved in a matter of seconds.
In addition, we analyzed the effectiveness of the proposed strategy in two
other well-known metaheuristics. Further experiments were also carried out on
benchmark instances of problem $1|s_{ij}|\sum T_j$.


  We study superconducting properties of the bulk states of a doped topological
insulator. We obtain that the hexagonal warping stabilizes the nematic
spin-triplet superconducting phase with $E_u$ pairing and the direction of the
nematic order parameter which opens the full gap is the ground state. This
order parameter exhibits non-BCS behavior. The ratio of the order parameter to
the critical temperature of $\Delta(0)/T_c$ differs from the BCS ratio. It
depends on the chemical potential and the value of the hexagonal warping. We
discuss the relevance of the obtained results for the explanation of the
experimental observations.


  In an effort to assist factcheckers in the process of factchecking, we tackle
the claim detection task, one of the necessary stages prior to determining the
veracity of a claim. It consists of identifying the set of sentences, out of a
long text, deemed capable of being factchecked. This paper is a collaborative
work between Full Fact, an independent factchecking charity, and academic
partners. Leveraging the expertise of professional factcheckers, we develop an
annotation schema and a benchmark for automated claim detection that is more
consistent across time, topics and annotators than previous approaches. Our
annotation schema has been used to crowdsource the annotation of a dataset with
sentences from UK political TV shows. We introduce an approach based on
universal sentence representations to perform the classification, achieving an
F1 score of 0.83, with over 5% relative improvement over the state-of-the-art
methods ClaimBuster and ClaimRank. The system was deployed in production and
received positive user feedback.


  We give a new proof of the fact that every planar graph is 5-choosable, and
use it to show that every graph drawn in the plane so that the distance between
every pair of crossings is at least 15 is 5-choosable. At the same time we may
allow some vertices to have lists of size four only, as long as they are far
apart and far from the crossings.


  Feynman loop integrals are a key ingredient for the calculation of higher
order radiation effects, and are responsible for reliable and accurate
theoretical prediction. We improve the efficiency of numerical integration in
sector decomposition by implementing a quasi-Monte Carlo method associated with
the CUDA/GPU technique. For demonstration we present the results of several
Feynman integrals up to two loops in both Euclidean and physical kinematic
regions in comparison with those obtained from FIESTA3. It is shown that both
planar and non-planar two-loop master integrals in the physical kinematic
region can be evaluated in less than half a minute with $\mathcal{O}(10^{-3})$
accuracy, which makes the direct numerical approach viable for precise
investigation of higher order effects in multi-loop processes, e.g. the
next-to-leading order QCD effect in Higgs pair production via gluon fusion with
a finite top quark mass.


  The vortex structure in superconducting stripe states is studied according to
the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with
nearest-neighbor sites pairing interaction. The vortex is trapped at the
outside region of the stripe line, where the superconductivity is weak. The
superconducting coherence length along the stripe direction becomes long. There
are no eminent low-energy electronic states even near the vortex core. These
characters resemble the Josephson vortex in layered superconductors under a
parallel field.


  We generalize the prior linked symplectic Grassmannian construction, applying
it to to prove smoothing results for rank-2 limit linear series with fixed
special determinant on chains of curves. We apply this general machinery to
prove new results on nonemptiness and dimension of rank-2 Brill-Noether loci in
a range of degrees.


  Multi-user multiple-input multiple-output (MU-MIMO) systems can be used to
meet high throughput requirements of 5G and beyond networks. A base station
serves many users in an uplink MU-MIMO system, leading to a substantial
multi-user interference (MUI). Designing a high-performance detector for
dealing with a strong MUI is challenging. This paper analyses the performance
degradation caused by the posterior distribution approximation used in the
state-of-the-art message passing (MP) detectors in the presence of high MUI. We
develop a graph neural network based framework to fine-tune the MP detectors'
cavity distributions and thus improve the posterior distribution approximation
in the MP detectors. We then propose two novel neural network based detectors
which rely on the expectation propagation (EP) and Bayesian parallel
interference cancellation (BPIC), referred to as the GEPNet and GPICNet
detectors, respectively. The GEPNet detector maximizes detection performance,
while GPICNet detector balances the performance and complexity. We provide
proof of the permutation equivariance property, allowing the detectors to be
trained only once, even in the systems with dynamic changes of the number of
users. The simulation results show that the proposed GEPNet detector
performance approaches maximum likelihood performance in various configurations
and GPICNet detector doubles the multiplexing gain of BPIC detector.


  Dust polarisation observations at optical wavelengths help understand the
dust grain properties and trace the plane-of-the-sky component of the magnetic
field. In this study, we make use of published optical polarisation data
acquired with AIMPOL along with distances ($d$) and extinction
($A_{\mathrm{V}}$) data. We study the variation of polarisation efficiency
($P/A_{\mathrm{V}}$) as a function of $A_{\mathrm{V}}$ in the diffuse
interstellar medium (ISM) and intracluster mediums (ICM) using the already
published polarisation data of six clusters. Among these clusters, NGC 2281,
NGC 1664, and NGC 1960 are old; while Stock 8, NGC 1931, and NGC 1893 are
young. We categorize stars towards each cluster into foreground, background,
and cluster members by employing two clustering algorithms GMM and DBSCAN.
Thus, classified field stars and cluster members are used to reveal the
polarisation properties of ISM and ICM dust, respectively. We find that the
dust grains located in the diffuse ISM show higher polarisation efficiencies
when compared to those located in the ICM of younger clusters.


  In the background of several holographic confining backgrounds, we present
the connections between the behaviors of string scattering amplitudes and
mutual information. We lay down the analogies between the logarithmic branch
cut behavior of the string scattering amplitude in $4d$, $ \mathcal{A}_4 $, at
low and medium Mandelstam variable $s$ observed in \cite{Bianchi:2021sug},
which is due to the dependence of the string tension on the holographic
coordinate, and the branch cut behavior observed in mutual information and
critical distance $D_c$ at low-cut-off variable $u_{KK}$ studied in our
previous work \cite{Ghodrati:2021ozc}. It can also be seen that in both cases,
as $s$ or $u_{KK}$ increases, the peaks in the branch cuts fade away in the
form of $\text{Re}\lbrack \mathcal{A}_4 \rbrack \propto s^{-1}$. Then, we used
modular flow and modular Hamiltonian as intermediary concept to further clarify
the observed connection. We discussed how mutual information itself can detect
chaos in various scenarios. In addition, we considered two examples of Compton
scattering between two photons and also the decay of a highly excited string
into two tachyons and scrutinized the pattern of entanglement entropy and the
change in the mutual information in these examples. Then, the kink-kink and
kink-antikink scatterings as simple models of scattering in confining
geometries have been used to examine the fractal structures in the scatterings
of topological defects. Finally, the relationships between Regge conformal
block and quantum error correction codes through pole-skipping and chaos bound
have been postulated. These observed connections can further establish the
ER$=$EPR conjecture and the general interdependence between the scattering
amplitudes and entanglement entropy.


  We explore trends in the morphology and line-of-sight (los) velocity of
stellar populations in the inner regions of disc galaxies, using N-body
simulations with both a thin (kinematically cold) and a thick (kinematically
hot) disc which form a bar and boxy/peanut (b/p) bulge. The bar in the thin
disc component is $\sim$50\% stronger than the thick disc bar and is more
elongated, with an axis ratio almost half that of the thick disc bar. The thin
disc b/p bulge has a pronounced X-shape, while the thick disc b/p is weaker
with a rather boxy shape. This leads to the signature of the b/p bulge in the
thick disc to be weaker and further away from the plane than in the thin disc.
Regarding the kinematics, we find that the los velocity of thick disc stars in
the outer parts of the b/p bulge can be \emph{larger} than that of thin disc
stars, by up to 40\% and 20\% for side-on and Milky Way-like orientations of
the bar respectively. This is due to the different orbits followed by thin and
thick disc stars in the bar-b/p region, which are affected by the fact that: i)
thin disc stars are trapped more efficiently in the bar - b/p instability and
thus lose more angular momentum than their thick disc counterparts and ii)
thick disc stars have large radial excursions and therefore stars from large
radii with high angular momenta can be found in the bar region. We also find
that the difference between the los velocities of the thin and thick disc in
the b/p bulge ($\Delta v_{los}$) correlates with the initial difference between
the radial velocity dispersions of the two discs ($\Delta \sigma$) . We
therefore conclude that stars in the bar - b/p bulge will have considerably
different morphologies and kinematics depending on the kinematic properties of
the disc population they originate from.


  We propose an arbitrary driven spin as the working fluid of a quantum Otto
cycle in the presence of internal friction. The role of total allocated time to
the adiabatic branches of the cycle, generated by different control field
profiles, on the extractable work and the thermal efficiency are analyzed in
detail. The internal friction is characterized by the excess entropy production
and quantitatively determined by studying the closeness of an actual unitary
process to an infinitely long one via quantum relative entropy. It is found
that the non-ideal, finite-time adiabatic transformations negatively effect the
work output and the thermal efficiency of the quantum heat engine. The
non-monotone dependence of the work output, thermal efficiency, entropy
production and the internal friction on the total adiabatic time are
elucidated. It is also found that almost frictionless adiabatic transformations
with small entropy production can be obtained in a short adiabatic time.


  A homological invariant of 3-manifolds is defined, using abelian Yang-Mills
gauge theory. It is shown that the construction, in an appropriate sense, is
functorial with respect to the families of 4-dimensional cobordisms. This
construction and its functoriality are used to define several link invariants.
The strongest version of these invariants has the form of a filtered chain
complex that can recover Khovanov homology of the mirror image as a bi-graded
group.


  According to the widely accepted statistical interpretation of black hole
entropy the mean separation between energy levels of black hole should be
exponentially small. But this sharply disagrees with the value obtained from
the quantization of black hole area. It is shown that the new statistical
interpretation of black hole entropy proposed in my paper arXiv:0911.5635 gives
the correct value.


  In the note, a new regularity condition for axisymmetric solutions to the
non-stationary 3D Navier-Stokes equations is proven. It is slightly
supercritical.


  The decay of any unstable quantum state can be inhibited or enhanced by
carefully tailored measurements, known as the quantum Zeno effect (QZE) or
anti-Zeno effect (QAZE). To date, studies of QZE (QAZE) transitions have since
expanded to various system-environment coupling, in which the time evolution
can be suppressed (enhanced) not only by projective measurement but also
through dissipation processes. However, a general criterion, which could extend
to arbitrary dissipation strength and periodicity, is still lacking. In this
letter, we show a general framework to unify QZE-QAZE effects and parity-time
(PT) symmetry breaking transitions, in which the dissipative Hamiltonian
associated to the measurement effect is mapped onto a PT-symmetric non-
Hermitian Hamiltonian, thus applying the PT symmetry transitions to distinguish
QZE (QAZE) and their crossover behavior. As a concrete example, we show that,
in a two-level system periodically coupled to a dissipative environment, QZE
starts at an exceptional point (EP), which separates the PT-symmetric (PTS)
phase and PT-symmetry broken (PTB) phase, and ends at the resonance point (RP)
of the maximum PT-symmetry breaking; while QAZE extends the rest of PTB phase
and remains the whole PTS phase. Such findings reveal a hidden relation between
QZE-QAZE and PTS-PTB phases in non-Hermitian quantum dynamics.


  Semi-supervised wrapper methods are concerned with building effective
supervised classifiers from partially labeled data. Though previous works have
succeeded in some fields, it is still difficult to apply semi-supervised
wrapper methods to practice because the assumptions those methods rely on tend
to be unrealistic in practice. For practical use, this paper proposes a novel
semi-supervised wrapper method, Dual Teaching, whose assumptions are easy to
set up. Dual Teaching adopts two external classifiers to estimate the false
positives and false negatives of the base learner. Only if the recall of every
external classifier is greater than zero and the sum of the precision is
greater than one, Dual Teaching will train a base learner from partially
labeled data as effectively as the fully-labeled-data-trained classifier. The
effectiveness of Dual Teaching is proved in both theory and practice.


  The Karman constant \kappa - widely used in atmospheric science and
engineering turbulence modelling, and proposed by Prandtl in 1925 and von
Karman in 1930 to describe the mean velocity of a turbulent wall-bounded flow -
leads to a logarithmic profile in an overlap region near the wall. For over
eighty years, its value was believed to be ~0.41. But more recently, many argue
that it is not a constant, because of measured variations in different flows
and at different Reynolds numbers (Re). Here, a multi-layer analytic theory is
shown to lead to a re-interpretation of \kappa as a global constant for both
the overlap region and outer flow, and to yield a new method for its
measurement. The newly determined value is 0.45 for both channel and pipe. It
is shown that this new \kappa, together with other wall constants, yields a 99%
accuracy in the prediction of mean velocity data at all points in high Re (up
to 40 million) pipe flow. The theory also describes finite Re effect, and
discovers a transition at the friction Re (i.e. Re_\tau)=5000. An accurate
model for the prediction of turbulent transport in canonical pipe and channel
flows is achieved here, and we propose the model to be valid for a wide class
of turbulent flows.


We give presentations of braid groups and pure braid groups on surfaces.


  we consider a system with homoclinic orbit, We decompose the corresponding
variational equation on the space of solutions and provide sufficient
conditions for the permanency of homoclinic in the space of $C^1$ vector
fields. We also provide new sufficient conditions for the persistence and
multiple bifurcations of the bounded solutions nearby. our results can be
verified numerically and do not meet the limitations of classic methods (like
Melnikon integrals and Poincare map)


  An outstanding challenge involves understanding the many-particle
entanglement of liquid states of quantum matter that arise in systems of
interacting electrons. The Fermi liquid (FL) in $D$ spatial dimensions shows a
violation of the area-law in real-space entanglement entropy of a subsystem (of
length $L$), $S_{EE} \sim L^{D-1}\ln L$, widely believed to be a hallmark
signature of the ground state of a gapless quantum critical system of
interacting fermions. In this work, we apply a $T=0$ renormalisation group
approach to a prototype of the FL in momentum (or, $k$)-space, unveiling
thereby the RG relevant quantum fluctuations (due to forward and tangential
scattering) from which long-range entanglement arises. A similar analysis of
non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D
Tomonaga-Luttinger liquid (TLL) reveals a universal logarithmic violation of
the area-law in gapless electronic liquids for a subsystem defined within a
$k$-space window (of size $\Lambda$) proximate to the Fermi surface, with a
proportionality constant that depends on the nature of the underlying Fermi
surface. We extend this analysis to the gapped quantum liquids emergent from
the destabilisation of the Fermi surface by quantum fluctuations arising from
backscattering processes. Indeed, we find that the $k$-space entanglement
signatures of gapped quantum liquids appear to be governed by the nature of the
Fermi surface (e.g., nested or not) from which they emerge, as well as the
nature of their parent gapless metallic liquid (e.g., FL, MFL etc.). This is
confirmed by our finding an enhanced entanglement entropy for the nodal MFL
present at the quantum critical point recently discovered in the 2D Hubbard
model at optimal hole-doping. Our work thus paves the way for an entanglement
based classification of quantum liquids emergent from the criticality of
interacting fermionic matter.


  Since the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120,
067003 (2018)], considerable research efforts have been dedicated to the study
of Cooper pairing order parameters constrained (or obstructed) by the
nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the
current work, we generalize the topologically obstructed pairings between Chern
states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper
pairing in 3D systems. The Euler obstructed Cooper pairing widely exists
between two Fermi surfaces with nontrivial band topology characterized by
nonzero Euler numbers; such Fermi surfaces can exist in 3D PT-protected
spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where
PT is the space-time inversion symmetry. An Euler obstructed pairing channel
must have pairing nodes on the pairing-relevant Fermi surfaces, and the total
winding number of the pairing nodes is determined by the sum or difference of
the Euler numbers on the Fermi surfaces. In particular, we find that when the
normal state is time-reversal invariant and the pairing is weak, a
sufficiently-dominant Euler obstructed pairing channel with zero total momentum
leads to nodal superconductivity. If the Fermi surface splitting is small, the
resultant nodal superconductor hosts hinge Majorana zero modes. The possible
dominance of the Euler obstructed pairing channel near the superconducting
transition and the robustness of the hinge Majorana zero modes against disorder
are explicitly demonstrated using effective or tight-binding models. Our work
presents the first class of higher-order nodal superconductivity originating
from the topologically obstructed Cooper pairing.


  An algorithm for reversible logic synthesis is proposed. The task is, for a
given $n$-bit substitution map $P_n: \{0,1\}^n \rightarrow \{0,1\}^n$, to find
a sequence of reversible logic gates that implements the map. The gate library
adopted in this work consists of multiple-controlled Toffoli gates denoted by
$C^m\!X$, where $m$ is the number of control bits that ranges from 0 to $n-1$.
Controlled gates with large $m \,\,(>2)$ are then further decomposed into
$C^0\!X$, $C^1\!X$, and $C^2\!X$ gates. A primary concern in designing the
algorithm is to reduce the use of $C^2\!X$ gate (also known as Toffoli gate)
which is known to be universal.
  The main idea is to view an $n$-bit substitution map as a rank-$2n$ tensor
and to transform it such that the resulting map can be written as a tensor
product of a rank-($2n-2$) tensor and the $2\times 2$ identity matrix. Let
$\mathcal{P}_n$ be a set of all $n$-bit substitution maps. What we try to find
is a size reduction map $\mathcal{A}_{\rm red}: \mathcal{P}_n \rightarrow
\{P_n: P_n = P_{n-1} \otimes I_2\}$. %, where $I_m$ is the $m\times m$ identity
matrix. One can see that the output $P_{n-1} \otimes I_2$ acts nontrivially on
$n-1$ bits only, meaning that the map to be synthesized becomes $P_{n-1}$. The
size reduction process is iteratively applied until it reaches tensor product
of only $2 \times 2$ matrices.


  In this paper we analyze a class of trace finite element methods (TraceFEM)
for the discretization of vector-Laplace equations. A key issue in the finite
element discretization of such problems is the treatment of the constraint that
the unknown vector field must be tangential to the surface (``tangent
condition''). We study three different natural techniques for treating the
tangent condition, namely a consistent penalty method, a simpler inconsistent
penalty method and a Lagrange multiplier method. A main goal of the paper is to
present an analysis that reveals important properties of these three different
techniques for treating the tangent constraint. A detailed error analysis is
presented that takes the approximation of both the geometry of the surface and
the solution of the partial differential equation into account. Error bounds in
the energy norm are derived that show how the discretization error depends on
relevant parameters such as the degree of the polynomials used for the
approximation of the solution, the degree of the polynomials used for the
approximation of the level set function that characterizes the surface, the
penalty parameter and the degree of the polynomials used for the approximation
of Lagrange multiplier.


  We have employed the multiple image method to compute the interparticle force
for a polydisperse electrorheological (ER) fluid in which the suspended
particles can have various sizes and different permittivites. The point-dipole
(PD) approximation being routinely adopted in computer simulation of ER fluids
is shown to err considerably when the particles approach and finally touch due
to multipolar interactions. The PD approximation becomes even worse when the
dielectric contrast between the particles and the host medium is large. From
the results, we show that the dipole-induced-dipole (DID) model yields very
good agreements with the multiple image results for a wide range of dielectric
contrasts and polydispersity. As an illustration, we have employed the DID
model to simulate the athermal aggregation of particles in ER fluids both in
uniaxial and rotating fields. We find that the aggregation time is
significantly reduced. The DID model accounts for multipolar interaction
partially and is simple to use in computer simulation of ER fluids.


  Due to the significant advancement of Natural Language Processing and
Computer Vision-based models, Visual Question Answering (VQA) systems are
becoming more intelligent and advanced. However, they are still error-prone
when dealing with relatively complex questions. Therefore, it is important to
understand the behaviour of the VQA models before adopting their results. In
this paper, we introduce an interpretability approach for VQA models by
generating counterfactual images. Specifically, the generated image is supposed
to have the minimal possible change to the original image and leads the VQA
model to give a different answer. In addition, our approach ensures that the
generated image is realistic. Since quantitative metrics cannot be employed to
evaluate the interpretability of the model, we carried out a user study to
assess different aspects of our approach. In addition to interpreting the
result of VQA models on single images, the obtained results and the discussion
provides an extensive explanation of VQA models' behaviour.


  Inspired by the seminal works of Khuller et al. (STOC 1994) and Chan (SoCG
2003) we study the bottleneck version of the Euclidean bounded-degree spanning
tree problem. A bottleneck spanning tree is a spanning tree whose largest
edge-length is minimum, and a bottleneck degree-$K$ spanning tree is a
degree-$K$ spanning tree whose largest edge-length is minimum. Let $\beta_K$ be
the supremum ratio of the largest edge-length of the bottleneck degree-$K$
spanning tree to the largest edge-length of the bottleneck spanning tree, over
all finite point sets in the Euclidean plane. It is known that $\beta_5=1$, and
it is easy to verify that $\beta_2\ge 2$, $\beta_3\ge \sqrt{2}$, and
$\beta_4>1.175$.
  It is implied by the Hamiltonicity of the cube of the bottleneck spanning
tree that $\beta_2\le 3$. The degree-3 spanning tree algorithm of Ravi et al.
(STOC 1993) implies that $\beta_3\le 2$. Andersen and Ras (Networks,
68(4):302-314, 2016) showed that $\beta_4\le \sqrt{3}$. We present the
following improved bounds: $\beta_2\ge\sqrt{7}$, $\beta_3\le \sqrt{3}$, and
$\beta_4\le \sqrt{2}$. As a result, we obtain better approximation algorithms
for Euclidean bottleneck degree-3 and degree-4 spanning trees. As parts of our
proofs of these bounds we present some structural properties of the Euclidean
minimum spanning tree which are of independent interest.


  We investigate the Cauchy problem for elliptic operators with
$C^\infty$-coefficients at a regular set $\Omega \subset R^2$, which is a
classical example of an ill-posed problem. The Cauchy data are given at the
subset $\Gamma \subset \partial\Omega$ and our objective is to reconstruct the
trace of the $H^1(\Omega)$ solution of an elliptic equation at $\partial \Omega
/ \Gamma$. The method described here is a generalization of the algorithm
developed by Maz'ya et al. [Ma] for the Laplace operator, who proposed a method
based on solving successive well-posed mixed boundary value problems (BVP)
using the given Cauchy data as part of the boundary data. We give an
alternative convergence proof for the algorithm in the case we have a linear
elliptic operator with $C^\infty$-coefficients. We also present some numerical
experiments for a special non linear problem and the obtained results are very
promisive.


  With the rise of AI, algorithms have become better at learning underlying
patterns from the training data including ingrained social biases based on
gender, race, etc. Deployment of such algorithms to domains such as hiring,
healthcare, law enforcement, etc. has raised serious concerns about fairness,
accountability, trust and interpretability in machine learning algorithms. To
alleviate this problem, we propose D-BIAS, a visual interactive tool that
embodies human-in-the-loop AI approach for auditing and mitigating social
biases from tabular datasets. It uses a graphical causal model to represent
causal relationships among different features in the dataset and as a medium to
inject domain knowledge. A user can detect the presence of bias against a
group, say females, or a subgroup, say black females, by identifying unfair
causal relationships in the causal network and using an array of fairness
metrics. Thereafter, the user can mitigate bias by acting on the unfair causal
edges. For each interaction, say weakening/deleting a biased causal edge, the
system uses a novel method to simulate a new (debiased) dataset based on the
current causal model. Users can visually assess the impact of their
interactions on different fairness metrics, utility metrics, data distortion,
and the underlying data distribution. Once satisfied, they can download the
debiased dataset and use it for any downstream application for fairer
predictions. We evaluate D-BIAS by conducting experiments on 3 datasets and
also a formal user study. We found that D-BIAS helps reduce bias significantly
compared to the baseline debiasing approach across different fairness metrics
while incurring little data distortion and a small loss in utility. Moreover,
our human-in-the-loop based approach significantly outperforms an automated
approach on trust, interpretability and accountability.


  In this paper we search for conditions on a countably compact
(pseudo-compact) topological semigroup under which: (i) each maximal subgroup
$H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part
$H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a
closed subset in $S$; (iii) the inversion $\operatorname{inv}\colon H(S)\to
H(S)$ is continuous; and (iv) the projection $\pi\colon H(S)\to E(S)$,
$\pi\colon x\longmapsto xx^{-1}$, onto the subset of idempotents $E(S)$ of $S$,
is continuous.


  Value iteration networks (VINs) enable end-to-end learning for planning tasks
by employing a differentiable "planning module" that approximates the value
iteration algorithm. However, long-term planning remains a challenge because
training very deep VINs is difficult. To address this problem, we embed highway
value iteration -- a recent algorithm designed to facilitate long-term credit
assignment -- into the structure of VINs. This improvement augments the
"planning module" of the VIN with three additional components: 1) an "aggregate
gate," which constructs skip connections to improve information flow across
many layers; 2) an "exploration module," crafted to increase the diversity of
information and gradient flow in spatial dimensions; 3) a "filter gate"
designed to ensure safe exploration. The resulting novel highway VIN can be
trained effectively with hundreds of layers using standard backpropagation. In
long-term planning tasks requiring hundreds of planning steps, deep highway
VINs outperform both traditional VINs and several advanced, very deep NNs.


  The ability to accurately track what happens during a conversation is
essential for the performance of a dialogue system. Current state-of-the-art
multi-domain dialogue state trackers achieve just over 55% accuracy on the
current go-to benchmark, which means that in almost every second dialogue turn
they place full confidence in an incorrect dialogue state. Belief trackers, on
the other hand, maintain a distribution over possible dialogue states. However,
they lack in performance compared to dialogue state trackers, and do not
produce well calibrated distributions. In this work we present state-of-the-art
performance in calibration for multi-domain dialogue belief trackers using a
calibrated ensemble of models. Our resulting dialogue belief tracker also
outperforms previous dialogue belief tracking models in terms of accuracy.


  While it is possible to build causal sets that approximate spacetime
manifolds, most causal sets are not at all manifold-like. We show that a
Lorentzian path integral with the Einstein-Hilbert action has a phase in which
one large class of non-manifold-like causal sets is strongly suppressed, and
suggest a direction for generalization to other classes. While we cannot yet
show our argument holds for all non-manifold-like sets, our results make it
plausible that the path integral might lead to emergent manifold-like behavior
with no need for further conditions.


  The Parareal algorithm is used to solve time-dependent problems considering
multiple solvers that may work in parallel. The key feature is a initial rough
approximation of the solution that is iteratively refined by the parallel
solvers. We report a derivation of the Parareal method that uses a convergence
acceleration technique to improve the accuracy of the solution. Our approach
uses firstly an explicit ODE solver to perform the parallel computations with
different time-steps and then, a decomposition of the solution into specific
convergent series, based on an extrapolation method, allows to refine the
precision of the solution. Our proposed method exploits basic explicit
integration methods, such as for example the explicit Euler scheme, in order to
preserve the simplicity of the global parallel algorithm. The first part of the
paper outlines the proposed method applied to the simple explicit Euler scheme
and then the derivation of the classical Parareal algorithm is discussed and
illustrated with numerical examples.


  We study the recent star formation histories of ten galaxies in the Fornax A
galaxy group, on the outskirts of the Fornax cluster. The group galaxies are
gas-rich, and their neutral atomic hydrogen (HI) was studied in detail with
observations from the MeerKAT telescope. This allowed them to be classified
into different stages of pre-processing (early, ongoing, advanced). We use
long-slit spectra obtained with the South African Large Telescope (SALT) to
analyse stellar population indicators to constrain quenching timescales and to
compare these to the HI gas content of the galaxies. The H$\alpha$ equivalent
width, EW(H$\alpha$), suggest that the pre-processing stage is closely related
to the recent (< 10 Myr) specific Star Formation Rate (sSFR). The early-stage
galaxy (NGC 1326B) is not yet quenched in its outer parts, while the
ongoing-stage galaxies mostly have a distributed population of very young
stars, though less so in their outer parts. The galaxies in the advanced stage
of pre-processing show very low recent sSFR in the outer parts. Our results
suggest that NGC 1326B, FCC 35 and FCC 46 underwent significantly different
histories from secular evolution during the last Gyr. The fact that most
galaxies are on the secular evolution sequence implies that pre-processing has
a negligible effect on these galaxies compared to secular evolution. We find
EW(H$\alpha$) to be a useful tool for classifying the stage of pre-processing
in group galaxies. The recent sSFR and HI morphology show that galaxies in the
Fornax A vicinity are pre-processing from the outside in.


  Understanding and even defining what constitutes animal interactions remains
a challenging problem. Correlational tools may be inappropriate for detecting
communication between a set of many agents exhibiting nonlinear behavior. A
different approach is to define coordinated motions in terms of an information
theoretic channel of direct causal information flow. In this work, we consider
time series data obtained by an experimental protocol of optical tracking of
the insect species Chironomus riparius. The data constitute reconstructed 3-D
spatial trajectories of the insects' flight trajectories and kinematics. We
present an application of the optimal causation entropy (oCSE) principle to
identify direct causal relationships or information channels among the insects.
The collection of channels inferred by oCSE describes a network of information
flow within the swarm. We find that information channels with a long spatial
range are more common than expected under the assumption that causal
information flows should be spatially localized. The tools developed herein are
general and applicable to the inference and study of intercommunication
networks in a wide variety of natural settings.


  An abelian processor is an automaton whose output is independent of the order
of its inputs. Bond and Levine have proved that a network of abelian processors
performs the same computation regardless of processing order (subject only to a
halting condition). We prove that any finite abelian processor can be emulated
by a network of certain very simple abelian processors, which we call gates.
The most fundamental gate is a "toppler", which absorbs input particles until
their number exceeds some given threshold, at which point it topples, emitting
one particle and returning to its initial state. With the exception of an adder
gate, which simply combines two streams of particles, each of our gates has
only one input wire. Our results can be reformulated in terms of the functions
computed by processors, and one consequence is that any increasing function
from N^k to N^l that is the sum of a linear function and a periodic function
can be expressed in terms of (possibly nested) sums of floors of quotients by
integers.


  Indoor ventilation is essential for a healthy and comfortable living
environment. A key issue is to discharge anthropogenic air contamination such
as CO2 gas or, more seriously, airborne respiratory droplets. Here, by
employing direct numerical simulations, we study the mechanical displacement
ventilation with the realistic range of air changes per hour (ACH) from 1 to
10. For this ventilation scheme, a cool lower zone is established beneath the
warm upper zone with the interface height h depending on ACH. For weak
ventilation, we find the scalings relation of the interface height h ~
ACH^{3/5}, as suggested by Hunt & Linden (Build. Environ., vol. 34, 1999, pp.
707-720). Also, the CO2 concentration decreases with ACH within this regime.
However, for too strong ventilation, the interface height h becomes insensitive
to ACH, and the CO2 concentration remains unchanged. Our results are in
contrast to the general belief that stronger flow is more helpful to remove
contaminants. We work out the physical mechanism governing the transition
between the low ACH and the high ACH regimes. It is determined by the relative
strength of the kinetic energy from the inflow, potential energy from the
stably-stratified layers, and energy loss due to drag. Our findings provide a
physics-based guideline to optimize displacement ventilation.


  Orbital angular momentum (OAM) light possesses in addition to its usual
helicity ($s=\pm \hbar$, depending on its circular polarization) an orbital
angular momentum $l$. This means that in principle one can transfer more than a
single quantum of $\hbar$ during an optical transition from light to a quantum
system. However, quantum objects are usually so small (typically in the nm
range) that they only locally probe the dipolar character of the local electric
field. In order to sense the complete macroscopic electric field, we utilize
Rydberg excitons in the semiconductor cuprite ($\text{Cu}_2\text{O}$), which
are single quantum objects of up to $\mu m$ size. Their interaction with
focused OAM light, allows for matching the focal spot size and the wavefunction
diameter. Here, the common dipole selection rules ($\Delta j=\pm 1$) should be
broken, and transitions of higher $\Delta j$ with higher order OAM states
should become more probable. Based on group theory, we analyze in detail the
optical selection rules governing this process. Then we are able to predict
what kind of new exciton transitions (quantum number $n$ and $l_{\text{exc}}$)
one would expect in absorption spectroscopy on $\text{Cu}_2\text{O}$ using
different kinds of OAM light.


  Using Visser's semi-analytical model for the stress-energy tensor
corresponding to the conformally coupled massless scalar field in the Unruh
vacuum, we examine, by explicitly evaluating the relevant integrals over
half-complete geodesics, the averaged weak (AWEC) and averaged null (ANEC)
energy conditions along with Ford-Roman quantum inequality-type restrictions on
negative energy in the context of four dimensional evaporating black hole
backgrounds. We find that in all cases where the averaged energy conditions
fail, there exist quantum inequality bounds on the magnitude and duration of
negative energy densities.


  Let $k$ be a positive integer and let $F$ be a finite unramified extension of
$\mathbb{Q}_2$ with ring of integers $\mathcal{O}_F$. An integral (resp.
classic) quadratic form over $\mathcal{O}_F$ is called $k$-universal (resp.
classically $k$-universal) if it represents all integral (resp. classic)
quadratic forms of dimension $k$. In this paper, we provide a complete
classification of $k$-universal and classically $k$-universal quadratic forms
over $\mathcal{O}_F$. The results are stated in terms of the fundamental
invariants associated to Jordan splittings of quadratic lattices.


  We consider a general system of n noninteracting identical particles which
evolve under a given dynamical law and whose initial microstates are a priori
independent. The time evolution of the n-particle average of a bounded function
on the particle microstates is then examined in the large n limit. Using the
theory of large deviations, we show that if the initial macroscopic average is
constrained to be near a given value, then the macroscopic average at a given
time converges in probability, as n goes to infinity, to a value given
explicitly in terms of a canonical expectation. Some general features of the
resulting deterministic curve are examined, particularly in regard to
continuity, symmetry, and convergence.


  Classical Cepheids (DCEPs) play a fundamental role in the calibration of the
extra-galactic distance ladder which eventually leads to the determination of
the Hubble constant($H_0$) thanks to the period-luminosity ($PL$) and
period-Wesenheit ($PW$) relations exhibited by these pulsating variables.
Therefore, it is of great importance to establish the dependence of $PL/PW$
relations on metallicity. We aim at quantifying the metallicity dependence of
the Galactic DCEPs' $PL/PW$ relations for a variety of photometric bands
ranging from optical to near-infrared. We gathered a literature sample of 910
DCEPs with available [Fe/H] values from high-resolution spectroscopy or
metallicities from \gaia\ Radial Velocity Spectrometer. For all these stars, we
collected photometry in the $G_{BP},G_{RP},G,I,V,J,H,K_S$ bands and astrometry
from the \gaia\ DR3. These data have been used to investigate the metal
dependence of both intercepts and slopes of a variety of $PL/PW$ relations at
multiple wavelengths. We find a large negative metallicity effect on the
intercept ($\gamma$ coefficient) of all the $PL/PW$ relations investigated in
this work, while present data still do not allow us to draw firm conclusions
regarding the metal dependence of the slope ($\delta$ coefficient). The typical
values of $\gamma$ are around $-0.4:-0.5$ mag/dex, i.e. larger than most of the
recent determinations present in the literature. We carried out several tests
which confirm the robustness of our results. As in our previous works, we find
that the inclusion of global zero point offset of \gaia\ parallaxes provides
smaller values of $\gamma$ (in an absolute sense). However, the assumption of
the geometric distance of the LMC seems to indicate that larger values of
$\gamma$ (in an absolute sense) would be preferred.


  These notes are based on lectures given by the author at the Summer School on
Teichm\"uller dynamics, mapping class groups and applications in Grenoble,
France, in June 2018 and at the Oberwolfach Seminar on Anisotropic Spaces and
their Applications to Hyperbolic and Parabolic Systems in June 2019. We derive
results about the so-called Ruelle resonances and the asymptotics of
correlations for several classes of systems from known results on cohomological
equations and invariant distributions for the respective unstable vector
fields. In particular, we consider pseudo-Anosov diffeomorphisms on surfaces of
higher genus, for horocycle flows on surfaces of constant negative curvature
and for partially hyperbolic automorphisms of Heisenberg 3-dimensional
nilmanfolds. Ruelles resonances for pseudo-Anosov maps with applications to the
cohomological equation for their unstable translation flows was recently
studied in depth by F. Faure, S. Gou\"ezel and E. Lanneau [FGL] by methods
based on the analysis of the transfer operator of the pseudo-Anosov map. Ruelle
resonances for geodesic flows on hyperbolic compact manifolds of any dimension
and of partially hyperbolic automorphisms of Heisenberg 3-dimensional
nilmanfolds are studied by general results of Dyatlov, Faure and Guillarmou
[DFG] and Faure and Tsujii [FT15] based on methods of semi-classical analysis.
These works do not derive results on cohomological equations for unstable flows
or horospherical foliations of these systems.


  The theory of q-analogs develops many combinatorial formulas for finite
vector spaces over a finite field with q elements--all in analogy with formulas
for finite sets (which are the special case of q=1). A direct-sum decomposition
of a finite vector space is the vector space analogue of a set partition. This
paper develops the formulas for the number of direct-sum decompositions that
are the q-analogs of the formulas for: (1) the number of set partitions with a
given number partition signature; (2) the number of set partitions of an
n-element set with m blocks (the Stirling numbers of the second kind); and (3)
for the total number of set partitions of an n-element set (the Bell numbers).


  The amplitude for $\gamma p \to \phi p$ is calculated in a pQCD $k_{T}$ -
factorization approach. The total cross section for this process is compared
with HERA data. Total cross section, as a function of photon-proton energy and
photon virtuality, is calculated. We also discuss the ratio of $\sigma_{L}$ /
$\sigma_{T}$ and the dependence on the mass of the strange quark. The amplitude
for $\gamma p \to \phi p$ is used to predict the cross section for exclusive
photoproduction of $\phi$ meson in proton-proton collisions. Absorption effects
are included. The results for RHIC, Tevatron and LHC energies are presented.


  The present work extends the randomized shortest-paths framework (RSP),
interpolating between shortest-path and random-walk routing in a network, in
three directions. First, it shows how to deal with equality constraints on a
subset of transition probabilities and develops a generic algorithm for solving
this constrained RSP problem using Lagrangian duality. Second, it derives a
surprisingly simple iterative procedure to compute the optimal, randomized,
routing policy generalizing the previously developed "soft" Bellman-Ford
algorithm. The resulting algorithm allows balancing exploitation and
exploration in an optimal way by interpolating between a pure random behavior
and the deterministic, optimal, policy (least-cost paths) while satisfying the
constraints. Finally, the two algorithms are applied to Markov decision
problems by considering the process as a constrained RSP on a bipartite
state-action graph. In this context, the derived "soft" value iteration
algorithm appears to be closely related to dynamic policy programming as well
as Kullback-Leibler and path integral control, and similar to a recently
introduced reinforcement learning exploration strategy. This shows that this
strategy is optimal in the RSP sense - it minimizes expected path cost subject
to relative entropy constraint. Simulation results on illustrative examples
show that the model behaves as expected.


  The topological color code and the toric code are two leading candidates for
realizing fault-tolerant quantum computation. Here we show that the color code
on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies
of the $d$-dimensional toric code up to local unitary transformations and
adding or removing ancilla qubits. Our result not only generalizes the proven
equivalence for $d=2$, but also provides an explicit recipe of how to decouple
independent components of the color code, highlighting the importance of
colorability in the construction of the code. Moreover, for the $d$-dimensional
color code with $d+1$ boundaries of $d+1$ distinct colors, we find that the
code is equivalent to multiple copies of the $d$-dimensional toric code which
are attached along a $(d-1)$-dimensional boundary. In particular, for $d=2$, we
show that the (triangular) color code with boundaries is equivalent to the
(folded) toric code with boundaries. We also find that the $d$-dimensional
toric code admits logical non-Pauli gates from the $d$-th level of the Clifford
hierarchy, and thus saturates the bound by Bravyi and K\"{o}nig. In particular,
we show that the $d$-qubit control-$Z$ logical gate can be fault-tolerantly
implemented on the stack of $d$ copies of the toric code by a local unitary
transformation.


  Let p be a prime. In this paper we provide a lower bound for the number of
almost p-rational characters of degree coprime to p in the principal p-block of
a finite group of order divisible by p. We further describe the p-local
structure of the groups for which the above-mentioned bound is sharp.


  We show that highly spinning primordial black holes of mass $M\sim 10^{12}$
kg, potentially born in a matter-dominated era after inflation, can produce
clouds of pions in their vicinity via the superradiant instability, with
densities up to that of nuclear matter. We discuss the electromagnetic
signatures of this process, via neutral pion decay and charged pion
annihilation into photons, computing in particular their contribution to the
isotropic gamma-ray background. This allows us to place upper bounds on the
abundance of such primordial black holes that are comparable to the ones
obtained from Hawking evaporation. We also discuss the possibility of directly
observing such clouds in high-redshift superclusters.


  Distributed data processing platforms such as MapReduce and Pregel have
substantially simplified the design and deployment of certain classes of
distributed graph analytics algorithms. However, these platforms do not
represent a good match for distributed graph mining problems, as for example
finding frequent subgraphs in a graph. Given an input graph, these problems
require exploring a very large number of subgraphs and finding patterns that
match some "interestingness" criteria desired by the user. These algorithms are
very important for areas such as social net- works, semantic web, and
bioinformatics. In this paper, we present Arabesque, the first distributed data
processing platform for implementing graph mining algorithms. Arabesque
automates the process of exploring a very large number of subgraphs. It defines
a high-level filter-process computational model that simplifies the development
of scalable graph mining algorithms: Arabesque explores subgraphs and passes
them to the application, which must simply compute outputs and decide whether
the subgraph should be further extended. We use Arabesque's API to produce
distributed solutions to three fundamental graph mining problems: frequent
subgraph mining, counting motifs, and finding cliques. Our implementations
require a handful of lines of code, scale to trillions of subgraphs, and
represent in some cases the first available distributed solutions.


  We study the growth of a crystal in presence of a correlated disorder on the
substrate. Using functional renormalization group, we show, for a long range
disorder correlation, an initial decay of the KPZ type nonlinearity, though
over a large length scale the behavior can be governed by the nonlinearity.


  We show that a generalized version of the holographic principle can be
derived from the Hamiltonian description of information flow within a quantum
system that maintains a separable state. We then show that this generalized
holographic principle entails a general principle of gauge invariance. When
this is realized in an ambient Lorentzian space-time, gauge invariance under
the Poincare group is immediately achieved. We apply this pathway to retrieve
the action of gravity. The latter is cast a la Wilczek through a similar
formulation derived by MacDowell and Mansouri, which involves the
representation theory of the Lie groups SO(3,2) and SO(4,1).


  This paper proposes AEDA (An Easier Data Augmentation) technique to help
improve the performance on text classification tasks. AEDA includes only random
insertion of punctuation marks into the original text. This is an easier
technique to implement for data augmentation than EDA method (Wei and Zou,
2019) with which we compare our results. In addition, it keeps the order of the
words while changing their positions in the sentence leading to a better
generalized performance. Furthermore, the deletion operation in EDA can cause
loss of information which, in turn, misleads the network, whereas AEDA
preserves all the input information. Following the baseline, we perform
experiments on five different datasets for text classification. We show that
using the AEDA-augmented data for training, the models show superior
performance compared to using the EDA-augmented data in all five datasets. The
source code is available for further study and reproduction of the results.


  Bismuth vanadate (BiVO4) has recently been under focus for its potential use
in photocatalysis thanks to its well-suited absorption edge in the visible
light range. Here, we characterize the optical absorption of a BiVO4 single
crystal as a function of temperature and polarization direction by reflectance
and transmittance spectroscopy. The optical band gap is found to be very
sensitive to temperature, and to the monoclinic-to-tetragonal ferroelastic
transition at 523K. The anisotropy, as measured by the difference in absorption
edge for light polarized parallel and perpendicular to the principal axis, is
reduced from 0.2 eV in the high-temperature tetragonal phase to 0.1 eV at
ambient temperature. We show that this evolution is dominantly controlled by
the ferroelastic shear strain. These findings provide a route for further
optimization of bismuth-vanadate-based light absorbers in photocatalytic
devices.


  Codes in the sum-rank metric have received many attentions in recent years,
since they have wide applications in the multishot network coding, the
space-time coding and the distributed storage. Fundamental bounds, some
explicit or probabilistic constructions of sum-rank codes and their decoding
algorithms have been developed in previous papers. In this paper, we construct
covering codes in the sum-rank metric from covering codes in the Hamming
metric. Then some upper bounds on sizes of covering codes in the sum-rank
metric are presented. Block length functions of covering codes in the sum-rank
metric are also introduced and studied. As applications of our upper bounds on
covering codes in the sum-rank metric and block length functions, several
strong Singleton-like bounds on sum-rank codes are proposed and proved. These
strong Singleton-like bounds are much stronger than the Singleton-like bound
for sum-rank codes, when block lengths are larger and minimum sum-rank
distances are small. An upper bound on sizes of list-decodable codes in the
sum-rank metric is also given, which leads to an asymptotic bound on
list-decodability of sum-rank codes. We also give upper bounds on block lengths
of general MSRD codes.


  Optoacoustic tomography (OAT), also known as photoacoustic tomography, is a
rapidly emerging hybrid imaging technique that possesses great potential for a
wide range of biomedical imaging applications. In OAT, a laser is employed to
illuminate the tissue of interest and acoustic signals are produced via the
photoacoustic effect. From these data, an estimate of the distribution of the
absorbed optical energy density within the tissue is reconstructed, referred to
as the object function. This quantity is defined, in part, by the distribution
of light fluence within the tissue that is established by the laser source.
When performing three-dimensional imaging of large objects, such as a female
human breast, it can be difficult to achieve a relatively uniform coverage of
light fluence within the volume of interest when the position of the laser
source is fixed. To circumvent this, researchers have proposed illumination
schemes in which the relative position of the laser source and ultrasound probe
is fixed, and both are rotated together to acquire a tomographic data set. A
problem with this rotating-illumination scheme is that the tomographic data are
inconsistent; namely, the acoustic data recorded at each tomographic view angle
(i.e., probe position) are produced by a distinct object function. In this
work, the impact of this data inconsistency on image reconstruction accuracy is
investigated systematically. This is accomplished by use of computer-simulation
studies and application of mathematical results from the theory of microlocal
analysis. These studies specify the set of image discontinuities that can be
stably reconstructed with a non-stationary optical illumination set-up. The
study also includes a comparison of the ability of iterative and analytic image
reconstruction methods to mitigate artifacts attributable to the data
inconsistency.


  Active learning (AL) is a subfield of machine learning (ML) in which a
learning algorithm could achieve good accuracy with less training samples by
interactively querying a user/oracle to label new data points. Pool-based AL is
well-motivated in many ML tasks, where unlabeled data is abundant, but their
labels are hard to obtain. Although many pool-based AL methods have been
developed, the lack of a comparative benchmarking and integration of techniques
makes it difficult to: 1) determine the current state-of-the-art technique; 2)
evaluate the relative benefit of new methods for various properties of the
dataset; 3) understand what specific problems merit greater attention; and 4)
measure the progress of the field over time. To conduct easier comparative
evaluation among AL methods, we present a benchmark task for pool-based active
learning, which consists of benchmarking datasets and quantitative metrics that
summarize overall performance. We present experiment results for various active
learning strategies, both recently proposed and classic highly-cited methods,
and draw insights from the results.


  Assuming humans are (approximately) rational enables robots to infer reward
functions by observing human behavior. But people exhibit a wide array of
irrationalities, and our goal with this work is to better understand the effect
they can have on reward inference. The challenge with studying this effect is
that there are many types of irrationality, with varying degrees of
mathematical formalization. We thus operationalize irrationality in the
language of MDPs, by altering the Bellman optimality equation, and use this
framework to study how these alterations would affect inference.
  We find that wrongly modeling a systematically irrational human as
noisy-rational performs a lot worse than correctly capturing these biases -- so
much so that it can be better to skip inference altogether and stick to the
prior! More importantly, we show that an irrational human, when correctly
modelled, can communicate more information about the reward than a perfectly
rational human can. That is, if a robot has the correct model of a human's
irrationality, it can make an even stronger inference than it ever could if the
human were rational. Irrationality fundamentally helps rather than hinder
reward inference, but it needs to be correctly accounted for.


  Existing system dealing with online complaint provides a final decision
without explanations. We propose to analyse the complaint text of internet
fraud in a fine-grained manner. Considering the complaint text includes
multiple clauses with various functions, we propose to identify the role of
each clause and classify them into different types of fraud element. We
construct a large labeled dataset originated from a real finance service
platform. We build an element identification model on top of BERT and propose
additional two modules to utilize the context of complaint text for better
element label classification, namely, global context encoder and label refiner.
Experimental results show the effectiveness of our model.


  We study regularizations of Schwartz distributions on a complete Riemannian
manifold $M$. These approximations are based on families of smoothing operators
obtained from the solution operator to the wave equation on $M$ derived from
the metric Laplacian. The resulting global regularization processes are optimal
in the sense that they preserve the microlocal structure of distributions,
commute with isometries and provide sheaf embeddings into algebras of
generalized functions on $M$.


  Element Method. The Finite Volume Method guarantees local and global mass
conservation. A property not satisfied by the Finite Volume Method. On the down
side, the Finite Volume Method requires non trivial modifications to attain
high order approximations unlike the Finite Volume Method. It has been
contended that the Discontinuous Galerkin Method, locally conservative and high
order, is a natural progression for Coastal Ocean Modeling. Consequently, as a
primer we consider the vertical ocean-slice model with the inclusion of density
effects. To solve these non steady Partial Differential Equations, we develop a
pressure projection method for solution. We propose a Hybridized Discontinuous
Galerkin solution for the required Poisson Problem in each time step. The
purpose, is to reduce the computational cost of classical applications of the
Discontinuous Galerkin method. The Hybridized Discontinuous Galerkin method is
first presented as a general elliptic problem solver. It is shown that a high
order implementation yields fast and accurate approximations on coarse meshes.


  The prevalence of coordinated information campaigns in social media platforms
has significant negative consequences across various domains, including social,
political, and economic processes. This paper proposes a multifaceted framework
for detecting and analysing coordinated message promotion on social media. By
simultaneously considering features related to content, time, and network
dimensions, our framework can capture the diverse nature of coordinated
activity and identify anomalous user accounts who likely engaged in suspicious
behaviour. Unlike existing solutions that rely on specific constraints, our
approach is more flexible as it employs specialised components to extract the
significant structures within a network and to detect the most unusual
interactions. We demonstrate the effectiveness of our framework using two
Twitter datasets, the Russian Internet Research Agency (IRA), and long-term
discussions on Data Science topics. The results demonstrate our framework's
ability to isolate unusual activity from expected normal behaviour and provide
valuable insights for further qualitative investigation.