  Changes in calcium concentration along the sperm flagellum regulate sperm
motility and hyperactivation, characterized by an increased flagellar bend
amplitude and beat asymmetry, enabling the sperm to reach and penetrate the
ovum (egg). The signaling pathways by which calcium increases within the
flagellum are well established. However, the exact mechanisms of how calcium
regulates flagellar bending are still under investigation. We extend our
previous model of planar flagellar bending by developing a fluid-structure
interaction model that couples the three-dimensional motion of the flagellum in
a viscous, Newtonian fluid with the evolving calcium concentration. The
flagellum is modeled as a Kirchhoff rod: an elastic rod with preferred
curvature and twist. The calcium dynamics are represented as a one-dimensional
reaction-diffusion model on a moving domain, the centerline of the flagellum.
The two models are coupled assuming that the preferred curvature and twist of
the sperm flagellum depend on the local calcium concentration. To investigate
the effect of calcium on sperm motility, we compare model results of flagellar
bend amplitude and swimming speed for three cases: planar, helical (spiral with
equal amplitude in both directions), and quasi-planar (spiral with small
amplitude in one direction). We observe that for the same parameters, the
planar swimmer is faster and a turning motion is more clearly observed when
calcium coupling is accounted for in the model. In the case of flagellar
bending coupled to the calcium concentration, we observe emergent trajectories
that can be characterized as a hypotrochoid for both quasi-planar and helical
bending.


  Machine learning approaches in sentiment analysis principally rely on the
abundance of resources. To limit this dependence, we propose a novel method
called Siamese Network Architecture for Sentiment Analysis (SNASA) to learn
representations of resource-poor languages by jointly training them with
resource-rich languages using a siamese network.
  SNASA model consists of twin Bi-directional Long Short-Term Memory Recurrent
Neural Networks (Bi-LSTM RNN) with shared parameters joined by a contrastive
loss function, based on a similarity metric. The model learns the sentence
representations of resource-poor and resource-rich language in a common
sentiment space by using a similarity metric based on their individual
sentiments. The model, hence, projects sentences with similar sentiment closer
to each other and the sentences with different sentiment farther from each
other. Experiments on large-scale datasets of resource-rich languages - English
and Spanish and resource-poor languages - Hindi and Telugu reveal that SNASA
outperforms the state-of-the-art sentiment analysis approaches based on
distributional semantics, semantic rules, lexicon lists and deep neural network
representations without sh


  The fastest pulsar and the slowest nova; the oldest galaxies and the youngest
stars; the weirdest life forms and the commonest dwarfs; the highest energy
particles and the lowest energy photons. These were some of the extremes of
Astrophysics 2006. We attempt also to bring you updates on things of which
there is currently only one (habitable planets, the Sun, and the universe) and
others of which there are always many, like meteors and molecules, black holes
and binaries.


  Because the cuprate superconductors are doped Mott insulators, it would be
advantageous to solve even a toy model that exhibits both Mottness and
superconductivity. We consider the Hatsugai-Kohmoto model, an exactly solvable
system that is a prototypical Mott insulator above a critical interaction
strength at half filling. Upon doping or reducing the interaction strength, our
exact calculations show that the system becomes a non-Fermi liquid metal with a
superconducting instability. In the presence of a weak pairing interaction, the
instability produces a thermal transition to a superconducting phase, which is
distinct from the BCS state, as evidenced by a gap-to-transition temperature
ratio exceeding the universal BCS limit. The elementary excitations of this
superconductor are not Bogoliubov quasiparticles but rather superpositions of
doublons and holons, composite excitations signaling that the superconducting
ground state of the doped Mott insulator inherits the non-Fermi liquid
character of the normal state. An unexpected feature of this model is that it
exhibits a superconductivity-induced transfer of spectral weight from high to
low energies as seen in the cuprates as well as a suppression of the superfluid
density relative to that in BCS theory.


  This work studies distributed primal-dual strategies for adaptation and
learning over networks from streaming data. Two first-order methods are
considered based on the Arrow-Hurwicz (AH) and augmented Lagrangian (AL)
techniques. Several revealing results are discovered in relation to the
performance and stability of these strategies when employed over adaptive
networks. The conclusions establish that the advantages that these methods have
for deterministic optimization problems do not necessarily carry over to
stochastic optimization problems. It is found that they have narrower stability
ranges and worse steady-state mean-square-error performance than primal methods
of the consensus and diffusion type. It is also found that the AH technique can
become unstable under a partial observation model, while the other techniques
are able to recover the unknown under this scenario. A method to enhance the
performance of AL strategies is proposed by tying the selection of the
step-size to their regularization parameter. It is shown that this method
allows the AL algorithm to approach the performance of consensus and diffusion
strategies but that it remains less stable than these other strategies.


  A dynamical pair breaking effect is evidenced at very low excitation
energies. For this purpose, a new set of time-dependent coupled channel
equations for pair-breaking in superfluid systems are deduced from the
variational principle. These equations give the probability to destroy or to
create a Cooper pair under the action of some perturbations or when the mean
field varies in time.
  The odd-even effect in fission is investigated within the model as an
example. For this purpose, the time-dependent probability to find the system in
a seniority-one or in a seniority-two state is restricted in the sense that the
perturbations are considered only in the avoided crossing regions.


  We study boundedness, compactness, and Schatten-class membership of the
canonical solution operator to dbar, restricted to (0,1)-forms with holomorphic
coefficients, on L^2(d mu) where mu is a measure with the property that the
monomials form an orthogonal family in L^2 (d mu). The characterizations are
formulated in terms of moment properties of mu. Our results generalize the
results of the first author to several variables, contain some known results
for several variables, and also cover new ground.


  Let $\alpha\in(0,1)\setminus{\Bbb Q}$ and $K=\{(e^z,e^{\alpha
z}):\,|z|\leq1\}\subset{\Bbb C}^2$. If $P$ is a polynomial of degree $n$ in
${\Bbb C}^2$, normalized by $\|P\|_K=1$, we obtain sharp estimates for
$\|P\|_{\Delta^2}$ in terms of $n$, where $\Delta^2$ is the closed unit bidisk.
For most $\alpha$, we show that $\sup_P\|P\|_{\Delta^2}\leq\exp(Cn^2\log n)$.
However, for $\alpha$ in a subset ${\mathcal S}$ of the Liouville numbers,
$\sup_P\|P\|_{\Delta^2}$ has bigger order of growth. We give a precise
characterization of the set ${\mathcal S}$ and study its properties.


  In this paper, we study the numerical method for the bi-Laplace problems with
inhomogeneous coefficients; particularly, we propose finite element schemes on
rectangular grids respectively for an inhomogeneous fourth-order elliptic
singular perturbation problem and for the Helmholtz transmission eigenvalue
problem. The new methods use the reduced rectangle Morley (RRM for short)
element space with piecewise quadratic polynomials, which are of the lowest
degree possible. For the finite element space, a discrete analogue of an
equality by Grisvard is proved for the stability issue and a locally-averaged
interpolation operator is constructed for the approximation issue. Optimal
convergence rates of the schemes are proved, and numerical experiments are
given to verify the theoretical analysis.


  We study uniform consistency in nonparametric mixture models as well as
closely related mixture of regression (also known as mixed regression) models,
where the regression functions are allowed to be nonparametric and the error
distributions are assumed to be convolutions of a Gaussian density. We
construct uniformly consistent estimators under general conditions while
simultaneously highlighting several pain points in extending existing pointwise
consistency results to uniform results. The resulting analysis turns out to be
nontrivial, and several novel technical tools are developed along the way. In
the case of mixed regression, we prove $L^1$ convergence of the regression
functions while allowing for the component regression functions to intersect
arbitrarily often, which presents additional technical challenges. We also
consider generalizations to general (i.e. non-convolutional) nonparametric
mixtures.


  We considered classical solutions to the initial boundary value problem for
non-isentropic compressible Euler equations with damping in multi-dimensions.
We obtained global a priori estimates and global existence results of classical
solutions to both non-isentropic Euler equations with damping and their
nonlinear diffusion equations under small data assumption. We proved the
pressure and velocity decay exponentially to constants, while the entropy and
density can not approach constants. Finally, we proved the pressure and
velocity of the non-isentropic Euler equations with damping converge
exponentially to those of their nonlinear diffusion equations when the time
goes to infinity.


  High sensitivity observations of radio halos in galaxy clusters at
frequencies lower than 330 MHz are still relatively rare, and very little is
known compared to the classical 1.4 GHz images. The few radio halos imaged down
to 150-240 MHz show a considerable spread in size, morphology and spectral
properties. All clusters belonging to the GMRT Radio Halo Survey with detected
or candidate cluster-scale diffuse emission have been imaged at 325 MHz with
the GMRT. Few of them were also observed with the GMRT at 240 MHz and 150 MHz.
For A1682, imaging is particularly challenging due to the presence of strong
and extended radio galaxies at the center. Our data analysis suggests that the
radio galaxies are superposed to very low surface brightness radio emission
extended on the cluster scale, which we present here.


  This letter presents studies of spin-transfer efficiency in electron
transport via discrete electron-in- a-box levels in individual nanometer-scale
Ni particles at 0.06K temperature. In a strong magnetic field, the
spin-transfer rates are estimated by measuring the amplitudes of the Zeeman
splitting of the levels. We find that the spin- and the charge-transfer rates
are comparable, demonstrating significant enhancement of the spin-transfer
efficiency compared to that in larger magnets. In a low magnetic field, we find
an additional energy splitting as evidence that the spin-transfer rate is far
higher than the charge-transfer rate. The effect is explained in terms of the
strong mesoscopic spin- orbit torques, which are exerted on the magnetization
in response to sequential electron tunneling.


  The concept of non-Gorenstein involutions on Calabi-Yau threefolds is a
higher dimensional generalization of non-symplectic involutions on $K3$
surfaces. We present some elementary facts about Calabi-Yau threefolds with
non-Gorenstein involutions. We give a classification of the Calabi-Yau
threefolds of Picard rank one with non-Gorenstein involutions whose fixed locus
is not zero-dimensional.


  A fundamental challenge for any intelligent system is prediction: given some
inputs, can you predict corresponding outcomes? Most work on supervised
learning has focused on producing accurate marginal predictions for each input.
However, we show that for a broad class of decision problems, accurate joint
predictions are required to deliver good performance. In particular, we
establish several results pertaining to combinatorial decision problems,
sequential predictions, and multi-armed bandits to elucidate the essential role
of joint predictive distributions. Our treatment of multi-armed bandits
introduces an approximate Thompson sampling algorithm and analytic techniques
that lead to a new kind of regret bound.


  There are various gate sets that can be used to describe a quantum
computation. A particularly popular gate set in the literature on quantum
computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A
CNOT gate is however not always the natural multi-qubit interaction that can be
implemented on a given physical quantum computer, necessitating a compilation
step that transforms these CNOT gates to the native gate set. A particularly
interesting case where compilation is necessary is for ion trap quantum
computers, where the natural entangling operation can act on more than 2 qubits
and can even act globally on all qubits at once. This calls for an entirely
different approach to constructing efficient circuits. In this paper we study
the problem of converting a given circuit that uses 2-qubit gates to one that
uses global gates. Our three main contributions are as follows. First, we find
an efficient algorithm for transforming an arbitrary circuit consisting of
Clifford gates and arbitrary phase gates into a circuit consisting of
single-qubit gates and a number of global interactions proportional to the
number of non-Clifford phases present in the original circuit. Second, we find
a general strategy to transform a global gate that targets all qubits into one
that targets only a subset of the qubits. This approach scales linearly with
the number of qubits that are not targeted, in contrast to the exponential
scaling reported in (Maslov & Nam, N. J. Phys. 2018). Third, we improve on the
number of global gates required to synthesise an arbitrary n-qubit Clifford
circuit from the 12n-18 reported in (Maslov & Nam, N. J. Phys. 2018) to 6n-8.


  In this paper, we develop a new discontinuous Galerkin method for solving
several types of partial differential equations (PDEs) with high order spatial
derivatives. We combine the advantages of local discontinuous Galerkin (LDG)
method and ultra-weak discontinuous Galerkin (UWDG) method. Firstly, we rewrite
the PDEs with high order spatial derivatives into a lower order system, then
apply the UWDG method to the system. We first consider the fourth order and
fifth order nonlinear PDEs in one space dimension, and then extend our method
to general high order problems and two space dimensions. The main advantage of
our method over the LDG method is that we have introduced fewer auxiliary
variables, thereby reducing memory and computational costs. The main advantage
of our method over the UWDG method is that no internal penalty terms are
necessary in order to ensure stability for both even and odd order PDEs. We
prove stability of our method in the general nonlinear case and provide optimal
error estimates for linear PDEs for the solution itself as well as for the
auxiliary variables approximating its derivatives. A key ingredient in the
proof of the error estimates is the construction of the relationship between
the derivative and the element interface jump of the numerical solution and the
auxiliary variable solution of the solution derivative. With this relationship,
we can then use the discrete Sobolev and Poincar\'{e} inequalities to obtain
the optimal error estimates. The theoretical findings are confirmed by
numerical experiments.


  One of the most important challenges in the field of software code audit is
the presence of vulnerabilities in software source code. These flaws are highly
likely ex-ploited and lead to system compromise, data leakage, or denial of
ser-vice. C and C++ open source code are now available in order to create a
large-scale, classical machine-learning and quantum machine-learning system for
function-level vulnerability identification. We assembled a siz-able dataset of
millions of open-source functions that point to poten-tial exploits. We created
an efficient and scalable vulnerability detection method based on a deep neural
network model Long Short Term Memory (LSTM), and quantum machine learning model
Long Short Term Memory (QLSTM), that can learn features extracted from the
source codes. The source code is first converted into a minimal intermediate
representation to remove the pointless components and shorten the de-pendency.
Therefore, We keep the semantic and syntactic information using state of the
art word embedding algorithms such as Glove and fastText. The embedded vectors
are subsequently fed into the classical and quantum convolutional neural
networks to classify the possible vulnerabilities. To measure the performance,
we used evaluation metrics such as F1 score, precision, re-call, accuracy, and
total execution time. We made a comparison between the results derived from the
classical LSTM and quantum LSTM using basic feature representation as well as
semantic and syntactic represen-tation. We found that the QLSTM with semantic
and syntactic features detects significantly accurate vulnerability and runs
faster than its classical counterpart.


  3D Voronoi's tessellation method was first applied to identify groups of
galaxies in the structure of a supercluster. The sample under consideration
consists of more than 7000 galaxies of the Local Supercluster (LS) with radial
velocities up to 3100 km/s. Because of an essential non-homogeneity of the LS
catalogue, it was proposed to overscale distances in such an ''artificial'' way
that the concentration of galaxies was varying as with increase of the distance
a power-behaved function with the same exponent beta as for the full
homogeneous catalogue. Various parameters of clustering were taking into
account: alpha (0.01, 0.1, 1%) as the part of galaxies, which have the relative
volume of a Voronoi's cell smaller than the critical one for the random
distribution; beta = 0, which fits to the random galaxy distribution; beta =
0.7, which is close to the pancake galaxy distribution. It is revealed that
Voronoi's tessellation method depends weakly on beta-parameter, and the number
of galaxies in rich structures is growing rather than in poor ones with
increase of alpha-parameter. The comparison of the groups derived with the
groups obtained by Karachentsev's dynamical method shows that the number of
groups, which coincides by all the components, is 22%. As a whole, the
dynamical method is more preferred for identifying sparsely populated galaxy
groups, whereas 3D Voronoi's tessellation method is preferred for more
populated ones.


  We report the discovery of four transiting hot Jupiters from the HATSouth
survey: HATS-39b, HATS-40b, HATS41b and HATS-42b. These discoveries add to the
growing number of transiting planets orbiting moderately bright (12.5 < V <
13.7) F dwarf stars on short (2-5 day) periods. The planets have similar radii,
ranging from 1.33(+0.29/-0.20) R_J for HATS-41b to 1.58(+0.16/-0.12) R_J for
HATS-40b. Their masses and bulk densities, however, span more than an order of
magnitude. HATS-39b has a mass of 0.63 +/- 0.13 M_J, and an inflated radius of
1.57 +/- 0.12 R_J, making it a good target for future transmission
spectroscopic studies. HATS-41b is a very massive 9.7 +/- 1.6 M_J planet and
one of only a few hot Jupiters found to date with a mass over 5 M_J. This
planet orbits the highest metallicity star ([Fe/H] = 0.470 +/- 0.010) known to
host a transiting planet and is also likely on an eccentric orbit. The high
mass, coupled with a relatively young age (1.34 +0.31/-0.51 Gyr) for the host
star, are factors that may explain why this planet's orbit has not yet
circularised.


  Recent research on spatial and spatio-temporal model checking provides novel
image analysis methodologies, rooted in logical methods for topological spaces.
Medical Imaging (MI) is a field where such methods show potential for
ground-breaking innovation. Our starting point is SLCS, the Spatial Logic for
Closure Spaces -- Closure Spaces being a generalisation of topological spaces,
covering also discrete space structures -- and topochecker, a model-checker for
SLCS (and extensions thereof). We introduce the logical language ImgQL ("Image
Query Language"). ImgQL extends SLCS with logical operators describing distance
and region similarity. The spatio-temporal model checker topochecker is
correspondingly enhanced with state-of-the-art algorithms, borrowed from
computational image processing, for efficient implementation of distancebased
operators, namely distance transforms. Similarity between regions is defined by
means of a statistical similarity operator, based on notions from statistical
texture analysis. We illustrate our approach by means of two examples of
analysis of Magnetic Resonance images: segmentation of glioblastoma and its
oedema, and segmentation of rectal carcinoma.


  Let $F$ be an archimedean field, $G$ a divisible ordered abelian group and
$h$ a group exponential on $G$. A triple $(F,G,h)$ is realised in a
non-archimedean exponential field $(K,\exp)$ if the residue field of $K$ under
the natural valuation is $F$ and the induced exponential group of $(K,\exp)$ is
$(G,h)$. We give a full characterisation of all triples $(F,G,h)$ which can be
realised in a model of real exponentiation in the following two cases: i) $G$
is countable. ii) $G$ is of cardinality $\kappa$ and $\kappa$-saturated for an
uncountable regular cardinal $\kappa$ with $\kappa^{<\kappa} = \kappa$.
Moreover, we show that for any o-minimal exponential field $(K, \exp)$
satisfying the differential equation $\exp' = \exp$, its residue exponential
field is a model of real exponentiation.


  We study the fluctuation-induced interaction between two impurities in a
weakly-interacting one-dimensional Bose gas using the field theoretical
approach. At separations between impurities shorter and of the order of the
healing length of the system, the induced interaction has a classical origin
and behaves exponentially. At separations longer than the healing length, the
interaction is of a quantum origin and scales as the third power of the inverse
distance. Finite temperature destroys the quasi-long-range order of the Bose
gas and, accordingly, the induced interaction becomes exponentially suppressed
beyond the thermal length. We obtain analytical expressions for the induced
interaction at zero and finite temperature that are valid at arbitrary
distances. We discuss experimental realizations as well as possible formation
of bound states of two impurities, known as bipolarons.


  It is well established that the onset of spatially periodic vortex states in
the Taylor-Couette flow between rotating cylinders occurs at the value of
Reynold's number predicted by local bifurcation theory. However, the symmetry
breaking induced by the top and bottom plates means that the true situation
should be a disconnected pitchfork. Indeed, experiments have shown that the
fold of the disconnected branch can occur at more than double the Reynold's
number of onset. This leads to an apparent contradiction: why should Taylor
vortices set in so sharply at the value Reynold's number predicted by the
symmetric theory, given such large symmetry-breaking effects caused by the
boundary conditions? This paper offers a generic explanation. The details are
worked out using a Swift-Hohenberg pattern formation model that shares the same
qualitative features as the Taylor-Couette flow. Onset occurs via a wall mode
whose exponential tail penetrates further into the bulk of the domain as the
driving parameter increases. In a large domain of length L, we show that the
wall mode creates significant amplitude in the centre at parameter values that
are O(L^{-2}) away from the value of onset in the problem with ideal boundary
conditions. We explain this as being due to a Hamiltonian Hopf bifurcation in
space, which occurs at the same parameter value as the pitchfork bifurcation of
the temporal dynamics. The disconnected anomalous branch remains O(1) away from
the onset parameter since it does not arise as a bifurcation from the wall
mode.


  The domination game is played on a graph $G$ by two players, Dominator and
Staller, who alternate in selecting vertices until each vertex in the graph $G$
is contained in the closed neighbourhood of the set of selected vertices.
Dominator's aim is to reach this state in as few moves as possible, whereas
Staller wants the game to last as long as possible. In this paper, we prove
that if $G$ has $n$ vertices and minimum degree at least 2, then Dominator has
a strategy to finish the domination game on $G$ within $10n/17+1/17$ moves,
thus making progress towards a conjecture by Bujt{\'a}s, Ir\v{s}i\v{c} and
Klav\v{z}ar.


  We discuss theoretical uncertainties of the measurement of the $W$ boson mass
at LEP2 energies, reconstructed with the help of the tandem of the Monte Carlo
event generators KoralW and YFSWW3. Exploiting numerical results obtained with
these programs, and the existing knowledge in the literature, we estimate that
the theoretical uncertainty of the $W$ mass due to electroweak corrections, as
reconstructed at LEP2 with the help of these programs, is $\sim 5 $MeV. Since
we use certain idealized event selections and a simple $M_W$-fitting procedure,
our numerical exercises can be (should be) repeated for the actual ``$M_W$
extraction methods'' of the LEP2 measurements, using KoralW and YFSWW3 or other
Monte Carlo programs.


  In this paper, we consider an inhomogeneous Doi model which was introduced by
W. E and P. Zhang [Meth. Appl. of Anal., 13 (2006), pp. 181 - 198]. We extend
their model, which couples a Smoluchowski equation to a Navier-Stokes type
equation, for active particles by introducing an additional stress tensor.
Exploiting the energetic and entropic structure of the system, we establish the
existence of global-in-time weak solutions in two and three space dimensions
for both passive and active particles. In particular, our result holds for
minimal regularity assumptions on the initial data and without restrictions on
the Reynolds and Deborah number.


  The relationship between charge and structure dictates the properties of
electrochemical systems. For example, reversible Na-ion intercalation - a
low-cost alternative to Li-ion technology - often induces detrimental
structural phase transformations coupled with charge compensation reactions.
However, little is known about the underpinning charge-structure mechanisms
because the reduction-oxidation (redox) reactions within coexisting structural
phases have so far eluded direct operando investigation. Here, we distinguish
x-ray spectra of individual crystalline phases operando during a redox-induced
phase transformation in P2-Na2/3Ni1/3Mn2/3O2 - an archetypal layered oxide for
sodium-ion batteries. We measure the resonant elastic scattering on the Bragg
reflection corresponding to the P2-phase lattice spacing. These resonant
spectra become static midway through the sodium extraction in an operando coin
cell, while the overall sodium extraction proceeds as evidenced by the X-ray
absorption averaging over all electrochemically active Ni atoms. The stop of
redox activity in the P2-structure signifies its inability to host Ni4+ ions.
The coincident emergence of the O2- structure reveals the rigid link between
the local redox and the long-range order during the phase transformation. The
structure-selective x-ray spectroscopy thus opens a powerful avenue for
resolving the dynamic chemistry of different structural phases in multi-phase
electrochemical systems.


  Communication technologies like voice over IP operate under constrained
real-time conditions, with voice packets being subject to delays and losses
from the network. In such cases, the packet loss concealment (PLC) algorithm
reconstructs missing frames until a new real packet is received. Recently,
autoregressive deep neural networks have been shown to surpass the quality of
signal processing methods for PLC, specially for long-term predictions beyond
60 ms. In this work, we propose a non-autoregressive adversarial auto-encoder,
named PLAAE, to perform real-time PLC in the waveform domain. PLAAE has a
causal convolutional structure, and it learns in an auto-encoder fashion to
reconstruct signals with gaps, with the help of an adversarial loss. During
inference, it is able to predict smooth and coherent continuations of such gaps
in a single feed-forward step, as opposed to autoregressive models. Our
evaluation highlights the superiority of PLAAE over two classic PLCs and two
deep autoregressive models in terms of spectral and intonation reconstruction,
perceptual quality, and intelligibility.


  Competing magnetic interactions in geometrically frustrated magnets give rise
to new forms of correlated matter, such as spin liquids and spin ices.
Characterizing the magnetic structure of these states has been difficult due to
the absence of long-range order. Here, we demonstrate that the spin Seebeck
effect (SSE) is a sensitive probe of magnetic short-range order (SRO) in
geometrically frustrated magnets. In low temperature (2 - 5 K) SSE measurements
on a model frustrated magnet \mathrm{Gd_{3}Ga_{5}O_{12}}, we observe
modulations in the spin current on top of a smooth background. By comparing to
existing neutron diffraction data, we find that these modulations arise from
field-induced magnetic ordering that is short-range in nature. The observed SRO
is anisotropic with the direction of applied field, which is verified by
theoretical calculation.


  We report on the magnetic properties of four isomorphous compounds of a
family of quinternary oxalates down to 60 mK. In all these materials, the
magnetic FeII ions with a strong magneto-crystalline anisotropy form a
distorted kagome lattice, topologically equivalent to a perfect kagome one if
nearest-neighbor interactions only are considered. All the compounds order at
low temperature in an antiferromagnetic arrangement with magnetic moments at
120{\deg}. A remarkable magnetic behavior emerges below the N\'eel temperature
in three compounds (with inter-kagome-layer Zr, Sn, Fe but not with Al): the
spin anisotropy combined with a low exchange path network connectivity lead to
domain walls intersecting the kagome planes through strings of free spins.
These produce an unfamiliar slow spin dynamics in the ordered phase observed by
AC susceptibility, evolving from exchange-released spin-flips towards a
cooperative behavior on decreasing the temperature.


  Regular functions of infinite words are (partial) functions realized by
deterministic two-way transducers with infinite look-ahead. Equivalently, Alur
et. al. have shown that they correspond to functions realized by deterministic
Muller streaming string transducers, and to functions defined by
MSO-transductions. Regular functions are however not computable in general (for
a classical extension of Turing computability to infinite inputs), and we
consider in this paper the class of deterministic regular functions of infinite
words, realized by deterministic two-way transducers without look-ahead. We
prove that it is a well-behaved class of functions: they are computable, closed
under composition, characterized by the guarded fragment of MSO-transductions,
by deterministic B\"uchi streaming string transducers, by deterministic two-way
transducers with finite look-ahead, and by finite compositions of sequential
functions and one fixed basic function called map-copy-reverse.


  We present novel homomorphic encryption schemes for integer arithmetic,
intended for use in secure single-party computation in the cloud. These schemes
are capable of securely computing only low degree polynomials homomorphically,
but this appears sufficient for most practical applications. In this setting,
our schemes lead to practical key and ciphertext sizes. We present a sequence
of generalisations of our basic schemes, with increasing levels of security,
but decreasing practicality. We have evaluated the first four of these
algorithms by computing a low-degree inner product. The timings of these
computations are extremely favourable. Finally, we use our ideas to derive a
fully homomorphic system, which appears impractical, but can homomorphically
evaluate arbitrary Boolean circuits.


  Huge astrospheres or stellar wind bubbles influence the propagation of cosmic
rays at energies up to the TeV range and can act as small-scale sinks
decreasing the cosmic ray flux. We model such a sink (in 2D) by a sphere of
radius 10\,pc embedded within a sphere of a radius of 1\,kpc. The cosmic ray
flux is calculated by means of backward stochastic differential equations from
an observer, which is located at $r_{0}$, to the outer boundary. It turns out
that such small-scale sinks can influence the cosmic ray flux at the observer's
location by a few permille (i.e\ a few 0.1\%), which is in the range of the
observations by IceCube, Milagro and other large area telescopes.


  A tantalizing conjecture in discrete mathematics is the one of Koml\'os,
suggesting that for any vectors $\mathbf{a}_1,\ldots,\mathbf{a}_n \in B_2^m$
there exist signs $x_1, \dots, x_n \in \{ -1,1\}$ so that $\|\sum_{i=1}^n
x_i\mathbf{a}_i\|_\infty \le O(1)$. It is a natural extension to ask what
$\ell_q$-norm bound to expect for $\mathbf{a}_1,\ldots,\mathbf{a}_n \in B_p^m$.
We prove that, for $2 \le p \le q \le \infty$, such vectors admit fractional
colorings $x_1, \dots, x_n \in [-1,1]$ with a linear number of $\pm 1$
coordinates so that $\|\sum_{i=1}^n x_i\mathbf{a}_i\|_q \leq
O(\sqrt{\min(p,\log(2m/n))}) \cdot n^{1/2-1/p+ 1/q}$, and that one can obtain a
full coloring at the expense of another factor of $\frac{1}{1/2 - 1/p + 1/q}$.
In particular, for $p \in (2,3]$ we can indeed find signs $\mathbf{x} \in \{
-1,1\}^n$ with $\|\sum_{i=1}^n x_i\mathbf{a}_i\|_\infty \le O(n^{1/2-1/p} \cdot
\frac{1}{p-2})$. Our result generalizes Spencer's theorem, for which $p = q =
\infty$, and is tight for $m = n$.
  Additionally, we prove that for any fixed constant $\delta>0$, in a centrally
symmetric body $K \subseteq \mathbb{R}^n$ with measure at least $e^{-\delta n}$
one can find such a fractional coloring in polynomial time. Previously this was
known only for a small enough constant -- indeed in this regime classical
nonconstructive arguments do not apply and partial colorings of the form
$\mathbf{x} \in \{ -1,0,1\}^n$ do not necessarily exist.


  We present novel approaches involving generative adversarial networks and
diffusion models in order to synthesize high quality, live and spoof
fingerprint images while preserving features such as uniqueness and diversity.
We generate live fingerprints from noise with a variety of methods, and we use
image translation techniques to translate live fingerprint images to spoof. To
generate different types of spoof images based on limited training data we
incorporate style transfer techniques through a cycle autoencoder equipped with
a Wasserstein metric along with Gradient Penalty (CycleWGAN-GP) in order to
avoid mode collapse and instability. We find that when the spoof training data
includes distinct spoof characteristics, it leads to improved live-to-spoof
translation. We assess the diversity and realism of the generated live
fingerprint images mainly through the Fr\'echet Inception Distance (FID) and
the False Acceptance Rate (FAR). Our best diffusion model achieved a FID of
15.78. The comparable WGAN-GP model achieved slightly higher FID while
performing better in the uniqueness assessment due to a slightly lower FAR when
matched against the training data, indicating better creativity. Moreover, we
give example images showing that a DDPM model clearly can generate realistic
fingerprint images.


  Silicon pixel detectors produced according to the ATLAS Pixel Detector design
were tested in a beam at CERN in the framework of the ATLAS collaboration. The
detectors used n+/n sensors with oxygenated silicon substrates. The
experimental behaviour of the detectors after irradiation to 1.1 10**15
n_eq/cm**2 and 600 kGy is discussed. At the sensor bias voltage of 600 V the
depleted depth is measured to be 229 um, the mean collected charge is 20000
electrons, the detection efficiency is 98.2% and the spatial resolution is 9.6
um


  Grigoriev and Podolskii (2018) have established a tropical analogue of the
effective Nullstellensatz, showing that a system of tropical polynomial
equations is solvable if and only if a linearized system obtained from a
truncated Macaulay matrix is solvable. They provided an upper bound of the
minimal admissible truncation degree, as a function of the degrees of the
tropical polynomials. We establish a tropical Nullstellensatz adapted to {\em
sparse} tropical polynomial systems. Our approach is inspired by a construction
of Canny-Emiris (1993), refined by Sturmfels (1994). This leads to an improved
bound of the truncation degree, which coincides with the classical Macaulay
degree in the case of $n+1$ equations in $n$ unknowns. We also establish a
tropical Positivstellensatz, allowing one to decide the inclusion of tropical
basic semialgebraic sets. This allows one to reduce decision problems for
tropical semi-algebraic sets to the solution of systems of tropical linear
equalities and inequalities.


  Extreme Classification (XC) seeks to tag data points with the most relevant
subset of labels from an extremely large label set. Performing deep XC with
dense, learnt representations for data points and labels has attracted much
attention due to its superiority over earlier XC methods that used sparse,
hand-crafted features. Negative mining techniques have emerged as a critical
component of all deep XC methods that allow them to scale to millions of
labels. However, despite recent advances, training deep XC models with large
encoder architectures such as transformers remains challenging. This paper
identifies that memory overheads of popular negative mining techniques often
force mini-batch sizes to remain small and slow training down. In response,
this paper introduces NGAME, a light-weight mini-batch creation technique that
offers provably accurate in-batch negative samples. This allows training with
larger mini-batches offering significantly faster convergence and higher
accuracies than existing negative sampling techniques. NGAME was found to be up
to 16% more accurate than state-of-the-art methods on a wide array of benchmark
datasets for extreme classification, as well as 3% more accurate at retrieving
search engine queries in response to a user webpage visit to show personalized
ads. In live A/B tests on a popular search engine, NGAME yielded up to 23%
gains in click-through-rates.


  We study the variational structure of the complex $k$-Hessian equation on
bounded domain $X\subset \mathbb C^n$ with boundary $M=\partial X$. We prove
that the Dirichlet problem $\sigma_k (\partial \bar{\partial} u) =0$ in $X$,
and $u=f$ on $M$ is variational and we give an explicit construction of the
associated functional $\mathcal{E}_k(u)$. Moreover we prove $\mathcal{E}_k(u)$
satisfies the Dirichlet principle. In a special case when $k=2$, our
constructed functional $\mathcal{E}_2(u)$ involves the Hermitian mean curvature
of the boundary, the notion first introduced and studied by X. Wang. Earlier
work of J. Case and and the first author of this article introduced a boundary
operator for the (real) $k$-Hessian functional which satisfies the Dirichlet
principle. The present paper shows that there is a parallel picture in the
complex setting.


  The symmetry of Nature under a Space Inversion is described by a Parity
operator. Contrary to popular belief, the Parity operator is not unique. The
choice of the Parity operator requires several arbitrary decisions to be made.
It is shown that alternative, equally plausible, choices leads to the
definition of a Parity operator that is conserved by the Weak Interactions. The
operator commonly known as CP is a more appropriate choice for a Parity
operator.


  Using 2D smoothed particle hydrodynamics, we investigate the distribution of
wait times between strong shocks in a turbulent, self-gravitating accretion
disc. We show the resulting distributions do not depend strongly on the cooling
time or resolution of the disc and that they are consistent with the
predictions of earlier work (Young & Clarke 2015; Cossins et al. 2009, 2010).
We use the distribution of wait times between shocks to estimate the likelihood
of stochastic fragmentation by gradual contraction of shear-resistant clumps on
the cooling time scale. We conclude that the stochastic fragmentation mechanism
(Paardekooper 2012) cannot change the radius at which fragmentation is possible
by more than ~20%, restricting direct gravitational collapse as a mechanism for
giant planet formation to the outer regions of protoplanetary discs.


  Nuclei segmentation and classification is the first and most crucial step
that is utilized for many different microscopy medical analysis applications.
However, it suffers from many issues such as the segmentation of small objects,
imbalance, and fine-grained differences between types of nuclei. In this paper,
multiple different contributions were done tackling these problems present.
Firstly, the recently released "ConvNeXt" was used as the encoder for HoVer-Net
model since it leverages the key components of transformers that make them
perform well. Secondly, to enhance the visual differences between nuclei, a
multi-channel color space-based approach is used to aid the model in extracting
distinguishing features. Thirdly, Unified Focal loss (UFL) was used to tackle
the background-foreground imbalance. Finally, Sharpness-Aware Minimization
(SAM) was used to ensure generalizability of the model. Overall, we were able
to outperform the current state-of-the-art (SOTA), HoVer-Net, on the
preliminary test set of the CoNiC Challenge 2022 by 12.489% mPQ+.


  We consider the low energy limit of three dimensional Quantum Chromodynamics
with an even number of flavors. We show that Parity is not spontaneously
broken, but the global (flavor) symmetry is spontaneously broken. The low
energy effective lagrangian is a nonlinear sigma model on the Grassmannian.
Some Chern--Simons terms are necessary in the lagrangian to realize the
discrete symmetries correctly. We consider also another parametrization of the
low energy sector which leads to a three dimensional analogue of the
Wess--Zumino--Witten--Novikov model. Since three dimensional QCD is believed to
be a model for quantum anti--ferromagnetism, our effective lagrangian can
describe their long wavelength excitations (spin waves).


  Motivated by the stringent flux limits for UHE neutrinos coming from gamma
ray burst or active galactic nuclei, we explore the possibility that the active
neutrinos generated in such astrophysical objects could oscillate to sterile
right handed states due to a neutrino magnetic moment mu_nu. We find that a
value as small as mu_nu ~1E-15 mu_B could produce such a transition thanks to
the intense magnetic fields that are expected in these objects.


  Voice assistants like Siri, Google Assistant, Alexa etc. are used widely
across the globe for home automation, these require the use of special phrases
also known as hotwords to wake it up and perform an action like "Hey Alexa!",
"Ok Google!" and "Hey Siri!" etc. These hotwords are detected with lightweight
real-time engines whose purpose is to detect the hotwords uttered by the user.
This paper presents the design and implementation of a hotword detection engine
based on one-shot learning which detects the hotword uttered by the user in
real-time with just one or few training samples of the hotword. This approach
is efficient when compared to existing implementations because the process of
adding a new hotword in the existing systems requires enormous amounts of
positive and negative training samples and the model needs to retrain for every
hotword. This makes the existing implementations inefficient in terms of
computation and cost. The architecture proposed in this paper has achieved an
accuracy of 94.51%.


  A multi-objective genetic algorithm is developed for optimizing
nonlinearities in diffraction limited storage rings. This algorithm determines
sextupole and octupole strengths for chromaticity correction that deliver
optimized dynamic aperture and beam lifetime. The algorithm makes use of
dominance constraints to breed desirable properties into the early generations.
The momentum aperture is optimized indirectly by constraining the chromatic
tune footprint and optimizing the off-energy dynamic aperture. The result is an
effective and computationally efficient technique for correcting chromaticity
in a storage ring while maintaining optimal dynamic aperture and beam lifetime.
This framework was developed for the Swiss Light Source (SLS) upgrade project.


  We consider different generalizations of the Fokker-Planck-equation devised
to describe Levy processes in potential force fields. We show that such
generalizations can proceed along different lines. On one hand,
  Levy statistics can emerge from the fractal temporal nature of the underlying
process, i.e. a high variability in the rate of microscopic events. On the
other hand, they may be a direct consequence of the scale-free spatial
structure on which the process evolves. Although both forms considered lead to
Boltzmann equilibrium, the relaxation patterns are quite different.
  As an example, generalized diffusion in a double-well potential is
considered.


  Motivated by the collective behaviour of biological swarms, we study the
critical dynamics of field theories with coupling between order parameter and
conjugate momentum in the presence of dissipation. By performing a dynamical
renormalization group calculation at one loop, we show that the violation of
momentum conservation generates a crossover between a conservative yet
IR-unstable fixed point, characterized by a dynamic critical exponent $z=d/2$,
and a dissipative IR-stable fixed point with $z=2$. Interestingly, the two
fixed points have different upper critical dimensions. The interplay between
these two fixed points gives rise to a crossover in the critical dynamics of
the system, characterized by a crossover exponent $\kappa=4/d$. Such crossover
is regulated by a conservation length scale, $\mathcal R_0$, which is larger
the smaller the dissipation: beyond $\mathcal R_0$ the dissipative fixed point
dominates, while at shorter distances dynamics is ruled by the conservative
fixed point and critical exponent, a behaviour which is all the more relevant
in finite-size systems with weak dissipation. We run numerical simulations in
three dimensions and find a crossover between the exponents $z=3/2$ and $z=2$
in the critical slowing down of the system, confirming the renormalization
group results. From the biophysical point of view, our calculation indicates
that in finite-size biological groups mode-coupling terms in the equation of
motion can significantly change the dynamical critical exponents even in the
presence of dissipation, a step towards reconciling theory with experiments in
natural swarms. Moreover, our result provides the scale within which fully
conservative Bose-Einstein condensation is a good approximation in systems with
weak symmetry-breaking terms violating number conservation, as quantum magnets
or photon gases.


  The validity of the affine assumption in model flexible polymer networks is
explored. To this end, the displacements of fluorescent tracer beads embedded
in polyacrylamide gels are quantified by confocal microscopy under shear
deformation, and the deviations of these displacements from affine responses
are recorded. Non-affinity within the gels is quantified as a function of
polymer chain density and cross-link concentration. Observations are in
qualitative agreement with current theories of polymer network non-affinity.
The measured degree of non-affinity in the polyacrylamide gels suggests the
presence of structural inhomogeneities which likely result from heterogeneous
reaction kinetics during gel preparation. In addition, the macroscopic
elasticity of the polyacrylamide gels is confirmed to behave in accordance with
standard models of flexible polymer network elasticity.


  The problem of the physical nature and the cosmological genesis of
Lambda-term is discussed. This problem can't be solved in terms of the current
quantum field theory which operates with Higgs and non-perturbative vacuum
condensates and takes into account the changes of these condensates during
relativistic phase transitions. The problem can't be completely solved also in
terms of the conventional global quantum theory: Wheeler-DeWitt quantum
geometrodynamics does not describe the evolution of the Universe in time (RPT
in particular). We have investigated this problem in the context of energies
density of different vacuum subsystems characteristic scales of which pervaid
all energetic scale of the Universe. At first the phemenological solution of
Lambda-term problem and then the hypothesis about the possible structure of a
new global quantum theory are proposed. The main feature of this theory is the
inreversible evolution of geometry and vacuum condensates in time in the regime
of their selforganization. The transformation of the cosmological constant in
dynamical variable is inevitably.


  In order to calculate correlation functions of the chiral Potts model, one
only needs to study the eigenvectors of the superintegrable model. Here we
start this study by looking for eigenvectors of the transfer matrix of the
periodic tau_2(t)model which commutes with the chiral Potts transfer matrix. We
show that the degeneracy of the eigenspace of tau_2(t) in the Q=0 sector is
2^r, with r=(N-1)L/N when the size of the transfer matrix L is a multiple of N.
We introduce chiral Potts model operators, different from the more commonly
used generators of quantum group U-tilde_q(sl-hat(2)). From these we can form
the generators of a loop algebra L(sl(2)). For this algebra, we then use the
roots of the Drinfeld polynomial to give new explicit expressions for the
generators representing the loop algebra as the direct sum of r copies of the
simple algebra sl(2).


  The problem of covariance of physical quantities has not been solved
fundamentally in the theory of relativity, which has caused a lot of confusion
in the community; a typical example is the Gordon metric tensor, which was
developed almost a century ago, and has been widely used to describe the
equivalent gravitational effect of moving media on light propagation,
predicting a novel physics of optical black hole. In this paper, it is shown
that under Lorentz transformation, a covariant tensor satisfies three rules:
(1) the tensor keeps invariant in mathematical form in all inertial frames; (2)
all elements of the tensor have the same physical definitions in all frames;
(3) the tensor expression in one inertial frame does not include any physical
quantities defined in other frames. The three rules constitute a criterion for
testing the covariance of physical laws, required by Einstein's principle of
relativity. Gordon metric does not satisfy Rule (3), and its covariance cannot
be identified before a general refractive index is defined. Finally, it is also
shown as well that in the relativistic quantum mechanics, the Lorentz
covariance of Dirac wave equation is not compatible with Einstein's mass-energy
equivalence.


  We study the Dirichlet problem for an elliptic equation involving the
$1$-Laplace operator and a reaction term, namely: $$ \left\{\begin{array}{ll}
\displaystyle -\Delta_1 u =h(u)f(x)&\hbox{in }\Omega\,,\\ u=0&\hbox{on
}\partial\Omega\,, \end{array}\right. $$ where $ \Omega \subset \mathbb{R}^N$
is an open bounded set having Lipschitz boundary, $f\in L^1(\Omega)$ is
nonnegative, and $h$ is a continuous real function that may possibly blow up at
zero. We investigate optimal ranges for the data in order to obtain existence,
nonexistence and (whenever expected) uniqueness of nonnegative solutions.


  We developed a minimum-cost circulation framework for solving the global data
association problem, which plays a key role in the tracking-by-detection
paradigm of multi-object tracking. The global data association problem was
extensively studied under the minimum-cost flow framework, which is
theoretically attractive as being flexible and globally solvable. However, the
high computational burden has been a long-standing obstacle to its wide
adoption in practice. While enjoying the same theoretical advantages and
maintaining the same optimal solution as the minimum-cost flow framework, our
new framework has a better theoretical complexity bound and leads to orders of
practical efficiency improvement. This new framework is motivated by the
observation that minimum-cost flow only partially models the data association
problem and must be accompanied by an additional and time-consuming searching
scheme to determine the optimal object number. By employing a minimum-cost
circulation framework, we eliminate the searching step and naturally integrate
the number of objects into the optimization problem. By exploring the special
property of the associated graph, that is, an overwhelming majority of the
vertices are with unit capacity, we designed an implementation of the framework
and proved it has the best theoretical complexity so far for the global data
association problem. We evaluated our method with 40 experiments on five MOT
benchmark datasets. Our method was always the most efficient and averagely 53
to 1,192 times faster than the three state-of-the-art methods. When our method
served as a sub-module for global data association methods using higher-order
constraints, similar efficiency improvement was attained. We further
illustrated through several case studies how the improved computational
efficiency enables more sophisticated tracking models and yields better
tracking accuracy.


  The unified theory of physics unifies various phenomena in our observable
universe and other universes. The unified theory is based on the zero-energy
universe and the space-object structures. Different universes in different
developmental stages are the different expressions of the space-object
structures. The unified theory is divided into five parts: the space-object
structures, cosmology, the periodic table of elementary particles, the galaxy
formation, and the extreme force field. The space-object structures explain
quantum mechanics, relativity, and the evolution of the universes. From the
zero-energy universe, our universe starts with the 11D (dimensional) membrane
dual universe followed by the 10D string dual universe and then by the 10D
particle dual universe, and ends with the asymmetrical light-dark dual
universe. This 4-stage process goes on in repetitive cycles. Such 4-stage
cosmology accounts for the origins of the four force fields. The theoretical
calculated percentages of dark energy, dark matter, and baryonic matter are
72.8. 22.7, and 4.53, respectively, in agreement with observed values.
According to the calculation, dark energy started in 4.47 billion years ago in
agreement with the observed 4.71 +/- 0.98 billion years ago. The unified theory
places all elementary particles in the periodic table of elementary particles
with the calculated masses in good agreement with the observed values,
including the mass of the Higgs boson. It explains the inflation, the Big Bang,
and the formation of various shapes of galaxies. It gives the structure for the
extreme force fields, including superconductivity, black hole, and supernova.


  We present a new scheme for quantum homomorphic encryption which is compact
and allows for efficient evaluation of arbitrary polynomial-sized quantum
circuits. Building on the framework of Broadbent and Jeffery and recent results
in the area of instantaneous non-local quantum computation, we show how to
construct quantum gadgets that allow perfect correction of the errors which
occur during the homomorphic evaluation of T gates on encrypted quantum data.
Our scheme can be based on any classical (leveled) fully homomorphic encryption
(FHE) scheme and requires no computational assumptions besides those already
used by the classical scheme. The size of our quantum gadget depends on the
space complexity of the classical decryption function -- which aligns well with
the current efforts to minimize the complexity of the decryption function.
  Our scheme (or slight variants of it) offers a number of additional
advantages such as ideal compactness, the ability to supply gadgets "on
demand", circuit privacy for the evaluator against passive adversaries, and a
three-round scheme for blind delegated quantum computation which puts only very
limited demands on the quantum abilities of the client.


  In this paper we find common features between the equations that are used for
pandemic or epidemic modeling and the renormalization group equations that are
used in high energy physics. Some of these features include the relation of
contact matrices in pandemic modeling and operator mixing in the
renormalization group equations. Another common feature are the use of flow
diagrams and the study of fixed points both in pandemic modeling and in
evolution under renormalization group equations. We illustrate these relations
through the study of some cases of interest to the current COVID-19 pandemic.
These include pandemic modeling with mixing between different age groups and
also contact matrices associated with contact between countries. For the final
example we study the effect on mortality of waning from nonspecific vaccines
which are designed to combat different pathogens but nevertheless may lessen
the severity and mortality of COVID-19 infections.


  The optimal $k$-thresholding (OT) and optimal $k$-thresholding pursuit (OTP)
are newly introduced frameworks of thresholding techniques for compressed
sensing and signal approximation. Such frameworks motivate the practical and
efficient algorithms called relaxed optimal $k$-thresholding
($\textrm{ROT}\omega$) and relaxed optimal $k$-thresholding pursuit
($\textrm{ROTP}\omega$) which are developed through the tightest convex
relaxations of OT and OTP, where $\omega$ is a prescribed integer number. The
preliminary numerical results demonstrated in \cite{Z19} indicate that these
approaches can stably reconstruct signals with a wide range of sparsity levels.
However, the guaranteed performance of these algorithms with parameter $ \omega
\geq 2 $ has not yet established in \cite{Z19}. The purpose of this paper is to
show the guaranteed performance of OT and OTP in terms of the restricted
isometry property (RIP) of nearly optimal order for the sensing matrix
governing the $k$-sparse signal recovery, and to establish the first guaranteed
performance result for $\textrm{ROT}\omega$ and $\textrm{ROTP}\omega$ with $
\omega\geq 2.$ In the meantime, we provide a numerical comparison between
ROTP$\omega$ and several existing thresholding methods.


  Reinforcement Learning (RL) or Deep Reinforcement Learning (DRL) is a
powerful approach to solving Markov Decision Processes (MDPs) when the model of
the environment is not known a priori. However, RL models are still faced with
challenges such as handling covariate shifts and ensuring the quality of human
demonstration. To address these challenges and further advance DRL models, our
work develops a human-in-the-loop DRL framework via digital twin that leverages
human intelligence after deployment to retrain the DRL model in real time.
First, we develop a pre-trained model fully based on learning through trial and
error in the simulated environment allowing scalability and automation while
eliminating variability and biases that can come from subjective human
guidance. Second, instead of deploying the trained model directly on the UGV,
we create a digital twin which controls the physical UGV from the virtual
environment. Third, to allow continuous learning without catastrophic
forgetting, we introduce the ability of the model to self-improve with the help
of small human guidance at the start of the retraining. We test the performance
of our proposed model in both simulation and real-world environments with both
static and dynamic obstacles. The results indicate that our proposed approach
not only outperforms the baseline models in terms of reward accumulation but
also demonstrates superior training efficiency.


  Learning to optimize (L2O) has gained increasing popularity, which automates
the design of optimizers by data-driven approaches. However, current L2O
methods often suffer from poor generalization performance in at least two
folds: (i) applying the L2O-learned optimizer to unseen optimizees, in terms of
lowering their loss function values (optimizer generalization, or
``generalizable learning of optimizers"); and (ii) the test performance of an
optimizee (itself as a machine learning model), trained by the optimizer, in
terms of the accuracy over unseen data (optimizee generalization, or ``learning
to generalize"). While the optimizer generalization has been recently studied,
the optimizee generalization (or learning to generalize) has not been
rigorously studied in the L2O context, which is the aim of this paper. We first
theoretically establish an implicit connection between the local entropy and
the Hessian, and hence unify their roles in the handcrafted design of
generalizable optimizers as equivalent metrics of the landscape flatness of
loss functions. We then propose to incorporate these two metrics as
flatness-aware regularizers into the L2O framework in order to meta-train
optimizers to learn to generalize, and theoretically show that such
generalization ability can be learned during the L2O meta-training process and
then transformed to the optimizee loss function. Extensive experiments
consistently validate the effectiveness of our proposals with substantially
improved generalization on multiple sophisticated L2O models and diverse
optimizees. Our code is available at:
https://github.com/VITA-Group/Open-L2O/tree/main/Model_Free_L2O/L2O-Entropy.


  We consider the vacuum Einstein field equations under the Belinski-Zakharov
symmetries. Depending on the chosen signature of the metric, these spacetimes
contain most of the well-known special solutions in General Relativity,
including well-known black holes. In this paper, we prove global existence of
small Belinski-Zakharov spacetimes under a natural nondegeneracy condition. We
also construct new energies and virial functionals to provide a description of
the energy decay of smooth global cosmological metrics inside the light cone.
Finally, some applications are presented in the case of generalized Kasner
solitons.


  We consider "cubes" in products of finite cyclic groups and we study their
tiling and spectral properties. (A set in a finite group is called a tile if
some of its translates form a partition of the group and is called spectral if
it admits an orhogonal basis of characters for the functions supported on the
set.) We show an analog of a theorem due to Iosevich and Pedersen, Lagarias,
Reeds and Wang, and the third author of this paper, which identified the tiling
complements of the unit cube in Euclidean space with the spectra of the same
cube.


  This research is to search for alternatives to the resolution of complex
medical diagnosis where human knowledge should be apprehended in a general
fashion. Successful application examples show that human diagnostic
capabilities are significantly worse than the neural diagnostic system. This
paper describes a modified feedforward neural network constructive algorithm
(MFNNCA), a new algorithm for medical diagnosis. The new constructive algorithm
with backpropagation; offer an approach for the incremental construction of
near-minimal neural network architectures for pattern classification. The
algorithm starts with minimal number of hidden units in the single hidden
layer; additional units are added to the hidden layer one at a time to improve
the accuracy of the network and to get an optimal size of a neural network. The
MFNNCA was tested on several benchmarking classification problems including the
cancer, heart disease and diabetes. Experimental results show that the MFNNCA
can produce optimal neural network architecture with good generalization
ability.


  In this kind of model, the main characteristic that determines population
viability in the long term is the stochastic growth rate (SGR) denoted
$\lambda_S$. When $\lambda_S$ is larger than one, the population grows
exponentially with probability one and when it is smaller than one, the
population goes extinct with probability one. However, even in very simple
situations it is not possible to calculate the SGR analytically. The literature
offers some approximations for the case in which environmental variability is
low, and there are also some lower and upper bounds, but there is no study of
the practical situations in which they would be tight. Some new bounds for the
SGR are built and the conditions under which each bound works best are
analyzed. These bounds are used to give some necessary and some sufficient
conditions for population explosion and extinction that are easy to check in
practice. The general results are applied to several cases, amongst them a
population structured as juveniles and adults living in an environment
switching randomly between "rich" and "poor".


  Phase-resolved spectroscopy of the newly discovered X-ray transient MAXI
J0556-332 has revealed the presence of narrow emission lines in the Bowen
region that most likely arise on the surface of the mass donor star in this low
mass X-ray binary. A period search of the radial velocities of these lines
provides two candidate orbital periods (16.43+/-0.12 and 9.754+/-0.048 hrs),
which differ from any potential X-ray periods reported. Assuming that MAXI
J0556-332 is a relatively high inclination system that harbors a precessing
accretion disk in order to explain its X-ray properties, it is only possible to
obtain a consistent set of system parameters for the longer period. These
assumptions imply a mass ratio of q~0.45, a radial velocity semi-amplitude of
the secondary of K_2~190 km/s and a compact object mass of the order of the
canonical neutron star mass, making a black hole nature for MAXI J0556-332
unlikely. We also report the presence of strong N III emission lines in the
spectrum, thereby inferring a high N/O abundance. Finally we note that the
strength of all emission lines shows a continuing decay over the ~1 month of
our observations.


  The effectiveness of ad creatives is greatly influenced by their visual
appearance. Advertising platforms can generate ad creatives with different
appearances by combining creative elements provided by advertisers. However,
with the increasing number of ad creative elements, it becomes challenging to
select a suitable combination from the countless possibilities. The industry's
mainstream approach is to select individual creative elements independently,
which often overlooks the importance of interaction between creative elements
during the modeling process. In response, this paper proposes a Cross-Element
Combinatorial Selection framework for multiple creative elements, termed CECS.
In the encoder process, a cross-element interaction is adopted to dynamically
adjust the expression of a single creative element based on the current
candidate creatives. In the decoder process, the creative combination problem
is transformed into a cascade selection problem of multiple creative elements.
A pointer mechanism with a cascade design is used to model the associations
among candidates. Comprehensive experiments on real-world datasets show that
CECS achieved the SOTA score on offline metrics. Moreover, the CECS algorithm
has been deployed in our industrial application, resulting in a significant
6.02% CTR and 10.37% GMV lift, which is beneficial to the business.


  We have studied a problem of the tachyon mediated D-brane - D-brane
annihilation from the underlying world-volume gauge field theory point of view.
The initial state was chosen in the form of two D-branes crossing at a non-zero
angle, which is non-supersymmetric configuration generically. This state was
not a groundstate of the theory and the problem at hand was a model, where we
had rather precise control over the behavior of the theory.Some applications of
this model to the D-brane physics and conclusions about stability of several
configurations were made. By taking a T-dual picture of this process on a T^2
torus, we derived known conclusion about the instability of a system consisting
of D-0 and D-2 branes, and found its decay modes.


  Well-known error detection and correction solutions in wireless
communications are slow or incur high transmission overhead. Recently, notable
solutions like PRAC and DAPRAC, implementing partial packet recovery with
network coding, could address these problems. However, they perform slowly when
there are many errors. We propose S-PRAC, a fast scheme for partial packet
recovery, particularly designed for very noisy wireless channels. S-PRAC
improves on DAPRAC. It divides each packet into segments consisting of a fixed
number of small RLNC encoded symbols and then attaches a CRC code to each
segment and one to each coded packet. Extensive simulations show that S-PRAC
can detect and correct errors quickly. It also outperforms DAPRAC significantly
when the number of errors is high.


  Context: In protoplanetary discs, micron-sized dust grows to form millimetre-
to centimetre-sized pebbles but encounters several barriers during its
evolution. Collisional fragmentation and radial drift impede further dust
growth to planetesimal size. Fluffy grains have been hypothesised to solve
these problems. While porosity leads to faster grain growth, the implied
porosity values obtained from previous simulations were larger than suggested
by observations. Aims: In this paper, we study the influence of porosity on
dust evolution taking into account growth, bouncing, fragmentation, compaction,
rotational disruption and snow lines, in order to understand their impact on
dust evolution. Methods: We develop a module for porosity evolution for the 3D
Smoothed Particle Hydrodynamics (SPH) code Phantom that accounts for dust
growth and fragmentation. This mono-disperse model is integrated into both a 1D
code and the 3D code to capture the overall evolution of dust and gas. Results:
We show that porosity helps dust growth and leads to the formation of larger
solids than when considering compact grains, as predicted by previous work. Our
simulations taking into account compaction during fragmentation show that large
millimetre grains are still formed, but are 10 to 100 times more compact. Thus,
mm sizes with typical filling factors of ~0.1 match the values measured on
comets or via polarimetric observations of protoplanetary discs.


  A fundamental astrobiological question is whether life can be transported
between extrasolar systems. We propose a new strategy to answer this question
based on the principle that life which arose via spreading will exhibit more
clustering than life which arose spontaneously. We develop simple statistical
models of panspermia to illustrate observable consequences of these excess
correlations. Future searches for biosignatures in the atmospheres of
exoplanets could test these predictions: a smoking gun signature of panspermia
would be the detection of large regions in the Milky Way where life saturates
its environment interspersed with voids where life is very uncommon. In a
favorable scenario, detection of as few as $\sim 25$ biologically active
exoplanets could yield a $5\sigma$ detection of panspermia. Detectability of
position-space correlations is possible unless the timescale for life to become
observable once seeded is longer than the timescale for stars to redistribute
in the Milky Way.


  Nanoelectromechanical Systems (NEMS) are among the best candidates to measure
interactions at nanoscale [1-6], especially when resonating oscillators are
used with high quality factor [7, 8]. Despite many efforts [9, 10], efficient
and easy actuation in NEMS remains an issue [11]. The mechanism that we
propose, thermally mediated Center Of Mass (COM) displacements, represents a
new actuation scheme for NEMS and MEMS. To demonstrate this scheme efficiency
we show how mechanical nanodis- placements of a MEMS is triggered using
modulated X-ray microbeams. The MEMS is a microswing constituted by a Ge
microcrystal attached to a Si microcantilever. The interaction is mediated by
the Ge absorption of the intensity modulated X-ray microbeam impinging on the
microcrystal. The small but finite thermal expansion of the Ge microcrystal is
large enough to force a nanodisplacement of the Ge microcrystal COM glued on a
Si microlever. The inverse mechanism can be envisaged: MEMS can be used to
shape X-ray beams. A Si microlever can be a high frequency X-ray beam chopper
for time studies in biology and chemistry.


  While the emergent field of quantum thermodynamics has the potential to
impact energy science, the performance of thermal machines is often classical.
We ask whether quantum effects can boost the performance of a thermal machine
to reach quantum supremacy, i.e., surpassing both the efficiency and power
achieved in classical thermodynamics. To this end, we introduce a nonadiabatic
quantum heat engine operating an Otto cycle with a many-particle working
medium, consisting of an interacting Bose gas confined in a time-dependent
harmonic trap. It is shown that thanks to the interplay of nonadiabatic and
many-particle quantum effects, this thermal machine can outperform an ensemble
of single-particle heat engines with same resources, demonstrating quantum
supremacy in many-particle thermal machines.


  With the growing humanlike nature of dialog agents, people are now engaging
in extended conversations that can stretch from brief moments to substantial
periods of time. Understanding the factors that contribute to sustaining these
interactions is crucial, yet existing studies primarily focusing on short-term
simulations that rarely explore such prolonged and real conversations.
  In this paper, we investigate the factors influencing retention rates in real
interactions with roleplaying models. By analyzing a large dataset of
interactions between real users and thousands of characters, we systematically
examine multiple factors and assess their impact on user retention rate.
Surprisingly, we find that the degree to which the bot embodies the roles it
plays has limited influence on retention rates, while the length of each turn
it speaks significantly affects retention rates. This study sheds light on the
critical aspects of user engagement with role-playing models and provides
valuable insights for future improvements in the development of large language
models for role-playing purposes.


  In this review article, we discuss the current status and future prospects of
perturbation theory as a means of studying the equilibrium thermodynamic and
near-equilibrium transport properties of deconfined QCD matter. We begin with a
brief introduction to the general topic, after which we review in some detail
the foundations and modern techniques of the real- and imaginary-time
formalisms of thermal field theory, covering e.g. the different bases used in
the real-time formalism and the resummations required to deal with soft and
collinear contributions. After this, we discuss the current status of
applications of these techniques, including topics such as electromagnetic
rates, transport coefficients, jet quenching, heavy quarks and quarkonia, and
the Equations of State of hot quark-gluon plasma as well as cold and dense
quark matter. Finally, we conclude with our view of the future directions of
the field, i.e. how we anticipate perturbative calculations to contribute to
our collective understanding of strongly interacting matter in the coming
years.


  The Hardy-Littlewood inequalities for $m$-linear forms on $\ell_{p}$ spaces
are stated for $p>m$. In this paper, among other results, we investigate
similar results for $1\leq p\leq m.$ Let $\mathbb{K}$ be $% \mathbb{R}$ or
$\mathbb{C}$ and $m\geq 2$ be a positive integer. Our main results are the
following sharp inequalities:
  (i) If $\left(r,p\right) \in \left(\lbrack 1,2]\times \lbrack 2,2m)\right)
\cup \left(\lbrack 1,\infty)\times \lbrack 2m,\infty \right)) $, then there is
a constant $D_{m,r,p}^{\mathbb{K}}>0$ (not depending on $% n $) such that
\begin{equation*} \textstyle\left(\sum\limits_{j_{1},...,j_{m}=1}^{n}\left\vert
T(e_{j_{1}},...,e_{j_{m}})\right\vert ^{r}\right) ^{\frac{1}{r}}\leq
D_{m,r,p}^{\mathbb{K}}n^{\max \left\{ \frac{2mr+2mp-mpr-pr}{2pr},0\right\}
}\left\Vert T\right\Vert \end{equation*} for all $m$--linear forms
$T:\ell_{p}^{n}\times \cdots \times \ell_{p}^{n}\rightarrow \mathbb{K}$ and all
positive integers $n$.
  (ii) If $\left(r,p\right) \in \lbrack 2,\infty)\times (m,2m]$, then
\begin{equation*} \textstyle\left(\sum\limits_{j_{1},...,j_{m}=1}^{n}\left\vert
T(e_{j_{1}},...,e_{j_{m}})\right\vert ^{r}\right) ^{\frac{1}{r}}\leq
\left(\sqrt{2}\right) ^{m-1}n^{\max \left\{ \frac{p+mr-rp}{pr},0\right\}
}\left\Vert T\right\Vert \end{equation*} for all $m$--linear forms
$T:\ell_{p}^{n}\times \cdots \times \ell_{p}^{n}\rightarrow \mathbb{K}$ and all
positive integers $n.$ Moreover the exponents $\max \{ (2mr+2mp-mpr-pr)/2pr,0
\} $ in (i) and $\max \{(p+mr-rp)/pr,0 \} $ in (ii) are optimal.


  We investigate the cosmological consequences of a brane-world theory which
incorporates time variations in the gravitational coupling G and the
cosmological term Lambda. We analyze in detail the model where (dG/dt)/G ~ H
and Lambda ~ H^2, which seems to be favored by observations. We show that these
conditions single out models with flat space sections. We determine the
behavior of the expansion scale factor, as well as, the variation of G, Lambda
and H for different possible scenarios where the bulk cosmological constant can
be zero, positive or negative. We demonstrate that the universe must
recollapse, if it is embedded in an Anti-de Sitter five-dimensional bulk, which
is the usual case in brane models. We evaluate the cosmological parameters,
using some observational data, and show that we are nowhere near the time of
recollapse. We conclude that the models with zero and negative bulk
cosmological constant agree with the observed accelerating universe, while
fitting simultaneously the observational data for the density and deceleration
parameters. The age of the universe, even in the recollapsing case, is much
larger than in the FRW universe.


  To each complex reflection group $\Gamma$ one can attach a canonical
symplectic singularity $\mathcal{M}_\Gamma$ arXiv:math/9903070. Motivated by
the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and
Rastelli arXiv:1810.03612 conjectured the existence of a supersymmetric vertex
operator superalgebra $\mathsf{W}_\Gamma$ whose associated variety is
isomorphic to $\mathcal{M}_\Gamma$. We prove this conjecture when the complex
reflection group $\Gamma$ is the symmetric group $S_N$ by constructing a sheaf
of $\hbar$-adic vertex operator superalgebras on the Hilbert scheme of $N$
points in the plane. For that case, we also show the free-field realisation of
$\mathsf{W}_\Gamma$ in terms of $\operatorname{rk}(\Gamma)$ many $\beta\gamma
bc$-systems proposed in arXiv:1810.03612, and identify the character of
$\mathsf{W}_\Gamma$ as a certain quasimodular form of mixed weight and multiple
$q$-zeta value.
  In physical terms, the vertex operator superalgebra $\mathsf{W}_{S_N}$
constructed in this article corresponds via the 4D/2D duality arXiv:1312.5344
to the four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory with
gauge group $\operatorname{SL}_N$.


  I report on the APOKASC catalog, a joint effort between the Kepler
Asteroseismic Science Consortium and the SDSS-III APOGEE spectroscopic survey.
It will contain both seismic and spectroscopic values for stars observed by
both surveys. I discuss the derivation of spectroscopic parameters and their
uncertainties from the H-band spectra delivered by the APOGEE spectrograph,
illustrating the sensitivity of stellar spectra to some parameters, such as
Teff, and lack of sensitivity to others, such as logg.


  This thesis is devoted to the Differential Geometry of curves and surfaces
along with applications in Quantum Mechanics. In the 1st part we introduce the
well known Frenet frame. Later, we show that the curvature function is a lower
bound for the scalar angular velocity of any other orthonormal moving frame,
from which one defines Rotation Minimizing (RM) frames as the ones that achieve
this minimum. Remarkably, RM frames are ideal to study spherical curves and
allow us to characterize them through a simple linear equation. We also apply
these ideas to curves that lie on level surfaces, by reinterpreting the problem
in the context of a metric induced by a Hessian, which may fail to be positive
or non-degenerate and naturally leads us to a Lorentz-Minkowski
$\mathbb{E}_1^3$ or isotropic $\mathbb{I}^3$ space. Here we develop a
systematic approach to construct RM frames and characterize spherical curves in
$\mathbb{E}_1^3$ and $\mathbb{I}^3$ and furnish a criterion for a curve to lie
on a level surface. Finally, we extend these tools to characterize geodesic
spherical curves in hyperbolic and spherical spaces. In the 2nd part we apply
the previous ideas in the quantum dynamics of a constrained particle. After
describing the confining potential formalism, from which emerges a
geometry-induced potential (GIP), we devote our attention to tubular surfaces
to model curved nanotubes. The use of RM frames offers a simpler description
for the constrained dynamics and allows us to show that the torsion of the
centerline of a tube gives rise to a geometric phase. Later, we study the
problem of prescribed GIP for surfaces. Here we explore the GIP for surfaces
invariant by a 1-parameter group of isometries, i.e., cylindrical, revolution,
and helicoidal surfaces. Finally, we devote a special attention to helicoidal
minimal surfaces and prove the existence of geometry-induced bound and
localized states.


  A converse method to the Construction of Salem (1945) of convergent families
of Salem numbers is investigated in terms of an association between Salem
polynomials and Hurwitz quotients via expansive polynomials of small Mahler
measure. This association makes use of Bertin-Boyd's Theorem A (1995) of
interlacing of conjugates on the unit circle; in this context, a Salem number
$\beta$ is produced and coded by an m-tuple of positive rational numbers
characterizing the (SITZ) Stieltjes continued fraction of the corresponding
Hurwitz quotient (alternant). The subset of Stieltjes continued fractions over
a Salem polynomial having simple roots, not cancelling at $\pm 1$, coming from
monic expansive polynomials of constant term equal to their Mahler measure, has
a semigroup structure. The sets of corresponding generalized Garsia numbers
inherit this semi-group structure.


  We employ a cryogenic High Electron Mobility Transistor (HEMT) amplifier to
increase the bandwidth of a charge detection setup with a quantum point contact
(QPC) charge sensor. The HEMT is operating at 1K and the circuit has a
bandwidth of 1 MHz. The noise contribution of the HEMT at high frequencies is
only a few times higher than that of the QPC shot noise. We use this setup to
monitor single-electron tunneling to and from an adjacent quantum dot and we
measure fluctuations in the dot occupation as short as 400 nanoseconds, 20
times faster than in previous work.


  In constructions of analytical solutions to open string field theories pure
gauge configurations parameterized by wedge states play an essential role.
These pure gauge configurations are constructed as perturbation expansions and
to guaranty that these configurations are asymptotical solutions to equations
of motions one needs to study convergence of the perturbation expansions. We
demonstrate that for the large parameter of the perturbation expansion these
pure gauge truncated configurations give divergent contributions to the
equation of motion on the subspace of the wedge states. We perform this
demonstration numerically for the pure gauge configurations related to tachyon
solutions for the bosonic and the NS fermionic SFT. By the numerical
calculations we also show that the perturbation expansions are cured by adding
extra terms. These terms are nothing but the terms necessary to make valued the
Sen conjectures.


  The La-based '214' cuprates host several symmetry breaking phases including
superconductivity, charge and spin order in the form of stripes, and a
structural othorhombic-to-tetragonal phase transition. Therefore, these
materials are an ideal system to study the effects of uniaxial stress onto the
various correlations that pervade the cuprate phase diagram. We report resonant
x-ray scattering experiments on
$\textrm{La}_{1.475}\textrm{Nd}_{0.4}\textrm{Sr}_{0.125}\textrm{Cu}\textrm{O}_{4}$
(LNSCO-125) that reveal a significant response of charge stripes to uniaxial
tensile-stress of $\sim$ 0.1 GPa. These effects include a reduction of the
onset temperature of stripes by $\sim$ 50 K, a 29 K reduction of the
low-temperature orthorhombic-to-tetragonal transition, competition between
charge order and superconductivity, and a preference for stripes to form along
the direction of applied stress. Altogether, we observe a dramatic response of
the electronic properties of LNSCO-125 to a modest amount of uniaxial stress.


  A rigorous definition of a path integral for a spinning particle in three
dimensions is given on a regular cubic lattice. The critical diffusion constant
and the associated critical exponents in each spin are calculated. Continuum
field theories such as Klein-Gordon, Dirac and massive Chern-Simons theories
are constructed near these critical points. The universality of obtained
results is argued on some other lattices.


  Time series clustering is an important data mining task with a wide variety
of applications. While most methods focus on time series taking values on the
real line, very few works consider functional time series. However, functional
objects frequently arise in many fields, such as actuarial science, demography
or finance. Functional time series are indexed collections of
infinite-dimensional curves viewed as random elements taking values in a
Hilbert space. In this paper, the problem of clustering functional time series
is addressed. To this aim, a distance between functional time series is
introduced and used to construct a clustering procedure. The metric relies on a
measure of serial dependence which can be seen as a natural extension of the
classical quantile autocorrelation function to the functional setting. Since
the dynamics of the series may vary over time, we adopt a fuzzy approach, which
enables the procedure to locate each series into several clusters with
different membership degrees. The resulting algorithm can group series
generated from similar stochastic processes, reaching accurate results with
series coming from a broad variety of functional models and requiring minimum
hyperparameter tuning. Several simulation experiments show that the method
exhibits a high clustering accuracy besides being computationally efficient.
Two interesting applications involving high-frequency financial time series and
age-specific mortality improvement rates illustrate the potential of the
proposed approach.


  Phantoms for surgical training are able to mimic cutting and suturing
properties and patient-individual shape of organs, but lack a realistic visual
appearance that captures the heterogeneity of surgical scenes. In order to
overcome this in endoscopic approaches, hyperrealistic concepts have been
proposed to be used in an augmented reality-setting, which are based on deep
image-to-image transformation methods. Such concepts are able to generate
realistic representations of phantoms learned from real intraoperative
endoscopic sequences. Conditioned on frames from the surgical training process,
the learned models are able to generate impressive results by transforming
unrealistic parts of the image (e.g.\ the uniform phantom texture is replaced
by the more heterogeneous texture of the tissue). Image-to-image synthesis
usually learns a mapping $G:X~\to~Y$ such that the distribution of images from
$G(X)$ is indistinguishable from the distribution $Y$. However, it does not
necessarily force the generated images to be consistent and without artifacts.
In the endoscopic image domain this can affect depth cues and stereo
consistency of a stereo image pair, which ultimately impairs surgical vision.
We propose a cross-domain conditional generative adversarial network approach
(GAN) that aims to generate more consistent stereo pairs. The results show
substantial improvements in depth perception and realism evaluated by 3 domain
experts and 3 medical students on a 3D monitor over the baseline method. In 84
of 90 instances our proposed method was preferred or rated equal to the
baseline.


  Driven by the proliferation of real-world application scenarios and scales,
time series anomaly detection (TSAD) has attracted considerable scholarly and
industrial interest. However, existing algorithms exhibit a gap in terms of
training paradigm, online detection paradigm, and evaluation criteria when
compared to the actual needs of real-world industrial systems. Firstly, current
algorithms typically train a specific model for each individual time series. In
a large-scale online system with tens of thousands of curves, maintaining such
a multitude of models is impractical. The performance of using merely one
single unified model to detect anomalies remains unknown. Secondly, most TSAD
models are trained on the historical part of a time series and are tested on
its future segment. In distributed systems, however, there are frequent system
deployments and upgrades, with new, previously unseen time series emerging
daily. The performance of testing newly incoming unseen time series on current
TSAD algorithms remains unknown. Lastly, although some papers have conducted
detailed surveys, the absence of an online evaluation platform prevents
answering questions like "Who is the best at anomaly detection at the current
stage?" In this paper, we propose TimeSeriesBench, an industrial-grade
benchmark that we continuously maintain as a leaderboard. On this leaderboard,
we assess the performance of existing algorithms across more than 168
evaluation settings combining different training and testing paradigms,
evaluation metrics and datasets. Through our comprehensive analysis of the
results, we provide recommendations for the future design of anomaly detection
algorithms. To address known issues with existing public datasets, we release
an industrial dataset to the public together with TimeSeriesBench. All code,
data, and the online leaderboard have been made publicly available.


  We present the status of the Farrell-Jones Conjecture for algebraic K-theory
for a group G and arbitrary coefficient rings R. We add new groups for which
the conjecture is known to be true and study inheritance properties. We discuss
new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture
and conjectures generalizing Moody's Induction Theorem. Thus we extend the
class of groups for which these conjectures are known considerably.


  Neural network architectures have been extensively employed in the fair
representation learning setting, where the objective is to learn a new
representation for a given vector which is independent of sensitive
information. Various "representation debiasing" techniques have been proposed
in the literature. However, as neural networks are inherently opaque, these
methods are hard to comprehend, which limits their usefulness. We propose a new
framework for fair representation learning which is centered around the
learning of "correction vectors", which have the same dimensionality as the
given data vectors. The corrections are then simply summed up to the original
features, and can therefore be analyzed as an explicit penalty or bonus to each
feature. We show experimentally that a fair representation learning problem
constrained in such a way does not impact performance.


  With the upcoming large-scale surveys like LSST, we expect to find
approximately $10^5$ strong gravitational lenses among data of many orders of
magnitude larger. In this scenario, the usage of non-automated techniques is
too time-consuming and hence impractical for science. For this reason, machine
learning techniques started becoming an alternative to previous methods. In our
previous work, we proposed a new machine learning architecture based on the
principle of self-attention, trained to find strong gravitational lenses on
simulated data from the Bologna Lens Challenge. Self-attention-based models
have clear advantages compared to simpler CNNs and highly competing performance
in comparison to the current state-of-art CNN models. We apply the proposed
model to the Kilo Degree Survey, identifying some new strong lens candidates.
However, these have been identified among a plethora of false positives, which
made the application of this model not so advantageous. Therefore, throughout
this paper, we investigate the pitfalls of this approach, and possible
solutions, such as transfer learning, are proposed.


  To any homogeneous polynomial $h$ we naturally associate a variety $\Omega_h$
which maps birationally onto the graph $\Gamma_h$ of the gradient map $\nabla
h$ and which agrees with the space of complete quadrics when $h$ is the
determinant of the generic symmetric matrix. We give a sufficient criterion for
$\Omega_h$ being smooth which applies for example when $h$ is an elementary
symmetric polynomial. In this case $\Omega_h$ is a smooth toric variety
associated to a certain generalized permutohedron. We also give examples when
$\Omega_h$ is not smooth.


  Semi-supervised semantic segmentation (SSS) has recently gained increasing
research interest as it can reduce the requirement for large-scale
fully-annotated training data. The current methods often suffer from the
confirmation bias from the pseudo-labelling process, which can be alleviated by
the co-training framework. The current co-training-based SSS methods rely on
hand-crafted perturbations to prevent the different sub-nets from collapsing
into each other, but these artificial perturbations cannot lead to the optimal
solution. In this work, we propose a new conflict-based cross-view consistency
(CCVC) method based on a two-branch co-training framework which aims at
enforcing the two sub-nets to learn informative features from irrelevant views.
In particular, we first propose a new cross-view consistency (CVC) strategy
that encourages the two sub-nets to learn distinct features from the same input
by introducing a feature discrepancy loss, while these distinct features are
expected to generate consistent prediction scores of the input. The CVC
strategy helps to prevent the two sub-nets from stepping into the collapse. In
addition, we further propose a conflict-based pseudo-labelling (CPL) method to
guarantee the model will learn more useful information from conflicting
predictions, which will lead to a stable training process. We validate our new
CCVC approach on the SSS benchmark datasets where our method achieves new
state-of-the-art performance. Our code is available at
https://github.com/xiaoyao3302/CCVC.


  Modern autonomous systems require extensive testing to ensure reliability and
build trust in ground vehicles. However, testing these systems in the
real-world is challenging due to the lack of large and diverse datasets,
especially in edge cases. Therefore, simulations are necessary for their
development and evaluation. However, existing open-source simulators often
exhibit a significant gap between synthetic and real-world domains, leading to
deteriorated mobility performance and reduced platform reliability when using
simulation data. To address this issue, our Scoping Autonomous Vehicle
Simulation (SAVeS) platform benchmarks the performance of simulated
environments for autonomous ground vehicle testing between synthetic and
real-world domains. Our platform aims to quantify the domain gap and enable
researchers to develop and test autonomous systems in a controlled environment.
Additionally, we propose using domain adaptation technologies to address the
domain gap between synthetic and real-world data with our SAVeS$^+$ extension.
Our results demonstrate that SAVeS$^+$ is effective in helping to close the gap
between synthetic and real-world domains and yields comparable performance for
models trained with processed synthetic datasets to those trained on real-world
datasets of same scale. This paper highlights our efforts to quantify and
address the domain gap between synthetic and real-world data for autonomy
simulation. By enabling researchers to develop and test autonomous systems in a
controlled environment, we hope to bring autonomy simulation one step closer to
realization.


  In [2], Bowen showed that for an expansive system (X, T) with specification
and a potential with the Bowen property, the equilibrium state is unique and
fully supported. We generalize that result by showing that the same conclusion
holds for non-uniform versions of Bowen's hypotheses in which constant
parameters are replaced by any increasing unbounded functions f(n) and g(n)
with sublogarithmic growth (in n). We prove results for two weakenings of
specification; the first is non-uniform specification, based on a definition of
Marcus in ([14]), and the second is a significantly weaker property which we
call non-uniform transitivity. We prove uniqueness of the equilibrium state in
the former case under the assumption that liminf (f(n) + g(n))/ln n = 0, and in
the latter case when lim (f(n) + g(n))/ln n = 0. In the former case, we also
prove that the unique equilibrium state has the K-property. It is known that
when f(n)/ln n or g(n)/ln n is bounded from below, equilibrium states may not
be unique, and so this work shows that logarithmic growth is in fact the
optimal transition point below which uniqueness is guaranteed. Finally, we
present some examples for which our results yield the first known proof of
uniqueness of equilibrium state.


  This paper gives an algorithm to determine whether a number in a cyclic
quartic field is a sum of two squares, mainly based on local-global principle
of isotropy of quadratic forms.