  We study the distribution of first-passage functionals ${\cal A}=
\int_0^{t_f} x^n(t)\, dt$, where $x(t)$ is a Brownian motion (with or without
drift) with diffusion constant $D$, starting at $x_0>0$, and $t_f$ is the
first-passage time to the origin. In the driftless case, we compute exactly,
for all $n>-2$, the probability density
$P_n(A|x_0)=\text{Prob}.(\mathcal{A}=A)$. This probability density has an
essential singular tail as $A\to 0$ and a power-law tail $\sim
A^{-(n+3)/(n+2)}$ as $A\to \infty$. The former is reproduced by the optimal
fluctuation method (OFM), which also predicts the optimal paths of the
conditioned process for small $A$. For the case with a drift toward the origin,
where no exact solution is known for general $n>-1$, the OFM predicts the
distribution tails. For $A\to 0$ it predicts the same essential singular tail
as in the driftless case. For $A\to \infty$ it predicts a stretched exponential
tail $-\ln P_n(A|x_0)\sim A^{1/(n+1)}$ for all $n>0$. In the limit of large
P\'eclet number $\text{Pe}= \mu x_0/(2D)\gg 1$, where $\mu$ is the drift
velocity, the OFM predicts a large-deviation scaling for all $A$: $-\ln
P_n(A|x_0)\simeq\text{Pe}\, \Phi_n\left(z= A/\bar{A}\right)$, where
$\bar{A}=x_0^{n+1}/{\mu(n+1)}$ is the mean value of $\mathcal{A}$. We compute
the rate function $\Phi_n(z)$ analytically for all $n>-1$. For $n>0$
$\Phi_n(z)$ is analytic for all $z$, but for $-1<n<0$ it is non-analytic at
$z=1$, implying a dynamical phase transition. The order of this transition is
$2$ for $-1/2<n<0$, while for $-1<n<-1/2$ the order of transition changes
continuously with $n$. Finally, we apply the OFM to the case of $\mu<0$ (drift
away from the origin). We show that, when the process is conditioned on
reaching the origin, the distribution of $\mathcal{A}$ coincides with the
distribution of $\mathcal{A}$ for $\mu>0$ with the same $|\mu|$.


  We consider the inverse problem of reconstructing the posterior measure over
the trajec- tories of a diffusion process from discrete time observations and
continuous time constraints. We cast the problem in a Bayesian framework and
derive approximations to the posterior distributions of single time marginals
using variational approximate inference. We then show how the approximation can
be extended to a wide class of discrete-state Markov jump pro- cesses by making
use of the chemical Langevin equation. Our empirical results show that the
proposed method is computationally efficient and provides good approximations
for these classes of inverse problems.


  In spite of the advancements made in the periocular recognition, the dataset
and periocular recognition in the wild remains a challenge. In this paper, we
propose a multilayer fusion approach by means of a pair of shared parameters
(dual-stream) convolutional neural network where each network accepts RGB data
and a novel colour-based texture descriptor, namely Orthogonal
Combination-Local Binary Coded Pattern (OC-LBCP) for periocular recognition in
the wild. Specifically, two distinct late-fusion layers are introduced in the
dual-stream network to aggregate the RGB data and OC-LBCP. Thus, the network
beneficial from this new feature of the late-fusion layers for accuracy
performance gain. We also introduce and share a new dataset for periocular in
the wild, namely Ethnic-ocular dataset for benchmarking. The proposed network
has also been assessed on one publicly available dataset, namely UBIPr. The
proposed network outperforms several competing approaches on these datasets.


  Block copolymer are ideal matrices to control the localisation of colloids.
Furthermore, anisotropic nanoparticles such as Janus nanoparticles possess an
additional orientational degree of freedom that can play a crucial role in the
formation of highly ordered materials made of block copolymers. This work
presents a mesoscopic simulation method to assert the co-assembly of Janus
nanoparticles in a block copolymer mixture, finding numerous instances of
aggregation and formation of ordered configurations which can be related to
dispersions of pure Janus colloids. Comparison with chemically homogeneous
neutral nanoparticles determines that Janus nanoparticles are less prone to
induce bridging along lamellar domains, thus being a less destructive way to
segregate nanoparticles at interfaces. The combination of asymmetric block
copolymer and asymmetric Janus nanoparticles can result in assembly of colloids
in an even number of layers within one of the block domains.


  We present two fast algorithms which apply inclusion-exclusion principle to
sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC)
and inchworm Monte Carlo method, respectively. In the case of inchworm Monte
Carlo, the proposed fast algorithm gives an extension to the work
["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B,
98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed
fast algorithms reduce the computational complexity from double factorial to
exponential. Numerical experiments are carried out to verify the theoretical
results and to compare the efficiency of the methods.


  We study three-body recombination in an ultracold Bose-Fermi mixture. We
first show theoretically that, for weak inter-species coupling, the loss rate
is proportional to Tan's contact. Second, using a 7 Li/ 6 Li mixture we probe
the recombination rate in both the thermal and dual superfluid regimes. We find
excellent agreement with our model in the BEC-BCS crossover. At unitarity where
the fermion-fermion scattering length diverges, we show that the loss rate is
proportional the 4/3 power of the fermionic density. Our results demonstrate
that impurity-induced losses can be used as a quantitative probe of many-body
correlations.


  We introduce a dust model for cosmological simulations implemented in the
moving-mesh code AREPO and present a suite of cosmological hydrodynamical
zoom-in simulations to study dust formation within galactic haloes. Our model
accounts for the stellar production of dust, accretion of gas-phase metals onto
existing grains, destruction of dust through local supernova activity, and dust
driven by winds from star-forming regions. We find that accurate stellar and
active galactic nuclei feedback is needed to reproduce the observed
dust-metallicity relation and that dust growth largely dominates dust
destruction. Our simulations predict a dust content of the interstellar medium
which is consistent with observed scaling relations at $z = 0$, including
scalings between dust-to-gas ratio and metallicity, dust mass and gas mass,
dust-to-gas ratio and stellar mass, and dust-to-stellar mass ratio and gas
fraction. We find that roughly two-thirds of dust at $z = 0$ originated from
Type II supernovae, with the contribution from asymptotic giant branch stars
below 20 per cent for $z \gtrsim 5$. While our suite of Milky Way-sized
galaxies forms dust in good agreement with a number of key observables, it
predicts a high dust-to-metal ratio in the circumgalactic medium, which
motivates a more realistic treatment of thermal sputtering of grains and dust
cooling channels.


  In this paper we introduce mutation of Brauer trees. We show that our
mutation of Brauer trees explicitly describes the tilting mutation of Brauer
tree algebras introduced by Okuyama and Rickard.


  Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots
\times T_N$, each of which is regular with degree at least three. We consider
Bernoulli bond percolation and the Ising model on this graph, giving a short
proof that the model undergoes a second order phase transition with mean-field
critical exponents in each case. The result concerning percolation recovers a
result of Kozma (2013), while the result concerning the Ising model is new.
  We also present a new proof, using similar techniques, of a lemma of Schramm
concerning the decay of the critical two-point function along a random walk, as
well as some generalizations of this lemma.


  Extending the approach of the paper [Mathieu, P. (1997) Hitting times and
spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we
prove that the Poincare inequality for a (possibly non-symmetric) Markov
process yields the exponential integrability of the hitting times of this
process. For symmetric elliptic diffusions, this provides a criterion for the
Poincare inequality in the terms of hitting times.


  It is shown that appearance of inertial range of scales, adjacent to
distributed chaos range, results in adiabatic invariance of an energy
correlation integral for isotropic homogeneous turbulence and for buoyancy
driven turbulence (with stable or unstable stratification, including
Rayleigh-Taylor mixing zone). Power spectrum of velocity field for distributed
chaos dominated by this adiabatic invariant has a stretched exponential form
$\propto \exp(-k/k_{\beta})^{3/5}$. Results of recent direct numerical
simulations have been used in order to support these conclusions.


  AGN feedback is invoked as one of the most relevant mechanisms that shape the
evolution of galaxies. Our goal is to understand the interplay between AGN
feedback and the interstellar medium in M51, a nearby spiral galaxy with a
modest AGN and a kpc-scale radio jet expanding through the disc of the galaxy.
For that purpose, we combine molecular gas observations in the CO(1-0) and
HCN(1-0) lines from the Plateau de Bure interferometer with archival radio,
X-ray, and optical data. We show that there is a significant scarcity of CO
emission in the ionisation cone, while molecular gas emission tends to
accumulate towards the edges of the cone. The distribution and kinematics of CO
and HCN line emission reveal AGN feedback effects out to r~500pc, covering the
whole extent of the radio jet, with complex kinematics in the molecular gas
which displays strong local variations. We propose that this is the result of
the almost coplanar jet pushing on molecular gas in different directions as it
expands; the effects are more pronounced in HCN than in CO emission, probably
as the result of radiative shocks. Following previous interpretation of the
redshifted molecular line in the central 5" as caused by a molecular outflow,
we estimate the outflow rates to be Mdot_H2~0.9Msun/yr and
Mdot_dense~0.6Msun/yr, which are comparable to the molecular inflow rates
(~1Msun/yr); gas inflow and AGN feedback could be mutually regulated processes.
The agreement with findings in other nearby radio galaxies suggests that this
is not an isolated case, and probably the paradigm of AGN feedback through
radio jets, at least for galaxies hosting low-luminosity active nuclei.


  We study 4 dimensional $(4d$) gravitational waves (GWs) with compact
wavefronts, generalizing Robinson-Trautman (RT) solutions in Einstein gravity
with an arbitrary cosmological constant. We construct the most general solution
of the GWs in the presence of a causal, timelike, or null boundary when the
usual tensor modes are turned off. Our solution space besides the shape and
topology of the wavefront which is a generic compact, smooth, and orientable
$2d$ surface $\Sigma$, is specified by a vector over $\Sigma$ satisfying the
conformal Killing equation and two scalars that are arbitrary functions over
the causal boundary, the boundary modes (soft hair). We work out the symplectic
form over the solution space using covariant phase space formalism and analyze
the boundary symmetries and charges. The algebra of surface charges is a
Heisenberg algebra. Only the overall size of the compact wavefront and not the
details of its shape appears in the boundary symplectic form and is canonical
conjugate to the overall mass of the GW. Hence, the information about the shape
of the wavefront can't be probed by the boundary observer. We construct a
boundary energy-momentum tensor and a boundary current, whose conservation
yields the RT equation for both asymptotically AdS and flat spacetimes. The
latter provides a hydrodynamic description for our RT solutions.


  A key step in any scanning-based asset creation workflow is to convert
unordered point clouds to a surface. Classical methods (e.g., Poisson
reconstruction) start to degrade in the presence of noisy and partial scans.
Hence, deep learning based methods have recently been proposed to produce
complete surfaces, even from partial scans. However, such data-driven methods
struggle to generalize to new shapes with large geometric and topological
variations. We present Points2Surf, a novel patch-based learning framework that
produces accurate surfaces directly from raw scans without normals. Learning a
prior over a combination of detailed local patches and coarse global
information improves generalization performance and reconstruction accuracy.
Our extensive comparison on both synthetic and real data demonstrates a clear
advantage of our method over state-of-the-art alternatives on previously unseen
classes (on average, Points2Surf brings down reconstruction error by 30% over
SPR and by 270%+ over deep learning based SotA methods) at the cost of longer
computation times and a slight increase in small-scale topological noise in
some cases. Our source code, pre-trained model, and dataset are available on:
https://github.com/ErlerPhilipp/points2surf


  The coefficients that appear in uniform asymptotic expansions for integrals
are typically very complicated. In the existing literature the majority of the
work only give the first two coefficients. In a limited number of papers where
more coefficients are given the evaluation of the coefficients near the
coalescence points is normally highly numerically unstable. In this paper, we
illustrate how well-known Cauchy type integral representations can be used to
compute the coefficients in a very stable and efficient manner. We discuss the
cases: (i) two coalescing saddles, (ii) two saddles coalesce with two branch
points, (iii) a saddle point near an endpoint of the interval of integration.
As a special case of (ii) we give a new uniform asymptotic expansion for Jacobi
polynomials $P_n^{(\alpha,\beta)}(z)$ in terms of Laguerre polynomials
$L_n^{(\alpha)}(x)$ as $n\to\infty$ that holds uniformly for $z$ near $1$.
Several numerical illustrations are included.


  We report the XMM-Newton/EPIC detection in 2008 March of a luminous (L_X ~
10^32-33 erg/s), variable X-ray source in the vicinity (within ~6") of the
enigmatic star V838 Mon, which underwent a spectacular outburst in early 2002.
Spectral modeling of the XMM-Newton X-ray source indicates the presence of two
plasma components with characteristic temperatures of TX ~ 2x10^6K and
~1.5x10^7K, attenuated by an absorbing column (N_H ~ 4 x 10^21cm^-2) that is
consistent with the visual extinction measured toward V838 Mon (A_V ~ 2). No
such luminous source was detected in the immediate vicinity of V838 Mon in
Chandra/ACIS-S observations obtained about one year after outburst or, most
recently, in 2010 January. The two XMM source spectral components appear to be
marginally spatially resolved, with the spatial centroid of the hard component
lying closer to (within ~2" of) the position of V838 Mon than the broad-band
source or the soft source component; however, if there are two sources at or
near V838 Mon, the Chandra nondetections would imply that both of them are
variable. An alternative is that there is a single variable source, and that
the apparent spatial separation may actually be due to photon-counting
statistics or is perhaps instrumental in origin. We consider constraints placed
by the X-ray detection and nondetections on a stellar merger model for the 2002
V838 Mon outburst, in which the spun-up merger product drives a powerful
magnetic dynamo. Alternatively, the transient behavior of the X-ray source
could indicate that the X-rays arose as a consequence of an interaction between
V838 Mon's ejecta and its early-type (B3 V) companion.


  We study the Landauer's principle of an Unruh-DeWitt detector linearly
coupled to Dirac field in $1 + 1$ dimensional cavity. When the initial state of
the field is vacuum, we obtain the heat transfer and von Neumann entropy change
perturbatively. For the thermal state, the heat transfer and entropy change are
approximately obtained in the case where the interaction time is long enough
and the Unruh-DeWitt detector is in resonance with one of the field mode.
Compared to the real scalar field, we find the results of vacuum initial state
differs solely from the helicity of the Dirac field and the distinguishablity
of fermion and anti-fermion comes into play when the initial state is thermal.
We also point out that the results for massless fermionic field can be obtained
by taking the particle $m\rightarrow 0$. We find that in both cases satisfy
Landauer's principle.


  Changes in the number of publications in a certain field might reflect the
dynamic of scientific progress in this field, since an increase in the number
of publications can be interpreted as an increase in the field-specific
knowledge. In this paper, we present a methodological approach to analyse the
dynamics of science on lower aggregation levels, i.e., the level of research
fields. Our trend analysis approach is able to uncover very recent trends, and
the methods used to study the trends are simple to understand for the possible
recipients of the results. In order to demonstrate the trend analysis approach,
we focused in this study on the annual number of publications (and patents) in
chemistry (and related areas) between 2014 and 2020 identifying those fields in
chemistry with the highest dynamics (largest rates of change in publication
counts). The study is based on the mono-disciplinary literature database
CAplus. Our results reveal that the number of publications in the CAplus
database is increasing since many years. Research regarding optical phenomena
and electrochemical technologies was found to be among the emerging topics in
recent years.


  This paper presents a novel Coprime Blurred Pair (CBP) model for visual
data-hiding for security in camera surveillance. While most previous approaches
have focused on completely encrypting the video stream, we introduce a spatial
encryption scheme by blurring the image/video contents to create a CBP. Our
goal is to obscure detail in public video streams by blurring while allowing
behavior to be recognized and to quickly deblur the stream so that details are
available if behavior is recognized as suspicious. We create a CBP by blurring
the same latent image with two unknown kernels. The two kernels are coprime
when mapped to bivariate polynomials in the z domain. To deblur the CBP we
first use the coprime constraint to approximate the kernels and sample the
bivariate CBP polynomials in one dimension on the unit circle. At each sample
point, we factor the 1D polynomial pair and compose the results into a 2D
kernel matrix. Finally, we compute the inverse Fast Fourier Transform (FFT) of
the kernel matrices to recover the coprime kernels and then the latent video
stream. It is therefore only possible to deblur the video stream if a user has
access to both streams. To improve the practicability of our algorithm, we
implement our algorithm using a graphics processing unit (GPU) to decrypt the
blurred video streams in real-time, and extensive experimental results
demonstrate that our new scheme can effectively protect sensitive identity
information in surveillance videos and faithfully reconstruct the unblurred
video stream when two blurred sequences are available.


  We revisit a fundamental open problem in quantum information theory, namely
whether it is possible to transmit quantum information at a rate exceeding the
channel capacity if we allow for a non-vanishing probability of decoding error.
Here we establish that the Rains information of any quantum channel is a strong
converse rate for quantum communication: For any sequence of codes with rate
exceeding the Rains information of the channel, we show that the fidelity
vanishes exponentially fast as the number of channel uses increases. This
remains true even if we consider codes that perform classical post-processing
on the transmitted quantum data. As an application of this result, for
generalized dephasing channels we show that the Rains information is also
achievable, and thereby establish the strong converse property for quantum
communication over such channels. Thus we conclusively settle the strong
converse question for a class of quantum channels that have a non-trivial
quantum capacity.


  After the successful completion of the SIDDHARTA experiment run with crab
waist collisions, the electron- positron collider DA{\Phi}NE has started
routine operations for the KLOE-2 detector. The new interaction region also
exploits the crab waist collision scheme, but features certain complications
including the experimental detector solenoid, compensating anti-solenoids, and
tilted quadrupole magnets. We have performed simulations of the beam-beam
collisions in the collider taking into account the real DA{\Phi}NE nonlinear
lattice. In particular, we have evaluated the effect of crab waist sextupoles
and beam-beam interactions on the DA{\Phi}NE dynamical aperture and energy
acceptance, and estimated the luminosity that can be potentially achieved with
and without crab waist sextupoles in the present working conditions. A
numerical analysis has been performed in order to propose possible steps for
further luminosity increase in DA{\Phi}NE such as a better working point
choice, crab sextupole strength optimization, correction of the phase advance
between the sextupoles and the interaction region. The proposed change of the
e- ring working point was implemented and resulted in a significant performance
increase.


  (Abridged) We present new K-band spectroscopy for a sample of 48 starburst
galaxies, obtained using UKIRT in Hawaii. This constitutes a fair sample of the
most common types of starburst galaxies found in the nearby Universe. The
variety of near infrared spectral features shown by these galaxies implies
different bursts characteristics, which suggests that we survey galaxies with
different star formation histories or at different stages of their burst
evolution.
  Using synthetic starburst models, we conclude that the best ensemble of
parameters which describe starburst galaxies in the nearby universe are a
constant rate of star formation, a Salpeter IMF with an upper mass cutoff equal
to 30 solar mass and bursts ages between 10 Myr and 1 Gyr. The model is fully
consistent with the differences observed in the optical and FIR between the
different types of starbursts. It suggests that HII galaxies have younger
bursts and lower metallicities than SBNGs, while LIRGs have younger bursts but
higher metallicities.
  Our observations suggest that the starburst phenomenon must be a sustained or
self--sustained phenomenon: either star formation is continuous in time or
multiple bursts happen in sequence over a relatively long period of time. The
generality of our observations implies that this is a characteristic of
starburst galaxies in the nearby Universe.


  We propose a framework for modeling and estimating the state of controlled
dynamical systems, where an agent can affect the system through actions and
receives partial observations. Based on this framework, we propose the
Predictive State Representation with Random Fourier Features (RFFPSR). A key
property in RFF-PSRs is that the state estimate is represented by a conditional
distribution of future observations given future actions. RFF-PSRs combine this
representation with moment-matching, kernel embedding and local optimization to
achieve a method that enjoys several favorable qualities: It can represent
controlled environments which can be affected by actions; it has an efficient
and theoretically justified learning algorithm; it uses a non-parametric
representation that has expressive power to represent continuous non-linear
dynamics. We provide a detailed formulation, a theoretical analysis and an
experimental evaluation that demonstrates the effectiveness of our method.


  We entertain the idea that robust theoretical expectations can become a tool
in removing hidden observational or data-reduction biases. We illustrate this
approach for a specific problem associated with gravitational microlensing.
Using the fact that a group is more than just a collection of individuals, we
derive formulae for correcting the distribution of the dimensionless impact
parameters of events, u_min. We refer to the case when undetected biases in the
u_min distribution can be alleviated by multiplication of impact parameters of
all events by a common constant factor. We show that in this case the general
maximum likelihood problem of solving an infinite number of equations reduces
to two constraints, and we find an analytic solution. Under the above
assumptions, this solution represents a state in which the ``entropy'' of a
microlensing ensemble is at its maximum, that is, the distribution of u_min
resembles a specific, theoretically expected, box-like distribution to the
highest possible extent. We also show that this technique does not allow one to
correct the parameters of individual events on the event by event basis
independently from each other.


  Past few years have seen an extensive use of RAM chips with wide I/O data
(e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly
vulnerable to a special type of byte error, called an $m$-spotty byte error,
which can be effectively detected or corrected using byte error-control codes.
The MacWilliams identity provides the relationship between the weight
distribution of a code and that of its dual. This paper introduces $m$-spotty
Hamming weight enumerator, joint $m$-spotty Hamming weight enumerator and split
$m$-spotty Hamming weight enumerator for byte error-control codes over finite
commutative Frobenius rings as well as $m$-spotty Lee weight enumerator over an
infinite family of rings. In addition, MacWilliams type identities are also
derived for these enumerators.


  Superresolution is a unique quantum feature generated by N00N states or
phase-controlled coherent photons via projection measurements in a Mach-Zehnder
interferometer (MZI). Superresolution has no direct relation with
supersensitivity in quantum sensing and has a potential application for the
precision measurement of an unknown signal frequency. Recently,
phase-controlled quantum erasers have been demonstrated for superresolution
using classical light of a continuous-wave laser to overcome the diffraction
limit in classical physics and to solve the limited scalability in N00N
state-based quantum sensing. Here, a quantum spectrometer is presented for the
macroscopic superresolution using phase-controlled spatial light modulators
(SLMs) in MZI. For validity, a general solution of the superresolution is
derived from the SLM-based projection measurements and an unprecedented
resolution is numerically confirmed for an unknown frequency of light.


  Testing the cosmological variation of fundamental constants of Nature can
provide valuable insights into new physics scenarios. While many such
constraints have been derived for Standard Model coupling constants and masses,
the $\bar\theta$ parameter of QCD has not been as extensively examined. This
letter discusses potentially promising paths to investigate the time dependence
of the $\bar\theta$ parameter. While laboratory searches for CP-violating
signals of $\bar\theta$ yield the most robust bounds on today's value of
$\bar\theta$, we show that CP-conserving effects provide constraints on the
variation of $\bar\theta$ over cosmological timescales. We find no evidence for
a variation of $\bar\theta$ that could have implied an "iron-deficient"
Universe at higher redshifts. By converting recent atomic clock constraints on
a variation of constants, we infer $ d({\bar\theta}^2)/dt \leq 6\times
10^{-15}\text{yr}^{-1}$, at 1-$\sigma$. Finally, we also sketch an axion model
that results in a varying $\bar\theta$ and could lead to excess diffuse gamma
ray background, from decays of axions produced in high redshift supernova
explosions.


  The Friedberg-Lee model is studied at finite temperature and density. By
using the finite temperature field theory, the effective potential of the
Friedberg-Lee model and the bag constant $B(T)$ and $B(T,\mu)$ have been
calculated at different temperatures and densities. It is shown that there is a
critical temperature $T_{C}\simeq 106.6 \mathrm{MeV}$ when $\mu=0 \mathrm{MeV}$
and a critical chemical potential $\mu \simeq 223.1 \mathrm{MeV}$ for fixing
the temperature at $T=50 \mathrm{MeV}$. We also calculate the soliton solutions
of the Friedberg-Lee model at finite temperature and density. It turns out that
when $T\leq T_{C}$ (or $\mu \leq \mu_C$), there is a bag constant $B(T)$ (or
$B(T,\mu)$) and the soliton solutions are stable. However, when $T>T_{C}$ (or
$\mu>\mu_C$) the bag constant $B(T)=0 \mathrm{MeV}$ (or $B(T,\mu)=0
\mathrm{MeV}$) and there is no soliton solution anymore, therefore, the
confinement of quarks disappears quickly.


  We have used the SINFONI near-infrared integral field unit on the VLT to
resolve the optical emission line structure of one of the brightest (L~1e44
erg/s) and nearest (z=2.38) of all Lya blobs (LABs). The target, known in the
literature as object 'B1' (Francis et al. 1996), lies at a redshift where the
main optical emission lines are accessible in the observed near-infrared. We
detect luminous [OIII]4959,5007A and Ha emission with a spatial extent of at
least 32x40 kpc (4"x5"). The dominant optical emission line component shows
relatively broad lines (600-800 km/s, FWHM) and line ratios consistent with
AGN-photoionization. The new evidence for AGN photoionization, combined with
previously detected CIV and luminous, warm infrared emission, suggest that B1
is the site of a hidden quasar. This is confirmed by the fact that [OII] is
relatively weak compared to [OIII] (extinction-corrected [OIII]/[OII] of about
3.8), which is indicative of a high, Seyfert-like ionization parameter. From
the [OIII] luminosity we infer a bolometric AGN luminosity of ~3e46 erg/s, and
further conclude that the obscured AGN may be Compton-thick given existing
X-ray limits. The large line widths observed are consistent with clouds moving
within the narrow line region of a luminous QSO. The AGN scenario is capable of
producing sufficient ionizing photons to power the Lya, even in the presence of
dust. By performing a census of similar objects in the literature, we find that
virtually all luminous LABs harbor obscured quasars. Based on simple duty-cycle
arguments, we conclude that AGN are the main drivers of the Lya in LABs rather
than the gravitational heating and subsequent cooling suggested by cold stream
models. We also conclude that the empirical relation between LABs and overdense
environments at high redshift must be due to a more fundamental correlation
between AGN (or massive galaxies) and environment.


  A class of differentiable solutions is proved for the isentropic Euler
equations in two and three space dimensions. The solutions are explicitly given
in terms of solutions to inviscid Burgers equations, and several directions of
propagation. The relative orientation of the directions is critical. Within the
directional constraints, the Burgers solutions are arbitrary. The several
velocities add, and the pressures combine nonlinearly. These solutions cannot
exist beyond the time when shocks develop in any of the Burgers solutions.


  Let $G$ be an undirected network with a distinguished set of terminals $T
\subseteq V(G)$ and edge capacities $cap: E(G) \rightarrow \mathbb{R}_+$. By an
odd $T$-walk we mean a walk in $G$ (with possible vertex and edge
self-intersections) connecting two distinct terminals and consisting of an odd
number of edges. Inspired by the work of Schrijver and Seymour on odd path
packing for two terminals, we consider packings of odd $T$-walks subject to
capacities $cap$.
  First, we present a strongly polynomial time algorithm for constructing a
maximum fractional packing of odd $T$-walks. For even integer capacities, our
algorithm constructs a packing that is half-integer. Additionally, if
$cap(\delta(v))$ is divisible by 4 for any $v \in V(G) - T$, our algorithm
constructs an integer packing.
  Second, we establish and prove the corresponding min-max relation.
  Third, if $G$ is inner Eulerian (i.e. degrees of all nodes in $V(G) - T$ are
even) and $cap(e) = 2$ for all $e \in E$, we show that there exists an integer
packing of odd $T$-trails (i.e. odd $T$-walks with no repeated edges) of the
same value as in case of odd $T$-walks, and this packing can be found in
polynomial time.
  To achieve the above goals, we establish a connection between packings of odd
$T$-walks and $T$-trails and certain multiflow problems in undirected and
bidirected graphs.


  The spectroscopy properties and angular momentum geometry for the wobbling
motion of a simple triaxial rotor are investigated within the triaxial rotor
model up to spin $I=40\hbar$. The obtained exact solutions of energy spectra
and reduced quadrupole transition probabilities are compared to the approximate
analytic solutions by harmonic approximation formula and Holstein-Primakoff
formula. It is found that the low lying wobbling bands can be well described by
the analytic formulas. The evolution of the angular momentum geometry as well
as the $K$-distribution with respect to the rotation and the wobbling phonon
excitation are studied in detail. It is demonstrated that with the increasing
of wobbling phonon number, the triaxial rotor changes its wobbling motions
along the axis with the largest moment of inertia to the axis with the smallest
moment of inertia. In this process, a specific evolutionary track that can be
used to depict the motion of a triaxial rotating nuclei is proposed.


  Quantum corrections coming from massless fields conformally coupled with
gravity are studied, in order to see if they can lead to avoidance of the
annoying Big Rip singularity which shows up in a flat
Friedmann-Robertson-Walker universe filled with dark energy and modeled by a
scalar phantom field. The dynamics of the model are discussed for all values of
the two parameters, named $\alpha>0$ and $\beta<0$, corresponding to the
regularization process. The new results are compared with the ones obtained in
\cite{hae11} previously, where dark energy was modeled by means of a phantom
fluid with equation of state $P=\omega\rho$, with $\omega<-1$.


  We measured organic volatiles (CH4, CH3OH, C2H6, H2CO), CO, and water in
comet 8P/Tuttle, a comet from the Oort cloud reservoir now in a short-period
Halley-type orbit. We compare its composition with two other comets in
Halley-type orbits, and with comets of the "organics-normal" and
"organics-depleted" classes. Chemical gradients are expected in the
comet-forming region of the proto-planetary disk, and an individual comet
should reflect its specific heritage. If Halley-type comets came from the inner
Oort cloud as proposed, we see no common characteristics that could distinguish
such comets from those that were stored in the outer Oort cloud.


  In this paper we prove that the generating series of the Poincare polynomials
of quasihomogeneous Hilbert schemes of points in the plane has a beautiful
decomposition into an infinite product. We also compute the generating series
of the numbers of quasihomogeneous components in a moduli space of sheaves on
the projective plane. The answer is given in terms of characters of the affine
Lie algebra $\hat{sl}_m$.


  Existing discourse formalisms use different taxonomies of discourse
relations, which require expert knowledge to understand, posing a challenge for
annotation and automatic classification. We show that discourse relations can
be effectively captured by some simple cognitively inspired dimensions proposed
by Sanders et al.(2018). Our experiments on cross-framework discourse relation
classification (PDTB & RST) demonstrate that it is possible to transfer
knowledge of discourse relations for one framework to another framework by
means of these dimensions, in spite of differences in discourse segmentation of
the two frameworks. This manifests the effectiveness of these dimensions in
characterizing discourse relations across frameworks. Ablation studies reveal
that different dimensions influence different types of discourse relations. The
patterns can be explained by the role of dimensions in characterizing and
distinguishing different relations. We also report our experimental results on
automatic prediction of these dimensions.


  We report on the results we obtained with XMM-Newton observations of HD49798
and BD+37 442, the only two sdO stars for which X-ray emission has been
observed so far. HD is a single-lined spectroscopic binary with orbital period
of 1.5 days. We could establish that its companion is a massive white dwarf
with M = 1.28 Msun, which makes it a candidate type Ia supernova progenitor; we
also detected a significant X-ray emission during the white-dwarf eclipse,
which could be X-ray emission of the sdO star itself. In the case of BD+37 442,
a luminous He-rich sdO that up to now was believed to be a single star, we
discovered soft X-ray emission with a periodicity of 19.2 s. This indicates
that also this hot subdwarf has a compact binary companion, either a white
dwarf or a neutron star, most likely powered by accretion from the wind of the
sdO star.


  We calculate the full counting statistics (FCS) of a subsystem energy in free
fermionic systems by means of the Grassmann variables. We demonstrate that the
generating function of these systems can be written as a determinant formula
with respect to the Hamiltonian couplings and by employing the Bell's
polynomials, we derive exact formulas for the subsystem energy moments. In
addition, we discuss the same quantities in the quantum XY spin chain, and we
demonstrate that at the critical regimes the fluctuations of the energy moments
decay like a power-law as we expect from the conformal field theory arguments,
while in non-critical regimes, the decay is exponential. Furthermore, we
discuss the full counting statistics of subsystem energy in the quantum XX
chain.


  This thesis is mainly about how to set up and carry out in a physically
meaningful way the idea of back-reaction, according to which dark energy could
be an effective source. There are, broadly speaking, two distinct approaches.
One is focused on how cosmological observables are affected by inhomogeneities,
while the other is focused on a theoretical description of the inhomogeneous
universe by means of a mean-field description. Both approaches, however, share
the idea of smoothing out inhomogeneities. We developed this duality in the
interpretation of the back-reaction by means of toy models based on the
Lemaitre-Tolman-Bondi solution of Einstein's equations. In particular we
focused on voids expanding faster than the background solution.


  A polyomino graph $H$ is a connected finite subgraph of the infinite plane
grid such that each finite face is surrounded by a regular square of side
length one and each edge belongs to at least one square. In this paper, we show
that if $K$ is a maximum resonant set of $H$, then $H-K$ has a unique perfect
matching. We further prove that the maximum forcing number of a polyomino graph
is equal to its Clar number. Based on this result, we have that the maximum
forcing number of a polyomino graph can be computed in polynomial time. We also
show that if $K$ is a maximal alternating set of $H$, then $H-K$ has a unique
perfect matching.


  In bosonic string theory, it is known that the Buscher rules for the
T-duality transformations receive quantum corrections at order $\alpha'$. In
this paper, we use the consistency of the gravity couplings on the D-brane
effective action at order $\alpha'$, with the above T-duality transformations
to find the B-field and the dilaton couplings. We show that these couplings are
fully consistent with the corresponding disk-level S-matrix elements in string
theory.


  We present a computational study into the adsorption properties of CO$_2$ on
amorphous and crystalline water surfaces under astrophysically relevant
conditions. Water and carbon dioxide are two of the most dominant species in
the icy mantles of interstellar dust grains and a thorough understanding of
their solid phase interactions at low temperatures is crucial for understanding
the structural evolution of the ices due to thermal segregation. In this paper,
a new H$_2$O-CO$_2$ interaction potential is proposed and used to model the
ballistic deposition of CO$_2$ layers on water ice surfaces, and to study the
individual binding sites at low coverages. Contrary to recent experimental
results, we do not observe CO$_2$ island formation on any type of water
substrate. Additionally, density functional theory calculations are performed
to assess the importance of induced electrostatic interactions.


  The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum
mechanics does not present the property of realism, the essence of the theorem
is the lack of a joint probability distributions for some experiment settings.
In this work, we exploit the information theoretic form of the theorem using
information measure instead of probabilistic measure and indicate that quantum
mechanics does not present such entropic realism neither. The entropic form of
Gleason's no-disturbance principle is developed and it turns out to be
characterized by the intersection of several entropic cones. Entropic
contextuality and entropic nonlocality are investigated in depth in this
framework. We show how one can construct monogamy relations using entropic cone
and basic Shannon-type inequalities. The general criterion for several entropic
tests to be monogamous is also developed, using the criterion, we demonstrate
that entropic nonlocal correlations are monogamous, entropic contextuality
tests are monogamous and entropic nonlocality and entropic contextuality are
also monogamous. Finally, we analyze the entropic monogamy relations for
multiparty and many-test case, which plays a crucial role in quantum network
communication.


  We study compact stars with hybrid equations of state consisting of a nuclear
outer region and two nested quark phases, each separated from the lower density
phase by a strong first-order phase transition. The stability of these models
is determined by calculating their radial oscillation modes with different
conversion rates between adjacent phases and hence junction conditions for the
modes at the phase separation interface between them. In the case when the
timescale of transition is faster than the period of oscillations, we recover
the traditional stability criterion implying that $\partial M/\partial\rho_c>0$
on the stable branch(es), where $M$ is the mass and $\rho_c$ is the central
density. In the opposite limit of slow conversion, we find stable stellar
multiplets beyond triplets consisting of stars that are stable by the usual
criterion plus slow-conversion (denoted by $s$) hybrid stars with $\partial
M/\partial\rho_c<0$ that are stabilized due to an alternative junction
condition on the fluid displacement field at the interface reflecting the slow
rate of conversion. We also study the properties of the reaction mode, the
radial mode that only exists for stars with rapid (abbreviated by $r$) phase
transitions, in stars with either two rapid phase transitions or alternating
rapid and slow phase transitions for the first time. The implications of
alternative junction conditions are also examined, with these conditions
generally being found to provide stability properties similar to those for a
slow conversion rate.


  The observation that SU(3)/SU(2) ~ S^5 implies the existence of a
particularly simple quantized topological action, or Wess-Zumino-Witten (WZW)
term. This action plays an important role in anomaly cancellation in extensions
of the Standard Model electroweak sector. A closed form is presented for the
action coupled to arbitrary gauge fields. The action is shown to be equivalent
to a limit of the WZW term for SU(3) x SU(3) / SU(3). By reduction of SU(3) x
U(1) / SU(2) x U(1) to SU(2) x U(1) / U(1), the construction gives a
topological derivation of the WZW term for the Standard Model Higgs field.


  We investigate the fractionalized Skyrmion excitations induced by spin-orbit
coupling in rotating and rapidly quenched spin-1 Bose-Einstein condensates. Our
results show that the fractionalized Skyrmion excitation depends on the
combination of spin-orbit coupling and rotation, and it originates from a
dipole structure of spin which is always embedded in three vortices constructed
by each condensate component respectively. When spin-orbit coupling is larger
than a critical value, the fractionalized Skyrmions encircle the center with
one or several circles to form a radial lattice, which occurs even in the
strong ferromagnetic/antiferromagnetic condensates. We can use both the
spin-orbit coupling and the rotation to adjust the radial lattice. The
realization and the detection of the fractionalized Skyrmions are compatible
with current experimental technology.


  In recent years, convolutional neural networks (CNNs) have been successfully
implemented to various image recognition applications, such as medical image
analysis, object detection, and image segmentation. Many studies and
applications have been working on improving the performance of CNN algorithms
and models. The strategies that aim to improve the performance of CNNs can be
grouped into three major approaches: (1) deeper and wider network architecture,
(2) automatic architecture search, and (3) convolutional attention block.
Unlike approaches (1) and (2), the convolutional attention block approach is
more flexible with lower cost. It enhances the CNN performance by extracting
more efficient features. However, the existing attention blocks focus on
enhancing the significant features, which lose some potential features in the
uncertainty information. Inspired by the test time augmentation and test-time
dropout approaches, we developed a novel convolutional uncertainty attention
block (CUAB) that can leverage the uncertainty information to improve CNN-based
models. The proposed module discovers potential information from the uncertain
regions on feature maps in computer vision tasks. It is a flexible functional
attention block that can be applied to any position in the convolutional block
in CNN models. We evaluated the CUAB with notable backbone models, ResNet and
ResNeXt, on a medical image segmentation task. The CUAB achieved a dice score
of 73% and 84% in pneumonia and pneumothorax segmentation, respectively,
thereby outperforming the original model and other notable attention
approaches. The results demonstrated that the CUAB can efficiently utilize the
uncertainty information to improve the model performance.


  Vanilla federated learning does not support learning in an online
environment, learning a personalized model on each client, and learning in a
decentralized setting. There are existing methods extending federated learning
in each of the three aspects. However, some important applications on
enterprise edge servers (e.g. online item recommendation at global scale)
involve the three aspects at the same time. Therefore, we propose a new
learning setting \textit{Decentralized Personalized Online Federated Learning}
that considers all the three aspects at the same time.
  In this new setting for learning, the first technical challenge is how to
aggregate the shared model parameters from neighboring clients to obtain a
personalized local model with good performance on each client. We propose to
directly learn an aggregation by optimizing the performance of the local model
with respect to the aggregation weights. This not only improves personalization
of each local model but also helps the local model adapting to potential data
shift by intelligently incorporating the right amount of information from its
neighbors. The second challenge is how to select the neighbors for each client.
We propose a peer selection method based on the learned aggregation weights
enabling each client to select the most helpful neighbors and reduce
communication cost at the same time. We verify the effectiveness and robustness
of our proposed method on three real-world item recommendation datasets and one
air quality prediction dataset.


  Observations of stellar activity cycles provide an opportunity to study
magnetic dynamos under many different physical conditions. Space-based
asteroseismology missions will soon yield useful constraints on the interior
conditions that nurture such magnetic cycles, and will be sensitive enough to
detect shifts in the oscillation frequencies due to the magnetic variations. We
derive a method for predicting these shifts from changes in the Mg II activity
index by scaling from solar data. We demonstrate this technique on the
solar-type subgiant beta Hyi, using archival International Ultraviolet Explorer
spectra and two epochs of ground-based asteroseismic observations. We find
qualitative evidence of the expected frequency shifts and predict the optimal
timing for future asteroseismic observations of this star.


  The relativistic amplitudes of pion photoproduction are evaluated by
dispersion relations at t=const. The imaginary parts of the amplitudes are
taken from the MAID model covering the absorption spectrum up to center-of-mass
energies W = 2.2 GeV. For sub-threshold kinematics the amplitudes are expanded
in powers of the two independent variables \nu and t related to energy and
momentum transfer. Subtracting the loop corrections from this power series
allows one to determine the counter terms of covariant baryon chiral
perturbation theory. The proposed continuation of the amplitudes into the
unphysical region provides a unique framework to derive the low-energy
constants to any given order as well as an estimate of the higher order terms
by global properties of the absorption spectrum.


  A three-dimensional granular system fluidized by vertical container
vibrations was studied using pulsed field gradient (PFG) NMR coupled with
one-dimensional magnetic resonance imaging (MRI). The system consisted of
mustard seeds vibrated vertically at 50 Hz, and the number of layers N_ell <= 4
was sufficiently low to achieve a nearly time-independent granular fluid. Using
NMR, the vertical profiles of density and granular temperature were directly
measured, along with the distributions of vertical and horizontal grain
velocities. The velocity distributions showed modest deviations from
Maxwell-Boltzmann statistics, except for the vertical velocity distribution
near the sample bottom which was highly skewed and non-Gaussian. Data taken for
three values of N_ell and two dimensionless accelerations Gamma=15,18 were fit
to a hydrodynamic theory, which successfully models the density and temperature
profiles including a temperature inversion near the free upper surface.


  The search for a top quark in association with a Z boson can be performed in
both top pair production as well as single top production. Targeting the three
lepton final state, the search can be used to identify the standard model (SM)
process of a single top quark associated with a Z boson and to search for
flavour changing neutral current (FCNC) interactions. The presented analysis
uses a data sample corresponding to an integrated luminosity of $19.7$
fb$^{-1}$ recorded by the CMS experiment at the LHC in proton collisions at
$\sqrt{s}=8$ TeV. The cross section for the SM tZq production is measured to be
$\sigma(tZq\rightarrow l\nu bl^+ l^- q)= 10^{+8}_{-7}$ fb with a significance
of $2.4 \sigma$. Exclusion limits at 95$\%$ confidence level on the branching
ratio of a top quark decaying to a Z boson and an up or charm quark are
determined to be $BR(t \rightarrow Zu) < 0.022\%$ and $BR(t \rightarrow Zc) <
0.049\%$ respectively.


  Studies of stellar magnetism at the pre-main sequence phase can provide
important new insights into the detailed physics of the late stages of star
formation, and into the observed properties of main sequence stars. This is
especially true at intermediate stellar masses, where magnetic fields are
strong and globally organised, and therefore most amenable to direct study.
This talk reviews recent high-precision ESPaDOnS observations of pre-main
sequence Herbig Ae-Be stars, which are yielding qualitatively new information
about intermediate-mass stars: the origin and evolution of their magnetic
fields, the role of magnetic fields in generating their spectroscopic activity
and in mediating accretion in their late formative stages, and the factors
influencing their rotational angular momentum.


  Following a recently manifested guide of how to team up infrared transparency
and high electrical conductivity within semimetal materials [C. Cui $et$ $al.$
Prog. Mater. Sci. 2023, 136, 101112], we evaluate an applicability of the
calcium digermanide (CaGe$_2$) thin film electrodes for the advanced Ge-based
optical devices. Rigorous growth experiments were conducted to define the
optimal annealing treatment and thickness of the Ca-Ge mixture for producing
stable CaGe$_2$ layers with high figure of merit (FOM) as transparent
conducting material. Ab-initio electronic band structure calculations and
optical modeling confirmed CaGe$_2$ semimetal nature, which is responsible for
a demonstrated high FOM. To test CaGe$_2$ electrodes under actual conditions, a
planar Ge photodetector (PD) with metal-semiconductor-metal structure was
fabricated, where CaGe$_2$/Ge interface acts as Schottky barrier. The resulting
Ge PD with semimetal electrodes outperformed commercially available Ge devices
in terms of both photoresponse magnitude and operated spectral range. Moreover,
by using femtosecond-laser projection lithography, a mesh CaGe$_2$ electrode
with the relative broadband transmittance of 90\% and sheet resistance of 20
$\Omega$/sq. was demonstrated, which further enhanced Ge PD photoresponse.
Thus, obtained results suggest that CaGe$_2$ thin films have a great potential
in numerous applications promoting the era of advanced Ge optoelectronics.


  A statistical study of 77 solar active regions (ARs) is conducted to
investigate the existence of identifiable correlations between the subsurface
structural disturbances and the activity level of the active regions. The
disturbances examined in this study are $<|\delta \Gamma_1/\Gamma_1|>$,
$<|\delta c^2/c^2|>$, and $<|\delta c^2/c^2-\delta \Gamma_1/\Gamma_1|>$. where
$\Gamma_1$ and $c$ are the thermodynamic properties of first adiabatic index
and sound speed modified by magnetic field, respectively. The averages are over
three depth layers: $0.975-0.98 R_\odot$, $0.98-0.99 R_\odot$ and $0.99-0.995
R_\odot$ to represent the structural disturbances in that layer. The level of
the surface magnetic activity is measured by the Magnetic Activity Index (MAI)
of active region and the relative and absolute MAI differences (rdMAI and dMAI)
between the active and quiet regions. The eruptivity of each active region is
quantified by its Flare Index, total number of coronal mass ejections (CMEs),
and total kinetic energy of the CMEs. The existence and level of the
correlations are evaluated by scatter plots and correlation coefficients. No
definitive correlation can be claimed from the results. While a weak positive
trend is visible between dMAI and $<|\delta \Gamma_1/\Gamma_1|>$ and $<|\delta
c^2/c^2|>$ in the layer $0.975-0.98 R_\odot$, their correlation levels, being
approximately 0.6, are not sufficiently high to justify the correlation. Some
subsurface disturbances are seen to increase with eruptivity indices among ARs
with high eruptivity. The statistical significance of such trend, however,
cannot be ascertained due to the small number of very eruptive ARs in our
sample.


  Many famous graphs are edge-primitive, for example, the Heawood graph, the
Tutte--Coxeter graph and the Higman--Sims graph. In this paper we
systematically analyse edge-primitive and edge-quasiprimitive graphs via the
O'Nan--Scott Theorem to determine the possible edge and vertex actions of such
graphs. Many interesting examples are given and we also determine all
$G$-edge-primitive graphs for $G$ an almost simple group with socle $PSL(2,q)$.


  It is well known that the dynamics of a quantum system is always
non-adiabatic in passage through a quantum critical point and the defect
density in the final state following a quench shows a power-law scaling with
the rate of quenching. However, we propose here a possible situation where the
dynamics of a quantum system in passage across quantum critical regions is
adiabatic and the defect density decays exponentially. This is achieved by
incorporating additional interactions which lead to quantum critical behavior
and gapless phases but do not participate in the time evolution of the system.
To illustrate the general argument, we study the defect generation in the
quantum critical dynamics of a spin-1/2 anisotropic quantum XY spin chain with
three spin interactions and a linearly driven staggered magnetic field.


  We generalize Givental's Theorem for complete intersections in smooth toric
varieties in the Fano case. In particular, we find Gromov--Witten invariants of
Fano varieties of dimension $\geq 3$, which are complete intersections in
weighted projective spaces and singular toric varieties. We generalize the
Riemann-Roch equations to weighted projective spaces. We compute counting
matrices of smooth Fano threefolds with Picard group Z and anticanonical
degrees 2, 8, and 16.


  In this paper we study conjugacy separability of subdirect products of two
free (or hyperbolic) groups. We establish necessary and sufficient criteria and
apply them to fibre products to produce a finitely presented group $G_1$ in
which all finite index subgroups are conjugacy separable, but which has an
index $2$ overgroup that is not conjugacy separable. Conversely, we construct a
finitely presented group $G_2$ which has a non-conjugacy separable subgroup of
index $2$ such that every finite index normal overgroup of $G_2$ is conjugacy
separable. The normality of the overgroup is essential in the last example, as
such a group $G_2$ will always posses an index $3$ overgroup that is not
conjugacy separable.
  Finally, we characterize $p$-conjugacy separable subdirect products of two
free groups, where $p$ is a prime. We show that fibre products provide a
natural correspondence between residually finite $p$-groups and $p$-conjugacy
separable subdirect products of two non-abelian free groups. As a consequence,
we deduce that the open question about the existence of an infinite finitely
presented residually finite $p$-group is equivalent to the question about the
existence of a finitely generated $p$-conjugacy separable full subdirect
product of infinite index in the direct product of two free groups.


  The analysis of fairness in process mining is a significant aspect of
data-driven decision-making, yet the advancement in this field is constrained
due to the scarcity of event data that incorporates fairness considerations. To
bridge this gap, we present a collection of simulated event logs, spanning four
critical domains, which encapsulate a variety of discrimination scenarios. By
simulating these event logs with CPN Tools, we ensure data with known ground
truth, thereby offering a robust foundation for fairness analysis. These logs
are made freely available under the CC-BY-4.0 license and adhere to the XES
standard, thereby assuring broad compatibility with various process mining
tools. This initiative aims to empower researchers with the requisite resources
to test and develop fairness techniques within process mining, ultimately
contributing to the pursuit of equitable, data-driven decision-making
processes.


  We present 237 new spectroscopically confirmed pre-main-sequence K and M-type
stars in the young Upper Scorpius subgroup of the Sco-Cen association, the
near- est region of recent massive star formation. Using the Wide-Field
Spectrograph at the Australian National University 2.3 m telescope at Siding
Spring, we observed 397 kinematically and photometrically selected candidate
members of Upper Scorpius, and identified new members by the presence of
Lithium absorption. The HR-diagram of the new members shows a spread of ages,
ranging from ~3-20 Myr, which broadly agrees with the current age estimates of
~5-10 Myr. We find a significant range of Li 6708 equivalent widths among the
members, and a minor dependence of HR-diagram position on the measured
equivalent width of the Li 6708A line, with members that appear younger having
more Lithium. This could indicate the presence of either popu- lations of
different age, or a spread of ages in Upper Scorpius. We also use Wide-Field
Infrared Survey Explorer data to infer circumstellar disk presence in 25 of the
members on the basis of infrared excesses, including two candidate transition
disks. We find that 11.2+-3.4% of the M0-M2 spectral type (0.4-0.8 M_sun) Upper
Sco stars display an excess that indicates the presence of a gaseous disk.


  Learning the distance metric between pairs of examples is of great importance
for learning and visual recognition. With the remarkable success from the state
of the art convolutional neural networks, recent works have shown promising
results on discriminatively training the networks to learn semantic feature
embeddings where similar examples are mapped close to each other and dissimilar
examples are mapped farther apart. In this paper, we describe an algorithm for
taking full advantage of the training batches in the neural network training by
lifting the vector of pairwise distances within the batch to the matrix of
pairwise distances. This step enables the algorithm to learn the state of the
art feature embedding by optimizing a novel structured prediction objective on
the lifted problem. Additionally, we collected Online Products dataset: 120k
images of 23k classes of online products for metric learning. Our experiments
on the CUB-200-2011, CARS196, and Online Products datasets demonstrate
significant improvement over existing deep feature embedding methods on all
experimented embedding sizes with the GoogLeNet network.


  Decentralized finance (DeFi) protocols are crypto projects developed on the
blockchain to manage digital assets. Attacks on DeFi have been frequent and
have resulted in losses exceeding \$77 billion. However, detection methods for
malicious DeFi events are still lacking. In this paper, we propose DeFiTail,
the first framework that utilizes deep learning to detect access control and
flash loan exploits that may occur on DeFi. Since the DeFi protocol events
involve invocations with multi-account transactions, which requires execution
path unification with different contracts. Moreover, to mitigate the impact of
mistakes in Control Flow Graph (CFG) connections, we validate the data path by
employing the symbolic execution stack. Furthermore, we feed the data paths
through our model to achieve the inspection of DeFi protocols. Experimental
results indicate that DeFiTail achieves the highest accuracy, with 98.39% in
access control and 97.43% in flash loan exploits. DeFiTail also demonstrates an
enhanced capability to detect malicious contracts, identifying 86.67% accuracy
from the CVE dataset.


  For an integer $k\geq 1$, the objective of \textsc{$k$-Geodesic Center} is to
find a set $\mathcal{C}$ of $k$ isometric paths such that the maximum distance
between any vertex $v$ and $\mathcal{C}$ is minimised. Introduced by Gromov,
\emph{$\delta$-hyperbolicity} measures how treelike a graph is from a metric
point of view. Our main contribution in this paper is to provide an additive
$O(\delta)$-approximation algorithm for \textsc{$k$-Geodesic Center} on
$\delta$-hyperbolic graphs. On the way, we define a coarse version of the
pairing property introduced by Gerstel \& Zaks (Networks, 1994) and show it
holds for $\delta$-hyperbolic graphs. This result allows to reduce the
\textsc{$k$-Geodesic Center} problem to its rooted counterpart, a main idea
behind our algorithm. We also adapt a technique of Dragan \& Leitert, (TCS,
2017) to show that for every $k\geq 1$, $k$-\textsc{Geodesic Center} is NP-hard
even on partial grids.


  STEM (Science, Technology, Engineering, and Mathematics) fields have become
increasingly central to U.S. economic competitiveness and growth. The shortage
in the STEM workforce has brought promoting STEM education upfront. The rapid
growth of social media usage provides a unique opportunity to predict users'
real-life identities and interests from online texts and photos. In this paper,
we propose an innovative approach by leveraging social media to promote STEM
education: matching Twitter college student users with diverse LinkedIn STEM
professionals using a ranking algorithm based on the similarities of their
demographics and interests. We share the belief that increasing STEM presence
in the form of introducing career role models who share similar interests and
demographics will inspire students to develop interests in STEM related fields
and emulate their models. Our evaluation on 2,000 real college students
demonstrated the accuracy of our ranking algorithm. We also design a novel
implementation that recommends matched role models to the students.


  The perfect fluid limit can be obtained from the Boltzmann equation in the
limit of vanishing Knudsen number. By treating the collision term in an
implicit manner, the implicit-explicit (IMEX) time stepping scheme allows this
limit to be achieved at finite values of the time step. We consider the 9th
order monotonicity-preserving (MP-9) scheme to implement the advection, which
is treated explicitly in the IMEX approach. We reduce the computational costs
using reduced distribution functions, which also permits the adiabatic index to
be varied. We validate the capabilities of our model by considering the
propagation of shock waves in one-dimensional and two-dimensional setups.


  The Kantowski-Sachs cosmological model sourced by a Skyrme field and a
cosmological constant is considered in the framework of General Relativity.
Assuming a constant radial profile function for the hedgehog ansatz, the Skyrme
contribution to Einstein equations is shown to be equivalent to an anisotropic
fluid. Using dynamical system techniques, a qualitative analysis of the
cosmological equations is presented. Physically interesting features of the
model such as isotropization, bounce and recollapse are discussed.


  The radiation dynamics of optical emitters can be manipulated by properly
designed material structures providing high local density of photonic states, a
phenomenon often referred to as the Purcell effect. Plasmonic nanorod
metamaterials with hyperbolic dispersion of electromagnetic modes are believed
to deliver a significant Purcell enhancement with both broadband and
non-resonant nature. Here, we have investigated finite-size cavities formed by
nanorod metamaterials and shown that the main mechanism of the Purcell effect
in these hyperbolic resonators originates from the cavity hyperbolic modes,
which in a microscopic description stem from the interacting cylindrical
surface plasmon modes of the finite number of nanorods forming the cavity. It
is found that emitters polarized perpendicular to the nanorods exhibit strong
decay rate enhancement, which is predominantly influenced by the rod length. We
demonstrate that this enhancement originates from Fabry-Perot modes of the
metamaterial cavity. The Purcell factors, delivered by those cavity modes,
reach several hundred, which is 4-5 times larger than those emerging at the
epsilon near zero transition frequencies. The effect of enhancement is less
pronounced for dipoles, polarized along the rods. Furthermore, it was shown
that the Purcell factor delivered by Fabry-Perot modes follows the dimension
parameters of the array, while the decay rate in the epsilon near-zero regime
is almost insensitive to geometry. The presented analysis shows a possibility
to engineer emitter properties in the structured metamaterials, addressing
their microscopic structure.


  On-demand and efficient storage of photons is an essential element in quantum
information processing and long-distance quantum communication. Most of the
quantum memory protocols require bulk systems in order to store photons.
However, with the advent of integrated photonic chip platforms for quantum
information processing, on-chip quantum memories are highly sought after. In
this paper, we propose a protocol for multi-mode photonic quantum memory using
only single-atom-cavity setup. We show that a single atom containing a
frequency comb coupled to an optical cavity can store photons efficiently.
Further, this scheme can also be used to store polarization states of light. As
examples, we show that the Rubidium and Cesium atoms coupled to nanophotonic
waveguide cavities can serve as promising candidates to realize our scheme.
This provides a possibility of a robust and efficient on-chip quantum memory to
be used in integrated photonic chips.


  We establish a relationship between the Small-World behavior found in complex
networks and a family of Random Walks trajectories using, as a linking bridge,
a maze iconography. Simple methods to generate mazes using Random Walks are
discussed along with related issues and it is explained how to interpret mazes
as graphs and loops as shortcuts. Small-World behavior was found to be
non-logarithmic but power-law in this model, we discuss the reason for this
peculiar scaling


  The analysis of domain wall dynamics is often simplified to one dimensional
physics. For domain walls in thin films, more realistic approaches require the
description as two dimensional objects. This includes the study of vortices and
curvatures along the domain walls as well as the influence of boundary effects.
Here we provide a theory in terms of soft modes that allows to analytically
study the physics of extended domain walls and their stability. By considering
irregular shaped skyrmions as closed domain walls, we analyze their plasticity
and compare their dynamics with those of circular skyrmions. Our theory
directly provides an analytical description of the the excitation modes of
magnetic skyrmions, previously only accessible by sophisticated micromagnetic
numerical calculations and spectral analysis. These analytical expressions
provide the scaling behaviour of the different physics on parameters that
experiments can test.


  We extend to the fermionic spin-1/2 case earlier work on quantum amplitudes
arising from gravitational collapse to a black hole. Boundary data are
specified on initial and final asymptotically-flat space-like hypersurfaces
$\Sigma_{I,F}$, separated by a Lorentzian proper-time interval $T$, measured at
spatial infinity. Following Feynman's $+i\epsilon$ prescription, one makes the
problem well-posed by rotating $T$ into the complex: $T\to{\mid}T{\mid}
\exp(-i\theta)$, with $0<\theta\leq\pi/2$. After calculating the amplitude for
$\theta>0$, one takes the 'Lorentzian limit' $\theta\to 0_+$. In this paper, we
treat quantum amplitudes for the case of fermionic massless spin-1/2 (neutrino)
final boundary data; working in the holomorphic representation, we take these
boundary data to be odd elements of a Grassmann algebra. Making use of boundary
conditions originally developed for local supersymmetry, we find that this
fermionic case can be treated in a way which parallels the bosonic case. With
these boundary conditions, for $\theta > 0$, one obtains a unique fermionic
classical solution, and we calculate its classical action as a functional of
the fermionic data on the late-time surface $\Sigma_F$; the quantum amplitude
follows straightforwardly from this.


  Several physically inspired problems have been proven undecidable; examples
are the spectral gap problem and the membership problem for quantum
correlations. Most of these results rely on reductions from a handful of
undecidable problems, such as the halting problem, the tiling problem, the Post
correspondence problem or the matrix mortality problem. All these problems have
a common property: they have an NP-hard bounded version. This work establishes
a relation between undecidable unbounded problems and their bounded NP-hard
versions. Specifically, we show that NP-hardness of a bounded version follows
easily from the reduction of the unbounded problems. This leads to new and
simpler proofs of the NP-hardness of bounded version of the Post correspondence
problem, the matrix mortality problem, the positivity of matrix product
operators, the reachability problem, the tiling problem, and the ground state
energy problem. This work sheds light on the intractability of problems in
theoretical physics and on the computational consequences of bounding a
parameter.


  Let $M$ be a compact $n$-dimensional Riemannian manifold with nonnegative
Ricci curvature and mean convex boundary $\partial M$. Assume that the mean
curvature $H$ of the boundary $\partial M$ satisfies $H \geq (n-1) k >0$ for
some positive constant $k$. In this paper, we prove that the distance function
$d$ to the boundary $\partial M$ is bounded from above by $\frac{1}{k}$ and the
upper bound is achieved if and only if $M$ is isometric to an $n$-dimensional
Euclidean ball of radius $\frac{1}{k}$.


  We investigate the limiting behavior of the Navier-Stokes-Cahn-Hilliard model
for binary-fluid flows as the diffuse-interface thickness passes to zero, in
the presence of fluid-fluid-solid contact lines. Allowing for motion of such
contact lines relative to the solid substrate is required to adequately model
multi-phase and multi-species fluid transport past and through solid media.
Even though diffuse-interface models provide an inherent slip mechanism through
the mobility-induced diffusion, this slip vanishes as the interface thickness
and mobility parameter tend to zero in the so-called sharp-interface limit. The
objective of this work is to present dynamic wetting and generalized Navier
boundary conditions for diffuse-interface models that are consistent in the
sharp-interface limit. We concentrate our analysis on the prototypical
binary-fluid Couette-flow problems. To verify the consistency of the
diffuse-interface model in the limit of vanishing interface thickness, we
provide reference limit solutions of a corresponding sharp-interface model. For
parameter values both at and away from the critical viscosity ratio, we present
and compare the results of both the diffuse- and sharp-interface models. The
close match between both model results indicates that the considered test case
lends itself well as a benchmark for further research.


  A key objective of the ESA Gaia satellite is the realization of a
quasi-inertial reference frame at visual wavelengths by means of global
astrometric techniques. This requires an accurate mathematical and numerical
modeling of relativistic light propagation, as well as double-blind-like
procedures for the internal validation of the results, before they are released
to the scientific community at large. Aim of this work is to specialize the
Time Transfer Functions (TTF) formalism to the case of the Gaia observer and
prove its applicability to the task of Global Sphere Reconstruction (GSR), in
anticipation of its inclusion in the GSR system, already featuring the suite of
RAMOD models, as an additional semi-external validation of the forthcoming Gaia
baseline astrometric solutions. We extend the current GSR framework and
software infrastructure (GSR2) to include TTF relativistic observation
equations compatible with Gaia's operations. We use simulated data generated by
the Gaia Data Reduction and Analysis Consortium (DPAC) to obtain different
least-squares estimations of the full stellar spheres and gauge results. These
are compared to analogous solutions obtained with the current RAMOD model in
GSR2 and to the catalog generated with GREM, the model baselined for Gaia and
used to generate the DPAC synthetic data. Linearized least-squares TTF
solutions are based on spheres of about 132,000 primary stars uniformly
distributed on the sky and simulated observations spanning the entire 5-yr
range of Gaia's nominal operational lifetime. The statistical properties of the
results compare well with those of GREM. Finally, comparisons to RAMOD@GSR2
solutions confirmed the known lower accuracy of that model and allowed us to
establish firm limits on the quality of the linearization point outside of
which an iteration for non-linearity is required for its proper convergence.


  We establish the stability of solutions to the entropically regularized
optimal transport problem with respect to the marginals and the cost function.
The result is based on the geometric notion of cyclical invariance and inspired
by the use of $c$-cyclical monotonicity in classical optimal transport. As a
consequence of stability, we obtain the wellposedness of the solution in this
geometric sense, even when all transports have infinite cost. More generally,
our results apply to a class of static Schr\"odinger bridge problems including
entropic optimal transport.


  We introduce a new method based on nonnegative matrix factorization, Neural
NMF, for detecting latent hierarchical structure in data. Datasets with
hierarchical structure arise in a wide variety of fields, such as document
classification, image processing, and bioinformatics. Neural NMF recursively
applies NMF in layers to discover overarching topics encompassing the
lower-level features. We derive a backpropagation optimization scheme that
allows us to frame hierarchical NMF as a neural network. We test Neural NMF on
a synthetic hierarchical dataset, the 20 Newsgroups dataset, and the MyLymeData
symptoms dataset. Numerical results demonstrate that Neural NMF outperforms
other hierarchical NMF methods on these data sets and offers better learned
hierarchical structure and interpretability of topics.


  The prediction of climate change and its impact on extreme weather events is
one of the great societal and intellectual challenges of our time. The first
part of the problem is to make the distinction between weather and climate. The
second part is to understand the dynamics of the fluctuations of the physical
variables. The third part is to predict how the variances of the fluctuations
are affected by statistical correlations in their fluctuating dynamics. This
paper investigates a framework called LA SALT which can meet all three parts of
the challenge for the problem of climate change. As a tractable example of this
framework, we consider the Euler--Boussinesq (EB) equations for an
incompressible stratified fluid flowing under gravity in a vertical plane with
no other external forcing. All three parts of the problem are solved for this
case. In fact, for this problem, the framework also delivers global
well-posedness of the dynamics of the physical variables and closed dynamical
equations for the moments of their fluctuations. Thus, in a well-posed
mathematical setting, the framework developed in this paper shows that the mean
field dynamics combines with an intricate array of correlations in the
fluctuation dynamics to drive the evolution of the mean statistics. The results
of the framework for 2D EB model analysis define its climate, as well as
climate change, weather dynamics, and change of weather statistics, all in the
context of a model system of SPDEs with unique global strong solutions.


  In this paper, we present a new distributional identity for the solutions of
elliptic equations involving Hardy potentials with singularities located on the
boundary of the domain. Then we use it to obtain the boundary isolated singular
solutions of nonhomogeneous problems.


  We have measured peak apparent speeds of 25.6 +/- 7.0c, 25.6 +/- 4.4c, and
28.2 +/- 6.6c in the jets of 0235+164, 0827+243, and 1406-076, respectively,
based on six epochs of high-sensitivity VLBA observations at 22 and 43 GHz
during 2002 and 2003 (H_{0}=71 km/(s Mpc), Omega_{m}=0.27, and
Omega_{Lambda}=0.73). These blazars had been identified as potentially having
apparent speeds exceeding 40c in an earlier VLBA survey of EGRET blazars by
Jorstad et al. We therefore confirm (with high confidence in 0827+243, and
lower confidence in 0235+164 and 1406-076) the presence of highly relativistic
pattern speeds in these three jets, although not at the >40c levels reported by
Jorstad et al. The lower limit to the bulk Lorentz factor implied by the
observed apparent speeds is Gamma>25-30 in these three sources, if the pattern
speeds are equal to or slower than the bulk flow speed.


  Graph density profiles are fundamental objects in extremal combinatorics.
Very few profiles are fully known, and all are two-dimensional. We show that
even in high dimensions ratios of graph densities and numbers often form the
power-sum profile (the limit of the image of the power-sum map) studied
recently by Acevedo, Blekherman, Debus and Riener. Our choice of graphs is
motivated by recent work by Blekherman, Raymond and Wei on undecidability of
polynomial inequalities in graph densities. While the ratios do not determine
the complete density profile, they contain high-dimensional information. For
instance, to reconstruct the density profile of $4k$-cycles from our results,
one needs to solve only one-parameter extremal problems, for any number of
$4k$-cycles.


  We prove an existence theorem for the Cauchy problem on a characteristic cone
for the vacuum Einstein equations.


  We explicitly determine all the relative generalized Hamming weights of
affine Cartesian codes using the notion of footprints and results from extremal
combinatorics. This generalizes the previous works on the determination of
relative generalized Hamming weights of Reed-Muller codes by Geil and Martin,
as well as the determination of all the generalized Hamming weights of the
affine Cartesian codes by Beelen and Datta.


  Time-reversal had always been assumed to be a symmetry of physics at the
fundamental level. In this paper we will explore the violations of
time-reversal symmetry at the fundamental level and the consequences on
thermodynamic systems. First, we will argue from from current physics that the
universe dynamics is not time-reversal invariant. Second, we will argue that
any thermodynamic system cannot be isolated from the rest of the universe. We
then discuss how these two make the dynamics of thermodynamics systems very
weakly irreversible at the classical and quantum level. Since time-reversal is
no longer a symmetry of realistic systems, the problem of how macroscopic
irreversibility arises from microscopic reversibility becomes irrelevant
becomes there is no longer microscopic reversibility. At the classical level of
thermodynamics system, we show that the H Theorem of Boltzmann is still valid
even without microscopic reversibility. We do this by deriving a modified H
Theorem, which still shows entropy monotonically increasing. At the quantum
level, we show the the effect of CP violation, small irreversible changes on
the internal states of the nuclear and atomic energy levels of thermodynamic
systems. Thus, we remove Loschmidts's objection to Boltzmann's ideas.


  The aim of this paper is to extend the aggregation convergence results given
in (Dacunha-Castelle and Fermin 2005, Dacunha-Castelle and Fermin 2008) to
doubly stochastic linear and nonlinear processes with weakly dependent
innovations. First, we introduce a weak dependence notion for doubly stochastic
processes, based in the weak dependence definition given in (Doukhan and
Louhichi 1999), and we exhibe several models satisfying this notion, such as:
doubly stochastic Volterra processes and doubly stochastic Bernoulli scheme
with weakly dependent innovations. Afterwards we derive a central limit theorem
for the partial aggregation sequence considering weakly dependent doubly
stochastic processes. Finally, show a new SLLN for the covariance function of
the partial aggregation process in the case of doubly stochastic Volterra
processes with interactive innovations.
  Keywords: Aggregation, weak dependence, doubly stochastic processes, Volterra
processes, Bernoulli shift, TCL, SLLN.


  It is suggested that the individual outcomes of a measurement process can be
understood within standard quantum mechanics in terms of the measuring
apparatus, treated as a quantum computer, executing Grover's search algorithm.


  Gravitational collapse of a shell of charged dust surrounded by the phantom
dark energy is probed by the minimal area surface, which is dual to probe the
thermalization in the boundary quantum field by expectation values of Wilson
loop in the framework of the AdS/CFT correspondence. We investigated mainly the
effect of the phantom dark energy parameter and chemical potential on the
thermalization. The result shows that the smaller the phantom dark energy
parameter is, the easier the plasma thermalizes as the chemical potential is
fixed, and the larger the chemical potential is, the harder the plasma
thermalizes as the dark energy parameter is fixed. We get the fitting function
of the thermalization curve and with it, the thermalization velocity and
thermalization acceleration are discussed.


  We prove the existence of uncountably many positive harmonic functions for
random walks on the euclidean lattice with non-zero drift, killed when leaving
two dimensional convex cones with vertex in 0. Our proof is an adaption of the
proof for the positive quadrant from [Ignatiouk-Robert, Loree]. We also make
the natural conjecture about the Martin boundary for general convex cones in
two dimensions. This is still an open problem and here we only indicate where
the proof technique for the positive quadrant breaks down.


  We go on with the definition of the theory of the non--Abelian two--tensor
fields and find the gauge transformation rules and curvature tensor for them.
To define the theory we use the surface {\it exponent} proposed in
hep--th/0503234. We derive the differential equation for the {\it exponent} and
make an attempt to give a matrix model formulation for it. We discuss
application of our constructions to the Yang--Baxter equation for integrable
models and to the String Field Theory.


  Histopathological images are widely used for the analysis of diseased (tumor)
tissues and patient treatment selection. While the majority of microscopy image
processing was previously done manually by pathologists, recent advances in
computer vision allow for accurate recognition of lesion regions with deep
learning-based solutions. Such models, however, usually require extensive
annotated datasets for training, which is often not the case in the considered
task, where the number of available patient data samples is very limited. To
deal with this problem, we propose a novel DeepCMorph model pre-trained to
learn cell morphology and identify a large number of different cancer types.
The model consists of two modules: the first one performs cell nuclei
segmentation and annotates each cell type, and is trained on a combination of 8
publicly available datasets to ensure its high generalizability and robustness.
The second module combines the obtained segmentation map with the original
microscopy image and is trained for the downstream task. We pre-trained this
module on the Pan-Cancer TCGA dataset consisting of over 270K tissue patches
extracted from 8736 diagnostic slides from 7175 patients. The proposed solution
achieved a new state-of-the-art performance on the dataset under consideration,
detecting 32 cancer types with over 82% accuracy and outperforming all
previously proposed solutions by more than 4%. We demonstrate that the
resulting pre-trained model can be easily fine-tuned on smaller microscopy
datasets, yielding superior results compared to the current top solutions and
models initialized with ImageNet weights. The codes and pre-trained models
presented in this paper are available at: https://github.com/aiff22/DeepCMorph


  In this paper, we construct a simple model for the complex heavy quark
potential which is defined through the Fourier transform of the static gluon
propagator. Besides the hard thermal loop resummed contribution, the gluon
propagator also includes a non-perturbative term induced by the dimension two
gluon condensate. Within the framework of thermal field theory, the real and
imaginary parts of the heavy quark potential are determined in a consistent way
without resorting to any extra assumption as long as the exact form of the
retarded/advanced gluon propagator is specified. The resulting potential model
has the desired asymptotic behaviors and reproduces the data from lattice
simulation reasonably well. By presenting a direct comparison with other
complex potential models on the market, we find the one proposed in this work
shows a significant improvement on the description of the lattice results,
especially for the imaginary part of the potential, in a temperature region
relevant to quarkonium studies.


  High-field electrical transport and point-contact tunneling spectroscopy were
used to investigate superconducting properties of the unique spinel oxide,
LiTi$_2$O$_{4-\delta}$ films with various oxygen content. We find that the
upper critical field $B_\mathrm{c2}$ gradually increases as more oxygen
impurities are brought into the samples by carefully tuning the deposition
atmosphere. It is striking that although the superconducting transition
temperature and energy gap are almost unchanged, an astonishing isotropic
$B_\mathrm{c2}$ up to $\sim$ 26 Tesla is observed in oxygen-rich sample, which
is doubled compared to the anoxic sample and breaks the Pauli limit. Such
anomalies of $B_\mathrm{c2}$ were rarely reported in other three dimensional
superconductors. Combined with all the anomalies, three dimensional spin-orbit
interaction induced by tiny oxygen impurities is naturally proposed to account
for the remarkable enhancement of $B_\mathrm{c2}$ in oxygen-rich
LiTi$_2$O$_{4-\delta}$ films. Such mechanism could be general and therefore
provides ideas for optimizing practical superconductors with higher
$B_\mathrm{c2}$.


  We obtain retarded Green's functions for massless scalar fields in the
background of near-extreme, near-horizon rotating charged black holes of
five-dimensional minimal gauged supergravity. The radial part of the
(separable) massless Klein-Gordon equation in such general black hole
backgrounds is Heun's equation, due to the singularity structure associated
with the three black hole horizons. On the other hand, we find the scaling
limit for the near-extreme, near-horizon background where the radial equation
reduces to a Hypergeometric equation whose $SL(2,{\bf R})^2$ symmetry signifies
the underlying two-dimensional conformal invariance, with the two sectors
governed by the respective Frolov-Thorne temperatures.


  We construct a general framework for deriving error bounds for conic
feasibility problems. In particular, our approach allows one to work with cones
that fail to be amenable or even to have computable projections, two previously
challenging barriers. For the purpose, we first show how error bounds may be
constructed using objects called one-step facial residual functions. Then, we
develop several tools to compute these facial residual functions even in the
absence of closed form expressions for the projections onto the cones. We
demonstrate the use and power of our results by computing tight error bounds
for the exponential cone feasibility problem. Interestingly, we discover a
natural example for which the tightest error bound is related to the
Boltzmann-Shannon entropy. We were also able to produce an example of sets for
which a H\"{o}lderian error bound holds but the supremum of the set of
admissible exponents is not itself an admissible exponent.


  The Polymer Quantization of the Fourier modes of the real scalar field is
studied within algebraic scheme. We replace the positive linear functional of
the standard Poincar\'e invariant quantization by a singular one. This singular
positive linear functional is constructed as mimicking the singular limit of
the complex structure of the Poincar\'e invariant Fock quantization. The
resulting symmetry group of such Polymer Quantization is the subgroup
$\mbox{SDiff}(\mathbb{R}^4)$ which is a subgroup of $\mbox{Diff}(\mathbb{R}^4)$
formed by spatial volume preserving diffeomorphisms. In consequence, this
yields an entirely different irreducible representation of the Canonical
Commutation Relations, non-unitary equivalent to the standard Fock
representation. We also compared the Poincar\'e invariant Fock vacuum with the
Polymer Fourier vacuum.


  In the maritime industry, the injection of air bubbles into the turbulent
boundary layer under the ship hull is seen as one of the most promising
techniques to reduce the overall fuel consumption. However, the exact mechanism
behind bubble drag reduction is unknown. Here we show that bubble drag
reduction in turbulent flow dramatically depends on the bubble size. By adding
minute concentrations (6 ppm) of the surfactant Triton X-100 into otherwise
completely unchanged strongly turbulent Taylor-Couette flow containing bubbles,
we dramatically reduce the drag reduction from more than 40% to about 4%,
corresponding to the trivial effect of the bubbles on the density and viscosity
of the liquid. The reason for this striking behavior is that the addition of
surfactants prevents bubble coalescence, leading to much smaller bubbles. Our
result demonstrates that bubble deformability is crucial for bubble drag
reduction in turbulent flow and opens the door for an optimization of the
process.


  We calculate the entanglement of a generalized elliptical vortex formed by
quantized radiation field, using Wigner quasiprobability distribution function
for such states. We find a critical squeezing parameter above which the
entanglement is less for higher vorticity, which is counter intuitive.


  Recent works showed that pressure-robust modifications of mixed finite
element methods for the Stokes equations outperform their standard versions in
many cases. This is achieved by divergence-free reconstruction operators and
results in pressure independent velocity error estimates which are robust with
respect to small viscosities. In this paper we develop a posteriori error
control which reflects this robustness.
  The main difficulty lies in the volume contribution of the standard
residual-based approach that includes the $L^2$-norm of the right-hand side.
However, the velocity is only steered by the divergence-free part of this
source term. An efficient error estimator must approximate this divergence-free
part in a proper manner, otherwise it can be dominated by the pressure error.
  To overcome this difficulty a novel approach is suggested that uses arguments
from the stream function and vorticity formulation of the Navier--Stokes
equations. The novel error estimators only take the $\mathrm{curl}$ of the
right-hand side into account and so lead to provably reliable, efficient and
pressure-independent upper bounds in case of a pressure-robust method in
particular in pressure-dominant situations. This is also confirmed by some
numerical examples with the novel pressure-robust modifications of the
Taylor--Hood and mini finite element methods.


  Capacitively coupled semiconductor spin qubits hold promise as the building
blocks of a scalable quantum computing architecture with long-range coupling
between distant qubits. However, the two-qubit gate fidelities achieved in
experiments to date have been severely limited by decoherence originating from
charge noise and hyperfine interactions with nuclear spins, and are currently
unacceptably low for any conceivable multi-qubit gate operations. Here, we
present control protocols that implement two-qubit entangling gates while
substantially suppressing errors due to both types of noise. These protocols
are obtained by making simple modifications to control sequences already used
in the laboratory and should thus be easy enough for immediate experimental
realization. Together with existing control protocols for robust single-qubit
gates, our results constitute an important step toward scalable quantum
computation using spin qubits in semiconductor platforms.


  We present a formulation of the coupling of vector multiplets to N=2
supergravity which is symplectic covariant (and thus is not based on a
prepotential) and uses superconformal tensor calculus. We do not start from an
action, but from the combination of the generalised Bianchi identities of the
vector multiplets in superspace, a symplectic definition of special Kahler
geometry, and the supersymmetric partners of the corresponding constraints.
These involve the breaking to super-Poincare symmetry, and lead to on-shell
vector multiplets. This symplectic approach gives the framework to formulate
vector multiplet couplings using a weaker defining constraint for special
Kahler geometry, which is an extension of older definitions of special Kahler
manifolds for some cases with only one vector multiplet.


  In this paper, we solve a longstanding open problem for determining the shape
of an obstacle from the knowledge of the electric (or magnetic) far field
pattern for the scattering of time-harmonic electromagnetic field. We show that
the electric (or magnetic) far field patten
${\mathbf{E}}^\infty(\boldsymbol{\beta}, {\boldsymbol{\alpha}}_0, k_0)$ (or
${\mathbf{H}}^\infty (\boldsymbol{\beta}, {\boldsymbol{\alpha}}_0, k_0)$),
known for all $\boldsymbol{\beta}\in {\mathbb S}^2$, where ${\mathbb {S}}^2$ is
the unit sphere in ${\mathbb{R}}^3$, ${\boldsymbol{\alpha}}_0\in
{\mathbb{S}}^2$ is fixed, $k_0>0$ is fixed, determines the obstacle $D$ and the
boundary condition on $\partial D$ uniquely. The boundary condition on
$\partial D$ is either the perfect conductor or the impedance one.


  We consider continuous semigroups of analytic functions $\{\Phi_t\}_{t\geq0}$
in the so-called Gordon-Hedenmalm class $\mathcal{G}$, that is, the family of
analytic functions $\Phi:\mathbb C_+\to \mathbb C_+$ giving rise to bounded
composition operators in the Hardy space of Dirichlet series $\mathcal{H}^2$.
We show that there is a one-to-one correspondence between continuous semigroups
$\{\Phi_{t}\}_{t\geq0}$ in the class $\mathcal G$ and strongly continuous
semigroups of composition operators $\{T_t\}_{t\geq0}$, where
$T_t(f)=f\circ\Phi_t$, $f\in\mathcal{H}^2$. We extend these results for the
range $p\in[1,\infty)$. For the case $p=\infty$, we prove that there is no
non-trivial strongly continuous semigroup of composition operators in
$\mathcal{H}^\infty$. We characterize the infinitesimal generators of
continuous semigroups in the class $\mathcal G$ as those Dirichlet series
sending $\mathbb C_{+}$ into its closure. Some dynamical properties of the
semigroups are obtained from a description of the Koenigs map of the semigroup.