  We are conducting a proper-motion survey for young brown dwarfs in the
Taurus-Auriga molecular cloud based on the Pan-STARRS1 3$\pi$ Survey. Our
search uses multi-band photometry and astrometry to select candidates, and is
wider (370 deg$^{2}$) and deeper (down to $\approx$3 M$_{\rm Jup}$) than
previous searches. We present here our search methods and spectroscopic
follow-up of our high-priority candidates. Since extinction complicates
spectral classification, we have developed a new approach using low-resolution
($R \approx 100$) near-infrared spectra to quantify reddening-free spectral
types, extinctions, and gravity classifications for mid-M to late-L ultracool
dwarfs ($\approx 100-3$ M$_{\rm Jup}$ in Taurus). We have discovered 25
low-gravity (VL-G) and the first 11 intermediate-gravity (INT-G) substellar
(M6-L1) members of Taurus, constituting the largest single increase of Taurus
brown dwarfs to date. We have also discovered 1 new Pleiades member and 13 new
members of the Perseus OB2 association, including a candidate very wide
separation (58 kAU) binary. We homogeneously reclassify the spectral types and
extinctions of all previously known Taurus brown dwarfs. Altogether our
discoveries have thus far increased the substellar census in Taurus by $\approx
40\%$ and added three more L-type members ($\approx 5-10$ M$_{\rm Jup}$). Most
notably, our discoveries reveal an older ($>$10 Myr) low-mass population in
Taurus, in accord with recent studies of the higher-mass stellar members. The
mass function appears to differ between the younger and older Taurus
populations, possibly due to incompleteness of the older stellar members or
different star formation processes.


  Topological states of matter such as quantum spin liquids (QSLs) are of great
interest because of their remarkable predicted properties including protection
of quantum information and the emergence of Majorana fermions. Such QSLs,
however, have proven difficult to identify experimentally. The most promising
approach is to study their exotic nature via the wave-vector and intensity
dependence of their dynamical response in neutron scattering. A major search
has centered on iridate materials which are proposed to realize the celebrated
Kitaev model on a honeycomb lattice - a prototypical topological QSL system in
two dimensions (2D). The difficulties of iridium for neutron measurements have,
however, impeded progress significantly. Here we provide experimental evidence
that a material based on ruthenium, {\alpha}-RuCl$_3$ realizes the same Kitaev
physics but is highly amenable to neutron investigation. Our measurements
confirm the requisite strong spin-orbit coupling, and a low temperature
magnetic order that matches the predicted phase proximate to the QSL. We also
show that stacking faults, inherent to the highly 2D nature of the material,
readily explain some puzzling results to date. Measurements of the dynamical
response functions, especially at energies and temperatures above that where
interlayer effects are manifest, are naturally accounted for in terms of
deconfinement physics expected for QSLs. Via a comparison to the recently
calculated dynamics from gauge flux excitations and Majorana fermions of the
pure Kitaev model we propose {\alpha}-RuCl$_3$ as the prime candidate for
experimental realization of fractionalized Kitaev physics.


  We discuss in which sense the so-called {\em regular pseudo-bosons}, recently
introduced by Trifonov and analyzed in some details by the author, are related
to ordinary bosons. We repeat the same analysis also for {\em pseudo-bosons},
and we analyze the role played by certain intertwining operators, which may be
bounded or not.


  The common pipeline in autonomous driving systems is highly modular and
includes a perception component which extracts lists of surrounding objects and
passes these lists to a high-level decision component. In this case, leveraging
the benefits of deep reinforcement learning for high-level decision making
requires special architectures to deal with multiple variable-length sequences
of different object types, such as vehicles, lanes or traffic signs. At the
same time, the architecture has to be able to cover interactions between
traffic participants in order to find the optimal action to be taken. In this
work, we propose the novel Deep Scenes architecture, that can learn complex
interaction-aware scene representations based on extensions of either 1) Deep
Sets or 2) Graph Convolutional Networks. We present the Graph-Q and DeepScene-Q
off-policy reinforcement learning algorithms, both outperforming
state-of-the-art methods in evaluations with the publicly available traffic
simulator SUMO.


  Recently there has been a growing interest in quantum gravity theories with
more than four derivatives, including both their quantum and classical aspects.
In this work we extend the recent results concerning the non-singularity of the
modified Newtonian potential to the most relevant case in which the propagator
has complex poles. The model we consider is Einstein-Hilbert action augmented
by curvature-squared higher-derivative terms which contain polynomials on the
d'Alembert operator. We show that the classical potential of these theories is
a real quantity and it is regular at the origin disregard the (complex or real)
nature or the multiplicity of the massive poles. The expression for the
potential is explicitly derived for some interesting particular cases. Finally,
the issue of the mechanism behind the cancellation of the singularity is
discussed; specifically we argue that the regularity of the potential can hold
even if the number of massive tensor modes and scalar ones is not the same.


  We study Killing tensors in the context of warped products and apply the
results to the problem of orthogonal separation of the Hamilton-Jacobi
equation. This work is motivated primarily by the case of spaces of constant
curvature where warped products are abundant. We first characterize Killing
tensors which have a natural algebraic decomposition in warped products. We
then apply this result to show how one can obtain the Killing-Stackel space
(KS-space) for separable coordinate systems decomposable in warped products.
This result in combination with Benenti's theory for constructing the KS-space
of certain special separable coordinates can be used to obtain the KS-space for
all orthogonal separable coordinates found by Kalnins and Miller in Riemannian
spaces of constant curvature. Next we characterize when a natural Hamiltonian
is separable in coordinates decomposable in a warped product by showing that
the conditions originally given by Benenti can be reduced. Finally we use this
characterization and concircular tensors (a special type of torsionless
conformal Killing tensor) to develop a general algorithm to determine when a
natural Hamiltonian is separable in a special class of separable coordinates
which include all orthogonal separable coordinates in spaces of constant
curvature.


  We study the representation capacity of deep hyperbolic neural networks
(HNNs) with a ReLU activation function. We establish the first proof that HNNs
can $\varepsilon$-isometrically embed any finite weighted tree into a
hyperbolic space of dimension $d$ at least equal to $2$ with prescribed
sectional curvature $\kappa<0$, for any $\varepsilon> 1$ (where $\varepsilon=1$
being optimal). We establish rigorous upper bounds for the network complexity
on an HNN implementing the embedding. We find that the network complexity of
HNN implementing the graph representation is independent of the representation
fidelity/distortion. We contrast this result against our lower bounds on
distortion which any ReLU multi-layer perceptron (MLP) must exert when
embedding a tree with $L>2^d$ leaves into a $d$-dimensional Euclidean space,
which we show at least $\Omega(L^{1/d})$; independently of the depth, width,
and (possibly discontinuous) activation function defining the MLP.


  We present the design and methodology for the large scale hybrid paper
recommender system used by Microsoft Academic. The system provides
recommendations for approximately 160 million English research papers and
patents. Our approach handles incomplete citation information while also
alleviating the cold-start problem that often affects other recommender
systems. We use the Microsoft Academic Graph (MAG), titles, and available
abstracts of research papers to build a recommendation list for all documents,
thereby combining co-citation and content based approaches. Tuning system
parameters also allows for blending and prioritization of each approach which,
in turn, allows us to balance paper novelty versus authority in recommendation
results. We evaluate the generated recommendations via a user study of 40
participants, with over 2400 recommendation pairs graded and discuss the
quality of the results using P@10 and nDCG scores. We see that there is a
strong correlation between participant scores and the similarity rankings
produced by our system but that additional focus needs to be put towards
improving recommender precision, particularly for content based
recommendations. The results of the user survey and associated analysis scripts
are made available via GitHub and the recommendations produced by our system
are available as part of the MAG on Azure to facilitate further research and
light up novel research paper recommendation applications.


  The stochastic Kronecker Graph model can generate large random graph that
closely resembles many real world networks. For example, the output graph has a
heavy-tailed degree distribution, has a (low) diameter that effectively remains
constant over time and obeys the so-called densification power law [1]. Aside
from this list of very important graph properties, one may ask for some
additional information about the output graph: What will be the expected number
of isolated vertices? How many edges, self loops are there in the graph? What
will be the expected number of triangles in a random realization? Here we try
to answer the above questions. In the first phase, we bound the expected values
of the aforementioned features from above. Next we establish the sufficient
conditions to generate stochastic Kronecker graph with a wide range of
interesting properties. Finally we show two phase transitions for the
appearance of edges and self loops in stochastic Kronecker graph.


  We construct embeddings of surface groups into the group of germs of analytic
diffeomorphisms in one variable.


  In this work, we show how to construct indistinguishability obfuscation from
subexponential hardness of four well-founded assumptions. We prove:
  Let $\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)$ be arbitrary
constants. Assume sub-exponential security of the following assumptions, where
$\lambda$ is a security parameter, and the parameters $\ell,k,n$ below are
large enough polynomials in $\lambda$:
  - The SXDH assumption on asymmetric bilinear groups of a prime order $p =
O(2^\lambda)$,
  - The LWE assumption over $\mathbb{Z}_{p}$ with subexponential
modulus-to-noise ratio $2^{k^\epsilon}$, where $k$ is the dimension of the LWE
secret,
  - The LPN assumption over $\mathbb{Z}_p$ with polynomially many LPN samples
and error rate $1/\ell^\delta$, where $\ell$ is the dimension of the LPN
secret,
  - The existence of a Boolean PRG in $\mathsf{NC}^0$ with stretch
$n^{1+\tau}$,
  Then, (subexponentially secure) indistinguishability obfuscation for all
polynomial-size circuits exists.


  The fractional heat operator $(\partial_t-\Delta_x)^s$ and Continuous Time
Random Walks (CTRWs) are interesting and sophisticated mathematical models that
can describe complex anomalous systems. In this paper, we prove asymptotic mean
value representation formulas for functions with respect to
$(\partial_t-\Delta_x)^s$ and we introduce new nonlocal, nonlinear parabolic
operators related to a tug-of-war which accounts for waiting times and
space-time couplings. These nonlocal, nonlinear parabolic operators and
equations can be seen as nonlocal versions of the evolutionary infinity Laplace
operator.


  In conventional FORC (First Order Reversal Curve) analysis of a magnetic
system, reversible and low-coercivity irreversible materials are treated as
being qualitatively different: the FORC distribution shows low-coercivity
materials but completely hides reversible (zero-coercivity) ones. This
distinction is artificial -- as the coercivity approaches zero, the physical
properties of an irreversible material change smoothly into those of a
reversible material. We have developed a method (called FORC+, implemented in
free software at http://MagVis.org) for displaying the reversible properties of
a system (a reversible switching-field distribution, R-SFD) together with the
irreversible ones (the usual FORC distribution), so that there is no sudden
discontinuity in the display when the coercivity becomes zero. We will define a
"FORC+ dataset" to include the usual FORC distribution, the R-SFD, the
saturation magnetization, and what we will call the "lost hysteron
distribution" (LHD) such that no information is lost -- the original FORC
curves can be exactly recovered from the FORC+ dataset. We also give some
examples of the application of FORC+ to real data -- it uses a novel
complementary-color display that minimizes the need for smoothing. In systems
which switch suddenly (thus having sharp structures in the FORC distribution)
direct display of un-smoothed raw data allows visualization of sharp structures
that would be washed out in a conventional smoothed FORC display. This is an
expanded version of paper GG-05, MMM-Intermag 2019, with a discrete derivation
of the FORC distribution (Eq. 1) and an additional example (Fig. 7).


  We study a simple model of a foraging animal that modifies the substrate on
which it moves. This substrate provides its only resource, and the forager
manage it by taking a limited portion at each visited site. The resource
recovers its value after the visit following a relaxation law. We study
different scenarios to analyze the efficiency of the managing strategy,
corresponding to control the bite size. We observe the non trivial emergence of
a home range, that is visited in a periodic way. The duration of the
corresponding cycles and the transient until it emerges is affected by the bite
size. Our results show that the most efficient use of the resource, measured as
the balance between gathering and travelled distance, corresponds to foragers
that take larger portions but without exhausting the resource. We also analyze
the use of space determining the number of attractors of the dynamics, and we
observe that it depends on the bite size and the recovery time of the resource.


  We propose a new complexity measure for Markov decision processes (MDPs), the
maximum expected hitting cost (MEHC). This measure tightens the closely related
notion of diameter [JOA10] by accounting for the reward structure. We show that
this parameter replaces diameter in the upper bound on the optimal value span
of an extended MDP, thus refining the associated upper bounds on the regret of
several UCRL2-like algorithms. Furthermore, we show that potential-based reward
shaping [NHR99] can induce equivalent reward functions with varying
informativeness, as measured by MEHC. We further establish that shaping can
reduce or increase MEHC by at most a factor of two in a large class of MDPs
with finite MEHC and unsaturated optimal average rewards.


  Set prediction is about learning to predict a collection of unordered
variables with unknown interrelations. Training such models with set losses
imposes the structure of a metric space over sets. We focus on stochastic and
underdefined cases, where an incorrectly chosen loss function leads to
implausible predictions. Example tasks include conditional point-cloud
reconstruction and predicting future states of molecules. In this paper, we
propose an alternative to training via set losses by viewing learning as
conditional density estimation. Our learning framework fits deep energy-based
models and approximates the intractable likelihood with gradient-guided
sampling. Furthermore, we propose a stochastically augmented prediction
algorithm that enables multiple predictions, reflecting the possible variations
in the target set. We empirically demonstrate on a variety of datasets the
capability to learn multi-modal densities and produce different plausible
predictions. Our approach is competitive with previous set prediction models on
standard benchmarks. More importantly, it extends the family of addressable
tasks beyond those that have unambiguous predictions.


  The formulation of quantum programs in terms of the fewest number of gate
operations is crucial to retrieve meaningful results from the noisy quantum
processors accessible these days. In this work, we demonstrate a use-case for
Field Programmable Gate Array (FPGA) based data-flow engines (DFEs) to scale up
variational quantum compilers to synthesize circuits up to $9$-qubit
programs.This gate decomposer utilizes a newly developed DFE quantum computer
simulator that is designed to simulate arbitrary quantum circuit consisting of
single qubit rotations and controlled two-qubit gates on FPGA chips. In our
benchmark with the QISKIT package, the depth of the circuits produced by the
SQUANDER package (with the DFE accelerator support) were less by $97\%$ on
average, while the fidelity of the circuits was still close to unity up to an
error of $\sim10^{-4}$.


  We report on the use of a single NV center to probe fluctuating AC magnetic
fields. Using engineered currents to induce random changes in the field
amplitude and phase, we show that stochastic fluctuations reduce the NV center
sensitivity and, in general, make the NV response field-dependent. We also
introduce two modalities to determine the field spectral composition, unknown a
priori in a practical application. One strategy capitalizes on the generation
of AC-field-induced coherence 'revivals', while the other approach uses the
time-tagged fluorescence intensity record from successive NV observations to
reconstruct the AC field spectral density. These studies are relevant for
magnetic sensing in scenarios where the field of interest has a non-trivial,
stochastic behavior, such as sensing unpolarized nuclear spin ensembles at low
static magnetic fields.


  The following thesis presents research which constitutes the first steps
towards the construction of a novel SiFi-CC detector intended for real-time
monitoring of proton therapy. The detector construction will be based on
inorganic scintillating fibers and silicon photomultipliers. The scope of the
presented thesis includes the design optimization of the components of the
proposed detector, as well as the construction, characterization, and tests of
a prototype. The design optimization comprised an extensive systematic
comparison of chosen inorganic scintillating materials, different types of
scintillator surface modifications (wrappings and coatings), and different
types of interface materials ensuring optical contact between the scintillators
and the photodetector. The propagation of scintillating light in all
investigated samples was described using two models: the exponential light
attenuation model (ELA), and the exponential light attenuation model with light
reflection (ELAR). The two models yielded the corresponding methods for energy
and position reconstruction. Furthermore, the samples were investigated for
energy and position resolution, light collection, and timing properties. Based
on the results obtained from the optimization study, the detector prototype was
constructed. Prototype tests were performed with two different photodetectors
and data acquisition systems. The performance of the prototype was evaluated
using the same metrics as in the case of single-fiber measurements. The best
results were obtained in measurements with Philips Digital Photon Counting
photosensor and the Hyperion platform, yielding a position resolution of 33.38
mm and an energy resolution of 7.73 %. The results obtained are satisfactory
and sufficient for the successful operation of the proposed SiFi-CC detector.


  In this paper, we generalize the arithmetic functions $\tau$ and
$\tau^{\left(e\right)}$ in algebraic number fields and we find some properties
of these functions.


  In this work, we experimentally investigate the frequency limit of Hall
effect sensor designs based on a 2 dimensional electron gas (2DEG) gallium
arsenide/aluminum gallium arsenide (GaAs/AlGaAs) heterostructure. The frequency
limit is measured and compared for four GaAs/AlGaAs Hall effect sensor designs
where the Ohmic contact length (contact geometry) is varied across the four
devices. By varying the geometry, the trade-off in sensitivity and frequency
limit is explored and the underlying causes of the frequency limit from the
resistance and capacitance perspective is investigated. Current spinning, the
traditional method to remove offset noise, imposes a practical frequency limit
on Hall effect sensors. The frequency limit of the Hall effect sensor, without
current spinning, is significantly higher. Wide-frequency Hall effect sensors
can measure currents in power electronics that operate at higher frequencies is
one such application.


  We present a simple encoding for unlabeled noncrossing graphs and show how
its latent counterpart helps us to represent several families of directed and
undirected graphs used in syntactic and semantic parsing of natural language as
context-free languages. The families are separated purely on the basis of
forbidden patterns in latent encoding, eliminating the need to differentiate
the families of non-crossing graphs in inference algorithms: one algorithm
works for all when the search space can be controlled in parser input.


  (Abridged) We present a spectral analysis of a new, flux-limited sample of 72
X-ray selected clusters of galaxies identified with the X-ray Telescope (XRT)
on board the Swift satellite down to a flux limit of ~10-14 erg/s/cm2 (SWXCS,
Tundo et al. 2012). We carry out a detailed X-ray spectral analysis with the
twofold aim of measuring redshifts and characterizing the properties of the
Intra-Cluster Medium (ICM). Optical counterparts and spectroscopic or
photometric redshifts are obtained with a cross-correlation with NED.
Additional photometric redshifts are computed with a dedicated follow-up
program with the TNG and a cross-correlation with the SDSS. We also detect the
iron emission lines in 35% of the sample, and hence obtain a robust measure of
the X-ray redshift zX. We use zX whenever the optical redshift is not
available. Finally, for all the sources with measured redshift,
background-subtracted spectra are fitted with a mekal model. We perform
extensive spectral simulations to derive an empirical formula to account for
fitting bias. The bias-corrected values are then used to investigate the
scaling properties of the X-ray observables. Overall, we are able to
characterize the ICM of 46 sources. The sample is mostly constituted by
clusters with temperatures between 3 and 10 keV, plus 14 low-mass clusters and
groups with temperatures below 3 keV. The redshift distribution peaks around
z~0.25 and extends up to z~1, with 60% of the sample at 0.1<z<0.4. We derive
the Luminosity-Temperature relation for these 46 sources, finding good
agreement with previous studies. The quality of the SWXCS sample is comparable
to other samples available in the literature and obtained with much larger
X-ray telescopes. Our results have interesting implications for the design of
future X-ray survey telescopes, characterised by good-quality PSF over the
entire field of view and low background.


  The real Jacobi group $G^J_n(\mathbb{R})$, defined as the semidirect product
of the Heisenberg group ${\rm H}_n(\R)$ with the symplectic group ${\mr
{Sp}}(n,\mathbb{R})$, admits a matrix embedding in $\text{Sp}(n+1,\mathbb{R})$.
The modified pre-Iwasawa decomposition of $\rm{Sp}(n,\mathbb{R})$ allows us to
introduce a convenient coordinatization $S_n$ of $G^J_n(\mathbb{R})$, which for
$G^J_1(\mathbb{R})$ coincides with the $S$-coordinates. Invariant one-forms on
$G^J_n(\mathbb{R})$ are determined. The formula of the 4-parameter invariant
metric on $G^J_1(\R)$ obtained as sum of squares of 6 invariant one-forms is
extended to $G^J_n(\R)$, $n\in\mathbb{N}$. We obtain a three parameter
invariant metric on the extended Siegel-Jacobi upper half space
$\tilde{\mathcal{X}}^J_n\approx\mathcal{X}^J_n\times \mathbb{R}$ by adding the
square of an invariant one-form to the two-parameter balanced metric on the
Siegel-Jacobi upper half space $ {\mathcal{X}}^J_n
=\frac{G^J_n(\mathbb{R})}{\mr{U}(n)\times\mathbb{R}}$.


  We outline a simple procedure designed for \emph{automatically} finding sets
of multiple images in strong lensing (SL) clusters. We show that by combining
(a) an arc-finding (or source extracting) program, (b) photometric redshift
measurements, and (c) a preliminary light-traces-mass lens model,
multiple-image systems can be identified in a fully automated (`blind') manner.
The presented procedure yields an assessment of the likelihood of each arc to
belong to one of the multiple-image systems, as well as the preferred redshift
for the different systems. These could be then used to automatically constrain
and refine the initial lens model for an accurate mass distribution. We apply
this procedure to \emph{Cluster Lensing And Supernova with Hubble} observations
of three galaxy clusters, MACS J0329.6-0211, MACS J1720.2+3536, and MACS
J1931.8-2635, comparing the results to published SL analyses where multiple
images were verified by eye on a particular basis. In the first cluster all
originally identified systems are recovered by the automated procedure, and in
the second and third clusters about half are recovered. Other known systems are
not picked up, in part due to a crude choice of parameters, ambiguous
photometric redshifts, or inaccuracy of the initial lens model. On top of real
systems recovered, some false images are also mistakenly identified by the
procedure, depending on the thresholds used. While further improvements to the
procedure and a more thorough scrutinisation of its performance are warranted,
the work constitutes another important step toward fully automatising SL
analyses for studying mass distributions of large cluster samples.


  Random walks on bipartite networks have been used extensively to design
personalized recommendation methods. While aging has been identified as a key
component in the growth of information networks, most research has focused on
the networks' structural properties and neglected the often available time
information. Time has been largely ignored both by the investigated
recommendation methods as well as by the methodology used to evaluate them. We
show that this time-unaware approach overestimates the methods' recommendation
performance. Motivated by microscopic rules of network growth, we propose a
time-aware modification of an existing recommendation method and show that by
combining the temporal and structural aspects, it outperforms the existing
methods. The performance improvements are particularly striking in systems with
fast aging.


  We investigate the physics of a charged scalar particle moving in conformally
flat spacetime with the conformal factor depending only on time in the
framework of quantum electrodynamics (QED). In particular, we show that the
radiation-reaction force derived from QED agrees with the classical counterpart
in the limit $\hbar \to 0$ using the fact that to lowest order in $\hbar$ the
charged scalar field theory with mass $m$ in conformally flat spacetime with
conformal factor $\Omega(t)$, which we call Model B, is equivalent to that in
flat spacetime with a time-dependent mass $m\Omega(t)$, which we call Model A,
at tree level in this limit. We also consider the one-loop QED corrections to
these two models in the semi-classical approximation. We find nonzero one-loop
corrections to the mass and Maxwell's equations in Model A at order
$\hbar^{-1}$. This does not mean, however, that the corresponding one-loop
corrections in Model B are nonzero because the equivalence of these models
through a conformal transformation breaks down at one loop. We find that the
one-loop corrections vanish in the limit $\hbar \to 0$ in Model B.


  The black hole candidate MAXI J1535-571 is a recently discovered X-ray
transient. We report on the monitoring observations of Swift Gamma-Ray Burst
Mission during outburst. The source transits from the hard state to the
intermediate state, and reaches the soft state; near the end of the outburst,
it returns to the hard state passing through the low intermediate state,
following a typical Q-shaped loop in the hardness-intensity diagram. During the
high intermediate state, detailed spectral analyses using a multi-temperature
disk model reveal that the disk luminosity is flatter than the inner disk
temperature to the fourth power, and the disk temperature profile varies as the
disk radius raised to the power of -0.5, consistent with the behavior of a slim
disk, implying that the disk structure has been modified due to the high
luminosity of ~ 10^{39} erg/s. Meanwhile, the column density increases with the
Eddington ratio, suggesting that the outflow matters are driven by radiation
pressure due to the high accretion rate.


  There are six orientable, compact, flat 3-manifolds that can occur as cusp
cross-sections of hyperbolic 4-manifolds. This paper provides criteria for
exactly when a given commensurability class of arithmetic hyperbolic
4-manifolds contains a representative with a given cusp type. In particular,
for three of the six cusp types, we provide infinitely many examples of
commensurability classes that contain no manifolds with cusps of the given
type; no such examples were previously known for any cusp type.


  Random Hermitian matrices with a source term arise, for instance, in the
study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and
sample covariance matrices \cite{Baik:2005}.
  We consider the case when the $n\times n$ external source matrix has two
distinct real eigenvalues: $a$ with multiplicity $r$ and zero with multiplicity
$n-r$. The source is small in the sense that $r$ is finite or $r=\mathcal
O(n^\gamma)$, for $0< \gamma<1$. For a Gaussian potential, P\'ech\'e
\cite{Peche:2006} showed that for $|a|$ sufficiently small (the subcritical
regime) the external source has no leading-order effect on the eigenvalues,
while for $|a|$ sufficiently large (the supercritical regime) $r$ eigenvalues
exit the bulk of the spectrum and behave as the eigenvalues of $r\times r$
Gaussian unitary ensemble (GUE). We establish the universality of these results
for a general class of analytic potentials in the supercritical and subcritical
regimes.


  Georges Lemaitre was a remarkable contributor to the advancement of cosmology
in the heady years following two great revolutions in theoretical physics in
the last century: general relativity and quantum mechanics. In the present
century, the impact of his key publications has advanced from very little to
enormous. The Big Bang universe has reigned supreme in cosmology for sixty
years, during which time it has acquired paradigmatic status as the most
important event in the entire history of cosmology. Lemaitre was the first
cosmologist to estimate the rate of expansion of the universe, later known as
the Hubble constant. In 2018 the International Astronomical Union renamed the
Hubble law as the Hubble-Lemaitre law in acknowledgement of his foundational
contribution to the theory of the expanding universe. This biographical review
examines: (a) factors that influenced his approach to the philosophy of
science, particularly cosmology; (b) his engagement with the network of
contemporary cosmologists; and (c) the circumstances of his withdrawal from
research in cosmology and the further promotion of the fireworks universe after
the early 1930s.


  Microdialysis is a well-established method for in vivo neurochemical
measurements of small molecules, with implanted concentric-design probes
offering minimized tissue damage and good temporal and spatial resolution.
However, the large majority of measurements do not allow the perfusate to reach
equilibrium with the brain, so that inferential methods of sample concentration
correction such as zero-net-flux must be used to determine actual brain
extracellular fluid glucose concentrations. In order for such methods to be
valid, steady-state transfer of the analyte of interest within the brain is
required, but this situation has not previously been confirmed. A
first-principles mathematical model of fluid flow and analyte diffusion around
an implanted microdialysis probe was developed and implemented in COMSOL in
order to validate the zero-net-flux approach, using measurement of
extracellular brain glucose levels as a well-explored example system against
which to compare the model. Results from the model accurately reproduced and
predicted results from in vivo experiments. Importantly, the model predicts
that the time for an implanted probe to achieve steady-state equilibrium with
the surrounding extracellular fluid is on the order of one to two minutes,
supporting the validity of this technique for quantitative measurement of in
vivo neurochemistry.


  We propose an experimentally feasible scheme to generate a superposition of
travelling field coherent states using extremely small Kerr effect and an
ancilla which could be a single photon or two entangled twin photons. The
scheme contains ingredients which are all within the current state of the art
and is robust against the main sources of errors which can be identified in our
setups.


  The main purpose of this paper is the study of second-order optimality
conditions for the bilinear control of a strongly degenerate parabolic
equation. The equation is degenerate at the boundary of the spatial domain. The
well-posedness of the state equation, as well as weak maximum principles are
established. We prove some differentiability properties of the control-to-state
operator and the existence of optimal solutions. Finally, we derive first- and
second-order optimality conditions for the system.


  We formulate a refined version of the Birch and Swinnerton-Dyer conjecture
for abelian varieties over global function fields. This refinement incorporates
both families of congruences between the leading terms of Artin-Hasse-Weil
$L$-series and also strong restrictions on the Galois structure of natural
Selmer complexes and constitutes a precise analogue for abelian varieties over
function fields of the equivariant Tamagawa number conjecture for abelian
varieties over number fields. We then provide strong supporting evidence for
this conjecture including giving a full proof, modulo only the assumed
finiteness of Tate-Shafarevich groups, in an important class of examples.


  We show how to obtain the difference function of the Weierstrass Zeta
function very directly, by choosing an appropriate order of summation for the
series defining this function. As a byproduct, we show how to obtain the
quasi-modularity of the weight 2 Eisenstein series immediately from the fact
that it appears in this difference function and the homogeneity properties of
the latter.


  The bulk-boundary correspondence establishes a connection between the bulk
topological index of an insulator or superconductor, and the number of
topologically protected edge bands or states. For topological superconductors
in two dimensions the first Chern number is related to the number of protected
bands within the bulk energy gap, and is therefore assumed to give the number
of Majorana band states in the system. Here we show that this is not
necessarily the case. As an example we consider a hexagonal-lattice topological
superconductor based on a model of graphene with Rashba spin orbit coupling,
proximity induced s-wave superconductivity, and a Zeeman magnetic field. We
explore the full Chern number phase diagram of this model, extending what is
already known about its parity. We then demonstrate that despite the high Chern
numbers that can be seen in some phases these do not strictly always contain
Majorana bound states.


  Polar magnetic states are realized in pseudocubic manganite thin films
fabricated on high-index substrates, in which a Jahn-Teller (JT) distortion
remains an active variable. Several types of orbital-orders were found to
develop large optical second harmonic generation, signaling
broken-inversion-symmetry distinct from their bulk forms and films on (100)
substrates. The observed symmetry-lifting and first-principles calculation both
indicate that the modified JT q2 mode drives Mn-site off-centering upon orbital
order, leading to the possible cooperation of "Mn-site polarization" and
magnetism.


  We study quadratic Lie algebras over a field K of null characteristic which
admit, at the same time, a symplectic structure. We see that if K is
algebraically closed every such Lie algebra may be constructed as the
T*-extension of a nilpotent algebra admitting an invertiblederivation and also
as the double extension of another quadratic symplectic Lie algebra by the
one-dimensional Lie algebra. Finally, we prove that every symplectic quadratic
Lie algebra is a special symplectic Manin algebra and we give an inductive
classification in terms of symplectic quadratic double extensions.


  Gravitational lenses with anomalous flux ratios are often cited as possible
evidence for dark matter satellites predicted by simulations of hierarchical
merging in cold dark matter cosmogonies. We show that the fraction of quads
with anomalous flux ratios depends primarily on the total mass and spatial
extent of the satellites, and the characteristic lengthscale R of their
distribution. If R is 100 kpc, then for a moderately elliptical galaxy with a
line-of-sight velocity dispersion of 250 km/s, a mass of 3 x 10^9 solar masses
in highly-concentrated (Plummer model) satellites is needed for 20% of
quadruplets to show anomalous flux ratios, rising to 1.25 x 10^10 solar masses
for 50%. Several times these masses are required if the satellites have more
extended Hernquist profiles. Compared to a typical elliptical, the flux ratios
of quads formed by typical edge-on disc galaxies with maximum discs are
significantly less susceptible to changes through substructure -- three times
the mass in satellite galaxies is needed to affect 50% of the systems. In many
of the lens systems with anomalous flux ratios, there is evidence for visible
satellites (e.g., B2045+265 or MG0414+0534). We show that optically identified
substructure should not be preponderant among lens systems with anomalies.
There are two possible resolutions of this difficulty. First, in some cases,
visible substructure may be projected within or close to the Einstein radius
and wrongly ascribed as the culprit, whereas dark matter substructure is
causing the flux anomaly. Second, bright satellites, in which baryon cooling
and condensation has taken place, may have higher central densities than dark
satellites, rendering them more efficient at causing flux anomalies.


  In combinatorics, a derangement is a permutation that has no fixed points.
The number of derangements of an n-element set is called the n-th derangement
number. In this paper, as natural companions to derangement numbers and
degenerate versions of the companions we introduce derangement polynomials and
degenerate derangement polynomials. We give some of their properties,
recurrence relations and identities for those polynomials which are related to
some special numbers and polynomials.


  With this study we want to test the validity of the well known "Verdoorn's
Law" which considers the relationship between the growth of productivity and
output in the case of the Portuguese economy at a regional and sectoral levels
(NUTs II) for the period 1995-1999. The importance of some additional variables
in the original specification of Verdoorn's Law is also tested, such as, trade
flows, capital accumulation and labour concentration. The main objective of the
study is to confirm the presence of economies to scale that characterise the
polarisation process with cumulative causation properties, explaining regional
divergence. By introducing new variables to the original specification of
Verdoorn's Law we intend to examine how the economies to scale are influenced
by the consideration of factors related to the Polarisation (Keynensian
tradition) and Agglomeration (spatial economics tradition) phenomena. The
results obtained from the regression analysis based on panel estimation show
that the original specification of Verdoorn's Law is more robust and confirm
the presence of increasing economies to scale at both, regional and sectoral
levels. However, the additional variables related to trade flows, capital
accumulation and labour concentration have few influence on the performance of
economies to scale (1)(Martinho, 2011).


  We perform a bifurcation analysis of the steady states of Rayleigh--B\'enard
convection with no-slip boundary conditions in two dimensions using a numerical
method called deflated continuation. By combining this method with an
initialisation strategy based on the eigenmodes of the conducting state, we are
able to discover multiple solutions to this non-linear problem, including
disconnected branches of the bifurcation diagram, without the need for any
prior knowledge of the solutions. One of the disconnected branches we find
contains an S-shaped curve with hysteresis, which is the origin of a flow
pattern that may be related to the dynamics of flow reversals in the turbulent
regime. Linear stability analysis is also performed to analyse the steady and
unsteady regimes of the solutions in the parameter space and to characterise
the type of instabilities.


  Gravitating monopoles and dyons in Einstein-Yang-Mills (EYM) or
Einstein-Yang-Mills-Higgs (EYMH) systems have been extensively studied for
various curved spacetimes, including those of black holes. We construct dyonic
solutions of the EYMH theory in Vaidya spacetime using a set of generalized
Julia-Zee ansatz for the fields. It is found that the dyonic charge is static
in nature and it does not contribute to the energy of the null dust.


  We present a new channel of the neutrinoless double beta decay. In this
scenario neutrinos not only oscillate inside the nucleus but also interact with
an external non-uniform magnetic field. We assume that the field rotates about
the direction of motion of the neutrino and show, that for a certain speed of
rotation the half-life of the $0\nu2\beta$ decay may be significantly lowered.


  We show how the inclusive $t\bar t$ production in $e^+e^-$, gluon~gluon and
photon~photon collisions could reveal the presence of new (visible or
invisible) particles connected to the Higgs sector and/or to the top quark.


  The interfacial Dzyaloshinskii-Moriya interaction (iDMI) is attracting great
interests for spintronics. An iDMI constant larger than 3 mJ/m^2 is expected to
minimize the size of skyrmions and to optimize the DW dynamics. In this study,
we experimentally demonstrate an enhanced iDMI in Pt/Co/X/MgO ultra-thin film
structures with perpendicular magnetization. The iDMI constants were measured
using a field-driven creep regime domain expansion method. The enhancement of
iDMI with an atomically thin insertion of Ta and Mg is comprehensively
understood with the help of ab-initio calculations. Thermal annealing has been
used to crystallize the MgO thin layer for improving tunneling
magneto-resistance (TMR), but interestingly it also provides a further increase
of the iDMI constant. An increase of the iDMI constant up to 3.3 mJ/m^2 is
shown, which could be promising for the scaling down of skyrmion electronics.


  Fourier ptychographic microscopy is a computational imaging technique that
provides quantitative phase information and high resolution over a large
field-of-view. Although the technique presents numerous advantages over
conventional microscopy, model mismatch due to unknown optical aberrations can
significantly limit reconstruction quality. Many attempts to address this issue
rely on embedding pupil recovery into the reconstruction algorithm. In this
paper we demonstrate the limitations of a purely algorithmic approach and
evaluate the merits of implementing a simple, dedicated calibration procedure.
In simulations, we find that for a target sample reconstruction error, we can
image without any aberration corrections up to a maximum aberration magnitude
of $\lambda$/40. When we use algorithmic self-calibration, we can increase the
aberration magnitude up to $\lambda$/10, and with our in situ speckle
calibration technique, this working range is extended further to a maximum
aberration magnitude of $\lambda$/3. Hence, one can trade-off complexity for
accuracy by using a separate calibration process, which is particularly useful
for larger aberrations.


  Let $P$ be a monic polynomial of degree $D \geq 3$ whose filled Julia set
$K_P$ has a non-degenerate periodic component $K$ of period $k \geq 1$ and
renormalization degree $2 \leq d<D$. Let $I=I_K$ denote the set of angles
$\theta$ on the circle ${\mathbb T}={\mathbb R}/{\mathbb Z}$ for which the
(smooth or broken) external ray $R^P_\theta$ for $P$ accumulates on $\partial
K$. We prove the following:
  $\bullet$ $I$ is a compact set of Hausdorff dimension $<1$ and there is an
essentially unique degree $1$ monotone map $\Pi: I \to {\mathbb T}$ which
semiconjugates $\theta \mapsto D^k \theta$ (mod 1) on $I$ to $\theta \mapsto d
\theta$ (mod 1) on $\mathbb T$.
  $\bullet$ Any hybrid conjugacy $\varphi$ between a renormalization of
$P^{\circ k}$ on a neighborhood of $K$ and a monic degree $d$ polynomial $Q$
induces a semiconjugacy $\Pi: I \to {\mathbb T}$ with the property that for
every $\theta \in I$ the external ray $R^P_\theta$ has the same accumulation
set as the curve $\varphi^{-1}(R^Q_{\Pi(\theta)})$. In particular, $R^P_\theta$
lands at $z \in \partial K$ if and only if $R^Q_{\Pi(\theta)}$ lands at
$\varphi(z) \in \partial K_Q$.
  $\bullet$ The ray correspondence established by the above result is
finite-to-one. In fact, the cardinality of each fiber of $\Pi$ is $\leq D-d+2$,
and the inequality is strict when the component $K$ has period $k=1$.
  Using a new type of quasiconformal surgery we construct a class of examples
with $k=1$ for which the upper bound $D-d+1$ is realized and the set $I$ has
isolated points.


  In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.


  We introduce a novel NMR approach that extends the capabilities of indirect
dynamic nuclear polarization (DNP) under magic-angle spinning to probe the
local environment of half-integer spin quadrupolar nuclei. Compared to
cross-polarization, this novel method based on the refocused INEPT scheme with
adiabatic dipolar recoupling is easier to optimize and does not distort the
quadrupolar line shapes. Furthermore, the use of this technique, instead of the
PRESTO (Phase-shifted Recoupling Effects a Smooth Transfer of Order) scheme or
direct DNP, greatly improves the sensitivity of DNP-NMR for the detection of
quadrupolar isotopes with small dipolar couplings to protons, including notably
those located in the subsurface of inorganic materials or with low gyromagnetic
ratio ($\gamma$). This technique has been applied to identify the atomic-level
structure of Br{\o}nsted acid sites of hydrated titania-supported MoO${}_3$,
MoO${}_3$/TiO${}_2$, a widely used heterogeneous catalyst. The spectra of
protonated and unprotonated ${}^{17}$O sites, acquired in natural abundance,
indicate the presence of various oxomolybdate species as well as HOMo${}_2$ and
HOMo${}_3$ Br{\o}nsted acid sites. The enhanced sensitivity of this new method
has also enabled the acquisition of the first DNP-enhanced spectra of
${}^{95}$Mo and ${}^{47,49}$Ti low-$\gamma$ quadrupolar isotopes. The proposed
polarization transfer is also employed to acquire the first DNPenhanced
spectrum of ${}^{67}$Zn, another low-$\gamma$ quadrupolar isotope. This
possibility is demonstrated for Al-doped ZnO nanoparticles used in
optoelectronic devices. The obtained ${}^{17}$O, ${}^{27}$Al, and ${}^{67}$Zn
DNP-NMR data prove that the surface region of these nanoparticles contains ZnO
phase as well as secondary phases, such as $\alpha$-Al${}_2$O${}_3$ and
partially inverse ZnAl${}_2$O${}_4$ spinel.


  We consider a class of iterated function systems (IFSs) of contracting
similarities of $R^n$, introduced by Hutchinson, for which the invariant set
possesses a natural H\"older continuous parameterization by the unit interval.
When such an invariant set is homeomorphic to an interval, we give necessary
conditions in terms of the similarities alone for it to possess a
quasisymmetric (and as a corollary, bi-H\"older) parameterization. We also give
a related necessary condition for the invariant set of such an IFS to be
homeomorphic to an interval.


  We consider the problem of setting a confidence interval on a parameter of
interest from a high-statistics counting experiment in the presence of
systematic uncertainties modeled as unconstrained nuisance parameters. We use
the profile-likelihood test statistic in the asymptotic limit for confidence
interval setting and focus on the case where the likelihood function is derived
from a finite sample of Monte Carlo simulated events. We prove as a general
result that statistical uncertainties in the Monte Carlo sample affect the
coverage of the confidence interval always in the same direction, namely they
lead to a systematic undercoverage of the interval. We argue that such spurious
effects might not be fully accounted for by statistical methods that are
usually adopted in HEP measurements to counteract the effects of finite-size MC
samples, such as those based on the Barlow-Beeston likelihood.


  The purpose of this bulletin board is to collect problems in higher
dimensional complex analysis. We are interested both in basic research
questions as well as interactive questions with other fields and sciences. We
encourage everybody to submit problems to the list. This includes not only
those coming up in your own work, but also others- maybe well known and
classical- that you see missing, but that you think workers in the field should
be aware of. Not only are we searching for basic research type questions in
several complex variables, we also solicit questions exploring relations to
other mathematical fields, one complex variable, partial differential
equations, differential geometry, dynamics, etc. and to other sciences such as
physics, engineering, biology etc. While some questions fall rather naturally
into one of the subject areas in this problem list and may lead to a
publishable paper, other questions may be non- specific or of a transient or
technical quality. Thus we have a section called ``Scratchpad'' for
conversational questions, vaguely formulated questions, or questions to which
you may hope to get a quick answer. In the ``open prize problems'' section, you
are welcome to offer a nice little prize to whoever does it. The miscellaneous
section is for announcements of conferences, jokes, remarks on the general
state of the field, etc.


  We establish the existence and uniqueness of local strong solutions to the
Navier-Stokes equations with arbitrary initial data and external forces in the
homogeneous Besov-Morrey space. The local solutions can be extended globally in
time provided the initial data and external forces are small. We adapt the
method introduced in \cite{ks6}, where the Besov space is considered, to the
setting of the homogeneous Besov-Morrey space.


  We design an insect-sized rolling microrobot driven by continuously rotating
wheels. It measures 18mm$\times$8mm$\times$8mm. There are 2 versions of the
robot - a 96mg laser-powered one and a 130mg supercapacitor powered one. The
robot can move at 27mm/s (1.5 body lengths per second) with wheels rotating at
300$^\circ$/s, while consuming an average power of 2.5mW. Neither version has
any electrical wires coming out of it, with the supercapacitor powered robot
also being self-sufficient and is able to roll freely for 8 seconds after a
single charge. Low-voltage electromagnetic actuators (1V-3V) along with a novel
double-ratcheting mechanism enable the operation of this device. It is, to the
best of our knowledge, the lightest and fastest self-sufficient rolling
microrobot reported yet.


  This study explores the age-old quest to construct a geometric model of a
quantum particle. While static classical particle models have largely been
dismissed, the focus has now shifted to intricate dynamic models that hold the
promise of reconciling general relativity with quantum mechanics. We propose
that matter particles can be described as radiation confined within dynamically
curved spacetime regions, without the need for quantization of space and time,
and using standard field equations and natural Planck units. Specifically, we
investigate a cyclic or oscillating radiation-dominated micro cosmos undergoing
repeated bouncing. Our methodology employs integration, with carefully defined
initial conditions. The results include several observable properties
characteristic of quantum particles. We calculate the total mass, revealing a
compelling inverse proportionality between mass and radius identical with the
de Broglie relationship. Applying this model to protons, we discover a profound
and surprisingly simple relationship between the proton's radius and mass
expressed in Planck units. This enables a definition of the proton radius that
aligns remarkably well with the 2018 CODATA value. Furthermore, our analysis
demonstrates that the radial density profile of the proton (or nucleon),
averaged over a cycle time, increases toward the center. The problem of
embedding the micro cosmos within a background spacetime is also described.
These results underscore the relevance of general relativity in the domain of
nuclear physics. Moreover, the model offers a fresh perspective that can
stimulate new ideas in the ongoing quest to unify general relativity with
quantum physics.


  We explore constraints on the equation of state (EOS) of neutron-rich matter
based on microscopic calculations up to nuclear densities and observations of
neutron stars. In a previous work we showed that predictions based on modern
nuclear interactions derived within chiral effective field theory and the
observation of two-solar-mass neutron stars result in a robust uncertainty
range for neutron star radii and the EOS over a wide range of densities. In
this work we extend this study, employing both the piecewise polytrope
extension from Hebeler et al. as well as the speed of sound model of Greif et
al., and show that moment of inertia measurements of neutron stars can
significantly improve the constraints on the EOS and neutron star radii.


  Let $K$ be a number field and $S$ a fixed finite set of places of $K$
containing all the archimedean ones. Let $R_S$ be the ring of $S$-integers of
$K$. In the present paper we study the cycles for rational maps of
$\mathbb{P}_1(K)$ of degree $\geq2$ with good reduction outside $S$. We say
that two ordered $n$-tuples $(P_0,P_1,...,P_{n-1})$ and $(Q_0,Q_1,...,Q_{n-1})$
of points of $\mathbb{P}_1(K)$ are equivalent if there exists an automorphism
$A\in{\rm PGL}_2(R_S)$ such that $P_i=A(Q_i)$ for every index
$i\in\{0,1,...,n-1\}$. We prove that if we fix two points
$P_0,P_1\in\mathbb{P}_1(K)$, then the number of inequivalent cycles for
rational maps of degree $\geq2$ with good reduction outside $S$ which admit
$P_0,P_1$ as consecutive points is finite and depends only on $S$. We also
prove that this result is in a sense best possible.


  Tremendous research effort was invested in audio browsers and machine
learning techniques to decode the structure of Web pages in order to put them
into an audio format. In this paper, we address a simpler and efficient
solution for the creation of an audio browser of VOICEXML generated from
RSS/Atom stream feeds. We developed a multimodal (audio and graphical) portal
application that offers RSS/Atom feeds. By utilizing sing our system, the user
can interact using voice or graphic commands, listen and watch digital content,
such as news, blogs feeds, podcasts, and even access email and personal
schedules. The portal system permits the use of security credentials
(user/password authentication) to collect secure RSS/Atom stream in the
multimodal browser to connect the user to specific personal services. A series
experiments have been conducted to evaluate the performance of the RSS reader
and navigator. Our system is extremely beneficial for a wide range of
applications, from interfaces for the visual impaired users to browsers for
mobile telephonic interfaces.


  Supersymmetric, asymptotically AdS5, black hole solutions of five dimensional
gauged supergravity coupled to arbitrarily many abelian vector multiplets are
presented. The general nature of supersymmetric solutions of this theory is
discussed. All maximally supersymmetric solutions of this theory (with or
without gauging) are obtained.


  In this paper we use character variety methods to study homomorphisms between
the fundamental groups of 3-manifolds, in particular those induced by non-zero
degree maps. A {\it knot manifold} is a compact, connected, irreducible,
orientable 3-manifold whose boundary is an incompressible torus. A {\it virtual
epimorphism} is a homomorphism whose image is of finite index in its range. We
show that the existence of such homomorphisms places constraints on the
algebraic decomposition of a knot manifold's $PSL_2(\mathbb C)$-character
variety and consequently determine a priori bounds on the number of virtual
epimorphisms between the fundamental groups of small knot manifolds with a
fixed domain. In the second part of the paper we fix a small knot manifold $M$
and investigate various sets of characters of representations with discrete
image in $PSL_2(\mathbb C)$. The topology of these sets is intimately related
to the algebraic structure of the $PSL_2(\mathbb C)$-character variety of $M$
as well as dominations of manifolds by $M$ and its Dehn fillings. In
particular, we apply our results to study families of non-zero degree maps
$f_n: M(\alpha_n) \to V_n$ where $M(\alpha_n)$ is the $\alpha_n$-Dehn filling
of $M$ and $V_n$ is either a hyperbolic manifold or $\widetilde{SL_2}$
manifold. We show that quite often, up to taking a subsequence, there is a knot
manifold $V$, slopes $\beta_j$ on $\partial V$ such that $V_j \cong
V(\beta_j)$, and a non-zero degree map $M \to V$ which induces $f_j$ up to
homotopy. The work of the first part of the paper is then applied to construct
infinite families of small, closed, connected, orientable 3-manifolds which do
not admit non-zero degree maps, other than homeomorphisms, to any hyperbolic
manifold, or even manifolds with infinite fundamental groups.


  It is shown that the baryon magnetic moment descriptions in the frameworks of
the chiral model ChPT and the quark soliton $\chi QSM $ one are practically
identical. The main difference from the traditional unitary symmetry models
proves to be in terms due to the pionic current contribution into the magnetic
moments of nucleons and in the prediction for the $\Lambda$ magnetic moment.


  Eisermann has shown that the Jones polynomial of a $n$-component ribbon link
$L\subset S^3$ is divided by the Jones polynomial of the trivial $n$-component
link. We improve this theorem by extending its range of application from links
in $S^3$ to colored knotted trivalent graphs in $\#_g(S^2\times S^1)$, the
connected sum of $g\geqslant 0$ copies of $S^2\times S^1$.
  We show in particular that if the Kauffman bracket of a knot in
$\#_g(S^2\times S^1)$ has a pole in $q=i$ of order $n$, the ribbon genus of the
knot is at least $\frac {n+1}2$. We construct some families of knots in
$\#_g(S^2\times S^1)$ for which this lower bound is sharp and arbitrarily big.
We prove these estimates using Turaev shadows.


  We present a detailed analysis of the far-IR properties of the bright,
lensed, z = 2.3, SMG, SMM J2135-0102, using new observations with Herschel,
SCUBA-2 and the VLA. These data allow us to constrain the galaxy's SED and show
that it has an intrinsic rest-frame 8-1000um luminosity, L(bol), of (2.3 +/-
0.2) x 10^12 L(sun) and a likely SFR of ~400 M(sun)/yr. The galaxy sits on the
far-IR/radio correlation for far-IR-selected galaxies. At ~>70um, the SED can
be described adequately by dust components with T(d) ~ 30 and 60K. Using
SPIRE's Fourier Transform Spectrometer we report a detection of the [CII] 158um
cooling line. If the [CII], CO and far-IR continuum arise in photo-dissociation
regions, we derive a characteristic gas density, n ~ 10^3 cm^-3, and a far-UV
radiation field, G_0, 10^3x stronger than the Milky Way. L([CII])/L(bol) is
significantly higher than in local ULIRGs but similar to the values found in
local star-forming galaxies and starburst nuclei. This is consistent with SMM
J2135-0102 being powered by starburst clumps distributed across ~2 kpc,
evidence that SMGs are not simply scaled-up ULIRGs. Our results show that
SPIRE's FTS has the ability to measure the redshifts of distant, obscured
galaxies via the blind detection of atomic cooling lines, but it will not be
competitive with ground-based CO-line searches. It will, however, allow
detailed study of the integrated properties of high-redshift galaxies, as well
as the chemistry of their ISM, once more suitably bright candidates have been
found.


  Recent experimental results on exclusive semi-tauonic B meson decays, B ->
D(*) tau nu, showing sizable deviations from the standard model prediction,
suggest a new physics in which the structure of the relevant weak charged
interaction may differ from that of the standard model. We study the exclusive
semi-tauonic B decays in a model-independent manner using the most general set
of four-Fermi interactions in order to clarify possible structures of the
charged current in new physics. It turns out that correlations among
observables including tau and D* polarizations and q^2 distributions are useful
to distinguish possible new physics operators. Further, we investigate some
interesting models to exhibit the advantage of our model-independent analysis.
As a result, we find that two Higgs doublet models without tree-level FCNC and
the minimal supersymmetric standard model with R-parity violation are unlikely
to explain the present experimental data, while two Higgs doublet models with
FCNC and a leptoquark model are consistent with the data.


  Cellular signaling involves the transmission of environmental information
through cascades of stochastic biochemical reactions, inevitably introducing
noise that compromises signal fidelity. Each stage of the cascade often takes
the form of a kinase-phosphatase push-pull network, a basic unit of signaling
pathways whose malfunction is linked with a host of cancers. We show this
ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov
(WK) optimal noise filter. Using concepts from umbral calculus, we generalize
the linear WK theory, originally introduced in the context of communication and
control engineering, to take nonlinear signal transduction and discrete
molecule populations into account. This allows us to derive rigorous
constraints for efficient noise reduction in this biochemical system. Our
mathematical formalism yields bounds on filter performance in cases important
to cellular function---like ultrasensitive response to stimuli. We highlight
features of the system relevant for optimizing filter efficiency, encoded in a
single, measurable, dimensionless parameter. Our theory, which describes noise
control in a large class of signal transduction networks, is also useful both
for the design of synthetic biochemical signaling pathways, and the
manipulation of pathways through experimental probes like oscillatory input.


  Let $\alpha$ be an arbritary ordinal, and $2<n<\omega$. In \cite{3} accepted
for publication in Quaestiones Mathematicae, we studied using algebraic logic,
interpolation, amalgamation using $\alpha$ many variables for topological logic
with $\alpha$ many variables briefly $\sf TopL_{\alpha}$. This is a sequel to
\cite{3}; the second part on modal cylindric algebras, where we study
algebraically other properties of $\sf TopL_{\alpha}$. Modal cylindric algebras
are cylindric algebras of infinite dimension expanded with unary modalities
inheriting their semantics from a unimodal logic $\sf L$ such as $\sf K5$ or
$\sf S4$. Using the methodology of algebraic logic, we study topological (when
$\sf L=S4$), in symbols $\sf TCA_{\alpha}$. We study completeness and omitting
types $\sf OTT$s for $\sf TopL_{\omega}$ and $\sf TenL_{\omega}$, by proving
several representability results for locally finite such algebras. Furthermore,
we study the notion of atom-canonicity for both ${\sf TCA}_{n}$ and ${\sf
TenL}_n$, a well known persistence property in modal logic, in connection to
$\sf OTT$ for ${\sf TopL}_n$ and ${\sf TeLCA}_n$, respectively. We study
representability, omitting types, interpolation and complexity isssues (such as
undecidability) for topological cylindric algebras. In a sequel to this paper,
we introduce temporal cyindric algebras and point out the way how to amalgamate
algebras of space (topological algebars) and algebras of time (temporal
algebras) forming topological-temporal cylindric algebras that lend themselves
to encompassing spacetime gemetries, in a purely algebraic manner.


  We prove the equality of three conjectural formulas for the Brumer--Stark
units. The first formula has essentially been proven, so the present paper also
verifies the validity of the other two formulas.


  We investigate the transmission of electrons through a quantum point contact
by using a quasi-one-dimensional model with a local bound state below the band
bottom. While the complete transmission in lower channels gives rise to
plateaus of conductance at multiples of $2e^{2}/h$, the electrons in the lowest
channel are scattered by the local bound state when it is singly occupied. This
scattering produces a wide zero-transmittance (anti-resonance) for a singlet
formed by tunneling and local electrons, and has no effect on triplets, leading
to an exact $0.75(2e^{2}/h)$ shoulder prior to the first $2e^{2}/h$ plateau.
Formation of a Kondo singlet from electrons in the Fermi sea screens the local
moment and reduces the effects of anti-resonance, complementing the shoulder
from 0.75 to 1 at low temperatures.


  In this work, we study self-supervised representation learning for 3D
skeleton-based action recognition. We extend Bootstrap Your Own Latent (BYOL)
for representation learning on skeleton sequence data and propose a new data
augmentation strategy including two asymmetric transformation pipelines. We
also introduce a multi-viewpoint sampling method that leverages multiple
viewing angles of the same action captured by different cameras. In the
semi-supervised setting, we show that the performance can be further improved
by knowledge distillation from wider networks, leveraging once more the
unlabeled samples. We conduct extensive experiments on the NTU-60 and NTU-120
datasets to demonstrate the performance of our proposed method. Our method
consistently outperforms the current state of the art on both linear evaluation
and semi-supervised benchmarks.


  Even though deep learning has shown unmatched performance on various tasks,
neural networks have been shown to be vulnerable to small adversarial
perturbations of the input that lead to significant performance degradation. In
this work we extend the idea of adding white Gaussian noise to the network
weights and activations during adversarial training (PNI) to the injection of
colored noise for defense against common white-box and black-box attacks. We
show that our approach outperforms PNI and various previous approaches in terms
of adversarial accuracy on CIFAR-10 and CIFAR-100 datasets. In addition, we
provide an extensive ablation study of the proposed method justifying the
chosen configurations.


  What is the time-optimal way of realizing quantum operations? Here, we show
how important instances of this problem can be related to the study of shortest
paths on the surface of a sphere under a special metric. Specifically, we
provide an efficient synthesis of a controlled NOT (CNOT) gate between qubits
coupled indirectly via Ising-type couplings to a third spin. Our implementation
of the CNOT gate is more than twice as fast as conventional approaches. The
pulse sequences for efficient manipulation of our coupled spin system are
obtained by explicit computation of geodesics on a sphere under the special
metric. These methods are also used for the efficient synthesis of indirect
couplings and of the Toffoli gate. We provide experimental realizations of the
presented methods on a linear three-spin chain with Ising couplings.


  Medical dialogue systems are promising in assisting in telemedicine to
increase access to healthcare services, improve the quality of patient care,
and reduce medical costs. To facilitate the research and development of medical
dialogue systems, we build two large-scale medical dialogue datasets:
MedDialog-EN and MedDialog-CN. MedDialog-EN is an English dataset containing
0.3 million conversations between patients and doctors and 0.5 million
utterances. MedDialog-CN is an Chinese dataset containing 1.1 million
conversations and 4 million utterances. To our best knowledge,
MedDialog-(EN,CN) are the largest medical dialogue datasets to date. The
dataset is available at https://github.com/UCSD-AI4H/Medical-Dialogue-System


  Few years ago, Cho and Vilenkin have proposed that topological defects can
arise in symmetry breaking models without having degenerate vacua. These types
of defects are known as vacuumless defects. In the present work, the
gravitational field of a vacuumless global string and global monopole have been
investigated in the context of Lyra geometry. We find the metric of the
vacuumless global string and global monopole in the weak field approximations.
It has been shown that the vacuumless global string can have repulsive whereas
global monopole exerts attractive gravitational effects on a test particle. It
is dissimilar to the case studied in general relativity.


  Let $K$ be a prime knot in $S^3$ and $G(K)=\pi_1(S^3-K)$ the knot group. We
write $K_1 \geq K_2$ if there exists a surjective homomorphism from $G(K_1)$
onto $G(K_2)$. In this paper, we determine this partial order on the set of
prime knots with up to 11 crossings. There exist such 801 prime knots and then
$640,800$ should be considered. The existence of a surjective homomorphism can
be proved by constructing it explicitly. On the other hand, the non-existence
of a surjective homomorphism can be proved by the Alexander polynomial and the
twisted Alexander polynomial. This work is an extension of the result of
\cite{KS1}.


  Generalising the recent method of Andreatta, Iovita, and Pilloni for cuspidal
forms, we construct an eigenvariety for symplectic and unitary groups that
parametrises systems of eigenvalues of overconvergent and locally analytic
$p$-adic automorphic forms. This is achieved by gluing some intermediates
eigenvarieties of a fixed 'degree of cuspidality'. The dimension of these
eigenvarieties is explicit and depends on the degree of cuspidality, it is
maximal for cuspidal forms and it is $1$ for forms that are 'not cuspidal at
all'. Under mild assumption, we are able to prove a conjecture of Urban about
the dimension of the irreducible components of Hansen's eigenvariety in the
case of the group $\mathrm{GSp}_4$ over $\mathbb{Q}$.


  Pancreatic cancer is one of the global leading causes of cancer-related
deaths. Despite the success of Deep Learning in computer-aided diagnosis and
detection (CAD) methods, little attention has been paid to the detection of
Pancreatic Cancer. We propose a method for detecting pancreatic tumor that
utilizes clinically-relevant features in the surrounding anatomical structures,
thereby better aiming to exploit the radiologist's knowledge compared to other,
conventional deep learning approaches. To this end, we collect a new dataset
consisting of 99 cases with pancreatic ductal adenocarcinoma (PDAC) and 97
control cases without any pancreatic tumor. Due to the growth pattern of
pancreatic cancer, the tumor may not be always visible as a hypodense lesion,
therefore experts refer to the visibility of secondary external features that
may indicate the presence of the tumor. We propose a method based on a
U-Net-like Deep CNN that exploits the following external secondary features:
the pancreatic duct, common bile duct and the pancreas, along with a processed
CT scan. Using these features, the model segments the pancreatic tumor if it is
present. This segmentation for classification and localization approach
achieves a performance of 99% sensitivity (one case missed) and 99%
specificity, which realizes a 5% increase in sensitivity over the previous
state-of-the-art method. The model additionally provides location information
with reasonable accuracy and a shorter inference time compared to previous PDAC
detection methods. These results offer a significant performance improvement
and highlight the importance of incorporating the knowledge of the clinical
expert when developing novel CAD methods.


  The Skyrme model is considered quantum mechanically ab initio in various
irreducible representations of the SU(2) group. The canonical quantization
procedure yields negative mass correction ensuring existence of stabile soliton
solution even in chiral limit. The evaluated static properties of nucleons
(masses, magnetic moments, radii etc.) are in a good agreement with
experimental data.


  Planetesimal formation is a crucial yet poorly understood process in planet
formation. It is widely believed that planetesimal formation is the outcome of
dust clumping by the streaming instability (SI). However, recent analytical and
numerical studies have shown that the SI can be damped or suppressed by
external turbulence, and at least the outer regions of protoplanetary disks are
likely weakly turbulent due to magneto-rotational instability (MRI). We conduct
high-resolution local shearing-box simulations of hybrid particle-gas
magnetohydrodynamics (MHD), incorporating ambipolar diffusion as the dominant
non-ideal MHD effect, applicable to outer disk regions. We first show that dust
backreaction enhances dust settling towards the midplane by reducing turbulence
correlation time. Under modest level of MRI turbulence, we find that dust
clumping is in fact easier than the conventional SI case, in the sense that the
threshold of solid abundance for clumping is lower. The key to dust clumping
includes dust backreaction and the presence of local pressure maxima, which in
our work is formed by the MRI zonal flows overcoming background pressure
gradient. Overall, our results support planetesimal formation in the
MRI-turbulent outer protoplanetary disks, especially in ring-like
substructures.


  We prove a result of the following type: given a Hida family of modular
forms, if there exists a weight two form in the family whose L-function
vanishes to exact order one at s=1, then all but finitely many weight two forms
in the family enjoy this same property. The analogous result for order of
vanishing zero is also true, and is an easy consequence of the existence of the
Mazur-Kitagawa two-variable p-adic L-function.


  We present the results on the distribution and kinematics of H$\sc{i}$ gas
with higher sensitivity and in one case of higher spectral resolution as well
than reported earlier, of three irregular galaxies CGCG 097073, 097079 and
097087 (UGC 06697) in the cluster Abell 1367. These galaxies are known to
exhibit long (50$-$75 kpc) tails of radio continuum and optical emission lines
(H$\alpha$) pointing away from the cluster centre and arcs of starformation on
the opposite sides of the tails. These features as well as the H{\sc i}
properties, with two of the galaxies (CGCG 097073 and 097079) exhibiting
sharper gradients in H{\sc i} intensity on the side of the tails, are
consistent with the H{\sc i} gas being affected by the ram pressure of the
intracluster medium. However the H{\sc i} emission in all the three galaxies
extends to much smaller distances than the radio-continuum and H$\alpha$ tails,
and are possibly still bound to the parent galaxies. Approximately 20$-$30 per
cent of the H{\sc i} mass is seen to accumulate on the downstream side due to
the effects of ram pressure.


  In a previous work, we proposed an extended Nambu--Jona-Lasinio (NJL) model
including heavy quark flavors. In this work, we will calculate strong and
radiative decays of vector mesons in this extended NJL model, including light
$\rho$, $\omega$, $K^*$, $\phi$ and heavy $D^*$, $D^*_s$, $B^*$, $B^*_s$.


  Recent analyses of photometric data on globular clusters and galaxies enabled
us to study more closely the long-periodic amplitude/phase modulation (Blazhko
effect) in classical variables. In the frequency spectra of these stars we see
either a doublet or an equally-spaced triplet with a very small frequency
separation close to the main component. None of the available theoretical
models are able to explain this behavior without invoking some form of
nonradial pulsation. In this review we describe the observational status of the
Blazhko variables, and discuss the limits of the applicability of the current
models to these stars.


  With the emergence of large language models (LLMs), investigating if they can
surpass humans in areas such as emotion recognition and empathetic responding
has become a focal point of research. This paper presents a comprehensive study
exploring the empathetic responding capabilities of four state-of-the-art LLMs:
GPT-4, LLaMA-2-70B-Chat, Gemini-1.0-Pro, and Mixtral-8x7B-Instruct in
comparison to a human baseline. We engaged 1,000 participants in a
between-subjects user study, assessing the empathetic quality of responses
generated by humans and the four LLMs to 2,000 emotional dialogue prompts
meticulously selected to cover a broad spectrum of 32 distinct positive and
negative emotions. Our findings reveal a statistically significant superiority
of the empathetic responding capability of LLMs over humans. GPT-4 emerged as
the most empathetic, marking approximately 31% increase in responses rated as
"Good" compared to the human benchmark. It was followed by LLaMA-2,
Mixtral-8x7B, and Gemini-Pro, which showed increases of approximately 24%, 21%,
and 10% in "Good" ratings, respectively. We further analyzed the response
ratings at a finer granularity and discovered that some LLMs are significantly
better at responding to specific emotions compared to others. The suggested
evaluation framework offers a scalable and adaptable approach for assessing the
empathy of new LLMs, avoiding the need to replicate this study's findings in
future research.


  We generalise an argument of Leader, Russell, and Walters to show that almost
all sets of d + 2 points on the (d - 1)-sphere S^{d-1} are not contained in a
transitive set in some R^n.


  The largest discs contained in a regular tetrahedron lie in its faces. The
proof is closely related to the theorem of Fritz John characterising ellipsoids
of maximal volume contained in convex bodies.


  Let $D$ be an integrally closed domain with quotient field $K$ and $n$ a
positive integer. We give a characterization of the polynomials in $K[X]$ which
are integer-valued over the set of matrices $M_n(D)$ in terms of their divided
differences. A necessary and sufficient condition on $f\in K[X]$ to be
integer-valued over $M_n(D)$ is that, for each $k$ less than $n$, the $k$-th
divided difference of $f$ is integral-valued on every subset of the roots of
any monic polynomial over $D$ of degree $n$. If in addition the intersection of
the maximal ideals of finite index is $(0)$ then it is sufficient to check the
above conditions on subsets of the roots of monic irreducible polynomials of
degree $n$, that is, conjugate integral elements of degree $n$ over $D$.


  We present recent results from a GALEX investigation of star formation in 16
cooling core clusters of galaxies, selected to span a broad range in both
redshift and central cooling time. Initial results demonstrate clear UV
excesses in most, but not all, brightest cluster galaxies in our sample. This
UV excess is a direct indication of the presence of young massive stars and,
therefore, recent star formation. We report on the physical extent of UV
emission in these objects as well as their FUV-NUV colors, and compare GALEX
inferred star formation rates to central cooling times, H-alpha and IR
luminosities for our sample.


  We review the theory of loss networks, including recent results on their
dynamical behaviour. We give also some new results.


  The experimental EXCITOR setup for obtaining the intense electron beams of
picosecond duration is presented in this work. Cathodes of tungsten, graphite,
copper and samarium of the same shape were used in these experiments. The
interelectrode gap varied from 0.5 to 6 mm. Interferometric technique to detect
anode rear side displacement was used. The time evolution of the displacement
and speed of the rear side of copper anode of 0.1 and 3.0 mm thickness was
experimentally obtained. Simulation of the space-time characteristics evolution
of the anode material is presented.


  In the present paper we consider a theory of gravity in which not only
curvature but also torsion is explicitly present in the Lagrangian, both with
their own coupling constant. In particular, we discuss the couplings to Dirac
fields and spin fluids: in the case of Dirac fields, we discuss how in our
approach, the Dirac self-interactions depend on the coupling constant as a
parameter that may even make these non-linearities manifest at subatomic
scales, showing different applications according to the value of the parameter
we have assigned; in the case of spin fluids, we discuss FLRW cosmological
models arising from the proposed theory.


  Deep learning's immense capabilities are often constrained by the complexity
of its models, leading to an increasing demand for effective sparsification
techniques. Bayesian sparsification for deep learning emerges as a crucial
approach, facilitating the design of models that are both computationally
efficient and competitive in terms of performance across various deep learning
applications. The state-of-the-art -- in Bayesian sparsification of deep neural
networks -- combines structural shrinkage priors on model weights with an
approximate inference scheme based on stochastic variational inference.
However, model inversion of the full generative model is exceptionally
computationally demanding, especially when compared to standard deep learning
of point estimates. In this context, we advocate for the use of Bayesian model
reduction (BMR) as a more efficient alternative for pruning of model weights.
As a generalization of the Savage-Dickey ratio, BMR allows a post-hoc
elimination of redundant model weights based on the posterior estimates under a
straightforward (non-hierarchical) generative model. Our comparative study
highlights the advantages of the BMR method relative to established approaches
based on hierarchical horseshoe priors over model weights. We illustrate the
potential of BMR across various deep learning architectures, from classical
networks like LeNet to modern frameworks such as Vision Transformers and
MLP-Mixers.


  Subgrid-scale (SGS) models are critical in large-eddy simulations (LES) of
turbulent flows. In this paper we conduct a comparative study on different SGS
models, including one-k-equation, wall-adapting local eddy-viscosity (WALE),
Sigma and shear-constrained model. Wall-resolved LES simulations of channel
flows are performed with a finite volume code at shear Reynolds number Re_\tau
= 395. In the simulations, the buffer sublayer turns out to be the most
sensitive to the SGS model. Through the analysis of the mean velocity, the
second-order moments, the SGS viscosity and the fluctuating vorticities, it is
shown that the WALE and Sigma model outperform others significantly in terms of
fluctuations while the constrained model improves slightly the mean velocity.
The results also indicate that the SGS dissipation influences strongly the
velocity fluctuations but not the mean flow nor the log-layer mismatch.


  Due to the hierarchical structure of many machine learning problems, bilevel
programming is becoming more and more important recently, however, the
complicated correlation between the inner and outer problem makes it extremely
challenging to solve. Although several intuitive algorithms based on the
automatic differentiation have been proposed and obtained success in some
applications, not much attention has been paid to finding the optimal
formulation of the bilevel model. Whether there exists a better formulation is
still an open problem. In this paper, we propose an improved bilevel model
which converges faster and better compared to the current formulation. We
provide theoretical guarantee and evaluation results over two tasks: Data
Hyper-Cleaning and Hyper Representation Learning. The empirical results show
that our model outperforms the current bilevel model with a great margin.
\emph{This is a concurrent work with \citet{liu2020generic} and we submitted to
ICML 2020. Now we put it on the arxiv for record.}


  Scanning tunneling spectroscopy at very low temperature on homogeneously
disordered superconducting Titanium Nitride thin films reveals strong spatial
inhomogeneities of the superconducting gap $\Delta$ in the density of states.
Upon increasing disorder, we observe suppression of the superconducting
critical temperature $T_c$ towards zero, enhancement of spatial fluctuations in
$\Delta$, and growth of the $\Delta/T_c$ ratio. These findings suggest that
local superconductivity survives across the disorder-driven
superconductor-insulator transition.


  We present experimental observation of a new phenomenon, that we interpret as
NMR-like effect on anisotropic magnetic moment of the surface Andreev bound
states in topological superfluid $^3$He-B at zero temperature limit. We show
that an anisotropic magnetic moment formed near the horizontal surface of a
mechanical resonator due to symmetry violation of the superfluid $^3$He-B order
parameter by the resonator's surface may lead to anomalous damping of the
resonator motion in magnetic field. In difference to classical NMR technique,
here NMR was excited using own harmonic motion of the mechanical resonator, and
nuclear magnetic resonance was detected as a maximum in damping when
resonator's angular frequency satisfied the Larmor resonance condition.


  We consider the optical Hall conductivity of a general electronic medium and
prove that the optical Hall angle obeys a new sum rule. This sum rule governs
the response of an electronic fluid to a Lorentz electric field and can thought
of as the transverse counterpart to the f-sum rule in optical conductivity. The
physical meaning of this sum rule is discussed, giving a number of examples of
its application to a variety of of electronic media.


  The purpose of the present study is to extend the simple concept of apparent
coefficient of restitution, widely approached in the literature for the case of
a single-contact-point between a sphere and a wall, to the case of bouncing
whose complexity is increased due to the shape of the contacting object.
  Experiments are carried out with a finite-length cylinder, freely falling in
a liquid at rest. Complex 3D motions of the cylinder with respect to the wall
occur during bouncing, including multi-contact-points between the cylinder and
the bottom as well as cavitation.
  We investigate numerical modelling of an idealized situation (2D infinite
cylinder falling parallel to the wall) with 2D simulations where the fluid
equations of motion were coupled to the particle equation of motion through an
Immersed Boundary Method. The particle equation of motion is coupled to an
elastic force to model bouncing, requiring a parameterization of the cut-off
length (interpreted as a roughness) and the contact time (associated with the
contact elasticity) used here to capture the experimental observations. The
simulations confirmed that i) the departure of the coefficient of restitution
from 0 is strictly dependent on the apparent roughness and ii) the coefficient
of restitution depends on the contact time.
  Finally, we model the coefficient of restitution as the product of two
contributions to the mechanical loss of energy: the collision-to-terminal
velocity ratio ($V_c/V_t$) of the approach-phase and the rebound-to-collision
velocity ratio ($-V_r/V_c$) of the contact-phase. This leads to a reasonably
good prediction of the coefficient of restitution in the intermediate regime in
$St$. This suggests the relevance of lumping the complex details of physical
phenomena involved during contact into a simple concept based on the contact
apparent roughness and elasticity.


  Half-supersymmetric geometries of N=2 five-dimensional gauged supergravity
have recently been fully classified using spinorial geometry techniques. We use
this classification to determine all possible regular half-supersymmetric
near-horizon geometries, assuming that all of the gauge-invariant spinor
bilinears are regular at the horizon. Four geometries are found, two of which
have been found previously in hep-th/0611351 and arXiv:0708.3695.


  The membership determination for open clusters in noisy environments of the
Milky Way is still an open problem. In this paper, our main aim is provide the
membership probability of stars using proper motions and parallax values of
stars using Gaia EDR3 astrometry. Apart from the Gaia astrometry, we have also
used other photometric data sets like UKIDSS, WISE, APASS and Pan-STARRS1 in
order to understand cluster properties from optical to mid-infrared regions. We
selected 438 likely members with membership probability higher than $50\%$ and
G$\le$20 mag. We obtained the mean value of proper motion as
$\mu_{x}=1.27\pm0.001$ and $\mu_{y}=-0.73\pm0.002$ mas yr$^{-1}$. The cluster's
radius is determined as 7.5 arcmin (5.67 pc) using radial density profile. Our
analysis suggests that NGC 1348 is located at a distance of $2.6\pm0.05$ kpc.
The mass function slope is found to be $1.30\pm0.18$ in the mass range
1.0$-$4.1 $M_\odot$, which is in fair agreement with Salpeter's value within
the 1$\sigma$ uncertainty. The present study validates that NGC 1348 is a
dynamically relaxed cluster. We computed the apex coordinates $(A, D)$ for NGC
1348 as $(A_\circ, D_\circ)$ = $(-23^{\textrm{o}}.815\pm 0^{\textrm{o}}.135$,
$-22^{\textrm{o}}.228\pm 0^{\textrm{o}}.105)$. In addition, calculations of the
velocity ellipsoid parameters (VEPs), matrix elements $\mu_{ij}$, direction
cosines ($l_j$, $m_j$, $n_j$) and the Galactic longitude of the vertex have
been also conducted in this analysis.


  We present high resolution measurements of the specific heat and the thermal
expansion of the inorganic spin--Peierls cuprate CuGeO_3 in a magnetic field of
16 Tesla. At the transition from the incommensurate to the uniform phase both
quantities show pronounced anomalies, which allow to derive the uniaxial
pressure dependencies of the transition temperature. In high magnetic fields
the specific heat is dominated by magnetic excitations and follows a T^3 law at
low temperatures. The thermal expansion measurements show the occurrence of
spontaneous strains along all three lattice constants and yield high resolution
measurements of the temperature dependence of the incommensurate structural
distortion. The sizes of the spontaneous strains in the incommensurate phase
are significantly reduced, but both their anisotropy as well as their
temperature dependencies are very similar to those in zero field.


  I report the discovery of a transient broad-H$\alpha$ point source in the
outskirts of the giant elliptical galaxy NGC 1404, discovered in archival
observations taken with the MUSE integral field spectrograph. The H$\alpha$
line width of 1950 km s$^{-1}$ FWHM, and luminosity of
(4.1$\pm$0.1)$\times$10$^{36}$ erg s$^{-1}$, are consistent with a nova
outburst, and the source is not visible in MUSE data obtained nine months
later. A transient soft X-ray source was detected at the same position (within
$<$1 arcsec), 14 years before the H$\alpha$ transient. If the X-ray and
H$\alpha$ emission are from the same object, the source may be a
short-timescale recurrent nova with a massive white dwarf accretor, and hence a
possible Type-Ia supernova progenitor. Selecting broad-H$\alpha$ point sources
in MUSE archival observations for a set of nearby early-type galaxies, I
discovered twelve more nova candidates with similar properties to the NGC 1404
source, including five in NGC 1380 and four in NGC 4365. Multi-epoch data are
available for four of these twelve sources; all four are confirmed to be
transient on $\sim$1 year timescales, supporting their identification as novae.


  Let $G$ be a locally compact group, and let ${\cal R}(G)$ denote the ring of
subsets of $G$ generated by the left cosets of open subsets of $G$. The
Cohen--Host idempotent theorem asserts that a set lies in ${\cal R}(G)$ if and
only if its indicator function is a coefficient function of a unitary
representation of $G$ on some Hilbert space. We prove related results for
representations of $G$ on certain Banach spaces. We apply our Cohen--Host type
theorems to the study of the Fig\`a-Talamanca--Herz algebras $A_p(G)$ with $p
\in (1,\infty)$. For arbitrary $G$, we characterize those closed ideals of
$A_p(G)$ that have an approximate identity bounded by 1 in terms of their
hulls. Furthermore, we characterize those $G$ such that $A_p(G)$ is 1-amenable
for some -- and, equivalently, for all -- $p \in (1,\infty)$: these are
precisely the abelian groups.


  We prove existence and multiplicity of small amplitude periodic solutions of
the completely resonant wave equation u_tt - u_xx + f(x,u)=0 with Dirichlet
boundary conditions where f(x,u)=a_2 u^2 + a_3(x) u^3 + O(u^4) or f(x,u)= a_4
u^4 + O(u^5) for a Cantor-like set of frequencies omega of asymptotically full
measure at omega=1.


  Aspect term extraction aims to extract aspect terms from review texts as
opinion targets for sentiment analysis. One of the big challenges with this
task is the lack of sufficient annotated data. While data augmentation is
potentially an effective technique to address the above issue, it is
uncontrollable as it may change aspect words and aspect labels unexpectedly. In
this paper, we formulate the data augmentation as a conditional generation
task: generating a new sentence while preserving the original opinion targets
and labels. We propose a masked sequence-to-sequence method for conditional
augmentation of aspect term extraction. Unlike existing augmentation
approaches, ours is controllable and allows us to generate more diversified
sentences. Experimental results confirm that our method alleviates the data
scarcity problem significantly. It also effectively boosts the performances of
several current models for aspect term extraction.


  Rayleigh-B\'enard (RB) convection with free-slip plates and horizontally
periodic boundary conditions is investigated using direct numerical
simulations. Two configurations are considered, one is two-dimension (2D) RB
convection and the other one three-dimension (3D) RB convection with a rotating
axis parallel to the plate. We explore the parameter range of Rayleigh numbers
Ra from $10^7 to $10^9$ and Prandtl numbers $Pr$ from $1$ to $100$. We show
that zonal flow, which was observed, for example, by Goluskin \emph{et al}.
\emph{J. Fluid. Mech.} 759, 360-385 (2014) for $\Gamma=2$, is only stable when
$\Gamma$ is smaller than a critical value, which depends on $Ra$ and $Pr$. With
increasing $\Gamma$, we find a second regime in which both zonal flow and
different convection roll states can be statistically stable. For even larger
$\Gamma$, in a third regime, only convection roll states are statistically
stable and zonal flow is not sustained. For the 3D simulations, we fix
$Ra=10^7$ and $Pr=0.71$, and compare the flow for
  $\Gamma=8$ and $\Gamma = 16$. We demonstrate that with increasing aspect
ratio $\Gamma$, zonal flow, which was observed for small $\Gamma=2\pi$ by von
Hardenberg \emph{et al}. \emph{Phys. Rev. Lett.} 15, 134501 (2015), completely
disappears for $\Gamma=16$. For such large $\Gamma$ only convection roll states
are statistically stable. In between, here for medium aspect ratio $\Gamma =
8$, the convection roll state and the zonal flow state are both statistically
stable. What state is taken depends on the initial conditions, similarly as we
found for the 2D case.


  Current status and future experimental plans for constraining the symmetry
energy at supra-normal densities are presented. A special emphasis is put on
significance of the results obtained by the ASY-EOS Collaboration in a broader
astrophysical context, including the recent interpretations of the first LIGO
and Virgo GW170817 gravitational wave signal. The plans for a high energy
campaign at FAIR using the NeuLAND and the KRAB detectors will be outlined.


  The decay K- -> pi0 mu- nu has been studied using in-flight decays detected
with the "ISTRA+" spectrometer. About 540K events were collected for the
analysis. The lambda+ and lambda0 slope parameters of the decay form-factors
f+(t), f0(t) have been measured : lambda+ = 0.0277+-0.0013 (stat)+-0.0009
(syst), lambda0 = 0.0183+-0.0011(stat)+-0.0006(syst), and
d(lambda0)/d(lambda+)=-0.348. The limits on the possible tensor and scalar
couplings have been derived: fT/f+(0)=-0.0007 +- 0.0071, fS/f+(0)=0.0017 +-
0.0014. No visible non-linearity in the form-factors have been observed.