  We study the task of cleaning scanned text documents that are strongly
corrupted by dirt such as manual line strokes, spilled ink etc. We aim at
autonomously removing dirt from a single letter-size page based only on the
information the page contains. Our approach, therefore, has to learn character
representations without supervision and requires a mechanism to distinguish
learned representations from irregular patterns. To learn character
representations, we use a probabilistic generative model parameterizing pattern
features, feature variances, the features' planar arrangements, and pattern
frequencies. The latent variables of the model describe pattern class, pattern
position, and the presence or absence of individual pattern features. The model
parameters are optimized using a novel variational EM approximation. After
learning, the parameters represent, independently of their absolute position,
planar feature arrangements and their variances. A quality measure defined
based on the learned representation then allows for an autonomous
discrimination between regular character patterns and the irregular patterns
making up the dirt. The irregular patterns can thus be removed to clean the
document. For a full Latin alphabet we found that a single page does not
contain sufficiently many character examples. However, even if heavily
corrupted by dirt, we show that a page containing a lower number of character
types can efficiently and autonomously be cleaned solely based on the
structural regularity of the characters it contains. In different examples
using characters from different alphabets, we demonstrate generality of the
approach and discuss its implications for future developments.


  We design spin filters for particles with potentially arbitrary spin S (=
1/2, 1, 3/2,....) using a one-dimensional periodic chain of magnetic atoms as a
quantum device. Describing the system within a tight-binding formalism we
present an analytical method to unravel the analogy between a one-dimensional
magnetic chain and a multi-strand ladder network. This analogy is crucial, and
is subsequently exploited to engineer gaps in the energy spectrum by an
appropriate choice of the magnetic substrate. We obtain an exact correlation
between the magnitude of the spin of the incoming beam of particles and the
magnetic moment of the substrate atoms in the chain desired for opening up of a
spectral gap. Results of spin polarized transport, calculated within a transfer
matrix formalism, are presented for particles having half-integer as well as
higher spin states. We find that the chain can be made to act as a quantum
device which opens a transmission window only for selected spin components over
certain ranges of the Fermi energy, blocking them in the remaining part of the
spectrum. The results appear to be robust even when the choice of the substrate
atoms deviates substantially from the ideal situation, as verified by extending
the ideas to the case of a spin spiral. Interestingly, the spin spiral
geometry, apart from exhibiting the filtering effect, is also seen to act as a
device flipping spins - an effect that can be monitored by an interplay of the
system size and the period of the spiral. Our scheme is applicable to ultracold
quantum gases, and might inspire future experiments in this direction.


  In gravitational lensing, the concept of optical depth assumes the lens is
dark. Several microlensing detections have now been made where the lens may be
bright. Relations are developed between apparent and absolute optical depth in
the regime of the apparent and absolute brightness of the lens. An apparent
optical depth through bright lenses is always less than the true, absolute
optical depth. The greater the intrinsic brightness of the lens, the more
likely it will be found nearer the source.


  The purpose of this work is to collect in one place available information on
line arrangements known in the literature as braid, monomial, Ceva or Fermat
arrangement. They have been studied for a long time and appeared recently in
connection with highly interesting problems, namely: the containment problem
between symbolic and ordinary powers of ideals and the existence of unexpected
hypersurfaces. We also study also derived configurations of points (or more
general: linear flats) which arise by intersecting hyperplanes in Fermat
arrangements or by taking duals of these hyperplanes. Furthermore we discuss
briefly higher dimensional generalizations and present results arising by
applying this approach to problems mentioned above. Some of our results are
original and appear for the first time in print.


  We derive a dynamical mean-field theory for mixtures of interacting bosons
and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive,
thermodynamically consistent framework for the theoretical investigation of
Bose-Fermi mixtures and is applicable for arbitrary values of the coupling
parameters and temperatures. It becomes exact in the limit of high spatial
dimensions d or coordination number Z of the lattice. In particular, the
BF-DMFT treats normal and condensed bosons on equal footing and thus includes
the effects caused by their dynamic coupling. Using the BF-DMFT we investigate
two different interaction models of correlated lattice bosons and fermions, one
where all particles are spinless (model I) and one where fermions carry a spin
one-half (model II). In model I the local, repulsive interaction between bosons
and fermions can give rise to an attractive effective interaction between the
bosons. In model II it can also lead to an attraction between the fermions.


  Let \beta : S^n \to S^n, for n = 2k + 1, k \geq 1, be one of the known
examples of a non-uniquely ergodic minimal diffeomorphism of an odd dimensional
sphere. For every such minimal dynamical system (S^n, \beta) there is a Cantor
minimal system (X, \alpha) such that the corresponding product system (X x S^n,
\alpha x \beta) is minimal and the resulting crossed product C*-algebra C(X x
S^n) \rtimes_{\alpha x \beta} \mathbb{Z} is tracially approximately an interval
algebra (TAI). This entails classification for such C*-algebras. Moreover, the
minimal Cantor system (X, \alpha) is such that each tracial state on C(X x S^n)
\rtimes_{\beta} \mathbb{Z} induces the same state on the K_0-group and such
that the embedding of C(S^n) \rtimes_{\beta} \mathbb{Z} into C(X x S^n)
\rtimes_{\alpha x \beta} \mathbb{Z} preserves the tracial state space. This
implies C(S^n) \rtimes_{\beta} \mathbb{Z} is TAI after tensoring with the
universal UHF algebra, which in turn shows that the C*-algebras of these
examples of minimal diffeomorphisms of odd dimensional spheres are classified
by their tracial state spaces.


  We use Kneser's neighbor method and isometry testing for lattices due to
Plesken and Souveigner to compute systems of Hecke eigenvalues associated to
definite forms of classical reductive algebraic groups.


  We proposed a new universal method for significantly increasing accuracy of
critical points of 2 and 3-dimensional Ising models and exploring fluctuation
mechanism. The method is based on analysis of block fractals and the
renormalization group theory. We discussed hierarchies and rescaling rule of
the self similar transformations, and define a fractal dimension of an ordered
block, which minimum corresponds to a fixed point of the transformations. By
the connectivity we divide the blocks into two types: irreducible and
reducible. We find there are two block spin states: single state and k-fold
state, each of which relates to a system or a subsystem described by a block
spin Gaussian model set up by mathematic map. Using the model we obtain a
universal formula of critical points by the minimal fractal dimensions. We
computed the critical points with high accuracy for three Ising models. It is
the first time to find a critical point only requires a fractal edge, which
causes fluctuations, and the point acts as a fluctuation attractor. Finally, we
discussed a possibility of different block spins at the critical point.


  It is shown that highly localized solitons can be created in lower
dimensional Bose-Einstein condensates (BEC), trapped in a regular harmonic
trap, by temporally varying the trap frequency. A BEC trapped in such a trap
can be effectively used to construct a pulsed atomic laser emitting coherent
atomic wave packets. It is also shown that one has complete control over the
spatio-temporal dynamics of the solitons. The dynamics of these solitons are
compared with those constructed in a BEC where the trap frequency is constant.


  In this paper we prove a tertiary index theorem which relates a spectral
geometric and a homotopy theoretic invariant of an almost complex manifold with
framed boundary. It is derived from the index theoretic and homotopy theoretic
versions of a complex elliptic genus and interestingly related with the
structure of the stable homotopy groups of spheres.


  The quantum sine-Gordon model is the simplest massive interacting integrable
quantum field theory whose two-particle scattering matrix is generally
non-diagonal. As such, it is a model that has been extensively studied,
especially in the context of the bootstrap programme. In this paper we compute
the form factors of a special local field known as the branch point twist
field, whose correlation functions are building blocks for measures of
entanglement. We consider the attractive regime where the theory posesses a
particle spectrum consisting of a soliton, an antisoliton (of opposite $U(1)$
charges) and several (neutral) breathers. In the breather sector we exploit the
fusion procedure to compute form factors of heavier breathers from those of
lighter ones. We apply our results to the study of the entanglement dynamics
after a small mass quench and for short times. We show that in the presence of
two or more breathers the von Neumann and R\'enyi entropies display undamped
oscillations in time, whose frequencies are proportional to the even breather
masses and whose amplitudes are proportional to the breather's one-particle
form factor.


  In this paper, martingales related to simple random walks and their maximum
process are investigated. First, a sufficient condition under which a function
with three arguments, time, the random walk, and its maximum process becomes a
martingale is presented, and as an application, an alternative way of deriving
the Kennedy martingale is provided. Then, a complete characterization of a
function with two arguments, the random walk and its maximum, being a
martingale is presented. This martingale can be regarded as a discrete version
of the Az\'ema--Yor martingale. As applications of discrete Az\'ema--Yor
martingale, a proof of the Doob's inequalities is provided and a discrete
Az\'ema--Yor solution for the Skorokhod embedding problem for the simple random
walk is formulated and examined in detail.


  Pre-training Reinforcement Learning agents in a task-agnostic manner has
shown promising results. However, previous works still struggle in learning and
discovering meaningful skills in high-dimensional state-spaces, such as
pixel-spaces. We approach the problem by leveraging unsupervised skill
discovery and self-supervised learning of state representations. In our work,
we learn a compact latent representation by making use of variational and
contrastive techniques. We demonstrate that both enable RL agents to learn a
set of basic navigation skills by maximizing an information theoretic
objective. We assess our method in Minecraft 3D pixel maps with different
complexities. Our results show that representations and conditioned policies
learned from pixels are enough for toy examples, but do not scale to realistic
and complex maps. To overcome these limitations, we explore alternative input
observations such as the relative position of the agent along with the raw
pixels.


  Common event-triggered state estimation (ETSE) algorithms save communication
in networked control systems by predicting agents' behavior, and transmitting
updates only when the predictions deviate significantly. The effectiveness in
reducing communication thus heavily depends on the quality of the dynamics
models used to predict the agents' states or measurements. Event-triggered
learning is proposed herein as a novel concept to further reduce communication:
whenever poor communication performance is detected, an identification
experiment is triggered and an improved prediction model learned from data.
Effective learning triggers are obtained by comparing the actual communication
rate with the one that is expected based on the current model. By analyzing
statistical properties of the inter-communication times and leveraging powerful
convergence results, the proposed trigger is proven to limit learning
experiments to the necessary instants. Numerical and physical experiments
demonstrate that event-triggered learning improves robustness toward changing
environments and yields lower communication rates than common ETSE.


  It has for ages been a rather constant feature of thinking in science to take
it for granted that the respective thinking happens in realms which are totally
outside and independent of all the other phenomena that constitute the objects
of such thinking. The imposition of this divide on two levels may conflict with
basic assumptions of Newtonian and Einsteinian mechanics, as well as with those
in Quantum Mechanics. It also raises the question whether the realms in which
thinking happens have no any other connection with the realms science deals
with, except to host and allow scientific thinking.


  In this paper, we will give convergence analysis for a family of 14-node
elements which was proposed by I. M. Smith and D. J. Kidger in 1992. The 14
DOFs are taken as the value at the eight vertices and six face-centroids. For
second-order elliptic problem, we will show that among all the Smith-Kidger
14-node elements, Type 1, Type 2 and type 5 elements can get the optimal
convergence order and Type 6 get lower convergence order. Motivated by the
proof, we also present a new 14-node nonconforming element. If we change the
DOFs into the value at the eight vertices and the integration value of six
faces, we show that Type 1, Type 2 and Type 5 keep the optimal convergence
order and Type 6 element improve one order accuracy which means that it also
get optimal convergence order.


  After reviewing known results on sensitiveness and also on robustness of
attractors together with observations on their proofs, we show that for
attractors of three-dimensional flows, robust chaotic behavior meaning
sensitiveness to initial conditions for the past as well for the future for all
nearby flows) is equivalent to the existence of certain hyperbolic structures.
These structures, in turn, are associated to the existence of physical
measures. In short in low dimensions, robust chaotic behavior for smooth flows
ensures the existence of a physical measure.


  We present an analysis of the neutrino oscillation solutions of the solar and
atmospheric neutrino problems in the framework of four-neutrino mixing where a
sterile neutrino is added to the three standard ones and the mass spectra
presents two separated doublets. Such scenarios allow for simultaneous
transitions of solar $\nu_e$, as well as atmospheric $\nu_\mu$, into active and
sterile neutrinos controlled by the additional mixing angles $\vartheta_{23}$
and $\vartheta_{24}$, and they contain as limiting cases the pure solar
$\nu_e$-active and $\nu_e$-sterile neutrino oscillations, and the pure
atmospheric $\nu_\mu\to\nu_s$ and $\nu_\mu\to\nu_\tau$ oscillations,
respectively. We evaluate the allowed active-sterile admixture in both solar
and atmospheric oscillations from the combined analysis. Our results show that,
although the Super-Kamiokande data disfavour both the pure $\nu_\mu\to\nu_s$
atmospheric channel and the pure $\nu_e\to\nu_s$ solar channel, the result from
the combined analysis still favours close-to-pure active and sterile
oscillations and disfavours oscillations into a near-maximal active-sterile
admixture.


  Van der Waals (vdW) magnets are promising owing to their tunable magnetic
properties with doping or alloy composition, where the strength of magnetic
interactions, their symmetry, and magnetic anisotropy can be tuned according to
the desired application. However, most of the vdW magnet based spintronic
devices are so far limited to cryogenic temperatures with magnetic anisotropies
favouring out-of-plane or canted orientation of the magnetization. Here, we
report room-temperature lateral spin-valve devices with strong in-plane
magnetic anisotropy of the vdW ferromagnet (Co0.15Fe0.85)5GeTe2 (CFGT) in
heterostructures with graphene. Magnetization measurements reveal above
room-temperature ferromagnetism in CFGT with a strong in-plane magnetic
anisotropy. Density functional theory calculations show that the magnitude of
the anisotropy depends on the Co concentration and is caused by the
substitution of Co in the outermost Fe layer. Heterostructures consisting of
CFGT nanolayers and graphene were used to experimentally realize basic building
blocks for spin valve devices such as efficient spin injection and detection.
The spin transport and Hanle spin precession measurements prove a strong
in-plane and negative spin polarization at the interface with graphene, which
is supported by the calculated spin-polarized density of states of CFGT. The
in-plane magnetization of CFGT at room temperature proves its usefulness in
graphene lateral spin-valve devices, thus opening further opportunities for
spintronic technologies.


  We have discovered heavy obscuration in the dual active galactic nucleus
(AGN) in the Swift/Burst Alert Telescope (BAT) source SWIFT J2028.5+2543 using
Nuclear Spectroscopic Telescope Array (NuSTAR). While an early XMM-Newton study
suggested the emission was mainly from NGC 6921, the superior spatial
resolution of NuSTAR above 10 keV resolves the Swift/BAT emission into two
sources associated with the nearby galaxies MCG +04-48-002 and NGC 6921 (z =
0.014) with a projected separation of 25.3 kpc (91"). NuSTAR's sensitivity
above 10 keV finds both are heavily obscured to Compton-thick levels (N
H=(1-2)x10^24 cm-2) and contribute equally to the BAT detection ({L}10-50
{keV}{{int}}= 6x10^42 erg s-1). The observed luminosity of both sources is
severely diminished in the 2-10 keV band, illustrating the importance of >10
keV surveys like those with NuSTAR and Swift/BAT. Compared to archival X-ray
data, MCG +04-48-002 shows significant variability (>3) between observations.
Despite being bright X-ray AGNs, they are difficult to detect using optical
emission-line diagnostics because MCG +04-48-002 is identified as a
starburst/composite because of the high rates of star formation from a luminous
infrared galaxy while NGC 6921 is only classified as a LINER using line
detection limits. SWIFT J2028.5+2543 is the first dual AGN resolved above 10
keV and is the second most heavily obscured dual AGN discovered to date in the
X-rays other than NGC 6240.


  Optical measurements under externally applied stresses allow us to study the
materials' electronic structure by comparing the pressure evolution of optical
peaks obtained from experiments and theoretical calculations. We examine the
stress-induced changes in electronic structure for the thermodynamically stable
1T polytype of selected MX2 compounds (M=Hf, Zr, Sn; X=S, Se), using the
density functional theory. We demonstrate that considered 1T-MX2 materials are
semiconducting with indirect character of the band gap, irrespective to the
employed pressure as predicted using modified Becke-Johnson potential. We
determine energies of direct interband transitions between bands extrema and in
band-nesting regions close to Fermi level. Generally, the studied transitions
are optically active, exhibiting in-plane polarization of light. Finally, we
quantify their energy trends under external hydrostatic, uniaxial, and biaxial
stresses by determining the linear pressure coefficients. Generally, negative
pressure coefficients are obtained implying the narrowing of the band gap. The
semiconducting-to-metal transition are predicted under hydrostatic pressure. We
discuss these trends in terms of orbital composition of involved electronic
bands. In addition, we demonstrate that the measured pressure coefficients of
HfS2 and HfSe2 absorption edges are in perfect agreement with our predictions.
Comprehensive and easy-to-interpret tables containing the optical features are
provided to form the basis for assignation of optical peaks in future
measurements.


  By studying the n-dimensional cube, the author finds a new way, and use it to
proves that the indefinite equation $x^n+y^n=z^n(n=>3)$ has no any solutions of
positive integers.


  We have carried out a search for massive white dwarfs (WDs) in the direction
of young open star clusters using the Gaia DR2 database. The aim of this survey
was to provide robust data for new and previously known high-mass WDs regarding
cluster membership, to highlight WDs previously included in the Initial Final
Mass Relation (IFMR) that are unlikely members of their respective clusters
according to Gaia astrometry and to select an unequivocal WD sample that could
then be compared with the host clusters' turnoff masses.
  All promising WD candidates in each cluster CMD were followed up with
spectroscopy from Gemini in order to determine whether they were indeed WDs and
derive their masses, temperatures and ages. In order to be considered cluster
members, white dwarfs were required to have proper motions and parallaxes
within 2, 3, or 4-$\sigma$ of that of their potential parent cluster based on
how contaminated the field was in their region of the sky, have a cooling age
that was less than the cluster age and a mass that was broadly consistent with
the IFMR. A number of WDs included in current versions of the IFMR turned out
to be non-members and a number of apparent members, based on Gaia's astrometric
data alone, were rejected as their mass and/or cooling times were incompatible
with cluster membership. In this way, we developed a highly selected IFMR
sample for high mass WDs that, surprisingly, contained no precursor masses
significantly in excess of ${\sim}$6 $M_{\odot}$.


  We use lattice simulations and the continuous renormalization-group method,
based on the gradient flow, to calculate the $\beta$ function and anomalous
dimensions of the SU(3) gauge theory with $N_f=10$ flavors of fermions in the
fundamental representation. We employ several improvements to extend the range
of available renormalized couplings, including the addition of heavy
Pauli-Villars bosons to reduce cutoff effects and the combination of a range of
gradient flow transformations. While in the weak coupling regime our result is
consistent with those of earlier studies, our techniques allow us to study the
system at much stronger couplings than previously possible. We find that the
renormalization group $\beta$ function develops a zero, corresponding to an
infrared-stable fixed point, at gradient-flow coupling $g^2=15.0(5)$. We also
determine the mass and tensor anomalous dimensions: At the fixed point we find
$\gamma_m\simeq0.6$, suggesting that this system might be deep inside the
conformal window.


  The occurrence of the nonzero leftmost digit, i.e., 1, 2, ..., 9, of numbers
from many real world sources is not uniformly distributed as one might naively
expect, but instead, the nature favors smaller ones according to a logarithmic
distribution, named Benford's law. We investigate three kinds of widely used
physical statistics, i.e., the Boltzmann-Gibbs (BG) distribution, the
Fermi-Dirac (FD) distribution, and the Bose-Einstein (BE) distribution, and
find that the BG and FD distributions both fluctuate slightly in a periodic
manner around the Benford distribution with respect to the temperature of the
system, while the BE distribution conforms to it exactly whatever the
temperature is. Thus the Benford's law seems to present a general pattern for
physical statistics and might be even more fundamental and profound in nature.
Furthermore, various elegant properties of Benford's law, especially the
mantissa distribution of data sets, are discussed.


  We propose multivariate nonstationary Gaussian processes for jointly modeling
multiple clinical variables, where the key parameters, length-scales, standard
deviations and the correlations between the observed output, are all time
dependent. We perform posterior inference via Hamiltonian Monte Carlo (HMC). We
also provide methods for obtaining computationally efficient gradient-based
maximum a posteriori (MAP) estimates. We validate our model on synthetic data
as well as on electronic health records (EHR) data from Kaiser Permanente (KP).
We show that the proposed model provides better predictive performance over a
stationary model as well as uncovers interesting latent correlation processes
across vitals which are potentially predictive of patient risk.


  We present a novel solver for an analogue to Poisson's equation in the
framework of modified Newtonian dynamics (MOND). This equation is highly
non-linear and hence standard codes based upon tree structures and/or FFT's in
general are not applicable; one needs to defer to multi-grid relaxation
techniques. After a detailed description of the necessary modifications to the
cosmological N-body code AMIGA (formerly known as MLAPM) we utilize the new
code to revisit the issue of cosmic structure formation under MOND. We find
that the proper (numerical) integration of a MONDian Poisson's equation has
some noticable effects on the final results when compared against simulations
of the same kind but based upon rather ad-hoc assumptions about the properties
of the MONDian force field. Namely, we find that the large-scale structure
evolution is faster in our revised MOND model leading to an even stronger
clustering of galaxies, especially when compared to the standard LCDM paradigm.


  The Cartan and Iwasawa decompositions of real reductive Lie groups play a
fundamental role in the representation theory of the groups and their
corresponding symmetric spaces. These decompositions are defined by an
involution with a compact fixed-point group, called a Cartan involution. For an
arbitrary involution, one can consider similar decompositions. We offer a
generalization of the Cartan and Iwasawa decompositions for algebraic groups
defined over an arbitrary field $k$ and a general involution.


  We develop a fermionic formulation of the triangular lattice Ising
antiferromagnet (TIAFM) which is both calculationally convenient and
intuitively appealing to imaginations steeped in conventional condensed matter
physics. It is used to elucidate a variety of aspects of zero-temperature
models. Cylindrical systems possess multiple "phases" distinguished by the
number of circumferential satisfied bonds and by entropy density. On the plane,
phases are labelled by densities of satisfied bonds of two different
orientations. A local particle (semi)conservation law in the fermionic picture
lies behind both these features as well as the classic power-law falloff of the
spin-spin correlation function, which is also derived from the fermionic
perspective.


  Recent studies have shown how disentangling images into content and feature
spaces can provide controllable image translation/ manipulation. In this paper,
we propose a framework to enable utilizing discrete multi-labels to control
which features to be disentangled, i.e., disentangling label-specific
fine-grained features for image manipulation (dubbed DLGAN). By mapping the
discrete label-specific attribute features into a continuous prior
distribution, we leverage the advantages of both discrete labels and reference
images to achieve image manipulation in a hybrid fashion. For example, given a
face image dataset (e.g., CelebA) with multiple discrete fine-grained labels,
we can learn to smoothly interpolate a face image between black hair and blond
hair through reference images while immediately controlling the gender and age
through discrete input labels. To the best of our knowledge, this is the first
work that realizes such a hybrid manipulation within a single model. More
importantly, it is the first work to achieve image interpolation between two
different domains without requiring continuous labels as the supervision.
Qualitative and quantitative experiments demonstrate the effectiveness of the
proposed method.


  Voice-Controllable Devices (VCDs) have seen an increasing trend towards their
adoption due to the small form factor of the MEMS microphones and their easy
integration into modern gadgets. Recent studies have revealed that MEMS
microphones are vulnerable to audio-modulated laser injection attacks. This
paper aims to develop countermeasures to detect and prevent laser injection
attacks on MEMS microphones. A time-frequency decomposition based on discrete
wavelet transform (DWT) is employed to decompose microphone output audio signal
into n + 1 frequency subbands to capture photo-acoustic related artifacts.
Higher-order statistical features consisting of the first four moments of
subband audio signals, e.g., variance, skew, and kurtosis are used to
distinguish between acoustic and photo-acoustic responses. An SVM classifier is
used to learn the underlying model that differentiates between an acoustic- and
laser-induced (photo-acoustic) response in the MEMS microphone. The proposed
framework is evaluated on a data set of 190 audios, consisting of 19 speakers.
The experimental results indicate that the proposed framework is able to
correctly classify $98\%$ of the acoustic- and laser-induced audio in a random
data partition setting and $100\%$ of the audio in speaker-independent and
text-independent data partition settings.


  Dynamical heterogeneity and the decoupling of diffusion and structural
relaxation in a supercooled liquid is investigated in terms of a
time-dependent, fourth-order density correlation function. The generalized
susceptibility $\chi_4(t)$ corresponding to this correlation function has a
maximum at an intermediate time $t_4^*$, and both $t_4^*$ and $\chi_4(t_4^*)$
grow strongly with decreasing temperature. We show that the main contribution
to $\chi_4(t)$ arises from spatial correlations between temporarily localized
(``caged'') particles. We compare $\chi_4(t)$ with a generalized susceptibility
$\chi_M(t)$ related to a correlation function of squared particle
displacements, and show that while $t_4^*$ is roughly proportional to the
$\alpha$-relaxation time, $t_M^*$ is proportional to the inverse of the
self-diffusion coefficient.


  We analyze Killing Initial Data on Cauchy surfaces in conformally rescaled
vacuum space-times satisfying Friedrich's conformal field equations. As an
application, we derive the KID equations on a spacelike $\mathcal{J}^-$.


  In the context of departures from Special Relativity written as a momentum
power expansion in the inverse of an ultraviolet energy scale M, we derive the
constraints that the relativity principle imposes between coefficients of a
deformed composition law, dispersion relation, and transformation laws, at
first order in the power expansion. In particular, we find that, at that order,
the consistency of a modification of the energy-momentum composition law fixes
the modification in the dispersion relation. We therefore obtain the most
generic modification of Special Relativity that preserves the relativity
principle at leading order in 1/M.


  We compute the contributions to the electron and muon anomalous magnetic
moment induced by heavy leptons up to four-loop order. Asymptotic expansion is
applied to obtain three analytic expansion terms which show rapid convergence.


  Extremely large antenna arrays (ELAAs) can provide higher spectral
efficiency. However, the use of narrower beams for data transmission
significantly increases the overhead associated with beam training. In this
letter, we propose a novel patterned beam training (PBT) scheme characterized
by its low overhead and complexity. This scheme requires only a single linear
operation by both the base station and the user equipment to determine the
optimal beam, reducing the training overhead to half or even less compared to
traditional exhaustive search methods. Furthermore, We discuss the pattern
design principles in detail and provide specific forms. Simulation results
demonstrate that the proposed scheme outperforms the compared methods in terms
of beam alignment accuracy and achieves a balance between signal-to-noise ratio
(SNR) conditions and training overhead, making it a promising alternative.


  The kinetics of non-ionic surfactant adsorption at a fluid-fluid interface
from a micellar solution is considered theoretically. Our model takes into
account the effect of micelle relaxation on the diffusion of the free
surfactant molecules. It is shown that non-ionic surfactants undergo either a
diffusion or a kinetically limited adsorption according to the characteristic
relaxation time of the micelles. This gives a new interpretation for the
observed dynamical surface tension of micellar solutions.


  It is proven that the rotation of the spin of a polarized neutron is
accompanied by a net nuclear force upon it. This force arises from the weak
nuclear self-interaction of its constituent quarks, whose chiral nature induces
the transfer of a net momentum to the fields of Z and W-bosons. This effect is
linear in Fermi's constant. As a result, it is estimated that along the
spin-flip of a polarized neutron its velocity undergoes a variation of the
order of meters per second.


  A procedure for solving the Maxwell equations in vacuum, under the additional
requirement that both scalar invariants are equal to zero, is presented. Such a
field is usually called a null electromagnetic field. Based on the complex
Euler potentials that appear as arbitrary functions in the general solution, a
vector potential for the null electromagnetic field is defined. This potential
is called natural vector potential of the null electromagnetic field. An
attempt is made to make the most of knowing the general solution. The
properties of the field and the potential are studied without fixing a specific
family of solutions. A equality, which is similar to the Dirac gauge condition,
is found to be true for both null field and Lienard-Wiechert field. It turns
out that the natural potential is a substantially complex vector, which is
equivalent to two real potentials. A modification of the coupling term in the
Dirac equation is proposed, that makes the equation work with both real
potentials. A solution, that corresponds to the Volkov's solution for a Dirac
particle in a linearly polarized plane electromagnetic wave, is found. The
solution found is directly compared to Volkov's solution under the same
conditions.


  We consider a model of $d$-dimensional interacting quantum Bose gas,
expressed in terms of an ensemble of interacting Brownian bridges in a large
box and undergoing the influence of all the interactions between the legs of
each of the Brownian bridges. We study the thermodynamic limit of the system
and give an explicit formula for the limiting free energy and a necessary and
sufficient criterion for the occurrence of a condensation phase transition. For
$d\geq 5$ and sufficiently small interaction, we prove that the condensate
phase is not empty. The ideas of proof rely on the similarity of the
interaction to that of the self-repellent random walk, and build on a lace
expansion method conducive to treating {\it paths} undergoing mutual repellence
within each bridge.


  Superiorization reduces, not necessarily minimizes, the value of a target
function while seeking constraints-compatibility. This is done by taking a
solely feasibility-seeking algorithm, analyzing its perturbations resilience,
and proactively perturbing its iterates accordingly to steer them toward a
feasible point with reduced value of the target function. When the perturbation
steps are computationally efficient, this enables generation of a superior
result with essentially the same computational cost as that of the original
feasibility-seeking algorithm. In this work, we refine previous formulations of
the superiorization method to create a more general framework, enabling target
function reduction steps that do not require partial derivatives of the target
function. In perturbations that use partial derivatives the step-sizes in the
perturbation phase of the superiorization method are chosen independently from
the choice of the nonascent directions. This is no longer true when
component-wise perturbations are employed. In that case, the step-sizes must be
linked to the choice of the nonascent direction in every step. Besides
presenting and validating these notions, we give a computational demonstration
of superiorization with component-wise perturbations for a problem of
computerized tomography image reconstruction.


  The Flora family resides in the densely populated inner main belt, bounded in
semimajor axis by the $\nu_6$ secular resonance and the Jupiter 3:1 mean motion
resonance. The presence of several large families that overlap dynamically with
the Floras (e.g., the Vesta, Baptistina, and Nysa-Polana families), and the
removal of a significant fraction of Floras via the nearby $\nu_6$ resonance
complicates the Flora family's distinction in both proper orbital elements and
reflectance properties. Here we use orbital information from the Asteroids
Dynamic Site, color information from the Sloan Digital Sky Survey, and albedo
information from the Wide-field Infrared Survey Explorer to obtain the median
orbital and reflectance properties of the Floras by sampling the core of the
family in multidimensional phase space. We find the median Flora SDSS colors to
be $a^*$ = 0.126 $\pm$ 0.007 and $i-z = -0.037 \pm 0.007$; the median Flora
albedo is $p_V$ = 0.291 $\pm$ 0.012. These properties allow us to define ranges
for the Flora family in orbital and reflectance properties, as required for a
detailed dynamical study. We use the young Karin family, for which we have an
age determined via direct backward integration of members' orbits, to calibrate
the Yarkovsky drift rates for the Flora family without having to estimate the
Floras' material properties. The size-dependent dispersion of the Flora members
in semimajor axis (the "V" plot) then yields an age for the family of
$910^{+160}_{-120}$ My, with the uncertainty dominated by the uncertainty in
the material properties of the family members (e.g., density and surface
thermal properties). We discuss the effects on our age estimate of two
independent processes that both introduce obliquity variations among the family
members on short (My) timescales: 1) the capture of Flora members in spin-orbit
resonance, and 2) YORP-driven obliquity variation.


  We obtained the spectral function of the graphite H point using high
resolution angle resolved photoelectron spectroscopy (ARPES). The extracted
width of the spectral function (inverse of the photo-hole lifetime) near the H
point is approximately proportional to the energy as expected from the linearly
increasing density of states (DOS) near the Fermi energy. This is well
accounted by our electron-phonon coupling theory considering the peculiar
electronic DOS near the Fermi level. And we also investigated the temperature
dependence of the peak widths both experimentally and theoretically. The upper
bound for the electron-phonon coupling parameter is ~0.23, nearly the same
value as previously reported at the K point. Our analysis of temperature
dependent ARPES data at K shows that the energy of phonon mode of graphite has
much higher energy scale than 125K which is dominant in electron-phonon
coupling.


  In a recent paper published in this Journal, Khordad and collaborators [J Low
Temp Phys (2018) 190:200] have studied the thermodynamics properties of a GaAs
double ring-shaped quantum dot under external magnetic and electric fields. In
that meritorious research the energy of system was obtained by solving the
Schr\"{o}dinger equation. The radial equation was mapped into a confluent
hypergeometric differential equation and the differential equation associated
to $z$ coordinate was mapped into a biconfluent Heun differential equation. In
this paper, it is pointed out a misleading treatment on the solution of the
biconfluent Heun equation. It is shown that the energy $E_{z}$ can not be
labeled with $n_{z}$ and this fact jeopardizes the results of this system. We
calculate the partition function with the correct energy spectrum and
recalculate the specific heat and entropy as a function of low and high
temperatures.


  In order to understand a boundary description of Hawking radiation in the
AdS/CFT correspondence, we investigate the trace anomaly method in AdS$_2$
space. In this method, Hawking radiation is derived from the trace anomaly of
the energy-momentum tensor in the bulk. We find a correspondence between the
energy-momentum tensor and a composite operator in CFT$_1$ and understand the
anomalous properties of the energy-momentum tensor in terms of this composite
operator. By using this correspondence, we reproduce Hawking radiation from the
boundary description. In addition, we find a correspondence between higher-spin
currents in the bulk and composite operators in the boundary.


  We characterize Lipschitz morphisms between quantum compact metric spaces as
those *-morphisms which preserve the domain of certain noncommutative analogues
of Lipschitz seminorms, namely lower semi-continuous Lip-norms. As a corollary,
lower semi-continuous Lip-norms with a shared domain are in fact equivalent. We
then note that when a family of lower semi-continuous Lip-norms are uniformly
equivalent, then they give rise to totally bounded classes of quantum compact
metric spaces, and we apply this observation to several examples of
perturbations of quantum metric spaces. We also construct the noncommutative
generalization of the Lipschitz distance between quantum compact metric spaces.


  Binary classification models which can assign probabilities to categories
such as "the tissue is 75% likely to be tumorous" or "the chemical is 25%
likely to be toxic" are well understood statistically, but their utility as an
input to decision making is less well explored. We argue that users need to
know which is the most probable outcome, how likely that is to be true and, in
addition, whether the model is capable enough to provide an answer. It is the
last case, where the potential outcomes of the model explicitly include "don't
know" that is addressed in this paper. Including this outcome would better
separate those predictions that can lead directly to a decision from those
where more data is needed. Where models produce an "Uncertain" answer similar
to a human reply of "don't know" or "50:50" in the examples we refer to
earlier, this would translate to actions such as "operate on tumour" or "remove
compound from use" where the models give a "more true than not" answer. Where
the models judge the result "Uncertain" the practical decision might be "carry
out more detailed laboratory testing of compound" or "commission new tissue
analyses". The paper presents several examples where we first analyse the
effect of its introduction, then present a methodology for separating
"Uncertain" from binary predictions and finally, we provide arguments for its
use in practice.


  We prove global existence for semilinear hyperbolic equations that satisfy
the null condition of Christodoulou and Klainerman in the exterior of convex
domains. We use a combination of the conformal method of Christodoulou and the
direct method of Klainerman.


  Given a constant vector field $Z$ in Minkowski space, a timelike surface is
said to have a canonical null direction with respect to $Z$ if the projection
of $Z$ on the tangent space of the surface gives a lightlike vector field. In
this paper we describe these surfaces in the ruled case. For example when the
Minkowski space has three dimensions then a surface with a canonical null
direction is minimal and flat. On the other hand, we describe several
properties in the non ruled case and we partially describe these surfaces in
four-dimensional Minkowski space. We give different ways for building these
surfaces in four-dimensional Minkowski space and we finally use the Gauss map
for describe another properties of these surfaces.


  It is well known that solutions of general relativity which allow for
traversable wormholes require the existence of exotic matter (matter that
violates weak or null energy conditions [WEC or NEC]). In this article, we
provide a class of exact solution for Einstein-Maxwell field equations
describing wormholes assuming the erstwhile cosmological term $\Lambda$ to be
space variable, viz., $\Lambda = \Lambda (r)$.
  The source considered here not only a matter entirely but a sum of matters
i.e. anisotropic matter distribution, electromagnetic field and cosmological
constant whose effective parts obey all energy conditions out side the wormhole
throat. Here violation of energy conditions can be compensated by varying
cosmological constant. The important feature of this article is that one can
get wormhole structure, at least theoretically, comprising with physically
acceptable matters.


  We study the Lipschitz structures on the geodesic compactification of a
regular tree, that are preserved by the automorphism group. They are shown to
be similar to the compactifications introduced by William Floyd, and a complete
description is given.


  We set up a new notion of local convergence for permutations and we prove a
characterization in terms of proportions of \emph{consecutive} pattern
occurrences. We also characterize random limiting objects for this new topology
introducing a notion of "shift-invariant" property (corresponding to the notion
of unimodularity for random graphs). We then study two models in the framework
of random pattern-avoiding permutations. We compute the local limits of uniform
$\rho$-avoiding permutations, for $|\rho|=3,$ when the size of the permutations
tends to infinity. The core part of the argument is the description of the
asymptotics of the number of consecutive occurrences of any given pattern. For
this result we use bijections between $\rho$-avoiding permutations and rooted
ordered trees, local limit results for Galton--Watson trees, the Second moment
method and singularity analysis.


  Deep learning techniques have recently shown to be successful in many natural
language processing tasks forming state-of-the-art systems. They require,
however, a large amount of annotated data which is often missing. This paper
explores the use of domain-adversarial learning as a regularizer to avoid
overfitting when training domain invariant features for deep, complex neural
networks in low-resource and zero-resource settings in new target domains or
languages. In case of new languages, we show that monolingual word vectors can
be directly used for training without prealignment. Their projection into a
common space can be learnt ad-hoc at training time reaching the final
performance of pretrained multilingual word vectors.


  We discuss present predictions for the total $\gamma \gamma$ and $\gamma p $
cross-sections, highlighting why predictions differ. We present results from
the Eikonal Minijet Model and improved predictions based on soft gluon
resummation.


  The use of unmanned aerial vehicle (UAV)-based communication in
millimeter-wave (mmWave) frequencies to provide on-demand radio access is a
promising approach to improve capacity and coverage in beyond-5G (B5G) systems.
There are several design aspects to be addressed when optimizing for the
deployment of such UAV base stations. As traffic demand of mobile users varies
across time and space, dynamic algorithms that correspondingly adjust the UAV
locations are essential to maximize performance. In addition to careful
tracking of spatio-temporal user/traffic activity, such optimization needs to
account for realistic backhaul constraints. In this work, we first review the
latest 3GPP activities behind integrated access and backhaul system design,
support for UAV base stations, and mmWave radio relaying functionality. We then
compare static and mobile UAV-based communication options under practical
assumptions on the mmWave system layout, mobility and clusterization of users,
antenna array geometry, and dynamic backhauling. We demonstrate that leveraging
the UAV mobility to serve moving users may improve the overall system
performance even in the presence of backhaul capacity limitations.


  We study the pointed or copointed liftings of Nichols algebras associated to
affine racks and constant cocycles for any finite group admitting a principal
YD-realization of these racks. In the copointed case we complete the
classification for the six affine racks whose Nichols algebra is known to be of
finite dimension. In the pointed case our method allows us to finish four of
them. In all of the cases the Hopf algebras obtained turn out to be cocycle
deformations of their associated graded Hopf algebras. All of them are new
examples of finite-dimensional copointed or pointed Hopf algebras over
non-abelian groups.


  Shrinking pattern dimensions leads to an increased variety of defect types in
semiconductor devices. This has spurred innovation in patterning approaches
such as Directed self-assembly (DSA) for which no traditional, automatic defect
inspection software exists. Machine Learning-based SEM image analysis has
become an increasingly popular research topic for defect inspection with
supervised ML models often showing the best performance. However, little
research has been done on obtaining a dataset with high-quality labels for
these supervised models. In this work, we propose a method for obtaining
coherent and complete labels for a dataset of hexagonal contact hole DSA
patterns while requiring minimal quality control effort from a DSA expert. We
show that YOLOv8, a state-of-the-art neural network, achieves defect detection
precisions of more than 0.9 mAP on our final dataset which best reflects DSA
expert defect labeling expectations. We discuss the strengths and limitations
of our proposed labeling approach and suggest directions for future work in
data-centric ML-based defect inspection.


  We show that two interacting physical systems may admit entangled pure or non
separable mixed states evolving in time as if the mutual interaction
hamiltonian were absent. In this paper we define these states Interaction Free
Evolving (IFE) states and characterize their existence for a generic binary
system described by a time independent Hamiltonian. A comparison between IFE
subspace and the decoherence free subspace is reported. The set of all pure IFE
states is explicitly constructed for a non homogeneous spin star system model.


  Computational workflow management systems power contemporary data-intensive
sciences. The slowly resolving reproducibility crisis presents both a sobering
warning and an opportunity to iterate on what science and data processing
entails. The Square Kilometre Array (SKA), the world's largest radio telescope,
is among the most extensive scientific projects underway and presents grand
scientific collaboration and data-processing challenges. This work presents a
scale and system-agnostic computational workflow model and extends five
well-known reproducibility tenets into seven defined for our workflow model.
Subsequent implementation of these definitions, powered by blockchain
primitives, into the Data Activated Flow Graph Engine (DALiuGE), a workflow
management system for the SKA, demonstrates the possibility of facilitating
automatic formal verification of scientific quality in amortized constant time.
We validate our approach with a simple yet representative astronomical
processing task; filtering a noisy signal with a lowpass filter with both CPU
and GPU methods. Our framework illuminates otherwise obscure scientific
discrepancies and similarities between principally identical workflow
executions.


  A solution of the vortex type is given in a six-dimensional $SU(2)\times
U(1)$ pure gauge theory coupled to Einstein gravity in a compactified
background geometry. We construct the solution of an effective abelian Higgs
model in terms of dimensional reduction. The solution, however, has a
peculiarity in its physically relevant quantity, a deficit angle, which is
given as a function of the ratio of the gauge couplings of $SU(2)$ and $U(1)$.
The size of the extra space (sphere) is shown to vary with the distance from
the axis of the "string".


  A single digital newsletter usually contains many messages (regions). Users'
reading time spent on, and read level (skip/skim/read-in-detail) of each
message is important for platforms to understand their users' interests,
personalize their contents, and make recommendations. Based on accurate but
expensive-to-collect eyetracker-recorded data, we built models that predict
per-region reading time based on easy-to-collect Javascript browser tracking
data.
  With eye-tracking, we collected 200k ground-truth datapoints on participants
reading news on browsers. Then we trained machine learning and deep learning
models to predict message-level reading time based on user interactions like
mouse position, scrolling, and clicking. We reached 27\% percentage error in
reading time estimation with a two-tower neural network based on user
interactions only, against the eye-tracking ground truth data, while the
heuristic baselines have around 46\% percentage error. We also discovered the
benefits of replacing per-session models with per-timestamp models, and adding
user pattern features. We concluded with suggestions on developing
message-level reading estimation techniques based on available data.


  In this work we present VCube-PS, a topic-based Publish/Subscribe system
built on the top of a virtual hypercube-like topology. Membership information
and published messages are broadcast to subscribers (members) of a topic group
over dynamically built spanning trees rooted at the publisher. For a given
topic, the delivery of published messages respects the causal order. VCube-PS
was implemented on the PeerSim simulator, and experiments are reported
including a comparison with the traditional Publish/Subscribe approach that
employs a single rooted static spanning-tree for message distribution. Results
confirm the efficiency of VCube-PS in terms of scalability, latency, number and
size of messages.


  Uncertainties in the real world mean that is impossible for system designers
to anticipate and explicitly design for all scenarios that a robot might
encounter. Thus, robots designed like this are fragile and fail outside of
highly-controlled environments. Causal models provide a principled framework to
encode formal knowledge of the causal relationships that govern the robot's
interaction with its environment, in addition to probabilistic representations
of noise and uncertainty typically encountered by real-world robots. Combined
with causal inference, these models permit an autonomous agent to understand,
reason about, and explain its environment. In this work, we focus on the
problem of a robot block-stacking task due to the fundamental perception and
manipulation capabilities it demonstrates, required by many applications
including warehouse logistics and domestic human support robotics. We propose a
novel causal probabilistic framework to embed a physics simulation capability
into a structural causal model to permit robots to perceive and assess the
current state of a block-stacking task, reason about the next-best action from
placement candidates, and generate post-hoc counterfactual explanations. We
provide exemplar next-best action selection results and outline planned
experimentation in simulated and real-world robot block-stacking tasks.


  In this manuscript, we address continuous unconstrained optimization problems
and we discuss descent type methods for the reconstruction of the Pareto set.
Specifically, we analyze the class of Front Descent methods, which generalizes
the Front Steepest Descent algorithm allowing the employment of suitable,
effective search directions (e.g., Newton, Quasi-Newton, Barzilai-Borwein). We
provide a deep characterization of the behavior and the mechanisms of the
algorithmic framework, and we prove that, under reasonable assumptions,
standard convergence results and some complexity bounds hold for the
generalized approach. Moreover, we prove that popular search directions can
indeed be soundly used within the framework. Then, we provide a completely
novel type of convergence results, concerning the sequence of sets produced by
the procedure. In particular, iterate sets are shown to asymptotically approach
stationarity for all of their points; additionally, in finite precision
settings, the sets are shown to only be enriched through exploration steps in
later iterations, and suitable stopping conditions can be devised. Finally, the
results from a large experimental benchmark show that the proposed class of
approaches far outperforms state-of-the-art methodologies.


  In this article we define new Fr\`Echet features for random cumulative
distribution functions using contrast. These contrasts allow to construct
Wasserstein costs and our new features minimize the average costs as the
Fr\`Echet mean minimizes the mean square Wasserstein$_2$ distance. An example
of new features is the median, and more generally the quantiles. From these
definitions, we are able to define sensitivity indices when the random
distribution is the output of a stochastic code. Associated to the Fr\`Echet
mean we extend the Sobol indices, and in general the indices associated to a
contrast that we previously proposed.


  Usual quantum mechanics predicts probabilities for the outcomes of
measurements carried out at definite moments of time. However, realistic
measurements do not take place in an instant, but are extended over a period of
time. The assumption of instantaneous alternatives in usual quantum mechanics
is an approximation whose validity can be investigated in the generalized
quantum mechanics of closed systems in which probabilities are predicted for
spacetime alternatives that extend over time. In this paper we investigate how
alternatives extended over time reduce to the usual instantaneous alternatives
in a simple model in non-relativistic quantum mechanics. Specifically, we show
how the decoherence of a particular set of spacetime alternatives becomes
automatic as the time over which they extend approaches zero and estimate how
large this time can be before the interference between the alternatives becomes
non-negligible. These results suggest that the time scale over which coarse
grainings of such quantities as the center of mass position of a massive body
may be extended in time before producing significant interference is much
longer than characteristic dynamical time scales.


  Complimenting recent work on the effective field theory of cosmological large
scale structures, here we present detailed approximate analytical results and
further pedagogical understanding of the method. We start from the
collisionless Boltzmann equation and integrate out short modes of a dark
matter/dark energy dominated universe (LambdaCDM) whose matter is comprised of
massive particles as used in cosmological simulations. This establishes a long
distance effective fluid, valid for length scales larger than the non-linear
scale ~ 10 Mpc, and provides the complete description of large scale structure
formation. Extracting the time dependence, we derive recursion relations that
encode the perturbative solution. This is exact for the matter dominated era
and quite accurate in LambdaCDM also. The effective fluid is characterized by
physical parameters, including sound speed and viscosity. These two fluid
parameters play a degenerate role with each other and lead to a relative
correction from standard perturbation theory of the form ~ 10^{-6}c^2k^2/H^2.
Starting from the linear theory, we calculate corrections to cosmological
observables, such as the baryon-acoustic-oscillation peak, which we compute
semi-analytically at one-loop order. Due to the non-zero fluid parameters, the
predictions of the effective field theory agree with observation much more
accurately than standard perturbation theory and we explain why. We also
discuss corrections from treating dark matter as interacting or wave-like and
other issues.


  The Moyal-Lax representation and the Moyal momentum algebra are introduced
and systematically investigated. It is shown that the Moyal-Lax equation can be
interpreted as a Hamiltonian equation and can be derived from an action. We
show that the parameter of non-commutativity, in this case, is related to the
central charge of the second Hamiltonian structure of the system. The Moyal-Lax
description leads in a natural manner to the dispersionless limit and provides
the second Hamiltonian structure of dispersionless integrable models, which has
been an open question for sometime.


  The radiation response and the MHD destabilization during the thermal quench
after a mixed species Shattered Pellet Injection (SPI) with impurity species
neon and argon are investigated via 3D non-linear MHD simulation using the
JOREK code. Both the $n=0$ global current profile contraction and the local
helical cooling at each rational surface caused by the pellet fragments are
found to be responsible for MHD destabilization after the injection.
Significant current driven mode growth is observed as the fragments cross low
order rational surfaces, resulting in rapidly inward propagating stochastic
magnetic field, ultimately causing the core temperature collapse. The Thermal
Quench (TQ) is triggered as the fragments arrive on the $q=1$ or $q=2$ surface
depending on the exact $q$ profile and thus mode structure. When injecting from
a single toroidal location, strong radiation asymmetry is found before and
during the TQ as a result of the unrelaxed impurity density profile along the
field line and asymmetric outward heat flux. Such asymmetry gradually relaxes
over the course of the TQ, and is entirely eliminated by the end of it.
Simulation results indicate that the aforementioned asymmetric radiation
behavior could be significantly mitigated by injection from toroidally opposite
locations, provided that the time delay between the two injectors is shorter
than $1ms$. It is also found that the MHD response are sensitive to the
relative timing and injection configuration in these multiple injection cases.


  The merger of two or more galaxies can enhance the inflow of material from
galactic scales into the close environments of Active Galactic Nuclei (AGN),
obscuring and feeding the supermassive black hole (SMBH). Both recent
simulations and observations of AGN in mergers have confirmed that mergers are
related to strong nuclear obscuration. However, it is still unclear how AGN
obscuration evolves in the last phases of the merger process. We study a sample
of 60 Luminous and Ultra-luminous IR galaxies (U/LIRGs) from the GOALS sample
observed by NuSTAR. We find that the fraction of AGN that are Compton-thick
(CT; $N_{\rm H}\geq 10^{24}\rm\,cm^{-2}$) peaks at $74_{-19}^{+14}\%$ at a late
merger stage, prior to coalescence, when the nuclei have projected separations
of $d_{\rm sep}\sim 0.4-6$ kpc. A similar peak is also observed in the median
$N_{\rm H}$ [$(1.6\pm0.5)\times10^{24}\rm\,cm^{-2}$]. The vast majority
($85^{+7}_{-9}\%$) of the AGN in the final merger stages ($d_{\rm sep}\lesssim
10$ kpc) are heavily obscured ($N_{\rm H}\geq 10^{23}\rm\,cm^{-2}$), and the
median $N_{\rm H}$ of the accreting SMBHs in our sample is systematically
higher than that of local hard X-ray selected AGN, regardless of the merger
stage. This implies that these objects have very obscured nuclear environments,
with the $N_{\rm H}\geq 10^{23}\rm\,cm^{-2}$ gas almost completely covering the
AGN in late mergers. CT AGN tend to have systematically higher
absorption-corrected X-ray luminosities than less obscured sources. This could
either be due to an evolutionary effect, with more obscured sources accreting
more rapidly because they have more gas available in their surroundings, or to
a selection bias. The latter scenario would imply that we are still missing a
large fraction of heavily obscured, lower luminosity ($L_{2-10}\lesssim
10^{43}\rm\,erg\,s^{-1}$) AGN in U/LIRGs.


  The analysis of absorption features along the line of sight to distant
sources is an invaluable tool for observational cosmology, giving a direct
insight into the physical and chemical state of the inter/circumgalactic
medium. Such endeavour entails the accessibility of bright QSOs as background
beacons, and the availability of software tools to extract the information in a
reproducible way. In this article, we will present the latest results we
obtained in both directions within the QUBRICS project: we will describe how
machine learning techniques were applied to detect hundreds of previously
unknown QSOs in the southern hemisphere, and how state-of-the art software like
QSFit and Astrocook was integrated in the analysis of the targets, opening up
new possibilities for the next era of observations.


  While the Vision Transformer (VT) architecture is becoming trendy in computer
vision, pure VT models perform poorly on tiny datasets. To address this issue,
this paper proposes the locality guidance for improving the performance of VTs
on tiny datasets. We first analyze that the local information, which is of
great importance for understanding images, is hard to be learned with limited
data due to the high flexibility and intrinsic globality of the self-attention
mechanism in VTs. To facilitate local information, we realize the locality
guidance for VTs by imitating the features of an already trained convolutional
neural network (CNN), inspired by the built-in local-to-global hierarchy of
CNN. Under our dual-task learning paradigm, the locality guidance provided by a
lightweight CNN trained on low-resolution images is adequate to accelerate the
convergence and improve the performance of VTs to a large extent. Therefore,
our locality guidance approach is very simple and efficient, and can serve as a
basic performance enhancement method for VTs on tiny datasets. Extensive
experiments demonstrate that our method can significantly improve VTs when
training from scratch on tiny datasets and is compatible with different kinds
of VTs and datasets. For example, our proposed method can boost the performance
of various VTs on tiny datasets (e.g., 13.07% for DeiT, 8.98% for T2T and 7.85%
for PVT), and enhance even stronger baseline PVTv2 by 1.86% to 79.30%, showing
the potential of VTs on tiny datasets. The code is available at
https://github.com/lkhl/tiny-transformers.


  We describe a new universality class for unitary invariant random matrix
ensembles. It arises in the double scaling limit of ensembles of random $n
\times n$ Hermitian matrices $Z_{n,N}^{-1} |\det M|^{2\alpha} e^{-N \Tr V(M)}
dM$ with $\alpha > -1/2$, where the factor $|\det M|^{2\alpha}$ induces
critical eigenvalue behavior near the origin. Under the assumption that the
limiting mean eigenvalue density associated with $V$ is regular, and that the
origin is a right endpoint of its support, we compute the limiting eigenvalue
correlation kernel in the double scaling limit as $n, N \to \infty$ such that
$n^{2/3}(n/N-1) = O(1)$. We use the Deift-Zhou steepest descent method for the
Riemann-Hilbert problem for polynomials on the line orthogonal with respect to
the weight $|x|^{2\alpha} e^{-NV(x)}$. Our main attention is on the
construction of a local parametrix near the origin by means of the
$\psi$-functions associated with a distinguished solution of the Painleve XXXIV
equation. This solution is related to a particular solution of the Painleve II
equation, which however is different from the usual Hastings-McLeod solution.


  We present a synthesis of the astronomical observations constraining the
wavelength-dependent extinction, emission, and polarization from interstellar
dust from UV to microwave wavelengths on diffuse Galactic sightlines.
Representative solid phase abundances for those sightlines are also derived.
Given the sensitive new observations of polarized dust emission provided by the
Planck satellite, we place particular emphasis on dust polarimetry, including
continuum polarized extinction, polarization in the carbonaceous and silicate
spectroscopic features, the wavelength-dependent polarization fraction of the
dust emission, and the connection between optical polarized extinction and
far-infrared polarized emission. Together, these constitute a set of
constraints that should be reproduced by models of dust in the diffuse
interstellar medium.


  The challenge in biomarker discovery using machine learning from omics data
lies in the abundance of molecular features but scarcity of samples. Most
feature selection methods in machine learning require evaluating various sets
of features (models) to determine the most effective combination. This process,
typically conducted using a validation dataset, involves testing different
feature sets to optimize the model's performance. Evaluations have performance
estimation error and when the selection involves many models the best ones are
almost certainly overestimated. Biomarker identification with feature selection
methods can be addressed as a multi-objective problem with trade-offs between
predictive ability and parsimony in the number of features. Genetic algorithms
are a popular tool for multi-objective optimization but they evolve numerous
solutions thus are prone to overestimation. Methods have been proposed to
reduce the overestimation after a model has already been selected in
single-objective problems, but no algorithm existed capable of reducing the
overestimation during the optimization, improving model selection, or applied
in the more general multi-objective domain. We propose DOSA-MO, a novel
multi-objective optimization wrapper algorithm that learns how the original
estimation, its variance, and the feature set size of the solutions predict the
overestimation. DOSA-MO adjusts the expectation of the performance during the
optimization, improving the composition of the solution set. We verify that
DOSA-MO improves the performance of a state-of-the-art genetic algorithm on
left-out or external sample sets, when predicting cancer subtypes and/or
patient overall survival, using three transcriptomics datasets for kidney and
breast cancer.


  New fundamental mathematical structures are introduced by the triples (left
semistructure,right semistructure,bisemistructure) associated with the
classical mathematical structures and such that the bisemistructures,resulting
from the reciprocal actions of left semistructures on right semistructures,are
composed of bielements which are either diagonal bielements or cross
bielements.


  We propose a geometric method to parameterize inequivalent vacua by dynamical
data. Introducing quantum Clifford algebras with arbitrary bilinear forms we
distinguish isomorphic algebras --as Clifford algebras-- by different
filtrations resp. induced gradings. The idea of a vacuum is introduced as the
unique algebraic projection on the base field embedded in the Clifford algebra,
which is however equivalent to the term vacuum in axiomatic quantum field
theory and the GNS construction in C^*-algebras. This approach is shown to be
equivalent to the usual picture which fixes one product but employs a variety
of GNS states. The most striking novelty of the geometric approach is the fact
that dynamical data fix uniquely the vacuum and that positivity is not
required. The usual concept of a statistical quantum state can be generalized
to geometric meaningful but non-statistical, non-definite, situations.
Furthermore, an algebraization of states takes place. An application to physics
is provided by an U(2)-symmetry producing a gap-equation which governs a phase
transition. The parameterization of all vacua is explicitly calculated from
propagator matrix elements. A discussion of the relation to BCS theory and
Bogoliubov-Valatin transformations is given.


  Recently, we have demonstrated that for a certain class of Casimir-type
systems ("devices") the energy of zero-point vacuum fluctuations reaches its
global minimum when the device rotates about a certain axis rather than remains
static. This rotational vacuum effect may lead to the emergence of permanently
rotating objects provided the negative rotational energy of zero-point
fluctuations cancels the positive rotational energy of the device itself. In
this paper, we show that for massless electrically charged particles the
rotational vacuum effect should be drastically (astronomically) enhanced in the
presence of a magnetic field. As an illustration, we show that in a background
of experimentally available magnetic fields the zero-point energy of massless
excitations in rotating torus-shaped doped carbon nanotubes may indeed
overwhelm the classical energy of rotation for certain angular frequencies so
that the permanently rotating state is energetically favored. The suggested
"zero-point driven" devices -- which have no internally moving parts --
correspond to a perpetuum mobile of a new, fourth kind: They do not produce any
work despite the fact that their equilibrium (ground) state corresponds to a
permanent rotation even in the presence of an external environment. We show
that our proposal is consistent with the laws of thermodynamics.


  Let M be a globally Riemannian symmetric space. We prove a duality estimate
between pairings of vector fields with divergence zero and and in L^1 with
vector fields in a critical Sobolev space on M. As a consequence we get a sharp
Calderon-Zygmund estimate for solutions to Poisson's equation on M, where the
right side data is manufactured from divergence free vector fields which are in
L^1. Such a result was proved earlier by Jean Bourgain and Haim Brezis on
Euclidean space.


  The performance of Federated Learning (FL) hinges on the effectiveness of
utilizing knowledge from distributed datasets. Traditional FL methods adopt an
aggregate-then-adapt framework, where clients update local models based on a
global model aggregated by the server from the previous training round. This
process can cause client drift, especially with significant cross-client data
heterogeneity, impacting model performance and convergence of the FL algorithm.
To address these challenges, we introduce FedAF, a novel aggregation-free FL
algorithm. In this framework, clients collaboratively learn condensed data by
leveraging peer knowledge, the server subsequently trains the global model
using the condensed data and soft labels received from the clients. FedAF
inherently avoids the issue of client drift, enhances the quality of condensed
data amid notable data heterogeneity, and improves the global model
performance. Extensive numerical studies on several popular benchmark datasets
show FedAF surpasses various state-of-the-art FL algorithms in handling
label-skew and feature-skew data heterogeneity, leading to superior global
model accuracy and faster convergence.


  We show that holomorphic vector fields on (C^3,0) have separatrices provided
that they are embedded in a rank 2 representation of a two-dimensional Lie
algebra. In turn, this result enables us to show that the second jet of a
holomorphic vector field defined on a compact complex manifold M of dimension 3
cannot vanish at an isolated singular point provided that M carries more than a
single holomorphic vector field.


  Adaptive importance sampling is a widely spread Monte Carlo technique that
uses a re-weighting strategy to iteratively estimate the so-called target
distribution. A major drawback of adaptive importance sampling is the large
variance of the weights which is known to badly impact the accuracy of the
estimates. This paper investigates a regularization strategy whose basic
principle is to raise the importance weights at a certain power. This
regularization parameter, that might evolve between zero and one during the
algorithm, is shown (i) to balance between the bias and the variance and (ii)
to be connected to the mirror descent framework. Using a kernel density
estimate to build the sampling policy, the uniform convergence is established
under mild conditions. Finally, several practical ways to choose the
regularization parameter are discussed and the benefits of the proposed
approach are illustrated empirically.


  We study a capacity theory based on a definition of Haj{\l} asz-Besov
functions. We prove several properties of this capacity in the general setting
of a metric space equipped with a doubling measure. The main results of the
paper are lower bound and upper bound estimates for the capacity in terms of a
modified Netrusov-Hausdorff content. Important tools are $\gamma$-medians, for
which we also prove a new version of a Poincar\'e type inequality.


  By expressing the time-independent Schrodinger equation in one dimension as a
system of two first-order differential equations, the transfer matrix for a
rectangular potential barrier is obtained making use of the matrix exponential.
It is shown that the transfer matrix allows one to find the bound states and
the quasinormal modes. A similar treatment for the one-dimensional propagation
of electromagnetic waves in a homogeneous medium is also presented.


  The different facets of the $R$-matrix method are presented pedagogically in
a general framework. Two variants have been developed over the years: $(i)$ The
"calculable" $R$-matrix method is a calculational tool to derive scattering
properties from the Schr\"odinger equation in a large variety of physical
problems. It was developed rather independently in atomic and nuclear physics
with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix
method is a technique to parametrize various types of cross sections. It was
mainly (or uniquely) used in nuclear physics. Both directions are explained by
starting from the simple problem of scattering by a potential. They are
illustrated by simple examples in nuclear and atomic physics. In addition to
elastic scattering, the $R$-matrix formalism is applied to transfer and
radiative-capture reactions. We also present more recent and more ambitious
applications of the theory in nuclear physics.


  The lowest order constrained variational method [Phys. Rev. Lett. {\bf 88},
210403 (2002)] has been generalized for a dilute (in the sense that the range
of interatomic potential is small compared with inter-particle spacing) uniform
gas of bosons near the Feshbach resonance using the multi-channel zero-range
potential model. The method has been applied to Na (F=1, m_F=1) atoms near the
907G Feshbach resonance. It is shown that at high densities there are
significant differences between our results for the real part of energy per
particle and the one-channel zero-range potential approximation. We point out
the possibility of stabilization of the uniform condensate for the case of
negative scattering length.


  In this paper, we focus on the variable selection techniques for a class of
semiparametric spatial regression models which allow one to study the effects
of explanatory variables in the presence of the spatial information. The
spatial smoothing problem in the nonparametric part is tackled by means of
bivariate splines over triangulation, which is able to deal efficiently with
data distributed over irregularly shaped regions. In addition, we develop a
unified procedure for variable selection to identify significant covariates
under a double penalization framework, and we show that the penalized
estimators enjoy the "oracle" property. The proposed method can simultaneously
identify non-zero spatially distributed covariates and solve the problem of
"leakage" across complex domains of the functional spatial component. To
estimate the standard deviations of the proposed estimators for the
coefficients, a sandwich formula is developed as well. In the end, Monte Carlo
simulation examples and a real data example are provided to illustrate the
proposed methodology. All technical proofs are given in the supplementary
materials.


  Symmetric non-expanding horizons are studied in arbitrary dimension. The
global properties -as the zeros of infinitesimal symmetries- are analyzed
particularly carefully. For the class of NEH geometries admitting helical
symmetry a quasi-local analog of Hawking's rigidity theorem is formulated and
proved: the presence of helical symmetry implies the presence of two
symmetries: null, and cyclic.
  The results valid for arbitrary-dimensional horizons are next applied in a
complete classification of symmetric NEHs in 4-dimensional space-times (the
existence of a 2-sphere crossection is assumed). That classification divides
possible NEH geometries into classes labeled by two numbers - the dimensions
of, respectively, the group of isometries induced in the horizon base space and
the group of null symmetries of the horizon.


  This paper is a tribute to Robert Bartnik and his work and conjectures on
quasi-local mass. We present a framework in which to clearly analyse Bartnik's
static vacuum extension conjecture. While we prove that this conjecture is not
true in general, it remains a fundamental open problem to understand the realm
of its validity.


  Cometary activity affects the orbital motion and rotation state due to
sublimation induced forces. The availability of precise rotation-axis
orientation and position data from the Rosetta mission allows one to accurately
determine the outgassing of comet Churyumov-Gerasimenko/67P. We derive the
observed non-gravitational acceleration of 67P directly from the Rosetta
spacecraft trajectory. From the non-gravitational acceleration we recover the
diurnal outgassing variations and study a possible delay of the sublimation
response with respect to the peak solar illumination. This allows us to compare
the non-gravitational acceleration of 67P with expectations based on empirical
models and common assumptions about the sublimation process. We use an
iterative orbit refinement and Fourier decomposition of the diurnal activity to
derive the outgassing induced non-gravitational acceleration. The uncertainties
of the data reduction are established by a sensitivity analysis of an ensemble
of best-fit orbits for comet 67P. We find that the Marsden non-gravitational
acceleration parameters reproduce part of the non-gravitational acceleration
but need to be augmented by an analysis of the nucleus geometry and surface
illumination to draw conclusions about the sublimation process on the surface.
The non-gravitational acceleration follows closely the subsolar latitude
(seasonal illumination), with a small lag angle with respect to local noon
around perihelion. The observed minor changes of the rotation axis do not
favour forced precession models for the non-gravitational acceleration. In
contrast to the sublimation induced torques, the non-gravitational acceleration
does not put strong constraints on localized active areas on the nucleus. We
find a close agreement of the orbit deduced non-gravitational acceleration and
the water production independently derived from Rosetta in-situ measurement.


  We make use of the first high--resolution hydrodynamic simulations of
structure formation which self-consistently follows the build up of
supermassive black holes introduced in Di Matteo et al. (2007) to investigate
the relation between black holes (BH), host halo and large--scale environment.
There are well--defined relations between halo and black hole masses and
between the activities of galactic nuclei and halo masses at low redshifts. A
large fraction of black holes forms anti--hierarchically, with a higher ratio
of black hole to halo mass at high than at low redshifts. At $z=1$, we predict
group environments (regions of enhanced local density) to contain the highest
mass and most active (albeit with a large scatter) BHs while the rest of the BH
population to be spread over all densities from groups to filaments and voids.
Density dependencies are more pronounced at high rather than low redshift.
These results are consistent with the idea that gas rich mergers are likely the
main regulator of quasar activity. We find star formation to be a somewhat
stronger and tighter function of local density than BH activity, indicating
some difference in the triggering of the latter versus the former. There exists
a large number of low--mass black holes, growing slowly predominantly through
accretion, which extends all the way into the most underdense regions, i.e. in
voids.


  We give a new construction of overconvergent modular forms of arbitrary
weights, defining them in terms of functions on certain affinoid subsets of
Scholze's infinite-level modular curve. These affinoid subsets, and a certain
canonical coordinate on them, play a role in our construction which is strongly
analogous with the role of the upper half-plane and its coordinate `z' in the
classical analytic theory of modular forms. As one application of these ideas,
we define and study an overconvergent Eichler-Shimura map in the context of
compact Shimura curves over $\mathbb{Q}$, proving stronger analogues of results
of Andreatta-Iovita-Stevens.


  In this essay, we discuss the notion of optimal transport on geodesic measure
spaces and the associated (2-)Wasserstein distance. We then examine
displacement convexity of the entropy functional on the space of probability
measures. In particular, we give a detailed proof that the Lott-Villani-Sturm
notion of generalized Ricci bounds agree with the classical notion on smooth
manifolds. We also give the proof that generalized Ricci bounds are preserved
under Gromov-Hausdorff convergence. In particular, we examine in detail the
space of probability measures over the interval, $P(X)$ equipped with the
Wasserstein metric $d^W$. We show that this metric space is isometric to a
totally convex subset of a Hilbert space, $L^2[0,1]$, which allows for concrete
calculations, contrary to the usual state of affairs in the theory of optimal
transport. We prove explicitly that $(P(X),d^W)$ has vanishing Alexandrov
curvature, and give an easy to work with expression for the entropy functional
on this space. In addition, we examine finite dimensional Gromov-Hausdorff
approximations to this space, and use these to construct a measure on the limit
space, the entropic measure first considered by Von Renesse and Sturm. We
examine properties of the measure, in particular explaining why one would
expect it to have generalized Ricci lower bounds. We then show that this is in
fact not true. We also discuss the possibility and consequences of finding a
different measure which does admit generalized Ricci lower bounds.


  Recently the 1/R gravity has been proposed in order to explain the
accelerated expansion of the universe. However, it was argued that the 1/R
gravity conflicts with solar system tests. While this statement is true if one
views the 1/R gravity as an effective theory, we find that this difficulty
might be avoided if one treats the 1/R term as a correction to the scalar
curvature term in the high curvature limit $R \gg \mu^2$.


  In this paper we prove the Pohozaev identity for the semilinear Dirichlet
problem $(-\Delta)^s u = f(u)$ in $\Omega$, $u \equiv 0$ in $\mathbb
R^n\setminus\Omega$. Here, $s\in(0,1)$, $(-\Delta)^s$ is the fractional
Laplacian in $\mathbb R^n$, and $\Omega$ is a bounded $C^{1,1}$ domain.
  To establish the identity we use, among other things, that if $u$ is a
bounded solution then $u/\delta^s|_{\Omega}$ is $C^\alpha$ up to the boundary
$\partial\Omega$, where $\delta(x)={\rm dist}(x,\partial\Omega)$. In the
fractional Pohozaev identity, the function $u/\delta^s|_{\partial\Omega}$ plays
the role that $\partial u/\partial\nu$ plays in the classical one.
Surprisingly, from a nonlocal problem we obtain an identity with a boundary
term (an integral over $\partial\Omega$) which is completely local.
  As an application of our identity, we deduce the nonexistence of nontrivial
solutions in star-shaped domains for supercritical nonlinearities.


  It is well known that the state operator of an open quantum system can be
generically represented as the solution of a time-local equation -- a quantum
master equation.
  Unraveling in quantum trajectories offers a picture of open system dynamics
dual to solving master equations. In the unraveling picture, physical
indicators are computed as Monte-Carlo averages over a stochastic process
valued in the Hilbert space of the system. This approach is particularly
adapted to simulate systems in large Hilbert spaces.
  We show that the dynamics of an open quantum system generically admits an
unraveling in the Hilbert space of the system described by a Markov process
generated by ordinary stochastic differential equations for which rigorous
concentration estimates are available. The unraveling can be equivalently
formulated in terms of norm-preserving state vectors or in terms of linear
``ostensible" processes trace preserving only on average. We illustrate the
results in the case of a two level system in a simple boson environment.
  Next, we derive the state-of-the-art form of the Diosi-Gisin-Strunz Gaussian
random ostensible state equation in the context of a model problem. This
equation provides an exact unraveling of open systems in Gaussian environments.
We compare and contrast the two unravelings and their potential for
applications to quantum error mitigation.


  Leaky integrate-and-fire (LIF) models are mean-field limits, with a large
number of neurons, used to describe neural networks. We consider inhomogeneous
networks structured by a connec-tivity parameter (strengths of the synaptic
weights) with the effect of processing the input current with different
intensities. We first study the properties of the network activity depending on
the distribution of synaptic weights and in particular its discrimination
capacity. Then, we consider simple learning rules and determine the synaptic
weight distribution it generates. We outline the role of noise as a selection
principle and the capacity to memorized a learned signal.


  We study a quantum (non-commutative) representation of the affine Weyl group
mainly of type $E_8^{(1)}$, where the representation is given by birational
actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau
variables, we also construct quantum "fundamental" polynomials $F(x,y)$ which
completely control the Weyl group actions. The geometric properties of the
polynomials $F(x,y)$ for the commutative case is lifted distinctively in the
quantum case to certain singularity structures as the $q$-difference operators.
This property is further utilized as the characterization of the quantum
polynomials $F(x,y)$. As an application, the quantum curve associated with
topological strings proposed recently by the first named author is rederived by
the Weyl group symmetry. The cases of type $D_5^{(1)}$, $E_6^{(1)}$,
$E_7^{(1)}$ are also discussed.


  Above the chiral symmetry restoration crossover around T_{ch} ~ 155 MeV a new
regime arises in QCD, a stringy fluid, which is characterized by an approximate
chiral spin symmetry of the thermal partition function. This symmetry is not a
symmetry of the Dirac Lagrangian and is a symmetry of the electric part of the
QCD Lagrangian. In this regime the medium consists of the chirally symmetric
and approximately chiral spin symmetric hadrons that are made of the chirally
symmetric quarks connected into the color singlet compounds by a confining
chromoelectric field. This regime is evidenced by the approximate chiral spin
symmetry of the spatial and temporal correlators and by the breakdown of the
thermal perturbation theory at the crossover between the partonic (the
quark-gluon plasma) and stringy fluid regimes at ~ 3 T_{ch}. The chiral spin
symmetry smoothly disappears above ~ 3T_{ch} which means that the
chromoelectric confining interaction gets screened. A direct evidence that the
stringy fluid medium consists of densely packed hadrons is the pion spectral
function that shows a distinct pion state and its first radial excitation above
T_{ch}. Another direct evidence of the hadron degrees of freedom in the stringy
fluid is the bottomonium spectrum with the 1S,2S,3S and 1P,2P radial and
orbital excitations that become broad with temperature. The hadrons between
T_{ch} and ~ 3 T_{ch} in the stringy fluid interact strongly which makes the
stringy fluid more a liquid rather than a gas. We discuss how this chiral spin
symmetric regime extends into the finite chemical potentials domain and present
a qualitative sketch of the QCD phase diagram.


  We study a weighted divisor function $\mathop{{\sum}'}\limits_{mn\leq
x}\cos(2\pi m\theta_1)\sin(2\pi n\theta_2)$, where $\theta_i (0<\theta_i<1)$ is
a rational number. By connecting it with the divisor problem with congruence
conditions, we establish the upper bound, mean-value, mean-square and some
power-moments.


  We studied anomalous Josephson effect (AJE) in Josephson trijunctions
fabricated on Bi$_2$Se$_3$, and found that the AJE in T-shaped trijunctions
significantly alters the Majorana phase diagram of the trijunctions, when an
in-plane magnetic field is applied parallel to two of the three single
junctions. Such a phenomenon in topological insulator-based Josephson
trijunction provides unambiguous evidence for the existence of AJE in the
system, and might provide an additional knob for controlling the Majorana bound
states in the Fu-Kane scheme of topological quantum computation.


  Square matrices represent linear self-maps of vector spaces, and their
eigenpoints are the fixed points of the induced map on projective space.
Likewise, polynomial self-maps of a projective space are represented by
tensors. We study the configuration of fixed points of a tensor or symmetric
tensor.


  We consider conformal actions of solvable Lie groups on closed Lorentzian
manifolds. With anterior results in which we addressed similar questions for
semi-simple Lie group actions, this work contributes to the understanding of
the identity component $G$ of the conformal group of closed Lorentzian
manifolds. In the first part of the article, we prove that $G$ is inessential
if and only if its nilradical is inessential. In the second, we assume the
nilradical essential and establish conformal flatness of the metric on an open
subset, under certain algebraic hypothesis on the solvable radical. This is
related to the Lorentzian Lichnerowicz conjecture. Finally, we consider the
remaining situations where our methods do not apply to prove conformal
flatness, and conclude that for an essential closed Lorentzian $n$-manifold, $n
\geq 3$, the radical of its conformal group admits a local embedding into
$O(2,n)$.


  Automl is the key technology for machine learning problem. Current state of
art hyperparameter optimization methods are based on traditional black-box
optimization methods like SMBO (SMAC, TPE). The objective function of black-box
optimization is non-smooth, or time-consuming to evaluate, or in some way
noisy. Recent years, many researchers offered the work about the properties of
hyperparameters. However, traditional hyperparameter optimization methods do
not take those information into consideration. In this paper, we use gradient
information and machine learning model analysis information to accelerate
traditional hyperparameter optimization methods SMBO. In our L2 norm
experiments, our method yielded state-of-the-art performance, and in many cases
outperformed the previous best configuration approach.


  Named entity recognition (NER) is used to identify relevant entities in text.
A bidirectional LSTM (long short term memory) encoder with a neural conditional
random fields (CRF) decoder (biLSTM-CRF) is the state of the art methodology.
In this work, we have done an analysis of several methods that intend to
optimize the performance of networks based on this architecture, which in some
cases encourage overfitting avoidance. These methods target exploration of
parameter space, regularization of LSTMs and penalization of confident output
distributions. Results show that the optimization methods improve the
performance of the biLSTM-CRF NER baseline system, setting a new state of the
art performance for the CoNLL-2003 Spanish set with an F1 of 87.18.


  The great success that deep models have achieved in the past is mainly owed
to large amounts of labeled training data. However, the acquisition of labeled
data for new tasks aside from existing benchmarks is both challenging and
costly. Active learning can make the process of labeling new data more
efficient by selecting unlabeled samples which, when labeled, are expected to
improve the model the most. In this paper, we combine a novel method of active
learning for object detection with an incremental learning scheme to enable
continuous exploration of new unlabeled datasets. We propose a set of
uncertainty-based active learning metrics suitable for most object detectors.
Furthermore, we present an approach to leverage class imbalances during sample
selection. All methods are evaluated systematically in a continuous exploration
context on the PASCAL VOC 2012 dataset.


  We study the dynamics of long-wavelength fluctuations in one-dimensional (1D)
many-particle systems as described by self-consistent mode-coupling theory. The
corresponding nonlinear integro-differential equations for the relevant
correlators are solved analytically and checked numerically. In particular, we
find that the memory functions exhibit a power-law decay accompanied by
relatively fast oscillations. Furthermore, the scaling behaviour and,
correspondingly, the universality class depends on the order of the leading
nonlinear term. In the cubic case, both viscosity and thermal conductivity
diverge in the thermodynamic limit. In the quartic case, a faster decay of the
memory functions leads to a finite viscosity, while thermal conductivity
exhibits an even faster divergence. Finally, our analysis puts on a more firm
basis the previously conjectured connection between anomalous heat conductivity
and anomalous diffusion.