  The effective field equations on a 3-brane are established considering the
massless bosonic sector of the type IIB string compactified on S^5. The
covariant embedding formalism in a space endowed with Z_2-symmetry is applied.
Recently the derivation of effective equations on the 3-brane, where only
gravity penetrates in the bulk has been performed by Shiromizu, Maeda, and
Sasaki. We extend this analysis to the situation when the bulk contains a set
of fields given by the type IIB string. The notion of the Einstein-Cartan space
is considered in order to avoid extra suppositions about the embedding of these
fields. The interactions between the brane and the bulk fields are understood
in a purely geometric way, which fixes the form of these interactions. Finally,
we present the dynamically equivalent effective equations have expressed
completely in Riemannian terms and make conclusions.


  We study $\kappa$-maximal cofinitary groups for $\kappa$ regular uncountable,
$\kappa = \kappa^{<\kappa}$. Revisiting earlier work of Kastermans and building
upon a recently obtained higher analogue of Bell's theorem, we show that:
  1. Any $\kappa$-maximal cofinitary group has ${<}\kappa$ many orbits under
the natural group action of $S(\kappa)$ on $\kappa$.
  2. If $\mathfrak{p}(\kappa) = 2^\kappa$ then any partition of $\kappa$ into
less than $\kappa$ many sets can be realized as the orbits of a
$\kappa$-maximal cofinitary group.
  3. For any regular $\lambda > \kappa$ it is consistent that there is a
$\kappa$-maximal cofinitary group which is universal for groups of size
${<}2^\kappa = \lambda$. If we only require the group to be universal for
groups of size $\kappa$ then this follows from $\mathfrak{p}(\kappa) =
2^\kappa$.


  This paper is concerned with the question of reconstructing a vector in a
finite-dimensional real or complex Hilbert space when only the magnitudes of
the coefficients of the vector under a redundant linear map are known. We
present new invertibility results as well an iterative algorithm that finds the
least-square solution and is robust in the presence of noise. We analyze its
numerical performance by comparing it to two versions of the Cramer-Rao lower
bound.


  Let $H$ be a complex Hilbert space and let ${\mathcal C}$ be a conjugacy
class of finite rank self-adjoint operators on $H$ with respect to the action
of unitary operators. We suppose that ${\mathcal C}$ is formed by operators of
rank $k$ and for every $A\in {\mathcal C}$ the dimensions of distinct maximal
eigenspaces are distinct. Under the assumption that $\dim H\ge 4k$ we establish
that every bijective transformation $f$ of ${\mathcal C}$ preserving the
commutativity in both directions is induced by a unitary or anti-unitary
operator, i.e. there is a unitary or anti-unitary operator $U$ such that
$f(A)=UAU^{*}$ for every $A\in {\mathcal C}$. A simple example shows that the
condition concerning the dimensions of maximal eigenspaces cannot be omitted.


  Panoptic segmentation brings together two separate tasks: instance and
semantic segmentation. Although they are related, unifying them faces an
apparent paradox: how to learn simultaneously instance-specific and
category-specific (i.e. instance-agnostic) representations jointly. Hence,
state-of-the-art panoptic segmentation methods use complex models with a
distinct stream for each task. In contrast, we propose Hierarchical Lov\'asz
Embeddings, per pixel feature vectors that simultaneously encode instance- and
category-level discriminative information. We use a hierarchical Lov\'asz hinge
loss to learn a low-dimensional embedding space structured into a unified
semantic and instance hierarchy without requiring separate network branches or
object proposals. Besides modeling instances precisely in a proposal-free
manner, our Hierarchical Lov\'asz Embeddings generalize to categories by using
a simple Nearest-Class-Mean classifier, including for non-instance "stuff"
classes where instance segmentation methods are not applicable. Our simple
model achieves state-of-the-art results compared to existing proposal-free
panoptic segmentation methods on Cityscapes, COCO, and Mapillary Vistas.
Furthermore, our model demonstrates temporal stability between video frames.


  This paper presents a comparative study of sampling methods within the
FedHome framework, designed for personalized in-home health monitoring. FedHome
leverages federated learning (FL) and generative convolutional autoencoders
(GCAE) to train models on decentralized edge devices while prioritizing data
privacy. A notable challenge in this domain is the class imbalance in health
data, where critical events such as falls are underrepresented, adversely
affecting model performance. To address this, the research evaluates six
oversampling techniques using Stratified K-fold cross-validation: SMOTE,
Borderline-SMOTE, Random OverSampler, SMOTE-Tomek, SVM-SMOTE, and SMOTE-ENN.
These methods are tested on FedHome's public implementation over 200 training
rounds with and without stratified K-fold cross-validation. The findings
indicate that SMOTE-ENN achieves the most consistent test accuracy, with a
standard deviation range of 0.0167-0.0176, demonstrating stable performance
compared to other samplers. In contrast, SMOTE and SVM-SMOTE exhibit higher
variability in performance, as reflected by their wider standard deviation
ranges of 0.0157-0.0180 and 0.0155-0.0180, respectively. Similarly, the Random
OverSampler method shows a significant deviation range of 0.0155-0.0176.
SMOTE-Tomek, with a deviation range of 0.0160-0.0175, also shows greater
stability but not as much as SMOTE-ENN. This finding highlights the potential
of SMOTE-ENN to enhance the reliability and accuracy of personalized health
monitoring systems within the FedHome framework.


  This paper gives a survey of known results concerning the Laplace transform
$$ L_k(s) := \int_0^\infty |\zeta(1/2+ ix)|^{2k}{\rm e}^{-sx}{\rm d} x \qquad(k
\in N, \R s > 0), $$ and the (modified) Mellin transform $$ {\cal Z}_k(s) :=
\int_1^\infty|\zeta(1/2+ ix)|^{2k}x^{-s}{\rm d} x\qquad(k\in N), $$ where the
integral is absolutely convergent for $\R s \ge c(k) > 1$. Also some new
results on these integral transforms of $|\zeta(1/2+ ix)|^{2k}$ are given,
which have important connections with power moments of the Riemann
zeta-function $\zeta(s)$.


  In prime characteristic there are important invariants that allow us to
measure singularities. For certain cases, it is known that they are rational
numbers. In this article, we show this property for Stanley-Reisner rings in
several cases.


  A new geometric background of graph invariants was introduced by Gutman, of
which the simplest is the second Sombor index $SO_2$, defined as
$SO_2=SO_2(G)=\sum_{uv\in E}\frac{|d^2_G(u)-d^2_G(v)|}{d^2_G(u)+d^2_G(v)}$,
where $G = (V, E)$ is a simple graph and $d_G(v)$ denotes the degree of $v$ in
$G$. In this paper, the chemical applicability of the second Sombor index is
investigated and it is shown that the the second Sombor index is useful in
predicting physicochemical properties with high accuracy compared to some
well-established and often used indices. Also, we obtain a bound for the second
Sombor index among all (molecular) trees with fixed numbers of vertices, and
characterize those molecular trees achieving the extremal value.


  We propose a precise reformulation of 3d quantum gravity with negative
cosmological constant in terms of a topological quantum field theory based on
the quantization of the Teichm\"uller space of Riemann surfaces that we refer
to as ``Virasoro TQFT.'' This TQFT is similar, but importantly not equivalent,
to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory. This sharpens the folklore
that 3d gravity is related to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory
into a precise correspondence, and resolves some well-known issues with this
lore at the quantum level. Our proposal is computationally very useful and
provides a powerful tool for the further study of 3d gravity. In particular, we
explain how together with standard TQFT surgery techniques this leads to a
fully algorithmic procedure for the computation of the gravity partition
function on a fixed topology exactly in the central charge. Mathematically, the
relation leads to many nontrivial conjectures for hyperbolic 3-manifolds,
Virasoro conformal blocks and crossing kernels.


  A detailed analysis to the [1,2] Pad\'e approximation to the $\pi\pi$
scattering 2--loop amplitudes in chiral perturbation theory is made.


  We present a new, explicit sum formula for symmetric Macdonald polynomials
$P_\lambda$ and show that they can be written as a trace over a product of
(infinite dimensional) matrices. These matrices satisfy the
Zamolodchikov--Faddeev (ZF) algebra. We construct solutions of the ZF algebra
from a rank-reduced version of the Yang--Baxter algebra. As a corollary, we
find that the normalization of the stationary measure of the multi-species
asymmetric exclusion process is a Macdonald polynomial with all variables set
equal to one.


  We propose a fixed wing unmanned aerial vehicles (UAV)-based millimeter wave
(mmWave) backhaul links, that is offered as a cost effective and easy to deploy
solution, to connect a disaster or remote area to the nearest core network.
First, we fully characterize the single relay fixed-wing UAV-based
communication system by taking into account the effects of realistic physical
parameters, such as the UAV's circular path, critical points of the flight
path, heights and positions of obstacles, flight altitude, tracking error, the
severity of UAV's vibrations, the real 3D antenna pattern, mmWave atmospheric
channel loss, temperature and air pressure. Second, we derive the distribution
of the signal-to-noise ratio (SNR) metric, which is based on the sum of a
series of Dirac delta functions. Using the SNR distribution, we derive
closed-form expressions for the outage probability and the ergodic capacity of
the considered system as a function of all system parameters. To provide an
acceptable quality of service for longer link lengths, we extend the analytical
expressions to a multi-relay system. The accuracy of the closed-form
expressions are verified by Monte-Carlo simulations. Finally, by providing
sufficient simulation results, we investigate the effects of key channel
parameters such as antenna pattern gain and flight path on the performance of
the considered system; and we carefully analyze the relationships between these
parameters in order to maximize the average channel capacity.


  We discuss the connection between colorings of a link diagram and the Goeritz
matrix.


  The emission processes responsible for the observed X-rays from radio jets
are commonly believed to be non-thermal, but in any particular case, it is
unclear if synchrotron emission or one or more varieties of inverse Compton
emission predominates. We present a formulation of inverse Compton emission
from a relativistically moving jet (``IC/beaming'') which relies on radio
emitting synchrotron sources for which the energy densities in particles and
fields are comparable. We include the non-isotropic nature of inverse Compton
scattering of the relativistic electrons on photons of the cosmic microwave
background (CMB) and provide beaming parameters for a number of jets. A list of
X-ray emitting jets is given and the jets are classified on the basis of their
morphology and spectral energy distribution to determine their likely emission
process. We conclude that these jets have significant bulk relativistic
velocities on kpc scales; that higher redshift sources require less beaming
because the energy density of the CMB is significantly greater than locally;
and that for some nearby sources, synchrotron X-ray emission predominates
because the jet makes a large angle to the line of sight.


  The model of spatial permutations is related to the Feynman-Kac
representation of the Bose gas. The transition to infinite cycles corresponds
to Bose-Einstein condensation. We review the general setting and some results,
and we derive a multi-body interaction between permutation jumps, that is due
to the original interactions between quantum particles.


  We consider the evolution of electromagnetic fields coupled to conduction
currents during the reheating era after inflation, and prior to the
establishing of the proton-electron plasma. We assume that the currents may be
described by second order causal hydrodynamics. The resulting theory is not
conformally invariant. The expansion of the Universe produces temperature
gradients which couple to the current and generally oppose Ohmic dissipation.
Although the effect is not strong, it suggests that the unfolding of
hydrodynamic instabilities in these models may follow a different pattern than
in first order theories, and even than in second order theories on non
expanding backgrounds.


  A novel bio-photonics approach based on the nonlinear optical process of
second harmonic generation by non-centrosymmetric nanoparticles is presented
and demonstrated on malignant human cell lines. The proposed method allows to
directly interact with DNA in absence of photosensitizing molecules, to enable
independent imaging and therapeutic modalities switching between the two modes
of operation by simply tuning the excitation laser wavelength, and to avoid any
risk of spontaneous activation by any natural or artificial light source.


  We consider the two-brane Randall-Sundrum (RS) model with bulk gauge fields.
We carefully match the bulk theory to a 4D low-energy effective Lagrangian. In
addition to the four-fermion operators induced by KK exchange we find that
large negative S and T parameters are induced in the effective theory. This is
a tree-level effect and is a consequence of the shapes of the W and Z wave
functions in the bulk. Such effects are generic in extra dimensional theories
where the standard model (SM) gauge bosons have non-uniform wave functions
along the extra dimension. The corrections to precision electroweak observables
in the RS model are mostly dominated by S. We fit the parameters of the RS
model to the experimental data and find somewhat stronger bounds than
previously obtained; however, the standard model bound on the Higgs mass from
precision measurements can only be slightly relaxed in this theory.


  We consider a class of stochastic dynamical networks whose governing dynamics
can be modeled using a coupling function. It is shown that the dynamics of such
networks can generate geometrically ergodic trajectories under some reasonable
assumptions. We show that a general class of coupling functions can be learned
using only one sample trajectory from the network. This is practically
plausible as in numerous applications it is desired to run an experiment only
once but for a longer period of time, rather than repeating the same experiment
multiple times from different initial conditions. Building upon ideas from the
concentration inequalities for geometrically ergodic Markov chains, we
formulate several results about the convergence of the empirical estimator to
the true coupling function. Our theoretical findings are supported by extensive
simulation results.


  We show that strong coupling between ions in an ultracold neutral plasma is
limited by electron screening. While electron screening reduces the
quasi-equilibrium ion temperature, it also reduces the ion-ion electrical
potential energy. The net result is that the ratio of nearest-neighbor
potential energy to kinetic energy in quasi-equilibrium is constant and limited
to approximately 2 unless the electrons are heated by some external source. We
support these conclusions by reporting new measurements of the ion velocity
distribution in an ultracold neutral calcium plasma. These results match
previously reported simulations of Yukawa systems. Theoretical considerations
are used to determine the screened nearest-neighbor potential energy in the
plasma.


  We address the problem of making Conformal Prediction (CP) intervals locally
adaptive. Most existing methods focus on approximating the object-conditional
validity of the intervals by partitioning or re-weighting the calibration set.
Our strategy is new and conceptually different. Instead of re-weighting the
calibration data, we redefine the conformity measure through a trainable change
of variables, $A \to \phi_X(A)$, that depends explicitly on the object
attributes, $X$. Under certain conditions and if $\phi_X$ is monotonic in $A$
for any $X$, the transformations produce prediction intervals that are
guaranteed to be marginally valid and have $X$-dependent sizes. We describe how
to parameterize and train $\phi_X$ to maximize the interval efficiency.
Contrary to other CP-aware training methods, the objective function is smooth
and can be minimized through standard gradient methods without approximations.


  This paper considers random Hill's equations in the limit where the periodic
forcing function becomes a Dirac delta function. For this class of equations,
the forcing strength $q_k$, the oscillation frequency $\af_k$, and the period
are allowed to vary from cycle to cycle. Such equations arise in astrophysical
orbital problems in extended mass distributions, in the reheating problem for
inflationary cosmologies, and in periodic Schr{\"o}dinger equations. The growth
rates for solutions to the periodic differential equation can be described by a
matrix transformation, where the matrix elements vary from cycle to cycle.
Working in the delta function limit, this paper addresses several coupled
issues: We find the growth rates for the $2 \times 2$ matrices that describe
the solutions. This analysis is carried out in the limiting regimes of both
large $q_k \gg 1$ and small $q_k \ll 1$ forcing strength parameters. For the
latter case, we present an alternate treatment of the dynamics in terms of a
Fokker-Planck equation, which allows for a comparison of the two approaches.
Finally, we elucidate the relationship between the fundamental parameters
$(\af_k,q_k)$ appearing in the stochastic differential equation and the matrix
elements that specify the corresponding discrete map. This work provides
analytic -- and accurate -- expressions for the growth rates of these
stochastic differential equations in both the $q_k \gg1 $ and the $q_k \ll 1$
limits.


  In this paper we describe a well-chosen discrete moving frame and their
associated invariants along projective polygons in $\RP^n$, and we use them to
write explicit general expressions for invariant evolutions of projective
$N$-gons. We then use a reduction process inspired by a discrete
Drinfeld-Sokolov reduction to obtain a natural Hamiltonian structure on the
space of projective invariants, and we establish a close relationship between
the projective $N$-gon evolutions and the Hamiltonian evolutions on the
invariants of the flow. We prove that {any} Hamiltonian evolution is induced on
invariants by an evolution of $N$-gons - what we call a projective realization
- and we give the direct connection. Finally, in the planar case we provide
completely integrable evolutions (the Boussinesq lattice related to the lattice
$W_3$-algebra), their projective realizations and their Hamiltonian pencil. We
generalize both structures to $n$-dimensions and we prove that they are
Poisson. We define explicitly the $n$-dimensional generalization of the planar
evolution (the discretization of the $W_n$-algebra) and prove that it is
completely integrable, providing also its projective realization.


  When $R$ is a non-archimedean real closed field we say that a function $f\in
R(\bar{X})$ is finitary at a point $\bar{b}\in R^n$ if on some neighborhood of
$\bar{b}$ the defined values of $f$ are in the finite part of $R$. In this note
we give a characterization of rational functions which are finitary on a set
defined by positivity and finiteness conditions. The main novel ingredient is a
proof that OVF-integrality has a natural topological definition, which allows
us to apply a known Ganzstellensatz for the relevant valuation. We also give
some information about the Kochen geometry associated with OVF-integrality.


  In this paper, a framework on a discrete observation of (marked) point
processes under the high-frequency observation is developed. Based on this
framework, we first clarify the relation between random coefficient
integer-valued autoregressive process with infinite order (RCINAR($\infty$))
and i.i.d.-marked self-exciting process, known as marked Hawkes process. For
this purpose, we show that the point process constructed of the sum of a
RCINAR($\infty$) converge weakly to a marked Hawkes process. This limit theorem
establish that RCINAR($\infty$) processes can be seen as a discretely observed
marked Hawkes processes when the observation frequency increases and thus build
a bridge between discrete-time series analysis and the analysis of
continuous-time stochastic process and give a new perspective in the point
process approach in extreme value theory. Second, we give a necessary and
sufficient condition of the stationarity of RCINAR($\infty$) process and give
its random coefficient autoregressive (RCAR) representation. Finally, as an
application of our results, we establish a rigorous theoretical justification
of self-exciting peaks over threshold (SEPOT) model, which is a well-known as a
(marked) Hawkes process model for the empirical analysis of extremal events in
financial econometrics and of which, however, the theoretical validity have
rarely discussed. Simulation results of the asymptotic properties of
RCINAR($\infty$) shows some interesting implications for statistical
applications.


  A recently-introduced function $\rho$ of spacetime event $P$ expressing
spacetime as made of 'spacetime atoms' of quantum origin is considered. Using
its defining relation, we provide an exact expression for $\rho$ involving the
van Vleck biscalar, and show it can be recast in terms of the extrinsic
curvature of suitable equi-geodesic surfaces centered at $P$. Moreover, looking
at the role $\rho$ plays in the statistical description of spacetime, we point
out that this quantity should actually be understood as counting the quantum
states of the collection of spacetime atoms rather than counting directly the
spacetime atoms themselves (or the degrees of freedom associated to them), and
would correspond to the ratio of the number of quantum states 'at $P$' for an
assigned spacetime configuration to the number of quantum states for flat
spacetime.


  We report on interferometric observations of a face-on accretion system
around the High-Mass young stellar object, G353.273+0.641. The innermost
accretion system of 100 au radius was resolved in a 45 GHz continuum image
taken with the Jansky-Very Large Array. Our spectral energy distribution
analysis indicated that the continuum could be explained by optically thick
dust emission. The total mass of the dusty system is $\sim$ 0.2 $M_{\sun}$ at
minimum and up to a few $M_{\sun}$ depending on the dust parameters. 6.7 GHz
CH$_{3}$OH masers associated with the same system were also observed with the
Australia Telescope Compact Array. The masers showed a spiral-like,
non-axisymmetric distribution with a systematic velocity gradient. The
line-of-sight velocity field is explained by an infall motion along a parabolic
streamline that falls onto the equatorial plane of the face-on system. The
streamline is quasi-radial and reaches the equatorial plane at a radius of 16
au. This is clearly smaller than that of typical accretion disks in High-Mass
star formation, indicating that the initial angular momentum was very small, or
the CH$_{3}$OH masers selectively trace accreting material that has small
angular momentum. In the former case, the initial specific angular momentum is
estimated to be 8 $\times$ 10$^{20}$ ($M_{*}$$/$10 $M_{\sun}$)$^{0.5}$ cm$^{2}$
s$^{-1}$, or a significant fraction of the initial angular momentum was removed
outside of 100 au. The physical origin of such a streamline is still an open
question and will be constrained by the higher-resolution ($\sim$ 10 mas)
thermal continuum and line observations with ALMA long baselines.


  We investigate the problems of ghosts and stability in the framework of
asymptotical safe theory of gravity in the Minkowski background. Within one
loop corrections, we obtain explicitly the constraints on the coupling
parameters. Applying them to the coupling constant recently-obtained at the
fixed point, we find that the corresponding theory is both ghost-free and
stable. Our results can be easily generalized to high order corrections.


  Graph-structured data appears frequently in domains including chemistry,
natural language semantics, social networks, and knowledge bases. In this work,
we study feature learning techniques for graph-structured inputs. Our starting
point is previous work on Graph Neural Networks (Scarselli et al., 2009), which
we modify to use gated recurrent units and modern optimization techniques and
then extend to output sequences. The result is a flexible and broadly useful
class of neural network models that has favorable inductive biases relative to
purely sequence-based models (e.g., LSTMs) when the problem is
graph-structured. We demonstrate the capabilities on some simple AI (bAbI) and
graph algorithm learning tasks. We then show it achieves state-of-the-art
performance on a problem from program verification, in which subgraphs need to
be matched to abstract data structures.


  We present a learning-based technique for estimating high dynamic range
(HDR), omnidirectional illumination from a single low dynamic range (LDR)
portrait image captured under arbitrary indoor or outdoor lighting conditions.
We train our model using portrait photos paired with their ground truth
environmental illumination. We generate a rich set of such photos by using a
light stage to record the reflectance field and alpha matte of 70 diverse
subjects in various expressions. We then relight the subjects using image-based
relighting with a database of one million HDR lighting environments,
compositing the relit subjects onto paired high-resolution background imagery
recorded during the lighting acquisition. We train the lighting estimation
model using rendering-based loss functions and add a multi-scale adversarial
loss to estimate plausible high frequency lighting detail. We show that our
technique outperforms the state-of-the-art technique for portrait-based
lighting estimation, and we also show that our method reliably handles the
inherent ambiguity between overall lighting strength and surface albedo,
recovering a similar scale of illumination for subjects with diverse skin
tones. We demonstrate that our method allows virtual objects and digital
characters to be added to a portrait photograph with consistent illumination.
Our lighting inference runs in real-time on a smartphone, enabling realistic
rendering and compositing of virtual objects into live video for augmented
reality applications.


  Let $X_1,...,X_n$ be iid random vectors and $f\ge 0$ be a non-negative
function. Let also $k(n) = {\rm Argmax}_{i=1,...,n} f(X_i)$. We are interested
in the distribution of $X_{k(n)}$ and their limit theorems. In other words,
what is the distribution the random vector where a function of its components
is extreme? This question is motivated by a kind of inverse problem where one
wants to determine the extremal behavior of $X$ when only explicitly observing
$f(X)$. We shall refer to such types of results as to implicit extremes. It
turns out that, as in the usual case of explicit extremes, all limit implicit
extreme value laws are implicit max-stable. We characterize the regularly
varying implicit max-stable laws in terms of their spectral and stochastic
representations. We also establish the asymptotic behavior of implicit order
statistics relative to a given homogeneous loss and conclude with several
examples drawing connections to prior work involving regular variation on
general cones.


  It has been observed that long time series of Stride Time (ST), Stride Length
(SL) and Stride Speed (SS=SL/ST) exhibited statistical persistence (long-range
auto-correlation) in overground walking. Rhythmic auditory cueing induced
anti-persistent (or anti-correlated) pattern in ST series, while SL and SS
remained persistent. On the other hand, it has been shown that SS became
anti-persistent in treadmill walking, while ST and SL remained persistent. The
aim of this study was to analyze the effect of the combination of treadmill
walking (imposed speed) and auditory cueing (imposed cadence) on gait dynamics.
Twenty middle-aged subjects performed 6 x 5min walking trials at various
imposed speeds on an instrumented treadmill. Freely-chosen walking cadences
were measured during the first three trials, and then imposed accordingly in
the last three trials by using a metronome. Detrended fluctuation analysis
(DFA) was performed on the times series of ST, SL, and SS. Treadmill induced
anti-persistent dynamics in the time series of SS, but preserved the
persistence of ST and SL. On the contrary, all the three parameters were
anti-persistent under dual-constraints condition. Anti-persistent dynamics may
be related to a tighter control: deviations are followed by a rapid
over-correction, what produces oscillations around target values. Under single
constraint condition, while SS is tightly regulated in order to follow the
treadmill speed, redundancy between ST and SL would likely allow persistent
pattern to occur. Conversely, under dual constraint conditions, the absence of
redundancy among SL, ST and SS would explain the generalized anti-persistent
pattern.


  We theoretically analyze the entanglement generation and dynamics by coupled
Josephson junction qubits. Considering a current-biased Josephson junction
(CBJJ), we generate maximally entangled states. In particular, the entanglement
dynamics is considered as a function of the decoherence parameters, such as the
temperature, the ratio $r\equiv\omega_c/\omega_0$ between the reservoir cutoff
frequency $\omega_c$ and the system oscillator frequency $\omega_0$, % between
$\omega_0$ the characteristic frequency of the %quantum system of interest, and
$\omega_c$ the cut-off frequency of %Ohmic reservoir and the energy levels
split of the superconducting circuits in the non-Markovian master equation. We
analyzed the entanglement sudden death (ESD) and entanglement sudden birth
(ESB) by the non-Markovian master equation. Furthermore, we find that the
larger the ratio $r$ and the thermal energy $k_BT$, the shorter the
decoherence. In this superconducting qubit system we find that the entanglement
can be controlled and the ESD time can be prolonged by adjusting the
temperature and the superconducting phases $\Phi_k$ which split the energy
levels.


  Learning a distribution conditional on a set of discrete-valued features is a
commonly encountered task. This becomes more challenging with a
high-dimensional feature set when there is the possibility of interaction
between the features. In addition, many frequently applied techniques consider
only prediction of the mean, but the complete conditional density is needed to
answer more complex questions. We demonstrate a novel nonparametric Bayes
method based upon a tensor factorization of feature-dependent weights for
Gaussian kernels. The method makes use of multistage feature selection for
dimension reduction. The resulting conditional density morphs flexibly with the
selected features.


  We calculate the small angle expansion of the four-loop QCD cusp anomalous
dimension. As a byproduct of our calculation, we also obtain the four-loop
anomalous dimension of the heavy-quark field in HQET. The validity of the
calculational setup is cross-checked by the independent calculation of the
four-loop QCD beta-function from heavy-quark-gluon vertex renormalization in
HQET. We check the obtained results for the cusp anomalous dimension and
heavy-quark field anomalous dimension against available analytical and
numerical results. Finally, we find that the maximal transcendentality
contribution to the QCD Bremsstrahlung function coincides, up to a factor 3/2,
with the Bremsstrahlung function in N = 4 supersymmetric Yang-Mills theory, at
least, through 4 loops.


  We shall discuss how some relevant analyticity and crossing-symmetry
properties of the "eikonal scattering amplitudes" of two Wilson loops in QCD,
when going from Euclidean to Minkowskian theory, can be related to the still
unsolved problem of the asymptotic s-dependence of the hadron-hadron total
cross-sections. In particular, we critically discuss the question if (and how)
a pomeron-like behaviour can be derived from this Euclidean-Minkowskian
duality.


  Motivated by the growing evidence for lepton flavour universality violation
after the first results from Fermilab's muon $(g-2)$ measurement, we revisit
one of the most widely studied anomaly free extensions of the standard model
namely, gauged $L_{\mu}-L_{\tau}$ model, known to be providing a natural
explanation for muon $(g-2)$. We also incorporate the presence of dark matter
(DM) in this model in order to explain the recently reported electron recoil
excess by the XENON1T collaboration. We show that the same neutral gauge boson
responsible for generating the required muon $(g-2)$ can also mediate
interactions between electron and dark fermions boosted by dark matter
annihilation. The required DM annihilation rate into dark fermion require a
hybrid setup of thermal and non-thermal mechanisms to generate DM relic
density. The tightly constrained parameter space from all requirements remain
sensitive to ongoing and near future experiments, keeping the scenario very
predictive.


  We revisit here and carry out further works on tumor-virotherapy
compartmental models of [Tian, 2011, Wang et al., 2013, Phan and Tian, 2017,
Guo et al., 2019]. The results of these papers are only slightly pushed
further. However, what is new is the fact that we make public our electronic
notebooks, since we believe that easy electronic reproducibility is crucial in
an era in which the role of the software becomes very important.


  Modularization is an important architectural principle underlying many types
of complex systems. It tends to tame the complexity of systems, to facilitate
their management, and to enhance their flexibility with respect to evolution.
In software, modularization has been practiced and studied thoroughly in local,
i.e. non-distributed systems. But very little attention has been paid so far to
modularization in distributed systems. This is, in part, because distributed
systems are inherently modularized, in the sense that the internals of each
component of such a system is inaccessible to other components, thus satisfying
the Parnas hiding principle. It is, however, the thesis of this paper that
there is much to be gained by being able to treat groups of distributed
components as modules, called here distributed modules. And that besides the
conventional hiding principle, distributed modularization should provide
additional capabilities, which rarely, if ever, figure in conventional
modularized systems. These capabilities include, but are not limited to: the
ability to impose constraints on which kind of messages can be sent from a
given distributed-module to its outside; and the ability to create AOP-like
crosscutting modules. This paper introduces a model of modular distributed
system, orMDS, which satisfies such capabilities, and which is implemented via
the LGI middleware.


  We report the isolation of thin flakes of cylindrite, a naturally occurring
van der Waals superlattice, by means of mechanical and liquid phase
exfoliation. We find that this material is a heavily doped p-type semiconductor
with a narrow gap (<0.85 eV) with intrinsic magnetic interactions that are
preserved even in the exfoliated nanosheets. Due to its environmental stability
and high electrical conductivity, cylindrite can be an interesting alternative
to the existing two-dimensional magnetic materials.


  Recently, we have shown how a colored-noise Langevin equation can be used in
the context of molecular dynamics as a tool to obtain dynamical trajectories
whose properties are tailored to display desired sampling features. In the
present paper, after having reviewed some analytical results for the stochastic
differential equations forming the basis of our approach, we describe in detail
the implementation of the generalized Langevin equation thermostat and the
fitting procedure used to obtain optimal parameters. We discuss in detail the
simulation of nuclear quantum effects, and demonstrate that, by carefully
choosing parameters, one can successfully model strongly anharmonic solids such
as neon. For the reader's convenience, a library of thermostat parameters and
some demonstrative code can be downloaded from an on-line repository.


  Fingerprint reconstruction is one of the most well-known and publicized
biometrics. Because of their uniqueness and consistency over time, fingerprints
have been used for identification over a century, more recently becoming
automated due to advancements in computed capabilities. Fingerprint
reconstruction is popular because of the inherent ease of acquisition, the
numerous sources (e.g. ten fingers) available for collection, and their
established use and collections by law enforcement and immigration.
Fingerprints have always been the most practical and positive means of
identification. Offenders, being well aware of this, have been coming up with
ways to escape identification by that means. Erasing left over fingerprints,
using gloves, fingerprint forgery; are certain examples of methods tried by
them, over the years. Failing to prevent themselves, they moved to an extent of
mutilating their finger skin pattern, to remain unidentified. This article is
based upon obliteration of finger ridge patterns and discusses some known cases
in relation to the same, in chronological order; highlighting the reasons why
offenders go to an extent of performing such act. The paper gives an overview
of different methods and performance measurement of the fingerprint
reconstruction.


  A two-dimensional extension of a recently developed formalism for slow-fast
quasilinear (QL) systems subject to fast instabilities is derived. Prior work
has demonstrated that the emergent dynamics of these systems is characterized
by a slow evolution of mean fields coupled to marginally stable, fast
fluctuation fields. By exploiting this emergent behavior, an efficient
fast-eigenvalue/slow-initial-value solution algorithm can be developed in which
the amplitude of the fast fluctuations is slaved to the slowly evolving mean
fields to ensure marginal stability (and temporal scale separation) is
maintained. For 2D systems that are spatially-extended in one direction, the
fluctuation eigenfunctions are labeled by their wavenumbers characterizing
spatial variability in that direction, and the marginal mode(s) also must
coincide with the fastest-growing mode(s) over all admissible wavenumbers.
Here, we introduce two equivalent procedures for deriving an ordinary
differential equation governing the slow evolution of the wavenumber of the
fastest-growing fluctuation mode that simultaneously must be slaved to the mean
dynamics to ensure the mode has zero growth rate. We illustrate the procedure
in the context of a 2D model partial differential equation that shares certain
attributes with the equations governing strongly stratified shear flows. The
slaved evolution follows one or more marginal stability manifolds, which
constitute select state-space structures that are not invariant under the full
flow dynamics yet capture quasi-coherent states in physical space in a manner
analogous to invariant solutions identified in, e.g., transitionally-turbulent
shear flows. Accordingly, we propose that marginal stability manifolds are
central organizing structures in a dynamical systems description of certain
classes of multiscale flows where scale separation justifies a QL approximation
of the dynamics.


  Seven and a half years of continuous monitoring of giant air showers
triggered by ultra high-energy cosmic rays have been recently summarized by the
AGASA collaboration. The resulting energy spectrum indicates clearly that the
cosmic ray spectrum extends well beyond the Greisen-Zatsepin-Kuzmin (GZK)
cut-off at $\sim 5 \times 10^{19}$ eV. Furthermore, despite the small number
statistics involved, some structure in the spectrum may be emerging. Using
numerical simulations, it is demonstrated in the present work that these
features are consistent with a spatial distribution of sources that follows the
distribution of luminous matter in the local Universe. Therefore, from this
point of view, there is no need for a second high-energy component of cosmic
rays dominating the spectrum beyond the GZK cut-off.


  The spectral envelope S(F) of a subset of integers is the set of probability
measures on the circle group that are weak star limits of squared moduli of
trigonometric polynomials with frequencies in F. Fourier transforms of these
measures are positive and supported in F - F but the converse generally fails.
The characteristic function chiF of F is a binary sequence whose orbit closure
gives a symbolic dynamical system O(F). Analytic properties of S(F) are related
to dynamical properties of chiF. The Riemann-Lebesque lemma implies that if
chiF is minimal, then S(F) is convex and hence S(F) is the closure of the
convex hull of its extreme points Se(F). In this paper we (i) review the
relationship between these concepts and the special case of the still open 1959
Kadison-Singer problem called Feichtinger's conjecture for exponential
functions, (ii) partially characterize of elements in Se(F), for minimal chiF,
in terms of ergodic properties of (O(F),lambda) where lambda is a shift
invariant probability measure whose existence in ensured by the 1937
Krylov-Bogoyubov theorem, (iii) refine previous numerical studies of the
Morse-Thue minimal binary sequence by exploiting a new MATLAB algorithm for
computing smallest eigenvalues of 4,000,000 x 4,000,000 matrices, (iv) describe
recent results characterizing S(F) for certain Bohr sets F related to
quasicrystals, (v) extend these concepts to general discrete groups including
those with Kazhdan's T-property, such as SL(n,Z), n > 2, which can be
characterized by several equivalent properties such as: any sequence of
positive definite functions converging to 1 uniformly on compact subsets
converges uniformly. This exotic property may be useful to construct a
counterexample to the generalization of Feichtinger's conjecture and hence to
provide a no answer to the question of Kadison and Singer whcih they themselves
tended to suspect.


  We consider the spin response of a normal Fermi liquid with noncentral
interactions under conditions intermediate between the collisionless and
hydrodynamic regimes. This problem is of importance for calculations of
neutrino properties in dense matter. By expressing the deviation of the
quasiparticle distribution function from equilibrium in terms of eigenfunctions
of the transport equation under the combined influence of collisions and an
external field, we derive a closed expression for the
spin-density--spin-density response function and compare its predictions with
that of a relaxation time approximation. Our results indicate that the
relaxation time approximation is reliable for neutrino properties under
astrophysically relevant conditions.


  We present evolutionary synthesis models of starbursts on top of old stellar
populations to investigate in detailed time evolution the relation between Ha
luminosity and star formation rate (SFR). The models show that several effects
have an impact on the ratio between L(Ha) and SFR. Metallicity different from
solar abundance, a time delay between star formation and maximum Ha-luminosity,
and a varying stellar initial mass function give rise to strong variations in
the ratio of Ha luminosity to SFR and can cause large errors in the
determination of the SFR when employing well-known calibrations. When studying
star-bursting dwarf galaxies, and sub-galactic fragments at high redshift,
which show SFR fluctuating on short timescales, these effects can add up to
errors of two orders of magnitude compared with the calibrations. To accurately
determine the true current SFR additional data in combination with models for
the spectral energy distribution are needed.


  We provide a detailed proof of the validity of the Minimal Model Program for
threefolds over excellent Dedekind separated schemes whose residue fields do
not have characteristic 2 or 3.


  We present high signal-to-noise ratio, multi-frequency polarization pulse
profiles for 24 millisecond pulsars that are being observed as part of the
Parkes Pulsar Timing Array (PPTA) project. The pulsars are observed in three
bands, centred close to 730, 1400 and 3100 MHz, using a dual-band 10 cm/50 cm
receiver and the central beam of the 20 cm multibeam receiver. Observations
spanning approximately six years have been carefully calibrated and summed to
produce high S/N profiles. This allows us to study the individual profile
components and in particular how they evolve with frequency. We also identify
previously undetected profile features. For many pulsars we show that pulsed
emission extends across almost the entire pulse profile. The pulse component
widths and component separations follow a complex evolution with frequency; in
some cases these parameters increase and in other cases they decrease with
increasing frequency. The evolution with frequency of the polarization
properties of the profile is also non-trivial. We provide evidence that the
pre- and post-cursors generally have higher fractional linear polarization than
the main pulse. We have obtained the spectral index and rotation measure for
each pulsar by fitting across all three observing bands. For the majority of
pulsars, the spectra follow a single power-law and the position angles follow a
$\lambda^2$ relation, as expected. However, clear deviations are seen for some
pulsars. We also present phase-resolved measurements of the spectral index,
fractional linear polarization and rotation measure. All these properties are
shown to vary systematically over the pulse profile.


  Using Easton collapses, we give a simplified construction of a model in which
Chang's Conjecture for triples holds.


We correct an error in the article "Property (RD) for Hecke pairs".


  The diffraction image of a quasicrystal admits a finite group G as a symmetry
group, and the quasicrystal can be regarded as a quasiperiodic packing of
copies of a G-cluster C, joined by glue atoms. The physical space E containing
C can be embedded into a higher-dimensional space R^k such that, up to an
inflation factor, C is the orthogonal projection of the set {(\pm 1,0,...,0),
(0,\pm 1,0,...,0), ... (0,...,0,\pm 1)}. The projections of the points of Z^k
lying in the strip S=E+[-1/2,1/2]^k+t obtained by shifting a hypercube
[-1/2,1/2]^k+t along E is a quasiperiodic packing of partially occupied copies
of C, but unfortunately, the occupation of clusters is very low. In our
modified strip projection method we firstly determine for each point x\in
Z^k\cap S the number n(x) of all the arithmetic neighbours of x lying in the
strip S, and project the points of Z^k\cap S on E in the decreasing order of
the occupation number n(x). In the case when n(x) represents more than p% of
all the points of the cluster C we project all the arithmetic neighbours of x
(lying inside or outside S). We choose p such that to avoid the superposition
of the fully occupied clusters. The projection of a point x with n(x) less than
p% of all the points of the cluster C is added to the pattern only if it is not
too close to the already obtained points.


  We study general teleportation scheme with an arbitrary state of the pair of
particles (2 and 3) shared by Alice and Bob, and arbitrary measurements on the
input particle 1 and one of the members (2) of the pair on Alice's side. We
find an efficient iterative algorithm for identifying optimum local operations
on Bob's side. In particular we find that simple unitary transformations on his
side are not always optimal even if particles 2 and 3 are perfectly entangled.
We describe the most interesting protocols in the language of extremal
completely-positive maps.


  We study collaborative machine learning systems where a massive dataset is
distributed across independent workers which compute their local gradient
estimates based on their own datasets. Workers send their estimates through a
multipath fading multiple access channel with orthogonal frequency division
multiplexing to mitigate the frequency selectivity of the channel. We assume
that there is no channel state information (CSI) at the workers, and the
parameter server (PS) employs multiple antennas to align the received signals.
To reduce the power consumption and the hardware costs, we employ
complex-valued low-resolution digital-to-analog converters (DACs) and
analog-to-digital converters (ADCs), at the transmitter and the receiver sides,
respectively, and study the effects of practical low-cost DACs and ADCs on the
learning performance. Our theoretical analysis shows that the impairments
caused by low-resolution DACs and ADCs, including those of one-bit DACs and
ADCs, do not prevent the convergence of the federated learning algorithm, and
the multipath channel effects vanish when a sufficient number of antennas are
used at the PS. We also validate our theoretical results via simulations, and
demonstrate that using low-resolution, even one-bit, DACs and ADCs causes only
a slight decrease in the learning accuracy.


  We consider a classically scale-invariant extension of the standard model in
which a dark, non-Abelian gauge symmetry is spontaneously broken via the
Coleman-Weinberg mechanism. Higgs portal couplings between the dark and
standard model sectors provide an origin for the Higgs mass squared parameter
and, hence, the electroweak scale. We find that choices for model parameters
exist in which the dark gauge multiplet is viable as dark matter.


  The presence of a heavy fermion doublet of fourth generation in the standard
model would lead to a anomalous decay with fermion number non-conservation. The
anomalous decay path in the background of the electroweak instanton is
demonstrated by numerical calculation. If the mass of fermion exceeds the
critical value $m_f^{\rm cr}$=9.2 TeV (for $M_H=M_W$), it is shown that there
exists the rapid anomalous decay of the heavy fermion in semi-classical
approximation. The dependence of the critical fermion mass on the Higgs mass is
also presented.


  We give conditions characterizing equality in the Minkowski inequality for
big divisors on a projective variety. Our results draw on the extensive history
of research on Minkowski inequalities in algebraic geometry.


  Phylogenetics is the study of the evolutionary relationships between
organisms. One of the main challenges in the field is to take biological data
for a group of organisms and to infer an evolutionary tree, a graph that
represents these relationships. Developing practical and efficient methods for
inferring phylogenetic trees has lead to a number of interesting mathematical
questions across a variety of fields. However, due to hybridization and gene
flow, a phylogenetic network may be a better representation of the evolutionary
history of some groups of organisms. In this chapter, we introduce some of the
basic concepts in phylogenetics, and present related undergraduate research
projects on phylogenetic networks that touch on areas of graph theory and
abstract algebra. In the first section, we describe several open research
questions related to the combinatorics of phylogenetic networks. In the second,
we describe problems related to understanding phylogenetic statistical models
as algebraic varieties.


  We introduce discrete systems in the form of straight (infinite) and
ring-shaped chains, with two symmetrically placed nonlinear sites. The systems
can be implemented in nonlinear optics (as waveguiding arrays) and BEC (by
means of an optical lattice). A full set of exact analytical solutions for
symmetric, asymmetric, and antisymmetric localized modes is found, and their
stability is investigated in a numerical form. The symmetry-breaking
bifurcation (SBB), through which the asymmetric modes emerge from the symmetric
ones, is found to be of the subcritical type. It is transformed into a
supercritical bifurcation if the nonlinearity is localized in relatively broad
domains around two central sites, and also in the ring of a small size, i.e.,
in effectively nonlocal settings. The family of antisymmetric modes does not
undergo bifurcations, and features both stable and unstable portions. The
evolution of unstable localized modes is investigated by means of direct
simulations. In particular, unstable asymmetric states, which exist in the case
of the subcritical bifurcation, give rise to breathers oscillating between the
nonlinear sites, thus restoring an effective dynamical symmetry between them.


  Evaluative bibliometrics compares the citation impact of researchers,
research groups and institutions with each other across time scales and
disciplines. Both factors - discipline and period - have an influence on the
citation count which is independent of the quality of the publication.
Normalizing the citation impact of papers for these two factors started in the
mid-1980s. Since then, a range of different methods have been presented for
producing normalized citation impact scores. The current study uses a data set
of over 50,000 records to test which of the methods so far presented correlate
better with the assessment of papers by peers. The peer assessments come from
F1000Prime - a post-publication peer review system of the biomedical
literature. Of the normalized indicators, the current study involves not only
cited-side indicators, such as the mean normalized citation score, but also
citing-side indicators. As the results show, the correlations of the indicators
with the peer assessments all turn out to be very similar. Since F1000 focuses
on biomedicine, it is important that the results of this study are validated by
other studies based on datasets from other disciplines or (ideally) based on
multi-disciplinary datasets.


  Non-classical states of light, such as number-squeezed light, with
fluctuations below the classical shot noise level, have important uses in
metrology, communication, quantum information processing, and quantum
simulation. However, generating these non-classical states of light, especially
with high intensity and high degree of squeezing, is challenging. To address
this problem, we introduce a new concept which uses gain to generate intense
sub-Poissonian light at optical frequencies. It exploits a strongly nonlinear
gain for photons which arises from a combination of frequency-dependent gain
and Kerr nonlinearity. In this laser architecture, the interaction between the
gain medium and Kerr nonlinearity suppresses the spontaneous emission at high
photon number states, leading to a strong "negative feedback" that suppresses
photon-number fluctuations. We discuss realistic implementations of this
concept based on the use of solid-state gain media in laser cavities with Kerr
nonlinear materials, showing how 90% squeezing of photon number fluctuations
below the shot noise level can be realized.


  Language modeling, a central task in natural language processing, involves
estimating a probability distribution over strings. In most cases, the
estimated distribution sums to 1 over all finite strings. However, in some
pathological cases, probability mass can ``leak'' onto the set of infinite
sequences. In order to characterize the notion of leakage more precisely, this
paper offers a measure-theoretic treatment of language modeling. We prove that
many popular language model families are in fact tight, meaning that they will
not leak in this sense. We also generalize characterizations of tightness
proposed in previous works.


  In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a
deformation of the metric tensor driven by its Ricci curvature. As a step
towards resolving the problem of time in quantum gravity, we attempt to merge
the Ricci flow equation with the Hamilton-Jacobi equation for general
relativity.


  In the present work, we investigate the thermoelectric properties of a
T-shaped double quantum dot system coupled to two metallic leads incorporating
the intra-dot Coulomb interaction. We explore the role of the interference
effects and Coulomb blockade on the thermoelectric efficiency of the system in
the linear and nonlinear regimes. We studied as well the effect of a Van-Hove
singularity of the leads density of states (DOS) at the neighborhood of the
Fermi energy, a situation that can be obtained using a carbon nanotube, a
graphene nano-ribbon or other contacts with one-dimensional properties. The
system is studied above the Kondo temperature. The Coulomb blockade of the
electronic charges is studied using the Hubbard III approximation, which
properly describes the transport properties of this regime. In the linear
response, our results show an enhancement of the thermopower and the figure of
merit of the system. For a nonlinear situation, we calculate the thermoelectric
efficiency and power output, concluding that the T-shaped double quantum dot is
an efficient thermoelectric device. Moreover, we demonstrate the great
importance of the DOS Van-Hove singularity at the neighborhood of the Fermi
energy to obtain a very significant increase of the thermoelectric efficiency
of the system.


  We performed the temperature diagnostics using inversions of data from nine
spectroscopic observations obtained with the IRIS spectrograph in the MgII h &
k lines. The sensitivity to the temperature of the emission peaks of these
lines was exploited to determine the temperature of the coronal rain plasma
using inversions of the spectroscopic profiles. Additional relationships
between different spectral features of these lines, derived from the use of 3D
radiative transfer line synthesis applied to simulations, were employed in
order to derive the line-of-sight (LoS) velocities in different parts of the
coronal rain plasma. For the first time, spectroscopic inversions of coronal
rain were successfully performed. Temperatures derived from the inversions
yield coronal rain clump temperatures at the formation height of the emission
peaks of the MgII h & k lines in the range between 5000 and 7000 K. This narrow
range of values remains consistent among all the different observations used in
this work. We obtained LoS velocities of up to 40 km/s, which are consistent
with the motion of the plasma being mostly constrained to the plane of the sky,
as the coronal rain was mostly detected shortly after its formation and the
observations took place in the disc. Furthermore, velocity diagnostics led to
the detection of larger velocities at higher layers of the coronal rain plasma
in some cases. This increased velocity seems to indicate that at some point (at
least) during the fall of coronal rain clumps towards the chromosphere, the
material in the upper part of the coronal rain plasma is falling with greater
velocity than the material below it. The conditions of the temperature and
density of the coronal rain plasma where the Mg II h line forms appear to be
slightly different that those of the Mg II k line, with the former found at
slightly colder and denser parts of the plasma.


  This paper concentrates on analyzing Witten deformation for a family of
non-Morse functions parametrized by $T\in \mathbb{R}_+$, resulting in a novel,
purely analytic proof of the gluing formula for analytic torsions in complete
generality. Intriguingly, the gluing formula in this article could be
reformulated as the Bismut-Zhang theorem for non-Morse functions, and from the
perspective of Vishik's theory of moving boundary problems, the deformation
parameter $T$ parametrizes a family of boundary conditions. Our proof also
makes use of an interesting connection between small eigenvalues of Witten
Laplacians and Mayer-Vietoris sequences. Finally, these new techniques could be
extended to analytic torsion forms and will play key roles in our future study
of the higher Cheeger-M\"uller theorem for general flat bundles.


  Density Functional Theory (DFT) calculations are being routinely used to
identify new material candidates that approach activity near fundamental limits
imposed by thermodynamics or scaling relations. DFT calculations have finite
uncertainty and this raises an issue related to the ability to delineate
materials that possess high activity. With the development of error estimation
capabilities in DFT, there is an urgent need to propagate uncertainty through
activity prediction models. In this work, we demonstrate a rigorous approach to
propagate uncertainty within thermodynamic activity models. This maps the
calculated activity into a probability distribution, and can be used to
calculate the expectation value of the distribution, termed as the expected
activity. We prove that the ability to distinguish materials increases with
reducing uncertainty. We define a quantity, prediction efficiency, which
provides a precise measure of the ability to distinguish the activity of
materials for a reaction scheme over an activity range. We demonstrate the
framework for 4 important electrochemical reactions, hydrogen evolution,
chlorine evolution, oxygen reduction and oxygen evolution. We argue that future
studies should utilize the expected activity and prediction efficiency to
improve the likelihood of identifying material candidates that can possess high
activity.


  Machine learning, as a tool to learn and model complicated (non)linear
relationships between input and output data sets, has shown preliminary success
in some HPC problems. Using machine learning, scientists are able to augment
existing simulations by improving accuracy and significantly reducing
latencies. Our ongoing research work is to create a general framework to apply
neural network-based models to HPC applications. In particular, we want to use
the neural network to approximate and replace code regions within the HPC
application to improve performance (i.e., reducing the execution time) of the
HPC application. In this paper, we present our preliminary study and results.
Using two applications (the Newton-Raphson method and the Lennard-Jones (LJ)
potential in LAMMP) for our case study, we achieve up to 2.7x and 2.46x
speedup, respectively.


  Many inverse problems in signal processing deal with the robust estimation of
unknown data from underdetermined linear observations. Low dimensional models,
when combined with appropriate regularizers, have been shown to be efficient at
performing this task. Sparse models with the 1-norm or low rank models with the
nuclear norm are examples of such successful combinations. Stable recovery
guarantees in these settings have been established using a common tool adapted
to each case: the notion of restricted isometry property (RIP). In this paper,
we establish generic RIP-based guarantees for the stable recovery of cones
(positively homogeneous model sets) with arbitrary regularizers. These
guarantees are illustrated on selected examples. For block structured sparsity
in the infinite dimensional setting, we use the guarantees for a family of
regularizers which efficiency in terms of RIP constant can be controlled,
leading to stronger and sharper guarantees than the state of the art.


  We extend the definition of algebraic entropy to endomorphisms of affine
varieties. We calculate algebraic entropy of the action of elements of mapping
class groups on various character varieties, and show that it is equal to a
quantity we call the spectral radius, a generalization of the dilatation of a
Pseudo-Anosov mapping class. Our calculations are compatible with all known
calculations of the topological entropy of this action.


  The study of nonequilibrium phenomena in interacting lattice systems can
provide new perspectives on correlation effects, and information on metastable
states of matter. Mott insulators are a promising class of systems for
nonequilibrium studies, since they exhibit exotic phenomena and complex phase
diagrams upon doping, and because a large Mott gap provides protection against
fast thermalization and heating after photo-excitations. We can thus expect the
emergence of interesting transient states and photo-induced phases in Mott
systems. This review presents the current understanding of the mechanisms which
control the time evolution of photo-doped charge carriers and the properties of
photo-induced metastable states. We focus on recent theoretical progress,
identify the relevant underlying concepts, and link them to experimental
observations. The review starts with a general discussion of field-induced
nonequilibrium setups and an overview of key experiments which revealed
characteristic properties of photo-excited Mott states, proceeds with a compact
overview of the theoretical tools which have been developed to investigate
these strongly correlated nonequilibrium states, and then analyzes Mott
insulators driven out of equilibrium by static electric fields, periodic
fields, and short laser pulses. We also discuss the appearance of nonthermal
electronic orders in photo-excited Mott systems, including nonthermal spin and
orbital orders, $\eta$ pairing states, and novel types of excitonic orders.


  R2 is a novel online any-angle path planner that uses heuristic bug-based or
ray casting approaches to find optimal paths in 2D maps with non-convex,
polygonal obstacles. R2 is competitive to traditional free-space planners,
finding paths quickly if queries have direct line-of-sight. On large sparse
maps with few obstacle contours, which are likely to occur in practice, R2
outperforms free-space planners, and can be much faster than state-of-the-art
free-space expansion planner Anya. On maps with many contours, Anya performs
faster than R2. R2 is built on RayScan, introducing lazy-searches and a
source-pledge counter to find successors optimistically on contiguous contours.
The novel approach bypasses most successors on jagged contours to reduce
expensive line-of-sight checks, therefore requiring no pre-processing to be a
competitive online any-angle planner.


  Charts are a powerful tool for visually conveying complex data, but their
comprehension poses a challenge due to the diverse chart types and intricate
components. Existing chart comprehension methods suffer from either heuristic
rules or an over-reliance on OCR systems, resulting in suboptimal performance.
To address these issues, we present ChartReader, a unified framework that
seamlessly integrates chart derendering and comprehension tasks. Our approach
includes a transformer-based chart component detection module and an extended
pre-trained vision-language model for chart-to-X tasks. By learning the rules
of charts automatically from annotated datasets, our approach eliminates the
need for manual rule-making, reducing effort and enhancing accuracy.~We also
introduce a data variable replacement technique and extend the input and
position embeddings of the pre-trained model for cross-task training. We
evaluate ChartReader on Chart-to-Table, ChartQA, and Chart-to-Text tasks,
demonstrating its superiority over existing methods. Our proposed framework can
significantly reduce the manual effort involved in chart analysis, providing a
step towards a universal chart understanding model. Moreover, our approach
offers opportunities for plug-and-play integration with mainstream LLMs such as
T5 and TaPas, extending their capability to chart comprehension tasks. The code
is available at https://github.com/zhiqic/ChartReader.


  Magnetic Resonance Force Microscopy (MRFM) is a powerful technique to detect
a small number of spins that relies on force-detection by an ultrasoft
magnetically tipped cantilever and selective magnetic resonance manipulation of
the spins. MRFM would greatly benefit from ultralow temperature operation,
because of lower thermomechanical noise and increased thermal spin
polarization. Here, we demonstrate MRFM operation at temperatures as low as 30
mK, thanks to a recently developed SQUID-based cantilever detection technique
which avoids cantilever overheating. In our experiment, we detect dangling bond
paramagnetic centers on a silicon surface down to millikelvin temperatures.
Fluctuations of such kind of defects are supposedly linked to 1/f magnetic
noise and decoherence in SQUIDs as well as in several superconducting and
single spin qubits. We find evidence that spin diffusion plays a key role in
the low temperature spin dynamics.


  We introduce the notion of the joint spectral flow, which is a generalization
of the spectral flow, by using Segal's model of the connective $K$-theory
spectrum. We apply it for some localization results of indices motivated by
Witten's deformation of Dirac operators and rephrase some analytic techniques
in terms of topology.


  In this paper, we study the local variational geometry of the optimal
solution set of the trust region subproblem (TRS), which minimizes a general,
possibly nonconvex, quadratic function over the unit ball. Specifically, we
demonstrate that a H\"olderian error bound holds globally for the TRS with
modulus 1/4 and the Kurdyka-{\L}ojasiewicz (KL) inequality holds locally for
the TRS with a KL exponent 3/4 at any optimal solution. We further prove that
unless in a special case, the H\"olderian error bound modulus, as well as the
KL exponent, is 1/2. Finally, based on the obtained KL property, we further
show that the projected gradient methods studied in [A. Beck and Y. Vaisbourd,
SIAM J. Optim., 28 (2018), pp. 1951--1967] for solving the TRS achieve a
sublinear or even linear rate of convergence.


  Modern PC workstations often provide more CPU power than required for most
control applications. On the other hand, the screen space is always in short
supply. One possible solution is to use more PCs, but in fact we need only more
screens, not more keyboards, mice etc. PC architecture allows using more than
one videocard, and X Window protocol is also aware that there can be more than
one screen. But until release of XFree86 version 4 there was no freely
available server capable of driving multiple ``heads''. We have been using
multiheaded workstations under XFree86 in the VEPP-5 control room since early
2000 (currently 4 4-headed PCs plus several dual-headed). The ``Xinerama'' mode
(one-large-screen) is better suited for accelerator control system than
``several separate screens''. When moving to this configuration we've
encountered a number of, mainly human-related, problems, some of which required
modifications to X server Additionaly, the ``style'' of performing control has
slightly changed.


  We derive an asymptotic formula for entropy rate of a hidden Markov chain
around a "weak Black Hole". We also discuss applications of the asymptotic
formula to the asymptotic behaviors of certain channels.


  The problem of finding necessary and sufficient conditions to decompose a
complete tripartite graph $K_{r,s,t}$ into 5-cycles was first considered by
E.S. Mahmoodian and Maryam Mirzakhani (1995). They stated some necessary
conditions and conjectured that those conditions are also sufficient. Since
then, many cases of the problem have been solved by various authors; however,
the case when the partite sets $r\leq s\leq t$ have odd and distinct sizes
remained open. We show the conjecture is true when $r$, $s$ and $t$ are all
multiples of 5, $t+90 \leq \frac{4rs}{r+s}$, and $t \neq s+10$.


  We destroy a finite tree of size $n$ by cutting its edges one after the other
and in uniform random order. Informally, the associated cut-tree describes the
genealogy of the connected components created by this destruction process. We
provide a general criterion for the convergence of the rescaled cut-tree in the
Gromov-Prohorov topology to an interval endowed with the Euclidean distance and
a certain probability measure, when the underlying tree has a small height of
order $o(\sqrt{n})$. In particular, we consider uniform random recursive trees,
binary search trees, scale-free random trees and a mixture of regular trees.
This yields extensions of a result in Bertoin for the cut-tree of uniform
random recursive trees and also allows us to generalize some results of Kuba
and Panholzer on the multiple isolation of vertices. The approach relies in the
close relationship between the destruction process and Bernoulli bond
percolation, which may be useful for studying the cut-tree of other classes of
trees.


  We analyze the data of low-energy cosmic-ray antiproton spectrum, recently
published by the BESS Collaboration, in terms of newly calculated fluxes for
secondary antiprotons and for a possible contribution of an exotic signal due
to neutralino annihilation in the galactic halo. We single out the relevant
supersymmetric configurations and discuss their explorability with experiments
of direct search for particle dark matter and at accelerators. We discuss how
future measurements with the Alpha Magnetic Spectrometer (AMS) on the Shuttle
flight may disentangle the possible neutralino-induced contribution from the
secondary one.


  In [1] the problem of finding a sharp lower bound on lower against number of
a general graph is mentioned as an open question. We solve the problem by
establishing a tight lower bound on lower against number of a general graph in
terms of order and maximum degree.


  The robustness of classifiers has become a question of paramount importance
in the past few years. Indeed, it has been shown that state-of-the-art deep
learning architectures can easily be fooled with imperceptible changes to their
inputs. Therefore, finding good measures of robustness of a trained classifier
is a key issue in the field. In this paper, we point out that averaging the
radius of robustness of samples in a validation set is a statistically weak
measure. We propose instead to weight the importance of samples depending on
their difficulty. We motivate the proposed score by a theoretical case study
using logistic regression, where we show that the proposed score is independent
of the choice of the samples it is evaluated upon. We also empirically
demonstrate the ability of the proposed score to measure robustness of
classifiers with little dependence on the choice of samples in more complex
settings, including deep convolutional neural networks and real datasets.


  Bose atoms in optical lattices are considered at low temperatures and weak
interactions, when Bose-Einstein condensate is formed. A self-consistent
approach, based on the use of a representative statistical ensemble, is
employed, ensuring a gapless spectrum of collective excitations and the
validity of conservation laws. In order to show that the approach is applicable
to both weak and tight binding, the problem is treated in the Bloch as well as
in the Wannier representations. Both these ways result in similar expressions
that are compared for the self-consistent Hartree-Fock-Bogolubov approximation.
A convenient general formula for the superfluid fraction of atoms in an optical
lattice is derived.


  The geometric flow theory and its applications turned into one of the most
intensively developing branches of modern geometry. Here, a brief introduction
to Finslerian Ricci flow and their self-similar solutions known as Ricci
solitons are given and some recent results are presented. They are a
generalization of Einstein metrics and are previously developed by the present
authors for Finsler manifolds. In the present work, it is shown that a complete
shrinking Ricci soliton Finsler manifold has a finite fundamental group.


  Increasingly sophisticated mathematical modelling processes from Machine
Learning are being used to analyse complex data. However, the performance and
explainability of these models within practical critical systems requires a
rigorous and continuous verification of their safe utilisation. Working towards
addressing this challenge, this paper presents a principled novel safety
argument framework for critical systems that utilise deep neural networks. The
approach allows various forms of predictions, e.g., future reliability of
passing some demands, or confidence on a required reliability level. It is
supported by a Bayesian analysis using operational data and the recent
verification and validation techniques for deep learning. The prediction is
conservative -- it starts with partial prior knowledge obtained from lifecycle
activities and then determines the worst-case prediction. Open challenges are
also identified.


  Computing systems have become increasingly complex with the emergence of
heterogeneous hardware combining multicore CPUs and GPUs. These parallel
systems exhibit tremendous computational power at the cost of increased
programming effort. This results in a tension between achieving performance and
code portability. Code is either tuned using device-specific optimizations to
achieve maximum performance or is written in a high-level language to achieve
portability at the expense of performance.
  We propose a novel approach that offers high-level programming, code
portability and high-performance. It is based on algorithmic pattern
composition coupled with a powerful, yet simple, set of rewrite rules. This
enables systematic transformation and optimization of a high-level program into
a low-level hardware specific representation which leads to high performance
code.
  We test our design in practice by describing a subset of the OpenCL
programming model with low-level patterns and by implementing a compiler which
generates high performance OpenCL code. Our experiments show that we can
systematically derive high-performance device-specific implementations from
simple high-level algorithmic expressions. The performance of the generated
OpenCL code is on par with highly tuned implementations for multicore CPUs and
GPUs written by experts


  We study the Cauchy problem for the (2+1) integrable nonlinear Schr\"odinger
equation by the inverse scattering transform (IST) method. This Cauchy problem
with given initial data and boundary data at infinity is reduced by IST to the
Cauchy problem for the linear Schr\"odinger equation, in which the potential is
expressed in terms of boundary data. The results on direct and inverse
scattering problems for a two-dimensional Dirac system with special potentials
are used and refined. The Cauchy problem admits an explicit solution if the IST
of the solution is an integral operator of rank 1. We give one such solution.


  A visible action on a complex manifold is a holomorphic action that admits a
$J$-transversal totally real submanifold $S$.
  It is said to be strongly visible if there exists an orbit-preserving
anti-holomorphic diffeomorphism $\sigma$ such that $\sigma |_S = \mathrm{id}$.
  In this paper, we prove that for any Hermitian symmetric space $D = G/K$ the
action of any symmetric subgroup $H$ is strongly visible.
  The proof is carried out by finding explicitly an orbit-preserving
anti-holomorphic involution and a totally real submanifold $S$.
  Our geometric results provide a uniform proof of various multiplicity-free
theorems of irreducible highest weight modules when restricted to reductive
symmetric pairs, for both classical and exceptional cases, for both finite and
infinite dimensional cases, and for both discrete and continuous spectra.


  The basic idea of fast Monte Carlo (MC) simulations is to perform
particle-based MC simulations with the excluded-volume interactions modeled by
"soft" repulsive potentials that allow particle overlapping. This gives much
faster system relaxation and better sampling of the configurational space than
conventional molecular simulations with "hard" repulsions that prevent particle
overlapping. Here we present fast lattice MC (FLMC) simulations for confined
homopolymers, where multiple occupancy of lattice sites is allowed with a
proper Boltzmann weight and thus the evaluation of nearest-neighbor
interactions can also be avoided. When compared with the corresponding lattice
field theories based on the \emph{same} Hamiltonian, FLMC simulations further
provide a powerful means for unambiguously and quantitatively revealing the
correlation/fluctuation effects.


  Axion-like particles (ALPs) are often considered as good candidates for dark
matter. Several mechanisms generating relic abundance of ALP dark matter have
been proposed. They may involve processes which take place before, during or
after cosmic inflation. In all cases an important role is played by the
potential of the corresponding Peccei-Quinn (PQ) field. Quite often this
potential is assumed to be dominated by a quartic term with a very small
coupling. We show that in such situation it is crucial to take into account
different kinds of corrections especially in models in which the PQ field
evolves during and after inflation. We investigate how such evolution changes
due to radiative, thermal and geometric corrections. In many cases those
changes are very important and result in strong modifications of the
predictions of a model. They may strongly influence the amount of ALP
contributions to cold and warm components of dark matter as well as the power
spectrum of associated isocurvature perturbations. Models with a
quasi-supersymmetric spectrum of particles to which the PQ field couples seem
to be especially interesting. Qualitative features of such models are discussed
with the help of approximate analytical formulae. However, the dynamics of the
PQ field with the considered corrections taken into account is more complicated
than in the case without corrections so dedicated numerical calculations are
necessary to obtain precise predictions. We present such results for some
characteristic benchmark points in the parameter space.


  Large Language Models (LLMs) are powerful zero-shot assessors used in
real-world situations such as assessing written exams and benchmarking systems.
Despite these critical applications, no existing work has analyzed the
vulnerability of judge-LLMs to adversarial manipulation. This work presents the
first study on the adversarial robustness of assessment LLMs, where we
demonstrate that short universal adversarial phrases can be concatenated to
deceive judge LLMs to predict inflated scores. Since adversaries may not know
or have access to the judge-LLMs, we propose a simple surrogate attack where a
surrogate model is first attacked, and the learned attack phrase then
transferred to unknown judge-LLMs. We propose a practical algorithm to
determine the short universal attack phrases and demonstrate that when
transferred to unseen models, scores can be drastically inflated such that
irrespective of the assessed text, maximum scores are predicted. It is found
that judge-LLMs are significantly more susceptible to these adversarial attacks
when used for absolute scoring, as opposed to comparative assessment. Our
findings raise concerns on the reliability of LLM-as-a-judge methods, and
emphasize the importance of addressing vulnerabilities in LLM assessment
methods before deployment in high-stakes real-world scenarios.


  Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging
task. In classical engineering literature simplified mathematical models and
simulation are widely used for its study. In this work the limitations of
classical engineering phase-locked loop analysis are demonstrated, e.g., hidden
oscillations, which can not be found by simulation, are discussed. It is shown
that the use of simplified dynamical models and the application of simulation
may lead to wrong conclusions concerning the operability of PLL-based circuits.


  We determine the abundances of neutron-capture elements from Sr to Eu for
five very-metal-poor stars (-3<[Fe/H]<-2) in the Milky Way halo to reveal the
origin of light neutron-capture elements. Previous spectroscopic studies have
shown evidence of at least two components in the r-process; one referred to as
the "main r-process" and the other as the "weak r-process," which is mainly
responsible for producing heavy and light neutron-capture elements,
respectively. Observational studies of metal-poor stars suggest that there is a
universal pattern in the main r-process, similar to the abundance pattern of
the r-process component of solar-system material. Still, it is uncertain
whether the abundance pattern of the weak r-process shows universality or
diversity, due to the sparseness of measured light neutron-capture elements. We
have detected the key elements, Mo, Ru, and Pd, in five target stars to give an
answer to this question. The abundance patterns of light neutron-capture
elements from Sr to Pd suggest a diversity in the weak r-process. In
particular, scatter in the abundance ratio between Ru and Pd is significant
when the abundance patterns are normalized at Zr. Our results are compared with
the elemental abundances predicted by nucleosynthesis models of supernovae with
parameters such as electron fraction or proto-neutron-star mass, to investigate
sources of such diversity in the abundance patterns of light neutron-capture
elements. This paper presents that the variation in the abundances of observed
stars can be explained with a small range of parameters, which can serve as
constraints on future modeling of supernova models.


  Chromatographic processes can be modeled by nonlinear, convection-dominated
partial differential equations, together with nonlinear relations: the
adsorption isotherms. In this paper we consider the nonlinear equilibrium
dispersive (ED) model with adsorption isotherms of Langmuir type. We show that
very efficient, fully conservative, numerical schemes can be designed for this
mode by exploiting the relation between the conserved variables of the model
and the physical concentrations of the multi-component mixtures. We show that
this relation is one to one and admits a smooth global inverse, which cannot be
given explicitly but can be easily computed by using a convenient root finder.
These results provide the necessary ingredients to implement fully conservative
numerical schemes for the model considered.
  Implicit-Explicit (IMEX) techniques can be used in the convection-dominated
regime in order to increase the efficiency of the numerical scheme. We propose
a second order IMEX scheme, combining an explicit
Weighted-Essentially-non-Oscillatory discretization of the convective fluxes
with an implicit treatment of the diffusive term, in order to illustrate the
numerical issues involved in the application of IMEX techniques to this model.
Through a series of numerical experiments, we show that the scheme provides
accurate numerical solutions which capture the sharp discontinuities present in
the chromatographic fronts, with the same stability restrictions as in the
purely hyperbolic case.


  We investigate the line element of spacetime around a linear cosmic string in
the presence of a cosmological constant. We obtain the metric and argue that it
should be discarded because of asymptotic considerations. Then a time dependent
and consistent form of the metric is obtained and its properties are discussed.


  We investigate the extent to which the eigenstate thermalization
hypothesis~(ETH) is valid or violated in the non-integrable and the integrable
spin-$1/2$ XXZ chain. We perform the energy-resolved analysis of the
statistical properties of matrix elements $\{O_{\gamma\alpha}\}$ of an
observable $\hat{O}$ in the energy eigenstate basis. The Hilbert space is
coarse-grained into energy shells of width $\Delta_E$, with which one can
define a block submatrix $\tilde{O}^{(b,a)}$ consisting of elements between
eigenstates in the $a$th and $b$th shells. Each block submatrix is
characterized by constant values of $E_{\gamma\alpha}=(E_\gamma+E_\alpha)/2
\simeq \tilde{E}$ and $\omega_{\gamma\alpha}= (E_\gamma-E_\alpha) \simeq
\omega$ up to $\Delta_E$. We will show that all matrix elements within a block
are statistically equivalent to each other in the non-integrable case. Their
distribution is characterized by $\bar{E}$ and $\omega$, and follows the
prediction of the ETH. In stark contrast, eigenstate-to-eigenstate fluctuations
persist in the integrable case. Consequently, matrix elements
$O_{\gamma\alpha}$ cannot be characterized by the energy parameters
$E_{\gamma\alpha}$ and $\omega_{\gamma\alpha}$ only. Our result explains the
origin for the breakdown of the fluctuation dissipation theorem in the
integrable system. The eigenstate-to-eigenstate fluctuations sheds a new light
on the meaning of the ETH.


  We show for several two-dimensional lattices that the nearest neighbor
valence bond states are linearly independent. To do so, we utilize and
generalize a method that was recently introduced and applied to the kagome
lattice by one of the authors. This method relies on the choice of an
appropriate cell for the respective lattice, for which a certain local linear
independence property can be demonstrated. Whenever this is achieved, linear
independence follows for arbitrarily large lattices that can be covered by such
cells, for {\em both} open and periodic boundary conditions. We report that
this method is applicable to the kagome, honeycomb, square, squagome, two types
of pentagonal, square-octagon, the star lattice, two types of archimedean
lattices, three types of "martini" lattices, and to fullerene-type lattices,
e.g., the well known "Buckyball". Applications of the linear independence
property, such as the derivation of effective quantum dimer models, or the
constructions of new solvable spin-1/2 models, are discussed.


  A review of the connections between K_2 of a field and universal central
extensions, quadratic forms, central simple algebras, differential forms,
abelian extensions, abelian coverings, explicit reciprocity laws, special
values of zeta functions, and special values of L-functions. No proofs, minimal
bibliography.


  We consider the problem of online boosting for regression tasks, when only
limited information is available to the learner. We give an efficient regret
minimization method that has two implications: an online boosting algorithm
with noisy multi-point bandit feedback, and a new projection-free online convex
optimization algorithm with stochastic gradient, that improves state-of-the-art
guarantees in terms of efficiency.


  We discuss the entropy change due to fragmentation for black hole solutions
in various dimensions. We find three different types of behavior. The entropy
may decrease, increase or have a mixed behavior, characterized by the presence
of a threshold mass. For two-dimensional (2D) black holes we give a complete
characterization of the entropy behavior under fragmentation, in the form of
sufficient conditions imposed on the function J, which defines the 2D
gravitational model. We compare the behavior of the gravitational solutions
with that of free field theories in d dimensions. This excludes the possibility
of finding a gravity/field theory realization of the holographic principle for
a broad class of solutions, including asymptotically flat black holes. We find
that the most natural candidates for holographic duals of the black hole
solutions with mixed behavior are field theories with a mass gap. We also
discuss the possibility of formulating entropy bounds that make reference only
to the energy of a system.


  The influence of surface enhanced covalency on the Madelung potential is
experimentally investigated using angle-resolved photoemission for (100), (110)
and (111) SrTiO$_3$ surfaces after annealing in UHV at 630 {\deg}C.
Deconvolution of the core level spectra (O 1s, Sr 3d and Ti 2p) distinguishes
bulk and surface components, which are interpreted in terms of surface enhanced
covalency (SEC). By comparing the experimentally measured binding energies with
theoretical calculations developed in the framework of the Localized-Hole
Point-Ion Model, we quantitatively determine the effective electron occupancy
at bulk and surface Sr and Ti sites. Our results confirm the essentially ionic
character of Sr$-$O bond and the partially covalent character of Ti$-$O bond in
bulk STO. The cation Ti and Sr electron occupation is greater for all the three
surfaces than in the bulk. Surface covalency shifts the Madelung potential at
the surface by {\Delta}EM. {\Delta}EM is a minimum for the (111) surface, and
increases through (100), attaining a maximum for (110). The angle-resolved
valence band spectra and the work function values also confirm this trend. The
results are consistent with d$-$d charge fluctuations dominating at the
surface, whereas metal-ligand charge transfers are more energetically
favourable in the bulk.


  Vacuum arcing poses significant challenges for high-field vacuum devices,
underscoring the importance of understanding it for their efficient design. A
detailed description of the physical mechanisms involved in vacuum arcing is
yet to be achieved, despite extensive research. In this work, we further
develop the modelling of the physical processes involved in the initiation of
vacuum arcing, starting from field emission and leading to plasma onset. Our
model concurrently combines particle-in-cell with Monte Carlo collisions
(PIC-MCC) simulations of plasma processes with finite element-based
calculations of electron emission and the associated thermal effects. Including
the processes of evaporation, impact ionization and direct field ionization
allowed us to observe the dynamics of plasma buildup from an initially cold
cathode surface. We simulated a static nanotip at various local fields to study
the thresholds for thermal runaway and plasma initiation, identifying the
significance of various interactions. We found that direct field ionization of
neutrals has a significant effect at high fields on the order of 10 GV/m.
Furthermore, we find that cathode surface interactions such as evaporation,
sputtering and bombardment heating play a major role in the initiation of
vacuum arcs. Consequently, the inclusion of these interactions in vacuum arc
simulations is imperative.


  We calculate the transverse and time-time components of the instantaneous
gluon propagator in Coulomb gauge QCD by using an SU(3) quenched lattice
simulation on isotropic and anisotropic lattices. We find that the gluon
propagators suffer from strong discretization effects on the isotropic lattice;
on the other hand, those on the anisotropic lattices give a better scaling.
Moreover, on these two type of lattices the transverse parts are significantly
suppressed in the infrared region and have a turnover at about 500 [MeV]. The
high resolution to the temporal direction due to the anisotropy yields small
discretization errors for the time-time gluon propagators, which also show an
infrared enhancement as expected in the Gribov-Zwanziger confinement scenario.


  High-latitude ($|b|>30^{\circ}$) molecular clouds have virial parameters that
exceed 1, but whether these clouds can form stars has not been studied
systematically. Using JCMT SCUBA-2 archival data, we surveyed 70 fields that
target high-latitude Planck galactic cold clumps (HLPCs) to find dense cores
with density of $10^{5}$-$10^{6}$ cm$^{-3}$ and size of $<0.1$ pc. The sample
benefits from both the representativeness of the parent sample and covering
densest clumps at the high column density end ($>1\times10^{21}$ cm$^{-2}$). At
an average noise rms of 15 mJy/beam, we detected Galactic dense cores in only
one field, G6.04+36.77 (L183), while also identifying 12 extragalactic objects
and two young stellar objects. Compared to the low-latitude clumps, dense cores
are scarce in HLPCs. With synthetic observations, the densities of cores are
constrained to be $n_c\lesssim10^5$ cm$^{-3}$, should they exist in HLPCs.
Low-latitude clumps, Taurus clumps, and HLPCs form a sequence where a higher
virial parameter corresponds to a lower dense core detection rate. If HLPCs
were affected by the Local Bubble, the scarcity should favor
turbulence-inhibited rather than supernova-driven star formation. Studies of
the formation mechanism of the L183 molecular cloud are warranted.


  We apply the recently developed slave fermion approach to study the doped
Mott insulator in the one-band Hubbard and Hubbard-Heisenberg models. Our
results produce several subtle features in the electron spectra and confirm the
key role of antiferromagnetic (AFM) correlations in the appearance of the
pseudogap. Upon hole doping, the electron spectra exhibit a single peak near
the Fermi energy in the local approximation of the Hubbard model where AFM
correlations are not included. When AFM correlations are included through an
explicit mean-field Heisenberg interaction, a second peak emerges at slightly
lower energy and pushes the other peak to higher energy, so that a pseudogap
emerges between the two peaks at small doping. Both peaks grow rapidly with
increasing doping and eventually merge together, where the pseudogap no longer
exists. Detailed analyses of the spectral evolution with doping and the
strength of the Heisenberg interaction confirm that the lower-energy peak comes
from a polaronic mechanism due to the holon-spinon interaction in the
AFM-correlated background and the higher-energy peak arises from the holon
hybridization to form the electron quasiparticles. Thus, the pseudogap arises
from the interplay of the polaronic and hybridization mechanisms. Our results
are in good agreement with previous numerical calculations using the dynamical
mean-field theory and its cluster extensions, but give a clearer picture of the
underlying physics. Our work provides a promising perspective for clarifying
the nature of doped Mott insulators and may serve as a starting point for more
elaborate investigations in the future.


  Doubly Special Relativity (DSR) is a theory with two observer-independent
scales, of velocity and mass, which is expected to replace Special Relativity
at ultra-high energies. In these notes we first discuss the postulates of DSR,
and then turn to presenting arguments supporting the hypothesis that DSR can be
regarded as a flat space, semiclassical limit of gravity. The notes are based
on the talk presented at the conference ``Special Relativity -- Will it Survive
the Next 100 Years?''