  Let $z_{1},z_{2},...,z_{N}$ be a sequence of distinct grid points. A finite
difference formula approximates the $m$-th derivative $f^{(m)}(0)$ as $\sum
w_{k}f(z_{k})$, with $w_{k}$ being the weights. We derive an algorithm for
finding the weights $w_{k}$ which is an improvement of an algorithm of Fornberg
(\emph{Mathematics of Computation}, vol. 51 (1988), p. 699-706). This algorithm
uses fewer arithmetic operations than that of Fornberg by a factor of
$4/(5m+5)$ while being equally accurate. The algorithm that we derive computes
finite difference weights accurately even when $m$, the order of the
derivative, is as high as 16. In addition, the algorithm generalizes easily to
the efficient computation of spectral differentiation matrices.
  The order of accuracy of the finite difference formula for $f^{(m)}(0)$ with
grid points $hz_{k}$, $1\leq k\leq N$, is typically $\mathcal{O}(h^{N-m})$.
However, the most commonly used finite difference formulas have an order of
accuracy that is higher than the typical. For instance, the centered difference
approximation $(f(h)-2f(0)+f(-h))/h^{2}$ to $f"(0)$ has an order of accuracy
equal to 2 not 1. Even unsymmetric finite difference formulas can exhibit such
superconvergence or boosted order of accuracy, as shown by the explicit
algebraic condition that we derive. If the grid points are real, we prove a
basic result stating that the order of accuracy can never be boosted by more
than 1.


  We prove the nonlinear inviscid damping for a class of monotone shear flows
with non-constant background density for the two-dimensional ideal
inhomogeneous fluids in $\mathbb{T}\times [0,1]$ when the initial perturbation
is in Gevrey-$\frac{1}{s}$ ($\frac{1}{2}<s<1$) class with compact support.


  We characterize the quasiprojective groups that appear as fundamental groups
of compact $3$-manifolds (with or without boundary). We also characterize all
closed $3$-manifolds that admit good complexifications. These answer questions
of Friedl--Suciu, \cite{fs}, and Totaro \cite{tot}


  Lead and tin chalcogenides have been studied widely due to their promising
thermoelectric (TE) properties. Further enhancement in their TE efficiency has
been reported upon the reduction of the dimension, which is an important
feature in modern device fabrications. Using density functional theory combined
with the Semi-classical Boltzmann transport theory, we studied the structural,
electronic and TE properties of two-dimensional (2D) MX (M = Sn, Pb; X = S, Te)
monolayers. Spin-orbit coupling was found to have significant effects on their
electronic structure, particularly for the heavy compounds. Structural
optimization followed by phonon transport studies prevailed that the
rectangular ({\gamma}-) phase is energetically the most favorable for SnS and
SnTe monolayers, whereas the square structure is found the most stable for PbS
and PbTe monolayers. Our results are in good agreement with previous studies.
These 2D materials exhibit high Seebeck coefficients and power factors along
with low lattice thermal conductivities, which are essential features of good
TE materials. The maximum figure of merits (ZT) of 1.04, 1.46, 1.51 and 1.94
are predicted for n-type SnS, SnTe, PBS and p-type PbTe monolayers respectively
at 700 K, which are higher than their bulk ZT values. Hence, these monolayers
are promising candidates for TE applications.


  We discuss variants of Cold Dark Matter (CDM) dominated cosmological models
that give good agreement with a range of observations. We consider models with
hot dark matter, tilt, $\Omega < 1$, or a cosmological constant. We also
discuss the sensitivity of the results to other parameters, such as the Hubble
parameter and the baryon fraction. We obtain constraints by combining the COBE
data, cluster abundances, abundance of damped Lyman-$\alpha$ systems at
$z\sim3$, the small-angle Cosmic Microwave Background anisotropy, and the
small-scale non-linear power spectrum. We present non-linear power spectra from
a new suite of N-body simulations for the ``best-bet'' models from each
category.


  Non-commutative gauge theory with a non-constant non-commutativity parameter
can be formulated as a decoupling limit of open strings ending on D3-branes
wrapping a Melvin universe. We construct the action explicitly and discuss
various physical features of this theory. The decoupled field theory is not
supersymmetric. Nonetheless, the Coulomb branch appears to remain flat at least
in the large N and large 't Hooft coupling limit. We also find the analogue of
Prasad-Sommerfield monopoles whose size scales with the non-commutativity
parameter and is therefore position dependent.


  The systematic errors inherent in the QCD sum rule approach to meson
wavefunctions are examined in the context of QCD in 1+1 spacetime dimensions in
the large N limit where the theory is exactly solvable. It is shown that the
truncation of high momentum modes induced in a lattice discretization
automatically produces a Chernyak-Zhitnitsky \cite{CZ} type meson wavefunction.
Such a truncation alters the balance of leading and higher twist terms in
correlators. We find that the reliable extraction of (a few) higher moments is
possible provided a reasonably accurate uniform approximation to the Euclidean
correlator over a suitable $Q^2$ range is available, but that the extracted
values are particularly sensitive to the balance of lower and higher twist
contributions. Underestimates of lower twist contributions or overestimates of
the highest twist term may lead to too high values for the second and fourth
moments of the pion wavefunction, suggesting a doubly peaked structure of the
Chernyak-Zhitnitsky type.


  Suspense is a crucial ingredient of narrative fiction, engaging readers and
making stories compelling. While there is a vast theoretical literature on
suspense, it is computationally not well understood. We compare two ways for
modelling suspense: surprise, a backward-looking measure of how unexpected the
current state is given the story so far; and uncertainty reduction, a
forward-looking measure of how unexpected the continuation of the story is.
Both can be computed either directly over story representations or over their
probability distributions. We propose a hierarchical language model that
encodes stories and computes surprise and uncertainty reduction. Evaluating
against short stories annotated with human suspense judgements, we find that
uncertainty reduction over representations is the best predictor, resulting in
near-human accuracy. We also show that uncertainty reduction can be used to
predict suspenseful events in movie synopses.


  Being motivated by the recent prediction of high-$Q$ supercavity modes in
subwavelength dielectric resonators, we study the second-harmonic generation
from isolated subwavelength AlGaAs nanoantennas pumped by a structured light.
We reveal that nonlinear effects at the nanoscale can be enhanced dramatically
provided the resonator parameters are tuned to the regime of the bound state in
the continuum. We predict a record-high conversion efficiency for nanoscale
resonators that exceeds by two orders of magnitude the conversion efficiency
observed at the conditions of magnetic dipole Mie resonance, thus opening the
way for highly-efficient nonlinear metadevices.


  In the pharmaceutical industry, the use of artificial intelligence (AI) has
seen consistent growth over the past decade. This rise is attributed to major
advancements in statistical machine learning methodologies, computational
capabilities and the increased availability of large datasets. AI techniques
are applied throughout different stages of drug development, ranging from drug
discovery to post-marketing benefit-risk assessment. Kolluri et al. provided a
review of several case studies that span these stages, featuring key
applications such as protein structure prediction, success probability
estimation, subgroup identification, and AI-assisted clinical trial monitoring.
From a regulatory standpoint, there was a notable uptick in submissions
incorporating AI components in 2021. The most prevalent therapeutic areas
leveraging AI were oncology (27%), psychiatry (15%), gastroenterology (12%),
and neurology (11%). The paradigm of personalized or precision medicine has
gained significant traction in recent research, partly due to advancements in
AI techniques \cite{hamburg2010path}. This shift has had a transformative
impact on the pharmaceutical industry. Departing from the traditional
"one-size-fits-all" model, personalized medicine incorporates various
individual factors, such as environmental conditions, lifestyle choices, and
health histories, to formulate customized treatment plans. By utilizing
sophisticated machine learning algorithms, clinicians and researchers are
better equipped to make informed decisions in areas such as disease prevention,
diagnosis, and treatment selection, thereby optimizing health outcomes for each
individual.


  Social networks (SNs) are increasingly important sources of news for many
people. The online connections made by users allows information to spread more
easily than traditional news media (e.g., newspaper, television). However, they
also make the spread of fake news easier than in traditional media, especially
through the users' social network connections. In this paper, we focus on
investigating if the SNs' users connection structure can aid fake news
detection on Twitter. In particular, we propose to embed users based on their
follower or friendship networks on the Twitter platform, so as to identify the
groups that users form. Indeed, by applying unsupervised graph embedding
methods on the graphs from the Twitter users' social network connections, we
observe that users engaged with fake news are more tightly clustered together
than users only engaged in factual news. Thus, we hypothesise that the embedded
user's network can help detect fake news effectively. Through extensive
experiments using a publicly available Twitter dataset, our results show that
applying graph embedding methods on SNs, using the user connections as network
information, can indeed classify fake news more effectively than most
language-based approaches. Specifically, we observe a significant improvement
over using only the textual information (i.e., TF.IDF or a BERT language
model), as well as over models that deploy both advanced textual features
(i.e., stance detection) and complex network features (e.g., users network,
publishers cross citations). We conclude that the Twitter users' friendship and
followers network information can significantly outperform language-based
approaches, as well as the existing state-of-the-art fake news detection models
that use a more sophisticated network structure, in classifying fake news on
Twitter.


  We extend an earlier proposal for a gauge invariant description of off-shell
open strings (at tree level), using loop variables, to off-shell closed strings
(at tree level). The basic idea is to describe the closed string amplitudes as
a product of two open string amplitudes (using the technique of kawai, Lewellen
and Tye). The loop variable techniques that were used earlier for open strings
can be applied here {\it mutatis mutandis}. It is a proposal for a theory whose
on-shell amplitudes coincide with those of the closed bosonic string in 26
dimensions. It is also gauge invariant off-shell. As was the case with the open
string, the interacting closed string looks like a free closed string thickened
to a band.


  We show spherical completeness of the ring of Colombeau generalized real (or
complex) numbers endowed with the sharp norm. As an application, we establish a
Hahn Banach extension theorem for ultra pseudo normed modules (over the ring of
generalized numbers) of generalized functions in the sense of Colombeau.


  We study the influence of network topology and connectivity on the
synchronization properties of chaotic logistic maps, interacting with random
delay times. Four different types of topologies are investigated: two regular
(a ring-type and a ring-type with a central node) and two random (free-scale
Barabasi-Albert and small-world Newman-Watts). The influence of the network
connectivity is studied by varying the average number of links per node, while
keeping constant the total input that each map receives from its neighbors. For
weak coupling the array does not synchronize regardless the topology or
connectivity of the network; however, for certain connectivity values there is
enhanced coherence. For strong coupling the array synchronizes in the
homogeneous steady-state, where the chaotic dynamics of the individual maps is
suppressed. For both, weak and strong coupling, the array propensity for
synchronization is largely independent of the network topology and depends
mainly on the average number of links per node.


  Mid-study design modifications are becoming increasingly accepted in
confirmatory clinical trials, so long as appropriate methods are applied such
that error rates are controlled. It is therefore unfortunate that the important
case of time-to-event endpoints is not easily handled by the standard theory.
We analyze current methods that allow design modifications to be based on the
full interim data, i.e., not only the observed event times but also secondary
endpoint and safety data from patients who are yet to have an event. We show
that the final test statistic may ignore a substantial subset of the observed
event times. Since it is the data corresponding to the earliest recruited
patients that is ignored, this neglect becomes egregious when there is specific
interest in learning about long-term survival. An alternative test
incorporating all event times is proposed, where a conservative assumption is
made in order to guarantee type I error control. We examine the properties of
our proposed approach using the example of a clinical trial comparing two
cancer therapies.


  New invariants for 2-dimensional cell complexes are defined, which can be
interpreted as curvature bounds. These invariants are proved to be rational and
computable in a companion article. This document is a survey that collects
theorems about these invariants, computes examples, and lays out a programme of
conjectures.


  Excitons -- quasiparticles formed by the binding of an electron and a hole
through electrostatic attraction -- hold promise in the fields of quantum light
confinement and optoelectronic sensing. Atomically thin transition metal
dichalcogenides (TMDs) provide a versatile platform for hosting and
manipulating excitons, given their robust Coulomb interactions and exceptional
sensitivity to dielectric environments. In this study, we introduce a cryogenic
scanning probe photoelectrical sensing platform, termed exciton-resonant
microwave impedance microscopy (ER-MIM). ER-MIM enables ultra-sensitive probing
of exciton polarons and their Rydberg states at the nanoscale. Utilizing this
technique, we explore the interplay between excitons and material properties,
including carrier density, in-plane electric field, and dielectric screening.
Furthermore, we employ deep learning for automated data analysis and
quantitative extraction of electrical information, unveiling the potential of
exciton-assisted nano-electrometry. Our findings establish an invaluable
sensing platform and readout mechanism, advancing our understanding of exciton
excitations and their applications in the quantum realm.


  The Quantum Fisher information (QFI) quantifies the ultimate precision of
estimating a parameter from a quantum state, and can be regarded as a
reliability measure of a quantum system as a quantum sensor. However,
estimation of the QFI for a mixed state is in general a computationally
demanding task. In this work we present a variational quantum algorithm called
Variational Quantum Fisher Information Estimation (VQFIE) to address this task.
By estimating lower and upper bounds on the QFI, based on bounding the
fidelity, VQFIE outputs a range in which the actual QFI lies. This result can
then be used to variationally prepare the state that maximizes the QFI, for the
application of quantum sensing. In contrast to previous approaches, VQFIE does
not require knowledge of the explicit form of the sensor dynamics. We simulate
the algorithm for a magnetometry setup and demonstrate the tightening of our
bounds as the state purity increases. For this example, we compare our bounds
to literature bounds and show that our bounds are tighter.


  It is elementary and well-known that if an element x of a bounded modular
lattice L has a complement in L then x has a relative complement in every
interval [a,b] containing x. We show that the relatively strong assumption of
modularity of L can be replaced by a weaker one formulated in the language of
so-called modular triples. We further show that, in general, we need not
suppose that x has a complement in L. By introducing the concept of modular
triples in posets, we extend our results obtained for lattices to posets. It
should be remarked that the notion of a complement can be introduced also in
posets that are not bounded.


  We show the existence of Gepner type Bridgeland stability conditions on the
triangulated categories of graded matrix factorizations associated with
homogeneous polynomials which define general cubic fourfolds containing a
plane. The key ingredient is to describe the grade shift functor of matrix
factorizations in terms of sheaves of Clifford algebras on the projective plane
under Orlov/Kuznetsov equivalence.


  In our previous work, based on the $SU(6)$ spin-flavor wave function, we
regard $\Lambda$ and $p$ as composed of different quark-diquark configurations
and established the Bethe-Salpeter (BS) equations of configurations for quark
and scalar diquark. In our present work, we apply this model to calculate the
form factors of the semileptonic transitions $\Lambda_b\rightarrow\Lambda
l^+l^-$ $(l=\mu,e,\tau)$ and $\Lambda_b\rightarrow p l\bar{\nu}$ within the
Standard Model (SM). The decay $\Lambda_b\rightarrow\Lambda \mu^+\mu^-$ is
especially interesting since it has been measured in CDF and LHCb
Collaborations and this rare decay is very sensitive to new physics effects.
The decay $\Lambda_b\rightarrow p l\bar{\nu}$ is a promising mode for the
measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ at the
Large Hadron Collider. In our calculations, depending on the ranges of the
parameters in the model including the diquark mass and the interaction strength
between the quark and the diquark in the kernel of the BS equation, we find
that the branching ratio of $\Lambda_b\rightarrow\Lambda\mu^+\mu^-$ in our
model is consistent with the experimental data and the current experimental
results from LHCb agree with the differential branching ratio of
$\Lambda_b\rightarrow\Lambda\mu^+\mu^-$ from our calculation except at the
lager momentum transfer region. This indicates that there is still room for
possible new physics effects. We also give comparisions of the total branching
ratios of $\Lambda_b\rightarrow\Lambda l^+l^-$ and $\Lambda_b\rightarrow p
l\bar{\nu}$ with those given by other phenomenological methods.


  This is a Reply to a Comment by Tanaka and Machida. We provide some details
of the derivation of the effective field theory for integer quantum Hall
transitions using the non-Abelian chiral anomaly.


  Autologous chemotaxis, in which cells secrete and detect molecules to
determine the direction of fluid flow, is thwarted at high cell density because
molecules from other cells interfere with a given cell's signal. Using a
minimal model of autologous chemotaxis, we determine the cell density at which
sensing fails and find that it agrees with experimental observations of
metastatic cancer cells. To understand this agreement, we derive a physical
limit to autologous chemotaxis in terms of the cell density, the P\'eclet
number, and the length scales of the cell and its environment. Surprisingly, in
an environment that is uniformly oversaturated in the signaling molecule, we
find that sensing not only can fail, but can be reversed, causing backwards
cell motion. Our results get to the heart of the competition between chemical
and mechanical cellular sensing and shed light on a sensory strategy employed
by cancer cells in dense tumor environments.


  We study the evidence for and possible origins of parity doubling among the
baryons. First we explore the experimental evidence, finding a significant
signal for parity doubling in the non-strange baryons, but little evidence
among strange baryons. Next we discuss potential explanations for this
phenomenon. Possibilities include suppression of the violation of the flavor
singlet axial symmetry ($U(1)_{A}$) of QCD, which is broken by the triangle
anomaly and by quark masses. A conventional Wigner-Weyl realization of the
$SU(2)_{L}\times SU(2)_{R}$ chiral symmetry would also result in parity
doubling. However this requires the suppression of families of \emph{chirally
invariant} operators by some other dynamical mechanism. In this scenario the
parity doubled states should decouple from pions. We discuss other explanations
including connections to chiral invariant short distance physics motivated by
large $N_{c}$ arguments as suggested by Shifman and others, and intrinsic
deformation of relatively rigid highly excited hadrons, leading to parity
doubling on the leading Regge trajectory. Finally we review the spectroscopic
consequences of chiral symmetry using a formalism introduced by Weinberg, and
use it to describe two baryons of opposite parity.


  PandaX-4T is a dark matter direct detection experiment located in China
jinping underground laboratory. The central apparatus is a dual-phase xenon
detector containing 4 ton liquid xenon in the sensitive volume, with about 500
photomultipliers instrumented in the top and the bottom of the detector. In
this paper we present a completely new system of readout electronics and data
acquisition in the PandaX-4T experiment. Compared to the one used in the
previous PandaX dark matter experiments, the new system features triggerless
readout and higher bandwidth. With triggerless readout, dark matter searches
are not affected by the efficiency loss of external triggers. The system
records single photelectron signals of the dominant PMTs with an average
efficiency of 96\%, and achieves the bandwidth of more than 450 MB/s. The
system has been used to successfully acquire data during the commissioning runs
of PandaX-4T.


  An in-flight beam of $^{16}$N was produced via the single-neutron adding
($d$,$p$) reaction in inverse kinematics at the recently upgraded Argonne
Tandem Linear Accelerator System (ATLAS) in-flight system. The amount of the
$^{16}$N beam which resided in its excited 0.120-MeV $J^{\pi}=0^-$ isomeric
state (T$_{1/2}\approx5$ $\mu$s) was determined to be 40(5)% at a reaction
energy of 7.9(3) MeV/$u$, and 24(2)% at a reaction energy of 13.2(2) MeV/$u$.
The isomer measurements took place at an experimental station $\approx30$ m
downstream of the production target and utilized an Al beam-stopping foil and a
HPGe Clover detector. Composite $^{16}$N beam rate determinations were made at
the experimental station and the focal plane of the Argonne in-flight
radioactive ion-beam separator (RAISOR) with Si $\Delta$E-E telescopes. A
Distorted Wave Born Approximation (DWBA) approach was coupled with the known
spectroscopic information on $^{16}$N in order to estimate the relative
$^{16}$N isomer yields and composite $^{16}$N beam rates. In addition to the
observed reaction-energy dependence of the isomer fraction, a large sensitivity
to angular acceptance of the recoils was also observed.


  We systematically investigate the mass spectra of
$\{Q\bar{s}\}\{\bar{Q}^{(')}s\}$ molecular states in the framework of QCD sum
rules. The interpolating currents representing the molecular states are
proposed. Technically, contributions of the operators up to dimension six are
included in operator product expansion (OPE). The masses for molecular states
with various $\{Q\bar{s}\}\{\bar{Q}^{(')}s\}$ configurations are presented. The
result $4.36\pm0.08 GeV$ for the $D_{s}^{*}\bar{D}_{s0}^{*}$ molecular state is
consistent with the mass $4350^{+4.6}_{-5.1}\pm0.7 MeV$ of the newly observed
$X(4350)$, which could support $X(4350)$ interpreted as a
$D_{s}^{*}\bar{D}_{s0}^{*}$ molecular state.


  Recently the Polish-American collaboration OGLE has reported the observation
of four possible microlensing events by monitoring, over several months, the
brightness of millions of stars in the region of the galactic bulge. If these
events are due to microlensing, the most accurate way to get information on the
mass of the dark compact objects, that acted as gravitational lenses, is to use
the method of the mass moments. Here I apply this method to the analysis of the
events detected by OGLE. The average mass turns out to be 0.28$M_{\odot}$,
suggesting that the lens objects are faint disk stars. The same method applied
to the five microlensing events detected so far by the EROS and MACHO
collaborations, which monitor stars in the Large Magellanic Cloud, leads to an
average value of 0.08$M_{\odot}$ for the dark compact halo objects.


  The formation and evolution of protoplanetary discs remains a challenge from
both a theoretical and numerical standpoint. In this work we first perform a
series of tests of our new hybrid algorithm presented in Glaschke, Amaro-Seoane
and Spurzem 2011 (henceforth Paper I) that combines the advantages of high
accuracy of direct-summation N-body methods with a statistical description for
the planetesimal disc based on Fokker-Planck techniques. We then address the
formation of planets, with a focus on the formation of protoplanets out of
planetesimals. We find that the evolution of the system is driven by encounters
as well as direct collisions and requires a careful modelling of the evolution
of the velocity dispersion and the size distribution over a large range of
sizes. The simulations show no termination of the protoplanetary accretion due
to gap formation, since the distribution of the planetesimals is only subjected
to small fluctuations. We also show that these features are weakly correlated
with the positions of the protoplanets. The exploration of different impact
strengths indicates that fragmentation mainly controls the overall mass loss,
which is less pronounced during the early runaway growth. We prove that the
fragmentation in combination with the effective removal of collisional
fragments by gas drag sets an universal upper limit of the protoplanetary mass
as a function of the distance to the host star, which we refer to as the mill
condition.


  Spoofing countermeasure (CM) systems are critical in speaker verification;
they aim to discern spoofing attacks from bona fide speech trials. In practice,
however, acoustic condition variability in speech utterances may significantly
degrade the performance of CM systems. In this paper, we conduct a
cross-dataset study on several state-of-the-art CM systems and observe
significant performance degradation compared with their single-dataset
performance. Observing differences of average magnitude spectra of bona fide
utterances across the datasets, we hypothesize that channel mismatch among
these datasets is one important reason. We then verify it by demonstrating a
similar degradation of CM systems trained on original but evaluated on
channel-shifted data. Finally, we propose several channel robust strategies
(data augmentation, multi-task learning, adversarial learning) for CM systems,
and observe a significant performance improvement on cross-dataset experiments.


  We investigate the classical communication over quantum channels when
assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT)
codes, for which both the optimal success probability of a given transmission
rate and the one-shot $\epsilon$-error capacity are formalized as semidefinite
programs (SDPs). Based on this, we obtain improved SDP finite blocklength
converse bounds of general quantum channels for entanglement-assisted codes and
unassisted codes. Furthermore, we derive two SDP strong converse bounds for the
classical capacity of general quantum channels: for any code with a rate
exceeding either of the two bounds of the channel, the success probability
vanishes exponentially fast as the number of channel uses increases. In
particular, applying our efficiently computable bounds, we derive an improved
upper bound on the classical capacity of the amplitude damping channel. We also
establish the strong converse property for the classical and private capacities
of a new class of quantum channels. We finally study the zero-error setting and
provide efficiently computable upper bounds on the one-shot zero-error capacity
of a general quantum channel.


  We study kinematic effects due to the approximation of on-shell, collinear
partons in shower Monte Carlo event generators. We observe that the
collinearity approximation, combined with the requirements of energy-momentum
conservation, gives rise to a kinematic shift, event by event, in longitudinal
momentum distributions. We present numerical results in the case of jet and
heavy flavor production processes measured at the LHC.


  We introduce two numerical conjugacy invariants for dynamical systems -- the
complexity and weak complexity indices -- which are well-suited for the study
of "completely integrable" Hamiltonian systems. These invariants can be seen as
"slow entropies", they describe the polynomial growth rate of the number of
balls (for the usual "dynamical" distances) of coverings of the ambient space.
We then define a new class of integrable systems, which we call decomposable
systems, for which one can prove that the weak complexity index is smaller than
the number of degrees of freedom. Hamiltonian systems integrable by means of
non-degenerate integrals (in Eliasson-Williamson sense), subjected to natural
additional assumptions, are the main examples of decomposable systems. We
finally give explicit examples of computation of the complexity index, for
Morse Hamiltonian systems on surfaces and for two-dimensional gradient systems.


  We adopt the Reall-Santos method to obtain the quadratic curvature
corrections to the thermodynamics of Myers-Perry rotating black holes in
diverse dimensions. We consider the corrections in canonical and grand
canonical ensembles, and also for fixed mass and angular momenta. We find that
there exist inevitable divergences for generic rotation parameters so that the
perturbative approach breaks down. We present a simple and universal formula to
determine where these divergences could arise, and argue, using an explicit
example, that these divergences are artefact of perturbation and may not exist
in the full nonlinear theory.


  Our main result is a new upper bound for the size of k-uniform,
L-intersecting families of sets, where L contains only positive integers. We
characterize extremal families in this setting. Our proof is based on the
Ray-Chaudhuri--Wilson Theorem. As an application, we give a new proof for the
Erd\H{o}s-Ko-Rado Theorem, improve Fisher's inequality in the uniform case and
give an uniform version of the Frankl-F\"uredi conjecture .


  The present paper introduces ad hoc communication networks as examples of
large scale real networks that can be prospected by statistical means. A
description of giant cluster formation based on the single parameter of node
neighbor numbers is given along with the discussion of some asymptotic aspects
of the giant cluster sizes.


  Irrespective of the specific definition of fairness in a machine learning
application, pruning the underlying model affects it. We investigate and
document the emergence and exacerbation of undesirable per-class performance
imbalances, across tasks and architectures, for almost one million categories
considered across over 100K image classification models that undergo a pruning
process.We demonstrate the need for transparent reporting, inclusive of bias,
fairness, and inclusion metrics, in real-life engineering decision-making
around neural network pruning. In response to the calls for quantitative
evaluation of AI models to be population-aware, we present neural network
pruning as a tangible application domain where the ways in which
accuracy-efficiency trade-offs disproportionately affect underrepresented or
outlier groups have historically been overlooked. We provide a simple,
Pareto-based framework to insert fairness considerations into value-based
operating point selection processes, and to re-evaluate pruning technique
choices.


  We argue that no notion of flavour is necessary when performing amplitude
calculations in perturbative QCD with massless quarks. We show this explicitly
at tree-level, using a flavour recursion relation to obtain multi-flavoured QCD
from one-flavour QCD. The method relies on performing a colour decomposition,
under which the one-flavour primitive amplitudes have a structure which is
restricted by planarity and cyclic ordering. An understanding of SU(3)_c group
theory relations between QCD primitive amplitudes and their organisation around
the concept of a Dyck tree is also necessary. The one-flavour primitive
amplitudes are effectively N=1 supersymmetric, and a simple consequence is that
all of tree-level massless QCD can be obtained from Drummond and Henn's closed
form solution to tree-level N=4 super Yang-Mills theory.


  Providing real time information about the arrival time of the transit buses
has become inevitable in urban areas to make the system more user-friendly and
advantageous over various other transportation modes. However, accurate
prediction of arrival time of buses is still a challenging problem in
dynamically varying traffic conditions especially under heterogeneous traffic
condition without lane discipline. One broad approach researchers have adopted
over the years is to segment the entire bus route into segments and work with
these segment travel times as the data input (from GPS traces) for prediction.
This paper adopts this approach and proposes predictive modelling approaches
which fully exploit the temporal correlations in the bus GPS data.
Specifically, we propose two approaches: (a) classical time-series approach
employing a seasonal AR model (b)unconventional linear, non-stationary AR
approach. The second approach is a novel technique and exploits the notion of
partial correlation for learning from data. A detailed analysis of the marginal
distributions of the data from Indian conditions (used here), revealed a
predominantly log-normal behavior. This aspect was incorporated into the above
proposed predictive models and statistically optimal prediction schemes in the
lognormal sense are utilized for all predictions. Both the above temporal
predictive modeling approaches predict ahead in time at each segment
independently. For real-time bus travel time prediction, one however needs to
predict across multiple segments ahead in space. Towards a complete solution,
the study also proposes an intelligent procedure to perform (real-time)
multi-section ahead travel-time predictions based on either of the above
proposed temporal models. Results showed a clear improvement in prediction
accuracy using the proposed methods,


  We have considered some results concerning gas and stars kinematics of nearby
galaxies recently obtained on the SAO RAS 6m telescope using the panoramic
spectroscopy methods. The circumnuclear regions of the galaxies were observed
with integral-field spectrograph MPFS. The large-scale ionized gas kinematics
was studied with the scanning Fabry-Perot interferometer (FPI) in the
multi-mode focal reducer SCORPIO. The main attention is given for kinematically
decoupled regions in the galaxies: bars, spirals, polar disks and rings.


  We present intermediate resolution spectroscopy and near infrared photometry
of NOVA Sco 2001 (V1178 Sco), which was first detected May 13th 2001 and
reported June 21th 2001, and obtained by us the same day. We also retrieved
very accurate astrometry of the target in this very crowded field. This is
needed to be able to do follow up observations of the postnova during the next
years. The spectrum shows an overall expansion of 2100 km/s and has clearly
complex, and most likely nonsymmetric, outflow substructures. We clearly
identify this object as classical nova, "Fe II" subclass.


  The century-long photometric record of the DASCH project provides a unique
window into the variability of stars normally considered to be photometrically
inactive. In this paper, we look for long-term trends in the brightness of F
stars, with particular attention to KIC 8462852,an F3 main sequence star that
has been identified as significant short-term variability according to Kepler
observations. Although a simple search for variability suggests long-term
dimming of a number of F stars, we find that such trends are artifacts of the
'Menzel Gap' in the DASCH data. That includes the behavior of KIC 8462852,
which we believe is consistent with constant flux over the full duration of
observations. We do, however, present a selection of F stars that do have
significant photometric trends, even after systematics are taken into account.


  The functional method, introduced to deal with systems endowed with a
continuous spectrum, is used to study the problem of decoherence and
correlations in a simple cosmological model.


  Most sales applications are characterized by competition and limited demand
information. For successful pricing strategies, frequent price adjustments as
well as anticipation of market dynamics are crucial. Both effects are
challenging as competitive markets are complex and computations of optimized
pricing adjustments can be time-consuming. We analyze stochastic dynamic
pricing models under oligopoly competition for the sale of perishable goods. To
circumvent the curse of dimensionality, we propose a heuristic approach to
efficiently compute price adjustments. To demonstrate our strategy's
applicability even if the number of competitors is large and their strategies
are unknown, we consider different competitive settings in which competitors
frequently and strategically adjust their prices. For all settings, we verify
that our heuristic strategy yields promising results. We compare the
performance of our heuristic against upper bounds, which are obtained by
optimal strategies that take advantage of perfect price anticipations. We find
that price adjustment frequencies can have a larger impact on expected profits
than price anticipations. Finally, our approach has been applied on Amazon for
the sale of used books. We have used a seller's historical market data to
calibrate our model. Sales results show that our data-driven strategy
outperforms the rule-based strategy of an experienced seller by a profit
increase of more than 20%.


  The space telescope MOST is now providing us with extremely accurate low
frequency p-mode oscillation data for the star Eta Boo. We demonstrate in this
paper that these data, when combined with ground based measurements of the high
frequency p-mode spectrum, can be reproduced with stellar models that include
the effects of turbulence in their outer layers. Without turbulence, the l=0
modes of our models deviate from either the ground based or the space data by
about 1.5-4.0 micro Hz. This discrepancy can be completely removed by including
turbulence in the models and we can exactly match 12 out of 13 MOST frequencies
that we identified as l=0 modes in addition to 13 out of 21 ground based
frequencies within their observational 2 sigma tolerances. The better agreement
between model frequencies and observed ones depends for the most part on the
turbulent kinetic energy which was taken from a 3D convection simulation for
the Sun.


  We have carried out an in-depth study of low-mass X-ray binaries (LMXBs)
detected in the nearby lenticular galaxy NGC 3115, using the Megasecond Chandra
X-Ray Visionary Project observation (total exposure time 1.1 Ms). In total we
found 136 candidate LMXBs in the field and 49 in globular clusters (GCs) above
2\sigma\ detection, with 0.3--8 keV luminosity L_X ~10^36-10^39 erg/s. Other
than 13 transient candidates, the sources overall have less long-term
variability at higher luminosity, at least at L_X > 2x10^37 erg/s. In order to
identify the nature and spectral state of our sources, we compared their
collective spectral properties based on single-component models (a simple power
law or a multicolor disk) with the spectral evolution seen in representative
Galactic LMXBs. We found that in the L_X versus photon index \Gamma_PL and L_X
versus disk temperature kT_MCD plots, most of our sources fall on a narrow
track in which the spectral shape hardens with increasing luminosity below
L_X~7x10^37 erg/s but is relatively constant (\Gamma_PL~1.5 or kT_MCD~1.5 keV)
above this luminosity, similar to the spectral evolution of Galactic neutron
star (NS) LMXBs in the soft state in the Chandra bandpass. Therefore we
identified the track as the NS LMXB soft-state track and suggested sources with
L_X<7x10^37 erg/s as atolls in the soft state and those with L_X>7x10^37 erg/s
as Z sources. Ten other sources (five are transients) displayed significantly
softer spectra and are probably black hole X-ray binaries in the thermal state.
One of them (persistent) is in a metal-poor GC.


  I discuss two related nonlinear mechanisms of tidal dissipation that require
finite tidal deformations for their operation: the elliptical instability and
the precessional instability. Both are likely to be important for the tidal
evolution of short-period extrasolar planets. The elliptical instability is a
fluid instability of elliptical streamlines, such as in tidally deformed
non-synchronously rotating or non-circularly orbiting planets. I summarise the
results of local and global simulations that indicate this mechanism to be
important for tidal spin synchronisation, planetary spin-orbit alignment and
orbital circularisation for the shortest period hot Jupiters. The precessional
instability is a fluid instability that occurs in planets undergoing axial
precession, such as those with spin-orbit misalignments (non-zero obliquities).
I summarise the outcome of local MHD simulations designed to study the
turbulent damping of axial precession, which suggest this mechanism to be
important in driving tidal evolution of the spin-orbit angle for hot Jupiters.
Avenues for future work are also discussed.


  We explore the possibility that a single relativistic shock, where the gas
dynamics is coupled with radiation, can fit the light curves of long GRBs. For
this we numerically solve the one dimensional relativistic radiation
hydrodynamics equations with a single initial shock. We calculate light curves
due to the evolution of this shock in terms of the velocity of the shock, the
opacity of the gas, mass density and density of radiated energy. We explore how
the variation of each of these parameters provides different features in the
light curves. As examples we include the fitting of two long GRBs.


  We study the quantum mechanical evolution of the tensor perturbations during
inflation with non-linear tensor interactions. We first obtain the Lindblad
terms generated by non-linear interactions by tracing out unobservable
sub-horizon modes. Then we calculate explicitly the reduced density matrix for
the super-horizon modes, and show that the probability of maintaining the
unitarity of the squeezed state decreases in time. The decreased probability is
transferred to other elements of the reduced density matrix including
off-diagonal ones, so the evolution of the reduced density matrix describes the
quantum-to-classical transition of the tensor perturbations. This is different
from the classicality accomplished by the squeezed state, the suppression of
the non-commutative effect, which is originated from the quadratic, linear
interaction, and also maintains the unitarity. The quantum-to-classical
transition occurs within 5 - 10 e-folds, faster than the curvature
perturbation.


  In this paper, the ergodic sum-rate of a fading cognitive multiple access
channel (C-MAC) is studied, where a secondary network (SN) with multiple
secondary users (SUs) transmitting to a secondary base station (SBS) shares the
spectrum band with a primary user (PU). An interference power constraint (IPC)
is imposed on the SN to protect the PU. Under such a constraint and the
individual transmit power constraint (TPC) imposed on each SU, we investigate
the power allocation strategies to maximize the ergodic sum-rate of a fading
C-MAC without successive interference cancellation (SIC). In particular, this
paper considers two types of constraints: (1) average TPC and average IPC, (2)
peak TPC and peak IPC. For the first case, it is proved that the optimal power
allocation is dynamic time-division multiple-access (D-TDMA), which is exactly
the same as the optimal power allocation to maximize the ergodic sum-rate of
the fading C-MAC with SIC under the same constraints. For the second case, it
is proved that the optimal solution must be at the extreme points of the
feasible region. It is shown that D-TDMA is optimal with high probability when
the number of SUs is large. Besides, we show that, when the SUs can be sorted
in a certain order, an algorithm with linear complexity can be used to find the
optimal power allocation.


  This work proposes provably-correct self-organizing strategies for platoons
of heterogeneous vehicles. We refer to self-organization as the capability of a
platoon to autonomously homogenize to a common group behavior. We show that
self-organization promotes resilience to acceleration limits and communication
failures, i.e., homogenizing to a common group behavior makes the platoon
recover from these causes of impairments. In the presence of acceleration
limits, resilience is achieved by self-organizing to a common constrained group
behavior that prevents the vehicles from hitting their acceleration limits. In
the presence of communication failures, resilience is achieved by
self-organizing to a common group observer to estimate the missing information.
Stability of the self-organization mechanism is studied analytically, and
correctness with respect to traffic actions (e.g. emergency braking, cut-in,
merging) is realized through a provably-correct safety layer. Numerical
validations via the platooning toolbox OpenCDA in CARLA and via the CommonRoad
platform confirm improved performance through self-organization and the
provably-correct safety layer.


  Utilization of event-based cameras is expected to improve the visual quality
of video frame interpolation solutions. We introduce a learning-based method to
exploit moving region boundaries in a video sequence to increase the overall
interpolation quality.Event cameras allow us to determine moving areas
precisely; and hence, better video frame interpolation quality can be achieved
by emphasizing these regions using an appropriate loss function. The results
show a notable average \textit{PSNR} improvement of $1.3$ dB for the tested
data sets, as well as subjectively more pleasing visual results with less
ghosting and blurry artifacts.


  It is found on the basis of the lowest Landau level approach for the
Ginzburg-Landau model that, in bulk type II superconductors with strong line
disorder directed {\it perpendicularly} to an applied field, the continuous
vortex-glass transition is depressed to the low $T$ limit in the limit of weak
{\it point} disorder. An anomalous resistive broadening in twin-free YBCO with
columnar defects in a field parallel to the layers is discussed based on this
theoretical finding. Other phenomena which, we argue, arise indirectly from
this mechanism in type II superconductors including correlated defects are also
discussed.


  In this paper, the Eddington-Finkelstein transformation is used as an
illustration of how the problem of singularities or infinities can be removed
by application of nonstandard analysis to the Schwarzschild line element
(metric). The evolution of a gravitationally collapsing spherical body with
radius greater than but near to the Schwarzschild radius is also investigated.


  We present a set of localized states for an even number of Dirac fermions
under Einsteinian gravity that have an infinite central redshift. Near the
center of the localized state the components of the Dirac spinor and the
spacetime metric all show simple power-law dependences on the radial distance;
further out the fermionic wave function decays to zero and the spacetime
becomes asymptotically flat. We show that this `central' solution of the
equations of motion can be used to understand much of the structure observed by
Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)] in their numerical
solutions of the same problem at finite central redshift.


  Exciton effects on conjugated polymers and the resulting optical
nonlinearities are investigated in soliton lattice states. We use the
Su-Schrieffer-Heeger model with long-range Coulomb interactions for electrons.
The third-harmonic generation (THG) at off-resonant frequencies is calculated
as functions of the soliton concentration and the chain length of the polymer.
The magnitude of the THG with 10 percent doping increases by the factor of
about 10^2 from that of the neutral system. The large increase of the order two
is common for several Coulomb interaction strengths, and is seen in open
systems as well as in periodic systems.


  The statistical distributions of active galactic nuclei (AGN), i.e. accreting
supermassive black holes (BHs), in mass, space and time, are controlled by a
series of key properties, namely the BH-galaxy scaling relations, Eddington
ratio distributions and fraction of active BHs (duty cycle). Shedding light on
these properties yields strong constraints on the AGN triggering mechanisms
whilst providing a clear baseline to create useful mock catalogues for the
planning of large galaxy surveys. We here delineate a robust methodology to
create mock AGN catalogs built on top of large N-body dark matter simulations
via state-of-the-art semi-empirical models. We show that by using as
independent tests the AGN clustering at fixed X-ray luminosity, galaxy stellar
mass and BH mass, along with the fraction of AGN in groups and clusters, it is
possible to significantly narrow down the choice in the relation between black
hole mass and host galaxy stellar mass, the duty cycle, and the average
Eddington ratio distribution, delivering well-suited constraints to guide
cosmological models for the co-evolution of BHs and galaxies. Avoiding such a
step-by-step methodology inevitably leads to strong degeneracies in the final
mock catalogs, severely limiting their usefulness in understanding AGN
evolution and in survey planning and testing.


  Given a valuation $v$ with quotient field $K$ and a sequence $\mathcal{K}
:K_0\subseteq K_1\subseteq\cdots$ of finite extensions of $K$, we construct a
weighted tree $\mathcal{T}(v,\mathcal{K})$ encoding information about the
ramification of $v$ in the extensions $K_i$; conversely, we show that a
weighted tree $\mathcal{T}$ can be expressed as $\mathcal{T}(v,\mathcal{K})$
under some mild hypothesis on $v$ or on $\mathcal{T}$. We use this construction
to construct, for every countable successor ordinal number $\alpha$, an almost
Dedekind domain $D$, integral over $V$ (the valuation domain of $v$) whose
SP-rank is $\alpha$. Subsequently, we extend this result to countable limit
ordinal numbers by considering integral extensions of Dedekind domains with
countably many maximal ideals.


  A study on cosmogenic activation in germanium was carried out to evaluate the
cosmogenic background level of natural and $^{70}$Ge depleted germanium
detectors. The production rates of long-lived radionuclides were calculated
with Geant4 and CRY. Results were validated by comparing the simulated and
experimental spectra of CDEX-1B detector. Based on the validated codes, the
cosmogenic background level was predicted for further tonne-scale CDEX
experiment. The suppression of cosmogenic background level could be achieved by
underground germanium crystal growth and high-purity germanium detector
fabrication to reach the sensitivity requirement for direct detection of dark
matter. With the low cosmogenic background, new physics channels, such as solar
neutrino research and neutrinoless double-beta decay experiments, were opened
and the corresponding simulations and evaluations were carried out.


  We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm
(RAGD), and show that for geodesically smooth and strongly convex problems,
within a neighborhood of the minimizer whose radius depends on the condition
number as well as the sectional curvature of the manifold, RAGD converges to
the minimizer with acceleration. Unlike the algorithm in (Liu et al., 2017)
that requires the exact solution to a nonlinear equation which in turn may be
intractable, our algorithm is constructive and computationally tractable. Our
proof exploits a new estimate sequence and a novel bound on the nonlinear
metric distortion, both ideas may be of independent interest.


  In this paper, we introduce a concept of weakly principally quasi-Baer
*-rings in terms of central cover. We prove that a *-rings is a principally
quasi-Baer *-rings if and only if it is weakly principally quasi-Baer *-rings
with unity. A partial solution to the problem similar to unitification problem
raised by S. K. Berberian is obtained.


  We study the relationship between the sigma-ideal generated by closed measure
zero sets and the ideals of null and meager sets. We show that the additivity
of the ideal of closed measure zero sets is not bigger than covering for
category. As a consequence we get that the additivity of the ideal of closed
measure zero sets is equal to the additivity of the ideal of meager sets.


  We report the discovery of one or more planet-mass companions to the K0-giant
HD 102272 with the Hobby-Eberly Telescope. In the absence of any correlation of
the observed periodicities with the standard indicators of stellar activity,
the observed radial velocity variations are most plausibly explained in terms
of a Keplerian motion of at least one planet-mass body around the star. With
the estimated stellar mass of 1.9M$_\odot$, the minimum mass of the confirmed
planet is 5.9M$_J$. The planet's orbit is characterized by a small but nonzero
eccentricity of $e$=0.05 and the semi-major axis of 0.61 AU, which makes it the
most compact one discovered so far around GK-giants. This detection adds to the
existing evidence that, as predicted by theory, the minimum size of planetary
orbits around intermediate-mass giants is affected by both planet formation
processes and stellar evolution. The currently available evidence for another
planet around HD 102272 is insufficient to obtain an unambiguous two-orbit
solution.


  This study describes a UWB and Machine Learning (ML)-based indoor positioning
system. We propose a simple mathematical strategy to create data to reduce the
job of measurements for fingerprint-based indoor localization systems. A
considerable number of measurements can be avoided this way. The paper compares
and contrasts the performance of four distinct models. Most test locations'
average error may be reduced to less than 150 mm using the best model.


  We investigate the properties of nonlinear excitations in different types of
soliton bearing systems with long-range dispersive interaction. We show that
length-scale competition in such systems universally results in a
multi-component structure of nonlinear excitations and can lead to a new type
of multistability: coexistence of different nonlinear excitations at the same
value of the spectral parameter (i.e., velocity in the case of anharmonic
lattices or frequency in nonlinear Schroedinger models).


  We briefly report on a recent computation, with the help of a fruitful
algebraic model, sketching the pion valence dressed-quark generalized parton
distribution. Then, preliminary, we introduce on a sensible procedure to get
reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and
Efremov-Radyushkin-Brodsky-Lepage (ERBL) kinematical regions, grounded on the
GPD overlap representation and its parametrization of a Radon transform of the
so-called double distribution (DD).


  We develop the theory of ultracoproducts and weak containment for flows of
arbitrary topological groups. This provides a nice complement to corresponding
theories for p.m.p. actions and unitary representations of locally compact
groups. For the class of locally Roelcke precompact groups, the theory is
especially rich, allowing us to define for certain families of $G$-flows a
suitable compact space of weak types. When $G$ is locally compact, all
$G$-flows belong to one such family, yielding a single compact space describing
all weak types of $G$-flows.


  Given a Hodge manifold, it is introduced a self-adjoint operator on the space
of endomorphisms of the global holomorphic sections of the polarization line
bundle. Such operator is shown to approximate the Laplace operator on functions
when composed with Berezin-Toeplitz quantization map and its adjoint up to an
error which tends to zero when taking higher powers of the polarization line
bundle.


  In symmetrical nuclear matter the solutions of pion dispersion equation are
investigated in the complex plane of the pion frequency \omega. There are three
well-known branches of solutions on the physical sheet : sound, pion and
isobar, at the matter density less than the critical one \rho <\rho_c. At \rho
>\rho_c the fourth branch appears on the physical sheet. For this branch the
condition \omega^2_c\leq0 (in general case Re\omega^2_c\leq0) takes place. This
points out the instability of the ground state which is possibly related to the
pion condensation.


  Liquid phase sensing applications at 1550~nm are highly desirable due to
widely available off-the-shelf components. Generally, liquids at 1550~nm induce
a high absorption loss that limits the overall sensor's sensitivity and
detection limit. One solution is to use an active fiber loop in conjunction
with cavity ring down spectroscopy to overcome these absorption losses.
However, the amplifier inside the fiber loop suffers from inherent gain
fluctuations that limit the sensing system's overall performance. Here, we
provide a novel sensor using the wavelength-scanned phase shift-cavity ring
down spectroscopy (PS-CRDS) in conjunction with a linear active fiber cavity
that potentially offers a more sensitive solution than traditional fiber loop
sensors. We use a tapered fiber as a sensing head inside the active cavity
built from fiber Bragg gratings. We derive a theoretical phase shift expression
for our system and simulate it using the finite element method to determine
optimum tapered fiber diameter for glucose sensing in DI water. Compared to a
non-amplified system, we find that our amplified system can increase the
sensitivity by fourteen times via the amplifier gain tuning. We also conduct
experimental measurements using 0-15.5~mM glucose solutions and find them in
excellent agreement with our theoretical predictions. Experimentally we obtain
the sensor's sensitivity of 0.768~$^o$/mM (1164~$^o$/RIU) and detection limit
of 0.75~mM ( 4.5~$\times$~10$^{-4}$~RIU) without any temperature stabilization
in the system. We anticipate that the present work will find a wide range of
sensing applications in fiber cavities, ring resonators, and other microcavity
structures.


  Birkhoff's theorem is one of the most important statements of Einstein's
general relativity, which generally can not be extended to modified theories of
gravity. Here we study the validity of the theorem in scalar-tensor theories
using a perturbative approach, and compare the results in the so-called
Einstein and Jordan frames. The implications of the results question the
physical equivalence between both frames, at least in perturbations.


  The cold dark matter (CDM) scenario predicts that galactic halos should host
a huge amount of subhalos possibly lighter than planets, depending on the
nature of dark matter. Predicting their abundance and distribution has
important implications for dark matter searches and searches for subhalos
themselves, as they could provide a decisive test of the CDM paradigm. A major
difficulty in subhalo population model building is to account for the
gravitational stripping induced by baryons, which strongly impact on the
overall dynamics inside galaxies. In this paper, we focus on these "baryonic"
tides from analytical perspectives, summarizing previous work on galactic disk
shocking, and thoroughly revisiting the impact of individual encounters with
stars. For the latter, we go beyond the reference calculation of Gerhard and
Fall (1983) to deal with penetrative encounters, and provide new analytical
results. Based upon a full statistical analysis of subhalo energy change during
multiple stellar encounters possibly occurring during disk crossing, we show
that subhalos lighter than $\sim 1$~M$_\odot$ are very efficiently pruned by
stellar encounters. This modifies their mass function in a stellar environment.
In contrast, disk shocking is more efficient at pruning massive subhalos. In
short, if reasonably resilient, subhalos surviving disk crossing have lost all
their mass but an inner cuspy part, with a tidal mass function strongly
departing from the cosmological one. If fragile, stellar encounters make their
number density drop by an additional order of magnitude with respect to
disk-shocking effects only (e.g., at the solar position in the Milky Way). Our
results can be incorporated to any analytical or numerical subhalo population
model, as we show for illustration. This study complements those based on
cosmological simulations, which cannot resolve dark matter subhalos on such
small scales.


  We demonstrate a wavelength spacing tunable, multiwavelength Q-switched
mode-locked fiber laser (QML) based on a fiber taper deposited with graphene
oxide. The operation of the laser can be understood in terms of the formation
of bunches of QMLs which possess small temporal intervals, and multiwavelength
spectra are generated due to the Fourier transformation. We find that the
temporal spacing of the QMLs is highly sensitive to the pump power, and as a
result, the wavelength spacing can be easily tuned by varying the pump power.
Our experimental laser provides a wavelength spacing tuning range from ~0.001
nm to 0.145 nm with a pump power variation less than 10 mW. The laser could be
developed into a low lost wavelength spacing tunable optical source for a wide
range of applications, such as spectroscopy, microwave/terahertz signal
generation, optical metrology, optical communications and sensing.


  As it is well-known, the year 2005 has been the centenary of the "annus
mirabilis" (1905) during which Albert Einstein published four fundamental
papers of his. But already in 1979, for the centenary of Einstein's birth, the
world celebrated his monumantal work. In Italy too, there appeared scientific
books, and many semi-popularization (or popularization) articles. The present
paper represents a talk delivered in Italian, at the invitation of the Nobel
Foundation (Sanremo, IM; Italy), in time for its publication in 1979. This
article has been however reprinted, much more recently, in 2002, by the "Centro
DIEA", Faculty of Engineering, University of Bologna, Bologna, Italy [and its
source-file, in html, has been prepared with DIEA's collaboration]. We present
here a description of the human, philosophycal and scientific background,
starting from which Einstein produced his amazing results: Indeed, we try to
show why Einstein's writings today are still so important not only for pure
physics (and technology!), but also for our epistemological understanding of
the procedures followed by science, and by our own mind, in their development,
as well as for our philosophical views about the world we live in; without
forgetting the teachings that come (or should come) from Einstein's life and
claims for modern pedagogy.


  For quantized universal enveloping algebras we construct weight modules by
inducing representations of the centralizer of the Cartan subalgebra in the
quantized universal enveloping algebra. The induced modules arising from
finite-dimensional weight modules the centralizer algebra are studied. In
particular, we study the induction of one-dimensional modules, and this is
related to the study of commutative subalgebras of the centralizer algebra. For
the special case of $U_q(\mathfrak{sl}(2,\mathbb{C}))$ we show that we get the
admissible unitary representations corresponding to the non-compact real form
$U_q(\mathfrak{su}(1,1))$.


  This paper expounds the modern theory of symplectic reduction in
finite-dimensional Hamiltonian mechanics. This theory generalizes the
well-known connection between continuous symmetries and conserved quantities,
i.e. Noether's theorem. It also illustrates one of mechanics' grand themes:
exploiting a symmetry so as to reduce the number of variables needed to treat a
problem. The exposition emphasises how the theory provides insights about the
rotation group and the rigid body. The theory's device of quotienting a state
space also casts light on philosophical issues about whether two apparently
distinct but utterly indiscernible possibilities should be ruled to be one and
the same. These issues are illustrated using ``relationist'' mechanics.


  Canonical Correlation Analysis (CCA) models are powerful for studying the
associations between two sets of variables. The canonically correlated
representations, termed \textit{canonical variates} are widely used in
unsupervised learning to analyze unlabeled multi-modal registered datasets.
Despite their success, CCA models may break (or overfit) if the number of
variables in either of the modalities exceeds the number of samples. Moreover,
often a significant fraction of the variables measures modality-specific
information, and thus removing them is beneficial for identifying the
\textit{canonically correlated variates}. Here, we propose $\ell_0$-CCA, a
method for learning correlated representations based on sparse subsets of
variables from two observed modalities. Sparsity is obtained by multiplying the
input variables by stochastic gates, whose parameters are learned together with
the CCA weights via an $\ell_0$-regularized correlation loss. We further
propose $\ell_0$-Deep CCA for solving the problem of non-linear sparse CCA by
modeling the correlated representations using deep nets. We demonstrate the
efficacy of the method using several synthetic and real examples. Most notably,
by gating nuisance input variables, our approach improves the extracted
representations compared to other linear, non-linear and sparse CCA-based
models.


  Because of the ambiguous and subjective property of the facial expression
recognition (FER) task, the label noise is widely existing in the FER dataset.
For this problem, in the training phase, current FER methods often directly
predict whether the label of the input image is noised or not, aiming to reduce
the contribution of the noised data in training. However, we argue that this
kind of method suffers from the low reliability of such noise data decision
operation. It makes that some mistakenly abounded clean data are not utilized
sufficiently and some mistakenly kept noised data disturbing the model learning
process. In this paper, we propose a more reliable noise-label suppression
method called ReSup (Reliable label noise Suppression for FER). First, instead
of directly predicting noised or not, ReSup makes the noise data decision by
modeling the distribution of noise and clean labels simultaneously according to
the disagreement between the prediction and the target. Specifically, to
achieve optimal distribution modeling, ReSup models the similarity distribution
of all samples. To further enhance the reliability of our noise decision
results, ReSup uses two networks to jointly achieve noise suppression.
Specifically, ReSup utilize the property that two networks are less likely to
make the same mistakes, making two networks swap decisions and tending to trust
decisions with high agreement. Extensive experiments on three popular
benchmarks show that the proposed method significantly outperforms
state-of-the-art noisy label FER methods by 3.01% on FERPlus becnmarks. Code:
https://github.com/purpleleaves007/FERDenoise


  Previous work has established that a person's demographics and speech style
affect how well speech processing models perform for them. But where does this
bias come from? In this work, we present the Speech Embedding Association Test
(SpEAT), a method for detecting bias in one type of model used for many speech
tasks: pre-trained models. The SpEAT is inspired by word embedding association
tests in natural language processing, which quantify intrinsic bias in a
model's representations of different concepts, such as race or valence
(something's pleasantness or unpleasantness) and capture the extent to which a
model trained on large-scale socio-cultural data has learned human-like biases.
Using the SpEAT, we test for six types of bias in 16 English speech models
(including 4 models also trained on multilingual data), which come from the
wav2vec 2.0, HuBERT, WavLM, and Whisper model families. We find that 14 or more
models reveal positive valence (pleasantness) associations with abled people
over disabled people, with European-Americans over African-Americans, with
females over males, with U.S. accented speakers over non-U.S. accented
speakers, and with younger people over older people. Beyond establishing that
pre-trained speech models contain these biases, we also show that they can have
real world effects. We compare biases found in pre-trained models to biases in
downstream models adapted to the task of Speech Emotion Recognition (SER) and
find that in 66 of the 96 tests performed (69%), the group that is more
associated with positive valence as indicated by the SpEAT also tends to be
predicted as speaking with higher valence by the downstream model. Our work
provides evidence that, like text and image-based models, pre-trained speech
based-models frequently learn human-like biases. Our work also shows that bias
found in pre-trained models can propagate to the downstream task of SER.


  Recommender systems are crucial tools to overcome the information overload
brought about by the Internet. Rigorous tests are needed to establish to what
extent sophisticated methods can improve the quality of the predictions. Here
we analyse a refined correlation-based collaborative filtering algorithm and
compare it with a novel spectral method for recommending. We test them on two
databases that bear different statistical properties (MovieLens and Jester)
without filtering out the less active users and ordering the opinions in time,
whenever possible. We find that, when the distribution of user-user
correlations is narrow, simple averages work nearly as well as advanced
methods. Recommender systems can, on the other hand, exploit a great deal of
additional information in systems where external influence is negligible and
peoples' tastes emerge entirely. These findings are validated by simulations
with artificially generated data.


  We study production of scalar dark matter via the freeze--in mechanism in the
relativistic regime, focussing on the simplest Higgs portal model. We derive
the corresponding relativistic reaction rates based on the Bose--Einstein
statistics taking into account the thermal mass effects as well as the change
in the Higgs degrees of freedom at the electroweak phase transition. The
consequent constraints on the Higgs portal coupling are obtained.


  A Skolem sequence is a sequence a_1,a_2,...,a_2n (where a_i \in A = {1,...,n
}), each a_i occurs exactly twice in the sequence and the two occurrences are
exactly a_i positions apart. A set A that can be used to construct Skolem
sequences is called a Skolem set. The problem of deciding which sets of the
form A = {1,...,n} are Skolem sets was solved by Thoralf Skolem in the late
1950's. We study the natural generalization where A is allowed to be any set of
n positive integers. We give necessary conditions for the existence of Skolem
sets of this generalized form. We conjecture these necessary conditions to be
sufficient, and give computational evidence in favor of our conjecture. We
investigate special cases of the conjecture and prove that the conjecture hold
for some of them. We also study enumerative questions and show that this
problem has strong connections with problems related to permutation
displacements.


  We investigated the effects of bulk scalar field in the braneworld
cosmological scenario. The Friedmann equations and acceleration condition in
presence of the bulk scalar field for a zero tension brane and cosmological
constant are studied. In DGP model the effective Einstein equation on the brane
is obtained with bulk scalar field. The rescaled bulk scalar field on the brane
in the DGP model behaves as an effective four dimensional field, thus standard
type cosmology is recovered. In present study of the DGP model, the late-time
accelerating phase of the universe can be explained .


  In this paper, we establish various maximum principles and develop the method
of moving planes and the sliding method (on general unbounded domains) for
equations involving the uniformly elliptic nonlocal Bellman operator. As a
consequence, we derive multiple applications of these maximum principles and
the moving planes method. For instance, we prove symmetry, monotonicity and
uniqueness results and asymptotic properties for solutions to various equations
involving the uniformly elliptic nonlocal Bellman operator in bounded domains,
unbounded domains, epigraph or $\mathbb{R}^{n}$. In particular, the uniformly
elliptic nonlocal Monge-Amp\`{e}re operator introduced by Caffarelli and Charro
in \cite{CC} is a typical example of the uniformly elliptic nonlocal Bellman
operator.


  It is shown that a Friedel type oscillations accompany skin effect in
degenerate plasma of a metal. It was learnt earlier that Friedel oscillations
take place under charge screening in quantum plasma. However the nature of
Friedel oscillations is not in the quantum character of the plasma, but in the
features of degenerate Fermi distribution, namely, in its sharp transformation
into zero directly just the other side of the Fermi surface. This circumstance
leads to the Frieldel-type oscillations under anomalous skin effect.


  In the history of quantum physics several no-go theorems have been proved,
and many of them have played a central role in the development of the theory,
such as Bell's or the Kochen-Specker theorem. A recent paper by F. Laudisa has
raised reasonable doubts concerning the strategy followed in proving some of
these results, since they rely on the standard framework of quantum mechanics,
a theory that presents several ontological problems. The aim of this paper is
twofold: on the one hand, I intend to reinforce Laudisa's methodological point
by critically discussing Malament's theorem in the context of the philosophical
foundation of Quantum Field Theory; secondly, I rehabilitate Gisin's theorem
showing that Laudisa's concerns do not apply to it.


  The odd signature operator is a Dirac operator which acts on the space of
differential forms of all degrees and whose square is the usual Laplacian. We
extend the result of [15] to prove the gluing formula of the zeta-determinants
of Laplacians acting on differential forms of all degrees with respect to the
boundary conditions ${\mathcal P}_{-, {\mathcal L}_{0}}$, ${\mathcal P}_{+,
{\mathcal L}_{1}}$. We next consider a double of de Rham complexes consisting
of differential forms of all degrees with the absolute and relative boundary
conditions. Using a similar method, we prove the gluing formula of the
zeta-determinants of Laplacians acting on differential forms of all degrees
with respect to the absolute and relative boundary conditions.


  In this survey, we describe controlled interacting particle systems (CIPS) to
approximate the solution of the optimal filtering and the optimal control
problems. Part I of the survey is focussed on the feedback particle filter
(FPF) algorithm, its derivation based on optimal transportation theory, and its
relationship to the ensemble Kalman filter (EnKF) and the conventional
sequential importance sampling-resampling (SIR) particle filters. The central
numerical problem of FPF -- to approximate the solution of the Poisson equation
-- is described together with the main solution approaches. An analytical and
numerical comparison with the SIR particle filter is given to illustrate the
advantages of the CIPS approach. Part II of the survey is focussed on adapting
these algorithms for the problem of reinforcement learning. The survey includes
several remarks that describe extensions as well as open problems in this
subject.


  We perform a detailed study of the phase diagram of the lattice Higgs SU(2)
model with fixed Higgs field length. Consistently with previsions based on the
Fradkin Shenker theorem we find a first order transition line with an endpoint
whose position we determined. The diagram also shows cross-over lines: the
cross-over corresponding to the pure SU(2) bulk is also present at nonzero
coupling with the Higgs field and merges with the one that continues the line
of first order transition beyond the critical endpoint. At high temperature the
first order line becomes a crossover, whose position moves by varying the
temperature.


  This paper considers the problem of estimating a mean pattern in the setting
of Grenander's pattern theory. Shape variability in a data set of curves or
images is modeled by the random action of elements in a compact Lie group on an
infinite dimensional space. In the case of observations contaminated by an
additive Gaussian white noise, it is shown that estimating a reference template
in the setting of Grenander's pattern theory falls into the category of
deconvolution problems over Lie groups. To obtain this result, we build an
estimator of a mean pattern by using Fourier deconvolution and harmonic
analysis on compact Lie groups. In an asymptotic setting where the number of
observed curves or images tends to infinity, we derive upper and lower bounds
for the minimax quadratic risk over Sobolev balls. This rate depends on the
smoothness of the density of the random Lie group elements representing shape
variability in the data, which makes a connection between estimating a mean
pattern and standard deconvolution problems in nonparametric statistics.


  Although infrared (IR) overall dust emission from clusters of galaxies has
been statistically detected using data from the Infrared Astronomical Satellite
(IRAS), it has not been possible to sample the spectral energy distribution
(SED) of this emission over its peak, and thus to break the degeneracy between
dust temperature and mass. By complementing the IRAS spectral coverage with
Planck satellite data from 100 to 857 GHz, we provide new constraints on the IR
spectrum of thermal dust emission in clusters of galaxies. We achieve this by
using a stacking approach for a sample of several hundred objects from the
Planck cluster sample; this procedure averages out fluctuations from the IR
sky, allowing us to reach a significant detection of the faint cluster
contribution. We also use the large frequency range probed by Planck, together
with component-separation techniques, to remove the contamination from both
cosmic microwave background anisotropies and the thermal Sunyaev-Zeldovich
effect (tSZ) signal, which dominate below 353 GHz. By excluding dominant
spurious signals or systematic effects, averaged detections are reported at
frequencies between 353 and 5000 GHz. We confirm the presence of dust in
clusters of galaxies at low and intermediate redshifts, yielding an SED with a
shape similar to that of the Milky Way. Planck's beam does not allow us to
investigate the detailed spatial distribution of this emission (e.g., whether
it comes from intergalactic dust or simply the dust content of the cluster
galaxies), but the radial distribution of the emission appears to follow that
of the stacked SZ signal, and thus the extent of the clusters. The recovered
SED allows us to constrain the dust mass responsible for the signal, as well as
its temperature. We additionally explore the evolution of the IR emission as a
function of cluster mass and redshift.


  Path integration over Euclidean chiral fermions is replaced by the quantum
mechanics of an auxiliary system of non--interacting fermions. Our construction
avoids the no--go theorem and faithfully maintains all the known important
features of chiral fermions, including the violation of some perturbative
conservation laws by gauge field configurations of non--trivial topology.


  We present a discussion on recent progress in high energy diffraction from
the perspective of AdS/CFT, through which a unified treatment for both
perturbative and nonperturbative Pomeron emerges. By working with Unitary
Irreducible Representation of Conformal group, a frame is provided in extending
AdS/CFT to both forward and nearforward scattering. We present an analysis
involving an exact solution to conformal blocks in Minkowski CFT and discuss
possible applications. Phenomenological applications can range from forward
scattering to DIS/DVCS/TMD at LHC energies and beyond.


  In this work, we report a direct measurement of the forces exerted by a
tubulin/kinesin active nematic gel as well as its complete rheological
characterization, including the quantification of its shear viscosity, {\eta},
and its activity parameter, {\alpha}. For this, we develop a novel method that
allows us to rapidly photo-polymerize compliant elastic inclusions in the
continuously remodelling active system. Moreover, we quantitatively settle
long-standing theoretical predictions, such as a postulated relationship
encoding the intrinsic time scale of the active nematic in terms of {\eta} and
{\alpha}. In parallel, we infer a value for the nematic elasticity constant, K,
by combining our measurements with the theorized scaling of the active length
scale. On top of the microrheology capatilities, we demonstrate novel
strategies for defect encapsulation, quantification of defect mechanics, and
defect interactions, enabled by the versatility of the new microfabrication
strategy that allows to combine elastic motifs of different shape and stiffness
that are fabricated in-situ and on-time.


  We examine interferometric experiments in systems that exhibit non-Abelian
braiding statistics, expressing outcomes in terms of the modular S-matrix. In
particular, this result applies to FQH interferometry, and we give a detailed
treatment of the Read-Rezayi states, providing explicit predictions for the
recently observed nu=12/5 plateau.


  We present the complete analytical classification of the atoms arising at the
critical points of rank 1 of the Kowalevski-Yehia gyrostat. To classify the
Smale-Fomenko diagrams, all separating values of the gyrostatic momentum are
found. We present a kind of constructor of the Fomenko graphs; its application
gives the complete description of the rough topology of this integrable case.
It is proved that there exists exactly nine groups of identical molecules (not
considering the marks). These groups contain 22 stable types of graphs and 6
unstable ones with respect to the number of critical circles on the critical
levels.


  Associating distinct groups of objects (clusters) with contiguous regions of
high probability density (high-density clusters), is central to many
statistical and machine learning approaches to the classification of unlabelled
data. We propose a novel hyperplane classifier for clustering and
semi-supervised classification which is motivated by this objective. The
proposed minimum density hyperplane minimises the integral of the empirical
probability density function along it, thereby avoiding intersection with high
density clusters. We show that the minimum density and the maximum margin
hyperplanes are asymptotically equivalent, thus linking this approach to
maximum margin clustering and semi-supervised support vector classifiers. We
propose a projection pursuit formulation of the associated optimisation problem
which allows us to find minimum density hyperplanes efficiently in practice,
and evaluate its performance on a range of benchmark datasets. The proposed
approach is found to be very competitive with state of the art methods for
clustering and semi-supervised classification.


  We show that general N=2 supersymmetric AdS_4 solutions of M-theory with
non-zero M2-brane charge admit a canonical contact structure. The free energy
of the dual superconformal field theory on S^3 and the scaling dimensions of
operators dual to supersymmetric wrapped M5-branes are expressed via AdS/CFT in
terms of contact volumes. In particular, this leads to topological and
localization formulae for the coefficient of N^{3/2} in the free energy of such
solutions.


  The generalized minimax concave (GMC) penalty is a nonconvex sparse
regularizer which can preserve the overall-convexity of the regularized
least-squares problem. In this paper, we focus on a significant instance of the
GMC model termed scaled GMC (sGMC), and present various notable findings on its
solution-set geometry and regularization path. Our investigation indicates that
while the sGMC penalty is a nonconvex extension of the LASSO penalty (i.e., the
$\ell_1$-norm), the sGMC model preserves many celebrated properties of the
LASSO model, hence can serve as a less biased surrogate of LASSO without losing
its advantages. Specifically, for a fixed regularization parameter $\lambda$,
we show that the solution-set geometry, solution uniqueness and sparseness of
the sGMC model can be characterized in a similar elegant way to the LASSO model
(see, e.g., Osborne et al. 2000, R. J. Tibshirani 2013). For a varying
$\lambda$, we prove that the sGMC solution set is a continuous polytope-valued
mapping of $\lambda$. Most noticeably, our study indicates that similar to
LASSO, the minimum $\ell_2$-norm regularization path of the sGMC model is
continuous and piecewise linear in $\lambda$. Based on these theoretical
results, an efficient regularization path algorithm is proposed for the sGMC
model, extending the well-known least angle regression (LARS) algorithm for
LASSO. We prove the correctness and finite termination of the proposed
algorithm under a mild assumption, and confirm its
correctness-in-general-situation, efficiency, and practical utility through
numerical experiments. Many results in this study also contribute to the
theoretical research of LASSO.


  We reformulate the zero-dimensional hermitean one-matrix model as a
(nonlocal) collective field theory, for finite~$N$. The Jacobian arising by
changing variables from matrix eigenvalues to their density distribution is
treated {\it exactly\/}. The semiclassical loop expansion turns out {\it not\/}
to coincide with the (topological) ${1\over N}$~expansion, because the
classical background has a non-trivial $N$-dependence. We derive a simple
integral equation for the classical eigenvalue density, which displays strong
non-perturbative behavior around $N\!=\!\infty$. This leads to IR singularities
in the large-$N$ expansion, but UV divergencies appear as well, despite
remarkable cancellations among the Feynman diagrams. We evaluate the free
energy at the two-loop level and discuss its regularization. A simple example
serves to illustrate the problems and admits explicit comparison with
orthogonal polynomial results.


  What restrictions are there on a spacetime for which the Ricci curvature is
such as to produce convergence of geodesics (such as the preconditions for the
Singularity Theorems) but for which there are no singularities? We answer this
question for a restricted class of spacetimes: static, geodesically complete,
and globally hyperbolic. The answer is that, in at least one spacelike
direction, the Ricci curvature must fall off at a rate inversely quadratic in a
naturally-occurring Riemannian metric on the space of static observers. Along
the way, we establish some global results on the static observer space,
regarding its completeness and its behavior with respect to universal covering
spaces.


  This essay delves into the ethical dilemmas encountered within the academic
peer review process and investigates the prevailing deficiencies in this
system. It highlights how established scholars often adhere to mainstream
theories not out of genuine belief, but to safeguard their own reputations.
This practice perpetuates intellectual conformity, fuels confirmation bias, and
stifles dissenting voices. Furthermore, as the number of incorrect papers
published by influential scientists increases, it inadvertently encourages more
researchers to follow suit, tacitly endorsing incorrect viewpoints. By
examining historical instances of suppressed ideas later proven valuable, this
essay calls for a reevaluation of academia's commitment to genuine innovation
and progress which is usually achieved by applications of fundamental
principles in from textbooks.


  Flow marks are common surface defects that occur in injection-molded
products. Their formation may be related to the flow process of the melt in the
mold. Through dimensional analysis, we have discovered that the geometric shape
of the flow field is controlled by specific dimensionless quantities. These
quantities can be summarized as follows: geometric dimensionless quantities
related to the shape of the mold, material dimensionless quantities related to
the melt and mold materials, and physical dimensionless quantities related to
the flow. When the geometric shape of the mold changes proportionally, with the
melt and mold material fixed, and the initial temperature of the melt and mold
fixed, the geometric shape of the flow field will be solely controlled by the
Weissenberg number Wi. If Wi is kept constant, changing the injection speed,
changing the relaxation time of the polypropylene melt, or scaling the mold
will result in similar geometric shapes of the flow field. If the size of the
mold is not changed, the geometric shape of the flow field will be the same.
Since the dimensionless equation represents a similar system of all sizes, we
verified the above conclusion through molecular dynamics simulations at a
smaller scale. After further improvement of the micro simulation system, there
is a possibility of visualizing the formation process of flow marks. This would
greatly aid in the advancement of theory and the elimination of flow marks in
production and experiments. This work also illustrates that the methodology of
dimensional analysis plus molecular dynamics simulation may be applied to a
wider range of other systems, scaling down large systems and thus significantly
reducing their computational effort.


  This paper considers the problem of inferring the structure of a network from
indirect observations. Each observation (a "trace") is the unordered set of
nodes which are activated along a path through the network. Since a trace does
not convey information about the order of nodes within the path, there are many
feasible orders for each trace observed, and thus the problem of inferring the
network from traces is, in general, illposed. We propose and analyze an
algorithm which inserts edges by ordering each trace into a path according to
which pairs of nodes in the path co-occur most frequently in the observations.
When all traces involve exactly 3 nodes, we derive necessary and sufficient
conditions for the reconstruction algorithm to exactly recover the graph.
Finally, for a family of random graphs, we present expressions for
reconstruction error probabilities (false discoveries and missed detections).


  In today's online advertising markets, it is common for advertisers to set
long-term budgets. Correspondingly, advertising platforms adopt budget control
methods to ensure that advertisers' payments lie within their budgets. Most
budget control methods rely on the value distributions of advertisers. However,
due to the complex advertising landscape and potential privacy concerns, the
platform hardly learns advertisers' true priors. Thus, it is crucial to
understand how budget control auction mechanisms perform under unassured
priors.
  This work answers this problem from multiple aspects. We consider the
unassured prior game among the seller and all buyers induced by different
mechanisms in the stochastic model. We restrict the parameterized mechanisms to
satisfy the budget-extracting condition, which maximizes the seller's revenue
by extracting buyers' budgets as effectively as possible. Our main result shows
that the Bayesian revenue-optimal mechanism and the budget-extracting
bid-discount first-price mechanism yield the same set of Nash equilibrium
outcomes in the unassured prior game. This implies that simple mechanisms can
be as robust as the optimal mechanism under unassured priors in the
budget-constrained setting. In the symmetric case, we further show that all
these five (budget-extracting) mechanisms share the same set of possible
outcomes. We further dig into the structural properties of these mechanisms. We
characterize sufficient and necessary conditions on the budget-extracting
parameter tuple for bid-discount/pacing first-price auctions. Meanwhile, when
buyers do not take strategic behaviors, we exploit the dominance relationships
of these mechanisms by revealing their intrinsic structures.


  The squashed 7-sphere $S^{7}$ is a 7-sphere with an Einstein metric given by
the canonical variation and its cone $\mathbb{R}^{8} - \{ 0 \}$ has full
holonomy ${\rm Spin}(7)$. There is a canonical calibrating 4-form $\Phi$ on
$\mathbb{R}^{8} - \{ 0 \}$. A minimal 3-submanifold in $S^{7}$ is called
associative if its cone is calibrated by $\Phi$. In this paper, we classify two
types of fundamental associative submanifolds in the squashed $S^{7}$. One is
obtained by the intersection with a 4-plane and the other is homogeneous. Then
we study their infinitesimal associative deformations and explicitly show that
all of them are integrable.


  We use resonant elastic x-ray scattering to determine the evolution of
magnetic order in EuCd$_2$As$_2$ below $T_\textrm{N}=9.5$\,K, as a function of
temperature and applied magnetic field. We find an A-type
antiferromagneticstructure with in-plane magnetic moments, and observe dramatic
magnetoresistive effects associated with field-induced changes in the magnetic
structure and domain populations. Our \textit{ab initio} electronic structure
calculations indicate that the Dirac dispersion found in the nonmagnetic Dirac
semimetal Cd$_3$As$_2$ is also present in EuCd$_2$As$_2$, but is gapped for $T
< T_\textrm{N}$ due to the breaking of $C_3$ symmetry by the magnetic
structure.


  This paper evaluates the dynamic response of economic activity to shocks in
uncertainty as percieved by agents.The study focuses on the comparison between
the perception of economic uncertainty by manufacturers and consumers.Since
uncertainty is not directly observable, we approximate it using the geometric
discrepancy indicator of Claveria et al.(2019).This approach allows us
quantifying the proportion of disagreement in business and consumer
expectations of eleven European countries and the Euro Area.First, we compute
three independent indices of discrepancy corresponding to three dimensions of
uncertainty (economic, inflation and employment) and we average them to obtain
aggregate disagreement measures for businesses and for consumers.Next, we use a
bivariate Bayesian vector autoregressive framework to estimate the impulse
response functions to innovations in disagreement in every country.We find that
the effect on economic activity of shocks to the perception of uncertainty
differ markedly between manufacturers and consumers.On the one hand, shocks to
consumer discrepancy tend to be of greater magnitude and duration than those to
manufacturer discrepancy.On the other hand, innovations in disagreement between
the two collectives have an opposite effect on economic activity:shocks to
manufacturer discrepancy lead to a decrease in economic activity, as opposed to
shocks to consumer discrepancy.This finding is of particular relevance to
researchers when using cross-sectional dispersion of survey-based expectations,
since the effect on economic growth of shocks to disagreement depend on the
type of agent.


  Recently, the multi-step inertial randomized Kaczmarz (MIRK) method for
solving large-scale linear systems was proposed in [17]. In this paper, we
incorporate the greedy probability criterion into the MIRK method, along with
the introduction of a tighter threshold parameter for this criterion. We prove
that the proposed greedy MIRK (GMIRK) method enjoys an improved deterministic
linear convergence compared to both the MIRK method and the greedy randomized
Kaczmarz method. Furthermore, we exhibit that the multi-step inertial
extrapolation approach can be seen geometrically as an orthogonal projection
method, and establish its relationship with the sketch-and-project method [15]
and the oblique projection technique [22]. Numerical experiments are provided
to confirm our results.


  In this paper, we establish a new improved Sobolev inequality based on a
weighted Morrey space. To be precise, there exists $C=C(n,m,s,\alpha)>0$ such
that for any $u,v \in {\dot{H}}^s(\mathbb{R}^{n})$ and for any $\theta \in
(\bar{\theta},1)$, it holds that \begin{equation} \label{eq0.3} \Big( \int_{
\mathbb{R}^{n} } \frac{ |(uv)(y)|^{\frac{2^*_{s}(\alpha)}{2} } } {
|y'|^{\alpha} } dy \Big)^{ \frac{1}{ 2^*_{s} (\alpha) }} \leq C
||u||_{{\dot{H}}^s(\mathbb{R}^{n})}^{\frac{\theta}{2}}
  ||v||_{{\dot{H}}^s(\mathbb{R}^{n})}^{\frac{\theta}{2}}
||(uv)||^{\frac{1-\theta}{2}}_{ L^{1,n-2s+r}(\mathbb{R}^{n},|y'|^{-r}) },
\end{equation} where $s \!\in\! (0,1)$, $0\!<\!\alpha\!<\!2s\!<\!n$,
$2s\!<\!m\!<\!n$, $\bar{\theta}=\max \{ \frac{2}{2^*_{s}(\alpha)},
1-\frac{\alpha}{s}\cdot\frac{1}{2^*_{s}(\alpha)},
\frac{2^*_{s}(\alpha)-\frac{\alpha}{s}}{2^*_{s}(\alpha)-\frac{2\alpha}{m}} \}$,
$r=\frac{2\alpha}{ 2^*_{s}(\alpha) }$ and $y\!=\!(y',y'') \in \mathbb{R}^{m}
\times \mathbb{R}^{n-m}$.
  By using mountain pass lemma and (\ref{eq0.3}), we obtain a nontrivial weak
solution to a doubly critical system involving fractional Laplacian in
$\mathbb{R}^{n}$ with partial weight in a direct way. Furthermore, we extend
inequality (\ref{eq0.3}) to more general forms on purpose of studying some
general systems with partial weight, involving p-Laplacian especially.