  Accurately finding and predicting dynamics based on the observational data
with noise perturbations is of paramount significance but still a major
challenge presently. Here, for the Hamiltonian mechanics, we propose the
Hamiltonian Neural Koopman Operator (HNKO), integrating the knowledge of
mathematical physics in learning the Koopman operator, and making it
automatically sustain and even discover the conservation laws. We demonstrate
the outperformance of the HNKO and its extension using a number of
representative physical systems even with hundreds or thousands of freedoms.
Our results suggest that feeding the prior knowledge of the underlying system
and the mathematical theory appropriately to the learning framework can
reinforce the capability of machine learning in solving physical problems.


  We present optical conductivity spectra for $Pb_{2}Ru_{2}O_{7-{\delta}}$
single crystal at different temperatures. Among reported pyrochlore ruthenates,
this compound exhibits metallic behavior in a wide temperature range and has
the least resistivity. At low frequencies, the optical spectra show typical
Drude responses, but with a knee feature around 1000 \cm. Above 20000 \cm, a
broad absorption feature is observed. Our analysis suggests that the low
frequency responses can be understood from two Drude components arising from
the partially filled Ru $t_{2g}$ bands with different plasma frequencies and
scattering rates. The high frequency broad absorption may be contributed by two
interband transitions: from occupied Ru $t_{2g}$ states to empty $e_{g}$ bands
and from the fully filled O 2p bands to unoccupied Ru $t_{2g}$ states.


  New precision in measuring extragalactic distances using supernovae has
confirmed with high probability an accelerating increase in redshift with
distance. This has been interpreted as implying the existence of dark energy in
an expanding and accelerating, flat universe. A more logical explanation of
these observations follows directly from an observation made by Erwin
Schrodinger in 1939 that in a closed Friedmann universe every quantum wave
function changes with spacetime geometry. Double the size of the universe and
both the wavelengths of photons and the sizes of atoms double. When the
evolution of atoms and photons are combined, the meaning of Hubble redshift is
reversed. Redshift is characteristic of contracting universes. The
magnitude-redshift curve for a contracting universe has exactly the
accelerating form recently observed and is in excellent quantitative agreement
with the data of Riess et al. 1998, Knop et al. 2003, and others. An observed
maximum redshift of 1.3 gives a minimum age estimate for the universe of 114
billion years. The time until collapse is estimated to be 15 billion years or
less.


  Traditional Internet of Things (IoT) sensors rely on batteries that need to
be replaced or recharged frequently which impedes their pervasive deployment. A
promising alternative is to employ energy harvesters that convert the
environmental energy into electrical energy. Kinetic Energy Harvesting (KEH)
converts the ambient motion/vibration energy into electrical energy to power
the IoT sensor nodes. However, most previous works employ KEH without
dynamically tracking the optimal operating point of the transducer for maximum
power output. In this paper, we systematically analyse the relation between the
operating point of the transducer and the corresponding energy yield. To this
end, we explore the voltage-current characteristics of the KEH transducer to
find its Maximum Power Point (MPP). We show how this operating point can be
approximated in a practical energy harvesting circuit. We design two hardware
circuit prototypes to evaluate the performance of the proposed mechanism and
analyse the harvested energy using a precise load shaker under a wide set of
controlled conditions typically found in human-centric applications. We analyse
the dynamic current-voltage characteristics and specify the relation between
the MPP sampling rate and harvesting efficiency which outlines the need for
dynamic MPP tracking. The results show that the proposed energy harvesting
mechanism outperforms the conventional method in terms of generated power and
offers at least one order of magnitude higher power than the latter.


  One of us got spins and charges of not only scalars and vectors but also of
spinors out of fields, which are antisymmetric tensor fields. Kahler got spins
of spinors out of differential forms, which again are antisymmetric tensor
fields. Using our simple Grassmann formulation of spins and charges of either
spinors or vectors and comparing it to the Dirac-Kahler formulation of spinors,
we generalize the Dirac-Kahler approach to vector internal degrees of freedom
and to charges of either spinors or vectors and tenzors and point out how at
all spinors can appear in both approaches.


  Thermal scene reconstruction exhibit great potential for applications across
a broad spectrum of fields, including building energy consumption analysis and
non-destructive testing. However, existing methods typically require dense
scene measurements and often rely on RGB images for 3D geometry reconstruction,
with thermal information being projected post-reconstruction. This two-step
strategy, adopted due to the lack of texture in thermal images, can lead to
disparities between the geometry and temperatures of the reconstructed objects
and those of the actual scene. To address this challenge, we propose
ThermoNeRF, a novel multimodal approach based on Neural Radiance Fields,
capable of rendering new RGB and thermal views of a scene jointly. To overcome
the lack of texture in thermal images, we use paired RGB and thermal images to
learn scene density, while distinct networks estimate color and temperature
information. Furthermore, we introduce ThermoScenes, a new dataset to palliate
the lack of available RGB+thermal datasets for scene reconstruction.
Experimental results validate that ThermoNeRF achieves accurate thermal image
synthesis, with an average mean absolute error of 1.5$^\circ$C, an improvement
of over 50% compared to using concatenated RGB+thermal data with Nerfacto, a
state-of-the-art NeRF method.


  With recent developments in smart technologies, there has been a growing
focus on the use of artificial intelligence and machine learning for affective
computing to further enhance the user experience through emotion recognition.
Typically, machine learning models used for affective computing are trained
using manually extracted features from biological signals. Such features may
not generalize well for large datasets and may be sub-optimal in capturing the
information from the raw input data. One approach to address this issue is to
use fully supervised deep learning methods to learn latent representations of
the biosignals. However, this method requires human supervision to label the
data, which may be unavailable or difficult to obtain. In this work we propose
an unsupervised framework reduce the reliance on human supervision. The
proposed framework utilizes two stacked convolutional autoencoders to learn
latent representations from wearable electrocardiogram (ECG) and electrodermal
activity (EDA) signals. These representations are utilized within a random
forest model for binary arousal classification. This approach reduces human
supervision and enables the aggregation of datasets allowing for higher
generalizability. To validate this framework, an aggregated dataset comprised
of the AMIGOS, ASCERTAIN, CLEAS, and MAHNOB-HCI datasets is created. The
results of our proposed method are compared with using convolutional neural
networks, as well as methods that employ manual extraction of hand-crafted
features. The methodology used for fusing the two modalities is also
investigated. Lastly, we show that our method outperforms current
state-of-the-art results that have performed arousal detection on the same
datasets using ECG and EDA biosignals. The results show the wide-spread
applicability for stacked convolutional autoencoders to be used with machine
learning for affective computing.


  The influence of neutrino flavor oscillations on the propagation of
magnetohydrodynamic (MHD) waves and instabilities is studied in neutrino-beam
driven magnetoplasmas. Using the neutrino MHD model, a general dispersion
relation is derived which manifests the resonant interactions of MHD waves, not
only with the neutrino beam, but also with the neutrino flavor oscillations. It
is found that the latter contribute to the wave dispersion and enhance the
magnitude of the instability of oblique magnetosonic waves. However, the
shear-Alfv{\'e}n wave remains unaffected by the neutrino beam and neutrino
flavor oscillations. Such an enhancement of the magnitude of the instability of
magnetosonic waves can be significant for relatively long-wavelength
perturbations in the regimes of high neutrino number density and/or strong
magnetic field, giving a convincing mechanism for type-II core-collapse
supernova explosion.


  We assume the vanishing of the quadratic divergences in the $SU(2)_L \otimes
U(1)$ electroweak theory. Using $\,$ the $\,$ top $\,$ mass $\,$ value reported
recently by the CDF Collaboration $m_t = 176 \pm 8 \pm 10 GeV$, we predict the
mass of the Higgs boson to be $m_H = 321 \pm 29 GeV$. If we assume the
vanishing of both quadratic and logarithmic divergencies of the top self-mass,
we predict $m_t = 170.5 \pm 0.3 GeV $ and $m_H = 308.6 \pm 0.7 GeV.$


  In this paper we disprove the following conjectured generalization of the
Contraction Mapping Theorem (due to J.D. Stein Jr.):
  Let X be a complete metric space and let F be a finite family of self-maps of
X. Suppose there is a postive constant strictly less than 1 such that, for any
two points x and y of X, some member of F contracts those points by a factor of
at most that constant. Then some composition of members of F has a fixed point.
  We also show that the above does hold for a (continuous) commuting F
containing only two maps. We conjecture that it holds for commuting F of any
finite size.


  Low energy electron diffraction (LEED) experiments, LEED simulations and
finite slab density functional calculations are combined to study the cleavage
surface of Co doped BaFe_{2-x}Co_{x}As_{2} (x = 0.1, 0.17). We demonstrate that
the energy dependence of the LEED data can only be understood from a
terminating 1/2 Ba layer accompanied by distortions of the underlying
As-Fe_2-As block. As a result, surface related Fe 3d states are present in the
electronic structure, which we identify in angle resolved photoemission
experiments. The close proximity of the surface-related states to the bulk
bands inevitably leads to broadening of the ARPES signals, which excludes the
use of the BaFe_{2-x}Co_{x}As_{2} system for accurate determination of
self-energies using ARPES.


  This paper studies the solvability of a class of Dirichlet problem associated
with non-linear integro-differential operator. The main ingredient is the
probabilistic construction of continuous supersolution via the identification
of the continuity set of the exit time operators under Skorohod topology.


  We report on the evolution of the magnetic structure of BiFeO3 thin films
grown on SrTiO3 substrates as a function of Sm doping. We determined the
magnetic structure using neutron diffraction. We found that as Sm increases,
the magnetic structure evolves from a cycloid to a G-type antiferromagnet at
the morphotropic phase boundary, where there is a large piezoelectric response
due to an electric-field induced structural transition. The occurrence of the
magnetic structural transition at the morphotropic phase boundary offers
another route towards room temperature multiferroic devices.


  This is an introduction to theories where the Higgs is a composite
Nambu-Goldstone boson of a new strongly-interacting dynamics not much above the
weak scale. A general discussion is presented based on the pattern of global
symmetries at low energy, and the analogy with the QCD pion is analyzed. The
last part of the lectures shows how a composite Higgs can emerge as the
hologram of a 5-dimensional gauge field.


  We consider multi-frequency inverse source problem for the discrete Helmholtz
operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this
problem for the cases with and without phase information. We prove uniqueness
results and present examples of non-uniqueness for this problem for the case of
compactly supported source function, and a Lipshitz stability estimate for the
phased case is established. Relations with inverse scattering problem for the
discrete Schr\"{o}dinger operators in the Born approximation are also provided.


  We study the behaviour of spinning strings in the background of various
distributions of smeared giant gravitons in supergravity. This gives insights
into the behaviour of operators of high dimension, spin and R-charge. Using a
new coordinate system recently presented in the literature, we find that it is
particularly natural to prepare backgrounds in which the probe operators
develop a variety of interesting new behaviours. Among these are the possession
of orbital angular momentum as well as spin, the breakdown of logarithmic
scaling of dimension with spin in the high spin regime, and novel
splitting/fractionation processes.


  We propose a completely unsupervised method to understand audio scenes
observed with random microphone arrangements by decomposing the scene into its
constituent sources and their relative presence in each microphone. To this
end, we formulate a neural network architecture that can be interpreted as a
nonnegative tensor factorization of a multi-channel audio recording. By
clustering on the learned network parameters corresponding to channel content,
we can learn sources' individual spectral dictionaries and their activation
patterns over time. Our method allows us to leverage deep learning advances
like end-to-end training, while also allowing stochastic minibatch training so
that we can feasibly decompose realistic audio scenes that are intractable to
decompose using standard methods. This neural network architecture is easily
extensible to other kinds of tensor factorizations.


  Position control devices enable precise selection, but significant clutching
degrades performance. Clutching can be reduced with high control-display gain
or pointer acceleration, but there are human and device limits. Elastic rate
control eliminates clutching completely, but can make precise selection
difficult. We show that hybrid position-rate control can outperform position
control by 20% when there is significant clutching, even when using pointer
acceleration. Unlike previous work, our RubberEdge technique eliminates
trajectory and velocity discontinuities. We derive predictive models for
position control with clutching and hybrid control, and present a prototype
RubberEdge position-rate control device including initial user feedback.


  A $\mu$-way $(v, k, t)$ trade $T = \{T_{1} , T_{2}, . . ., T_{\mu} \}$ of
volume $m$ consists of $\mu$ disjoint collections $T_{1}, T_{2}, \ldots,
T_{\mu}$, each of $m$ blocks of size $k$, such that for every $t$-subset of
$v$-set $V$ the number of blocks containing this $t$-subset is the same in each
$T_{i}$ (for $1 \leq i \leq \mu$). A $\mu$-way $(v, k, t)$ trade is called
$\mu$-way $(v, k, t)$ Steiner trade if any $t$-subset of found$(T)$ occurs at
most once in $T_{1}$ $(T_{j},\ j \geq 2)$. A $\mu$-way $(v,k,t)$ trade is
called $d$-homogeneous if each element of $V$ occurs in precisely $d$ blocks of
$T_{1}$ $(T_{j},~ j \geq 2)$. In this paper we characterize the $3$-way
$3$-homogeneous $(v,3,2)$ Steiner trades of volume $v$. Also we show how to
construct a $3$-way $d$-homogeneous $(v,3,2)$ Steiner trade for $d\in
\{4,5,6\}$, except for seven small values of $v$.


  The two-dimensional ghost systems with negative integral central charge
received much attention in the last years for their role in a number of
applications and in connection with logarithmic conformal field theory. We
consider the free massive bosonic and fermionic ghost systems and concentrate
on the non-trivial sectors containing the disorder operators. A unified
analysis of the correlation functions of such operators can be performed for
ghosts and ordinary complex bosons and fermions. It turns out that these
correlators depend only on the statistics although the scaling dimensions of
the disorder operators change when going from the ordinary to the ghost case.
As known from the study of the ordinary case, the bosonic and fermionic
correlation functions are the inverse of each other and are exactly expressible
through the solution of a non-linear differential equation.


  We present a Bayesian approach to modelling galaxy clusters using
multi-frequency pointed observations from telescopes that exploit the
Sunyaev--Zel'dovich effect. We use the recently developed MultiNest technique
(Feroz, Hobson & Bridges, 2008) to explore the high-dimensional parameter
spaces and also to calculate the Bayesian evidence. This permits robust
parameter estimation as well as model comparison. Tests on simulated Arcminute
Microkelvin Imager observations of a cluster, in the presence of primary CMB
signal, radio point sources (detected as well as an unresolved background) and
receiver noise, show that our algorithm is able to analyse jointly the data
from six frequency channels, sample the posterior space of the model and
calculate the Bayesian evidence very efficiently on a single processor. We also
illustrate the robustness of our detection process by applying it to a field
with radio sources and primordial CMB but no cluster, and show that indeed no
cluster is identified. The extension of our methodology to the detection and
modelling of multiple clusters in multi-frequency SZ survey data will be
described in a future work.


  We consider the Goursat problem in the plane for partial differential
operators whose principal part is the $p$th power of the standard Laplace
operator. The data is posed on a union of $2p$ distinct lines through the
origin. We show that the solvability of this Goursat problem depends on
Diophantine properties of the geometry of lines on which the data is posed.


  There have been many versions of spin-dependent parton distributions in the
literature. Although most agree with present data within uncertainties, they
are based upon different physical assumptions. Some physical models are
discussed and the corresponding predictions for double spin asymmetries are
shown. A summary of the most feasible measurements in the appropriate kinematic
regions at RHIC, which should yield the most useful information about the
polarized gluon distribution, is given.


  This study presents the integrated control/structure design of a Large
Flexible Structure, the Extra Long Mast Observatory (ELMO). The integrated
design is performed using structured $\mathcal{H}_\infty$ control tools,
developing the Two-Input Two-Output Port (TITOP) model of the flexible
multi-body structure and imposing integrated design specifications as
$\mathcal{H}_\infty$ constraints. The integrated control/structure design for
ELMO consists of optimizing simultaneously its payload mass and control system
for low-frequency perturbation rejection respecting bandwidth requirements.


  The design of cable-stayed bridges requires the determination of several
design variables' values. Civil engineers usually perform this task by hand as
an iteration of steps that stops when the engineer is happy with both the cost
and maintaining the structural constraints of the solution. The problem's
difficulty arises from the fact that changing a variable may affect other
variables, meaning that they are not independent, suggesting that we are facing
a deceptive landscape. In this work, we compare two approaches to a baseline
solution: a Genetic Algorithm and a CMA-ES algorithm. There are two objectives
when designing the bridges: minimizing the cost and maintaining the structural
constraints in acceptable values to be considered safe. These are conflicting
objectives, meaning that decreasing the cost often results in a bridge that is
not structurally safe. The results suggest that CMA-ES is a better option for
finding good solutions in the search space, beating the baseline with the same
amount of evaluations, while the Genetic Algorithm could not. In concrete, the
CMA-ES approach is able to design bridges that are cheaper and structurally
safe.


  In our experience, some ontology users find it much easier to convey logical
statements using rules rather than OWL (or description logic) axioms. Based on
recent theoretical developments on transformations between rules and
description logics, we develop ROWL, a Protege plugin that allows users to
enter OWL axioms by way of rules; the plugin then automatically converts these
rules into OWL DL axioms if possible, and prompts the user in case such a
conversion is not possible without weakening the semantics of the rule.


  Microquasars, Galactic binary systems showing extended and variable radio
emission, are potential gamma-ray emitters. Indications of gamma-ray transient
episodes have been reported in at least two systems, Cyg X-1 and Cyg X-3. The
identification of additional gamma-ray emitting microquasars is key for a
better understanding of these systems. Very-high-energy gamma-ray emission from
microquasars has been predicted to happen during periods of transient outbursts
potentially connected with the formation of a jet-like outflow. Contemporaneous
observations using the H.E.S.S. telescope array and the RXTE satellite were
obtained on three microquasars: GRS 1915+105, Circinus X-1 and V4641 Sgr with
the aim of detecting a broadband flaring event in the very-high-energy
gamma-ray and X-ray bands. We report here on the analysis of these data for
each system, including a detailed X-ray analysis assessing the location of the
sources in a hardness-intensity diagram during the observations. Finally we
discuss the derived upper limits on their very-high-energy gamma-ray flux.


  We propose a model for a power-counting renormalizable field theory living in
a fractal spacetime. The action is Lorentz covariant and equipped with a
Stieltjes measure. The system flows, even in a classical sense, from an
ultraviolet regime where spacetime has Hausdorff dimension 2 to an infrared
limit coinciding with a standard $D$-dimensional field theory. We discuss the
properties of a scalar field model at classical and quantum level. Classically,
the field lives on a fractal which exchanges energy-momentum with the bulk of
integer topological dimension D. Although an observer experiences dissipation,
the total energy-momentum is conserved. The field spectrum is a continuum of
massive modes. The gravitational sector and Einstein equations are discussed in
detail, also on cosmological backgrounds. We find ultraviolet cosmological
solutions and comment on their implications for the early universe.


  Gene expression levels are important molecular quantitative traits that link
genotypes to molecular functions and fitness. In Drosophila, population-genetic
studies in recent years have revealed substantial adaptive evolution at the
genomic level. However, the evolutionary modes of gene expression have remained
controversial. Here we present evidence that adaptation dominates the evolution
of gene expression levels in flies. We show that 63% of the observed expression
divergence across seven Drosophila species are adaptive changes driven by
directional selection. Our results are derived from the variation of expression
within species and the time-resolved divergence across a family of related
species, using a new inference method for selection. We identify functional
classes of adaptively regulated genes, as well as sex-specific adaptation
occurring predominantly in males. Our analysis opens a new avenue to map
system-wide selection on molecular quantitative traits independently of their
genetic basis.


  We consider the pebble game on DAGs with bounded fan-in introduced in
[Paterson and Hewitt '70] and the reversible version of this game in [Bennett
'89], and study the question of how hard it is to decide exactly or
approximately the number of pebbles needed for a given DAG in these games. We
prove that the problem of eciding whether $s$~pebbles suffice to reversibly
pebble a DAG $G$ is PSPACE-complete, as was previously shown for the standard
pebble game in [Gilbert, Lengauer and Tarjan '80]. Via two different graph
product constructions we then strengthen these results to establish that both
standard and reversible pebbling space are PSPACE-hard to approximate to within
any additive constant. To the best of our knowledge, these are the first
hardness of approximation results for pebble games in an unrestricted setting
(even for polynomial time). Also, since [Chan '13] proved that reversible
pebbling is equivalent to the games in [Dymond and Tompa '85] and [Raz and
McKenzie '99], our results apply to the Dymond--Tompa and Raz--McKenzie games
as well, and from the same paper it follows that resolution depth is
PSPACE-hard to determine up to any additive constant. We also obtain a
multiplicative logarithmic separation between reversible and standard pebbling
space. This improves on the additive logarithmic separation previously known
and could plausibly be tight, although we are not able to prove this. We leave
as an interesting open problem whether our additive hardness of approximation
result could be strengthened to a multiplicative bound if the computational
resources are decreased from polynomial space to the more common setting of
polynomial time.


  For a new class of topological vector spaces, namely $\kappa $-normed spaces,
and associated quasisemilinear topological preordered space is defined and
investigated. This structure arise naturally from the consideration of a
$\kappa $-norm, that is a distance function between a point and a
$G_{\delta}$-subset. For it, analogs of the Hahn-Banach theorem are proved.


  Within the Kotliar-Ruckenstein slave-boson approach, we have studied the
antiferromagnetic (AF) properties for the $t$-$t'$-$t''$-$U$ model applied to
electron-doped cuprate superconductors. Due to inclusion of spin fluctuations
the AF order decreases with doping much faster than obtained in the
Hartree-Fock theory. Under an intermediate {\it constant} $U$ the calculated
doping evolution of the spectral intensity has satisfactorily reproduced the
experimental results, without need of a strongly doping-dependent $U$ as argued
earlier. This may reconcile a discrepancy suggested in recent studies on
photoemission and optical conductivity.


  Recent advances in deep generative models have lead to remarkable progress in
synthesizing high quality images. Following their successful application in
image processing and representation learning, an important next step is to
consider videos. Learning generative models of video is a much harder task,
requiring a model to capture the temporal dynamics of a scene, in addition to
the visual presentation of objects. While recent attempts at formulating
generative models of video have had some success, current progress is hampered
by (1) the lack of qualitative metrics that consider visual quality, temporal
coherence, and diversity of samples, and (2) the wide gap between purely
synthetic video data sets and challenging real-world data sets in terms of
complexity. To this extent we propose Fr\'{e}chet Video Distance (FVD), a new
metric for generative models of video, and StarCraft 2 Videos (SCV), a
benchmark of game play from custom starcraft 2 scenarios that challenge the
current capabilities of generative models of video. We contribute a large-scale
human study, which confirms that FVD correlates well with qualitative human
judgment of generated videos, and provide initial benchmark results on SCV.


  Solving math word problems is a challenging task that requires accurate
natural language understanding to bridge natural language texts and math
expressions. Motivated by the intuition about how human generates the equations
given the problem texts, this paper presents a neural approach to automatically
solve math word problems by operating symbols according to their semantic
meanings in texts. This paper views the process of generating equation as a
bridge between the semantic world and the symbolic world, where the proposed
neural math solver is based on an encoder-decoder framework. In the proposed
model, the encoder is designed to understand the semantics of problems, and the
decoder focuses on tracking semantic meanings of the generated symbols and then
deciding which symbol to generate next. The preliminary experiments are
conducted in a dataset Math23K, and our model significantly outperforms both
the state-of-the-art single model and the best non-retrieval-based model over
about 10% accuracy, demonstrating the effectiveness of bridging the symbolic
and semantic worlds from math word problems.


  Contrastive representation learning has gained much attention due to its
superior performance in learning representations from both image and sequential
data. However, the learned representations could potentially lead to
performance disparities in downstream tasks, such as increased silencing of
underrepresented groups in toxicity comment classification. In light of this
challenge, in this work, we study learning fair representations that satisfy a
notion of fairness known as equalized odds for text classification via
contrastive learning. Specifically, we first theoretically analyze the
connections between learning representations with a fairness constraint and
conditional supervised contrastive objectives, and then propose to use
conditional supervised contrastive objectives to learn fair representations for
text classification. We conduct experiments on two text datasets to demonstrate
the effectiveness of our approaches in balancing the trade-offs between task
performance and bias mitigation among existing baselines for text
classification. Furthermore, we also show that the proposed methods are stable
in different hyperparameter settings.


  Kato's theory on the construction of strongly continuous evolution systems
associated with hyperbolic equations is applied to the linear equation
describing an age-structured population that is subject to time-dependent
diffusion. The evolution system is used to provide conditions for the
well-posedness of the corresponding quasilinear equation.


  Let $A$ be an $AH$ algebra $A=\lim\limits_{n\to
\infty}(A_{n}=\bigoplus\limits_{i=1}\limits^{t_{n}}P_{n,i}M_{[n,i]}(C(X_{n,i}))P_{n,i},
\phi_{n,m})$, where $X_{n,i}$ are compact metric spaces, $t_{n}$ and $[n,i]$
are positive integers, and $P_{n,i}\in M_{[n,i]}(C(X_{n,i}))$ are projections.
Suppose that $A$ has the ideal property: each closed two-sided ideal of $A$ is
generated by the projections inside the ideal, as a closed two sided ideal. In
this article, we will classify all $AH$ algebras with ideal property of no
dimension growth---that is, $sup_{n,i}dim(X_{n,i})<+\infty$. This result
generalizes and unifies the classification of $AH$ algebras of real rank zero
in [EG] and [DG] and the classification of simple $AH$ algebras in [G5] and
[EGL1]. This completes one of two important possible generalizations of [EGL1]
suggested in the introduction of [EGL1]. The invariants for the classification
include the scaled ordered total $K$-group $(\underline{K}(A),
\underline{K}(A)_{+},\Sigma A)$ (as already used in real rank zero case in
[DG]), for each $[p]\in\Sigma A$, the tracial state space $T(pAp)$ of cut down
algebra $pAp$ with a certain compatibility, (which is used by [Stev] and
[Ji-Jiang] for $AI$ algebras with the ideal property), and a new ingredient,
the invariant $U(pAp)/\overline{DU(pAp)}$ with a certain compatibility
condition, where $\overline{DU(pAp)}$ is the closure of commutator subgroup
$DU(pAp)$ of the unitary group $U(pAp)$ of the cut down algebra $pAp$. In [GJL]
a counterexample is presented to show that this new ingredient must be included
in the invariant. The discovery of this new invariant is analogous to that of
the order structure on the total K-theory when one advances from the
classification of simple real rank zero $C^*$-algebras to that of non simple
real rank zero $C^*$-algebras in [G2], [Ei], [DL] and [DG] (see Introduction
below).


  We continue the effort to optimise and generalise the solution of the
spectral problem of AdS$_5$/CFT$_4$ in the planar limit via integrability. We
present a simple strategy to solve the quantum spectral curve perturbatively
for general states by focusing on the $\mathbf{P}\mu$-system. A Mathematica
notebook with an implementation of this algorithm is provided, as well as an
extensive database with a user-friendly interface containing more than 8.000
solutions of the QSC. When investigating the solution space, we observe a
curious phenomenon: existence of solutions for which the Q-system degenerates
in the limit $g\to 0$. These degeneracies are lifted at higher orders in
perturbation theory. The degenerating solutions have auxiliary Bethe roots
merging with branch points at weak coupling.


  Nowadays the state of the art Density Functional Theory (DFT) codes are based
on local (LDA) or semilocal (GGA) energy functionals. Recently the theory of a
truly nonlocal energy functional has been developed. It has been used mostly as
a post DFT calculation approach, i.e. by applying the functional on the charge
density calculated using any standard DFT code, thus obtaining a new improved
value for the total energy of the system. Nonlocal calculation is
computationally quite expensive and scales as N^2 where N is the number of
points in which charge density is defined, and a massively parallel calculation
is essential for a wider applicability of the new approach. In this article we
present a code which acomplishes this goal.


  The distribution function for the first eigenvalue spacing in the Laguerre
unitary ensemble of finite size may be expressed in terms of a solution of the
fifth Painleve transcendent. The generating function of a certain discontinuous
linear statistic of the Laguerre unitary ensemble can similarly be expressed in
terms of a solution of the fifth Painleve equation. The methodology used to
derive these results rely on two theories regarding differential equations for
orthogonal polynomial systems, one involving isomonodromic deformations and the
other ladder operators. We compare the two theories by showing how either can
be used to obtain a characterization of a more general Laguerre unitary
ensemble average in terms of the Hamiltonian system for Painleve V.


  The Motzkin numbers can be derived as coefficients of hybrid polynomials.
Such an identification allows the derivation of new identities for this family
of numbers and offers a tool to investigate previously unnoticed links with the
theory of special functions and with the relevant treatment in terms of
operational means. The use of umbral methods opens new directions for further
developments and generalizations, which leads, e.g., to the identification of
new Motzkin associated forms.


  Adversarial examples are crafted by adding indistinguishable perturbations to
normal examples in order to fool a well-trained deep learning model to
misclassify. In the context of computer vision, this notion of
indistinguishability is typically bounded by $L_{\infty}$ or other norms.
However, these norms are not appropriate for measuring indistinguishiability
for time series data. In this work, we propose adversarial examples in the
Wasserstein space for time series data for the first time and utilize
Wasserstein distance to bound the perturbation between normal examples and
adversarial examples. We introduce Wasserstein projected gradient descent
(WPGD), an adversarial attack method for perturbing univariant time series
data. We leverage the closed-form solution of Wasserstein distance in the 1D
space to calculate the projection step of WPGD efficiently with the gradient
descent method. We further propose a two-step projection so that the search of
adversarial examples in the Wasserstein space is guided and constrained by
Euclidean norms to yield more effective and imperceptible perturbations. We
empirically evaluate the proposed attack on several time series datasets in the
healthcare domain. Extensive results demonstrate that the Wasserstein attack is
powerful and can successfully attack most of the target classifiers with a high
attack success rate. To better study the nature of Wasserstein adversarial
example, we evaluate a strong defense mechanism named Wasserstein smoothing for
potential certified robustness defense. Although the defense can achieve some
accuracy gain, it still has limitations in many cases and leaves space for
developing a stronger certified robustness method to Wasserstein adversarial
examples on univariant time series data.


  Spoken Question Answering (SQA) is to find the answer from a spoken document
given a question, which is crucial for personal assistants when replying to the
queries from the users. Existing SQA methods all rely on Automatic Speech
Recognition (ASR) transcripts. Not only does ASR need to be trained with
massive annotated data that are time and cost-prohibitive to collect for
low-resourced languages, but more importantly, very often the answers to the
questions include name entities or out-of-vocabulary words that cannot be
recognized correctly. Also, ASR aims to minimize recognition errors equally
over all words, including many function words irrelevant to the SQA task.
Therefore, SQA without ASR transcripts (textless) is always highly desired,
although known to be very difficult.
  This work proposes Discrete Spoken Unit Adaptive Learning (DUAL), leveraging
unlabeled data for pre-training and fine-tuned by the SQA downstream task. The
time intervals of spoken answers can be directly predicted from spoken
documents. We also release a new SQA benchmark corpus, NMSQA, for data with
more realistic scenarios. We empirically showed that DUAL yields results
comparable to those obtained by cascading ASR and text QA model and robust to
real-world data. Our code and model will be open-sourced.


  To open up new possibilities to assess the multimodal perceptual quality of
omnidirectional media formats, we proposed a novel open source 360 audiovisual
(AV) quality dataset. The dataset consists of high-quality 360 video clips in
equirectangular (ERP) format and higher-order ambisonic (4th order) along with
the subjective scores. Three subjective quality experiments were conducted for
audio, video, and AV with the procedures detailed in this paper. Using the data
from subjective tests, we demonstrated that this dataset can be used to
quantify perceived audio, video, and audiovisual quality. The diversity and
discriminability of subjective scores were also analyzed. Finally, we
investigated how our dataset correlates with various objective quality metrics
of audio and video. Evidence from the results of this study implies that the
proposed dataset can benefit future studies on multimodal quality evaluation of
360 content.


  The path lengths of monochromatic muons emerging in the $\pi \to \mu\nu_{\mu}
$ decay were measured by the coordinate method with the view to determine their
energy by path length. The dispersion of muon energy measurements by this
method was $ \sigma_{\mu} = (0.11 \pm 0.01)$ MeV, which corresponds to the
accuracy of $ \sigma \approx 2.7%$ of the energy of a charged particle
estimated by its path length in nuclear emulsion. The developed method will
enable measurements of electron energies in $2\beta $ decay ($\sim 3$ MeV) to
an accuracy of $ \sigma \approx 5%$.


  We study last-mile delivery problems where trucks and drones collaborate to
deliver goods to final customers. In particular, we focus on problem settings
where either a single truck or a fleet with several homogeneous trucks work in
parallel to drones, and drones have the capability of collaborating for
delivering missions. This cooperative behaviour of the drones, which are able
to connect to each other and work together for some delivery tasks, enhance
their potential, since connected drone has increased lifting capabilities and
can fly at higher speed, overcoming the main limitations of the setting where
the drones can only work independently.
  In this work, we contribute a Constraint Programming model and a valid
inequality for the version of the problem with one truck, namely the
\emph{Parallel Drone Scheduling Traveling Salesman Problem with Collective
Drones} and we introduce for the first time the variant with multiple trucks,
called the \emph{Parallel Drone Scheduling Vehicle Routing Problem with
Collective Drones}. For the latter variant, we propose two Constraint
Programming models and a Mixed Integer Linear Programming model.
  An extensive experimental campaign leads to state-of-the-art results for the
problem with one truck and some understanding of the presented models'
behaviour on the version with multiple trucks. Some insights about future
research are finally discussed.


  We study the connected components G^00, G^000 and their quotients for a group
G definable in a saturated o-minimal expansion of a real closed field. We show
that G^00/G^000 is naturally the quotient of a connected compact commutative
Lie group by a dense finitely generated subgroup. We also highlight the role of
universal covers of semisimple Lie groups.


  In a model extraction attack, an adversary steals a copy of a remotely
deployed machine learning model, given oracle prediction access. We taxonomize
model extraction attacks around two objectives: *accuracy*, i.e., performing
well on the underlying learning task, and *fidelity*, i.e., matching the
predictions of the remote victim classifier on any input.
  To extract a high-accuracy model, we develop a learning-based attack
exploiting the victim to supervise the training of an extracted model. Through
analytical and empirical arguments, we then explain the inherent limitations
that prevent any learning-based strategy from extracting a truly high-fidelity
model---i.e., extracting a functionally-equivalent model whose predictions are
identical to those of the victim model on all possible inputs. Addressing these
limitations, we expand on prior work to develop the first practical
functionally-equivalent extraction attack for direct extraction (i.e., without
training) of a model's weights.
  We perform experiments both on academic datasets and a state-of-the-art image
classifier trained with 1 billion proprietary images. In addition to broadening
the scope of model extraction research, our work demonstrates the practicality
of model extraction attacks against production-grade systems.


  Inspired by the success of Google's Pregel, many systems have been developed
recently for iterative computation over big graphs. These systems provide a
user-friendly vertex-centric programming interface, where a programmer only
needs to specify the behavior of one generic vertex when developing a parallel
graph algorithm. However, most existing systems require the input graph to
reside in memories of the machines in a cluster, and the few out-of-core
systems suffer from problems such as poor efficiency for sparse computation
workload, high demand on network bandwidth, and expensive cost incurred by
external-memory join and group-by.
  In this paper, we introduce the GraphD system for a user to process very
large graphs with ordinary computing resources. GraphD fully overlaps
computation with communication, by streaming edges and messages on local disks,
while transmitting messages in parallel. For a broad class of Pregel algorithms
where message combiner is applicable, GraphD eliminates the need of any
expensive external-memory join or group-by. These key techniques allow GraphD
to achieve comparable performance to in-memory Pregel-like systems without
keeping edges and messages in memories. We prove that to process a graph G=(V,
E) with n machines using GraphD, each machine only requires O(|V|/n) memory
space, allowing GraphD to scale to very large graphs with a small cluster.
Extensive experiments show that GraphD beats existing out-of-core systems by
orders of magnitude, and achieves comparable performance to in-memory systems
running with enough memories.


  Learning agent behaviors from observational data has shown to improve our
understanding of their decision-making processes, advancing our ability to
explain their interactions with the environment and other agents. While
multiple learning techniques have been proposed in the literature, there is one
particular setting that has not been explored yet: multi agent systems where
agent identities remain anonymous. For instance, in financial markets labeled
data that identifies market participant strategies is typically proprietary,
and only the anonymous state-action pairs that result from the interaction of
multiple market participants are publicly available. As a result, sequences of
agent actions are not observable, restricting the applicability of existing
work. In this paper, we propose a Policy Clustering algorithm, called K-SHAP,
that learns to group anonymous state-action pairs according to the agent
policies. We frame the problem as an Imitation Learning (IL) task, and we learn
a world-policy able to mimic all the agent behaviors upon different
environmental states. We leverage the world-policy to explain each anonymous
observation through an additive feature attribution method called SHAP (SHapley
Additive exPlanations). Finally, by clustering the explanations we show that we
are able to identify different agent policies and group observations
accordingly. We evaluate our approach on simulated synthetic market data and a
real-world financial dataset. We show that our proposal significantly and
consistently outperforms the existing methods, identifying different agent
strategies.


  We propose a general strategy to determine universal properties induced by a
nearby phase transition on a non-order parameter field. A general
renormalizable Lagrangian is used, which contains the order parameter and a
non-order parameter field, and respects all the symmetries present. We
investigate the case in which the order parameter field depends only on space
coordinates and the case in which this field is also time dependent. We find
that the spatial correlators of the non-order parameter field, in both cases,
are infrared dominated and can be used to determine properties of the phase
transition. We predict a universal behavior for the screening mass of a generic
singlet field, and show how to extract relevant information from such a
quantity. We also demonstrate that the pole mass of the non-order parameter
field is not infrared sensitive. Our results can be applied to any continuous
phase transition. As an example we consider the deconfining transition in pure
Yang-Mills theory, and show that our findings are supported by lattice data.
Our analysis suggests that monitoring the spatial correlators of different
hadron species, more specifically the derivatives of these, provides an
efficient and sufficient way to experimentally uncover the deconfining phase
transition and its features.


  Three-dimensional imaging of biological cells is crucial for the
investigation of cell biology, provide valuable information to reveal the
mechanisms behind pathophysiology of cells and tissues. Recent advances in
optical diffraction tomography (ODT) have demonstrated the potential for the
study of various cells with its unique advantages of quantitative and
label-free imaging capability. To provide insight on this rapidly growing field
of research and to discuss its applications in biology and medicine, we present
the summary of the ODT principle and highlight recent studies utilizing ODT
with the emphasis on the applications to the pathophysiology of cells.


  Motivated by certain problems of statistical physics we consider a stationary
stochastic process in which deterministic evolution is interrupted at random
times by upward jumps of a fixed size. If the evolution consists of linear
decay, the sample functions are of the "random sawtooth" type and the level
dependent persistence exponent \theta can be calculated exactly. We then
develop an expansion method valid for small curvature of the deterministic
curve. The curvature parameter g plays the role of the coupling constant of an
interacting particle system. The leading order curvature correction to \theta
is proportional to g^{2/3}. The expansion applies in particular to exponential
decay in the limit of large level, where the curvature correction considerably
improves the linear approximation. The Langevin equation, with Gaussian white
noise, is recovered as a singular limiting case.


  Invariance properties of a physical system govern its behavior: energy
conservation in turbulence drives a wide distribution of energy among modes, as
observed in geophysics, astrophysics and engineering. In hydrodynamic
turbulence, the role of helicity (which measures departures from mirror
symmetry) remains unclear since it does not alter this distribution. However,
the interplay of rotation and helicity leads to significant differences. Using
numerical simulations we show the occurence of long-lived laminar cyclonic
vortices together with turbulent vortices, reminiscent of recent tornado
observations. Furthermore, the small scales are completely self-similar with no
deviations from Gaussianity. This result points to the discovery of a small
parameter in rotating helical turbulence.


  The non-linear second order Born-Infeld equation is reduced to a simpler
first order complex equation, which can be trivially solved for the coordinates
as functions of the field. Each solution is determined by the choice of a
holomorphic function subjected to boundary conditions. The explanation of the
method is accompanied by applications to Born-Infeld electrostatics,
magnetostatics and wave propagation.


  Motivated by recent interest in redshifted 21 cm emission of intergalactic
hydrogen, we investigate the 8.7 GHz ^2S_{1/2} F=0-1 hyperfine transition of
^3He^+. While the primordial abundance of 3He relative to hydrogen is 10^-5,
the hyperfine spontaneous decay rate is 680 times larger. Furthermore, the
antenna temperature is much lower at the frequencies relevant for the ^3He^+
transition compared to that of z>6 21 cm emission. We find that the spin
temperature of this 8.7 GHz line in the intergalactic medium is approximately
the cosmic microwave background temperature, such that this transition is best
observed in absorption against high-redshift, radio-bright quasars. We show
that intergalactic 8.7 GHz absorption is a promising, unsaturated observable of
the ionization history of intergalactic helium (for which HeII->HeIII
reionization is believed to be complete at z~3) and of the primordial 3He
abundance. Instruments must reach ~1 \mu Jy RMS noise in bands of 1 MHz on a 1
Jy source to directly resolve this absorption. However, in combination with HI
Ly\alpha forest measurements, an instrument can statistically detect this
absorption from z > 3 with 30 \mu Jy RMS noise in 0.1 MHz spectral bands over
100 MHz, which may be within the reach of present instruments.


  In this study, we analyzed the weak decays induced by $J^P = \frac{1}{2}^{+}
\to \frac{3}{2}^{-} $ transitions within the light-cone sum rules.
Specifically, semileptonic decays of the bottom baryons into the P-wave baryons
$\Lambda_b \to \Lambda_c(2625) \ell \nu_l$ and $\Xi_b \to \Xi_c(2815) \ell
\nu_l$ as well as nonleptonic $\Lambda_b \to \Lambda_c(2625) \pi (\rho)$ and
$\Xi_b \to \Xi_c(2815) \pi (\rho)$ decays are investigated. The form factors
for the considered transitions are obtained within the sum rules method. With
the calculated form factors, the decay widths of the processes are determined.
Up to now, only the decay width for $\Lambda_b^0 \to \Lambda_c^+ \mu^- \nu_\mu$
has been measured among the considered decays, and we observe that our finding
is quite compatible with the measurement. We also compare our results with the
predictions of other approaches.


  We initiate the study of degree-bounded network design problems in the online
setting. The degree-bounded Steiner tree problem { which asks for a subgraph
with minimum degree that connects a given set of vertices { is perhaps one of
the most representative problems in this class. This paper deals with its
well-studied generalization called the degree-bounded Steiner forest problem
where the connectivity demands are represented by vertex pairs that need to be
individually connected. In the classical online model, the input graph is given
online but the demand pairs arrive sequentially in online steps. The selected
subgraph starts off as the empty subgraph, but has to be augmented to satisfy
the new connectivity constraint in each online step. The goal is to be
competitive against an adversary that knows the input in advance. We design a
simple greedy-like algorithm that achieves a competitive ratio of O(log n)
where n is the number of vertices. We show that no (randomized) algorithm can
achieve a (multiplicative) competitive ratio o(log n); thus our result is
asymptotically tight. We further show strong hardness results for the group
Steiner tree and the edge-weighted variants of degree-bounded connectivity
problems. Fourer and Raghavachari resolved the online variant of degree-bounded
Steiner forest in their paper in SODA'92. Since then, the natural family of
degree-bounded network design problems has been extensively studied in the
literature resulting in the development of many interesting tools and numerous
papers on the topic. We hope that our approach in this paper, paves the way for
solving the online variants of the classical problems in this family of network
design problems.


  3D object detection is an important yet demanding task that heavily relies on
difficult to obtain 3D annotations. To reduce the required amount of
supervision, we propose 3DIoUMatch, a novel semi-supervised method for 3D
object detection applicable to both indoor and outdoor scenes. We leverage a
teacher-student mutual learning framework to propagate information from the
labeled to the unlabeled train set in the form of pseudo-labels. However, due
to the high task complexity, we observe that the pseudo-labels suffer from
significant noise and are thus not directly usable. To that end, we introduce a
confidence-based filtering mechanism, inspired by FixMatch. We set confidence
thresholds based upon the predicted objectness and class probability to filter
low-quality pseudo-labels. While effective, we observe that these two measures
do not sufficiently capture localization quality. We therefore propose to use
the estimated 3D IoU as a localization metric and set category-aware
self-adjusted thresholds to filter poorly localized proposals. We adopt VoteNet
as our backbone detector on indoor datasets while we use PV-RCNN on the
autonomous driving dataset, KITTI. Our method consistently improves
state-of-the-art methods on both ScanNet and SUN-RGBD benchmarks by significant
margins under all label ratios (including fully labeled setting). For example,
when training using only 10\% labeled data on ScanNet, 3DIoUMatch achieves 7.7%
absolute improvement on<EMAIL_ADDRESS>and 8.5% absolute improvement on<EMAIL_ADDRESS>upon
the prior art. On KITTI, we are the first to demonstrate semi-supervised 3D
object detection and our method surpasses a fully supervised baseline from 1.8%
to 7.6% under different label ratios and categories.


  Evaluation plays a significant role in modern natural language processing.
Most modern NLP benchmarks consist of arbitrary sets of tasks that neither
guarantee any generalization potential for the model once applied outside the
test set nor try to minimize the resource consumption needed for model
evaluation. This paper presents a theoretical instrument and a practical
algorithm to calculate similarity between benchmark tasks, we call this
similarity measure "Vygotsky distance". The core idea of this similarity
measure is that it is based on relative performance of the "students" on a
given task, rather that on the properties of the task itself. If two tasks are
close to each other in terms of Vygotsky distance the models tend to have
similar relative performance on them. Thus knowing Vygotsky distance between
tasks one can significantly reduce the number of evaluation tasks while
maintaining a high validation quality. Experiments on various benchmarks,
including GLUE, SuperGLUE, CLUE, and RussianSuperGLUE, demonstrate that a vast
majority of NLP benchmarks could be at least 40% smaller in terms of the tasks
included. Most importantly, Vygotsky distance could also be used for the
validation of new tasks thus increasing the generalization potential of the
future NLP models.


  We show that under certain conditions the Gelfand-Kazhdan criterion for the
Gelfand property is a necessary condition. We work in the generality of finite
groups, however part of the argument carries over to p-adic and real groups.


  We invesigate analytically both the intermediate and late-time behaviour of
the massive scalar field in the background of static spherically symmetric
black hole solution in dilaton gravity with arbitrary coupling constant. The
intermediate asymptotic behaviour of scalar field depends on the field's
parameter mass as well as the multiple number l. On its turn, the late-time
behaviour has the power law decay rate independent on coupling constant in the
theory under consideration.


  We prove a vanishing theorem of the cohomology arising from the two Quantized
Drinfeld-Sokolov reductions (``+'' and ``-'' reduction) introduced by
Feigin-Frenkel and Frenkel-Kac-Wakimoto. As a consequence, the vanishing
conjecture of Frenkel-Kac-Wakimoto is proved for the ``-'' reduction and
partially for the ``+'' reduction.


  Much of the recent progress in String Theory can be traced to a precise
strategy: a careful study of the few models known since the beginnings of the
subject, and the abstraction from them of basic properties that one would like
to demand from other models. This could be termed a set of "model-building
rules". The approach corresponds to the fact, often a source of embarrassment
to specialists, that String Theory, born as a set of rules rather than as a set
of principles, has long resisted attempts to reduce it to a logically
satisfying structure.
  Talk presented at the Cargese Summer Institute on Non-Perturbative Methods in
Field Theory, Cargese, France, July 16-30, 1987.


  We propose a novel numerical algorithm for computing the electronic structure
related eigenvalue problem of incommensurate systems. Unlike the conventional
practice that approximates the system by a large commensurate supercell, our
algorithm directly discretizes the eigenvalue problem under the framework of a
plane wave method. The emerging ergodicity and the interpretation from higher
dimensions give rise to many unique features compared to what we have been
familiar with in the periodic system. The numerical results of 1D and 2D
quantum eigenvalue problems are presented to show the reliability and
efficiency of our scheme. Furthermore, the extension of our algorithm to full
Kohn-Sham density functional theory calculations are discussed.


  The contribution of an astrophysics group based in Milan to the science with
the IUE satellite during its almost 20 years lifetime has focussed on high
energy sources, of both galactic (LMXRB, HMXRB, and black hole candidates) and
extragalactic (AGN) nature. The results of this long term research and in
particular of the latest multiwavelength campaigns conducted simultaneously
with IUE are reviewed here.


  The formation of primordial black hole (PBH) dark matter and the generation
of scalar induced secondary gravitational waves (SIGWs) have been studied in
the generic no-scale supergravity inflationary models. By adding an exponential
term to the K\"ahler potential, the inflaton experiences a period of
ultraslow-roll and the amplitude of primordial power spectrum at small scales
is enhanced to $\mathcal{O}(10^{-2})$. The enhanced power spectra of primordial
curvature perturbations can have both sharp and broad peaks. A wide mass range
of PBHs can be produced in our model, and the frequencies of the accompanied
SIGWs are ranged form nanohertz to kilohertz. We show four benchmark points
where the generated PBH masses are around $\mathcal{O}(10^{-16}M_{\odot})$,
$\mathcal{O}(10^{-12}M_{\odot})$, $\mathcal{O}(10^{-2}M_{\odot})$ and
$\mathcal{O}(10^{2}M_{\odot})$. The PBHs with masses around
$\mathcal{O}(10^{-16}M_{\odot})$ and $ \mathcal{O}(10^{-12}M_{\odot})$ can make
up almost all the dark matter, and the accompanied SIGWs can be probed by the
upcoming space-based gravitational wave observatory. Also, the SIGWs
accompanied with the formation of stellar mass PBHs can be used to interpret
the stochastic GW background in the nanohertz band, detected by the North
American Nanohertz Observatory for gravitational waves, and can be tested by
future interferometric gravitational wave observatory.


  I give a geometric construction of certain first order natural dynamical
observables in multifield cosmological models with arbitrary target space
topology and discuss a system of related dynamical approximations and regimes
for such models.


  We study F-term inflation in M-theory with and without five-brane moduli
fields. We show the slow rolling condition is not satisfied in M-theory without
five-brane moduli fields, but it can be satisfied in the case with
non-vanishing F-terms of five-brane moduli fields.


  Let $\mathbf{f} = \left(f_1, \dots, f_p\right) $ be a polynomial tuple in
$\mathbb{Q}[z_1, \dots, z_n]$ and let $d = \max_{1 \leq i \leq p} \deg f_i$. We
consider the problem of computing the set of asymptotic critical values of the
polynomial mapping, with the assumption that this mapping is dominant,
$\mathbf{f}: z \in \mathbb{K}^n \to (f\_1(z), \dots, f\_p(z)) \in \mathbb{K}^p$
where $\mathbb{K}$ is either $\mathbb{R}$ or $\mathbb{C}$. This is the set of
values $c$ in the target space of $\mathbf{f}$ such that there exists a
sequence of points $(\mathbf{x}_i)_{i\in \mathbb{N}}$ for which
$\mathbf{f}(\mathbf{x}_i)$ tends to $c$ and $\|\mathbf{x}_i\| \kappa {\rm d}
\mathbf{f}(\mathbf{x}_i))$ tends to $0$ when $i$ tends to infinity where ${\rm
d} \mathbf{f}$ is the differential of $\mathbf{f}$ and $\kappa$ is a function
measuring the distance of a linear operator to the set of singular linear
operators from $\mathbb{K}^n$ to $\mathbb{K}^p$. Computing the union of the
classical and asymptotic critical values allows one to put into practice
generalisations of Ehresmann's fibration theorem. This leads to natural and
efficient applications in polynomial optimisation and computational real
algebraic geometry. Going back to previous works by Kurdyka, Orro and Simon, we
design new algorithms to compute asymptotic critical values. Through
randomisation, we introduce new geometric characterisations of asymptotic
critical values. This allows us to dramatically reduce the complexity of
computing such values to a cost that is essentially $O(d^{2n(p+1)})$ arithmetic
operations in $\mathbb{Q}$. We also obtain tighter degree bounds on a
hypersurface containing the asymptotic critical values, showing that the degree
is at most $p^{n-p+1}(d-1)^{n-p}(d+1)^{p}$. Next, we show how to apply these
algorithms to unconstrained polynomial optimisation problems and the problem of
computing sample points per connected component of a semi-algebraic set defined
by a single inequality/inequation. We report on the practical capabilities of
our implementation of this algorithm. It shows how the practical efficiency
surpasses the current state-of-the-art algorithms for computing asymptotic
critical values by tackling examples that were previously out of reach.


  We study boundary value problems posed in a semistrip for the elliptic
sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in
two variables. We use the method introduced by one of the authors, which
provides a substantial generalization of the inverse scattering transform and
can be used for the analysis of boundary as opposed to initial-value problems.
We first express the solution in terms of a $2\times 2$ matrix Riemann-Hilbert
problem formulated in terms of both the Dirichlet and the Neumann boundary
values on the boundary of a semistrip. We then concentrate on the case that the
prescribed boundary conditions are zero along the unbounded sides of the
semistrip and constant along the bounded side; in this particular case we show
that the "jump matrices" of the above Riemann-Hilbert problem can be expressed
explicitly in terms of the width of the semistrip and the constant value of the
solution along the bounded side. This Riemann-Hilbert problem has a unique
solution.


  We revisit the problem of \emph{missing mass concentration}, developing a new
method of estimating concentration of heterogenic sums, in spirit of celebrated
Rosenthal's inequality. As a result we slightly improve the state-of-art bounds
due to Ben-Hamou at al., and simplify the proofs.


  The extraction of transverse momentum dependent distributions (TMDs) in
semi-inclusive deep inelastic scattering (SIDIS) is complicated by the presence
of both initial- and final-state nonperturbative physics. We recently proposed
measuring jets (instead of hadrons) as a solution, showing that for the
Winner-Take-All jet axis the same factorization formulae valid for hadrons
applied to jets of arbitrary size. This amounts to simply replacing TMD
fragmentation functions by our TMD jet functions. In this paper we present the
calculation of these jet functions at one loop. We obtain phenomenological
results for $e^+e^- \to$ dijet (Belle II, LEP) and SIDIS (HERA, EIC) with a
jet, building on the arTeMiDe code. Surprisingly, we find that the limit of
large jet radius describes the full $R$ results extremely well, and we extract
the two-loop jet function in this limit using Event2, allowing us to achieve
N$^3$LL accuracy. We demonstrate the perturbative convergence of our
predictions and explore the kinematic dependence of the cross section. Finally,
we investigate the sensitivity to nonperturbative physics, demonstrating that
jets are a promising probe of proton structure.


  This paper presents CRESM, a novel collision resolution method for decoding
collided packets in random-access wireless networks. In a collision,
overlapping signals from several sources are received simultaneously at a
receiver. CRESM exploits symbol misalignment among the overlapping signals to
recover the individual packets. CRESM can be adopted in 802.11 networks without
modification of the transmitter design; only a simple DSP technique is needed
at the receiver to decode the overlapping signals. Our simulations indicate
that CRESM has better BER performance than the simplistic Successive
Interference Cancellation (SIC) technique that treats interference as noise,
for almost all SNR regimes. The implication of CRESM for random-access
networking is significant: in general, using CRESM to resolve collisions of up
to n packets, network throughput can be boosted by more than n times if the
transmitters are allowed to transmit more aggressively in the MAC protocol.


  We consider an approach to deciding isomorphism of rigid n-vertex graphs (and
related isomorphism problems) by solving a nonabelian hidden shift problem on a
quantum computer using the standard method. Such an approach is arguably more
natural than viewing the problem as a hidden subgroup problem. We prove that
the hidden shift approach to rigid graph isomorphism is hard in two senses.
First, we prove that Omega(n) copies of the hidden shift states are necessary
to solve the problem (whereas O(n log n) copies are sufficient). Second, we
prove that if one is restricted to single-register measurements, an exponential
number of hidden shift states are required.


  Machine learning has recently made significant strides in reducing design
cycle time for complex products. Ship design, which currently involves years
long cycles and small batch production, could greatly benefit from these
advancements. By developing a machine learning tool for ship design that learns
from the design of many different types of ships, tradeoffs in ship design
could be identified and optimized. However, the lack of publicly available ship
design datasets currently limits the potential for leveraging machine learning
in generalized ship design. To address this gap, this paper presents a large
dataset of thirty thousand ship hulls, each with design and functional
performance information, including parameterization, mesh, point cloud, and
image representations, as well as thirty two hydrodynamic drag measures under
different operating conditions. The dataset is structured to allow human input
and is also designed for computational methods. Additionally, the paper
introduces a set of twelve ship hulls from publicly available CAD repositories
to showcase the proposed parameterizations ability to accurately reconstruct
existing hulls. A surrogate model was developed to predict the thirty two wave
drag coefficients, which was then implemented in a genetic algorithm case study
to reduce the total drag of a hull by sixty percent while maintaining the shape
of the hulls cross section and the length of the parallel midbody. Our work
provides a comprehensive dataset and application examples for other researchers
to use in advancing data driven ship design.


  We present a decoherence-based interpretation for the quantum Zeno effect
(QZE) where measurements are dynamically treated as dispersive couplings of the
measured system to the apparatus, rather than the von Neumann's projections. It
is found that the explicit dependence of the survival probability on the
decoherence time quantitatively distinguishes this dynamic QZE from the usual
one based on projection measurements. By revisiting the cavity-QED experiment
of the QZE [J. Bernu, et al., Phys. Rev. Lett, 101, 180402 (2008)], we suggest
an alternative scheme to verify our theoretical consideration that frequent
measurements slow down the increase of photon number inside a microcavity due
to the nondemolition couplings with the atoms in large detuning.


  Optimum nuclear parton distributions are obtained by analyzing available
experimental data on electron and muon deep inelastic scattering (DIS). The
distributions are given at Q^2=1 GeV^2 with a number of parameters, which are
determined by a chi^2 analysis of the data. Valence-quark distributions are
relatively well determined at medium x, but they are slightly dependent on the
assumed parametrization form particularly at small x. Although antiquark
distributions are shadowed at small x, their behavior is not obvious at medium
x from the F_2 data. The gluon distributions could not be restricted well by
the inclusive DIS data; however, the analysis tends to support the gluon
shadowing at small x. We provide analytical expressions and computer
subroutines for calculating the nuclear parton distributions, so that other
researchers could use them for applications to other high-energy nuclear
reactions.


  Microstructure reconstruction is a key enabler of process-structure-property
linkages, a central topic in materials engineering. Revisiting classical
optimization-based reconstruction techniques,they are recognized as a powerful
framework to reconstruct random heterogeneous media, especially due to their
generality and controllability. The stochasticity of the available approaches
is, however, identified as a performance bottleneck. In this work,
reconstruction is approached as a differentiable optimization problem, where
the error of a generic prescribed descriptor is minimized under consideration
of its derivative. As an exemplary descriptor, a suitable differentiable
version of spatial correlations is formulated, along with a multigrid scheme to
ensure scalability. The applicability of differentiable optimization realized
through this descriptor is demonstrated using a wide variety of heterogeneous
media, achieving exact statistical equivalence with errors as low as 0 in a
short time. We conclude that, while still in an early stage of development,
this approach has the potential to significantly alleviate the computational
effort currently associated with reconstructing general random heterogeneous
media.


  We consider the classical problem of sequential resource allocation where a
decision maker must repeatedly divide a budget between several resources, each
with diminishing returns. This can be recast as a specific stochastic
optimization problem where the objective is to maximize the cumulative reward,
or equivalently to minimize the regret. We construct an algorithm that is {\em
adaptive} to the complexity of the problem, expressed in term of the regularity
of the returns of the resources, measured by the exponent in the {\L}ojasiewicz
inequality (or by their universal concavity parameter). Our
parameter-independent algorithm recovers the optimal rates for strongly-concave
functions and the classical fast rates of multi-armed bandit (for linear reward
functions). Moreover, the algorithm improves existing results on stochastic
optimization in this regret minimization setting for intermediate cases.


  The cross-section for inclusive phi meson production in pp collisions at a
centre-of-mass energy of sqrt(s) = 7 TeV has been measured with the LHCb
detector at the Large Hadron Collider. The differential cross-section is
measured as a function of the phi transverse momentum p_T and rapidity y in the
region 0.6 < p_T < 5.0 GeV/c and 2.44 < y < 4.06. The cross-section for
inclusive phi production in this kinematic range is sigma(pp -> phi X) = 1758
pm 19(stat) ^{+43}_{-14}(syst) pm 182(scale) microbarn, where the first
systematic uncertainty depends on the p_T and y region and the second is
related to the overall scale. Predictions based on the Pythia 6.4 generator
underestimate the cross-section.


  We give a simple argument that if a quasiperiodic multi-frequency
Schr\"odinger cocycle is reducible to a constant rotation for almost all
energies with respect to the density of states measure, then the spectrum of
the dual operator is purely point for Lebesgue almost all values of the ergodic
parameter $\theta$. The result holds in the $L^2$ setting provided, in
addition, that the conjugation preserves the fibered rotation number.
Corollaries include localization for (long-range) 1D analytic potentials with
dual ac spectrum and Diophantine frequency as well as a new result on
multidimensional localization.


  We analyse the respective benefits and drawbacks of ground-based and
space-based transit surveys for extrasolar planets. Based on simple but
realistic assumptions about the fraction of lower main sequence stars harboring
telluric and giant planets within the outer limit of the habitable zone, we
predict the harvests of fictitious surveys with three existing wide field
optical and near-IR cameras: the CFHT-Megacam, SUBARU-Suprime and VISTA-IR. An
additional promising instrument is considered, VISTA-Vis, currently under
development. The results are compared with the harvests predicted under exactly
the same assumptions, for the space missions COROT and KEPLER. We show that
ground-based wide field surveys may discover more giant planets than space
missions. However, space surveys seem to constitute the best strategy to search
for telluric planets. In this respect, the KEPLER mission appears 50 times more
efficient than any of the ground--based surveys considered here. KEPLER might
even discover telluric planets in the habitable zone of their host star.


  Smart glasses have become more prevalent as they provide an increasing number
of applications for users. They store various types of private information or
can access it via connections established with other devices. Therefore, there
is a growing need for user identification on smart glasses. In this paper, we
introduce a low-power and minimally-obtrusive system called SonicID, designed
to authenticate users on glasses. SonicID extracts unique biometric information
from users by scanning their faces with ultrasonic waves and utilizes this
information to distinguish between different users, powered by a customized
binary classifier with the ResNet-18 architecture. SonicID can authenticate
users within 0.12 seconds, with an energy consumption of 19.8 mAs per trial. A
user study involving 24 participants confirms that SonicID achieves a true
positive rate of 96.5%, a false positive rate of 4.1%, and a balanced accuracy
of 96.2% using just 4 minutes of training data collected for each new user.
This performance is relatively consistent across different remounting sessions
and days. Given this promising performance, we further discuss the potential
applications of SonicID and methods to improve its performance in the future.


  Two separated sequences of blue straggler stars (BSSs) have been revealed by
Ferraro et al. (2009) in the color-magnitude diagram (CMD) of the Milky Way
globular cluster M30. Their presence has been suggested to be related to the
two BSS formation channels (namely, collisions and mass-transfer in close
binaries) operating within the same stellar system. The blue sequence was
indeed found to be well reproduced by collisional BSS models. In contrast, no
specific models for mass transfer BSSs were available for an old stellar system
like M30. Here we present binary evolution models, including case-B mass
transfer and binary merging, specifically calculated for this cluster. We
discuss in detail the evolutionary track of a $0.9+0.5 M_\odot$ binary, which
spends approximately 4 Gyr in the BSS region of the CMD of a 13 Gyr old
cluster. We also run Monte-Carlo simulations to study the distribution of mass
transfer BSSs in the CMD and to compare it with the observational data. Our
results show that: (1) the color and magnitude distribution of synthetic mass
transfer BSSs defines a strip in the CMD that nicely matches the observed red
BSS sequence, thus providing strong support to the mass transfer origin for
these stars; (2) the CMD distribution of synthetic BSSs never attains the
observed location of the blue BSS sequence, thus reinforcing the hypothesis
that the latter formed through a different channel (likely collisions); (3)
most ($\sim 60\%$) of the synthetic BSSs are produced by mass-transfer models,
while the remaining $< 40\%$ requires the contribution from merger models.


  Klauder's recent generalization of the harmonic oscillator coherent states
[J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems,
requiring some additional structure if applied to systems with degeneracies.
The author suggests how this structure could be added, and applies the complete
method to the hydrogen atom problem. To illustrate how a certain degree of
freedom in the construction may be exercised, states are constructed which are
initially localized and evolve semi-classically, and whose long time evolution
exhibits "fractional revivals."


  Vision Transformers (ViTs) are built on the assumption of treating image
patches as ``visual tokens" and learn patch-to-patch attention. The patch
embedding based tokenizer has a semantic gap with respect to its counterpart,
the textual tokenizer. The patch-to-patch attention suffers from the quadratic
complexity issue, and also makes it non-trivial to explain learned ViTs. To
address these issues in ViT, this paper proposes to learn Patch-to-Cluster
attention (PaCa) in ViT. Queries in our PaCa-ViT starts with patches, while
keys and values are directly based on clustering (with a predefined small
number of clusters). The clusters are learned end-to-end, leading to better
tokenizers and inducing joint clustering-for-attention and
attention-for-clustering for better and interpretable models. The quadratic
complexity is relaxed to linear complexity. The proposed PaCa module is used in
designing efficient and interpretable ViT backbones and semantic segmentation
head networks. In experiments, the proposed methods are tested on ImageNet-1k
image classification, MS-COCO object detection and instance segmentation and
MIT-ADE20k semantic segmentation. Compared with the prior art, it obtains
better performance in all the three benchmarks than the SWin and the PVTs by
significant margins in ImageNet-1k and MIT-ADE20k. It is also significantly
more efficient than PVT models in MS-COCO and MIT-ADE20k due to the linear
complexity. The learned clusters are semantically meaningful. Code and model
checkpoints are available at https://github.com/iVMCL/PaCaViT.


  We study production of dark relics during reheating after the end of
inflation in a system consisting of a non-minimally coupled spectator scalar
field and the inflaton. We derive a set of renormalized quantum transport
equations for the one-point function and the two-point function of the
spectator field and solve them numerically. We find that our system can embody
both tachyonic and parametric instabilities. The former is an expected result
due to the non-minimal coupling, but the latter displays new features driven by
a novel interplay of the two-point function with the Ricci scalar. We find that
when the parametric instability driven by the two-point function takes place,
it dominates the total particle production. The quantitative results are also
found to be highly sensitive to the model parameters.


  Muon spin spectroscopy is one of the most powerful tools to investigate the
microscopic properties of superconductors. In this manuscript, an overview on
some of the main achievements obtained by this technique in the iron-based
superconductors (IBS) are presented. It is shown how the muons allow to probe
the whole phase diagram of IBS, from the magnetic to the superconducting phase,
and their sensitivity to unravel the modifications of the magnetic and the
superconducting order parameters, as the phase diagram is spanned either by
charge doping, by an external pressure or by introducing magnetic and
non-magnetic impurities. Moreover, it is highlighted that the muons are unique
probes for the study of the nanoscopic coexistence between magnetism and
superconductivity taking place at the crossover between the two ground-states.


  Given a wedge V with generic edge in a submanifold M of $C^N$, in general,
CR-functions on V do not extend to a wedge in $C^N$ in the direction of each
nontrivial value of the Levi form of M as was recently observed by Eastwood and
Graham. In this paper we propose an invariant geometric way of selecting those
Levi form directions that are responsible for the extension. These are the Levi
form directions of the complex tangent vectors, whose complex planes intersect
the tangent cone to the wedge in angles larger than $\pi/2$. We show by several
examples the optimality of this criterion. Applications to regularity of
CR-functions are also given generalizing the edge-of-the-wedge theorem of
Ajrapetyan-Henkin.


  We give a detailed description of a novel method for time-resolved
experiments on single non-luminescent nanoparticles. The method is based on the
combination of pump-probe spectroscopy and a common-path interferometer. In our
interferometer, probe and reference arms are separated in time and polarization
by a birefringent crystal. The interferometer, fully described by an analytical
model, allows us to separately detect the real and imaginary contributions to
the signal. We demonstrate the possibilities of the setup by time-resolved
detection of single gold nanoparticles as small as 10 nm in diameter, and of
acoustic oscillations of particles larger than 40 nm in diameter.


  Synchronization in networks of coupled oscillators is a widely studied topic
with extensive scientific and engineering applications. In this paper, we study
the frequency synchronization problem for networks of Kuramoto oscillators with
arbitrary topology and heterogeneous edge weights. We propose a novel
equivalent transcription for the equilibrium synchronization equation. Using
this transcription, we develop a power series expansion to compute the
synchronized solution of the Kuramoto model as well as a sufficient condition
for the strong convergence of this series expansion. Truncating the power
series provides (i) an efficient approximation scheme for computing the
synchronized solution, and (ii) a simple-to-check, statistically-correct
hierarchy of increasingly accurate synchronization tests. This hierarchy of
tests provides a theoretical foundation for and generalizes the best-known
approximate synchronization test in the literature. Our numerical experiments
illustrate the accuracy and the computational efficiency of the truncated
series approximation compared to existing iterative methods and existing
synchronization tests.


  We propose a scheme to control quantum coherence of a two-component
Bose-Einstein condensate (BEC) by a single impurity atom immersed in the BEC.
We show that the single impurity atom can act as a single atom valve (SAV) to
control quantum coherence of the two-component BEC. It is demonstrated that the
SAV can realize the on-demand control over quantum coherence at an arbitrary
time. Specially, it is found that the SAV can also control higher-order quantum
coherence of two-component BEC. We investigate the long-time evolution of
quantum coherence of the two-component BEC. It is indicated that the single
impurity atom can induce collapse and revival phenomenon of quantum coherence
of the two-component BEC. Collapse-revival configurations of quantum coherence
can be manipulated by the initial-state parameters of the impurity atom and the
impurity-BEC interaction strengths.


  We show that a version of the nearly Minimal Supersymmetric Standard Model
(nMSSM), extended only in the singlet sector to include the additional
superfields of right-handed neutrinos and very heavy Dirac particles conserving
$B-L$, admits a viable scenario for Dirac leptogenesis and naturally small
Dirac neutrino masses. The origin of the ($B-L$)-conserving high singlet
neutrino scale and the desired supersymmetry breaking terms is associated with
dynamical supersymmetry breaking in the hidden sector.


  We reanalyze cosmology of a non-minimally coupled massive scalar field which
was originally discussed by Futamase and Maeda in the context of chaotic
inflation scenario. We find a new type of inflationary solution where inflation
occurs inside a domain wall. This new solution relaxes constraints on the
coupling constant for successful inflation.


  We extend variational quantum optimization algorithms for Quadratic
Unconstrained Binary Optimization problems to the class of Mixed Binary
Optimization problems. This allows us to combine binary decision variables with
continuous decision variables, which, for instance, enables the modeling of
inequality constraints via slack variables. We propose two heuristics and
introduce the Transaction Settlement problem to demonstrate them. Transaction
Settlement is defined as the exchange of securities and cash between parties
and is crucial to financial market infrastructure. We test our algorithms using
classical simulation as well as real quantum devices provided by the IBM
Quantum Computation Center.


  We report on measurements of the collisional properties of a mixture of
$^{133}$Cs and $^{87}$Rb atoms in a magnetic trap at $\mu\mathrm{K}$
temperatures. By selectively evaporating the Rb atoms using a radio-frequency
field, we achieved sympathetic cooling of Cs down to a few $\mu\mathrm{K}$. The
inter-species collisional cross-section was determined through rethermalization
measurements, leading to an estimate of $a_s=595 a_0$ for the s-wave scattering
length for Rb in the $|F=2, m_F=2>$ and Cs in the $|F=4, m_F=4>$ magnetic
states. We briefly speculate on the prospects for reaching Bose-Einstein
condensation of Cs inside a magnetic trap through sympathetic cooling.


  We have studied the nuclei of 28 radio galaxies from the 3CR sample in the UV
band. Unresolved nuclei (central compact cores, CCC) are observed in 10 of the
13 FR I, and in 5 of the 15 FR II. All sources that do not have a CCC in the
optical, do not have a CCC in the UV. Two FR I (3C 270 and 3C 296) have a CCC
in the optical but do not show the UV counterpart. Both of them show large
dusty disks observed almost edge-on, possibly implying that they play a role in
obscuring the nuclear emission. We have measured optical-UV spectral indices
alpha_o,UV between ~0.6 and ~7.0. BLRG have the flattest spectra and their
values of alpha_o,UV are also confined to a very narrow range. This is
consistent with radiation produced in a geometrically thin, optically thick
accretion disk. On the other hand, FR I nuclei, which are most plausibly
originated by synchrotron emission from the inner relativistic jet, show a wide
range of alpha_o,UV. There is a clear trend with orientation in that sources
observed almost edge-on or with clear signs of dust absorption have the
steepest spectra. These observations imply that in FR I obscuration can be
present, but the obscuring material is not in a ``standard'' geometrically
thick torus. The most striking difference between these absorbing structures
and the classic AGN ``tori'' resides in the lower optical depth of the FR I
obscuring material.


  Superparamagnetic tunnel junctions are important devices for a range of
emerging technologies, but most existing compact models capture only their mean
switching rates. Capturing qualitatively accurate analog dynamics of these
devices will be important as the technology scales up. Here we present results
using a one-dimensional overdamped Langevin equation that captures statistical
properties of measured time traces, including voltage histograms, drift and
diffusion characteristics as measured with Kramers-Moyal coefficients, and
dwell times distributions. While common macrospin models are more
physically-motivated magnetic models than the Langevin model, we show that for
the device measured here, they capture even fewer of the measured experimental
behaviors.


  The aim of this note is to give a simplified proof of the induced version of
the Ramsey theorem for vector spaces first proved by H. J. Pr\"{o}mel.


  Lorentz violation (LV) is predicted by some quantum gravity theories, where
photon dispersion relation is modified, and the speed of light becomes
energy-dependent. Consequently, it results in a tiny time delay between high
energy photons and low energy ones. Very high energy (VHE) photon emissions
from cosmological distance can amplify these tiny LV effects into observable
quantities. Here we analyze four VHE $\gamma$-ray bursts (GRBs) from Fermi
observations, and briefly review the constraints from three TeV flares of
active galactic nuclei (AGNs) as well. One step further, we present a first
robust analysis of VHE GRBs taking the intrinsic time lag caused by sources
into account, and give an estimate to quantum gravity energy $\sim 2 \times
10^{17}$ GeV for linear energy dependence, and $\sim 5 \times 10^9$ GeV for
quadratic dependence. However, the statistics is not sufficient due to the lack
of data, and further observational results are desired to constrain LV effects
better.


  We consider a bounded domain $\Omega$ of $\mathbb{R}^N$, $N\geq 3$, and $h$ a
continuous function on $\Omega$. Let $\Gamma$ be a closed curve contained in
$\Omega$. We study existence of positive solutions $u\in H^1_0(\Omega)$ to the
equation $$ -\Delta u+h u=\rho^{-\sigma}_\Gamma u^{2^*_\sigma-1} \qquad
\textrm{ in } \Omega $$ where $2^*_\sigma:=\frac{2(N-\sigma)}{N-2}$, $\sigma\in
(0,2)$, and $\rho_\Gamma$ is the distance function to $\Gamma$. For $N\geq 4$,
we find a sufficient condition, given by the local geometry of the curve, for
the existence of a ground-state solution. In the case $N=3$, we obtain
existence of ground-state solution provided the trace of the regular part of
the Green of $-\Delta+h$ is positive at a point of the curve.


  A comprehensive study of the $S$-wave heavy tetraquark states with identical
quarks and antiquarks, specifically $QQ{\bar Q'}\bar Q'$ ($Q, Q'=c,b$), $QQ\bar
s\bar s$/$\bar Q\bar Q ss$, and $QQ\bar q\bar q$/$\bar Q\bar Q qq$ ($q=u,d$),
are studied in a unified constituent quark model. This model contains the
one-gluon exchange and confinement potentials. The latter is modeled as the sum
of all two-body linear potentials. We employ the Gaussian expansion method to
solve the full four-body Schr\"{o}dinger equations, and search bound and
resonant states using the complex-scaling method. We then identify $3$ bound
and $62$ resonant states. The bound states are all $QQ\bar q\bar q$ states with
the isospin and spin-parity quantum numbers $I(J^P)=0(1^+)$: two bound
$bb\bar{q}\bar{q}$ states with the binding energies, 153 MeV and 4 MeV below
the $BB^*$ threshold, and a shallow $cc\bar{q}\bar{q}$ state at $-15$ MeV from
the $DD^*$ threshold. The deeper $bb\bar q \bar q$ bound state aligns with the
lattice QCD predictions, while $cc\bar q\bar q$ bound state, still has a much
larger binding energy than the recently observed $T^+_{cc}$ by LHCb
collaboration. No bound states are identified for the $QQ\bar Q'\bar Q'$,
$QQ\bar s\bar s$ and $QQ\bar q\bar q$ with $I=1$. Our analysis shows that the
bound $QQ\bar Q'\bar Q'$ states are more probable with a larger mass ratio,
$m_Q/m_{Q'}$. Experimental investigation for these states is desired, which
will enrich our understanding of hadron spectroscopy and probe insights into
the confinement mechanisms within tetraquarks.


  Once you have invented digital money, you may need a ledger to track who owns
what -- and an interface to that ledger so that users of your money can
transact. On the Tezos blockchain this implies: a smart contract (distributed
program), storing in its state a ledger to map owner addresses to token
quantities, and standardised entrypoints to transact on accounts.
  A bank does a similar job -- it maps account numbers to account quantities
and permits users to transact -- but in return the bank demands trust, it
incurs expense to maintain a centralised server and staff, it uses a
proprietary interface ... and it may speculate using your money and/or display
rent-seeking behaviour. A blockchain ledger is by design decentralised,
inexpensive, open, and it won't just bet your tokens on risky derivatives
(unless you ask).
  The FA1.2 standard is an open standard for ledger-keeping smart contracts on
the Tezos blockchain. Several FA1.2 implementations already exist.
  Or do they? Is the standard sensible and complete? Are the implementations
correct? And what are they implementations \emph{of}? The FA1.2 standard is
written in English, a specification language favoured by wet human brains but
notorious for its incompleteness and ambiguity when rendered into dry and
unforgiving code.
  In this paper we report on a formalisation of the FA1.2 standard as a Coq
specification, and on a formal verification of three FA1.2-compliant smart
contracts with respect to that specification. Errors were found and ambiguities
were resolved; but also, there now exists a \emph{mathematically precise} and
battle-tested specification of the FA1.2 ledger standard.
  We will describe FA1.2 itself, outline the structure of the Coq theories --
which in itself captures some non-trivial and novel design decisions of the
development -- and review the detailed verification of the implementations.


  The Ising model, originally developed as a spin-glass model for ferromagnetic
elements, has gained popularity as a network-based model for capturing
dependencies in agents' outputs. Its increasing adoption in healthcare and the
social sciences has raised privacy concerns regarding the confidentiality of
agents' responses. In this paper, we present a novel
$(\varepsilon,\delta)$-differentially private algorithm specifically designed
to protect the privacy of individual agents' outcomes. Our algorithm allows for
precise estimation of the natural parameter using a single network through an
objective perturbation technique. Furthermore, we establish regret bounds for
this algorithm and assess its performance on synthetic datasets and two
real-world networks: one involving HIV status in a social network and the other
concerning the political leaning of online blogs.


  Self-supervised monocular depth estimation has been widely investigated to
estimate depth images and relative poses from RGB images. This framework is
attractive for researchers because the depth and pose networks can be trained
from just time sequence images without the need for the ground truth depth and
poses.
  In this work, we estimate the depth around a robot (360 degree view) using
time sequence spherical camera images, from a camera whose parameters are
unknown. We propose a learnable axisymmetric camera model which accepts
distorted spherical camera images with two fisheye camera images. In addition,
we trained our models with a photo-realistic simulator to generate ground truth
depth images to provide supervision. Moreover, we introduced loss functions to
provide floor constraints to reduce artifacts that can result from reflective
floor surfaces. We demonstrate the efficacy of our method using the spherical
camera images from the GO Stanford dataset and pinhole camera images from the
KITTI dataset to compare our method's performance with that of baseline method
in learning the camera parameters.


  We study hypersurfaces with fractional mean curvature in N-dimensional
Euclidean space. These hypersurfaces are critical points of the fractional
perimeter under a volume constraint. We use local inversion arguments to prove
existence of smooth branches of multiply-periodic hypersurfaces bifurcating
from suitable parallel hyperplanes.