  We study here the error of numerical integration on metric measure spaces
adapted to a decomposition of the space into disjoint subsets. We consider both
the error for a single given function, and the worst case error for all
functions in a given class of potentials. The main tools are the classical
Marcinkiewicz-Zygmund inequality and ad hoc definitions of function spaces on
metric measure spaces. The same techniques are used to prove the existence of
point distributions in metric measure spaces with small $L^p$ discrepancy with
respect to certain classes of subsets, for example metric balls.


  Graph contrastive learning is a general learning paradigm excelling at
capturing invariant information from diverse perturbations in graphs. Recent
works focus on exploring the structural rationale from graphs, thereby
increasing the discriminability of the invariant information. However, such
methods may incur in the mis-learning of graph models towards the
interpretability of graphs, and thus the learned noisy and task-agnostic
information interferes with the prediction of graphs. To this end, with the
purpose of exploring the intrinsic rationale of graphs, we accordingly propose
to capture the dimensional rationale from graphs, which has not received
sufficient attention in the literature. The conducted exploratory experiments
attest to the feasibility of the aforementioned roadmap. To elucidate the
innate mechanism behind the performance improvement arising from the
dimensional rationale, we rethink the dimensional rationale in graph
contrastive learning from a causal perspective and further formalize the
causality among the variables in the pre-training stage to build the
corresponding structural causal model. On the basis of the understanding of the
structural causal model, we propose the dimensional rationale-aware graph
contrastive learning approach, which introduces a learnable dimensional
rationale acquiring network and a redundancy reduction constraint. The
learnable dimensional rationale acquiring network is updated by leveraging a
bi-level meta-learning technique, and the redundancy reduction constraint
disentangles the redundant features through a decorrelation process during
learning. Empirically, compared with state-of-the-art methods, our method can
yield significant performance boosts on various benchmarks with respect to
discriminability and transferability. The code implementation of our method is
available at https://github.com/ByronJi/DRGCL.


  In this study, we introduce an intelligent Test Time Augmentation (TTA)
algorithm designed to enhance the robustness and accuracy of image
classification models against viewpoint variations. Unlike traditional TTA
methods that indiscriminately apply augmentations, our approach intelligently
selects optimal augmentations based on predictive uncertainty metrics. This
selection is achieved via a two-stage process: the first stage identifies the
optimal augmentation for each class by evaluating uncertainty levels, while the
second stage implements an uncertainty threshold to determine when applying TTA
would be advantageous. This methodological advancement ensures that
augmentations contribute to classification more effectively than a uniform
application across the dataset. Experimental validation across several datasets
and neural network architectures validates our approach, yielding an average
accuracy improvement of 1.73% over methods that use single-view images. This
research underscores the potential of adaptive, uncertainty-aware TTA in
improving the robustness of image classification in the presence of viewpoint
variations, paving the way for further exploration into intelligent
augmentation strategies.


  We study the Glauber dynamics at zero temperature of spins placed on the
vertices of an uncorrelated network with a power-law degreedistribution.
Application of mean-field theory yields as main prediction that for symmetric
disordered initial conditions the mean time to reach full order is finite or
diverges as a logarithm of the system size N, depending on the exponent of the
degree distribution. Extensive numerical simulations contradict these results
and clearly show that the mean-field assumption is not appropriate to describe
this problem.


  Piecewise divergence-free nonconforming virtual elements are designed for
Stokes problem in any dimensions. After introducing a local energy projector
based on the Stokes problem and the stabilization, a divergence-free
nonconforming virtual element method is proposed for Stokes problem. A detailed
and rigorous error analysis is presented for the discrete method. An important
property in the analysis is that the local energy projector commutes with the
divergence operator. With the help of a divergence-free interpolation operator
onto a generalized Raviart-Thomas element space, a pressure-robust
nonconforming virtual element method is developed by simply modifying the right
hand side of the previous discretization. A reduced virtual element method is
also discussed. Numerical results are provided to verify the theoretical
convergence.


  Let A be an abelian variety defined over a number field k and F a finite
Galois extension of k. Let p be a prime number. Then under certain
not-too-stringent conditions on A and F we investigate the explicit Galois
structure of the p-primary Selmer group of A over F. We also use the results so
obtained to derive new bounds on the growth of the Selmer rank of A over
extensions of k.


  In this paper, we study relay selection and power allocation in two-way
relaying networks consisting of a source, a destination and multiply
half-duplex decode-and-forward (DF) relays. A transmission model with three
time subslots is purposely introduced. In the first subslot, selected relay
applies time-switching protocol to harvest radio frequency energy radiated by
source and destination; in the remaining subslots, selected relay facilitates
source and destination to exchange information. Due to finite-size data buffer
and finite-size battery of relay, an optimal relay selection and power
allocation policy is proposed, in order to maximize networks sum-throughput.
One obstacle is the inherent non-convex property of the underlying
sum-throughput optimization problem. By carefully decoupling the multiplicative
variables and relaxing binary variable to a real number, we convert this
problem into a convex optimization one and then Karush-Kuhn-Tucker (KKT)
conditions are used to solve it. Extensive simulations have been conducted to
demonstrate the improved sum-throughput with our proposed strategy.


  We discuss stability of spherically symmetric static solutions in Newtonian
limit of Jordan, Brans-Dicke field equations. The behavior of the stable
equilibrium solutions for the spherically symmetric configurations considered
here, it emerges that the more compact a model is, the more stable it is.
Moreover, linear stability analysis shows the existence of stable
configurations for any polytropic index.


  We prove that every quasiconformal mapping from the harmonic $\beta$-Bloch
space between the unit ball and a spatial domain with $C^1$ boundary is
globally $\alpha$-H\"older continuous for $\alpha<1-\beta$, with the H\"older
coefficient that does not depend neither on the mapping nor on $\beta$. An
analogous result also holds for Lipschitz continuous, quasiconformal harmonic
mappings for $\alpha <1$. This extends some results from the complex plane
obtained by Warschawski in \cite{Warschawski} for conformal mappings and Kalaj
in \cite{Kalaj6} for quasiconformal harmonic mappings.


  The {\em rank $n$ swapping algebra} is a Poisson algebra defined on the set
of ordered pairs of points of the circle using linking numbers, whose geometric
model is given by a certain subspace of $(\mathbb{K}^n \times
\mathbb{K}^{n*})^r/\operatorname{GL}(n,\mathbb{K})$. For any ideal
triangulation of $D_k$---a disk with $k$ points on its boundary, using
determinants, we find an injective Poisson algebra homomorphism from the
fraction algebra generated by the Fock--Goncharov coordinates for
$\mathcal{X}_{\operatorname{PGL}_n,D_k}$ to the rank $n$ swapping multifraction
algebra for $r=k\cdot(n-1)$ with respect to the (Atiyah--Bott--)Goldman Poisson
bracket and the swapping bracket. This is the building block of the general
surface case. Two such injective Poisson algebra homomorphisms related to two
ideal triangulations $\mathcal{T}$ and $\mathcal{T}'$ are compatible with each
other under the flips.


  Topological spin textures such as skyrmions hold high potential for use as
magnetically active elements in diverse near-future applications. While
skyrmions in metallic multilayers attract great attention in this context,
unleashing the myriad potential of skyrmions for various applications requires
the discovery and customization of alternative host system paradigms. Here we
developed and applied a chemical method to synthesize octahedral particles of
the chiral insulating skyrmion host Cu2OSeO3 with both narrow size
distribution, and tailored dimensions approaching the nanoscale. Combining
magnetometry and neutron scattering experiments with micromagnetic simulations,
we show that the bulk phase diagram of Cu2OSeO3 changes dramatically below
octahedral heights of 400 nm. Further particle size-dependent regimes are
identified where various topological spin textures such as skyrmions, merons
and bobbers can stabilize, prior to a lower critical octahedral height of
approx. 190 nm below which no topological spin texture is found stable. These
findings suggest conditions under which sparse topological spin textures
confined to chiral magnet nanoparticles can be stable, and provide fresh
potential for insulator-based application paradigms.


  Electromagnetic source imaging (ESI) requires solving a highly ill-posed
inverse problem. To seek a unique solution, traditional ESI methods impose
various forms of priors that may not accurately reflect the actual source
properties, which may hinder their broad applications. To overcome this
limitation, in this paper a novel data-synthesized spatio-temporally
convolutional encoder-decoder network method termed DST-CedNet is proposed for
ESI. DST-CedNet recasts ESI as a machine learning problem, where discriminative
learning and latent-space representations are integrated in a convolutional
encoder-decoder network (CedNet) to learn a robust mapping from the measured
electroencephalography/magnetoencephalography (E/MEG) signals to the brain
activity. In particular, by incorporating prior knowledge regarding dynamical
brain activities, a novel data synthesis strategy is devised to generate
large-scale samples for effectively training CedNet. This stands in contrast to
traditional ESI methods where the prior information is often enforced via
constraints primarily aimed for mathematical convenience. Extensive numerical
experiments as well as analysis of a real MEG and Epilepsy EEG dataset
demonstrate that DST-CedNet outperforms several state-of-the-art ESI methods in
robustly estimating source signals under a variety of source configurations.


  We propose scattering matrices for N=1 supersymmetric integrable quantum
field theories in 1+1 dimensions which involve unstable particles in their
spectra. By means of the thermodynamic Bethe ansatz we analyze the ultraviolet
behaviour of some of these theories and identify the effective Virasoro central
charge of the underlying conformal field theories.


  In this paper we report on a measurement of the Cotton Mouton effect of water
vapour. Measurement performed at room temperature ($T=301$ K) with a wavelength
of 1064 nm gave the value $\Delta n_u = (6.67 \pm 0.45) \cdot 10^{-15}$ for the
unit magnetic birefringence (1 T magnetic field and atmospheric pressure).


  A Feynman-Kac-type formula for a L\'evy and an infinite dimensional Gaussian
random process associated with a quantized radiation field is derived. In
particular, a functional integral representation of $e^{-t\PF}$ generated by
the Pauli-Fierz Hamiltonian with spin $\han$ in non-relativistic quantum
electrodynamics is constructed. When no external potential is applied $\PF$
turns translation invariant and it is decomposed as a direct integral $\PF =
\int_\BR^\oplus \PF(P) dP$. The functional integral representation of
$e^{-t\PF(P)}$ is also given. Although all these Hamiltonians include spin,
nevertheless the kernels obtained for the path measures are scalar rather than
matrix expressions. As an application of the functional integral
representations energy comparison inequalities are derived.


  We provide a quantum picture for the emergence of a bouncing cosmology,
according to the idea that a semiclassical behavior of the Universe towards the
singularity is not available in many relevant Minisuperspace models. In
particular, we study the Bianchi I model in vacuum adopting the isotropic
Misner variable as an internal clock for the quantum evolution. The isomorphism
between the Wheeler-DeWitt equation in this Minisuperspace representation and
the Klein-Gordon one for a relativistic scalar field allows to identify the
positive and negative frequency solutions as associated to the collapsing and
expanding Universe respectively. We clarify how any Bianchi I localized wave
packet unavoidably spreads when the singularity is approached and therefore the
semiclassical description of the model evolution in the Planckian region loses
its predictability. Then, we calculate the transition amplitude that a
collapsing Universe is turned into an expanding one, according to the standard
techniques of relativistic quantum mechanics, thanks to the introduction of an
ekpyrotic-like matter component which mimics a time-dependent potential term
and breaks the frequency separation. In particular, the transition probability
of this "Quantum Big Bounce" acquires a maximum value when the mean values of
the momenta conjugate to the anisotropies in the collapsing Universe are close
enough to the corresponding mean values in the expanding one, depending on the
variances of the in-going and out-going Universe wave packets. This symmetry
between the pre-Bounce and post-Bounce mean values reflects what happens in the
semiclassical bouncing cosmology, with the difference that here the connection
of the two branches takes place on a pure probabilistic level.


  In this paper, we focus on a novel knowledge reuse scenario where the
knowledge in the source schema needs to be translated to a semantically
heterogeneous target schema. We refer to this task as "knowledge translation"
(KT). Unlike data translation and transfer learning, KT does not require any
data from the source or target schema. We adopt a probabilistic approach to KT
by representing the knowledge in the source schema, the mapping between the
source and target schemas, and the resulting knowledge in the target schema all
as probability distributions, specially using Markov random fields and Markov
logic networks. Given the source knowledge and mappings, we use standard
learning and inference algorithms for probabilistic graphical models to find an
explicit probability distribution in the target schema that minimizes the
Kullback-Leibler divergence from the implicit distribution. This gives us a
compact probabilistic model that represents knowledge from the source schema as
well as possible, respecting the uncertainty in both the source knowledge and
the mapping. In experiments on both propositional and relational domains, we
find that the knowledge obtained by KT is comparable to other approaches that
require data, demonstrating that knowledge can be reused without data.


  Time-delay strong lensing provides a unique way to directly measure the
Hubble constant ($H_{0}$). The precision of the $H_{0}$ measurement depends on
the uncertainties in the time-delay measurements, the mass distribution of the
main deflector(s), and the mass distribution along the line of sight. Tie and
Kochanek (2018) have proposed a new microlensing effect on time delays based on
differential magnification of the coherent accretion disc variability of the
lensed quasar. If real, this effect could significantly broaden the uncertainty
on the time delay measurements by up to $30\%$ for lens systems such as
PG1115+080, which have relatively short time delays and monitoring over several
different epochs. In this paper we develop a new technique that uses the
time-delay ratios and simulated microlensing maps within a Bayesian framework
in order to limit the allowed combinations of microlensing delays and thus to
lessen the uncertainties due to the proposed effect. We show that, under the
assumption of Tie and Kochanek (2018), the uncertainty on the time-delay
distance ($D_{\Delta t}$, which is proportional to 1/$H_{0}$) of short
time-delay ($\sim18$ days) lens, PG1115+080, increases from $\sim7\%$ to
$\sim10\%$ by simultaneously fitting the three time-delay measurements from the
three different datasets across twenty years, while in the case of long
time-delay ($\sim90$ days) lens, the microlensing effect on time delays is
negligible as the uncertainty on $D_{\Delta t}$ of RXJ1131-1231 only increases
from $\sim2.5\%$ to $\sim2.6\%$.


  Let (X_0,B_0) be the canonical limit of a one-parameter family of stable
pairs, provided by the log Minimal Model Program. We prove that X_0 is S2 and
that [B_0] is S_1, as an application of a general local statement: if
(X,B+\epsilon D) is log canonical and D is Q-Cartier then D is S2 and [B] \cap
D is S1, i.e. has no embedded components. When B has coefficients smaller than
1, examples due to Hacking and Hassett show that B_0 may indeed have embedded
primes. We resolve this problem by introducing a category of stable
branchpairs. We prove that the corresponding moduli functor is proper for
families with normal generic fiber.


  For H\"older continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of
finite type and $\Theta\subset \mathbb \R^d$ we consider a parametrized family
of potentials $\{F_\theta= f_0+\sum_{i=1}^d \theta_i f_i : \theta\in \Theta\}$.
We show that the maximum likelihood estimator of $\theta$ for a family of Gibbs
measures with potentials $F_\theta$ is consistent and determine its asymptotic
distribution under the associated shift-invariant distribution. A second part
discusses applications; from confidence intervals through testing problems to
connections to Bernoulli distributions and stationary Markov chains.


  Spectral geometric methods have brought revolutionary changes to the field of
geometry processing. Of particular interest is the study of the Laplacian
spectrum as a compact, isometry and permutation-invariant representation of a
shape. Some recent works show how the intrinsic geometry of a full shape can be
recovered from its spectrum, but there are approaches that consider the more
challenging problem of recovering the geometry from the spectral information of
partial shapes. In this paper, we propose a possible way to fill this gap. We
introduce a learning-based method to estimate the Laplacian spectrum of the
union of partial non-rigid 3D shapes, without actually computing the 3D
geometry of the union or any correspondence between those partial shapes. We do
so by operating purely in the spectral domain and by defining the union
operation between short sequences of eigenvalues. We show that the approximated
union spectrum can be used as-is to reconstruct the complete geometry [MRC*19],
perform region localization on a template [RTO*19] and retrieve shapes from a
database, generalizing ShapeDNA [RWP06] to work with partialities. Working with
eigenvalues allows us to deal with unknown correspondence, different sampling,
and different discretizations (point clouds and meshes alike), making this
operation especially robust and general. Our approach is data-driven and can
generalize to isometric and non-isometric deformations of the surface, as long
as these stay within the same semantic class (e.g., human bodies or horses), as
well as to partiality artifacts not seen at training time.


  The pseudo-rapidity dependence of the elliptic flow at various excitation
energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is
one of the surprising results that has not been explained before in terms of
hydrodynamical models. Here we show that these data are in agreement with
theoretical predictions based on perfect fluid hydrodynamics.
  We also show that these PHOBOS data satisfy the universal scaling relation
predicted by the Buda-Lund hydrodynamical model, based on exact solutions of
perfect fluid hydrodynamics.


  Restoration of images degraded by spatially varying blurs is an issue of
increasing importance in the context of photography, satellite or microscopy
imaging. One of the main difficulty to solve this problem comes from the huge
dimensions of the blur matrix. It prevents the use of naive approaches for
performing matrix-vector multiplications. In this paper, we propose to
approximate the blur operator by a matrix sparse in the wavelet domain. We
justify this approach from a mathematical point of view and investigate the
approximation quality numerically. We finish by showing that the sparsity
pattern of the matrix can be pre-defined, which is central in tasks such as
blind deconvolution.


  We construct a divided difference operator using GKM theory. This generalizes
the classical divided difference operator for the cohomology of the complete
flag variety. This construction proves a special case of a recent conjecture of
Shareshian and Wachs. Our methods are entirely combinatorial and algebraic, and
rely heavily on the combinatorics of root systems and Bruhat order.


  We present a full set of wave equations describing a dense Bose fluid,
applicable both to non- ideal gases and to liquid 4He. The phonon spectrum in
liquid 4He is found and the fraction of condensed particles is calculated at
zero temperature for a wide range of densities. The theory also yields the
ground-state energy for the quantum liquid 4He in agreement to high accuracy
with Monte Carlo simulations and experimental data at low pressure. We also
present the derivation of a generalized Hartree-Fock equation describing roton
clusters in low temperature liquid 4He, allowing us to confirm that, at low
enough temperatures and for a wide range of pressures, the stable clusters
consist of 13 bound atoms.


  Static flexoelectric effect in a finite sample of a solid is addressed in
terms of phenomenological theory for the case of a thin plate subjected to
bending. It has been shown that despite an explicit asymmetry inherent to the
bulk constitutive electromechanical equations which take into account the
flexoelectric coupling, the electromechanical response for a finite sample is
"symmetric". "Symmetric" means that if a sensor and an actuator are made of a
flexoelectric element, performance of such devices can be characterized by the
same effective piezoelectric coefficient. This behavior is consistent with the
thermodynamic arguments offered earlier, being in conflict with the current
point of view on the matter in literature. This result was obtained using
standard mechanical boundary conditions valid for the case where the
polarization vanishes at the surface. It was shown that, for the case where
there is the polarization is nonzero at the surface, the aforementioned
symmetry of electromechanical response may be violated if standard mechanical
boundary conditions are used, leading to a conflict with the thermodynamic
arguments. It was argued that this conflict may be resolved when using modified
mechanical boundary conditions. It was also shown that the contribution of
surface piezoelectricity to the flexoelectric response of a finite sample is
expected to be comparable to that of the static bulk contribution (including
the material with high values of the dielectric constant) and to scale as the
bulk value of the dielectric constant (similar to the bulk contribution). This
finding implies that if the experimentally measured flexoelectric coefficient
scales as the dielectric constant of the material, this does not imply that the
measured flexoelectric response is controlled by the static bulk contribution
to the flexoelectric effect.


  Deep reinforcement learning (DRL) is a promising approach for developing
legged locomotion skills. However, the iterative design process that is
inevitable in practice is poorly supported by the default methodology. It is
difficult to predict the outcomes of changes made to the reward functions,
policy architectures, and the set of tasks being trained on. In this paper, we
propose a practical method that allows the reward function to be fully
redefined on each successive design iteration while limiting the deviation from
the previous iteration. We characterize policies via sets of Deterministic
Action Stochastic State (DASS) tuples, which represent the deterministic policy
state-action pairs as sampled from the states visited by the trained stochastic
policy. New policies are trained using a policy gradient algorithm which then
mixes RL-based policy gradients with gradient updates defined by the DASS
tuples. The tuples also allow for robust policy distillation to new network
architectures. We demonstrate the effectiveness of this iterative-design
approach on the bipedal robot Cassie, achieving stable walking with different
gait styles at various speeds. We demonstrate the successful transfer of
policies learned in simulation to the physical robot without any dynamics
randomization, and that variable-speed walking policies for the physical robot
can be represented by a small dataset of 5-10k tuples.


  In this paper, we consider statistical estimation of time-inhomogeneous
aggregate Markov models. Unaggregated models, which corresponds to Markov
chains, are commonly used in multi-state life insurance to model the biometric
states of an insured. By aggregating microstates to each biometric state, we
are able to model dependencies between transitions of the biometric states as
well as the distribution of occupancy in these. This allows for non--Markovian
modelling in general. Since only paths of the macrostates are observed, we
develop an expectation-maximization (EM) algorithm to obtain maximum likelihood
estimates of transition intensities on the micro level. Special attention is
given to a semi-Markovian case, known as the reset property, which leads to
simplified estimation procedures where EM algorithms for inhomogeneous
phase-type distributions can be used as building blocks. We provide a numerical
example of the latter in combination with piecewise constant transition rates
in a three-state disability model with data simulated from a time-inhomogeneous
semi-Markov model. Comparisons of our fits with more classic GLM-based fits as
well as true and empirical distributions are provided to relate our model with
existing models and their tools.


  Given a huge set of applicants, how should a firm allocate sequential resume
screenings, phone interviews, and in-person site visits? In a tiered interview
process, later stages (e.g., in-person visits) are more informative, but also
more expensive than earlier stages (e.g., resume screenings). Using accepted
hiring models and the concept of structured interviews, a best practice in
human resources, we cast tiered hiring as a combinatorial pure exploration
(CPE) problem in the stochastic multi-armed bandit setting. The goal is to
select a subset of arms (in our case, applicants) with some combinatorial
structure. We present new algorithms in both the probably approximately correct
(PAC) and fixed-budget settings that select a near-optimal cohort with provable
guarantees. We show via simulations on real data from one of the largest
US-based computer science graduate programs that our algorithms make better
hiring decisions or use less budget than the status quo.


  Ground state energies are obtained using the unrestricted Hartree Fock method
for up to four interacting electrons parabolically confined in a quantum dot
subject to a magnetic field. Restoring spin and rotational symmetries we
recover Hund first rule. With increasing magnetic field, crossovers between
ground states with different quantum numbers are found for fixed electron
number that are not reproduced by the unrestricted Hartree Fock approximation.
These are consistent with the ones obtained with more refined techniques. We
confirm the presence of a spin blockade due to a spin mismatch in the ground
states of three and four electrons.


  We provide a generalisation of Kripke semantics for Petr Hajek's Basic Logic
and prove soundness and completeness of the same with respect to our semantics.
We find this semantics easily specialises to the linearly-ordered Kripke frames
for Godel-Dummett logic, which BL properly contains. Our soundness, deduction
theorem and completeness arguments further strengthen this analogy. This paper
extends the insights of our previous paper, "A Kripke Semantics for
Intuitionistic Lukasiewicz logic," to the case of Hajeks' BL.


  One of the main neutron sources for the astrophysical s-process is the
reaction 13C({\alpha},n)16O, taking place in thermally pulsing Asymptotic Giant
Branch stars at temperatures around 90 MK. To model the nucleosynthesis during
this process the reaction cross section needs to be known in the 150-230keV
energy window (Gamow peak). At these sub-Coulomb energies cross section direct
measurements are severely affected by the low event rate, making us rely on
input from indirect methods and extrapolations from higher-energy direct data.
This leads to an uncertainty in the cross section at the relevant energies too
high to reliably constrain the nuclear physics input to s-process calculations.
We present the results from a new deep-underground measurement of
13C({\alpha},n)16O, covering the energy range 230-300keV, with drastically
reduced uncertainties over previous measurements and for the first time
providing data directly inside the s-process Gamow peak. Selected stellar
models have been computed to estimate the impact of our revised reaction rate.
For stars of nearly solar composition, we find sizeable variations of some
isotopes, whose production is influenced by the activation of close-by
branching points that are sensitive to the neutron density, in particular the
two radioactive nuclei 60Fe and 205Pb, as well as 152Gd


  PtBi$_2$ is a polymorphic system with interesting electronic properties. Here
we report optimized crystal growth and structural characterization of
pyrite-type and trigonal modification of PtBi$_2$. Selected area electron
diffraction, X-ray powder diffraction and further Rietveld refinement confirms
that trigonal PtBi$_2$ crystallizes in non-centrosymmetric $P31m$ space group,
pyrite-type PtBi$_2$ in $Pa\bar{3}$ space group. Series of
Pt$_{1-x}$Rh$_x$Bi$_2$ samples was obtained for $x=0, 0.03, 0.35$ in the
trigonal PtBi$_2$ structure. These Pt$_{1-x}$Rh$_x$Bi$_2$ compounds become
superconducting where critical temperature increases from $T_c=600$ mK for
$x=0$ up to $T_c=2.7$ K for $x=0.35$. Furthermore we calculate the electronic
band structure, using the structure parameters obtained. The calculated density
of states (DOS) shows a minimum for the stochiometric compound at the Fermi
level. These findings warrant further research by broader array of experimental
techniques, as well as the effect of the substitution on the non-trivial band
structure.


  We show that under repeated differentiation, the zeros of the Selberg
$\Xi$-function become more evenly spaced out, but with some scaling towards the
origin. We do this by showing the high derivatives of the $\Xi$-function
converge to the cosine function, and this is achieved by expressing a product
of Gamma functions as a single Fourier transform.


  The growth in the number of users in mobile communications networks and the
rise in the traffic generated by each user, are responsible for the increasing
importance of Mobility Management. Within Mobility Management, the main
objective of Location Management is to enable the roaming of the user in the
coverage area. In this paper, we analyze the savings in Location Management
costs obtained leveraging the users' statistics, in comparison with the
classical strategy. In particular, we introduce two novel algorithms to obtain
the Beta parameters (useful terms in the calculation of location update costs
for different Location Management strategies), utilizing a geographical study
of relative positions of the cells within the location areas. Eventually, we
discuss the influence of the different network parameters on the total Location
Management costs savings for both the radio interface and the fixed network
part, providing useful guidelines for the optimum design of the networks.


  We consider the problem of data classification where the training set
consists of just a few data points. We explore this phenomenon mathematically
and reveal key relationships between the geometry of an AI model's feature
space, the structure of the underlying data distributions, and the model's
generalisation capabilities. The main thrust of our analysis is to reveal the
influence on the model's generalisation capabilities of nonlinear feature
transformations mapping the original data into high, and possibly infinite,
dimensional spaces.


  An experiment is proposed to show that after initial frequency and
polarization selection, classical thermal light from two independent sources
can be made path-polarization entangled. Such light will show new
intensity-intensity correlations involving both path and polarization phases,
formally similar to those for four-particle GHZ states. For fixed polarization
phases, the correlations reduce to the Hanbury Brown-Twiss phase correlations.
It is also shown that these classical correlations violate noncontextuality.


  Elasto-inertial turbulence (EIT) is a new, two-dimensional chaotic flow state
observed in polymer solutions with possible connections to inertialess elastic
turbulence and drag-reduced Newtonian turbulence. In this Letter, we argue that
the origins of EIT are fundamentally different from Newtonian turbulence by
finding a dynamical connection between EIT and an elasto-inertial linear
instability recently found at high Weissenberg numbers (Garg et al. Phys. Rev.
Lett. 121, 024502, 2018). This link is established by isolating the first known
exact coherent structures in viscoelastic parallel flows - nonlinear
elasto-inertial travelling waves (TWs) - borne at the linear instability and
tracking them down to substantially lower Weissenberg numbers where EIT exists.
These TWs have a distinctive ``arrowhead'' structure in the polymer stretch
field and can be clearly recognised, albeit transiently, in EIT, as well as
being attractors for EIT dynamics if the Weissenberg number is sufficiently
large. Our findings suggest that the dynamical systems picture in which
Newtonian turbulence is built around the co-existence of many (unstable) simple
invariant solutions populating phase space carries over to EIT, though these
solutions rely on elasticity to exist.


  We present a slightly more general version of Boole's additive formula for
factorials as a simple consequence of Lagrange's Interpolating Polynomial
theorem.


  Conversational recommender systems (CRS) aim to provide the recommendation
service via natural language conversations. To develop an effective CRS,
high-quality CRS datasets are very crucial. However, existing CRS datasets
suffer from the long-tail issue, \ie a large proportion of items are rarely (or
even never) mentioned in the conversations, which are called long-tail items.
As a result, the CRSs trained on these datasets tend to recommend frequent
items, and the diversity of the recommended items would be largely reduced,
making users easier to get bored.
  To address this issue, this paper presents \textbf{LOT-CRS}, a novel
framework that focuses on simulating and utilizing a balanced CRS dataset (\ie
covering all the items evenly) for improving \textbf{LO}ng-\textbf{T}ail
recommendation performance of CRSs. In our approach, we design two pre-training
tasks to enhance the understanding of simulated conversation for long-tail
items, and adopt retrieval-augmented fine-tuning with label smoothness strategy
to further improve the recommendation of long-tail items. Extensive experiments
on two public CRS datasets have demonstrated the effectiveness and
extensibility of our approach, especially on long-tail recommendation.


  Invariant geodesic orbit Finsler $(\alpha,\beta)$ metrics $F$ which arise
from Riemannian geodesic orbit metrics $\alpha$ on spheres are determined. The
relation of Riemannian geodesic graphs with Finslerian geodesic graphs proved
in a previous work is now illustrated with explicit constructions. Interesting
examples are found such that $(G/H,\alpha)$ is Riemannian geodesic orbit space,
but for the geodesic orbit property of $(G/H,F)$ the isometry group has to be
extended. It is also shown that projective spaces other than ${\mathbb{R}}P^n$
do not admit invariant purely Finsler $(\alpha,\beta)$ metrics.


  We present laboratory mid-infrared transmission/absorption spectra obtained
from matrix of the hydrated Murchison CM meteorite experimentally shocked at
peak pressures of 10 to 49 GPa, and compare them to astronomical observations
of circumstellar dust in different stages of the formation of planetary
systems. The laboratory spectra of the Murchison samples exhibit characteristic
changes in the infrared features. A weakly shocked sample (shocked at 10 GPa)
shows almost no changes from the unshocked sample dominated by hydrous silicate
(serpentine). Moderately shocked samples (21 to 34 GPa) have typical serpentine
features gradually replaced by bands of amorphous material and olivine with
increasing shock pressure. A strongly shocked sample (36 GPa) shows major
changes due to decomposition of the serpentine and due to devolatilization. A
shock melted sample (49 GPa) shows features of olivine recrystallized from
melted material. The spectra of highly shocked Murchison samples (36 and 49
GPa) are similar to those of dust in the debris disks of HD113766 and HD69830,
and the transitional disk of HD100546. The moderately shocked samples (21 to 34
GPa) exhibit spectra similar to those of dust in the debris disks of Beta
Pictoris and BD+20307, and the transitional disk of GM Aur. An average of the
spectra of all Murchison samples (0 to 49 GPa) has a similarity to the spectrum
of the older protoplanetary disk of SU Auriga. In the gas-rich transitional and
protoplanetary disks, the abundances of amorphous silicates and gases have
widely been considered to be a primary property. However, our study suggests
that impact processing may play a significant role in generating secondary
amorphous silicates and gases in those disks. Infrared spectra of the shocked
Murchison samples are also suggesting that the comets also contain shocked
Murchison-like material.


  Research on damage detection of road surfaces has been an active area of
re-search, but most studies have focused so far on the detection of the
presence of damages. However, in real-world scenarios, road managers need to
clearly understand the type of damage and its extent in order to take effective
action in advance or to allocate the necessary resources. Moreover, currently
there are few uniform and openly available road damage datasets, leading to a
lack of a common benchmark for road damage detection. Such dataset could be
used in a great variety of applications; herein, it is intended to serve as the
acquisition component of a physical asset management tool which can aid
governments agencies for planning purposes, or by infrastructure mainte-nance
companies. In this paper, we make two contributions to address these issues.
First, we present a large-scale road damage dataset, which includes a more
balanced and representative set of damages. This dataset is composed of 18,034
road damage images captured with a smartphone, with 45,435 in-stances road
surface damages. Second, we trained different types of object detection
methods, both traditional (an LBP-cascaded classifier) and deep learning-based,
specifically, MobileNet and RetinaNet, which are amenable for embedded and
mobile and implementations with an acceptable perfor-mance for many
applications. We compare the accuracy and inference time of all these models
with others in the state of the art.


  In this paper, by employing Gaussian type estimate of heat kernel, we
establish Krylov's estimate and Khasminskill's estimate for EM algorithm. As
applications, by taking Zvonkin's transformation into account, we investigate
convergence rate of EM algorithm for a class of multidimensional SDEs under
integrability conditions, where the drifts need not to be piecewise Lipschitz
and are much more singular in some sense.


  Supersymmetry predicts the identity of Yukawa and gauge couplings in the QCD
sector: quark-squark-gluino = squark-squark-gluon = quark-quark-gluon. We
examine whether the quark-squark-gluino Yukawa coupling can be determined, by
methods complementary to LHC, by analyzing squark-gluino final states at a TeV
e+e- collider.


  This review presents an entry-level introduction to topological quantum
computation -- quantum computing with anyons. We introduce anyons at the
system-independent level of anyon models and discuss the key concepts of
protected fusion spaces and statistical quantum evolutions for encoding and
processing quantum information. Both the encoding and the processing are
inherently resilient against errors due to their topological nature, thus
promising to overcome one of the main obstacles for the realisation of quantum
computers. We outline the general steps of topological quantum computation, as
well as discuss various challenges faced by it. We also review the literature
on condensed matter systems where anyons can emerge. Finally, the appearance of
anyons and employing them for quantum computation is demonstrated in the
context of a simple microscopic model -- the topological superconducting
nanowire -- that describes the low-energy physics of several experimentally
relevant settings. This model supports localised Majorana zero modes that are
the simplest and the experimentally most tractable types of anyons that are
needed to perform topological quantum computation.


  An exponential interaction is constructed so that one-dimensional atoms and
chains of atoms mimic the general behavior of their three-dimensional
counterparts. Relative to the more commonly used soft-Coulomb interaction, the
exponential greatly diminishes the computational time needed for calculating
highly accurate quantities with the density matrix renormalization group. This
is due to the use of a small matrix product operator and to exponentially
vanishing tails. Furthermore, its more rapid decay closely mimics the screened
Coulomb interaction in three dimensions. Choosing parameters to best match
earlier calculations, we report results for the one dimensional hydrogen atom,
uniform gas, and small atoms and molecules both exactly and in the local
density approximation.


  We study real-time correlators for $N=4$ super Yang Mill fields coupled to a
pair of entangled quarks using holography, in the setup that energy quanta sent
from one quark perturb the quantum state of the fields and affect the other
quark. We make the connection with the ER=EPR conjecture by considering the
situation when two quarks are uniformly accelerating opposite to each other.
The dynamics of quarks, in the gravity dual, is described by the string
worldsheet theory, which in this case has the induced metric describing a
two-sided AdS black hole, or a wormhole. Energy quanta sent by one of the
quarks produce the shock wave on the worldsheet. We find the effect of shock
wave on the boundary field correlators and we discuss the consequence for the
ER=EPR conjecture.


  Cold collisions of ground state oxygen molecules with Helium have been
investigated in a wide range of cold collision energies (from 1 $\mu$K up to 10
K) treating the oxygen molecule first as a rigid rotor and then introducing the
vibrational degree of freedom. The comparison between the two models shows that
at low energies the rigid rotor approximation is very accurate and able to
describe all the dynamical features of the system. The comparison between the
two models has also been extended to cases where the interaction potential He -
O$_2$ is made artificially stronger. In this case vibration can perturb rate
constants, but fine-tuning the rigid rotor potential can alleviate the
discrepancies between the two models.


  We study the simplest optomechanical system with a focus on the bistable
regime. The covariance matrix formalism allows us to study both cooling and
entanglement in a unified framework. We identify two key factors governing
entanglement, namely the bistability parameter, i.e. the distance from the end
of a stable branch in the bistable regime, and the effective detuning, and we
describe the optimum regime where entanglement is greatest. We also show that
in general entanglement is a non-monotonic function of optomechanical coupling.
This is especially important in understanding the optomechanical entanglement
of the second stable branch.


  Parity violation in the cosmic microwave background (CMB) radiation has been
confirmed by recent Planck observation. In this paper, we extend our previous
work [P. Naselsky et al. Astrophys. J. {\bf 749}, 31 (2012)] on the directional
properties of CMB parity asymmetry by considering the Planck data of the CMB
temperature anisotropy. We define six kinds of the directional statistics and
find that they all indicate the odd-parity preference of CMB data. In addition,
we find the preferred axes of all these statistics strongly correlate with the
preferred axes of the CMB kinematic dipole, quadrupole, and octopole. The
alignment between them is confirmed at more than $3\sigma$ confidence level,
which implies that the CMB parity asymmetry, and the anomalies of the CMB
quadrupole and octopole, may have the common physical, contaminated or
systematic origin. In addition, they all should be connected with the possible
contamination of the residual dipole component.


  We consider two problems regarding arithmetic progressions in symmetric sets
in the finite field (product space) model.
  First, we show that a symmetric set $S\subseteq\mathbb{Z}_q^n$ containing
$|S|=\mu\cdot q^n$ elements must contain at least $\delta(q,\mu)\cdot q^n\cdot
2^n$ arithmetic progressions $x,x+d,\ldots,x+(q-1)\cdot d$ such that the
difference $d$ is restricted to lie in $\{0,1\}^n$.
  Second, we show that for prime $p$ a symmetric set $S\subseteq\mathbb{F}^n_p$
with $|S|=\mu\cdot p^n$ elements contains at least $\mu^{C(p)}\cdot p^{2n}$
arithmetic progressions of length $p$. This establishes that the qualitative
behavior of longer arithmetic progressions in symmetric sets is the same as for
progressions of length three.


  We introduce a technique for improving document-level language models (LM) by
leveraging "ancient history": text that is outside the LM's current context
window. We learn an auxiliary function to select spans from the ancient history
which can help the LM to predict future text. The selected text spans are then
copied directly into the LM's context window, replacing less predictive spans.
This method can improve perplexity of pretrained LMs with no updates to the
LM's own parameters. We further observe that an auxiliary function trained in a
specific textual domain like Wikipedia will also work in a substantially
different domain such as scientific publications. With this technique we see a
7 percent perplexity reduction on Wikipedia articles, and a 12 percent
perplexity reduction on scientific texts.


  The free boundary problem for a two-dimensional fluid filtered in porous
media is studied. This is known as the one-phase Muskat problem and is
mathematically equivalent to the vertical Hele-Shaw problem driven by gravity
force. We prove that if the initial free boundary is the graph of a periodic
Lipschitz function, then there exists a global-in-time Lipschitz solution in
the strong $L^\infty_t L^2_x$ sense and it is the unique viscosity solution.
The proof requires quantitative estimates for layer potentials and pointwise
elliptic regularity in Lipschitz domains. This is the first construction of
unique global strong solutions for the Muskat problem with initial data of
arbitrary size.


  The behaviors of coupled oscillators, each of which has periodic motion with
random natural frequency in the absence of coupling, are investigated. Some
novel collective phenomena are revealed. At the onset of instability of the
phase-locking state, simultaneous phase slips of all oscillators and quantized
phase shifts in these phase slips are observed. By incresing the coupling, a
bifurcation tree from high-dimensional quasiperiodicity to chaos to
quasiperiodicity and periodicity is found. Different orders of phase
synchronizations of chaotic oscillators and chaotic clusters play the key role
for constructing this tree structure.


  The oscillatory force F_b^ac on the bottom of a rigid, vertically vibrated,
grain filled column, reveals rich granular dynamics, even when the peak
acceleration of the vibrations is signicantly less than the gravitational
acceleration at the earth's surface. For loose packings or high frequencies,
F_b^ac 's dynamics are dominated by grain motion. For moderate driving
conditions in more compact samples, grain motion is virtually absent, but
F_b^ac nevertheless exhibits strongly nonlinear and hysteretic behavior,
evidencing a granular regime dominated by nontrivial force-network dynamics.


  A model for spontaneous symmetry breaking using a specific form of the
bumblebee model is analyzed in the context of a Schwarzschild background
metric. The resulting back reaction of the symmetry-breaking field on the
metric is computed to second order. Consistency with conventional
(pseudo)Riemannian geometry is demonstrated. This background field is coupled
to fermions via a spin-dependent CPT-violating coupling term of a type commonly
considered in the Standard-Model Extension. The perturbations of various
orbital trajectories are discussed. Specifically, a spin-dependent orbital
velocity is found as well as a spin-dependent precession rate.


  We present a brief review of observational results contributing to modern
ideas on the evolution of stellar activity. Basic laws, derived for both
rotation-age and activity-rotation relationships, allow us to trace how the
activity of low-mass stars changes with age during their stay on the main
sequence. We focus on the evaluation of the activity properties of stars that
could be analogs of the young Sun. Our study includes joint consideration of
different tracers of activity, rotation and magnetic fields of Sun-like stars
of various ages. We identify rotation periods, when the saturated regime of
activity changes to the unsaturated mode, when the solar-type activity is
formed: for G- and K-type stars, they are 1.1 and 3.3 days, respectively. This
corresponds to an age interval of about 0.2-0.6 Gyr, when regular sunspot cycle
began to be established on the early Sun. We discuss properties of the coronal
and chromospheric activity in young Suns. Our evaluation of the EUV-fluxes in
the spectral range of 1350-1750 A shows that the far-UV radiation of the early
Sun was a factor of 7 times more intense than that of the present-day Sun, and
twice higher when the regular sunspot cycle was established. For the young Sun,
we can estimate the possible mass loss rate associated with quasi-steady
outflow as $10^{-12} M_\odot$/yr. The results of observations of the largest
flares on solar-type stars are also discussed, leading to conclusion that the
most powerful phenomena occur on the fast-rotating stars in the saturated
activity regime. Our estimate of the stellar magnetic fields makes it possible
to evaluate the maximal possible flare energy. This could help us better
understand the origin of extreme events on the Sun in the past.


  We consider mixed Monge-Amp\`ere products of quasiplurisubharmonic functions
with analytic singularities, and show that such products may be regularized as
explicit one parameter limits of mixed Monge-Amp\`ere products of smooth
functions, generalizing results of Andersson, B{\l}ocki and the last author in
the case of non-mixed Monge-Amp\`ere products. Connections to the theory of
residue currents, going back to Coleff-Herrera, Passare and others, play an
important role in the proof. As a consequence we get an approximation of Chern
and Segre currents of certain singular hermitian metrics on vector bundles by
smooth forms in the corresponding Chern and Segre classes.


  Click-through rate (CTR) prediction is a critical task in online advertising
systems. A large body of research considers each ad independently, but ignores
its relationship to other ads that may impact the CTR. In this paper, we
investigate various types of auxiliary ads for improving the CTR prediction of
the target ad. In particular, we explore auxiliary ads from two viewpoints: one
is from the spatial domain, where we consider the contextual ads shown above
the target ad on the same page; the other is from the temporal domain, where we
consider historically clicked and unclicked ads of the user. The intuitions are
that ads shown together may influence each other, clicked ads reflect a user's
preferences, and unclicked ads may indicate what a user dislikes to certain
extent. In order to effectively utilize these auxiliary data, we propose the
Deep Spatio-Temporal neural Networks (DSTNs) for CTR prediction. Our model is
able to learn the interactions between each type of auxiliary data and the
target ad, to emphasize more important hidden information, and to fuse
heterogeneous data in a unified framework. Offline experiments on one public
dataset and two industrial datasets show that DSTNs outperform several
state-of-the-art methods for CTR prediction. We have deployed the
best-performing DSTN in Shenma Search, which is the second largest search
engine in China. The A/B test results show that the online CTR is also
significantly improved compared to our last serving model.


  Dataspaces have recently gained adoption across various sectors, including
traditionally less digitized domains such as culture. Leveraging Semantic Web
technologies helps to make dataspaces FAIR, but their complexity poses a
significant challenge to the adoption of dataspaces and increases their cost.
The advent of Large Language Models (LLMs) raises the question of how these
models can support the adoption of FAIR dataspaces. In this work, we
demonstrate the potential of LLMs in dataspaces with a concrete example. We
also derive a research agenda for exploring this emerging field.


  Product quantization-based approaches are effective to encode
high-dimensional data points for approximate nearest neighbor search. The space
is decomposed into a Cartesian product of low-dimensional subspaces, each of
which generates a sub codebook. Data points are encoded as compact binary codes
using these sub codebooks, and the distance between two data points can be
approximated efficiently from their codes by the precomputed lookup tables.
Traditionally, to encode a subvector of a data point in a subspace, only one
sub codeword in the corresponding sub codebook is selected, which may impose
strict restrictions on the search accuracy. In this paper, we propose a novel
approach, named Optimized Cartesian $K$-Means (OCKM), to better encode the data
points for more accurate approximate nearest neighbor search. In OCKM, multiple
sub codewords are used to encode the subvector of a data point in a subspace.
Each sub codeword stems from different sub codebooks in each subspace, which
are optimally generated with regards to the minimization of the distortion
errors. The high-dimensional data point is then encoded as the concatenation of
the indices of multiple sub codewords from all the subspaces. This can provide
more flexibility and lower distortion errors than traditional methods.
Experimental results on the standard real-life datasets demonstrate the
superiority over state-of-the-art approaches for approximate nearest neighbor
search.


  A complex scalar $\lambda$ is said to be an extended eigenvalue of a bounded
linear operator $T$ on a complex Banach space if there is a nonzero operator
$X$ such that $TX= \lambda XT.$ Such an operator $X$ is called an extended
eigenoperator of $T$ corresponding to the extended eigenvalue $\lambda.$ The
purpose of this paper is to give a description of the extended eigenvalues for
the discrete Ces\`aro operator $C_0,$ the finite continuous Ces\`aro operator
$C_1$ and the infinite continuous Ces\`aro operator $C_\infty$ defined on the
complex Banach spaces $\ell^p,$ $L^p[0,1]$ and $L^p[0,\infty)$ for $1 < p
<\infty$ by the expressions \begin{align*} (C_0f)(n) \colon & = \frac{1}{n+1}
\sum_{k=0}^n f(k),\\ (C_1f)(x) \colon & = \frac{1}{x} \int_0^x f(t)\,dt,\\
(C_\infty f)(x) \colon & = \frac{1}{x} \int_0^x f(t)\,dt. \end{align*} It is
shown that the set of extended eigenvalues for $C_0$ is the interval
$[1,\infty),$ for $C_1$ it is the interval $(0,1],$ and for $C_\infty$ it
reduces to the singleton $\{1\}.$


  In this paper we generalize correspondence theorems of Mikhalkin and
Nishinou-Siebert providing a correspondence between algebraic and parameterized
tropical curves. We also give a description of a canonical tropicalization
procedure for algebraic curves motivated by Berkovich's construction of
skeletons of analytic curves. Under certain assumptions, we construct a
one-to-one correspondence between algebraic curves satisfying toric constraints
and certain combinatorially defined objects, called "stacky tropical
reductions", that can be enumerated in terms of tropical curves satisfying
linear constraints. Similarly, we construct a one-to-one correspondence between
elliptic curves with fixed $j$-invariant satisfying toric constraints and
"stacky tropical reductions" that can be enumerated in terms of tropical
elliptic curves with fixed tropical $j$-invariant satisfying linear
constraints. Our theorems generalize previously published correspondence
theorems in tropical geometry, and our proofs are algebra-geometric. In
particular, the theorems hold in large positive characteristic.


  A decentralized coded caching scheme has been proposed by Maddah-Ali and
Niesen, and has been shown to alleviate the load of networks. Recently,
placement delivery array (PDA) was proposed to characterize the coded caching
scheme. In this paper, a neural architecture is first proposed to learn the
construction of PDAs. Our model solves the problem of variable size PDAs using
mechanism of neural attention and reinforcement learning. It differs from the
previous attempts in that, instead of using combined optimization algorithms to
get PDAs, it uses sequence-to-sequence model to learn construct PDAs. Numerical
results are given to demonstrate that the proposed method can effectively
implement coded caching. We also show that the complexity of our method to
construct PDAs is low.


  We use high-resolution N-body simulations to follow the formation and
evolution of tidal streams associated to dwarf spheroidal galaxies (dSphs). The
dSph models are embedded in dark matter (DM) haloes with either a
centrally-divergent 'cusp', or an homogeneous-density 'core'. In agreement with
previous studies, we find that as tides strip the galaxy the evolution of the
half-light radius and the averaged velocity dispersion follows well-defined
tracks that are mainly controlled by the amount of mass lost. Crucially, the
evolutionary tracks behave differently depending on the shape of the DM
profile: at a fixed remnant mass, dSphs embedded in cored haloes have larger
sizes and higher velocity dispersions than their cuspy counterparts. The
divergent evolution is particularly pronounced in galaxies whose stellar
component is strongly segregated within their DM halo and becomes more
disparate as the remnant mass decreases. Our analysis indicates that the DM
profile plays an important role in defining the internal dynamics of tidal
streams. We find that stellar streams associated to cored DM models have
velocity dispersions that lie systematically above their cuspy counterparts.
Our results suggest that the dynamics of streams with known dSph progenitors
may provide strong constraints on the distribution of DM on the smallest
galactic scales.


  We examine a possibility to explain the signals of dark matter direct
detection from DAMA and CoGeNT experiments, under the framework of
supersymmetric extension of the standard model. For this purpose, we introduce
four Higgs doublet fields and assume that one pair of Higgs fields which have
very small vacuum expectation values gives sizable effects for annihilation and
scattering processes of dark matter. We show that the preferred parameter
regions for DAMA and CoGeNT results can be simultaneously explained by
supersymmetric four-Higgs doublet model with the parameters consistent with the
observed value of dark matter relic abundance. The extra Higgs fields
introduced as an explanation of the light dark matter scenario also explain the
Wjj anomaly reported by CDF.


  For circuit-based quantum computation, experimental implementation of
universal set of quantum logic gates with high-fidelity and strong robustness
is essential and central. Quantum gates induced by geometric phases, which
depend only on global properties of the evolution paths, have built-in
noise-resilience features. Here, we propose and experimentally demonstrate
nonadiabatic holonomic single-qubit quantum gates on two dark paths in a
trapped $^{171}\mathrm{Yb}^{+}$ ion based on four-level systems with resonant
drives. We confirm the implementation with measured gate fidelity through both
quantum process tomography and randomized benchmarking methods. Meanwhile, we
find that nontrivial holonomic two-qubit quantum gates can also be realized
within current experimental technologies. Compared with previous
implementations on three-level systems, our experiment share both the advantage
of fast nonadiabatic evolution and the merit of robustness against systematic
errors, and thus retains the main advantage of geometric phases. Therefore, our
experiment confirms a promising method for fast and robust holonomic quantum
computation.


  Predicting the dissolution rates of silicate glasses in aqueous conditions is
a complex task as the underlying mechanism(s) remain poorly understood and the
dissolution kinetics can depend on a large number of intrinsic and extrinsic
factors. Here, we assess the potential of data-driven models based on machine
learning to predict the dissolution rates of various aluminosilicate glasses
exposed to a wide range of solution pH values, from acidic to caustic
conditions. Four classes of machine learning methods are investigated, namely,
linear regression, support vector machine regression, random forest, and
artificial neural network. We observe that, although linear methods all fail to
describe the dissolution kinetics, the artificial neural network approach
offers excellent predictions, thanks to its inherent ability to handle
non-linear data. Overall, we suggest that a more extensive use of machine
learning approaches could significantly accelerate the design of novel glasses
with tailored properties.


  Engineering high-fidelity two-qubit gates is an indispensable step toward
practical quantum computing. For superconducting quantum platforms, one
important setback is the stray interaction between qubits, which causes
significant coherent errors. For transmon qubits, protocols for mitigating such
errors usually involve fine-tuning the hardware parameters or introducing
usually noisy flux-tunable couplers. In this work, we propose a simple scheme
to cancel these stray interactions. The coupler used for such cancellation is a
driven high-coherence resonator, where the amplitude and frequency of the drive
serve as control knobs. Through the resonator-induced-phase (RIP) interaction,
the static ZZ coupling can be entirely neutralized. We numerically show that
such a scheme can enable short and high-fidelity entangling gates, including
cross-resonance CNOT gates within 40 ns and adiabatic CZ gates within 140 ns.
Our architecture is not only ZZ free but also contains no extra noisy
components, such that it preserves the coherence times of fixed-frequency
transmon qubits. With the state-of-the-art coherence times, the error of our
cross-resonance CNOT gate can be reduced to below 1e-4.


  We define a signed count of real rational pseudo-holomorphic curves appearing
in a one-parameter family of real Spin symplectic K3 surfaces. We show that
this count is an invariant of the deformation class of the family. In the case
of a real projective K3 surface, this invariant specializes to count real
rational curves appearing in a linear system on the surface.


  For an operator of a certain class in Hilbert space, we introduce axioms of
an abstract intersection theory, which we prove to be equivalent to the Riemann
Hypothesis concerning the spectrum of that operator. In particular if the
nontrivial zeros of the Riemann zeta-function arise from an operator of this
class, the original Riemann Hypothesis is equivalent to the existence of an
abstract intersection theory.


  We study the Ginzburg-Landau stochastic models in infinite domains with some
special geometry and prove that without the help of external forces there are
stationary measures with non zero current in three or more dimensions.


  Among the diverse progenitor channels leading to Type Ia Supernovae (SNe Ia),
there are explosions originating from white dwarfs with sub-Chandrasekhar
masses. These white dwarfs undergo detonation and explosion triggered by
primary detonation in the helium shell, which has been accreted from a
companion star. The double-detonation model predicts a correlation between the
age of the progenitor system and the near peak brightness: the younger the
exploding progenitors, the brighter the SNe. In this paper, we present our
recent achievements on the study of SNe Ia properties in different locations
within host galactic discs and the estimation of their progenitor population
ages. Observationally, we confirm the validity of the anticipated correlation
between the SN photometry and the age of their progenitors.


  Emerging technologies, such as big data, Internet of things, cloud computing,
mobile Internet, and robotics, breed and expedite new applications and fields.
In the mean while, the long-term prosperity and happiness of human race demands
advanced technologies. In this paper, the aforementioned emerging technologies
are applied to management and governance for the long-term prosperity and
happiness of human race. The term "machine ruling" is coined, introduced, and
justified. Moreover, the framework and architecture of machine ruling are
proposed. Enabling technologies and challenges are discussed.


  Cell-free massive MIMO (CF-M-MIMO) systems represent an evolution of the
classical cellular architecture that has dominated the mobile landscape for
decades. In CF-M-MIMO, a central processing unit (CPU) controls a multitude of
access points (APs) that are irregularly scattered throughout the coverage area
effectively becoming a fully distributed implementation of the M-MIMO
technology. As such, it inherits many of the key properties that have made
M-MIMO one of the physical layer pillars of 5G systems while opening the door
to new features not available in M-MIMO. Among the latest is the possibility of
performing the precoding at the CPU (centralized) or at the APs (distributed)
with the former known to offer much better performance at the cost of having to
collect all the relevant channel state information (CSI) at the CPU. Realistic
deployments of cell-free systems are likely to require more than one CPU when
the area to be covered is large, thus a critical issue that needs to be solved
is how these multiple CPUs should be interconnected. This paper analyzes and
proposes designs for different degrees of interconnectivity among the CPUs for
the specific case of centralized zero-forcing precoding. Results show that a
modest form of CPU interconnection can boost very significantly the max-min
rate performance so prevalent in CF-M-MIMO architectures.


  In this paper, we establish a standard $L^p$-theory of solutions to one
dimensional nonlinear Schr\"odinger equations with the power like nonlinearity.
More precisely, we extend the following three well-known results in the $L^2$
space into $L^p$ setting: 1. Large data local well-posedness for subcritical
nonlinearities, 2. Small data global well-posedness for critical
nonlinearities, 3. Large data global well-posedness if the subcritical
nonlinearity is given by $|u|^{\alpha-1}u$.


  Let $A_\Phi$ be a matrix valued truncated Toeplitz operator-the compression
of multiplication operator to vector-valued model space $H^2(E)\ominus \Theta
H^2(E)$, where $\Theta$ is a matrix valued non constant inner function. Under
supplementary assumptions, we find necessary and sufficient condition that the
product $A_\Phi A_\Psi$ is itself a matrix valued truncated Toeplitz operator.


  It is now well established that FGK post-AGB stars that are surrounded by
both hot and cold dust (as derived from the spectral energy distribution), are
almost always part of a binary system with $100 < P_{orb} < 5000$~days. The
properties and long-term stability of the dust emission requires it to arise
from a gas- and dust-rich, puffed-up and (semi-)stable circumbinary disk. This
interpretation has been confirmed with spatially resolved observations at a
range of wavelengths for various individual objects. Here I present the first
results of the first mid-IR interferometric survey of this class of objects.
Our sample comprises 18 sources, most of which are confirmed binaries and which
cover a range in IR excess. Our analysis clearly shows the compactness of the
dust structures in these systems. We perform a statistical comparison with
radiative transfer disk models, showing that most objects are indeed continuous
disks from the sublimation radius outwards.


  We discuss the concept of the shadow boundary of a centrally symmetric convex
ball $K$ (actually being the unit ball of a Minkowski normed space) with
respect to a direction ${\bf x}$ of the Euclidean n-space $R^n$. We introduce
the concept of general parameter spheres of $K$ corresponding to this direction
and prove that the shadow boundary is a topological manifold if all of the
non-degenerated general parameter spheres are, too. In this case, using the
approximation theorem of cell-like maps we get that they are homeomorphic to
the $(n-2)$-dimensional sphere $S^{(n-2)}$. We also prove that the bisector
(equidistant set of the corresponding normed space) in the direction ${\bf x}$
is homeomorphic to $R^{(n-1)}$ iff all of the non-degenerated general parameter
spheres are $(n-2)$-manifolds implying that if the bisector is a homeomorphic
copy of $R^{(n-1)}$ then the corresponding shadow boundary is a topological
$(n-2)$-sphere.


  Recently discovered long-term oscillations of the solar background magnetic
field associated with double dynamo waves generated in inner and outer layers
of the Sun indicate that the solar activity is heading in the next three
decades (2019-2055) to a Modern grand minimum similar to Maunder one. On the
other hand, a reconstruction of solar total irradiance suggests that since the
Maunder minimum there is an increase in the cycle-averaged total solar
irradiance (TSI) by a value of about $1-1.5$ $Wm^{-2}$ closely correlated with
an increase of the baseline (average) terrestrial temperature. In order to
understand these two opposite trends, we calculated the double dynamo summary
curve of magnetic field variations backward one hundred thousand years allowing
us to confirm strong oscillations of solar activity in regular (11 year) and
recently reported grand (350-400 year) solar cycles caused by actions of the
double solar dynamo. In addition, oscillations of the baseline (zero-line) of
magnetic field with a period of $1950\pm95$ years (a super-grand cycle) are
discovered by applying a running averaging filter to suppress large-scale
oscillations of 11 year cycles. Latest minimum of the baseline oscillations is
found to coincide with the grand solar minimum (the Maunder minimum) occurred
before the current super-grand cycle start. Since then the baseline magnitude
became slowly increasing towards its maximum at $~$2700 to be followed by its
decrease and minimum at $~$3700. These oscillations of the baseline solar
magnetic field are found associated with a long-term solar inertial motion
about the barycenter of the solar system that can lead to a further natural
increase of the terrestrial temperature by 2.5-3.0$^\circ$C.


  Chaos synchronization between Josephson junctions driven by a central
junction is studied under the parameter mismatches and noise. It is
demonstrated that chaos synchronization quality is robust to 10-15 % parameter
mismatches. It is also elucidated that for the intermediary noise intensity
correlation between the synchronized junctions can be even enhanced; however
for larger intensities of noise synchronization quality deteriorates. It is
also established that synchronization quality between some junctions remains
unchanged, despite the fact that all the driven junctions and the driver
junction were subject to the same amount of noise. These results are of certain
importance for obtaining the high power system of Josephson junctions in
real-life situations and are promising for practical applications in the
Terahertz region.


  The essential minimum and equidistribution of small points are two
well-established interrelated subjects in arithmetic geometry. However, there
is lack of an analogue of essential minimum dealing with higher dimensional
subvarieties, and the equidistribution of these is a far less explored topic.
  In this paper, we introduce a new notion of higher dimensional essential
minimum and use it to prove equidistribution of generic and small effective
cycles. The latter generalizes the previous higher dimensional equidistribution
theorems by considering cycles and by allowing more fexibility on the
arithmetic datum.


  The construction of atomically-precise carbon nanostructures holds promise
for developing novel materials for scientific study and nanotechnology
applications. Here we show that graphene origami is an efficient way to convert
graphene into atomically-precise, complex, and novel nanostructures. By
scanning-tunneling-microscope manipulation at low temperature, we repeatedly
fold and unfold graphene nanoislands (GNIs) along arbitrarily chosen direction.
A bilayer graphene stack featuring a tunable twist angle and a tubular edge
connection between the layers are formed. Folding single-crystal GNIs creates
tubular edges with specified chirality and one-dimensional electronic features
similar to those of carbon nanotubes, while folding bi-crystal GNIs creates
well-defined intramolecular junctions. Both origami structural models and
electronic band structures were computed to complement analysis of the
experimental results. The present atomically-precise graphene origami provides
a platform for constructing novel carbon nanostructures with engineered quantum
properties and ultimately quantum machines.


  We explain a highly efficient algorithm for playing the simplest type of dots
and boxes endgame optimally (by which we mean "in such a way so as to maximise
the number of boxes that you take"). The algorithm is sufficiently simple that
it can be learnt and used in over-the-board games by humans. The types of
endgames we solve come up commonly in practice in well-played games on a 5x5
board and were in fact developed by the authors in order to improve their
over-the-board play.


  The dispersion interaction between two point-like particles confined in a
dielectric slab between two plates of another dielectric medium is studied
within a continuum (Lifshitz) theory. The retarded (Casimir-Polder) interaction
at large inter-particle distances is found to be strongly enhanced as the
mismatch between the dielectric permittivities of the two media is increased.
The large-distance interaction is multiplied due to confinement by a factor of
$(33\gamma^{5/2}+13\gamma^{-3/2})/46$ at zero temperature, and by
$(5\gamma^2+\gamma^{-2})/6$ at finite temperature, $\gamma=\ein(0)/\eout(0)$
being the ratio between the static dielectric permittivities of the inner and
outer media. This confinement-induced amplification of the dispersion
interaction can reach several orders of magnitude.


  In this work we present a novel approach to solving concurrent multiagent
planning problems in which several agents act in parallel. Our approach relies
on a compilation from concurrent multiagent planning to classical planning,
allowing us to use an off-the-shelf classical planner to solve the original
multiagent problem. The solution can be directly interpreted as a concurrent
plan that satisfies a given set of concurrency constraints, while avoiding the
exponential blowup associated with concurrent actions. Our planner is the first
to handle action effects that are conditional on what other agents are doing.
Theoretically, we show that the compilation is sound and complete. Empirically,
we show that our compilation can solve challenging multiagent planning problems
that require concurrent actions.


  The main results in this note concern the characterization of the length of
continua 1 (Theorems 2.5) and the parametrization of continua with finite
length (Theorem 4.4). Using these results we give two independent and
relatively elementary proofs of Golab's semicontinuity theorem.


  We apply classical quartet techniques to the problem of phylogenetic
decisiveness and find a value $k$ such that all collections of at least $k$
quartets are decisive. Moreover, we prove that this bound is optimal and give a
lower-bound on the probability that a collection of quartets is decisive.


  Optimal contribution selection (OCS) is a mathematical optimization problem
that aims to maximize the total benefit from selecting a group of individuals
under a constraint on genetic diversity. We are specifically focused on OCS as
applied to forest tree breeding, when selected individuals will contribute
equally to the gene pool. Since the diversity constraint in OCS can be
described with a second-order cone, equal deployment in OCS can be
mathematically modeled as mixed-integer second-order cone programming
(MI-SOCP). If we apply a general solver for MI-SOCP, non-linearity embedded in
OCS requires a heavy computation cost. To address this problem, we propose an
implementation of lifted polyhedral programming (LPP) relaxation and a
cone-decomposition method (CDM) to generate effective linear approximations for
OCS. In particular, CDM successively solves OCS problems much faster than
generic approaches for MI-SOCP. The approach of CDM is not limited to OCS, so
that we can also apply the approach to other MI-SOCP problems.


  The {\em hypermetric cone} is defined as the cone of semimetrics satisfying
the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds
to a ray of this polyhedral cone. The Delaunay polytopes, which correspond to
extreme rays are called {\em extreme}.
  We use this polyhedral cone and the {\em closest vector problem} to present a
new technique that allow to find, from a given extreme Delaunay polytope, some
new ones.
  Then, we show some examples of applications of this technique in
low-dimensions.


  An efficient, low-complexity, soft-output detector for general lattices is
presented, based on their Tanner graph (TG) representations. Closest-point
searches in lattices can be performed as non-binary belief propagation on
associated TGs; soft-information output is naturally generated in the process;
the algorithm requires no backtrack (cf. classic sphere decoding), and extracts
extrinsic information. A lattice's coding gain enables equivalence relations
between lattice points, which can be thereby partitioned in cosets. Total and
extrinsic a posteriori probabilities at the detector's output further enable
the use of soft detection information in iterative schemes. The algorithm is
illustrated via two scenarios that transmit a 32-point, uncoded
super-orthogonal (SO) constellation for multiple-input multiple-output (MIMO)
channels, carved from an 8-dimensional non-orthogonal lattice (a direct sum of
two 4-dimensional checkerboard lattice): it achieves maximum likelihood
performance in quasistatic fading; and, performs close to interference-free
transmission, and identically to list sphere decoding, in independent fading
with coordinate interleaving and iterative equalization and detection. Latter
scenario outperforms former despite the absence of forward error correction
coding---because the inherent lattice coding gain allows for the refining of
extrinsic information. The lattice constellation is the same as the one
employed in the SO space-time trellis codes first introduced for 2-by-2 MIMO by
Ionescu et al., then independently by Jafarkhani and Seshadri. Complexity is
log-linear in lattice dimensionality, vs. cubic in sphere decoders.


  Fourier series approximations of continuous but nonperiodic functions on an
interval suffer the Gibbs phenomenon, which means there is a permanent
oscillatory overshoot in the neighbourhoods of the endpoints. Fourier
extensions circumvent this issue by approximating the function using a Fourier
series which is periodic on a larger interval. Previous results on the
convergence of Fourier extensions have focused on the error in the L2 norm, but
in this paper we analyze pointwise and uniform convergence of Fourier
extensions (formulated as the best approximation in the L2 norm). We show that
the pointwise convergence of Fourier extensions is more similar to Legendre
series than classical Fourier series. In particular, unlike classical Fourier
series, Fourier extensions yield pointwise convergence at the endpoints of the
interval. Similar to Legendre series, pointwise convergence at the endpoints is
slower by an algebraic order of a half compared to that in the interior. The
proof is conducted by an analysis of the associated Lebesgue function, and
Jackson- and Bernstein-type theorems for Fourier extensions. Numerical
experiments are provided. We conclude the paper with open questions regarding
the regularized and oversampled least squares interpolation versions of Fourier
extensions.


  Polaron dephasing processes are investigated in InAs/GaAs dots using
far-infrared transient four wave mixing (FWM) spectroscopy. We observe an
oscillatory behaviour in the FWM signal shortly (< 5 ps) after resonant
excitation of the lowest energy conduction band transition due to coherent
acoustic phonon generation. The subsequent single exponential decay yields long
intraband dephasing times of 90 ps. We find excellent agreement between our
measured and calculated FWM dynamics, and show that both real and virtual
acoustic phonon processes are necessary to explain the temperature dependence
of the polarization decay.


  Quantum information can provide a lens for characterizing the operational
implications of spacetime physics. A well-known result in this area is that
quantum entanglement is degraded in the vicinity of a black hole. This result
treats the black hole and its spacetime as classical. But what if these were to
be treated quantum-mechanically? Here, we show that quantum coherence in black
hole, and thus spacetime, degrees of freedom can limit the degradation of
entanglement, thereby improving the performance of nearby quantum communication
protocols. This finding indicates that quantum features of spacetime could
serve as resources for quantum information processing.


  This study considers the linear stability of Poiseuille-Rayleigh-B\'enard
flows, subjected to a transverse magnetic field to understand the instabilities
that arise from the complex interaction between the effects of shear, thermal
stratification and magnetic damping. This fundamental study is motivated in
part by the desire to enhance heat transfer in the blanket ducts of nuclear
fusion reactors. In pure MHD flows, the imposed transverse magnetic field
causes the flow to become quasi-2D and exhibit disturbances that are localised
to the horizontal walls. However, the vertical temperature stratification in
Rayleigh-B\'enard flows feature convection cells that occupy the interior
region and therefore the addition of this aspect provides an interesting point
for investigation.
  The linearised governing equations are described by the \qtwod\ model
proposed by Sommeria and Moreau (1982) which incorporates a Hartmann friction
term, and the base flows are considered fully developed and 1D. The neutral
stability curves for critical Reynolds and Rayleigh numbers, $Re_c$ and $Ra_c$,
respectively, as functions of Hartmann friction parameter $H$ have been
obtained over $10^{-2}\leq H\leq10^4$. Asymptotic trends are observed as
$H\rightarrow\infty$ following $Re_c\propto H^{\,1/2}$ and $Ra_c\propto H$. The
linear stability analysis reveals multiple instabilities which alter the flow
both within the Shercliff boundary layers and the interior flow, with
structures consistent with features from plane Poiseuille and Rayleigh-B\'enard
flows.


  Large terrestrial planets are expected to have muted topography and deep
oceans, implying that most super-Earths should be entirely covered in water,
so-called waterworlds. This is important because waterworlds lack a silicate
weathering thermostat so their climate is predicted to be less stable than that
of planets with exposed continents. In other words, the continuously habitable
zone for waterworlds is much narrower than for Earth-like planets. A planet's
water is partitioned, however, between a surface reservoir, the ocean, and an
interior reservoir, the mantle. Plate tectonics transports water between these
reservoirs on geological timescales. Degassing of melt at mid-ocean ridges and
serpentinization of oceanic crust depend negatively and positively on seafloor
pressure, respectively, providing a stabilizing feedback on long-term ocean
volume. Motivated by Earth's approximately steady-state deep water cycle, we
develop a two-box model of the hydrosphere and derive steady-state solutions to
the water partitioning on terrestrial planets. Critically, hydrostatic seafloor
pressure is proportional to surface gravity, so super-Earths with a deep water
cycle will tend to store more water in the mantle. We conclude that a
tectonically active terrestrial planet of any mass can maintain exposed
continents if its water mass fraction is less than ~0.2%, dramatically
increasing the odds that super-Earths are habitable. The greatest source of
uncertainty in our study is Earth's current mantle water inventory: the greater
its value, the more robust planets are to inundation. Lastly, we discuss how
future missions can test our hypothesis by mapping the oceans and continents of
massive terrestrial planets.


  Large language models (LLMs) have shown impressive capabilities in natural
language understanding and generation. Their potential for deeper user
understanding and improved personalized user experience on recommendation
platforms is, however, largely untapped. This paper aims to address this gap.
Recommender systems today capture users' interests through encoding their
historical activities on the platforms. The generated user representations are
hard to examine or interpret. On the other hand, if we were to ask people about
interests they pursue in their life, they might talk about their hobbies, like
I just started learning the ukulele, or their relaxation routines, e.g., I like
to watch Saturday Night Live, or I want to plant a vertical garden. We argue,
and demonstrate through extensive experiments, that LLMs as foundation models
can reason through user activities, and describe their interests in nuanced and
interesting ways, similar to how a human would.
  We define interest journeys as the persistent and overarching user interests,
in other words, the non-transient ones. These are the interests that we believe
will benefit most from the nuanced and personalized descriptions. We introduce
a framework in which we first perform personalized extraction of interest
journeys, and then summarize the extracted journeys via LLMs, using techniques
like few-shot prompting, prompt-tuning and fine-tuning. Together, our results
in prompting LLMs to name extracted user journeys in a large-scale industrial
platform demonstrate great potential of these models in providing deeper, more
interpretable, and controllable user understanding. We believe LLM powered user
understanding can be a stepping stone to entirely new user experiences on
recommendation platforms that are journey-aware, assistive, and enabling
frictionless conversation down the line.


  Based on the tick-by-tick price changes of the companies from the U.S. and
from the German stock markets over the period 1998-99 we reanalyse several
characteristics established by the Boston Group for the U.S. market in the
period 1994-95, which serves to verify their space and time-translational
invariance. By increasing the time scales we find a significantly more
accelerated crossover from the power-law (alpha approximately 3) asymptotic
behaviour of the distribution of returns towards a Gaussian, both for the U.S.
as well as for the German stock markets. In the latter case the crossover is
even faster. Consistently, the corresponding autocorrelation functions of
returns and of the time averaged volatility also indicate a faster loss of
memory with increasing time. This route towards efficiency may reflect a
systematic increase of the information processing when going from past to
present.


  We describe a technique that can be used for the fusion of multiple sources
of information as well as for the evaluation and selection of alternatives
under multi-criteria. Three important properties contribute to the uniqueness
of the technique introduced. The first is the ability to do all necessary
operations and aggregations with information that is of a nonnumeric linguistic
nature. This facility greatly reduces the burden on the providers of
information, the experts. A second characterizing feature is the ability
assign, again linguistically, differing importance to the criteria or in the
case of information fusion to the individual sources of information. A third
significant feature of the approach is its ability to be used as method to find
a consensus of the opinion of multiple experts on the issue of concern. The
techniques used in this approach are base on ideas developed from the theory of
approximate reasoning. We illustrate the approach with a problem of project
selection.


  Radio-Frequency Quadrupoles (RFQs) are multi-purpose linear particle
accelerators that simultaneously bunch and accelerate charged particle beams.
They are ubiquitous in accelerator physics, especially as injectors to
higher-energy machines, owing to their impressive efficiency. The design and
optimization of these devices can be lengthy due to the need to repeatedly
perform high-fidelity simulations. Several recent papers have demonstrated that
machine learning can be used to build surrogate models (fast-executing
replacements of computationally costly beam simulations) for order-of-magnitude
computing time speedups. However, while these pilot studies are encouraging,
there is room to improve their predictive accuracy. Particularly, beam summary
statistics such as emittances (an important figure of merit in particle
accelerator physics) have historically been challenging to predict. For the
first time, we present a surrogate model trained on 200,000 samples that yields
<6% mean average percent error for the predictions of all relevant beam output
parameters, solving the problem of poor emittance predictions by identifying
and including hidden variables which were not accounted for previously. These
surrogate models were made possible by using the Julia language and GPU
computing; we briefly discuss both. We demonstrate the utility of surrogate
modeling by performing a multi-objective optimization using our best model as a
callback in the objective function to select an optimal RFQ design. We consider
trade-offs in RFQ performance for various choices of Pareto-optimal design
variables: common issues for any multi-objective optimization scheme. Lastly,
we make recommendations for input data preparation, selection, and neural
network architectures that pave the way for future development of
production-capable surrogate models for RFQs and other particle accelerators.


  Starting from the Fock space representation of hadron bound states in a quark
model, a change of representation is implemented by a unitary transformation
such that the composite hadrons are redescribed by elementary-particle field
operators. Application of the unitary transformation to the microscopic quark
Hamiltonian gives rise to effective hadron-hadron, hadron-quark, and
quark-quark Hamiltonians. An effective baryon Hamiltonian is derived using a
simple quark model. The baryon Hamiltonian is free of the post-prior
discrepancy which usually plagues composite-particle effective interactions.


  In this paper we introduce a new method to study the influence of thermal
conduction and viscous processes in anisotropic gravitational collapse. To this
end we employ the HJR method to solve the Einstein equations. The
Maxwell-Cattaneo type transport equations are used to find the temperature and
bulk and shear viscous pressures. Under some conditions Maxwell-Cattaneo
transport equations comply with relativistic causality. Thus, it is advisable
to use them instead of Eckart transport equations. In the inner layers of the
star the temperature ceases to be sensitive to the boundary condition. This
behavior, which can be explained in terms of the Eddington approximation,
allows us to find the thickness of the neutrinosphere. The dynamics of
collapsing dense stars is deeply influenced by the neutrino emission/absorption
processes. These cool the star and drive it to a new equilibrium state.
Therefore, the calculation of transport coefficients is based on these
processes.


  We present the HOLCF-Prelude, a formalization of a large part of Haskell's
standard prelude in Isabelle/HOLCF. Applying this formalization to the hints
suggested by HLint allows us to certify them formally.


  Extracting building footprints from remote sensing images has been attracting
extensive attention recently. Dominant approaches address this challenging
problem by generating vectorized building masks with cumbersome refinement
stages, which limits the application of such methods. In this paper, we
introduce a new refinement-free and end-to-end building footprint extraction
method, which is conceptually intuitive, simple, and effective. Our method,
termed as BiSVP, represents a building instance with ordered vertices and
formulates the building footprint extraction as predicting the serialized
vertices directly in a bidirectional fashion. Moreover, we propose a
cross-scale feature fusion (CSFF) module to facilitate high resolution and rich
semantic feature learning, which is essential for the dense building vertex
prediction task. Without bells and whistles, our BiSVP outperforms
state-of-the-art methods by considerable margins on three building instance
segmentation benchmarks, clearly demonstrating its superiority. The code and
datasets will be made public available.


  I introduce a simple continuous probability theory based on the
Ginzburg-Landau equation that provides for the first time a common analytical
basis to relate and describe the main features of two seemingly different
phenomena of condensed-matter physics, namely self-organized criticality and
multifractality. Numerical support is given by a comparison with reported
simulation data. Within the theory the origin of self-organized critical
phenomena is analysed in terms of a nonlinear singularity spectrum different
from the typical convex shape due to multifractal measures.


  Serverless computing has emerged as a promising alternative to
infrastructure- (IaaS) and platform-as-a-service (PaaS)cloud platforms for
applications with ample parallelism and intermittent activity. Serverless
promises greater resource elasticity, significant cost savings, and simplified
application deployment. All major cloud providers, including Amazon, Google,
and Microsoft, have introduced serverless to their public cloud offerings. For
serverless to reach its potential, there is a pressing need for programming
frameworks that abstract the deployment complexity away from the user. This
includes simplifying the process of writing applications for serverless
environments, automating task and data partitioning, and handling scheduling
and fault tolerance.
  We present Ripple, a programming framework designed to specifically take
applications written for single-machine execution and allow them to take
advantage of the task parallelism of serverless. Ripple exposes a simple
interface that users can leverage to express the high-level dataflow of a wide
spectrum of applications, including machine learning (ML) analytics, genomics,
and proteomics. Ripple also automates resource provisioning, meeting
user-defined QoS targets, and handles fault tolerance by eagerly detecting
straggler tasks. We port Ripple over AWS Lambda and show that, across a set of
diverse applications, it provides an expressive and generalizable programming
framework that simplifies running data-parallel applications on serverless, and
can improve performance by up to 80x compared to IaaS/PaaS clouds for similar
costs.


  Let $(X_1, \dots, X_n)$ be multivariate normal, with mean vector
$\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$, and
$S_n=\mathrm{e}^{X_1}+\cdots+\mathrm{e}^{X_n}$. The Laplace transform ${\cal
L}(\theta)=\mathbb{E}\mathrm{e}^{-\theta S_n} \propto \int
\exp\{-h_\theta(\boldsymbol{x})\} \,\mathrm{d} \boldsymbol{x}$ is represented
as $\tilde{\cal L}(\theta)I(\theta)$, where $\tilde{\cal L}(\theta)$ is given
in closed-form and $I(\theta)$ is the error factor ($\approx 1$). We obtain
$\tilde{\cal L}(\theta)$ by replacing $h_\theta(\boldsymbol{x})$ with a second
order Taylor expansion around its minimiser $\boldsymbol{x}^*$. An algorithm
for calculating the asymptotic expansion of $\boldsymbol{x}^*$ is presented,
and it is shown that $I(\theta)\to 1$ as $\theta\to\infty$. A variety of
numerical methods for evaluating $I(\theta)$ are discussed, including Monte
Carlo with importance sampling and quasi-Monte Carlo. Numerical examples
(including Laplace transform inversion for the density of $S_n$) are also
given.