  In this report the Co2 based Heusler compounds are discussed as potential
materials for spin voltage generation. The compounds were synthesized by
arcmelting and consequent annealing. Band structure calculations were performed
and revealed the compounds to be half-metallic ferromagnets. Magnetometry was
performed on the samples and the Curie temperatures and the magnetic moments
were determined. The Seebeck coefficients were measured from low to ambient
temperatures for all compounds. For selected compounds high temperature
measurements up to 900 K were performed.


  In this note I give a description of Lyubeznik's local cohomology invariants
for a certain natural class of local rings, namely the ones which have the same
local cohomology vanishing as one expects from an isolated singularity. This
strengthens the results of Bondu and myself in math.AG/0406265 while at the
same time somewhat simplifying the proofs. Through examples I further point out
the bad behavior of these invariants under reduction to positive
characteristic.


  We study the efficiency of the noble gases sequestration by the ion H3+ in
the form of XH3+ complexes (with X = argon, krypton or xenon) in gas phase
conditions similar to those encountered during the cooling of protoplanetary
disks, at the epoch of icy planetesimals formation. We show that XH3+ complexes
form very stable structures in the gas phase and that their binding energies
are much higher than those involved in the structures of X-H2O hydrates or pure
X-X condensates. This implies that, in presence of H3+ ions, argon, krypton or
xenon are likely to remain sequestrated in the form of XH3+ complexes embedded
in the gas phase rather than forming ices during the cooling of protoplanetary
disks. The amount of the deficiency depends on how much H3+ is available and
efficient in capturing noble gases. In the dense gas of the mid-plane of solar
nebula, H3+ is formed by the ionization of H2 from energetic particles, as
those in cosmic rays or those ejected by the young Sun. Even using the largest
estimate of the cosmic rays ionization rate, we compute that the H3+ abundance
is two and three orders of magnitude lower than the xenon and krypton
abundance, respectively. Estimating the ionization induced by the young Sun, on
the other hand, is very uncertain but leaves the possibility to have enough H3+
to make krypton and xenon trapping efficent. Finally, additional source of H3+
formation may be provided by the presence of a nearby supernova, as discussed
in the literature. Recent solar system observations show a deficiency of Ar,
and, even more, of Kr and Xe in Titan and in comets. In this article, we
consider the possibility that this deficiency is caused by the afore-mentioned
process, namely trapping of those noble gases by H3+ ions in the solar nebula.


  A new approach to effective theory of quarks in the instanton vacuum is
presented. Exact equations for the quark propagator and Lagrangian are derived
which contain contributions of all quark modes with known coefficients. The
resulting effective Lagrangian resembles that of the Nambu--Jona--Lasinio
model. The commonly used zero--mode approximation is shown to be invalid in the
chiral limit.


  In an abelian topologically massive gauge theory, any eigenstate of the
Hamiltonian can be decomposed into a factor describing massive propagating
gauge bosons and a Chern-Simons wave function describing a set of
nonpropagating ``topological'' excitations. The energy depends only on the
propagating modes, and energy eigenstates thus occur with a degeneracy that can
be parametrized by the Hilbert space of the pure Chern-Simons theory. We show
that for a {\em nonabelian} topologically massive gauge theory, this degeneracy
is lifted: although the Gauss law constraint can be solved with a similar
factorization, the Hamiltonian couples the propagating and nonpropagating
(topological) modes.


  This paper studies the relationship between generalization and privacy
preservation in iterative learning algorithms by two sequential steps. We first
establish an alignment between generalization and privacy preservation for any
learning algorithm. We prove that $(\varepsilon, \delta)$-differential privacy
implies an on-average generalization bound for multi-database learning
algorithms which further leads to a high-probability bound for any learning
algorithm. This high-probability bound also implies a PAC-learnable guarantee
for differentially private learning algorithms. We then investigate how the
iterative nature shared by most learning algorithms influence privacy
preservation and further generalization. Three composition theorems are
proposed to approximate the differential privacy of any iterative algorithm
through the differential privacy of its every iteration. By integrating the
above two steps, we eventually deliver generalization bounds for iterative
learning algorithms, which suggest one can simultaneously enhance privacy
preservation and generalization. Our results are strictly tighter than the
existing works. Particularly, our generalization bounds do not rely on the
model size which is prohibitively large in deep learning. This sheds light to
understanding the generalizability of deep learning. These results apply to a
wide spectrum of learning algorithms. In this paper, we apply them to
stochastic gradient Langevin dynamics and agnostic federated learning as
examples.


  Recent advances in quantum thermodynamics have been focusing on ever more
elementary systems of interest, approaching the limit of a single qubit, with
correlations, strong coupling and non-equilibrium environments coming into
play. Under such scenarios, it is clear that fundamental physical quantities
must be revisited. This article questions whether a universal definition of
internal energy for open quantum systems may be devised, setting limits on its
possible properties. We argue that, for such a definition to be regarded as
local, it should be implemented as a functional of the open system's reduced
density operator and its time derivatives. Then we show that it should involve
at least up to the second-order derivative, otherwise failing to recover the
previously-known internal energy of the "universe". Possible implications of
this general result are discussed.


  The CHY-integrand of bi-adjoint cubic scalar theory is a product of two
PT-factors. This pair of PT-factors can be interpreted as defining a
permutation. We introduce the cycle representation of permutation in this paper
for the understanding of cubic scalar amplitude. We show that, given a
permutation related to the pair of PT-factors, the pole and vertex information
of Feynman diagrams of corresponding CHY-integrand is completely characterized
by the cycle representation of permutation. Inversely, we also show that, given
a set of Feynman diagrams, the cycle representation of corresponding PT-factor
can be recursively constructed. In this sense, there exists a deep connection
between cycles of a permutation and amplitude. Based on these results, we have
investigated the relations among different independent pairs of PT-factors in
the context of cycle representation as well as the multiplication of
cross-ratio factors.


  We present a high-resolution laser spectroscopic study of the
$\tilde{A}\,^2B_2- \tilde{X}\,^2A_1$ and $\tilde{B}\,^2B_1- \tilde{X}\,^2A_1$
transitions of calcium (I) phenoxide, CaOPh (CaOC$_6$H$_5$). The rotationally
resolved band systems are analyzed using an effective Hamiltonian model and are
accurately modeled as independent perpendicular ($b$- or $c$-type) transitions.
The structure of calcium monophenoxide is compared to previously observed
Ca-containing radicals and implications for direct laser cooling are discussed.
This work demonstrates that functionalization of aromatic molecules with
optical cycling centers can preserve many of the properties needed for
laser-based control.


  Bell conjectured that a positive Wigner function does not allow violation of
the inequalities imposed by local hidden variable theories. A requirement for
this conjecture is "when phase space measurements are performed". We introduce
the theory-independent concept of "operationally local transformations" which
refers to the change of the switch on a local measurement apparatus. We show
that two separated parties, performing only phase space measurements on a
composite quantum system with a positive Wigner function and performing only
operationally local transformations that preserve this positivity, can
nonetheless violate Bell's inequality. Such operationally local transformations
are realized using entangled ancillae.


  We suggest that the large single spin asymmetries observed at high momentum
fractions x_F and transverse momenta k_T of the pion in p^\uparrow p ->
\pi(x_F,k_T)+X arise from the coherence of the soft interactions with the hard
parton scattering process. Such coherence can be maintained if x_F -> 1 as k_T
-> \infty, while k_T^2(1-x_F) ~ \Lambda_{QCD}^2 stays fixed. Analogous
coherence effects have been seen experimentally in the Drell-Yan process at
high x_F. We find that the p^\uparrow p -> \pi X production amplitudes have
large dynamic phases and that helicity flip contributions are unsuppressed in
this limit, giving rise to potentially large single spin asymmetries.


  We consider emitting nanoparticles in dielectric nanocomposites with varying
refractive index contrast and geometry. For that we develop a simple and
universal method to calculate the emission enhancement in nanocomposites that
employs solely the calculation of the effective refractive index and electric
field distributions from three quasistatic calculations with orthogonal
polarizations. The method is exemplified for dilute nanocomposites without
electromagnetic interaction between emitting particles as well as for dense
nanocomposites with strong particle interaction. We show that the radiative
decay in dielectric nanocomposites is greatly affected by the shape and
arrangement of its constituents and give guidelines for larger enhancement.


  For orthogonal polynomials defined by compact Jacobi matrix with exponential
decay of the coefficients, precise properties of orthogonality measure is
determined. This allows showing uniform boundedness of partial sums of
orthogonal expansions with respect to $L^\infty$ norm, which generalize
analogous results obtained for little $q$-Legendre, little $q$-Jacobi and
little $q$-Laguerre polynomials, by the authors.


  We present a Quantum Monte Carlo study of a hardcore boson model with
ring-only exchanges on a square lattice, where a $K_1$ term acts on 1$\times$1
plaquettes and a $K_2$ term acts on 1$\times$2 and 2$\times$1 plaquettes. At
half-filling, the phase diagram reveals charge density wave for small $K_2$,
valence bond solid for intermediate $K_2$, and possibly for large $K_2$ the
novel Exciton Bose Liquid (EBL) phase first proposed by Paramekanti, et
al[Phys. Rev. B {\bf 66}, 054526 (2002)]. Away from half-filling, the EBL phase
is present already for intermediate $K_2$ and remains stable for a range of
densities below 1/2 before phase separation sets in at lower densities


  Several philosophical problems arising from the physics of consciousness,
including identity, duplication, teleportation, simulation, self-location, and
the Boltzmann Brain problem, hinge on one of the most deeply held but
unnecessary convictions of physicalism: the assumption that brain states and
their corresponding conscious states can in principle be copied. In this paper
I will argue against this assumption by attempting to prove the Unique History
Theorem, which states, essentially, that conscious correlations to underlying
quantum mechanical measurement events must increase with time and that every
conscious state uniquely determines its history from an earlier conscious
state. By assuming only that consciousness arises from an underlying physical
state, I will argue that the physical evolution from a first physical state
giving rise to a conscious state to a second physical state giving rise to a
later conscious state is unique. Among the consequences of this theorem are
that: consciousness is not algorithmic and a conscious state cannot be uploaded
to or simulated by a digital computer; a conscious state cannot be copied by
duplicating a brain or any other physical state; and a conscious state cannot
be repeated or created de novo. These conclusions shed light on the physical
nature of consciousness by rendering moot a variety of seemingly paradoxical
philosophy and science fiction problems.


  We report electrical conductance measurements of Bi nanocontacts created by
repeated tip-surface indentation using a scanning tunneling microscope at
temperatures of 4 K and 300 K. As a function of the elongation of the
nanocontact we measure robust, tens of nanometers long plateaus of conductance
G0 = 2e^2/h at room temperature. This observation can be accounted for by the
mechanical exfoliation of a Bi(111) bilayer, a predicted QSH insulator, in the
retracing process following a tip-surface contact. The formation of the bilayer
is further supported by the additional observation of conductance steps below
G0 before break-up at both temperatures. Our finding provides the first
experimental evidence of the possibility of mechanical exfoliation of Bi
bilayers, of the existence of the QSH phase in a two-dimensional crystal, and,
most importantly, of the observation of the QSH phase at room temperature.


  In the paper we develop the dressing method for the solution of the
two-dimensional periodic Volterra system with a period N. We derive soliton
solutions of arbitrary rank $k$ and give a full classification of rank 1
solutions. We have found a new class of exact solutions corresponding to wave
fronts which represent smooth interfaces between two nonlinear periodic waves
or a periodic wave and a trivial (zero) solution. The wave fronts are
non-stationary and they propagate with a constant average velocity. The system
also has soliton solutions similar to breathers, which resembles soliton webs
in the KP theory. We associate the classification of soliton solutions with the
Schubert decomposition of the Grassmanians ${\rm Gr}_{\mathbb{R}}(k,N)$ and
${\rm Gr}_{\mathbb{C}}(k,N)$.


  This paper addresses the computational challenges of learning strong
substitutes demand when given access to a demand (or valuation) oracle. Strong
substitutes demand generalises the well-studied gross substitutes demand to a
multi-unit setting. Recent work by Baldwin and Klemperer shows that any such
demand can be expressed in a natural way as a finite list of weighted bid
vectors. A simplified version of this bidding language has been used by the
Bank of England.
  Assuming access to a demand oracle, we provide an algorithm that computes the
unique list of weighted bid vectors corresponding to a bidder's demand
preferences. In the special case where their demand can be expressed using
positive bids only, we have an efficient algorithm that learns this list in
linear time. We also show super-polynomial lower bounds on the query complexity
of computing the list of bids in the general case where bids may be positive
and negative. Our algorithms constitute the first systematic approach for
bidders to construct a bid list corresponding to non-trivial demand, allowing
them to participate in `product-mix' auctions.


  In a number of experimental situations, single polymer molecules can be
suspended in a vacuum. Here collisions between such molecules are considered.
The limit of high collision velocity is investigated numerically for a variety
of conditions. The distribution of contact times, scattering angles, and final
velocities are analyzed. In this limit, self avoiding chains are found to
become highly stretched as they collide with each other, and have a
distribution of scattering times that depends on the scattering angle. The
velocity of the molecules after the collisions is similar to predictions of a
model assuming thermal equilibration of molecules during the collision. The
most important difference is a significant subset of molecules that
inelastically scatter but do not substantially change direction.


  The richness of the mean-field solution of simple glasses leaves many of its
features challenging to interpret. A minimal model that illuminates glass
physics the same way the random energy model clarifies spin glass behavior
would therefore be beneficial. Here, we propose such a real-space model that is
amenable to infinite-dimensional analysis and is exactly solvable at high and
low densities in finite dimension. By joining analysis with numerical
simulations, we uncover geometrical signatures of the dynamical and jamming
transitions and provides insight into the origin of activated processes.
Translating these findings to the context of standard glass formers further
reveals the role played by non-convexity in the emergence of Gardner physics.


  We prove a uniform Fourier extension-restriction estimate for a certain class
of curves in d-dimensional Euclidean space.


  The stellar abundance ratio of Mg/Fe is an important tool in diagnostics of
galaxy evolution. In order to make reliable measurements of the Mg abundance of
stars, it is necessary to have accurate values for the oscillator strength
(f-value) of each of the observable transitions. In metal-poor stars the Mg I
3p-4s triplet around 5175 AA (Fraunhofer's so-called b lines) are the most
prominent magnesium lines. The lines also appear as strong features in the
solar spectrum. We present new and improved experimental oscillator strengths
for the optical Mg I 3p-4s triplet, along with experimental radiative lifetimes
for six terms in Mg I. With these data we discuss the implications on previous
and future abundance analyses of metal-poor stars. The oscillator strengths
have been determined by combining radiative lifetimes with branching fractions,
where the radiative lifetimes are measured using the laser induced fluorescence
technique and the branching fractions are determined using intensity calibrated
Fourier Transform (FT) spectra. The FT spectra are also used for determining
new accurate laboratory wavelengths for the 3p-4s transitions. The f-values of
the Mg I 3p-4s lines have been determined with an absolute uncertainty of 9 %,
giving an uncertainty of +-0.04 dex in the log gf values. Compared to values
previously used in abundance analyses of metal-poor stars, rescaling to the new
values implies an increase of typically 0.04 dex in the magnesium abundance.


  In this paper we continue the investigation of the regularity of the
so-called weak $\frac{n}{p}$-harmonic maps in the critical case. These are
critical points of the following nonlocal energy \[
{\mathcal{L}}_s(u)=\int_{\mathbb{R}^n}| ( {-\Delta})^{\frac{s}{2}} u(x)|^p
dx\,, \] where $u\in \dot{H}^{s,p}(\mathbb{R}^n,\mathcal{N})$ and
${\mathcal{N}}\subset\mathbb{R}^N$ is a closed $k$ dimensional smooth manifold
and $s=\frac{n}{p}$. We prove H\"older continuity for such critical points for
$p \leq 2$. For $p > 2$ we obtain the same under an additional Lorentz-space
assumption. The regularity theory is in the two cases based on regularity
results for nonlocal Schr\"odinger systems with an antisymmetric potential.


  Measuring the faint polarization signal of the cosmic microwave background
(CMB) not only requires high optical throughput and instrument sensitivity but
also control over systematic effects. Polarimetric cameras or receivers used in
this setting often employ dielectric vacuum windows, filters, or lenses to
appropriately prepare light for detection by cooled sensor arrays. These
elements in the optical chain are typically designed to minimize reflective
losses and hence improve sensitivity while minimizing potential imaging
artifacts such as glint and ghosting. The Primordial Inflation Polarization
ExploreR (PIPER) is a balloon-borne instrument designed to measure the
polarization of the CMB radiation at the largest angular scales and
characterize astrophysical dust foregrounds. PIPER's twin telescopes and
detector systems are submerged in an open-aperture liquid helium bucket dewar.
A fused-silica window anti-reflection (AR) coated with polytetrafluoroethylene
(PTFE) is installed on the vacuum cryostat that houses the cryogenic detector
arrays. Light passes from the skyward portions of the telescope to the detector
arrays though this window, which utilizes an indium seal to prevent superfluid
helium leaks into the vacuum cryostat volume. The AR coating implemented
reduces reflections from each interface to <1% compared to ~10% from an
uncoated window surface. The AR coating procedure and room temperature optical
measurements of the window are presented. The indium vacuum sealing process is
also described in detail and test results characterizing its integrity to
superfluid helium leaks are provided.


  We prove that the mod Z reduction of the torsion of a rational homology
3-sphere is completely determined by three data: a certain canonical spin^c
structure, the linking form and a Q/Z-valued constant c. This constant is a new
topological invariant of the rational homology sphere. Experimentations with
lens spaces suggest this constant may be as powerful an invariant as the
torsion itself.


  Consider a finite sequence of independent random permutations, chosen
uniformly either among all permutations or among all matchings on n points. We
show that, in probability, as n goes to infinity, these permutations viewed as
operators on the (n-1) dimensional vector space orthogonal to the vector with
all coordinates equal to 1, are asymptotically strongly free. Our proof relies
on the development of a matrix version of the non-backtracking operator theory
and a refined trace method.
  As a byproduct, we show that the non-trivial eigenvalues of random n-lifts of
a fixed based graphs approximately achieve the Alon-Boppana bound with high
probability in the large n limit. This result generalizes Friedman's Theorem
stating that with high probability, the Schreier graph generated by a finite
number of independent random permutations is close to Ramanujan.
  Finally, we extend our results to tensor products of random permutation
matrices. This extension is especially relevant in the context of quantum
expanders.


  We propose a mechanism for system-induced spontaneous time reparametrization
symmetry breaking in canonical gravity. We consider a model of extended
canonical gravity, based on Sen's spinorial expression of the
spatial-diffeomorphism-gauge independent part of the shift vector, with one
additional long-range self-interacting massive spin-$1/2$ particle whose spin
is coupled to Sen's spinor in the Hamiltonian. This additional particle plays
the role of creating the system-induced time reparametrization invariant
potential. We use this potential to break time reparametrization symmetry
spontaneously. We identify the symmetry breaking with the origin of the quantum
energy measurement processes in the ensemble interpretation of quantum
mechanics. Our theory uses a novel interpretation of quantum mechanics with
respect to quantum mechanical position uncertainties of particles. The
spatial-diffeomorphism-gauge independent part of the shift vector is attributed
to this novel interpretation of quantum mechanics.


  A lightweight underwater image enhancement network is of great significance
for resource-constrained platforms, but balancing model size, computational
efficiency, and enhancement performance has proven difficult for previous
approaches. In this work, we propose the Five A$^{+}$ Network (FA$^{+}$Net), a
highly efficient and lightweight real-time underwater image enhancement network
with only $\sim$ 9k parameters and $\sim$ 0.01s processing time. The
FA$^{+}$Net employs a two-stage enhancement structure. The strong prior stage
aims to decompose challenging underwater degradations into sub-problems, while
the fine-grained stage incorporates multi-branch color enhancement module and
pixel attention module to amplify the network's perception of details. To the
best of our knowledge, FA$^{+}$Net is the only network with the capability of
real-time enhancement of 1080P images. Thorough extensive experiments and
comprehensive visual comparison, we show that FA$^{+}$Net outperforms previous
approaches by obtaining state-of-the-art performance on multiple datasets while
significantly reducing both parameter count and computational complexity. The
code is open source at https://github.com/Owen718/FiveAPlus-Network.


  We present a novel spectral embedding of graphs that incorporates weights
assigned to the nodes, quantifying their relative importance. This spectral
embedding is based on the first eigenvectors of some properly normalized
version of the Laplacian. We prove that these eigenvectors correspond to the
configurations of lowest energy of an equivalent physical system, either
mechanical or electrical, in which the weight of each node can be interpreted
as its mass or its capacitance, respectively. Experiments on a real dataset
illustrate the impact of weighting on the embedding.


  Stellar magnetic activity induces both distortions and Doppler-shifts in the
absorption line profiles of Sun-like stars. Those effects produce apparent
radial velocity (RV) signals which greatly hamper the search for potentially
habitable, Earth-like planets. In this work, we investigate these distortions
in the Sun using cross-correlation functions (CCFs), derived from intensive
monitoring with the high-precision spectrograph HARPS-N. We show that the RV
signal arising from line-shape variations on time-scales associated with the
solar rotation and activity cycle can be robustly extracted from the data,
reducing the RV dispersion by half. Once these have been corrected,
activity-induced Doppler-shifts remain, that are modulated at the solar
rotation period, and that are most effectively modelled in the time domain,
using Gaussian Processes (GPs). Planet signatures are still best retrieved with
multi-dimensonal GPs, when activity is jointly modelled from the raw RVs and
indicators of the line width or of the Ca II H and K emission. After GP
modelling, the residual RVs exhibit a dispersion of 0.6-0.8 m/s, likely to be
dominated by signals induced by super-granulation. Finally, we find that the
statistical properties of the RVs evolve significantly over time, and that this
evolution is primarily driven by sunspots, which control the smoothness of the
signal. Such evolution, which reduces the sensitivity to long-period planet
signatures, is no longer seen in the activity-induced Doppler-shifts, which is
promising for long term RV monitoring surveys such as the Terra Hunting
Experiment or the PLATO follow-up campaign.


  We propose a new deep learning based framework to identify pedestrians, and
caution distracted drivers, in an effort to prevent the loss of life and
property. This framework uses two Convolutional Neural Networks (CNN), one
which detects pedestrians and the second which predicts the onset of drowsiness
in a driver, is implemented on a Raspberry Pi 3 Model B+, shows great promise.
The algorithm for implementing such a low-cost, low-compute model is presented
and the results discussed.


  In this letter, we bootstrap the 4-point correlators on the 1D celestial
circle using 3D symmetries in the Aharony-Bergman-Jafferis-Maldacena theory as
constraints. We find that the dual inversion property is strong enough to
replace the crossing symmetry condition (or cyclic invariant condition) when
bootstrapping. We also give some results about the conformal block expansion
coefficients which contain the spectrum and the leading multi-OPE of this
celestial CFT. Furthermore, we find a non-local 2-particle operator from the
multi-OPE at the leading OPE. Although we studied a specific theory, the
methods used are valid for general cases. Finally, we try to find how the
relations between the Grassmannians of $\mathcal{N}=4$ super Yang-Mills theory
and the Aharony-Bergman-Jafferis-Maldacena theory with reduced supersymmetry
are realized on the celestial sphere in the four-point case.


  Medical image processing has been highlighted as an area where deep
learning-based models have the greatest potential. However, in the medical
field in particular, problems of data availability and privacy are hampering
research progress and thus rapid implementation in clinical routine. The
generation of synthetic data not only ensures privacy, but also allows to
\textit{draw} new patients with specific characteristics, enabling the
development of data-driven models on a much larger scale. This work
demonstrates that three-dimensional generative adversarial networks (GANs) can
be efficiently trained to generate high-resolution medical volumes with finely
detailed voxel-based architectures. In addition, GAN inversion is successfully
implemented for the three-dimensional setting and used for extensive research
on model interpretability and applications such as image morphing, attribute
editing and style mixing. The results are comprehensively validated on a
database of three-dimensional HR-pQCT instances representing the bone
micro-architecture of the distal radius.


  We show that the dissipation rate bounds the rate at which physical processes
can be performed in stochastic systems far from equilibrium. Namely, for rare
processes we prove the fundamental tradeoff $\langle \dot S_\text{e} \rangle
\mathcal{T} \geq k_{\text{B}} $ between the entropy flow $\langle \dot
S_\text{e} \rangle$ into the reservoirs and the mean time $\mathcal{T}$ to
complete a process. This dissipation-time uncertainty relation is a novel form
of speed limit: the smaller the dissipation, the larger the time to perform a
process.


  Eshelby showed that if an inclusion is of elliptic or ellipsoidal shape then
for any uniform elastic loading the field inside the inclusion is uniform. He
then conjectured that the converse is true, i.e., that if the field inside an
inclusion is uniform for all uniform loadings, then the inclusion is of
elliptic or ellipsoidal shape. We call this the weak Eshelby conjecture. In
this paper we prove this conjecture in three dimensions. In two dimensions, a
stronger conjecture, which we call the strong Eshelby conjecture, has been
proved: If the field inside an inclusion is uniform for a single uniform
loading, then the inclusion is of elliptic shape. We give an alternative proof
of Eshelby's conjecture in two dimensions using a hodographic transformation.
As a consequence of the weak Eshelby's conjecture, we prove in two and three
dimensions a conjecture of Polya and Szego on the isoperimetric inequalities
for the polarization tensors. The Polya-Szego conjecture asserts that the
inclusion whose electrical polarization tensor has the minimal trace takes the
shape of a disk or a ball.


  The aim of this note is to characterize briefly main components of
theoretical error of the small angle Bhabha measurement at LEP and to discuss
critically how solid these estimates really are, from todays perspective. We
conclude that the existing theoretical error of the LEP luminometer process
(small angle Bhabha) is rather solid, and we add some new discussion concerning
the remaining uncertainties and prospects of the future improvements toward the
$\le 0.025%$ precision.


  This paper presents theoretical analysis and software implementation for real
harmonics analysis on the special orthogonal group. Noncommutative harmonic
analysis for complex-valued functions on the special orthogonal group has been
studied extensively. However, it is customary to treat real harmonic analysis
as a special case of complex harmonic analysis, and there have been limited
results developed specifically for real-valued functions. Here, we develop a
set of explicit formulas for real-valued irreducible unitary representations on
the special orthogonal group, and provide several operational properties, such
as derivatives, sampling, and Clebsch-Gordon coefficients. Furthermore, we
implement both of complex and real harmonics analysis on the special orthogonal
group into an open source software package that utilizes parallel processing
through the OpenMP library. The efficacy of the presented results are
illustrated by benchmark studies and an application to spherical shape
matching.


  In previous work we showed that a semi-empirical model in which galaxies in
host dark matter haloes are assigned stellar masses via a stellar mass-halo
mass (SMHM) relation and sizes ($R_e$) via a linear and tight $R_e-R_h$
relation, can faithfully reproduce the size function of local SDSS central
galaxies and the strong size evolution of massive galaxies (MGs, $M_{\rm
star}>10^{11.2}M_\odot$). In this third paper of the series, we focus on the
population of satellite MGs. We find that without any additional calibration
and irrespective of the exact SMHM relation, fraction of quenched galaxies or
level of stellar stripping, the same model is able to reproduce the local size
function of quiescent satellite MGs in SDSS. In addition, the same model can
reproduce the puzzling weak dependence of mean size on host halo mass for both
central and satellite galaxies. The model also matches the size function of
starforming satellite MGs, after assuming that some of them transform into
massive lenticulars in a few Gyr after infalling in the group/cluster
environment. However, the vast majority of satellite lenticulars is predicted
to form before infall. The $R_e-R_h$ appears to be fundamental to connect
galaxies and their host haloes.


  In the framework of the effective field theory (EFT) we discuss the
electroweak (EW) corrections at LEP energies. We obtain the effective
Lagrangian in the large m_t limit, and reproduce analytically the dominant EW
corrections to the LEP2 processes e+ e- --> gamma Z and e+ e- --> Z Z. To
include effects of finite top-quark and Higgs masses, we use the effective
Lagrangian at tree level and fit LEP1/SLD observables with four arbitrary
parameters, plus alpha_s(m_Z). The EFT approach works remarkably well. Using
the effective couplings determined from the fit, and tree-level EFT formulae,
we predict the cross sections for e+ e- --> Z Z, gamma Z at a level better than
1%.


  In recent years it has been shown that the tidal coupling between extrasolar
planets and their stars could be an important mechanism leading to orbital
evolution. Both the tides the planet raises on the star and vice versa are
important and dissipation efficiencies ranging over four orders of magnitude
are being used. In addition, the discovery of extrasolar planets extremely
close to their stars has made it clear that the estimates of the tidal quality
factor, Q, of the stars based on Jupiter and its satellite system and on main
sequence binary star observations are too low, resulting in lifetimes for the
closest planets orders of magnitude smaller than their age. We argue that those
estimates of the tidal dissipation efficiency are not applicable for stars with
spin periods much longer than the extrasolar planets' orbital period. We
address the problem by applying our own values for the dissipation efficiency
of tides, based on our numerical simulations of externally perturbed volumes of
stellar-like convection. The range of dissipation we find for main-sequence
stars corresponds to stellar $Q_*$ of $10^8$ to $3{\times}10^9$. The derived
orbit lifetimes are comparable to, or much longer than the ages of the observed
extrasolar planetary systems. The predicted orbital decay transit timing
variations due to the tidal coupling are below the rate of ms/yr for currently
known systems, but within reach of an extended Kepler mission provided such
objects are found in its field.


  A conjecture appears in \cite{milsteinscheme}, in the form of a remark, where
it is stated that it is possible to construct, in a specified way, any high
order explicit numerical schemes to approximate the solutions of SDEs with
superlinear coefficients. We answer this conjecture affirmatively for the case
of order 1.5 approximations and show that the suggested methodology works.
Moreover, we explore the case of having H\"{o}lder continuous derivatives for
the diffusion coefficients.


  The process of multicomponent condensation is considered. The theory taking
into account several channels of nucleation is constructed. The analytical
approximate description of the whole condensation process is given. The
specific phenomena of the secondary nucleation is described analytically. The
possibility of the partial reverse condensation is discussed.


  We discuss the two-loop evolution of the flavor-nonsinglet meson distribution
amplitude in perturbative QCD. After reviewing previous two-loop computations,
we outline the incompatibility of these solutions with the group property of
the renormalization-group transformations. To cure this deficiency, we compute
a correction factor for the non-diagonal part of the meson evolution equation
and prove that with this modification the two-loop solution conforms with the
group properties of the renormalization-group transformations. The special case
of a fixed strong coupling (no Q^2 dependence) is also discussed and comparison
is given to previously obtained results.


  Quantification of Uncertainty in predictions is a challenging problem. In the
classification settings, although deep learning based models generalize well,
class probabilities often lack reliability. Calibration errors are used to
quantify uncertainty, and several methods exist to minimize calibration error.
We argue that between the choice of having a minimum calibration error on
original distribution which increases across distortions or having a (possibly
slightly higher) calibration error which is constant across distortions, we
prefer the latter
  We hypothesize that the reason for unreliability of deep networks is - The
way neural networks are currently trained, the probabilities do not generalize
across small distortions. We observe that quantile based approaches can
potentially solve this problem. We propose an innovative approach to decouple
the construction of quantile representations from the loss function allowing us
to compute quantile based probabilities without disturbing the original
network. We achieve this by establishing a novel duality property between
quantiles and probabilities, and an ability to obtain quantile probabilities
from any pre-trained classifier.
  While post-hoc calibration techniques successfully minimize calibration
errors, they do not preserve robustness to distortions. We show that, Quantile
probabilities (QuantProb), obtained from Quantile representations, preserve the
calibration errors across distortions, since quantile probabilities generalize
better than the naive Softmax probabilities.


  We prove scattering for small solutions to of nonlinear Schroedinger
equations in 1D with a space periodic potential


  One of the remarkable features of quantum mechanics is the ability to ensure
secrecy. Private states embody this effect, as they are precisely those
multipartite quantum states from which two parties can produce a shared secret
that cannot in any circumstance be correlated to an external system. Naturally,
these play an important role in quantum key distribution (QKD) and quantum
information theory. However, a general distillation method has heretofore been
missing. Inspired by Koashi's complementary control scenario (arXiv:0704.3661v1
[quant-ph]), we give a new definition of private states in terms of one party's
potential knowledge of two complementary measurements made on the other and use
this to construct a general method of private state distillation using quantum
error-correcting codes. The procedure achieves the same key rate as recent,
more information-theoretic approaches while demonstrating the physical
principles underlying privacy of the key. Additionally, the same approach can
be used to establish the hashing inequality for entanglement distillation, as
well as the direct quantum coding theorem.


  Though deep learning has achieved advanced performance recently, it remains a
challenging task in the field of medical imaging, as obtaining reliable labeled
training data is time-consuming and expensive. In this paper, we propose a
double-uncertainty weighted method for semi-supervised segmentation based on
the teacher-student model. The teacher model provides guidance for the student
model by penalizing their inconsistent prediction on both labeled and unlabeled
data. We train the teacher model using Bayesian deep learning to obtain
double-uncertainty, i.e. segmentation uncertainty and feature uncertainty. It
is the first to extend segmentation uncertainty estimation to feature
uncertainty, which reveals the capability to capture information among
channels. A learnable uncertainty consistency loss is designed for the
unsupervised learning process in an interactive manner between prediction and
uncertainty. With no ground-truth for supervision, it can still incentivize
more accurate teacher's predictions and facilitate the model to reduce
uncertain estimations. Furthermore, our proposed double-uncertainty serves as a
weight on each inconsistency penalty to balance and harmonize supervised and
unsupervised training processes. We validate the proposed feature uncertainty
and loss function through qualitative and quantitative analyses. Experimental
results show that our method outperforms the state-of-the-art uncertainty-based
semi-supervised methods on two public medical datasets.


  This is the last of three papers on Conformal General Relativity (CGR), which
ascribes inflation to a spontaneous breakdown of conformal symmetry, followed
by a sudden energy transfer from geometry to matter identified as big bang.
This process is driven by a conformal-invariant, unitarity-preserving
interaction of two Nambu-Goldstone fields: a ghost scalar field $\sigma$,
invested with geometric meaning, and a physical scalar field $\varphi$ behaving
like a Higgs field of varying mass. The big bang generates a bulk of Higgs
bosons at temperature $T_B\simeq 141$ GeV, after which the universe evolves
adiabatically while the Higgs bosons decay into Standard-Model particles and
the magnitude of the gravitational coupling constant decreases. The process
ends when the $\sigma$-$\varphi$ interaction potential vanishes, the amplitudes
of these fields converge to their expectation values in a final stable vacuum
and the Higgs-boson mass converges to about 126 GeV. The main aspects of this
phenomenology are qualitatively described and accurately exemplified by
numerical simulations. The combination of CGR gravitational equation at time
zero with entropy conservation equation results in striking predictions. The
best fit to astronomic data is obtained from only standard Higgs boson
parameters and a universe age of 19.5 Gyr. The cosmological constant
$\Lambda\simeq 1.35\times 10^{-35}$s$^{-2}$, the scale factor across inflation
$Z\simeq 4.54\times 10^{27}$, and the lower bound of the power spectrum of
cosmic background anisotropies $W_{min}\!\simeq 37.5\,\mu$K$^2$ are thus
predicted.


  This paper studies efficient distributed optimization methods for multi-agent
networks. Specifically, we consider a convex optimization problem with a
globally coupled linear equality constraint and local polyhedra constraints,
and develop distributed optimization methods based on the alternating direction
method of multipliers (ADMM). The considered problem has many applications in
machine learning and smart grid control problems. Due to the presence of the
polyhedra constraints, agents in the existing methods have to deal with
polyhedra constrained subproblems at each iteration. One of the key issues is
that projection onto a polyhedra constraint is not trivial, which prohibits
from closed-form solutions or the use of simple algorithms for solving these
subproblems. In this paper, by judiciously integrating the proximal
minimization method with ADMM, we propose a new distributed optimization method
where the polyhedra constraints are handled softly as penalty terms in the
subproblems. This makes the subproblems efficiently solvable and consequently
reduces the overall computation time. Furthermore, we propose a randomized
counterpart that is robust against randomly ON/OFF agents and imperfect
communication links. We analytically show that both the proposed methods have a
worst-case $\mathcal{O}(1/k)$ convergence rate, where $k$ is the iteration
number. Numerical results show that the proposed methods offer considerably
lower computation time than the existing distributed ADMM method.


  Using the Clauser-Horne model of Bell's theorem, the locality condition is
examined and it is shown the corresponding formulation is equivalent to a
factorization process consisting of three stages. The first stage is introduced
based on the conditional probability definition in classical theory of
probability and the other two stages are based on previously-known relations
named as outcome and parameter independence conditions.


  Supersaturated design (SSD) has received much recent interest because of its
potential in factor screening experiments. In this paper, we provide equivalent
conditions for two columns to be fully aliased and consequently propose methods
for constructing $E(f_{\mathrm{NOD}})$- and $\chi^2$-optimal mixed-level SSDs
without fully aliased columns, via equidistant designs and difference matrices.
The methods can be easily performed and many new optimal mixed-level SSDs have
been obtained. Furthermore, it is proved that the nonorthogonality between
columns of the resulting design is well controlled by the source designs. A
rather complete list of newly generated optimal mixed-level SSDs are tabulated
for practical use.


  Resource reservation is an essential step to enable wireless data networks to
support a wide range of user demands. In this paper, we consider the problem of
joint resource reservation in the backhaul and Radio Access Network (RAN) based
on the statistics of user demands and channel states, and also network
availability. The goal is to maximize the sum of expected traffic flow rates,
subject to link and access point budget constraints, while minimizing the
expected outage of downlinks. The formulated problem turns out to be non-convex
and difficult to solve to global optimality. We propose an efficient Block
Coordinate Descent (BCD) algorithm to approximately solve the problem. The
proposed BCD algorithm optimizes the link capacity reservation in the backhaul
using a novel multipath routing algorithm that decomposes the problem down to
link-level and parallelizes the computation across backhaul links, while the
reservation of transmission resources in RAN is carried out via a novel
scalable and distributed algorithm based on Block Successive Upper-bound
Minimization (BSUM). We prove that the proposed BCD algorithm converges to a
Karush-Kuhn-Tucker solution. Simulation results verify the efficiency and the
efficacy of our BCD approach against two heuristic algorithms.


  Sources of long wavelength radiation are naturally described by an effective
field theory (EFT) which takes the form of a multipole expansion. Its action is
given by a derivative expansion where higher order terms are suppressed by
powers of the ratio of the size of the source over the wavelength. In order to
determine the Wilson coefficients of the EFT, i.e. the multipole moments, one
needs the mapping between a linear source term action and the multipole
expansion form of the action of the EFT. In this paper we perform the multipole
expansion to all orders by Taylor expanding the field in the source term and
then decomposing the action into symmetric trace free tensors which form
irreducible representations of the rotation group. We work at the level of the
action, and we obtain the action to all orders in the multipole expansion and
the exact expressions for the multipole moments for a scalar field,
electromagnetism and linearized gravity. Our results for the latter two cases
are manifestly gauge invariant. We also give expressions for the energy flux
and the (gauge dependent) radiation field to all orders in the multipole
expansion. The results for linearized gravity are a component of the EFT
framework NRGR and will greatly simplify future calculations of gravitational
wave observables in the radiation sector of NRGR.


  In this work we study the dynamical generation of mass in the massless N=1
Wess-Zumino model in a three dimensional spacetime. Using the tadpole method to
compute the effective potential, we observe that supersymmetry is dynamicaly
broken together with the discrete symmetry A(x) -> - A(x). We show that this
model, differently from non-supersymmetric scalar models, exhibits a consistent
perturbative dynamical generation of mass after two loop corrections to the
effective potential.


  We present a new phenomenological Nucleon-Nucleon chiral potential fitted to
925 pp and 1743 np scattering data selected from the Granada-2013 NN-database
up to a laboratory energy of $125$ MeV with 20 short distance parameters and
three chiral constants $c_1$, $c_3$ and $c_4$ with $\chi^2/\nu = 1.02$. Special
attention is given to testing the normality of the residuals which allows for a
sound propagation of statistical errors from the experimental data to the
potential parameters, phase-shifts, scattering amplitudes and counter-terms.
This fit allows for a new determination of the chiral constants $c_1$, $c_3$
and $c_4$ compatible with previous determinations from NN data. This new
interactions is found to be softer than other high quality potentials by
undertaking a Weinberg eigenvalue analysis. We further explore the interplay
between the error analysis and the assumed form of the short distance
interaction. The present work shows that it is possible to fit NN scattering
with a TPE chiral potential fulfilling all necessary statistical requirements
up to 125 MeV and shows unequivocal non-vanishing D-wave short distance pieces.


  The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using
the exact renormalization group equations has been studied, motivated by the
recently found non-trivial fixed point in $4<d<6$ dimensions with metastable
critical potential. Particular attention is paid to the case of $d=5$ where the
scaling exponent $\nu$ has the value $1/3$, which coincides with the scaling
exponent of quantum gravity in one fewer dimensions. Convincing results show
that this relation could be generalized to arbitrary number of dimensions above
five. Some aspects of AdS/CFT correspondence are also discussed.


  The Golden-Thompson trace inequality which states that $Tr\, e^{H+K} \leq
Tr\, e^H e^K$ has proved to be very useful in quantum statistical mechanics.
Golden used it to show that the classical free energy is less than the quantum
one. Here we make this G-T inequality more explicit by proving that for some
operators, notably the operators of interest in quantum mechanics, $H=\Delta$
or $H= -\sqrt{-\Delta +m}$ and $K=$ potential, $Tr\, e^{H+(1-u)K}e^{uK}$ is a
monotone increasing function of the parameter $u$ for $0\leq u \leq 1$. Our
proof utilizes an inequality of Ando, Hiai and Okubo (AHO): $Tr\,
X^sY^tX^{1-s}Y^{1-t} \leq Tr\, XY$ for positive operators X,Y and for
$\tfrac{1}{2} \leq s,\,t \leq 1 $ and $s+t \leq \tfrac{3}{2}$. The obvious
conjecture that this inequality should hold up to $s+t\leq 1$, was proved false
by Plevnik. We give a different proof of AHO and also give more counterexamples
in the $\tfrac{3}{2}, 1$ range. More importantly we show that the inequality
conjectured in AHO does indeed hold in this range if $X,Y$ have a certain
positivity property -- one which does hold for quantum mechanical operators,
thus enabling us to prove our G-T monotonicity theorem.


  We investigate the computational power of periodically iterated morphisms,
also known as D0L systems with periodic control, PD0L systems for short. These
systems give rise to a class of one-sided infinite sequences, called PD0L
words.
  We construct a PD0L word with exponential subword complexity, thereby
answering a question raised by Lepisto (1993) on the existence of such words.
We solve another open problem concerning the decidability of the first-order
theories of PD0L words; we show it is already undecidable whether a certain
letter occurs in a PD0L word. This stands in sharp contrast to the situation
for D0L words (purely morphic words), which are known to have at most quadratic
subword complexity, and for which the monadic theory is decidable.
  The main result of our paper, leading to these answers, is that every
computable word w over an alphabet Sigma can be embedded in a PD0L word u over
an extended alphabet Gamma in the following two ways: (i) such that every
finite prefix of w is a subword of u, and (ii) such that w is obtained from u
by erasing all letters from Gamma not in Sigma. The PD0L system generating such
a word u is constructed by encoding a Fractran program that computes the word
w; Fractran is a programming language as powerful as Turing Machines.
  As a consequence of (ii), if we allow the application of finite state
transducers to PD0L words, we obtain the set of all computable words. Thus the
set of PD0L words is not closed under finite state transduction, whereas the
set of D0L words is. It moreover follows that equality of PD0L words (given by
their PD0L system) is undecidable. Finally, we show that if erasing morphisms
are admitted, then the question of productivity becomes undecidable, that is,
the question whether a given PD0L system defines an infinite word.


  We consider a discrete-time random walk on a line starting at $x_0\geq 0$
where a cost is incurred at each jump. We obtain an exact analytical formula
for the distribution of the total cost of a trajectory until the process
crosses the origin for the first time. The formula is valid for arbitrary jump
distribution and cost function (heavy- and light-tailed alike), provided they
are symmetric and continuous. We analyze the formula in different scaling
regimes, and find a high degree of universality with respect to the details of
the jump distribution and the cost function. Applications are given to the
motion of an active run-and-tumble particle in one dimension and extensions to
multiple cost variables are considered. The analytical results are in perfect
agreement with numerical simulations.


  Let X be e quasi-compact and semi-separated scheme. If every at quasi-
coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for
some n > 0. If X is coherent and n-perfect(not necessarily of finite krull
dimension), we prove that every at quasi-coherent sheaf has finite pure
injective dimension. Also, we show that there is an equivalence K(PinfX)--->
D(FlatX) of homotopy categories, whenever K(PinfX) is the homotopy category of
pure injective at quasi-coherent sheaves and D(FlatX) is the pure derived
category of at quasi-coherent sheaves.


  In 1980 J. Powell proposed that five specific elements sufficed to generate
the Goeritz group of any Heegaard splitting of $S^3$. This conjecture remains
unresolved for genus $g \geq 4$. Here a short argument shows that one of his
proposed generators is redundant, in fact a consequence of three of the other
four.


  Dust particles immersed within a plasma environment, such as those found in
planetary rings or cometary environments, will acquire an electric charge. If
the ratio of interparticle potential energy to average kinetic energy is high
enough the particles will form either a 'liquid' structure with short-range
ordering or a crystalline structure with long-range ordering. Since their
discovery in laboratory environments in 1994, such crystals have been the
subject of a variety of experimental, theoretical, and numerical
investigations. Laboratory experiments analyzing the behavior of dust grains in
a plasma rely on optical diagnostics to provide data about the system in a
non-perturbative manner. In the past, capturing, imaging, and analyzing
crystalline structure in dusty plasmas has been a non-trivial problem.
Utilizing digital imaging and analysis systems, data capture, image formatting,
and analysis can be done quickly. Following data capture, image analysis is
conducted using modified Particle Image Velocimetry (PIV) and Particle Tracking
Velocimetry (PTV) algorithms. The data extracted is then used to construct
Voronoi diagrams, calculate particle density, inter-particle spacing, pair
correlation functions, and thermal energy. From this data other dust plasma
parameters can be inferred such as inter-particle forces and grain charges.


  In the last years there has been a growing interest in the applications of
diffusion tractography for target identification in neurofunctional disorders
for an increasingly tailored approach. The growing diffusion of
well-established neurosurgical procedures as deep brain stimulation (DBS) and
trans-cranial Magnetic Resonance-guided Focused Ultrasound (tcMRgFUS) favored
this trend. Tractography can indeed provide more accurate, patient-specific,
information about the targeted region if compared to stereotactic atlases. On
the other hand, this tractography-based approachs is not very
physician-friendly, and its heavily time consuming since needs several hours
for Magnetic Resonance Imaging (MRI) data processing. In this study we propose
a novel open-source deep learning framework called DeLTA-BIT (acronym of
Deep-learning Local TrActography for BraIn Targeting) for reconstructing
thalamic probabilistic tractography maps enabling a personalized
(patient-specific) target identification for functional neurological disorders.
The proposed framework exploits two convolutional neural networks (CNNs) to
segment the thalamus and reconstruct the connectivity map between each voxel
inside the thalamus and any user-specified target cortical or subcortical
masks. These CNNs were trained, validated, and tested on the datasets from the
Human Connectome Project (HCP) database. Our results are comparable with the
state-of-the-art data-driven segmentation and probabilistic tractography and
demonstrate the high performance of proposed networks for personalized thalamic
target identification with a Dice coefficient of 0.93 +/- 0.01 for thalamus
segmentation and a Dice Similarity Coefficient for the projection to the
precentral gyrus from the thalamus of 0.80 +/- 0.06. The code of these models
is freely available on GitHub.


  In a reasonably self-contained and explicit presentation we illustrate the
efficiency of the Feynman-Kac formula for the rigorous derivation of three
inequalities of interest in non-relativistic quantum mechanics.


  From the perspective of network analysis, the ubiquitous networks are
comprised of regular and irregular components, which makes uncovering the
complexity of network structures to be a fundamental challenge. Exploring the
regular information and identifying the roles of microscopic elements in
network data can help us recognize the principle of network organization and
contribute to network data utilization. However, the intrinsic structural
properties of networks remain so far inadequately explored and theorised. With
the realistic assumption that there are consistent features across the local
structures of networks, we propose a low-rank pursuit based self-representation
network model, in which the principle of network organization can be uncovered
by a representation matrix. According to this model, original true networks can
be reconstructed based on the observed unreliable network topology. In
particular, the proposed model enables us to estimate the extent to which the
networks are regulable, i.e., measuring the reconstructability of networks. In
addition, the model is capable of measuring the importance of microscopic
network elements, i.e., nodes and links, in terms of network regularity thereby
allowing us to regulate the reconstructability of networks based on them.
Extensive experiments on disparate real-world networks demonstrate the
effectiveness of the proposed network reconstruction and regulation algorithm.
Specifically, the network regularity metric can reflect the reconstructability
of networks, and the reconstruction accuracy can be improved by removing
irregular network links. Lastly, our approach provides an unique and novel
insight into the organization exploring of complex networks.


  I present the reduction of phase space of the theory of an antisymmetric
tensor potential coupled to an abelian gauge field, using Dirac's procedure.
Duality transformations on the reduced phase space are also discussed.


  Results are presented on $\psi(2S)$ and $J/\psi$ hadronic decays to
$K^0_SpK^-\bar n$ and $K^0_S\bar p K^+n$ final states from data samples of 14
million $\psi(2S)$ and 58 million $J/\psi$ events accumulated at the BES II
detector. No $\Theta(1540)$ signal, the pentaquark candidate, is observed, and
upper limits for ${\cal B}(\psi(2S)\to\Theta\bar\Theta\to K^0_S p K^-\bar n +
K^0_S \bar p K^+ n) < 0.84\times 10^{-5}$ and ${\cal
B}(J/\psi\to\Theta\bar\Theta\to K^0_S p K^-\bar n + K^0_S \bar p K^+ n) <
1.1\times 10^{-5}$ at the 90% confidence level are set. For single
$\Theta(1540)$ production, the upper limits determined by our analysis are also
on the order of $10^{-5}$ in both $\psi(2S)$ and $J/\psi$ decays.


  We study a limit of the Kerr-(A)dS spacetime in a general dimension where an
arbitrary number of its rotational parameters is set equal. The resulting
metric after the limit formally splits into two parts - the first part has the
form of the Kerr-NUT-(A)dS metric analogous to the metric of the entire
spacetime, but only for the directions not subject to the limit, and the second
part can be interpreted as the K\"{a}hler metrics. However, this separation is
not integrable, thus it does not lead to a product of independent manifolds. We
also reconstruct the original number of explicit and hidden symmetries
associated with Killing vectors and Killing tensors. Therefore, the resulting
spacetime represents a special subcase of the generalized Kerr-NUT-(A)dS metric
that retains the full Killing tower of symmetries. In $D=6$, we present
evidence of an enhanced symmetry structure after the limit. Namely, we find
additional Killing vectors and show that one of the Killing tensors becomes
reducible as it can be decomposed into Killing vectors.


  Studies of the kinematics of gaseous halos in some spiral galaxies have shown
that the rotational velocity of the gas decreases with height above the
midplane (z). This vertical velocity gradient has been observed in both the
neutral and ionized components of halos. We present imaging Fabry-Perot Halpha
observations of the edge-on galaxy NGC 5775. These observations allow us to
study the variation in the rotation curve (and, to some extent, the radial
profile) of the ionized gas component as a function of z. We have used an
iterative technique to infer the major axis rotation curve from the ionized gas
observations as well as CO data. A preliminary analysis of position-velocity
(PV) diagrams parallel to the major axis implies the presence of a vertical
velocity gradient. The magnitude of this gradient is tentatively found to be ~2
km/s/arcsec, consistent with the results of Rand (2000) and Tullmann et al.
(2000).


  Limits of classical constitutive laws such as Fourier and Navier-Stokes
equations are discovered since decades. However, the proper extensions --
generalizations of these are not unique. They differ in the underlying physical
principles and in modeling capabilities. In this paper, two different theories
are discussed and compared to each other, namely the kinetic theory-based
Rational Extended Thermodynamics (RET) and non-equilibrium thermodynamics with
internal variables (NET-IV).
  First, the paper starts with the case of rigid heat conductors summarizing
the result achieved so far. Then a typical example of compressible bodies is
shown by presenting the first generalization for rarefied gases, called
Meixner's theory. It is further extended using generalized entropy current in
the framework of NET-IV. It is shown how its structure is related to RET and
how the compatibility between them can be acquired.


  The identification of groups' prototypes, i.e. elements of a dataset that
represent different groups of data points, may be relevant to the tasks of
clustering, classification and mixture modeling. The R package pivmet presented
in this paper includes different methods for extracting pivotal units from a
dataset. One of the main applications of pivotal methods is a Markov Chain
Monte Carlo (MCMC) relabelling procedure to solve the label switching in
Bayesian estimation of mixture models. Each method returns posterior estimates,
and a set of graphical tools for visualizing the output. The package offers
JAGS and Stan sampling procedures for Gaussian mixtures, and allows for
user-defined priors' parameters. The package also provides functions to perform
consensus clustering based on pivotal units, which may allow to improve
classical techniques (e.g. k-means) by means of a careful seeding. The paper
provides examples of applications to both real and simulated datasets.


  Given a C*-dynamical system (A,G,\alpha), we say that A is a weakly proper
(X\rtimes G)-algebra if there exists a proper G-space X together with a
nondegenerate G-equivariant *-homomorphism \phi:C_0(X)->M(A). Weakly proper
G-algebras form a large subclass of the class of proper G-algebras in the sense
of Rieffel. In this paper we show that weakly proper (X\rtimes G)-algebras
allow the construction of full fixed-point algebras A^G corresponding to the
full crossed product A\rtimes_{\alpha}G, thus solving, in this setting, a
problem stated by Rieffel in his 1988's original article on proper actions. As
an application we obtain a general Landstad duality result for arbitrary
coactions together with a new and functorial construction of maximalizations of
coactions.
  The same methods also allow the construction of exotic generalized
fixed-point algebras associated to crossed-product norms lying between the
reduced and universal ones. Using these, we give complete answers to some
questions on duality theory for exotic crossed products recently raised by
Kaliszewski, Landstad and Quigg.


  Signature-based algorithms have become a standard approach for computing
Gr\"obner bases in commutative polynomial rings. However, so far, it was not
clear how to extend this concept to the setting of noncommutative polynomials
in the free algebra. In this paper, we present a signature-based algorithm for
computing Gr\"obner bases in precisely this setting. The algorithm is an
adaptation of Buchberger's algorithm including signatures. We prove that our
algorithm correctly enumerates a signature Gr\"obner basis as well as a
Gr\"obner basis of the module generated by the leading terms of the generators'
syzygies, and that it terminates whenever the ideal admits a finite signature
Gr\"obner basis. Additionally, we adapt well-known signature-based criteria
eliminating redundant reductions, such as the syzygy criterion, the F5
criterion and the singular criterion, to the case of noncommutative
polynomials. We also generalize reconstruction methods from the commutative
setting that allow to recover, from partial information about signatures, the
coordinates of elements of a Gr\"obner basis in terms of the input polynomials,
as well as a basis of the syzygy module of the generators. We have written a
toy implementation of all the algorithms in the Mathematica package OperatorGB
and we compare our signature-based algorithm to the classical Buchberger
algorithm for noncommutative polynomials.


  Building a successful community means governing active populations and
limited resources. This challenge often requires communities to design formal
governance systems from scratch. But the characteristics of successful
institutional designs are unclear. Communities that are more mature and
established may have more elaborate formal policy systems. Alternatively, they
may require less formalization precisely because of their maturity. Indeed,
scholars often downplay the role that formal rules relative to unwritten rules,
norms, and values. But in a community with formal rules, decisions are more
consistent, transparent, and legitimate. To understand the relationship of
formal institutions to community maturity and governance style, we conduct a
large-scale quantitative analysis applying institutional analysis frameworks of
self-governance scholar Elinor Ostrom to 80,000 communities across 3 platforms:
the sandbox game Minecraft, the MMO game World of Warcraft, and Reddit. We
classify communities' written rules to test predictors of institutional
formalization. From this analysis we extract two major findings. First,
institutional formalization, the size and complexity of an online community's
governance system, is generally positively associated with maturity, as
measured by age, population size, or degree of user engagement. Second, we find
that online communities employ similar governance styles across platforms,
strongly favoring "weak" norms to "strong" requirements. These findings suggest
that designers and founders of online communities converge on styles of
governance practice that are correlated with successful self-governance. With
deeper insights into the patterns of successful self-governance, we can help
more communities overcome the challenges of self-governance and create for
their members powerful experiences of shared meaning and collective
empowerment.


  Three-dimensional magnetic nanostructures have recently emerged as artificial
magnetic material types with unique properties bearing potential for
applications, including magnonic devices. Interconnected magnetic nanowires are
a sub-category within this class of materials that is attracting particular
interest. We investigate the high-frequency magnetization dynamics in a cubic
array of cylindrical magnetic nanowires through micromagnetic simulations based
on a frequency-domain formulation of the linearized Landau-Lifshitz-Gilbert
equation. The small-angle high-frequency magnetization dynamics excited by an
external oscillatory field displays clear resonances at distinct frequencies.
These resonances are identified as oscillations connected to specific geometric
features and micromagnetic configurations. The geometry- and
configuration-dependence of the nanowire array's absorption spectrum
demonstrates the potential of such magnetic systems for tuneable and
reprogrammable magnonic applications.


  In an effort to understand ``rafts'' in biological membranes, we propose
phenomenological models for saturated and unsaturated lipid mixtures, and
lipid-cholesterol mixtures. We consider simple couplings between the local
composition and internal membrane structure, and their influence on transitions
between liquid and ``gel'' membrane phases. Assuming that the gel transition
temperature of the saturated lipid is shifted by the presence of the
unsaturated lipid, and that cholesterol acts as an external field on the chain
melting transition, a variety of phase diagrams are obtained. The phase
diagrams for binary mixtures of saturated/unsaturated lipids and
lipid/cholesterol are in semi-quantitative agreement with the experiments. Our
results also apply to regions in the ternary phase diagram of
lipid/lipid/cholesterol systems.


  Research into, and design and construction of mobile systems and algorithms
requires access to large-scale mobility data. Unfortunately, the wireless and
mobile research community lacks such data. For instance, the largest available
human contact traces contain only 100 nodes with very sparse connectivity,
limited by experimental logistics. In this paper we pose a challenge to the
community: how can we collect mobility data from billions of human
participants? We re-assert the importance of large-scale datasets in
communication network design, and claim that this could impact fundamental
studies in other academic disciplines. In effect, we argue that planet-scale
mobility measurements can help to save the world. For example, through
understanding large-scale human mobility, we can track and model and contain
the spread of epidemics of various kinds.


  We present observational estimates of the magnitude difference between the
luminosity function RGB bump and the HB (Delta(bump-zahb)), and of star counts
in the bump region (R_bump), for a sample of 54 Galactic globular clusters
(GCs) observed by the HST. The large sample of stars resolved in each cluster,
and the high photometric accuracy of the data allowed us to detect the bump
also in a number of metal poor clusters. To reduce the photometric
uncertainties, empirical values are compared with theoretical predictions
obtained from a set of updated canonical stellar evolution models which have
been transformed directly into the HST flight system. We found an overall
qualitative agreement between theory and observations. Quantitative estimates
of the confidence level are hampered by current uncertainties on the GCs
metallicity scale, and by the strong dependence of Delta(bump-zahb) on the
cluster metallicity. In case of the R_bump parameter, which is only weakly
affected by the metallicity, we find a very good quantitative agreement between
theoretical canonical models and observations. For our full cluster sample the
average difference between predicted and observed R_bump values is practically
negligible, and ranges from -0.002 to -0.028, depending on the employed
metallicity scale. The observed dispersion around these values is entirely
consistent with the observational errors on R_bump. As a comparison, the value
of R_bump predicted by theory in case of spurious bump detections would be
\~0.10 smaller than the observed ones. We have also tested the influence on the
predicted Delta(bump-zahb) and R_bump values of an He-enriched component in the
cluster stellar population. We find that the predicted Delta(bump-zahb) and
R_bump values are only marginally affected.


  We report on a study of exclusive radiative decays of the Upsilon(1S)
resonance into a final state consisting of a photon and two K0s candidates. We
find evidence for a signal for Upsilon(1S)->gamma f_2'(1525);
f_2'(1525)->K0sK0s, at a rate (4.0+/-1.3+/-0.6)x10^{-5}, consistent with
previous observations of Upsilon(1S)->gamma f_2'(1525); f_2'(1525)->K+K-, and
isospin. Combining this branching fraction with existing branching fraction
measurements of Upsilon(1S)->gamma f_2'(1525) and J/psi->gamma f_2'(1525), we
obtain the ratio of branching fractions: B(Upsilon(1S)->gamma
f_2'(1525))/B(J/psi->gamma f_2'(1525))=0.09+/-0.02, approximately consistent
with expectations based on soft collinear effective theory.


  A parent insulator of the Bi-based high-$T_c$ superconductor
Bi$_2$Sr$_{2-x}$La$_x$CaCu$_2$O$_{8+\delta}$ was successfully grown by a
traveling solvent floating zone method. The in-plane resistivity $\rho_{ab}$
shows metallic behavior ($d\rho_{ab}/dT >$ 0) near room temperature, although
the magnitude of the resistivity is far above the Mott limit for metallic
conduction. The Hall mobility of the parent insulator does not so much differ
from that of an optimally doped sample. These results suggest that the system
is not a simple insulator with a well-defined gap, and the hole in the parent
insulator is essentially itinerant, as soon as it is doped.


  We study sound in Galilean invariant systems of one-dimensional fermions. At
low temperatures, we find a broad range of frequencies in which in addition to
the waves of density there is a second sound corresponding to ballistic
propagation of heat in the system. The damping of the second sound mode is
weak, provided the frequency is large compared to a relaxation rate that is
exponentially small at low temperatures. At lower frequencies the second sound
mode is damped, and the propagation of heat is diffusive.


  This paper investigates the energy savings that near-subthreshold processors
can obtain in edge AI applications and proposes strategies to improve them
while maintaining the accuracy of the application. The selected processors
deploy adaptive voltage scaling techniques in which the frequency and voltage
levels of the processor core are determined at the run-time. In these systems,
embedded RAM and flash memory size is typically limited to less than 1 megabyte
to save power. This limited memory imposes restrictions on the complexity of
the neural networks model that can be mapped to these devices and the required
trade-offs between accuracy and battery life. To address these issues, we
propose and evaluate alternative 'big-little' neural network strategies to
improve battery life while maintaining prediction accuracy. The strategies are
applied to a human activity recognition application selected as a demonstrator
that shows that compared to the original network, the best configurations
obtain an energy reduction measured at 80% while maintaining the original level
of inference accuracy.


  It is known that the wavelength of the ripples on icicles in nature is of
centimeter-scale. Such study on morphological instability of ice-water
interface during ice growth from flowing supercooled water film with one side
being a free surface has recently been made [K. Ueno, Phys. Rev. E 68, 021603
(2003)]. This is a first theoretical study taking into account the influence of
the shape of the water-air surface on the growth condition of infinitesimal
disturbances of the ice-water interface. A simpler formula to determine the
wavelength of the ripples than that in the previous paper is derived. It seems
that the wavelength of ripples is insensitive to the water supply rates,
diameters of the icicles and surrounding air temperatures. The details of
dependence of the wavelengh of ripples on these parameters are investigated.


  The importance of center vortices for the understanding of the confining
properties of SU(N) Yang-Mills theories is well established in the lattice.
However, in the continuum, there is a problem concerning the relevance of
center vortex backgrounds. They display the so called Savvidy-Nielsen-Olesen
instability, associated with a gyromagnetic ratio $g^{(b)}_m=2$ for the
off-diagonal gluons.
  In this work, we initially consider the usual definition of a {\it thin}
center vortex and rewrite it in terms of a local color frame in SU(N)
Yang-Mills theories. Then, we define a thick center vortex as a diagonal
deformation of the thin object. Besides the usual thick background profile,
this deformation also contains a frame defect coupled with gyromagnetic ratio
$g^{(d)}_m=1$, originated from the charged sector. As a consequence, the
analysis of stability is modified. In particular, we point out that the defect
should stabilize a vortex configuration formed by a pair of straight components
separated by an appropriate finite distance.


  Time-Varying meshes (TVMs), characterized by their varying connectivity and
number of vertices, hold significant potential in immersive media and other
various applications. However, their practical utilization is challenging due
to their time-varying features and large file sizes. Creating a reference mesh
that contains the most essential information is a promising approach to
utilizing shared information within TVMs to reduce storage and transmission
costs. We propose a novel method that employs volume tracking to extract
reference meshes. First, we adopt as-rigid-as-possible (ARAP) volume tracking
on TVMs to get the volume centers for each mesh. Then, we use multidimensional
scaling (MDS) to get reference centers that ensure the reference mesh avoids
self-contact regions. Finally, we map the vertices of the meshes to reference
centers and extract the reference mesh. Our approach offers a feasible solution
for extracting reference meshes that can serve multiple purposes such as
establishing surface correspondence, deforming the reference mesh to different
shapes for I-frame based mesh compression, or defining the global shape of the
TVMs.


  In this study, we employ analytical and numerical techniques to examine a
phase transition model with moving boundaries. The model displays two relevant
spatial scales pointing out to a macroscopic phase and a microscopic phase,
interacting on disjoint inclusions. The shrinkage or the growth of the
inclusions is governed by a modified Gibbs-Thomson law depending on the
macroscopic temperature, but without accessing curvature information. We use
the Hanzawa transformation to transform the problem onto a fixed reference
domain. Then a fixed-point argument is employed to demonstrate the
well-posedness of the system for a finite time interval. Due to the model's
nonlinearities and the macroscopic parameters, which are given by differential
equations that depend on the size of the inclusions, the problem is
computationally expensive to solve numerically. We introduce a precomputing
approach that solves multiple cell problems in an offline phase and uses an
interpolation scheme afterward to determine the needed parameters.
Additionally, we propose a semi-implicit time-stepping method to resolve the
nonlinearity of the problem. We investigate the errors of both the precomputing
and time-stepping procedures and verify the theoretical results via numerical
simulations.


  We prove that the solution map associated with the $1D$ half-wave cubic
equation in the periodic setting cannot be uniformly continuous on bounded sets
of the periodic Sobolev spaces $H^s$ with $s\in (1/4, 1/2)$


  We show that static sources coupled to a massless scalar field in
Schwarzschild spacetime give rise to emission and absorption of zero-energy
particles due to the presence of Hawking radiation. This is in complete analogy
with the description of the bremsstrahlung by a uniformly accelerated charge
from the coaccelerated observers' point of view. The response rate of the
source is found to coincide with that in Minkowski spacetime as a function of
its proper acceleration. This result may be viewed as restoration of the
equivalence principle by the Hawking effect.


  To optimize a neural network one often thinks of optimizing its parameters,
but it is ultimately a matter of optimizing the function that maps inputs to
outputs. Since a change in the parameters might serve as a poor proxy for the
change in the function, it is of some concern that primacy is given to
parameters but that the correspondence has not been tested. Here, we show that
it is simple and computationally feasible to calculate distances between
functions in a $L^2$ Hilbert space. We examine how typical networks behave in
this space, and compare how parameter $\ell^2$ distances compare to function
$L^2$ distances between various points of an optimization trajectory. We find
that the two distances are nontrivially related. In particular, the
$L^2/\ell^2$ ratio decreases throughout optimization, reaching a steady value
around when test error plateaus. We then investigate how the $L^2$ distance
could be applied directly to optimization. We first propose that in multitask
learning, one can avoid catastrophic forgetting by directly limiting how much
the input/output function changes between tasks. Secondly, we propose a new
learning rule that constrains the distance a network can travel through
$L^2$-space in any one update. This allows new examples to be learned in a way
that minimally interferes with what has previously been learned. These
applications demonstrate how one can measure and regularize function distances
directly, without relying on parameters or local approximations like loss
curvature.


  Let $(X_1,\ldots,X_n)$ be an exchangeable random vector with distribution
function $F$, and denote by $Y_1\leq \cdots\leq Y_n$ the corresponding order
statistics. We show that the conditional distribution of $(X_1,\ldots,X_n)$
given $(Y_1,\ldots,Y_n)$ does not depend on $F$.


  This note surveys how energy generation and strengthening has been used to
prove Morawetz estimates for various field equations in Minkowski space, the
exterior of the Schwarzschild spacetime, and the exterior of the Kerr
spacetime. It briefly outlines an approach to proving a decay estimate for the
Maxwell equation outside a Kerr black hole.


  In "On the Heavens" Aristotle criticizes the Pythagorean point of view which
claims the existence of a cosmic music and a cosmic sound. According to the
Pythagorean argument, there exists a cosmic music produced by stars and
planets. These celestial bodies generate sound in its movements, and the music
appears due to the cosmic harmony. For Aristotle, there is no sound produced by
celestial bodies. Then, there is no music as well. However, recently, LIGO
(Laser Interferometer Gravitational-Waves Observatory) has detected the
gravitational waves predicted by Einstein. In some sense, a sound originated
from black holes has been heard. That is, Einstein or the General Relativity
and LIGO appear to be with the Pythagoreanism and against the master of the
Lyceum.


  This is the writeup of an expository talk. It is intended as an introduction
to the work of Hopkins, Kuhn, and Ravenel on generalized group characters,
which seems to fit very well with the theory of what physicists call higher
twisted sectors in the theory of orbifolds.


  This short report is concerned with the well known and not yet satisfactorily
answered problem of the existence of two well distinct typical mass scales of
primordial halo objects: solar size objects (halo field stars) and globular
cluster size objects (10^5 solar masses and more). A likely possibility is that
almost all the gaseous content of the halo fragmented into massive clouds,
which, in their turn, recycled part of their gas to the environment in either a
quiescent either a violent way.
  The modes and quantity of mass loss depends on thermodynamic properties of
gas clouds, determined, in a zero-metal environment, mainly by hydrogenic
components evolution and influence on the equation of state.
  It is logical to expect that, due to the different dynamical and
thermodynamical conditions of the recycled gas, another typical fragmenting
mass scale is settled.


  This review article aims at illustrating the recent progresses in the
electrical control of magnetism in oxides with profound physics and enormous
potential applications. In the first part, we provide a comprehensive summary
of the electrical control of magnetism in the classic multiferroic
heterostructures and clarify their various mechanisms lying behind. The second
part focuses on the novel route of electric double layer gating for driving a
significantly electronic phase transition in magnetic oxides by a small
voltage. The electric field applied on the ordinary dielectric oxide in the
third part is used to control the magnetic phenomenon originated from the
charge transfer and orbital reconstruction at the interface between dissimilar
correlated oxides. At last, we analyze the challenges in electrical control of
magnetism in oxides, both on mechanism and practical application, which would
inspire more in-depth researches and advance the development in this field.


  We examine excitons formed in the bulk of a topological insulator as the
system is tuned via a parameter between topological and trivial insulating
phases, arguing that nontrivial topology has fingerprints in the spectrum of
these excitons. The closely related hydrogen atom problem is well known to have
a degeneracy due to a hidden symmetry, and the changes to the excitonic
spectrum that we find can be understood as a result of breaking of this
underlying symmetry due to the Berry phase. Furthermore, this phase is found to
affect the spectrum in the topological parameter regime much more strongly than
in the trivial regime. We first construct a semiclassical model of the system
to develop qualitative intuition for the effects at play, then move to a more
robust numerical simulation of the full quantum system, working with the
Bernevig-Hughes-Zhang model of a 2D topological insulator.


  We have developed a quantitative theory of Cooper pair pumping in gated
one-dimensional arrays of Josephson junctions. The pumping accuracy is limited
by quantum tunneling of Cooper pairs out of the propagating potential well and
by direct supercurrent flow through the array. Both corrections decrease
exponentially with the number N of junctions in the array, but give a serious
limitation of accuracy for any practical array. The supercurrent at resonant
gate voltages decreases with N only as sin(v/N)/N, where v is the Josephson
phase difference across the array.


  We present a Bayesian analysis of the energies and arrival times of the
neutrinos from supernova SN 1987A detected by the Kamiokande II, IMB, and
Baksan detectors, and find strong evidence for two components in the neutrino
signal: a long time scale component from thermal Kelvin-Helmholtz cooling of
the nascent neutron star, and a brief (~< 1 s), softer component similar to
that expected from emission by accreting material in the delayed supernova
scenario. In the context of this model, we show that the data constrain the
electron antineutrino rest mass to be less than 5.7 eV with 95% probability.
Our analysis takes advantage of significant advances that have occured in the
years since the detections in both our understanding of the supernova mechanism
and our ability to analyze sparse data. As a result there are substantial
differences between our inferences and those found in earlier studies. We find
that two-component models for the neutrino signal make the data >100 times more
probable than single-component models. In addition, the radius and binding
energy of the nascent neutron star implied by single-component models deviates
significantly from the values predicted by current neutron star models, whereas
those implied by models with an accretion component are in complete agreement
with the predictions. As a result, two-component models are hundreds to
thousands of times more probable than single-component models. The neutrino
data thus provide the first direct observational evidence in favor of the
delayed supernova scenario over the prompt scenario. (Abridged abstract)


  Despite recent advances in video-based action recognition and robust
spatio-temporal modeling, most of the proposed approaches rely on the abundance
of computational resources to afford running huge and computation-intensive
convolutional or transformer-based neural networks to obtain satisfactory
results. This limits the deployment of such models on edge devices with limited
power and computing resources. In this work we investigate an important smart
home application, video based delivery detection, and present a simple and
lightweight pipeline for this task that can run on resource-constrained
doorbell cameras. Our method relies on motion cues to generate a set of coarse
activity proposals followed by their classification with a mobile-friendly
3DCNN network. To train we design a novel semi-supervised attention module that
helps the network to learn robust spatio-temporal features and adopt an
evidence-based optimization objective that allows for quantifying the
uncertainty of predictions made by the network. Experimental results on our
curated delivery dataset shows the significant effectiveness of our pipeline
and highlights the benefits of our training phase novelties to achieve free and
considerable inference-time performance gains.


  We study the collective charge-density modes (plasmons) of two-dimensional
nonsymmorphic Dirac semimetals, within the random-phase approximation (RPA) in
presence of Coulomb interaction. Without loss of generality, we consider a
system in a two-dimensional square-lattice, based on the model originally
predicted by Young and Kane (https://doi.org/10.1103/PhysRevLett.115.126803),
where the non-interacting band-structure consists of three band-touching
points, near which the electronic states follow Dirac equations. Two of these
Dirac nodes, at the momentum points $X_1$ and $X_2$, are anisotropic, i.e.,
disperse with different velocities in different directions, whereas the third
Dirac point at $M$ is isotropic. Interestingly we find that the system of these
three Dirac nodes hold a single low-energy plasmon mode, within its
particle-hole gap, that disperses in isotropic manner, in the case when the
nodes at $X_1$ and $X_2$ are related by symmetry, which we further show in a
long-wavelength approximation. We also discuss the effects of possible
perturbations that can give rise to anisotropic plasmon dispersions. Our
results suggest, in similarity with graphene, plasmon modes of such
non-symmorphic semimetals are highly tunable and hold promise for possible
applications.


  We consider the hypothetical quantum network case where Alice wishes to
transmit one qubit of information (specifically a pure quantum state) to $M$
parties, where $M$ is some large number. The remote receivers locally perform
single qubit quantum state tomography on the transmitted qubits in order to
compute the quantum state within some error rate (dependent on the tomography
technique and number of qubits used). We show that with the use of an
intermediate optimal symmetric universal quantum cloning machine (between Alice
and the remote receivers) as a repeater-type node in a hypothetical quantum
network, Alice can send significantly fewer qubits compared to direct
transmission of the message qubits to each of the $M$ remote receivers. This is
possible due to two properties of quantum cloning. The first being that single
qubit quantum clones retain the same angle, in the Bloch sphere representation,
as the initial quantum state. This means that if the mixed state of the quantum
clone can be computed to high enough accuracy, the pure quantum state can be
computed by extrapolating that vector to the surface of the Bloch sphere. The
second property is that the state overlap of approximate quantum clones, with
respect to the original pure quantum state, quickly converges (specifically for
$1 \rightarrow M$ the limit of the fidelity as M goes to infinity is
$\frac{2}{3}$). This means that Alice can prepare a constant number of qubits
(which are then passed through the quantum cloning machine) in order to achieve
a desired error rate, if $M$ is large enough. Combined, these two properties
mean that for large $M$, Alice can prepare orders of magnitude fewer qubits in
order to achieve the same single qubit transmission accuracy compared to the
naive direct qubit transmission approach.


  We show that Hilbert schemes of points on supersingular Enriques surface in
characteristic 2 are simply connected, symplectic varieties but are not
irreducible symplectic as the hodge number $h^{2,0} > 1$, even though a
supersingular Enriques surface is an irreducible symplectic variety. These are
the classes of varieties which appear only in characteristic 2 and they show
that the hodge number formula for G\"ottsche-Soergel does not hold over
characteristic 2. It also gives examples of varieties with trivial canonical
class which are neither irreducible symplectic nor Calabi-Yau, thereby showing
that there are strictly more classes of simply connected varieties with trivial
canonical class in characteristic 2 than over $\mathbb{C}$ as given by
Beauville-Bogolomov decomposition theorem.


  We give the description of three-dimensional Lie triple systems and their
corresponding Lie algebras with invomorphisme, The description of
three-dimensional Bol algebras linked with the distinguished Lie triple systems
above is given. The construction of the object describing the isotopy of Bol
algebras. The description of Bol 3-Webs, connected with the selected Bol
algebras.


  The static pair correlation (distribution) function and the structure factor
of particle distributions in three-dimensional homogeneous isotropic systems
are explicitly restored from two-dimensional data observed in a thin slab
sliced out from original systems. The result is given as an expansion with
respect to the thickness of the slab and applied to the critical density
fluctuations.


  We estimate the near-Sun axial magnetic field of a coronal mass ejection
(CME) on 10 March 2022. Solar Orbiter's in situ measurements, 7.8 degrees east
of the Sun-Earth line at 0.43 AU, provided a unique vantage point, along with
the WIND measurements at 0.99 AU. We determine a single power-law index from
near-Sun to L1, including in situ measurements from both vantage points. We
tracked the temporal evolution of the instantaneous relative magnetic helicity
of the source active region (AR), NOAA AR 12962. By estimating the helicity
budget of the pre-and post-eruption AR, we estimated the helicity transported
to the CME. Assuming a Lundquist flux-rope model and geometrical parameters
obtained through the graduated cylindrical shell (GCS) CME forward modelling,
we determined the CME axial magnetic field at a GCS-fitted height. Assuming a
power-law variation of the axial magnetic field with heliocentric distance, we
extrapolated the estimated near-Sun axial magnetic field to in situ
measurements at 0.43 AU and 0.99 AU. The net helicity difference between the
post-and pre-eruption AR is $(-7.1 \pm 1.2) \times 10^{41} \mathrm{Mx^{2}}$,
which is assumed to be bodily transported to the CME. The estimated CME axial
magnetic field at a near-Sun heliocentric distance of 0.03 AU is 2067 $\pm$ 405
nT. From 0.03 AU to L1, a single power-law falloff, including both vantage
points at 0.43 AU and 0.99 AU, gives an index $-1.23 \pm 0.18$. We observed a
significant decrease in the pre-eruptive AR helicity budget. Extending previous
studies on inner-heliospheric intervals from 0.3 AU to $\sim$1 AU, referring to
estimates from 0.03 AU to measurements at $\sim$1 AU. Our findings indicate a
less steep decline in the magnetic field strength with distance compared to
previous studies, but they align with studies that include near-Sun in situ
magnetic field measurements, such as from Parker Solar Probe.