  Dark matter searches in gamma ray final states often make use of the fact
that photons can be produced from final state muons. Modern Monte Carlo
generators and DM codes include the effects of final state radiation from muons
produced in the dark matter annihilation process itself, but neglect the O(1%)
radiative correction that arises from the subsequent muon decay. After
implementing this correction we demonstrate the effect that it can have on dark
matter phenomenology by considering the case of dark matter annihilation to
four muons via scalar mediator production. We first show that the AMS-02
positron excess can no longer easily be made consistent with this final state
once the Fermi-LAT dwarf limits are calculated with the inclusion of radiative
muon decays, and we next show that the Fermi-LAT galactic centre gamma excess
can be improved with this final state after inclusion of the same effect. We
provide code and tables for the implementation of this effect in the popular
dark matter code micrOMEGAs, providing a solution for any model producing final
state muons.


  The possibility of reconstructing a spherically symmetric inhomogeneous
Lemaitre-Tolman-Bondi (LTB) model with $\Lambda$CDM observations has drawn a
lot of attention. Recently, a LTB model having the same luminosity-distance and
light-cone mass density as the $\Lambda$CDM model was reconstructed. We
calculate the cosmic age at our position in this model, and get the age
$t_{LTB}<11.7$Gyr in 2$\sigma$ confidence level from the Seven-Year WMAP
observations. This result is inconsistent with some Milky Way observations.


  In this paper, we present our studies of the phase diagram of the cuprate
superconductors performed in recent years. We describe how a few
field-theoretical concepts can be used to account for the puzzling properties
of these compounds. Starting with a short exposition of recent experimental
developments, we then introduce the concept of an emergent SU(2) symmetry,
which rotates between the superconducting and charge order parameters. We
describe a solvable model for which this symmetry turns out to be exact and
derive the corresponding effective field theory in terms of a non-linear
{\sigma} model. We then turn to the experimental consequences of our model with
the presence of skyrmions inside the vortex core and an elegant account of the
B-T phase diagram. Next, we move on to the second concept, which is the one of
an emergent U(1) gauge field in the theory. Within this more general framework,
the pseudogap transition can be viewed as a confining/deconfining transition.
Experimental consequences for a few spectroscopic probes like inelastic neutron
scattering, Raman spectroscopy, phonon line in x-ray scattering and
angle-resolved photoemission experiments are studied. This theory suggests the
presence of incoherent bosons at moderate temperatures in the phase diagram of
the cuprates, which would undergo a jamming transition at optimal doping [1].
Consequences of the presence of such bosons on the transport properties of
these materials are examined.


  In this paper we introduce the concept of von Neumann-Schatten Bessel
multipliers and obtain some of their characterizations. Finally, special
attention is devoted to the study of invertible Hilbert--Schmidt frame
multipliers. These results are not only of interest in their own right, but
also they pave the way for obtaining some new results for diagonalization of
matrices in finite dimensional setting as well as for dual $g$-frames. In
particular, we show that a $g$-frame is uniquely determined by the set of its
$g$-frames.


  The set of terms of an infinite sequence expressed by a recurrence relation
is equal to the set of maximum numbers of all primitive Pythagorean triples
such that the difference between the two non-maximum numbers is 1, which
Cimmino showed. By reference to Cimmino's researches, we show a recurrence
relation for the case where the difference between the two non-maximum numbers
is not 1, but 7.


  Linear Temporal Logic (LTL) is the de-facto standard temporal logic for
system specification, whose foundational properties have been studied for over
five decades. Safety and cosafety properties define notable fragments of LTL,
where a prefix of a trace suffices to establish whether a formula is true or
not over that trace. In this paper, we study the complexity of the problems of
satisfiability, validity, and realizability over infinite and finite traces for
the safety and cosafety fragments of LTL. As for satisfiability and validity
over infinite traces, we prove that the majority of the fragments have the same
complexity as full LTL, that is, they are PSPACE-complete. The picture is
radically different for realizability: we find fragments with the same
expressive power whose complexity varies from 2EXPTIME-complete (as full LTL)
to EXPTIME-complete. Notably, for all cosafety fragments, the complexity of the
three problems does not change passing from infinite to finite traces, while
for all safety fragments the complexity of satisfiability (resp.,
realizability) over finite traces drops to NP-complete (resp.,
${\Pi}^P_2$-complete).


  We consider quantum Hall droplets on complex projective spaces with a
combination of abelian and nonabelian background magnetic fields. Carrying out
an analysis similar to what was done for abelian backgrounds, we show that the
effective action for the edge excitations is given by a chiral, gauged
Wess-Zumino-Witten (WZW) theory generalized to higher dimensions.


  In this paper, we present a Hamiltonian identification method for a closed
quantum system whose time trace observables are measured with colored
measurement noise. The dynamics of the quantum system are described by a
Liouville equation which can be converted to a coherence vector representation.
Since the measurement process is disturbed by classical colored noise, we
introduce an augmented system model to describe the total dynamics, where the
classical colored noise is parameterized. Based on the augmented system model
as well as the measurement data, we can find a realization of the quantum
system with unknown parameters by employing an Eigenstate Realization
Algorithm. The unknown parameters can be identified using a
transfer-function-based technique. An example of a two-qubit system with
colored measurement noise is demonstrated to verify the effectiveness of our
method.


  We study the effect of magnetic fields on a simulated galaxy and its
surrounding gaseous halo, or circumgalactic medium (CGM), within cosmological
'zoom-in' simulations of a Milky Way-mass galaxy as part of the 'Simulating the
Universe with Refined Galaxy Environments' (SURGE) project. We use three
different galaxy formation models, each with and without magnetic fields, and
include additional spatial refinement in the CGM to improve its resolution. The
central galaxy's star formation rate and stellar mass are not strongly affected
by the presence of magnetic fields, but the galaxy is more disc-dominated and
its central black hole is more massive when $B>0$. The physical properties of
the CGM change significantly. With magnetic fields, the circumgalactic gas
flows are slower, the atomic hydrogen-dominated extended discs around the
galaxy are more massive and the densities in the inner CGM are therefore
higher, the temperatures in the outer CGM are higher, and the pressure in the
halo is higher and smoother. The total gas fraction and metal mass fraction in
the halo are also higher when magnetic fields are included, because less gas
escapes the halo. Additionally, we find that the CGM properties depend on
azimuthal angle and that magnetic fields reduce the scatter in radial velocity,
whilst enhancing the scatter in metallicity at fixed azimuthal angle. The
metals are thus less well-mixed throughout the halo, resulting in more
metal-poor halo gas. These results together show that magnetic fields in the
CGM change the flow of gas in galaxy haloes, making it more difficult for
metal-rich outflows to mix with the metal-poor CGM and to escape the halo, and
therefore should be included in simulations of galaxy formation.


  There has been recent progress in understanding chaotic features in many-body
quantum systems. Motivated by the scrambling of information in black holes, it
has been suggested that the time dependence of out-of-time-ordered (OTO)
correlation functions such as $\langle O_2(t) O_1(0) O_2(t) O_1(0) \rangle $ is
a faithful measure of quantum chaos. Experimentally, these correlators are
challenging to access since they apparently require access to both forward and
backward time evolution with the system Hamiltonian. Here, we propose a
protocol to measure such OTO correlators using an ancilla which controls the
direction of time. Specifically, by coupling the state of ancilla to the system
Hamiltonian of interest, we can emulate the forward and backward time
propagation, where the ancilla plays the role of a 'quantum clock'. Within this
scheme, the continuous evolution of the entire system (the system of interest
and the ancilla) is governed by a time-independent Hamiltonian. Our protocol is
immune to errors that could occur when the direction of time evolution is
externally controlled by a classical switch.


  Federated learning (FL) is an emerging machine learning paradigm involving
multiple clients, e.g., mobile phone devices, with an incentive to collaborate
in solving a machine learning problem coordinated by a central server. FL was
proposed in 2016 by Kone\v{c}n\'{y} et al. and McMahan et al. as a viable
privacy-preserving alternative to traditional centralized machine learning
since, by construction, the training data points are decentralized and never
transferred by the clients to a central server. Therefore, to a certain degree,
FL mitigates the privacy risks associated with centralized data collection.
  Unfortunately, optimization for FL faces several specific issues that
centralized optimization usually does not need to handle. In this thesis, we
identify several of these challenges and propose new methods and algorithms to
address them, with the ultimate goal of enabling practical FL solutions
supported with mathematically rigorous guarantees.


  We analytically investigate the quasinormal modes of the massive scalar field
with a nonminimal coupling in the higher-dimensional de Sitter black hole with
a single rotation. According to the separated scalar field equation, the
boundary conditions of quasinormal modes are well constructed at the outer and
cosmological horizons. Then, under near-extremal conditions, where the outer
horizon closes to the cosmological horizon, the quasinormal frequencies are
obtained and generalized to universal form in the higher-dimensional spacetime.
Here, the real part of the frequency includes the scalar field contents, and
its imaginary part only depends on the surface gravity at the outer horizon of
the black hole.


  Extensions to General Relativity (GR) allow the polarization of gravitational
waves (GW) from astrophysical sources to suffer from amplitude and velocity
birefringence, which respectively induce changes in the ellipticity and
orientation of the polarization tensor. We introduce a multi-messenger approach
to test this polarization behavior of GWs during their cosmological propagation
using binary sources, for which the initial polarization is determined by the
inclination and orientation angles of the orbital angular momentum vector with
respect to the line of sight. In particular, we use spatially-resolved radio
imaging of the jet from a binary neutron star (BNS) merger to constrain the
orientation angle and hence the emitted polarization orientation of the GW
signal at the site of the merger, and compare to that observed on Earth by GW
detectors. For GW170817 we constrain the deviation from GR due to amplitude
birefringence to $\kappa_A = -0.12^{+0.60}_{-0.61}$, while the velocity
birefringence parameter $\kappa_V$ remains unconstrained. The inability to
constrain $\kappa_V$ is due to the fact that Virgo did not detect GW170817, and
measurements of the polarization orientation require information from a
combination of multiple detectors with different alignments. For this reason,
we also mock future BNS mergers with resolved afterglow proper motion and
project that $\kappa_V$ could be constrained to a precision of $5\,$rad
(corresponding to an angular shift of the GW polarization of
$\delta\phi_V\approx 0.2\,$rad for a BNS at $100\,$Mpc) by a future network of
third-generation ground-based GW detectors such as Cosmic Explorer and the
radio High Sensitivity Array. Crucially, this velocity birefringence effect
cannot be constrained with dark binary mergers as it requires polarization
information at the emission time, which can be provided only by electromagnetic
emission.


  {\small The Wiener index $W(G)$ of a graph $G$ is the sum of the distances
between all pairs of vertices in the graph. The Szeged index $Sz(G)$ of a graph
$G$ is defined as $Sz(G)=\sum_{e=uv \in E}n_u(e)n_v(e)$ where $n_u(e)$ and
$n_v(e)$ are, respectively, the number of vertices of $G$ lying closer to
vertex $u$ than to vertex $v$ and the number of vertices of $G$ lying closer to
vertex $v$ than to vertex $u$. Hansen used the computer programm AutoGraphiX
and made the following conjecture about the Szeged index and the Wiener index
for a bipartite connected graph $G$ with $n \geq 4$ vertices and $m \geq n$
edges: $$ Sz(G)-W(G) \geq 4n-8. $$ Moreover the bound is best possible as shown
by the graph composed of a cycle on 4 vertices $C_4$ and a tree $T$ on $n-3$
vertices sharing a single vertex. This paper is to give a confirmative proof to
this conjecture.


  We study the statistics of matrix elements of local operators in the basis of
energy eigenstates in a paradigmatic integrable many-particle quantum theory,
the Lieb-Liniger model of bosons with repulsive delta-function interaction.
Using methods of quantum integrability we determine the scaling of matrix
elements with system size. As a consequence of the extensive number of
conservation laws the structure of matrix elements is fundamentally different
from, and much more intricate than, the predictions of the eigenstate
thermalization hypothesis for generic models. We uncover an interesting
connection between this structure for local operators in interacting integrable
models, and the one for local operators that are not local with respect to the
elementary excitations in free theories. We find that typical off-diagonal
matrix elements $\langle\boldsymbol{\mu}|O|\boldsymbol{\lambda}\rangle$ in the
same macro-state scale as $\exp(-c^{
O}L\ln(L)-LM^{O}_{\boldsymbol{\mu},\boldsymbol{\lambda}})$ where the
probability distribution function for
$M^{O}_{\boldsymbol{\mu},\boldsymbol{\lambda}}$ are well described by Fr\'echet
distributions and $c^{O}$ depends only on macro-state information. In contrast,
typical off-diagonal matrix elements between two different macro-states scale
as $\exp(-d^{ O}L^2)$, where $d^{O}$ depends only on macro-state information.
Diagonal matrix elements depend only on macro-state information up to
finite-size corrections.


  Seed scheduling, the order in which seeds are selected, can greatly affect
the performance of a fuzzer. Existing approaches schedule seeds based on their
historical mutation data, but ignore the structure of the underlying Control
Flow Graph (CFG). Examining the CFG can help seed scheduling by revealing the
potential edge coverage gain from mutating a seed. An ideal strategy will
schedule seeds based on a count of all reachable and feasible edges from a seed
through mutations, but computing feasibility along all edges is prohibitively
expensive. Therefore, a seed scheduling strategy must approximate this count.
We observe that an approximate count should have 3 properties -- (i) it should
increase if there are more edges reachable from a seed; (ii) it should decrease
if mutation history information suggests an edge is hard to reach or is located
far away from currently visited edges; and (iii) it should be efficient to
compute over large CFGs. We observe that centrality measures from graph
analysis naturally provide these three properties and therefore can efficiently
approximate the likelihood of reaching unvisited edges by mutating a seed. We
therefore build a graph called the edge horizon graph that connects seeds to
their closest unvisited nodes and compute the seed node's centrality to measure
the potential edge coverage gain from mutating a seed. We implement our
approach in K-scheduler and compare with many popular seed scheduling
strategies. We find that K-scheduler increases feature coverage by 25.89%
compared to Entropic and edge coverage by 4.21% compared to the next-best
AFL-based seed scheduler, in arithmetic mean on 12 Google FuzzBench programs.
It also finds 3 more previously-unknown bugs than the next-best AFL-based seed
scheduler.


  We design a system of phase oscillators that is able to produce temporally
periodic sequences of patterns. Patterns are cluster partitions which encode
information as phase differences between phase oscillators. The architecture of
our system consists of a retrieval network with N globally coupled phase
oscillators, a pacemaker that controls the sequence retrieval, and a set of
patterns stored in the couplings between the pacemaker and the retrieval
network. The system performs in analogy to a central pattern generator of
neural networks and is very robust against perturbations in the retrieval
process.


  To date, testing interactions in high dimensions has been a challenging task.
Existing methods often have issues with sensitivity to modeling assumptions and
heavily asymptotic nominal p-values. To help alleviate these issues, we propose
a permutation-based method for testing marginal interactions with a binary
response. Our method searches for pairwise correlations which differ between
classes. In this manuscript, we compare our method on real and simulated data
to the standard approach of running many pairwise logistic models. On simulated
data our method finds more significant interactions at a lower false discovery
rate (especially in the presence of main effects). On real genomic data,
although there is no gold standard, our method finds apparent signal and tells
a believable story, while logistic regression does not. We also give asymptotic
consistency results under not too restrictive assumptions.


  We establish two results on three-dimensional del Pezzo fibrations in
positive characteristic. First, we give an explicit bound for torsion index of
relatively torsion line bundles. Second, we show the existence of purely
inseparable sections with explicit bounded degree. To prove these results, we
study log del Pezzo surfaces defined over imperfect fields.


  In this paper, we construct the wavelet eigenvalue regression methodology in
high dimensions. We assume that possibly non-Gaussian, finite-variance
$p$-variate measurements are made of a low-dimensional $r$-variate ($r \ll p$)
fractional stochastic process with non-canonical scaling coordinates and in the
presence of additive high-dimensional noise. The measurements are correlated
both time-wise and between rows. Building upon the asymptotic and large scale
properties of wavelet random matrices in high dimensions, the wavelet
eigenvalue regression is shown to be consistent and, under additional
assumptions, asymptotically Gaussian in the estimation of the fractal structure
of the system. We further construct a consistent estimator of the effective
dimension $r$ of the system that significantly increases the robustness of the
methodology. The estimation performance over finite samples is studied by means
of simulations.


  We consider the superheterodyning system discovered by Armstrong and Schottky
in 1924. This system is the basic piece of any communication system. We prove
that the frequency spectrum of this system is governed by arithmetical rule. We
provide a number theoritical framework which allows us to predict all the
particular features of the experimental frequency spectrum. We also introduce a
new natural dynamical system on numbers and study its first properties.


  Important features of certain economic models may be revealed by studying
positive eigenfunctions of appropriately chosen linear operators. Examples
include long-run risk-return relationships in dynamic asset pricing models and
components of marginal utility in external habit formation models. This paper
provides identification conditions for positive eigenfunctions in nonparametric
models. Identification is achieved if the operator satisfies two mild
positivity conditions and a power compactness condition. Both existence and
identification are achieved under a further non-degeneracy condition. The
general results are applied to obtain new identification conditions for
external habit formation models and for positive eigenfunctions of pricing
operators in dynamic asset pricing models.


  We provide a set of analytic fits to the radii of pre-mainsequence stars in
the mass range 0.1 < M/Msun < 8.0. We incorporate the formulae in N-body
cluster models for evolution from the beginning of pre-main sequence. In models
with 1,000 stars and high initial cluster densities, pre-mainsequence evolution
causes roughly twice the number of collisions between stars than in similar
models with evolution begun only from the zero-age main sequence. The
collisions are often all part of a runaway sequence that creates one relatively
massive star.


  There is often a mixture of very frequent labels and very infrequent labels
in multi-label datatsets. This variation in label frequency, a type class
imbalance, creates a significant challenge for building efficient multi-label
classification algorithms. In this paper, we tackle this problem by proposing a
minority class oversampling scheme, UCLSO, which integrates Unsupervised
Clustering and Label-Specific data Oversampling. Clustering is performed to
find out the key distinct and locally connected regions of a multi-label
dataset (irrespective of the label information). Next, for each label, we
explore the distributions of minority points in the cluster sets. Only the
minority points within a cluster are used to generate the synthetic minority
points that are used for oversampling. Even though the cluster set is the same
across all labels, the distributions of the synthetic minority points will vary
across the labels. The training dataset is augmented with the set of
label-specific synthetic minority points, and classifiers are trained to
predict the relevance of each label independently. Experiments using 12
multi-label datasets and several multi-label algorithms show that the proposed
method performed very well compared to the other competing algorithms.


  This document contains large-format Adams-Novikov charts that compute the
classical 2-complete stable homotopy groups. The charts are essentially
complete through the 60-stem. We believe that these are the most accurate and
extensive charts of their kind. We also include a motivic Adams-Novikov
E-infinity chart.


  The X-ray transient MAXI J1631-479 went into outburst on 2018 December 21 and
remained active for about seven months. Owing to various constraints it was
monitored by NICER only during the decay phase of the outburst for about four
months. The NICER observations were primarily in the soft state with a brief
excursion to the hard intermediate state. While the soft state spectrum was
dominated by thermal disk emission, the hard intermediate state spectrum had
maximum contribution from the thermal Comptonization. Almost all
intermediate-state power spectra had a Type-C low frequency quasi-periodic
oscillation (within 4 - 10 Hz), often accompanied by a harmonic component. The
frequency of these oscillations increased and the fractional rms decreased with
inner-disk temperature suggesting a geometric origin. One observation in the
middle of the outburst during the hard intermediate state had two
non-harmonically related peaks. While one of them was definitely a Type-C QPO,
the identification of the other one is uncertain. The rms spectra during the
intermediate state had a hard shape from above 1 keV. Below 1 keV the shape
could not be constrained in most cases, while only a few observations showed a
rise in amplitude.


  Despite suggestions to the contrary, we show in this paper that the usual
dispersive form of the electromagnetic energy must be used to derive the
Lifshitz force between parallel dielectric media. This conclusion follows from
the general form of the quantum vacuum energy, which is the basis of the
multiple-scattering formalism. As an illustration, we explicitly derive the
Lifshitz formula for the interaction between parallel dielectric semispaces,
including dispersion, starting from the expression for the total energy of the
system. The issues of constancy of the energy between parallel plates and of
the observability of electrostrictive forces are briefly addressed.


  We consider two K3 surfaces defined over an arbitrary field, together with a
smooth proper moduli space of stable sheaves on each. When the moduli spaces
have the same dimension, we prove that if the \'etale cohomology groups (with
Q_ell coefficients) of the two surfaces are isomorphic as Galois
representations, then the same is true of the two moduli spaces. In particular,
if the field of definition is finite and the K3 surfaces have equal zeta
functions, then so do the moduli spaces, even when the moduli spaces are not
birational.


  The objective of this paper is a neural network model that controls the pose
and expression of a given face, using another face or modality (e.g. audio).
This model can then be used for lightweight, sophisticated video and image
editing.
  We make the following three contributions. First, we introduce a network,
X2Face, that can control a source face (specified by one or more frames) using
another face in a driving frame to produce a generated frame with the identity
of the source frame but the pose and expression of the face in the driving
frame. Second, we propose a method for training the network fully
self-supervised using a large collection of video data. Third, we show that the
generation process can be driven by other modalities, such as audio or pose
codes, without any further training of the network.
  The generation results for driving a face with another face are compared to
state-of-the-art self-supervised/supervised methods. We show that our approach
is more robust than other methods, as it makes fewer assumptions about the
input data. We also show examples of using our framework for video face
editing.


  We present an improved partial wave analysis of the dominant LSP annihilation
channel to a fermion-antifermion pair which avoids the non-relativistic
expansion being therefore applicable near thresholds and poles. The method we
develop allows of contributions of any partial wave in the total angular
momentum J in contrast to partial wave analyses in terms of the orbital angular
momentum L of the initial state, which is usually truncated to p-waves, and
yields very accurate results. The method is formulated in such a way as to
allow easy handling of CP-violating phases residing in supersymmetric
parameters. We apply this refined partial wave technique in order to calculate
the neutralino relic density in the constrained MSSM (CMSSM) in the presence of
CP-violating terms occurring in the Higgs - mixing parameter \mu and trilinear
A coupling for large tanb. The inclusion of CP-violating phases in mu and A
does not upset significantly the picture and the annihilation of the LSP's to a
b b_bar, through Higgs exchange, is still the dominant mechanism in obtaining
cosmologically acceptable neutralino relic densities in regions far from the
stau-coannihilation and the `focus point'. Significant changes can occur if we
allow for phases in the gaugino masses and in particular the gluino mass.


  This paper studies the magnetic topology of successively erupting active
regions (ARs) 11429 and 12371. Employing vector magnetic field observations
from Helioseismic and Magnetic Imager, the pre-eruptive magnetic structure is
reconstructed by a model of non-linear force-free field (NLFFF). For all the
five CMEs from these ARs, the pre-eruptive magnetic structure identifies an
inverse-S sigmoid consistent with the coronal plasma tracers in EUV
observations. In all the eruption cases, the quasi-separatrix layers (QSLs) of
Large Q values are continuously enclosing core field bipolar regions in which
inverse-S shaped flare ribbons are observed. These QSLs essentially represent
the large connectivity gradients between the domains of twisted core flux
within the inner bipolar region and the surrounding potential like arcade. It
is consistent with the observed field structure largely with the sheared
arcade. The QSL maps in the chromosphere are compared with the flare-ribbons
observed at the peak time of the flares. The flare ribbons are largely
inverse-S shape morphology with their continuity of visibility is missing in
the observations. For the CMEs in the AR 12371, the QSLs outline the flare
ribbons as a combination of two inverse J-shape sections with their straight
parts being separated. These QSLs are typical with the weakly twisted flux
rope. Similarly, for the CMEs in the AR 11429, the QSLs are co-spatial with the
flare ribbons both in the middle of the PIL and in the hook sections. In the
frame work of standard model of eruptions, the observed flare ribbons are the
characteristic of the pre-eruptive magnetic structure being sigmoid which is
reproduced by {\bf the} NLFFF model with a weakly twisted flux rope at the
core.


  We consider a class of conformal models describing closed strings in axially
symmetric stationary magnetic flux tube backgrounds. These models are closed
string analogs of the Landau model of a particle in a magnetic field or the
model of an open string in a constant magnetic field. They are interesting
examples of solvable unitary conformal string theories with non-trivial
4-dimensional curved space-time interpretation. In particular, their quantum
Hamiltonian can be expressed in terms of free fields and the physical spectrum
and string partition function can be explicitly determined. In addition to the
presence of tachyonic instabilities and existence of critical values of
magnetic field the closed string spectrum exhibits also some novel features
which were absent in the open string case. (Contribution to the Proceedings of
"Strings 95" Conference)


  We present a qutrit quantum computer design using trapped ions in the
presence of a magnetic field gradient. The magnetic field gradient induces a
"spin-spin" type coupling, similar to the J-coupling observed in molecules,
between the qutrits which allows conditional quantum logic to take place. We
describe in some detail, how one can execute specific one and two qutrit
quantum gates, required for universal qutrit quantum computing.


  In this paper, we construct four infinite families of binary linear codes
associated with double cosets with respect to certain maximal parabolic
subgroup of the orthogonal group O^+(2n,2^r). Here q is a power of two. Then we
obtain two infinite families of recursive formulas for the power moments of
Kloosterman sums and those of 2-dimensional Kloosterman sums in terms of the
frequencies of weights in the codes. This is done via Pless power moment
identity and by utilizing the explicit expressions of exponential sums over
those double cosets related to the evaluations of "Gauss sums" for the
orthogonal groups O^+(2n,2^r).


  Many recent observational studies have concluded that planetary systems
commonly exist in multiple-star systems. At least ~20% of the known extrasolar
planetary systems are associated with one or more stellar companions. The
orbits of stellar binaries hosting planetary systems are typically wider than
100 AU and often highly inclined with respect to the planetary orbits. The
effect of secular perturbations from such an inclined binary orbit on a coupled
system of planets, however, is little understood theoretically. In this paper
we investigate various dynamical classes of double-planet systems in binaries
through numerical integrations and we provide an analytic framework based on
secular perturbation theories. Differential nodal precession of the planets is
the key property that separates two distinct dynamical classes of multiple
planets in binaries: (1) dynamically-rigid systems in which the orbital planes
of planets precess in concert as if they were embedded in a rigid disk, and (2)
weakly-coupled systems in which the mutual inclination angle between initially
coplanar planets grows to large values on secular timescales. In the latter
case, the quadrupole perturbation from the outer planet induces additional
Kozai cycles and causes the orbital eccentricity of the inner planet to
oscillate with large amplitudes. The cyclic angular momentum transfer from a
stellar companion propagating inward through planets can significantly alter
the orbital properties of the inner planet on shorter timescales. This
perturbation propagation mechanism may offer important constraints on the
presence of additional planets in known single-planet systems in binaries.


  Extending computational harmonic analysis tools from the classical setting of
regular lattices to the more general setting of graphs and networks is very
important and much research has been done recently. The Generalized Haar-Walsh
Transform (GHWT) developed by Irion and Saito (2014) is a multiscale transform
for signals on graphs, which is a generalization of the classical Haar and
Walsh-Hadamard Transforms. We propose the extended Generalized Haar-Walsh
Transform (eGHWT), which is a generalization of the adapted time-frequency
tilings of Thiele and Villemoes (1996). The eGHWT examines not only the
efficiency of graph-domain partitions but also that of "sequency-domain"
partitions simultaneously. Consequently, the eGHWT and its associated
best-basis selection algorithm for graph signals significantly improve the
performance of the previous GHWT with the similar computational cost, $O(N \log
N)$, where $N$ is the number of nodes of an input graph. While the GHWT
best-basis algorithm seeks the most suitable orthonormal basis for a given task
among more than $(1.5)^N$ possible orthonormal bases in $\mathbb{R}^N$, the
eGHWT best-basis algorithm can find a better one by searching through more than
$0.618\cdot(1.84)^N$ possible orthonormal bases in $\mathbb{R}^N$. This article
describes the details of the eGHWT best-basis algorithm and demonstrates its
superiority using several examples including genuine graph signals as well as
conventional digital images viewed as graph signals. Furthermore, we also show
how the eGHWT can be extended to 2D signals and matrix-form data by viewing
them as a tensor product of graphs generated from their columns and rows and
demonstrate its effectiveness on applications such as image approximation.


  Spectral clustering is one of the most popular methods for community
detection in graphs. A key step in spectral clustering algorithms is the eigen
decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$
leading eigenvectors, where $k$ is the desired number of clusters among $n$
objects. This is prohibitively complex to implement for very large datasets.
However, it has recently been shown that it is possible to bypass the eigen
decomposition by computing an approximate spectral embedding through graph
filtering of random signals. In this paper, we analyze the working of spectral
clustering performed via graph filtering on the stochastic block model.
Specifically, we characterize the effects of sparsity, dimensionality and
filter approximation error on the consistency of the algorithm in recovering
planted clusters.


  Secret data hiding in binary images is more difficult than other formats
since binary images require only one bit representation to indicate black and
white. This study proposes a new method for data hiding in binary images using
optimized bit position to replace a secret bit. This method manipulates blocks,
which are sub-divided. The parity bit for a specified block decides whether to
change or not, to embed a secret bit. By finding the best position to insert a
secret bit for each divided block, the image quality of the resulting
stego-image can be improved, while maintaining low computational complexity.The
experimental results show that the proposed method has an improvement with
respect to a previous work.


  Statistical calculations by K. G. Karlsson (Astron Astrophys. 239, 50, 1990),
G. R. Burbidge and other authors, show that the redshifts Z of the spectral
lines emitted by quasars and galaxies accumulate close to Z(m) = mK, where K =
0061 is the "Karlsson's constant" and m some integers. We demonstrate this
formula and find exactly K and the allowed values of m, using only rules
commonly used in laser spectroscopy, the hypothesis of low pressure atomic
hydrogen in 1S state around these stars and the observation of an initially
continuous spectrum of a very hot star.


  We present a new simple relativistic model for planetary motion describing
accurately the anomalous precession of the perihelion of Mercury and its
origin. The model is based on transforming Newton's classical equation for
planetary motion from absolute to real spacetime influenced by the
gravitational potential and introducing the concept of influenced direction.


  We show that the transfer map on Floer homotopy types associated to an exact
Lagrangian embedding is an equivalence. This provides an obstruction to
representing isotopy classes of Lagrangian immersions by Lagrangian embeddings,
which, unlike previous obstructions, is sensitive to information that cannot be
detected by Floer cochains. We show this by providing a concrete computation in
the case of spheres.


  The nature of fractional quantum Hall (FQH) states is determined by the
interplay between the Coulomb interaction and the symmetries of the system. The
unique combination of spin, valley, and orbital degeneracies in bilayer
graphene is predicted to produce novel and tunable FQH ground states. Here we
present local electronic compressibility measurements of the FQH effect in the
lowest Landau level of bilayer graphene. We observe incompressible FQH states
at filling factors v = 2p + 2/3 with hints of additional states appearing at v
= 2p + 3/5, where p = -2,-1, 0, and 1. This sequence of states breaks
particle-hole symmetry and instead obeys a v --> v + 2 symmetry, which
highlights the importance of the orbital degeneracy for many-body states in
bilayer graphene.


  Despite the significant progress made in practical applications of aligned
language models (LMs), they tend to be overconfident in output answers compared
to the corresponding pre-trained LMs. In this work, we systematically evaluate
the impact of the alignment process on logit-based uncertainty calibration of
LMs under the multiple-choice setting. We first conduct a thoughtful empirical
study on how aligned LMs differ in calibration from their pre-trained
counterparts. Experimental results reveal that there are two distinct
uncertainties in LMs under the multiple-choice setting, which are responsible
for the answer decision and the format preference of the LMs, respectively.
Then, we investigate the role of these two uncertainties on aligned LM's
calibration through fine-tuning in simple synthetic alignment schemes and
conclude that one reason for aligned LMs' overconfidence is the conflation of
these two types of uncertainty. Furthermore, we examine the utility of common
post-hoc calibration methods for aligned LMs and propose an easy-to-implement
and sample-efficient method to calibrate aligned LMs. We hope our findings
could provide insights into the design of more reliable alignment processes for
LMs.


  We show that the Hilbert scheme of two points on the Vinberg $K3$ surface has
a 2:1 map onto a very symmetric EPW sextic $Y$ in $\mathbb{P}^5$. The fourfold
$Y$ is singular along $60$ planes, $20$ of which form a complete family of
incident planes. This solves a problem of Morin and O'Grady and establishes
that $20$ is the maximal cardinality of such a family of planes. Next, we show
that this Hilbert scheme is birationally isomorphic to the Kummer type IHS
fourfold $X_0$ constructed in [DW]. We find that $X_0$ is also related to the
Debarre-Varley abelian fourfold.


  The aim of this paper is studying the problem of existence of asymptotically
periodic solutions of the scalar differential equation $x'=f(t,x),$ where
$f:\mathbb R\times \mathbb R\to \mathbb R$ is a continuous asymptotically
$\tau$-periodic function. We prove that every bounded on semi-axis $\mathbb
R_{+}$ solution $\varphi$ of this equation is S-asymptotically $\tau$-periodic,
i.e., $\lim\limits_{t\to +\infty}|\varphi(t+\tau)-\varphi(t)|=0$. This
statement is a generalization of the well-known Massera's theorem for
asymptotically periodic scalar differential equations. We also establish a
similar statement for scalar difference equations.


  An effective Coulomb gauge Hamiltonian, H_eff, is used to calculate the light
(u-ubar-g), strange (s-sbar-g) and charmed (c-cbar-g) hybrid meson spectra. For
the same two parameter H_eff providing glueball masses consistent with lattice
results and a good description of the observed u,d,s and c quark mesons, a
large-scale variational treatment predicts the lightest hybrid has
J^{PC}=0^{++} and mass 2100 MeV. The lightest exotic 1^{-+} state is just above
2200 MeV, near the upper limit of lattice and Flux Tube predictions. These
theoretical formulations all indicate the observed 1^{-+} pi_1(1600) and, more
clearly, pi_1(1400) are not hybrid states. The Coulomb gauge approach further
predicts that in the strange and charmed sectors, respectively, the ground
state hybrids have 1^{+-} with masses 2125 and 3830 MeV, while the first exotic
1^{-+} states are at 2395 and 4020 MeV. Finally, using our hybrid
wavefunctions, dimensional counting rules and the Franck-Condon principle,
novel experimental signatures are presented to assist light and heavy hybrid
meson searches.


  Many algorithms have been recently proposed for causal machine learning. Yet,
there is little to no theory on their quality, especially considering finite
samples. In this work, we propose a theory based on generalization bounds that
provides such guarantees. By introducing a novel change-of-measure inequality,
we are able to tightly bound the model loss in terms of the deviation of the
treatment propensities over the population, which we show can be empirically
limited. Our theory is fully rigorous and holds even in the face of hidden
confounding and violations of positivity. We demonstrate our bounds on
semi-synthetic and real data, showcasing their remarkable tightness and
practical utility.


  In a recent paper, A. Libgober showed that the multiplicative sequence
{Q_i(c_1,...,c_i)} of Chern classes corresponding to the power series
Q(z)=1/Gamma(1+z) appears in a relation between the Chern classes of certain
Calabi-Yau manifolds and the periods of their mirrors. We show that the
polynomials Q_i can be expressed in terms of multiple zeta values.


  We show how the continuous Almkvist-Zeilberger algorithm can be used to
efficiently discover and prove differential equations satisfied by generating
functions of sequences defined as integrals of powers of C-finite polynomial
sequences (like the Chebyshev polynomials) from which one can automatically
derive linear recurrences with polynomial coefficients for the sequences
themselves. We fully implement this with a Maple package, CfiniteIntergal.txt .


  We compute the spin-orbit correlations of quarks and gluons at small-$x$ and
show that the helicity and the orbital angular momentum of individual partons
are strongly anti-aligned even in unpolarized or spinless hadrons and nuclei.
Combined with the fact that gluons in the Color Glass Condensate are linearly
polarized, our finding indicates that the helicity and the orbital angular
momentum of single gluons are maximally entangled in a quantum mechanical
sense.


  Motivated by the fact that the gradient-based optimization algorithms can be
studied from the perspective of limiting ordinary differential equations
(ODEs), here we derive an ODE representation of the accelerated triple momentum
(TM) algorithm. For unconstrained optimization problems with strongly convex
cost, the TM algorithm has a proven faster convergence rate than the Nesterov's
accelerated gradient (NAG) method but with the same computational complexity.
We show that similar to the NAG method to capture accurately the
characteristics of the TM method, we need to use a high-resolution modeling to
obtain the ODE representation of the TM algorithm. We use a Lyapunov analysis
to investigate the stability and convergence behavior of the proposed
high-resolution ODE representation of the TM algorithm. We show through this
analysis that this ODE model has robustness to deviation from the parameters of
the TM algorithm. We compare the rate of the ODE representation of the TM
method with that of the NAG method to confirm its faster convergence. Our study
also leads to a tighter bound on the worst rate of convergence for the ODE
model of the NAG method. Lastly, we discuss the use of the integral quadratic
constraint (IQC) method to establish an estimate on the rate of convergence of
the TM algorithm. A numerical example demonstrates our results.


  We present the results of study of the Galactic candidate luminous blue
variable Wray 15-906, revealed via detection of its infrared circumstellar
shell (of \approx2 pc in diameter) with the Wide-field Infrared Survey Explorer
and the Herschel Space Observatory. Using the stellar atmosphere code CMFGEN
and the Gaia parallax, we found that Wray 15-906 is a relatively
low-luminosity, log(L/Lsun)\approx5.4, star of temperature of 25\pm2 kK, with a
mass-loss rate of \approx3\times10^{-5} Msun/yr, a wind velocity of 280\pm50
km/s, and a surface helium abundance of 65\pm2 per cent (by mass). In the
framework of single star evolution, the obtained results suggest that Wray
15-906 is a post-red supergiant star with initial mass of \approx26\pm2 Msun
and that before exploding as a supernova it could transform for a short time
into a WN11h star. Our spectroscopic monitoring with the Southern African Large
Telescope (SALT) does not reveal significant changes in the spectrum of Wray
15-906 during the last 8 yr, while the V-band light curve of this star over
years 1999--2019 shows quasi-periodic variability with a period of \approx1700
d and an amplitude of \approx0.1 mag. We estimated the mass of the shell to be
2.9\pm0.5 Msun assuming the gas-to-dust mass ratio of 200. The presence of such
a shell indicates that Wray 15-906 has suffered substantial mass loss in the
recent past. We found that the open star cluster C1128-631 could be the birth
place of Wray 15-906 provided that this star is a rejuvenated product of binary
evolution (a blue straggler).


  Rapidly convergent expansions of a one-loop contribution to the partition
function of quantum fields with ellipsoid constant-energy surface dispersion
law are derived. The omega-potential is naturally decomposed into three parts:
the quasiclassical contribution, the contribution from the branch cut of the
dispersion law, and the oscillating part. The low- and high-temperature
expansions of the quasiclassical part are obtained. An explicit expression and
a relation of the contribution from the cut with the Casimir term and vacuum
energy are established. The oscillating part is represented in the form of the
Chowla-Selberg expansion for the Epstein zeta function. Various resummations of
this expansion are considered. The developed general procedure is applied to
two models: massless particles in a box both at zero and non-zero chemical
potential; electrons in a thin metal film. The rapidly convergent expansions of
the partition function and average particle number are obtained for these
models. In particular, the oscillations of the chemical potential of conduction
electrons in graphene and a thin metal film due to a variation of sizes of the
crystal are described.


  We calculate the soft function for the global event variable 1-jettiness at
next-to-next-to-leading order (NNLO) in QCD. We focus specifically on the
non-Abelian contribution, which, unlike the Abelian part, is not determined by
the next-to-leading order result. The calculation uses the known general forms
for the emission of one and two soft partons and is performed using a
sector-decomposition method that is spelled out in detail. Results are
presented in the form of numerical fits to the 1-jettiness soft function for
LHC kinematics (as a function of the angle between the incoming beams and the
final-state jet) and for generic kinematics (as a function of three independent
angles). These fits represent one of the needed ingredients for NNLO
calculations that use the N-jettiness event variable to handle infrared
singularities.


  The exact relation between the response function $R(t,t^{\prime})$ and the
two time correlation function $C(t,t^{\prime})$ is derived analytically in the
one dimensional kinetic Ising model subjected to a temperature quench. The
fluctuation dissipation ratio $X(t,t^{\prime})$ is found to depend on time
through $C(t,t^{\prime})$ in the time region where scaling $C(t,t^{\prime}) =
f(t/t^{\prime})$ holds. The crossover from the nontrivial form
$X(C(t,t^{\prime}))$ to $X(t,t^{\prime}) \equiv 1$ takes place as the waiting
time $t_w$ is increased from below to above the equilibration time $t_{eq}$.


  In the neutron-rich internal shocks model for gamma-ray bursts (GRBs), the
Lorentz factors (LFs) of ion shells are variable, and so are the LFs of
accompanying neutron shells. For slow neutron shells with a typical LF of
approximate tens, the typical $\beta$-decay radius is $\sim 10^{14}-10^{15}$
cm. As GRBs last long enough [$T_{90}>14(1+z)$ s], one earlier but slower
ejected neutron shell will be swept successively by later ejected ion shells in
the range $\sim10^{13}-10^{15}$ cm, where slow neutrons have decayed
significantly. Part of the thermal energy released in the interaction will be
given to the electrons. These accelerated electrons will be mainly cooled by
the prompt soft $\gamma-$rays and give rise to GeV emission. This kind of GeV
emission is particularly important for some very long GRBs and is detectable
for the upcoming satellite {\it Gamma-Ray Large Area Space Telescope} (GLAST).


  Given a root system $\mathsf{R}$, the vector system $\tilde{\mathsf{R}}$ is
obtained by taking a representative $v$ in each antipodal pair $\{v, -v\}$. The
matroid $M(\mathsf{R})$ is formed by all independent subsets of
$\tilde{\mathsf{R}}$. The automorphism group of a matroid is the group of
permutations preserving its independent subsets. We prove that the automorphism
groups of all irreducible root systems matroids $M(\mathsf{R})$ are uniquely
determined by their independent sets of size 3. As a corollary, we compute
these groups explicitly, and thus complete the classification of the
automorphism groups of root systems matroids.


  Recent years have witnessed many exciting breakthroughs in neutrino physics.
The detection of neutrino oscillations has proved that neutrinos are massive
particles but the assessment of their absolute mass scale is still an
outstanding challenge in today particle physics and cosmology. Since low
temperature detectors were first proposed for neutrino physics experiments in
1984, there have been tremendous technical progresses: today this technique
offers the high energy resolution and scalability required to perform
competitive experiments challenging the lowest electron neutrino masses. This
paper reviews the thirty-year effort aimed at realizing a calorimetric
measurements with sub-eV neutrino mass sensitivity using low temperature
detectors.


  Let $\mathbb F$ be a field $\mathbb F $ of characteristic zero. Let
$W_{n}(\mathbb F)$ be the Lie algebra of all $\mathbb F$-derivations with the
Lie bracket $[D_1, D_2]:=D_1D_2-D_2D_1$ on the polynomial ring $\mathbb F [x_1,
\ldots , x_n]$. The problem of classifying finite dimensional subalgebras of
$W_{n}(\mathbb F)$ was solved if $ n\leq 2$ and $\mathbb F=\mathbb C$ or
$\mathbb F=\mathbb R.$ We prove that this problem is wild if $n\geq 4$, which
means that it contains the classical unsolved problem of classifying matrix
pairs up to similarity. The structure of finite dimensional subalgebras of
$W_{n}(\mathbb F)$ is interesting since each derivation in case $\mathbb
F=\mathbb R$ can be considered as a vector field with polynomial coefficients
on the manifold $\mathbb R^{n}.$


  It is well-known that for expansive maps and continuous potential functions,
the specification property (for the map) and the Bowen property (for the
potential) together imply the existence of a unique equilibrium state. We
consider symbolic spaces that may not have specification, and potentials that
may not have the Bowen property, and give conditions under which uniqueness of
the equilibrium state can still be deduced. Our approach is to ask that the
collection of cylinders which are obstructions to the specification property or
the Bowen property is small in an appropriate quantitative sense. This allows
us to construct an ergodic equilibrium state with a weak Gibbs property, which
we then use to prove uniqueness. We do not use inducing schemes or the
Perron--Frobenius operator, and we strengthen some previous results obtained
using these approaches. In particular, we consider $\beta$-shifts and show that
the class of potential functions with unique equilibrium states strictly
contains the set of potentials with the Bowen property. We give applications to
piecewise monotonic interval maps, including the family of geometric potentials
for examples which have both indifferent fixed points and a non-Markov
structure.


  We present a machine learning system that can quantify fine art paintings
with a set of visual elements and principles of art. This formal analysis is
fundamental for understanding art, but developing such a system is challenging.
Paintings have high visual complexities, but it is also difficult to collect
enough training data with direct labels. To resolve these practical
limitations, we introduce a novel mechanism, called proxy learning, which
learns visual concepts in paintings though their general relation to styles.
This framework does not require any visual annotation, but only uses style
labels and a general relationship between visual concepts and style. In this
paper, we propose a novel proxy model and reformulate four pre-existing methods
in the context of proxy learning. Through quantitative and qualitative
comparison, we evaluate these methods and compare their effectiveness in
quantifying the artistic visual concepts, where the general relationship is
estimated by language models; GloVe or BERT. The language modeling is a
practical and scalable solution requiring no labeling, but it is inevitably
imperfect. We demonstrate how the new proxy model is robust to the
imperfection, while the other models are sensitively affected by it.


  We review different neutron methods which allow extracting directly the value
of the magnetic induction in thick films: Larmor precession, Zeeman spatial
beam-splitting and neutron spin resonance. Resulting parameters obtained by the
neutron methods and standard magnetometry technique are presented and compared.
The possibilities and specificities of the neutron methods are discussed.


  The origin of the radio synchrotron background (RSB) is currently unknown.
Its understanding might have profound implications in fundamental physics or
might reveal a new class of radio emitters. In this work, we consider the
scenario in which the RSB is due to extragalactic radio sources and measure the
angular cross-correlation of LOFAR images of the diffuse radio sky with matter
tracers at different redshifts, provided by galaxy catalogs and CMB lensing. We
compare these measured cross-correlations to those expected for models of RSB
sources. We find that low-redshift populations of discrete sources are excluded
by the data, while higher redshift explanations are compatible with available
observations. We also conclude that at least 20\% of the RSB surface brightness
level must originate from populations tracing the large-scale distribution of
matter in the universe, indicating that at least this fraction of the RSB is of
extragalactic origin. Future measurements of the correlation between the RSB
and tracers of high-redshift sources will be crucial to constraining the source
population of the RSB.


  The relative arbitrage portfolio outperforms a benchmark portfolio over a
given time-horizon with probability one. With market price of risk processes
depending on the market portfolio and investors, this paper analyzes the
multi-agent optimization of relative arbitrage opportunities in the coupled
system of market and wealth dynamics. We construct a well-posed market
dynamical system of McKean-Vlasov type under an empirical measure of investors,
where each investor seeks for relative arbitrage with respect to a benchmark
dependent on market and all the agents. We show the conditions to guarantee
relative arbitrage opportunities among competitive investors through the
Fichera drift. Under mild conditions, we derive the optimal strategies for
investors and the unique Nash equilibrium that depends on the smallest
nonnegative solution of a Cauchy problem.


  We introduce a new notion of a relational word as a finite totally ordered
set of positions endowed with three binary relations that describe which
positions are labeled by equal data, by unequal data and those having an
undefined relation between their labels. We define the operations of insertion
and deletion on relational words generalizing corresponding operations on
strings. We prove that the transitive and reflexive closure of these operations
has a decidable membership problem for the case of short insertion-deletion
rules (of size two/three and three/two). At the same time, we show that in the
general case such systems can produce a coding of any recursively enumerable
language leading to undecidabilty of reachability questions.


  This study evaluates two approaches applied to computed tomography (CT)
images of patients with abdominal aortic aneurysm: one deterministic, based on
tools of Approximation Theory, and one based on Artificial Intelligence. Both
aim to segment the basal CT images to extract the patent area of the aortic
vessel, in order to propose an alternative to nephrotoxic contrast agents for
diagnosing this pathology. While the deterministic approach employs sampling
Kantorovich operators and the theory behind, leveraging the reconstruction and
enhancement capabilities of these operators applied to images, the artificial
intelligence-based approach lays on a U-net neural network. The results
obtained from testing the two methods have been compared numerically and
visually to assess their performances, demonstrating that both models yield
accurate results.


  Recently, we have introduced and modified two graph-decomposition theorems
based on a new graph product, motivated by applications in the context of
synchronising periodic real-time processes. This vertex-removing synchronised
product (VRSP), is based on modifications of the well-known Cartesian product
and is closely related to the synchronised product due to W\"ohrle and Thomas.
Here, we introduce a new graph-decomposition theorem based on the VRSP that
provides a Cartesian decomposition of graphs.


  We review and elaborate on some aspects of the classically scale-invariant
renormalizable 4-derivative scalar theory $L= \phi\, \partial^4 \phi + g
(\partial \phi)^4$. Similar models appear, e.g., in the context of conformal
supergravity or in the description of the crystalline phase of membranes.
Considering this theory in Minkowski signature we suggest how to define
Poincare-invariant scattering amplitudes by assuming that only massless
oscillating (non-growing) modes appear as external states. In such
shift-symmetric interacting theory there are no IR divergences despite the
presence of $1/q^4$ internal propagators. We discuss how non-unitarity of this
theory manifests itself at the level of the one-loop massless scattering
amplitude.


  Autoregressive models have proven to be very powerful in NLP text generation
tasks and lately have gained popularity for image generation as well. However,
they have seen limited use for the synthesis of 3D shapes so far. This is
mainly due to the lack of a straightforward way to linearize 3D data as well as
to scaling problems with the length of the resulting sequences when describing
complex shapes. In this work we address both of these problems. We use octrees
as a compact hierarchical shape representation that can be sequentialized by
traversal ordering. Moreover, we introduce an adaptive compression scheme, that
significantly reduces sequence lengths and thus enables their effective
generation with a transformer, while still allowing fully autoregressive
sampling and parallel training. We demonstrate the performance of our model by
comparing against the state-of-the-art in shape generation.


  We study the generalized Drazin invertibility as well as the Drazin and
ordinary invertbility of an operator matrix (A C \\ 0 B) acting on a Banach or
on a Hilbert space. As a consequence some recent results are extended.


  The normal-conducting state of the superconductor UTe$_2$ is studied by
entropy analysis for magnetic fields along the $b$-axis, obtained from
magnetization using the relation $(\partial M/\partial T)_B=(\partial
S/\partial B)_T$. We observe a strong increase in entropy with magnetic field
due to metamagnetic fluctuations (spatially uniform, $Q=0$). The field
dependence is well described by the Hertz-Millis-Moriya theory for quantum
criticality of itinerant metamagnetism. Notably, the lower bound of the
quantum-critical region coincides well with the position of the minimum in the
superconducting transition temperature $T_c(B)$. Hence, our results suggest
that $Q=0$ fluctuations reinforce the superconductivity.


  An earthquake-proof seismic negative belt of an artificial seismic shadow
zone is introduced. The belt is composed of acoustic materials which has one of
the constituent parameter between density and modulus is negative effectively.
It converts the velocity of the seismic wave imaginary, and then creates a
stop-band for the seismic frequency range. The belt is an attenuator of a
seismic wave that reduces the amplitude of the wave exponentially. Passing the
belt underground, the seismic energy turns into sound and heat in air and the
magnitude of the seismic wave is weakened to be defended by conventional
method. Models of the negative density and negative modulus for engineering are
suggested.


  The generalised Proca (GP) theory is a modified gravity model in which the
acceleration of the cosmic expansion rate can be explained by self interactions
of a cosmological vector field. In this paper we study a particular sub-class
of the GP theory, with up to cubic order Lagrangian, known as the cubic vector
Galileon (cvG) model. This model is similar to the cubic scalar Galileon (csG)
in many aspects, including a fifth force and the Vainshtein screening
mechanism, but with the additional flexibility that the strength of the fifth
force depends on an extra parameter -- interpolating between zero and the full
strength of the csG model -- while the background expansion history is
independent of this parameter. It offers an interesting alternative to
LambdaCDM in explaining the cosmic acceleration, as well as a solution to the
tension between early- and late-time measurements of the Hubble constant H_0.
To identify the best ways to test this model, in this paper we conduct a
comprehensive study of the phenomenology of this model in the nonlinear regime
of large-scale structure formation, using a suite of N-body simulations run
with the modified gravity code ECOSMOG. By inspecting thirteen statistics of
the dark matter field, dark matter haloes and weak lensing maps, we find that
the fifth force in this model can have particularly significant effects on the
large-scale velocity field and lensing potential at late times, which suggest
that redshift-space distortions and weak lensing can place strong constraints
on it.


  Global climate models aim to reproduce physical processes on a global scale
and predict quantities such as temperature given some forcing inputs. We
consider climate ensembles made of collections of such runs with different
initial conditions and forcing scenarios. The purpose of this work is to show
how the simulated temperatures in the ensemble can be reproduced (emulated)
with a global space/time statistical model that addresses the issue of
capturing nonstationarities in latitude more effectively than current
alternatives in the literature. The model we propose leads to a computationally
efficient estimation procedure and, by exploiting the gridded geometry of the
data, we can fit massive data sets with millions of simulated data within a few
hours. Given a training set of runs, the model efficiently emulates temperature
for very different scenarios and therefore is an appealing tool for impact
assessment.


  Motivated by condensed matter physical systems, in which a finite-time
singularity indicates that the topology of the system changes, we critically
examine the possibility of the Universe's topology change at a finite-time
cosmological singularity. We emphasize on Big Rip and Type II and IV
cosmological singularities, which we classify to future spacelike and timelike
singularities. For the Type IV and Type II singularities, since no geodesics
incompleteness occurs, no topological change is allowed, by using Geroch's
theorem arguments. However, for the Big Rip case, Tipler's arguments allow a
topology change, if the spacetime in which the topology change occurs is
non-compact and the boundary of this region are two topologically distinct
three dimensional spacelike partial Cauchy hypersurfaces. Also, some additional
requirements must hold true, among which the weak energy condition, which can
be satisfied in a geometric way in the context of a modified gravity. We
critically examine Tipler's arguments for the Big Rip case, and we discuss the
mathematical implications of such a topological change, with regard to the
final hypersurface on which geodesics incompleteness occurs.


  RX J1856.5$-$3754 is the brightest and nearest ($\sim 120$ pc) source among
thermally emitting isolated neutron stars. Its spectra observed with {\sl
XMM-Newton} and {\sl Chandra} satellites are well-fitted with the
two-temperature ($kT^\infty \sim$ 32 and 63 eV) blackbody model. Fitting ten
sets of the data from {\sl Suzaku} XIS0, XIS1, XIS3 and {\sl XMM-Newton}
EPIC-pn with the two-temperature blackbody model, we discover an excess
emission, 16--26\% in 0.8--1.2\,keV. We examine possible causes of this
keV-X-ray excess; uncertainty in the background, pile up of the low energy
photons and confusion of other sources. None of them succeeds in explaining the
keV-X-ray excess observed with different instruments. We thus consider this
keV-X-ray excess is most likely originated in RX J1856.5$-$3754. However, it is
difficult to constrain the spectral shape of the keV-X-ray excess. The third
blackbody component with $kT^\infty = 137^{+18}_{-14}$ eV, additional power-law
component with a photon index $\Gamma = 3.4^{+0.5}_{-0.6}$, or Comptonization
of blackbody seed photons into power-law with a photon index $\Gamma_c =
4.3^{+0.8}_{-0.8}$ can reproduce the keV-X-ray excess. We also search for the
periodicity of 0.8--1.2\,keV data, since 7.055 s pulsation is discovered from
0.15--1.2\,keV band in the XMM Newton EPIC-pn data ($\sim$1.5\%). We only
obtain the upper limit of pulsed fraction $<$ 3\% in the keV-X-ray excess. We
shortly discuss the possible origin of the keV-X-ray excess, such as
synchrotron radiation and Comptonization of blackbody photons.


  We introduce adaptive sampling methods for stochastic programs with
deterministic constraints. First, we propose and analyze a variant of the
stochastic projected gradient method where the sample size used to approximate
the reduced gradient is determined on-the-fly and updated adaptively. This
method is applicable to a broad class of expectation-based risk measures and
leads to a significant reduction in the individual gradient evaluations used to
estimate the objective function gradient. Numerical experiments with expected
risk minimization and conditional value-at-risk minimization support this
conclusion and demonstrate practical performance and efficacy for both
risk-neutral and risk-averse problems. Second, we propose an SQP-type method
based on similar adaptive sampling principles. The benefits of this method are
demonstrated in a simplified engineering design application featuring
risk-averse shape optimization of a steel shell structure subject to uncertain
loading conditions and model uncertainty.


  We investigate wave transport properties of Parity-Time (PT) symmetric
lattices that are periodically modulated along the direction of propagation. We
demonstrate that in the regime of unbroken PT-symmetry the system Floquet-Bloch
modes may interfere constructively leading to either controlled oscillations or
linear power absorption and amplification occurring exactly at the phase
transition point. The differential power response is effected by the overlap of
the gain and loss system distribution with wave intensity pattern that is
formed through Rabi oscillations engaging the coupled Floquet-Bloch modes.


  The nearby dwarf elliptical galaxy NGC 205 offers a unique opportunity for
high resolution studies of the interstellar medium in an elliptical galaxy.
This paper investigates the distribution of molecular gas, molecular line
ratios, and the relationships between atomic gas, molecular gas, and dust in
NGC 205. The line ratios 12CO(2-1)/(1-0) and 12CO(1-0)/13CO(1-0) in one of the
molecular clouds in NGC 205 are consistent with the ratios found in other
elliptical galaxies and in Galactic giant molecular clouds; they suggest that
the CO in this cloud is probably subthermally excited. Atomic gas, molecular
gas, and dust are very closely associated on scales of 100 pc; the atomic gas
can be understood as photodissociated envelopes around the molecular clouds.
The atomic column densities in this galaxy are quite low (10^20 cm^-2) because
the interstellar UV field is relatively low. The total gas-to-dust column
density ratios are consistent with Galactic gas-to-dust ratios. In short, the
molecular gas in NGC 205 seems to have very similar properties to the familiar
molecular clouds in our own Galaxy, except for the low atomic column densities.


  We explore the scenario of a Coronal Mass Ejection (CME) being the cause of
the observed continuous X-ray absorption of the August 30 1997 superflare on
the eclipsing binary Algol (the Demon Star). The temporal decay of the
absorption is consistent with absorption by a CME undergoing self-similar
evolution with uniform expansion velocity. We investigate the kinematic and
energetic properties of the CME using the ice-cream cone model for its
three-dimensional structure in combination with the observed profile of the
hydrogen column density decline with time. Different physically justified
length scales were used that allowed us to estimate lower and upper limits of
the possible CME characteristics. Further consideration of the maximum
available magnetic energy in starspots leads us to quantify its mass as likely
lying in the range $2\times 10^{21}$-$2\times 10^{22}$ g and kinetic energy in
the range $7\times 10^{35}$-$3\times 10^{38}$ erg. The results are in
reasonable agreement with extrapolated relations between flare X-ray fluence
and CME mass and kinetic energy derived for solar CMEs.


  Using the full CDF Run II data sample, we report evidence for a new
resonance, which we refer to as $B(5970)$, found simultaneously in the
$B^0\pi^+$ and $B^+\pi^-$ mass distributions with a significance of 4.4
standard deviations. We further report the first study of resonances consistent
with orbitally excited $B^{+}$ mesons and an updated measurement of the
properties of orbitally excited $B^0$ and $B_s^0$ mesons. We measure the masses
and widths of all states, as well as the relative production rates of $B_1$,
$B_2^*$, and $B(5970)$ states and the branching fraction of the $B_{s2}^{*0}$
state to either $B^{*+} K^-$ and $B^{+} K^-$. Furthermore, we measure the
production rates of the orbitally excited $B^{0,+}$ states relative to the
$B^{0,+}$ ground state. The masses of the new $B(5970)$ resonances are
$5978\pm5(\textrm{stat})\pm12(\textrm{syst}) \textrm{ MeV/c}^{2}$ for the
neutral state and $5961\pm5(\textrm{stat})\pm12(\textrm{syst}) \textrm{
MeV/c}^{2}$ for the charged state, assuming that the resonance decays into
$B\pi$ final states. The properties of the orbitally excited and the new
$B(5970)^{0,+}$ states are compatible with isospin symmetry.


  We prove that the quantum group inclusion $O_n \subset O_n^*$ is "maximal",
where $O_n$ is the usual orthogonal group and $O_n^*$ is the half-liberated
orthogonal quantum group, in the sense that there is no intermediate compact
quantum group $O_n\subset G\subset O_n^*$. In order to prove this result, we
use: (1) the isomorphism of projective versions $PO_n^*\simeq PU_n$, (2) some
maximality results for classical groups, obtained by using Lie algebras and
some matrix tricks, and (3) a short five lemma for cosemisimple Hopf algebras.


  The quasi-equilibrium approximation is acceptable when molecular interactions
are fast enough compared to circuit dynamics, but is no longer allowed when
cellular activities are governed by rare events. A typical example is the
lactose operon (lac), one of the most famous paradigms of transcription
regulation, for which several theories still coexist to describe its behaviors.
The lac system is generally analyzed by using equilibrium constants,
contradicting single-event hypotheses long suggested by Novick and Weiner
(1957). Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci.
USA 43, 553-566) and recently refined in the study of (Choi et al., 2008. A
stochastic single-molecule event triggers phenotype switching of a bacterial
cell. Science 322, 442-446). In the present report, a lac repressor
(LacI)-mediated DNA immunoprecipitation experiment reveals that the natural
LacI-lac DNA complex built in vivo is extremely tight and long-lived compared
to the time scale of lac expression dynamics, which could functionally
disconnect the abortive expression bursts and forbid using the standard modes
of lac bistability. As alternatives, purely kinetic mechanisms are examined for
their capacity to restrict induction through: (i) widely scattered derepression
related to the arrival time variance of a predominantly backward asymmetric
random walk and (ii) an induction threshold arising in a single window of
derepression without recourse to nonlinear multimeric binding and Hill
functions. Considering the complete disengagement of the lac repressor from the
lac promoter as the probabilistic consequence of a transient stepwise
mechanism, is sufficient to explain the sigmoidal lac responses as functions of
time and of inducer concentration. This sigmoidal shape can be misleadingly
interpreted as a phenomenon of equilibrium cooperativity classically used to
explain bistability, but which has been reported to be weak in this system.


  Many classification problems focus on maximizing the performance only on the
samples with the highest relevance instead of all samples. As an example, we
can mention ranking problems, accuracy at the top or search engines where only
the top few queries matter. In our previous work, we derived a general
framework including several classes of these linear classification problems. In
this paper, we extend the framework to nonlinear classifiers. Utilizing a
similarity to SVM, we dualize the problems, add kernels and propose a
componentwise dual ascent method.


  We have studied non-stationary and non-axisymmetric perturbations of a
magnetohydrodynamic accretion onto a rotating (Kerr) black hole. Assuming that
the magnetic field dominates the plasma accretion, we find that the accretion
suffers a large radial acceleration resulting from the Lorentz force, and
becomes highly variable compared with the electromagnetic field there. In fact,
we further find an interesting perturbed structure of the plasma velocity with
a large peak in some narrow region located slightly inside of the
fast-magnetosonic surface. This is due to the concentrated propagation of the
fluid disturbances in the form of fast-magnetosonic waves along the separatrix
surface. If the fast-magnetosonic speed is smaller in the polar regions than in
the equatorial regions, the critical surface has a prolate shape for radial
poloidal field lines. In this case, only the waves that propagate towards the
equator can escape from the super-fast-magnetosonic region and collimate
polewards as they propagate outwards in the sub-fast-magnetosonic regions. We
further discuss the capabilities of such collimated waves in accelerating
particles due to cyclotron resonance in an electron-positron plasma.


  Logistic regression models with $n$ observations and $q$ linearly-independent
covariates are shown to have Fisher information volumes which are bounded below
by $\pi^q$ and above by ${n \choose q} \pi^q$. This is proved with a novel
generalization of the classical theorems of Pythagoras and de Gua, which is of
independent interest. The finding that the volume is always finite is new, and
it implies that the volume can be directly interpreted as a measure of model
complexity. The volume is shown to be a continuous function of the design
matrix $X$ at generic $X$, but to be discontinuous in general. This means that
models with sparse design matrices can be significantly less complex than
nearby models, so the resulting model-selection criterion prefers sparse
models. This is analogous to the way that $\ell^1$-regularisation tends to
prefer sparse model fits, though in our case this behaviour arises
spontaneously from general principles. Lastly, an unusual topological duality
is shown to exist between the ideal boundaries of the natural and expectation
parameter spaces of logistic regression models.


  The emergence of eusocial species is both very rare in evolutionary history
and results in remarkably successful species. By inverting an agent based
model, agent rules are discovered that display behaviors characteristic of
eusocial species as well as other behaviors that lead to unexpected population
dynamics. By holding the agents' genome constant across the colony and allowing
the agents' rules to evolve, the individual behaviors exhibit phenotypic
plasticity in response to environmental cues. The phenotypically driven
reduction of intrinsic growth rates and the emergence of non-reproducing
phenotypes both demonstrate selection pressure at the colony (system) level.
The efficiency of an evolved colony is shown to have a strong relationship to
the computational capacity of the agents. Various other emergent behaviors,
both eusocial and otherwise novel, are identified and discussed. A path forward
to more capable eusocial populations and inter-colony evolution is outlined.


  We study flavour neutrinos confined to our 4-dimensional world coupled to one
"bulk" state, i.e. a Kaluza-Klein tower. We discuss the spatial development of
the neutrino disappearance, the possibility of resurgence and the effective
flavour transitions induced in this mechanism. We show that even a simple model
can produce an energy-independent suppression at large distances, and relate
this to experimental data.


  Due to dynamical friction stellar mass black holes and neutron stars are
expected to form high density cusps in the inner parsec of our Galaxy. These
compact remnants, expected to number around 20000, may be accreting cold dense
gas present there, and give rise to potentially observable X-ray emission. Here
we build a simple but detailed time-dependent model of such emission. We find
that at least several X-ray sources of this nature should be detectable with
Chandra at any one time. Turning this issue around, we also ask a question of
what current observational constraints might be telling us about the total
number of compact remnants. A cusp with ~ 40 thousand black holes over-predicts
the number of discrete sources and the total X-ray luminosity of the inner
parsec, and is hence ruled out. Future observations of the distribution and
orbits of the cold ionised gas in the inner parsec of Sgr A* will put tighter
constraints on the cusp of compact remnants.


  Collective effects, such as Dicke superradiant emission, can enhance the
performance of a quantum device. Here, we study the heat current flowing
between a cold and a hot bath through an ensemble of $N$ qubits, which are
collectively coupled to the thermal baths. We find a regime where the
collective coupling leads to a quadratic scaling of the heat current with $N$
in a finite-size scenario. Conversely, when approaching the thermodynamic
limit, we prove that the collective scenario exhibits a parametric enhancement
over the non-collective case. We then consider the presence of a third
uncontrolled {\it parasitic} bath, interacting locally with each qubit, that
models unavoidable couplings to the external environment. Despite having a
non-perturbative effect on the steady-state currents, we show that the
collective enhancement is robust to such an addition. Finally, we discuss the
feasibility of realizing such a Dicke heat valve with superconducting circuits.
Our findings indicate that in a minimal realistic experimental setting with two
superconducting qubits, the collective advantage offers an enhancement of
approximately $10\%$ compared to the non-collective scenario.


  Generation of automated clinical notes have been posited as a strategy to
mitigate physician burnout. In particular, an automated narrative summary of a
patient's hospital stay could supplement the hospital course section of the
discharge summary that inpatient physicians document in electronic health
record (EHR) systems. In the current study, we developed and evaluated an
automated method for summarizing the hospital course section using
encoder-decoder sequence-to-sequence transformer models. We fine tuned BERT and
BART models and optimized for factuality through constraining beam search,
which we trained and tested using EHR data from patients admitted to the
neurology unit of an academic medical center. The approach demonstrated good
ROUGE scores with an R-2 of 13.76. In a blind evaluation, two board-certified
physicians rated 62% of the automated summaries as meeting the standard of
care, which suggests the method may be useful clinically. To our knowledge,
this study is among the first to demonstrate an automated method for generating
a discharge summary hospital course that approaches a quality level of what a
physician would write.


  We present polarisation observations of five pulsars whose profiles exhibit
two distinct emission regions separated by close to 180 degrees of longitude.
We fitted the position angle of the linear polarisation using the rotating
vector model and convincingly show that all the pulsars have the angle between
their magnetic and rotation axes close to 90 degrees. The simplest
interpretation of the results is that we see `main pulse' emission from one
pole and `interpulse' emission from the opposite pole. We have attempted to
produce emission maps of the magnetosphere above the polar caps for each pulsar
and find that the maps support the view that the emission region in pulsars is
complex, even when the profile appears simple. For three pulsars, we can derive
emission heights and polar maps which are consistent with emission regions
located symmetrically about the magnetic axis and confined to the open field
lines. For two pulsars, we find that either the emission arises from `closed'
field lines or that the profiles are highly asymmetric with respect to the
magnetic axis.


  We present a strong lensing system, composed of 4 multiple images of a source
at z = 2.387, created by two lens galaxies, G1 and G2, belonging to the galaxy
cluster MACS J1115.9+0129 at z = 0.353. We use observations taken as part of
the Cluster Lensing and Supernova survey with Hubble, CLASH, and its
spectroscopic follow-up programme at the Very Large Telescope, CLASH-VLT, to
estimate the total mass distributions of the two galaxies and the cluster
through strong gravitational lensing models. We find that the total projected
mass values within the half-light radii, R_{e}, of the two lens galaxies are
M_{T,G1}(< R_{e,G1}) = (3.6 +/- 0.4) x 10^{10}M_{Sun} and M_{T,G2}(< R_{e,G2})
= (4.2 +/- 1.6) x 10^{10}M_{Sun}. The effective velocity dispersion values of
G1 and G2 are (122 +/- 7) km/s and (137 +/- 27) km/s, respectively. We remark
that these values are relatively low when compared to those of ~200-300 km/s,
typical of lens galaxies found in the field by previous surveys. By fitting the
spectral energy distributions of G1 and G2, we measure projected luminous over
total mass fractions within R_{e} of 0.11 +/- 0.03, for G1, and 0.73 +/- 0.32,
for G2. The fact that the less massive galaxy, G1, is dark-matter dominated in
its inner regions raises the question of whether the dark matter fraction in
the core of early-type galaxies depends on their mass. Further investigating
strong lensing systems will help us understand the influence that dark matter
has on the structure and evolution of the inner regions of galaxies.


  Many promising approaches to symbolic regression have been presented in
recent years, yet progress in the field continues to suffer from a lack of
uniform, robust, and transparent benchmarking standards. In this paper, we
address this shortcoming by introducing an open-source, reproducible
benchmarking platform for symbolic regression. We assess 14 symbolic regression
methods and 7 machine learning methods on a set of 252 diverse regression
problems. Our assessment includes both real-world datasets with no known model
form as well as ground-truth benchmark problems, including physics equations
and systems of ordinary differential equations. For the real-world datasets, we
benchmark the ability of each method to learn models with low error and low
complexity relative to state-of-the-art machine learning methods. For the
synthetic problems, we assess each method's ability to find exact solutions in
the presence of varying levels of noise. Under these controlled experiments, we
conclude that the best performing methods for real-world regression combine
genetic algorithms with parameter estimation and/or semantic search drivers.
When tasked with recovering exact equations in the presence of noise, we find
that deep learning and genetic algorithm-based approaches perform similarly. We
provide a detailed guide to reproducing this experiment and contributing new
methods, and encourage other researchers to collaborate with us on a common and
living symbolic regression benchmark.


  The cerebrum of mammals spans a vast range of sizes and yet has a very
regular structure. The amount of folding of the cortical surface and the
proportion of white matter gradually increase with size, but the underlying
mechanisms remain elusive. Here, two laws are derived to fully explain these
cerebral scaling relations. The first law holds that the long-range information
flow in the cerebrum is determined by the total cortical surface (i.e., the
number of neurons) and the increasing information resistance of long-range
connections. Despite having just one free parameter, the first law fits the
mammalian cerebrum better than any existing function, both across species and
within humans. According to the second law, the white matter volume scales,
with a few minor corrections, to the cortical surface area. It follows from the
first law that large cerebrums have much local processing and little global
information flow. Moreover, paradoxically, a further increase in long-range
connections would decrease the efficiency of information flow.


  In this work, we address the challenge of uncovering patterns in variational
optimal protocols for taking the system to ground states of many-body
Hamiltonians, using variational quantum algorithms. We develop highly optimized
classical Monte Carlo (MC) algorithms to find the optimal protocols for
transformations between the ground states of the square-lattice XXZ model for
finite systems sizes. The MC method obtains optimal bang-bang protocols, as
predicted by Pontryagin's minimum principle. We identify the minimum time
needed for reaching an acceptable error for different system sizes as a
function of the initial and target states and uncover correlations between the
total time and the wave-function overlap. We determine a dynamical phase
diagram for the optimal protocols, with different phases characterized by a
topological number, namely the number of on-pulses. Bifurcation transitions as
a function of initial and final states, associated with new jumps in the
optimal protocols, demarcate these different phases. The number of pulses
correlates with the total evolution time. In addition to identifying the
topological characteristic above, i.e., the number of pulses, we introduce a
correlation function to characterize bang-bang protocols' quantitative
geometric similarities. We find that protocols within one phase are indeed
geometrically correlated. Identifying and extrapolating patterns in these
protocols may inform efficient large-scale simulations on quantum devices.


  With the rapid increase in the number of Anthropogenic Space Objects (ASOs),
Low Earth Orbit (LEO) is facing significant congestion, thereby posing
challenges to space operators and risking the viability of the space
environment for varied uses. Current models for examining this evolution, while
detailed, are computationally demanding. To address these issues, we propose a
novel machine learning-based model, as an extension of the MIT Orbital Capacity
Tool (MOCAT). This advanced model is designed to accelerate the propagation of
ASO density distributions, and it is trained on hundreds of simulations
generated by an established and accurate model of the space environment
evolution. We study how different deep learning-based solutions can potentially
be good candidates for ASO propagation and manage the high-dimensionality of
the data. To assess the model's capabilities, we conduct experiments in long
term forecasting scenarios (around 100 years), analyze how and why the
performance degrades over time, and discuss potential solutions to make this
solution better.


  Let $M$ be an open (complete and non-compact) manifold with $\mathrm{Ric}\ge
0$ and escape rate not $1/2$. It is known that under these conditions, the
fundamental group $\pi_1(M)$ has a finitely generated torsion-free nilpotent
subgroup $\mathcal{N}$ of finite index, as long as $\pi_1(M)$ is an infinite
group. We show that the nilpotency step of $\mathcal{N}$ must be reflected in
the asymptotic geometry of the universal cover $\widetilde{M}$, in terms of the
Hausdorff dimension of an isometric $\mathbb{R}$-orbit: there exist an
asymptotic cone $(Y,y)$ of $\widetilde{M}$ and a closed $\mathbb{R}$-subgroup
$L$ of the isometry group of $Y$ such that its orbit $Ly$ has Hausdorff
dimension at least the nilpotency step of $\mathcal{N}$. This resolves a
question raised by Wei and the author, and extends previous results on virtual
abelianness by the author.


  Transport is one of the most important physical processes in all energy and
length scales. Ideal gases and hydrodynamics are, respectively, two opposite
limits of transport. Here, we present an unexpected mathematical connection
between these two limits; that is, there exist situations that the solution to
a class of interacting hydrodynamic equations with certain initial conditions
can be exactly constructed from the dynamics of noninteracting ideal gases. We
analytically provide three such examples. The first two examples focus on
scale-invariant systems, which generalize fermionization to the hydrodynamics
of strongly interacting systems, and determine specific initial conditions for
perfect density oscillations in a harmonic trap. The third example recovers the
dark soliton solution in a one-dimensional Bose condensate. The results can
explain a recent puzzling experimental observation in ultracold atomic gases by
the Paris group and make further predictions for future experiments. We
envision that extensive examples of such an ideal-gas approach to hydrodynamics
can be found by systematical numerical search, which can find broad
applications in different problems in various subfields of physics.


  We study the $B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K
decays with perturbative QCD approach (pQCD) based on $k_T$ factorization. The
new orbitally excited charmonium distribution amplitudes $\psi(1^{3}D_{1})$
based on the Schr\"{o}dinger wave function of the $n=1$, $l=2$ state for the
harmonic-oscillator potential are employed. By using the corresponding
distribution amplitudes, we calculate the branching ratio of
$B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K decays and the
form factors $A_{0,1,2}$ and $V$ for the transition
$B_{c}$$\rightarrow$$\psi(1^{3}D_{1})$. We obtain the branching ratio of both
$B_{c}$$\rightarrow$$\psi(2S)$K and $B_{c}$$\rightarrow$$\eta_{c}(2S)$K are at
the order of $10^{-5}$. The effects of two sets of the S-D mixing angle
$\theta=-12^{\circ}$ and $\theta=27^{\circ}$ for the decay
$B_{c}$$\rightarrow$$\psi(3770)$K are studied firstly in this paper. Our
calculations show that the branching ratio of the decay
$B_{c}$$\rightarrow$$\psi(3770)$K can be raised from the order of $10^{-6}$ to
the order of $10^{-5}$ at the mixing angle $\theta=-12^{\circ}$, which can be
tested by the running LHC-b experiments.


  Twisted graphene multilayers have demonstrated to yield a versatile
playground to engineer controllable electronic states. Here, by combining
first-principles calculations and low-energy models, we demonstrate that
twisted graphene trilayers provide a tunable system where van Hove
singularities can be controlled electrically. In particular, it is shown that
besides the band flattening, bulk valley currents appear, which can be quenched
by local chemical dopants. We finally show that in the presence of electronic
interactions, a non-uniform superfluid density emerges, whose non-uniformity
gives rise to spectroscopic signatures in dispersive higher energy bands. Our
results put forward twisted trilayers as a tunable van der Waals
heterostructure displaying electrically controllable flat bands and bulk valley
currents.


  We study the current-voltage characteristics of a superconducting junction
with particle losses at the contacts. We adopt the Keldysh formalism to compute
the steady-state current for varying transmission of the contact. In the low
transmission regime, the dissipation leads to an enhancement of the current at
low bias, a nonmonotonic dependence of current on dissipation, and the
emergence of new structures in the current-voltage curves. The effect of
dissipation by particle loss is found to be qualitatively different from that
of a finite temperature and a finite inelastic scattering rate in the
reservoirs.


  The structure of very complicated irregular "microscopic" (local) entropy
fluctuations around a big separated "macroscopic" (global) fluctuation in the
statistical equilibrium was studied in numerical experiments on a simple
2--freedom strongly chaotic Hamiltonian model described by the modified Arnold
cat map. A comparison of transient nonequilibrium rise and relaxation process
of the big fluctuation out of the statistical equilibrium with a nonequilibrium
steady state in a model without statistical equilibrium is considered and
discussed with respect to the so-called Fluctuation Law (or "theorem")
introduced and intensively studied recently in the latter case. A new transient
fluctuation law was found on the basis of a simple semiempirical theory
developed. Preliminary results of numerical experiments on some fractal
properties of the "microscopic" fluctuations are presented and briefly
discussed.


  Condensed matter materials have shown great potential in searching for light
dark matter (DM) via detecting the phonon or magnon signals induced by the
scattering of DMs off the materials. In this paper, we study the possibility of
detecting electromagnetic form factors of fermionic DM and axion-like particles
(ALPs) using superfluid Helium-4. The phonon induced by a sub-GeV fermionic DM
scattering off the superfluid can be described using the effective field theory
with the interaction between DM and the bulk ${}^4$He. Signals arising from the
electromagnetic form factors of light DM in the presence of an external
electric field are calculated. Projected constraints on the charge radius, the
anapole moment, and the magnetic moment of the DM are derived with 1
kg$\cdot$year exposure. The phonon signal induced by the scattering of ALPs off
the superfluid is also calculated, which can put competitive and the first
direct detection bounds on ALP-photon-dark photon couplings in the projected
experiments.


  We report on the retrieval of directional sea surface roughness, in terms of
its full directional mean square slope (including direction and isotropy), from
Global Navigation Satellite System Reflections (GNSS-R) Delay-Doppler-Map (DDM)
data collected during an experimental flight at 1 km altitude. This study
emphasizes the utilization of the entire DDM to more precisely infer ocean
roughness directional parameters. In particular, we argue that the DDM exhibits
the impact of both roughness and scatterer velocity. Obtained estimates are
analyzed and compared to co-located Jason-1 measurements, ECMWF numerical
weather model outputs and optical data.