  We present results from the first near-IR imaging of the weak X-ray sources
discovered in the Chandra/ACIS-I survey (Wang et al. 2002) towards the Galactic
Centre (GC). These ~800 discrete sources, which contribute significantly to the
GC X-ray emission, represent an important and previously unknown population
within the Galaxy. From our VLT observations we will identify likely IR
counterparts to a sample of the hardest sources, which are most likely X-ray
binaries. With these data we can place constraints on the nature of the
discrete weak X-ray source population of the GC.


  Thermally conductive polymers are of fundamental interest and can also be
exploited in thermal management applications. Recent studies have shown
stretched polymers can achieve high thermal conductivity. However, the
transport mechanisms of heat in thermally conductive polymers have yet to be
elucidated. Here we report a method for scalable fabrication of polyethylene
films with a high thermal conductivity of 62 W/m-K. The achieved thermal
conductivity is over two orders-of-magnitude greater than that of typical
polymers (~0.1 W/m-K), and exceeds those of many metals and ceramics used as
traditional heat conductors. Careful structural studies are carried out and
reveal that the film consists of nanofibers with crystalline and amorphous
regions. Contrary to conventional wisdom, we reveal the importance of the
amorphous morphology in achieving such high thermal conductivity, rather than
simply from enhancements in the degree of crystallinity and crystallite
alignment. The amorphous phase reaches a remarkably high thermal conductivity
of ~16 W/m-K. Even still, we identify that the presence of this amorphous phase
is the dominant factor as the film thermal conductivity is still much lower
than the predicted values for bulk single-crystal polyethylene (237 K/m-K).
This work lays the foundation for the rational design and synthesis of
thermally conductive polymers, and opens up new opportunities for advanced heat
management, particularly when flexible, lightweight, chemically inert and
electrically insulating thermal conductors are desired.


  We develop a convolution theory for quasianalytic ultradistributions of
Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and
use it as a base for the parametrix method in the study of new topological and
structural properties of several quasianalytic spaces of functions and
ultradistributions. In particular, our results apply to Fourier hyperfunctions
and Fourier ultra-hyperfunctions.


  We present a systematic investigation of attractive binary mixtures in
presence of both spin- and mass-imbalance in one dimensional setups described
by the Hubbard model. After discussing typical cold atomic experimental
realizations and the relation between microscopic and effective parameters, we
study several many-body features of trapped Fermi-Fermi and Bose-Bose mixtures
such as density profiles, momentum distributions and correlation functions by
means of numerical density-matrix-renormalization-group and Quantum Monte Carlo
simulations. In particular, we focus on the stability of
Fulde-Ferrell-Larkin-Ovchinnikov, dimer and trimer fluids in inhomogeneous
situations, as typically realized in cold gas experiments due to the harmonic
confinement. We finally consider possible experimental signatures of these
phases both in the presence of a finite polarization and of a finite
temperature.


  This paper considers mean field games in a multi-agent Markov decision
process (MDP) framework. Each player has a continuum state and binary action.
By active control, a player can bring its state to a resetting point. All
players are coupled through their cost functions. The structural property of
the individual strategies is characterized in terms of threshold policies when
the mean field game admits a solution. We further introduce a stationary
equation system of the mean field game and analyze uniqueness of its solution
under positive externalities.


  The pulsational method to estimate the absolute magnitudes of RR Lyrae stars
is updated with new data on field-star metallicities by Layden, a new
calibration of the (B-V)_0-temperature correlation from recent atmospheric
models by Bell and Tripicco, and new mass estimates by Bono et al. New linear
and non-linear calibrations of M_V(RR)=f([Fe/H]) are derived that depend on the
nature of the adopted envelope in a diagram of log period versus metallicity
fitted to the shortest period field variables in each metallicity range,
together with the stated assumptions on the colour of the stars at that
envelope. These new cali- brations are compared with a recent non-linear
calibration by Caputo et al. The theoretical luminosity zero points for each of
the three new calibrations derived here agree with each other to within 0.1 mag
over the metallicity range of -1.0>[Fe/H]>-2.0. Comparison with the empirical
absolute magnitude calibra- tion of M_V(RR)=+0.52 at [Fe/H]=-1.5 by Clementini
at al. from RR Lyraes in LMC also shows agreement at the 0.05 mag level at the
stated metallicity. Our final compromise pulsational calibration is,
M_V(RR)=0.82 + 0.20([Fe/H]) with the caveat that the true relation is likely to
be non-linear at the 0.1 mag level for [Fe/H] values between -0.5 and -2.0,
hence with variable dM_V/d([Fe/H]) slopes that cover the range from 0 to 0.6
for different metallicities. (...)


  The Dialog State Tracking Challenge 4 (DSTC 4) proposes several pilot tasks.
In this paper, we focus on the spoken language understanding pilot task, which
consists of tagging a given utterance with speech acts and semantic slots. We
compare different classifiers: the best system obtains 0.52 and 0.67 F1-scores
on the test set for speech act recognition for the tourist and the guide
respectively, and 0.52 F1-score for semantic tagging for both the guide and the
tourist.


  It is known that there exist non-local correlations that respect no-signaling
criterion, but violate Bell-type inequalities more than quantum-mechanical
correlations. Such super quantum correlations were introduced as the
Popescu-Rohrlich (PR) box. We consider such non-local boxes with two/three
inputs and two/three outputs. We show that these super quantum correlations can
lead to signaling when at least one of the input bit has access to a word line
along a closed time-like curve.


  Recent studies suggest that artificial neural networks (ANNs) that match the
spectral properties of the mammalian visual cortex -- namely, the $\sim 1/n$
eigenspectrum of the covariance matrix of neural activities -- achieve higher
object recognition performance and robustness to adversarial attacks than those
that do not. To our knowledge, however, no previous work systematically
explored how modifying the ANN's spectral properties affects performance. To
fill this gap, we performed a systematic search over spectral regularizers,
forcing the ANN's eigenspectrum to follow $1/n^\alpha$ power laws with
different exponents $\alpha$. We found that larger powers (around 2--3) lead to
better validation accuracy and more robustness to adversarial attacks on dense
networks. This surprising finding applied to both shallow and deep networks and
it overturns the notion that the brain-like spectrum (corresponding to $\alpha
\sim 1$) always optimizes ANN performance and/or robustness. For convolutional
networks, the best $\alpha$ values depend on the task complexity and evaluation
metric: lower $\alpha$ values optimized validation accuracy and robustness to
adversarial attack for networks performing a simple object recognition task
(categorizing MNIST images of handwritten digits); for a more complex task
(categorizing CIFAR-10 natural images), we found that lower $\alpha$ values
optimized validation accuracy whereas higher $\alpha$ values optimized
adversarial robustness. These results have two main implications. First, they
cast doubt on the notion that brain-like spectral properties ($\alpha \sim 1$)
\emph{always} optimize ANN performance. Second, they demonstrate the potential
for fine-tuned spectral regularizers to optimize a chosen design metric, i.e.,
accuracy and/or robustness.


  Let $D$ be a smoothly bounded pseudoconvex domain in $\mathbf C^n$, $n > 1$.
Using the Robin function $\La(p)$ that arises from the Green function $G(z, p)$
for $D$ with pole at $p \in D$ associated with the standard sum-of-squares
Laplacian, N. Levenberg and H. Yamaguchi had constructed a K\"{a}hler metric
(the so-called $\La$-metric) on $D$. Assume that $D$ is strongly pseudoconvex
and $ds^2$ denotes the $\La$-metric on $D$. In this article, first we prove
that the holomorphic sectional curvature of $ds^2$ along normal directions
converges to a negative constant near the boundary of $D$. Then, we prove that
if $D$ is not simply connected, then any nontrivial homotopy class of
$\pi_1(D)$ contains a closed geodesic for $ds^2$. Finally, we prove that the
diminesion of the space of square integrable harmonic $(p, q)$-forms on $D$
relative to $ds^2$ is zero except when $p+q=n$ in which case it is infinite.


  We investigate quantum transport through a rectangular potential barrier in
Weyl semimetals (WSMs) and multi-Weyl semimetals (MSMs), within the framework
of Landauer-B\"uttiker formalism. Our study uncovers the role of nodal topology
imprinted in the electric current and the shot noise. We find that, in contrast
to the finite odd-order conductance and noise power, the even-order
contributions vanish at the nodes. Additionally, depending on the topological
charge ($J$), the linear conductance ($G_1$) scales with the Fermi energy
($E_F$) as $G_1^{E_F>U}\propto E_F^{2/J}$. We demonstrate that the
$E_F$-dependence of the second-order conductance and shot noise power could
quite remarkably distinguish an MSM from a WSM depending on the band topology,
and may induce several smoking gun experiments in nanostructures made out of
WSMs and MSMs. Analyzing shot noise and Fano factor, we show that the transport
across the rectangular barrier follows the sub-Poissonian statistics.
Interestingly, we obtain universal values of Fano factor at the nodes unique to
their topological charges. The universality for a fixed $J$, however, indicates
that only a fixed number of open channels participate in the transport through
evanescent waves at the nodes. The proposed results can serve as a potential
diagnostic tool to identify different topological systems in experiments.


  A version of the classical Vieta theorem for free noncommuting variables is
given. It leads to a new start in a construction of noncommutative symmetric
functions


  We report an NMR investigation of the superconductivity in BaFe(2)As(2)
induced by Co doping (Tc=22K). We demonstrate that Co atoms form an alloy with
Fe atoms and donate carriers without creating localized moments. Our finding
strongly suggests that the underlying physics of iron-pnictide superconductors
is quite different from the widely accepted physical picture of high Tc
cuprates as doped Mott insulators. We also show a crossover of electronic
properties into a low temperature pseudo-gap phase with a pseudo-gap Delta
560K, where chi(spin) constant and resisitivty T. The NMR Knight shift below Tc
decreases for both along the c-axis and ab-plane, and is consistent with the
singlet pairing scenario.


  We measure the mean frequencies of acoustic waves propagating toward and away
from a sunspot employing a spot-centered Fourier-Hankel decomposition of p-mode
amplitudes as measured from a set of observations made at the South Pole in
1991. We demonstrate that there is a significant frequency shift between the
inward and outward traveling waves which is consistent with the Doppler effect
of a radial outflow from the sunspot. For p-modes of temporal frequencies of 3
mHz it is observed that the frequency shift decreases slightly with spatial
frequency, for modes with degree l between 160 to 600. From the l dependence of
the frequency shift, we infer that the mean radial outflow within the observed
annular region (which extends between 30 and 137 Mm from the spot) increases
nearly linearly with depth, reaching a magnitude of about 200 m/s at a depth of
20 Mm. This outflow exhibits properties similar to flows recently reported by
Lindsey, et al. (1996) using spatially sensitive local helioseismic techniques.


  We present a neutron diffraction study of NaYbO$_2$, a candidate quantum spin
liquid compound hosting a geometrically frustrated triangular lattice of
magnetic Yb$^{3+}$ ions. We observe diffuse magnetic scattering that persists
to at least 20 K, demonstrating the presence of short-range magnetic
correlations in this system up to a relatively high energy scale. Using reverse
Monte Carlo and magnetic pair distribution function analysis, we confirm the
predominant antiferromagnetic nature of these correlations and show that the
diffuse scattering data can be well described by noninteracting layers of XY
spins on the triangular lattice. We rule out Ising spins and
short-range-ordered stripe or 120$^{\circ}$ phases as candidate ground states
of NaYbO$_2$. These results are consistent with a possible QSL ground state in
NaYbO$_2$ and showcase the benefit of combined reciprocal- and real-space
analysis of materials with short-range magnetic correlations.


  To understand the dynamical and conformational properties of deformable
active agents in porous media, we computationally investigate the dynamics of
linear chains and rings made of active Brownian monomers. In porous media,
flexible linear chains and rings always migrate smoothly and undergo
activity-induced swelling. However, semiflexible linear chains though navigate
smoothly, shrink at lower activities, followed by swelling at higher
activities, while semiflexible rings exhibit a contrasting behavior.
Semiflexible rings shrink, get trapped at lower activities, and escape at
higher activities. This demonstrates how activity and topology interplay and
control the structure and dynamics of linear chains and rings in porous media.
We envision that our study will shed light on understanding the mode of
transport of shape-changing active agents in porous media.


  We study the range of a classifiable class ${\cal A}$ of unital separable
simple amenable $C^*$-algebras which satisfy the Universal Coefficient Theorem.
The class ${\cal A}$ contains all unital simple AH-algebras. We show that all
unital simple inductive limits of dimension drop circle $C^*$-algebras are also
in the class. This unifies some of the previous known classification results
for unital simple amenable $C^*$-algebras. We also show that there are many
other $C^*$-algebras in the class. We prove that, for any partially ordered,
simple weakly unperforated rationally Riesz group $G_0$ with order unit $u,$
any countable abelian group $G_1,$ any metrizable Choquet simplex $S,$ and any
surjective affine continuous map $r: S\to S_u(G_0)$ (where $S_u(G_0)$ is the
state space of $G_0$) which preserves extremal points, there exists one and
only one (up to isomorphism) unital separable simple amenable $C^*$-algebra $A$
in the classifiable class ${\cal A}$ such that $$ ((K_0(A), K_0(A)_+, [1_A]),
K_1(A), T(A), \lambda_A)=((G_0, (G_0)_+, u), G_1,S, r).


  A generalization of the notion of a (pseudo-) Riemannian space is proposed in
a framework of noncommutative geometry. In particular, there are parametrized
families of generalized Riemannian spaces which are deformations of classical
geometries. We also introduce harmonic maps on generalized Riemannian spaces
into Hopf algebras and make contact with integrable models in two dimensions.


  A celebrated conjecture due to De Giorgi states that any bounded solution of
the equation $\Delta u + (1-u^2) u = 0 \hbox{in} \R^N $ with $\pp_{y_N}u >0$
must be such that its level sets $\{u=\la\}$ are all hyperplanes, {\em \bf at
least} for dimension $N\le 8$. A counterexample for $N\ge 9$ has long been
believed to exist. Based on a minimal graph $\Gamma$ which is not a hyperplane,
found by Bombieri, De Giorgi and Giusti in $\R^N$, $N\ge 9$, we prove that for
any small $\alpha >0$ there is a bounded solution $u_\alpha(y)$ with
$\pp_{y_N}u_\alpha >0$, which resembles $ \tanh (\frac t{\sqrt{2}}) $, where
$t=t(y)$ denotes a choice of signed distance to the blown-up minimal graph
$\Gamma_\alpha := \alpha^{-1}\Gamma$. This solution constitutes a
counterexample to De Giorgi conjecture for $N\ge 9$.


  Most stars form in multiple systems whose properties can significantly impact
circumstellar disk evolution. We investigate the physical and chemical
properties of the equal-mass, small separation (~66 mas, ~9 au) DF Tau binary
system. Previous observations indicated that only DF Tau A has a circumstellar
disk. We present JWST-MIRI MRS observations of DF Tau. The MIRI spectrum shows
a forest of H2O lines and emission from CO, C2H2, HCN, CO2, and OH. LTE slab
models are used to determine the properties of the gas, and we analyze high
angular spatial and spectral resolution data from ALMA, VLTI-GRAVITY, and
IRTF-iSHELL to aid in the interpretation of the JWST data. The 1.3 mm ALMA
continuum data show two equal-brightness sources of compact (R<3 au) emission,
with separations and movement consistent with astrometry from VLTI-GRAVITY and
the known orbit. This is interpreted as a robust detection of a disk around DF
Tau B, which we suggest may host a small (~1 au) cavity to reconcile all
observations. The disk around DF Tau A is expected to be a full disk, and
spatially and spectrally resolved dust and gas emission points to hot, close-in
(<0.2 au) material. Hot (~500-1000 K) H2O, HCN, and C2H2 emission in the MIRI
data likely originate in the DF Tau A disk, while a cold (<200 K) H2O component
with an extended emitting area is consistent with an origin from both disks.
Despite the very compact outer disks, the inner disk composition and conditions
are similar to isolated systems, suggesting that the close binary nature is not
a driving factor in setting the inner disk chemistry. However, constraining the
geometry of the disks, for instance, via higher resolution ALMA observations,
would provide additional insight into the mid-infrared gas emission. JWST
observations of spatially resolved binaries will be important for understanding
the impact of binarity on inner disk chemistry more generally.


  In this work we prove global stability for the Boltzmann equation (1872) with
the physical collision kernels derived by Maxwell in 1866 for the full range of
inverse power intermolecular potentials, $r^{-(p-1)}$ with $p>2$. This
completes the work which we began in (arXiv:0912.0888v1). We more generally
cover collision kernels with parameters $s\in (0,1)$ and $\gamma$ satisfying
$\gamma > -(n-2)-2s$ in arbitrary dimensions $\mathbb{T}^n \times \mathbb{R}^n$
with $n\ge 2$. Moreover, we prove rapid convergence as predicted by the
Boltzmann H-Theorem. When $\gamma + 2s \ge 0$, we have exponential time decay
to the Maxwellian equilibrium states. When $\gamma + 2s < 0$, our solutions
decay polynomially fast in time with any rate. These results are constructive.
Additionally, we prove sharp constructive upper and lower bounds for the
linearized collision operator in terms of a geometric fractional Sobolev norm;
we thus observe that a spectral gap exists only when $\gamma + 2s \ge 0$, as
conjectured in Mouhot-Strain (2007).


  Deep learning techniques have been used recently to tackle the audio source
separation problem. In this work, we propose to use deep fully convolutional
denoising autoencoders (CDAEs) for monaural audio source separation. We use as
many CDAEs as the number of sources to be separated from the mixed signal. Each
CDAE is trained to separate one source and treats the other sources as
background noise. The main idea is to allow each CDAE to learn suitable
spectral-temporal filters and features to its corresponding source. Our
experimental results show that CDAEs perform source separation slightly better
than the deep feedforward neural networks (FNNs) even with fewer parameters
than FNNs.


  The Split SUSY scenario with light Higgsino states is treated as an
application to the Dark Matter problem. We have considered the structure of the
neutralino-nucleon interaction and calculated cross-section of the
neutralino-nucleon scattering. The decay properties of the lightest chargino
and next lightest neutralino are analyzed in details.


  We introduce a stochastic partial differential equation (SPDE) with elliptic
operator in divergence form, with measurable and bounded coefficients and
driven by space-time white noise. Such SPDEs could be used in mathematical
modelling of diffusion phenomena in medium consisting of different kinds of
materials and undergoing stochastic perturbations. We characterize the solution
and, using the Stein--Malliavin calculus, we prove that the sequence of its
recentered and renormalized spatial quadratic variations satisfies an almost
sure central limit theorem. Particular focus is given to the interesting case
where the coefficients of the operator are piecewise constant.


  We generalize the concept of optical state truncation and noiseless linear
amplification to enable truncation of the Fock-state expansion of an optical
state to higher order and to simultaneously amplify it using linear optics. The
resulting generalized quantum scissors are more efficient for noiseless linear
amplification than employing multiple scissors in parallel and are
experimentally practical. As a particular example, we focus on a third-order
scissor device and demonstrate advantages in terms of fidelity with the target
state, probability of success, distillable entanglement, and the amount of
non-Gaussianity introduced.


  In this note we prove that any affine algebraic monoid can be obtained as the
endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.


  Anomalous X-ray Pulsars and Soft-Gamma Repeaters groups are magnetar
candidates featuring low characteristic ages ($\tau = {P\over{2 {\dot P}}}$).
At least some of them they should still be associated with the remnants of the
explosive events in which they were born, giving clues to the type of events
leading to their birth and the physics behind the apparent high value of the
magnetar magnetic fields. To explain the high values of $B$, a self-consistent
picture of field growth also suggests that energy injection into the SNR is
large and unavoidable, in contrast with the evolution of {\it conventional}
SNR. This modified dynamics, in turn, has important implications for the
proposed associations. We show that this scenario yields low ages for the new
candidates CXOU J171405.7-381031/CTB 37B and XMMU J173203.3-344518/G353.6-0.7,
and predicted values agree with recently found ${\dot P}$, giving support to
the overall picture.


  This paper considers base station cooperation (BSC) strategies for the uplink
of a multi-user multi-cell high frequency reuse scenario where distributed
iterative detection (DID) schemes with soft/hard interference cancellation
algorithms are studied. The conventional distributed detection scheme exchanges
{soft symbol estimates} with all cooperating BSs. Since a large amount of
information needs to be shared via the backhaul, the exchange of hard bit
information is preferred, however a performance degradation is experienced. In
this paper, we consider a reduced message passing (RMP) technique in which each
BS generates a detection list with the probabilities for the desired symbol
that are sorted according to the calculated probability. The network then
selects the best {detection candidates} from the lists and conveys the index of
the constellation symbols (instead of double-precision values) among the
cooperating cells. The proposed DID-RMP achieves an inter-cell-interference
(ICI) suppression with low backhaul traffic overhead compared with {the
conventional soft bit exchange} and outperforms the previously reported
hard/soft information exchange algorithms.


  Quantum key distribution (QKD) offers an unconditionally secure means of
communication based on the laws of quantum mechanics. Currently, a major
challenge is to achieve a QKD system with a 40 dB channel loss, which is
required if we are to realize global scale QKD networks using communication
satellites. Here we report the first QKD experiment in which secure keys were
distributed over 42 dB channel loss and 200 km of optical fibre. We employed
the differential phase shift quantum key distribution (DPS-QKD) protocol
implemented with a 10-GHz clock frequency, and superconducting single photon
detectors (SSPD) based on NbN nanowire. The SSPD offers a very low dark count
rate (a few Hz) and small timing jitter (60 ps full width at half maximum).
These characteristics allowed us to construct a 10-GHz clock QKD system and
thus distribute secure keys over channel loss of 42 dB. In addition, we
achieved a 17 kbit/s secure key rate over 105 km of optical fibre, which is two
orders of magnitude higher than the previous record, and a 12.1 bit/s secure
key rate over 200 km of optical fibre, which is the longest terrestrial QKD yet
demonstrated. The keys generated in our experiment are secure against both
general collective attacks on individual photons and a specific collective
attack on multi-photons, known as a sequential unambiguous state discrimination
(USD) attack.


  Background: Due to the societal, economic, and health costs of COVID-19
non-pharmaceutical interventions (NPIs), it is important to assess their
effects. Human mobility serves as a surrogate for human contacts and compliance
to NPIs. In Nordic countries, NPIs have mostly been advised and sometimes made
mandatory. It is unclear if making NPIs mandatory further reduced mobility.
  Aim: We investigated the effect of non-compulsory and follow-up mandatory
measures in major cities and rural regions on human mobility in Norway. We
identified NPI categories that most affected mobility.
  Methods: We used mobile phone mobility data from the largest Norwegian
operator. We analysed non-compulsory and mandatory measures with before-after
and synthetic difference-in-differences approaches. By regression, we
investigated the impact of different NPIs on mobility.
  Results: Nationally and in less populated regions, follow-up mandatory
measures further decreased time, but not distance travelled. In urban areas,
however, follow-up mandates also decreased distance, and the effect exceeded
that of initial non-compulsory measures. Stricter metre rules, gyms closing and
reopening, restrictions on guests in homes, and face mask recommendations most
impacted distance travelled. Time travelled was most affected by gyms closing
and restaurants and shops reopening.
  Conclusion: Overall, non-compulsory measures appeared to decrease distance
travelled from home, while mandates further decreased this metric in urban
areas. Time travelled is reduced more by mandates than by non-compulsory
measures for all regions and interventions. Stricter distancing and restricted
number of guests were associated with decreases in mobility.


  We develop the theory of continuous-variable quantum secret sharing and
propose its interferometric realization using passive and active optical
elements. In the ideal case of infinite squeezing, a fidelity ${\cal F}$ of
unity can be achieved with respect to reconstructing the quantum secret. We
quantify the reduction in fidelity for the (2,3) threshold scheme due to finite
squeezing and establish the condition for verifying that genuine quantum secret
sharing has occurred.


  In this paper some aspects on chaotic behavior and minimality in planar
piecewise smooth vector fields theory are treated. The occurrence of
non-deterministic chaos is observed and the concept of orientable minimality is
introduced. It is also investigated some relations between minimality and
orientable minimality and observed the existence of new kinds of non-trivial
minimal sets in chaotic systems. The approach is geometrical and involve the
ordinary techniques of non-smooth systems.


  We present the comaprative study of semileptonic and leptonic decays of
D_{s},D^{\pm} and D^0 meson (D\rightarrowM
l_{{\alpha}}^+l_{{\beta}}^-,D\rightarrowl_{{\alpha}}^+l_{{\beta}}^-,D\rightarrowl_{{\alpha}}^+v_{{\alpha}};{\alpha},{\beta}=e,{\mu})
within the framework of R-parity violating (R_{p}) Minimal Supersymmetric
Standard Model (MSSM). The comparison shows that combination and product
couplings ({\lambda}_{{\beta}i{\alpha}}{\lambda}_{ijq}^{'\ast} or
{\lambda}_{{\beta}qk}'{\lambda}_{{\alpha}jk}^{'\ast}) contribution to the
branching fractions of the said processes rocesses(under consideration) is
consistent or comparable to the experimental measurements in most of the cases.
However, there exists some cases, where these contributions are suppressed but
still comparable to that of standard model.


  We introduce the notion of "quasi-symmetric" polynomials, which is a
generalization of the notion of symmetry, and is particularly suited to the
setting of polynomial rings over finite fields. The properties of this new
class of functions are studied. It is then shown that quasi-symmetric
polynomials are very useful in splitting rational places in extensions of
function fields over finite fields and thus may be used in constructing
extensions with many rational places.


  The mechanical behavior of inelastic materials with microstructure is very
complex and hard to grasp with heuristic, empirical constitutive models. For
this purpose, multiscale, homogenization approaches are often used for
performing reliable, accurate predictions of the macroscopic mechanical
behavior of solids and structures. Nevertheless, the calculation cost of such
approaches is extremely high and prohibitive for real-scale applications
involving inelastic materials.
  Here, we propose the so-called Thermodynamics-based Artificial Neural
Networks (TANN) for the constitutive modeling of materials with inelastic and
complex microstructure. Our approach integrates thermodynamics-aware
dimensionality reduction techniques and thermodynamics-based deep neural
networks to identify, in an autonomous way, the constitutive laws and discover
the internal state variables of complex inelastic materials. The efficiency and
accuracy of TANN in predicting the average and local stress-strain response,
the free-energy and the dissipation rate is demonstrated for both regular and
perturbed two- and three-dimensional lattice microstructures in inelasticity.
TANN manage to identify the internal state variables that characterize the
inelastic deformation of the complex microstructural fields. These internal
state variables are then used to reconstruct the microdeformation fields of the
microstructure at a given state. Finally, a double-scale homogenization scheme
(FEMxTANN) is used to solve a large scale boundary value problem. The high
performance of the homogenized model using TANN is illustrated through detailed
comparisons with microstructural calculations at large scale. An excellent
agreement is shown for a variety of monotonous and cyclic stress-strain paths.


  As the space industry approaches a period of rapid change, securing both
emerging and legacy satellite missions will become vital. However, space
technology has been largely overlooked by the systems security community. This
systematization of knowledge paper seeks to understand why this is the case and
to offer a starting point for technical security researchers seeking impactful
contributions beyond the Earth's mesosphere.
  The paper begins with a cross-disciplinary synthesis of relevant threat
models from a diverse array of fields, ranging from legal and policy studies to
aerospace engineering. This is presented as a "threat matrix toolbox" which
security researchers may leverage to motivate technical research into given
attack vectors and defenses. We subsequently apply this model to an original
chronology of more than 100 significant satellite hacking incidents spanning
the previous 60 years. Together, these are used to assess the state-of-the-art
in satellite security across four sub-domains: satellite radio-link security,
space hardware security, ground station security, and operational/mission
security. In each area, we note significant findings and unresolved questions
lingering in other disciplines which the systems security community is aptly
poised to tackle. By consolidating this research, we present the case that
satellite systems security researchers can build on strong, but disparate,
academic foundations and rise to meet an urgent need for future space missions.


  Prior information is often incorporated informally when planning a clinical
trial. Here, we present an approach on how to incorporate prior information,
such as data from historical clinical trials, into the nuisance parameter based
sample size re-estimation in a design with an internal pilot study. We focus on
trials with continuous endpoints in which the outcome variance is the nuisance
parameter. For planning and analyzing the trial frequentist methods are
considered. Moreover, the external information on the variance is summarized by
the Bayesian meta-analytic-predictive (MAP) approach. To incorporate external
information into the sample size re-estimation, we propose to update the MAP
prior based on the results of the internal pilot study and to re-estimate the
sample size using an estimator from the posterior. By means of a simulation
study, we compare the operating characteristics such as power and sample size
distribution of the proposed procedure with the traditional sample size
re-estimation approach which uses the pooled variance estimator. The simulation
study shows that, if no prior-data conflict is present, incorporating external
information into the sample size re-estimation improves the operating
characteristics compared to the traditional approach. In the case of a
prior-data conflict, that is when the variance of the ongoing clinical trial is
unequal to the prior location, the performance of the traditional sample size
re-estimation procedure is in general superior, even when the prior information
is robustified. When considering to include prior information in sample size
re-estimation, the potential gains should be balanced against the risks.


  In the framework of the ESA Athena mission, the X-ray Integral Field Unit
(X-IFU) instrument to be on board the X-ray Athena Observatory is a cryogenic
micro-calorimeter array of Transition Edge Sensor (TES) detectors aimed at
providing spatially resolved high-resolution spectroscopy. As a part of the
on-board Event Processor (EP), the reconstruction software will provide the
energy, spatial location and arrival time of the incoming X-ray photons hitting
the detector and inducing current pulses on it. Being the standard optimal
filtering technique the chosen baseline reconstruction algorithm, different
modifications have been analyzed to process pulses shorter than those
considered of high resolution (those where the full length is not available due
to a close pulse after them) in order to select the best option based on energy
resolution and computing performance results. It can be concluded that the best
approach to optimize the energy resolution for short filters is the 0-padding
filtering technique, benefiting also from a reduction in the computational
resources. However, its high sensitivity to offset fluctuations currently
prevents its use as the baseline treatment for the X-IFU application for lack
of consolidated information on the actual stability it will get in flight.


  We investigate the behavior of antiferromagnetic integer-spin chains in a
staggered magnetic field, by means of the density-matrix renormalization group,
carefully addressing the role of finite-size effects within the Haldane phase
at small fields. In the case of spin S=2, we determine the dependence of the
groundstate energy and magnetization on the external field, in the
thermodynamic limit, and show how the peculiar finite-size behavior can be
connected with the crossover in the groundstate from a spin liquid to a
polarized N\'eel state.


  The linearized Korteweg-De Vries equation can be written as a Hamilton-like
system. However, the Hamilton energy depends on the time, and is a nonsymmetric
operator on $L^2({\bf R})$. By performing suitable unitary transforms on the
Hamilton energy, we can reduce this operator into one that is not independent
on the time but nonsymmetric. In this study, we consider the $L^2$-stability
issues and smoothing estimates for this operator, and prove that it has no
eigenvalues.


  A simple proof of a key inequality required by the paper's analysis is
presented. An introductory section discussing the paper's setup may be helpful
to some readers. An alternative statistical analysis is suggested.


  Consider an analytical function $f:V\subset\mathbb R^2\rightarrow\mathbb R$
having $0$ as its regular value, a switching manifold $\Sigma=f^{-1}(0)$ and a
piecewise analytical vector field $X=(X^+,X^-)$, i.e. $X^\pm$ are analytical
vector fields defined on $\Sigma^\pm=\{p\in V: \pm f(p)>0\}$. We characterize
when the vector field $X$ has a monodromic singular point in $\Sigma$, called
$\Sigma$-monodromic singular point. Moreover, under certain conditions, we show
that a $\Sigma$-monodromic singular point of $X$ has a neighborhood free of
limit cycles.


  Sampling proper negatives from a large document pool is vital to effectively
train a dense retrieval model. However, existing negative sampling strategies
suffer from the uninformative or false negative problem. In this work, we
empirically show that according to the measured relevance scores, the negatives
ranked around the positives are generally more informative and less likely to
be false negatives. Intuitively, these negatives are not too hard (\emph{may be
false negatives}) or too easy (\emph{uninformative}). They are the ambiguous
negatives and need more attention during training. Thus, we propose a simple
ambiguous negatives sampling method, SimANS, which incorporates a new sampling
probability distribution to sample more ambiguous negatives. Extensive
experiments on four public and one industry datasets show the effectiveness of
our approach. We made the code and models publicly available in
\url{https://github.com/microsoft/SimXNS}.


  The perturbation theory with respect to the potential energy of three
particles is considered. The first-order correction to the continuum wave
function of three free particles is derived. It is shown that the use of the
collective multipole expansion of the free three-body Green function over the
set of Wigner $D$-functions can reduce the dimensionality of perturbative
matrix elements from twelve to six. The explicit expressions for the
coefficients of the collective multipole expansion of the free Green function
are derived. It is found that the $S$-wave multipole coefficient depends only
upon three variables instead of six as higher multipoles do. The possible
applications of the developed theory to the three-body molecular break-up
processes are discussed.


  We calculate the evolution of a jet shower due to medium induced splittings
in the deep LPM regime. Due to the characteristic energy dependence of the
formation time $t_{\rm form}(\omega)= \sqrt{\omega /\hat{\bar{q}}}$, the
radiative break-up process exhibits turbulent characteristics, allowing for
analytic predictions of various inclusive properties of the medium induced
cascade in an inertial range of energies $T \ll \omega \ll E$, where $E$ is the
energy of the jet and $T$ is the temperature of the medium.


  The recent proliferation of smart devices has given rise to ubiquitous
computing, an emerging computing paradigm which allows anytime & anywhere
computing possible. In such a ubiquitous computing environment, customers
release different computing or sensing tasks, and people, also known as data
processors, participate in these tasks and get paid for providing their idle
computing and communication resources. Thus, how to select an appropriate and
reliable customer while not disclosing processors' privacy has become an
interesting problem. In this article, we present a trust-based and
privacy-preserving customer selection scheme in ubiquitous computing, called
TPCS, to enable potential processors select the customers with good reputation.
The basic concept of TPCS is that each data processor holds a trust value, and
the reputation score of the customer is calculated based on processors' trust
values and feedbacks via a truth discovery process. To preserve processors'
privacy, pseudonyms and Paillier cryptosystem are applied to conceal each
processor's real identity. In addition, three authentication protocols are
designed to ensure that only the valid data processors (i.e., the processors
registering in the system, holding the truthful trust values, and joining the
computing tasks) can pass the authentication. A comprehensive security analysis
is conducted to prove that our proposed TPCS scheme is secure and can defend
against several sophisticated attacks. Moreover, extensive simulations are
conducted to demonstrate the correctness and effectiveness of the proposed
scheme.


  We consider parameter estimation in a regression model corresponding to an
iid sequence of censored observations of a finite state modulated renewal
process. The model assumes a similar form as in Cox regression except that the
baseline intensities are functions of the backwards recurrence time of the
process and a time dependent covariate. As a result of this it falls outside
the class of multiplicative intensity models. We use kernel estimation to
construct estimates of the regression coefficints and the baseline cumulative
hazards. We give conditions for consistency and asymptotic normality of
estimates. Data from a bone marrow transplant study are used to illustrate the
results.


  Multilingual transformer-based models demonstrate remarkable zero and
few-shot transfer across languages by learning and reusing language-agnostic
features. However, as a fixed-size model acquires more languages, its
performance across all languages degrades, a phenomenon termed interference.
Often attributed to limited model capacity, interference is commonly addressed
by adding additional parameters despite evidence that transformer-based models
are overparameterized. In this work, we show that it is possible to reduce
interference by instead identifying and pruning language-specific parameters.
First, we use Shapley Values, a credit allocation metric from coalitional game
theory, to identify attention heads that introduce interference. Then, we show
that removing identified attention heads from a fixed model improves
performance for a target language on both sentence classification and
structural prediction, seeing gains as large as 24.7\%. Finally, we provide
insights on language-agnostic and language-specific attention heads using
attention visualization.


  The possibility is indicated of applying the theory of superconductors with
overlapping energy bands to describe the thermodynamic and electromagnetic
properties of the high-temperature compounds $La_{2-x}(Ba,Sr)_xCuO_4$ and
$YBa_2Ci_3O_{7-\delta}$. The two-band model was used to obtain high values of
$T_c$, two energy gaps $2\Delta_1/T_c > 3.5$ and $2\Delta_2/T_c < 3.5$, large
negative values of $d\ln T_c/d\ln V$ ($V$ is the volume) in lanthanum ceramics,
small values of the jump in the electron heat capacity at $T=T_c$, negative
curvature of the upper critical magnetic field $H_{c2}$ near the transition
temperature, etc. Such behavior of the above quantities is observed
experimentally. A description is also obtained of the decrease in $T_c$ as the
disordering of oxygen increases, and also as copper atoms are replaced by a
nonmagnetic impurity (Al, Zn, etc.). The main mechanism responsible for this
decrease is the interband scattering of electrons by impurities and by randomly
distributed oxygen vacancies. A theory has been developed of multiband
superconductors which takes into account the points of high symmetry in
momentum space. On the basis of this theory one can explain the existence of a
plateau in the dependence of $T_c$ on $\delta$ for $YBa_2Cu_3O_{7-\delta}$, and
also in the dependence of $T_c$ on $x$ for $La_{2-x}(Ba,Sr)_xCuO_4$, that has
been observed in a number of experiments. Moreover, this theory also explains
the presence of two maxima in the dependence of $T_c$ on pressure for
$Bi_2Sr_2CaCu_2O_8$.


  Drake and Szekeres have extended the Newman-Janis algorithm to produce
stationary axisymmetric spacetimes from general static spherically symmetric
solutions of the Einstein equations. The algorithm mathematically generates an
energy-momentum tensor for the rotating solution, but the rotating and
nonrotating system may or may not represent the same physical system, in the
sense of both being a perfect fluid, or an electromagnetic field, or a
$\Lambda$-term, and so on. In Part I (arxiv:2104.02255), we compared the
structure of the eigenvalues and eigenvectors of the rotating and nonrotating
energy-momentum tensors (their Segre types) and looked for the existence of
equations of state relating the rotating energy density and principal pressures
for Kerr-Schild systems. Here we extend our analysis to general static
spherically symmetric systems obtained according to the Drake-Szekeres
generalization of the Newman-Janis algorithm. We find that these rotating
systems can have almost all Segre types except [31] and [(31)]. Moreover, the
Segre type of the spacetime can change severely in passing from the nonrotating
to the rotating configurations, for example to $[11Z\bar{Z}]$ from seed systems
which were initially [(111,1)]. We also find conditions dictating how many
equations of state may exist in a Drake-Szekeres system.


  We present a comprehensive first principles electronic structure study of the
magnetoelastic and magnetostrictive properties in the Co-based Co$_2$XAl (X =
V, Ti, Cr, Mn, Fe) full Heusler compounds. In addition to the commonly used
total energy approach, we employ torque method to calculate the magnetoelastic
tensor elements. We show that the torque based methods are in general
computationally more efficient, and allow to unveil the atomic- and
orbital-contributions to the magnetoelastic constants in an exact manner, as
opposed to the conventional approaches based on second order perturbation with
respect to the spin-orbit coupling. The magnetostriction constants are in good
agreement with available experimental data. The results reveal that the main
contribution to the magnetostriction constants, $\lambda_{100}$ and
$\lambda_{111}$, arises primarily from the strained-induced modulation of the
$\langle d_{x^2-y^2}|\hat{L}_z|d_{xy}\rangle$ and $\langle
d_{z^2}|\hat{L}_x|d_{yz}\rangle$ spin orbit coupling matrix elements,
respectively, of the Co atoms.


  By applying the Atiyah-Bott-Berline-Vergne equivariant integration formula
upon double dimensional integrals, we find a way to compute the matrix integral
representations of $4d$ $\mathcal{N}=1$ superconformal indices. The final
formula allows us to easily extract analytic results in the large-rank
expansion of certain theories. As an example, we compute the leading one-loop
corrections to the effective action of the known complex saddles in those
theories. For a superconformal index of $SU(N)$ $\mathcal{N}=4$ SYM, we use the
equivariant integration formula and the Picard-Lefschetz method to show that at
large enough values of $N$, only two, among the known complex saddles, dominate
the counting of large operators i.e. of operators with charges of order $N^2$.
Contributions from other known complex saddles are present, but we show they
are exponentially suppressed in that range of charges; the smaller the charges
the less suppressed they are, and eventually, to count small operators i.e.
operators with charges smaller than $N^{2/3}$, like multi-gravitons, they can
not be neglected.


  Solar flares are associated with intense soft X-ray emission generated by the
hot flaring plasma. Kink unstable twisted flux-ropes provide a source of
magnetic energy which can be released impulsively and account for the flare
plasma heating. We compute the temporal evolution of the thermal X-ray emission
in kink-unstable coronal loops using MHD simulations and discuss the results of
with respect to solar flare observations. The model consists of a highly
twisted loop embedded in a region of uniform and untwisted coronal magnetic
field. We let the kink instability develop, compute the evolution of the plasma
properties in the loop (density, temperature) without accounting for mass
exchange with the chromosphere. We then deduce the X-ray emission properties of
the plasma during the whole flaring episode. During the initial phase of the
instability plasma heating is mostly adiabatic. Ohmic diffusion takes over as
the instability saturates, leading to strong and impulsive heating (> 20 MK),
to a quick enhancement of X-ray emission and to the hardening of the thermal
X-ray spectrum. The temperature distribution of the plasma becomes broad, with
the emission measure depending strongly on temperature. Significant emission
measures arise for plasma at temperatures T > 9 MK. The magnetic flux-rope then
relaxes progressively towards a lower energy state as it reconnects with the
background flux. The loop plasma suffers smaller sporadic heating events but
cools down conductively. The total thermal X-ray emission slowly fades away
during this phase, and the high temperature component of emission measure
distribution converges to the power-law distribution $EM\propto T^{-4.2}$. The
amount of twist deduced directly from the X-ray emission patterns is
considerably lower than the maximum magnetic twist in the simulated flux-ropes.


  Previous studies of gravitationally bound states of ultracold neutrons showed
the quantization of energy levels, and confirmed quantum mechanical predictions
for the average size of the two lowest energy states wave functions.
Improvements in position-like measurements can increase the accuracy by an
order of magnitude only. We therefore develop another approach, consisting in
accurate measurements of the energy levels. The GRANIT experiment is devoted to
the study of resonant transitions between quantum states induced by an
oscillating perturbation.
  According to Heisenberg's uncertainty relations, the accuracy of measurement
of the energy levels is limited by the time available to perform the
transitions. Thus, trapping quantum states will be necessary, and each source
of losses has to be controlled in order to maximize the lifetime of the states.
We discuss the general principles of transitions between quantum states, and
consider the main systematical losses of neutrons in a trap.


  The abnormal pause or rate reduction in breathing is known as the sleep-apnea
hypopnea syndrome and affects the quality of sleep of an individual. A novel
method for the detection of sleep apnea events (pause in breathing) from
peripheral oxygen saturation (SpO2) signals obtained from wearable devices is
discussed in this paper. The paper details an apnea detection algorithm of a
very high resolution on a per-second basis for which a 1-dimensional
convolutional neural network -- which we termed SomnNET -- is developed. This
network exhibits an accuracy of 97.08% and outperforms several lower resolution
state-of-the-art apnea detection methods. The feasibility of model pruning and
binarization to reduce the computational complexity is explored. The pruned
network with 80% sparsity exhibited an accuracy of 89.75%, and the binarized
network exhibited an accuracy of 68.22%. The performance of the proposed
networks is compared against several state-of-the-art algorithms.


  Forthcoming astrometric missions such as the Gaia satellite will bring to the
fore the problem of estimating the enclosed mass from a set of positions,
radial velocities and proper motions of tracer stars. Here, we show how to
construct the tracer mass estimator when the proper motion data are available
in addition to the usual line-of-sight velocity data. Notably, the mass
estimators do not require any assumption on the anisotropy, as it is naturally
incorporated through the different components of proper motions. In addition,
the separate treatment of the proper motions and the line-of-sight velocities
is desirable because they are observationally independent and thus the
propagation of the combined uncertainties is rather straightforward. The
extension to projected data is also sketched, together with a possible
application of measuring the masses of Galactic globular clusters.


  We investigate the relationship between the extensor electromyogram (EMG) and
tremor time series in physiological hand tremor by cross-spectral analysis.
Special attention is directed to the phase spectrum and the effects of
observational noise. We calculate the theoretical phase spectrum for a second
order linear stochastic process and compare the results to measured tremor data
recorded from subjects who did not show a synchronized EMG activity in the
corresponding extensor muscle. The results show that physiological tremor is
well described by the proposed model and that the measured EMG represents a
Newtonian force by which the muscle acts on the hand.


  This paper describes the processing applied to the Planck High Frequency
Instrument (HFI) cleaned, time-ordered information to produce photometrically
calibrated maps in temperature and (for the first time) in polarization. The
data from the entire 2.5 year HFI mission include almost five independent
full-sky surveys. HFI observes the sky over a broad range of frequencies, from
100 to 857 GHz. To obtain the best accuracy on the calibration over such a
large range, two different photometric calibration schemes have been used. The
545 and 857 GHz data are calibrated using models of planetary atmospheric
emission. The lower frequencies (from 100 to 353 GHz) are calibrated using the
time-variable cosmological microwave background dipole, which we call the
"orbital dipole". This source of calibration only depends on the satellite
velocity with respect to the solar system. Using a CMB temperature of 2.7255
+/- 0.0006 K, it permits an independent measurement of the amplitude of the CMB
solar dipole (3364.3 +/- 1.5 \mu K) which is approximatively 1\sigma\ higher
than the WMAP measurement with a direction that is consistent between both
experiments. We describe the pipeline used to produce the maps of intensity and
linear polarization from the HFI timelines, and the scheme used to set the zero
level of the maps a posteriori. We also summarize the noise characteristics of
the HFI maps in the 2015 Planck data release and present some null tests to
assess their quality. Finally, we discuss the major systematic effects and in
particular the leakage induced by flux mismatch between the detectors that
leads to spurious polarization signal.


  Under a weak assumption of the existence of a geodesic null congruence, we
present the general solution of the Einstein field equations in three
dimensions with any value of the cosmological constant, admitting an aligned
null matter field, and also gyratons (a matter field in the form of a null dust
with an additional internal spin). The general local solution consists of the
expanding Robinson-Trautman class and the non-expanding Kundt class. The
gyratonic solutions reduce to spacetimes with a pure radiation matter field
when the spin is set to zero. Without matter fields, we obtain new forms of the
maximally symmetric vacuum solutions. We discuss these complete classes of
solutions and their various subclasses. In particular, we identify the
gravitational field of an arbitrarily accelerating source (the Kinnersley
photon rocket, which reduces to a Vaidya-type non-moving object) in the
Robinson-Trautman class, and pp-waves, vanishing scalar invariants (VSI)
spacetimes, and constant scalar invariants (CSI) spacetimes in the Kundt class.


  The Coronavirus Disease 2019 (COVID-19) is affecting increasingly large
number of people worldwide, posing significant stress to the health care
systems. Early and accurate diagnosis of COVID-19 is critical in screening of
infected patients and breaking the person-to-person transmission. Chest X-ray
(CXR) based computer-aided diagnosis of COVID-19 using deep learning becomes a
promising solution to this end. However, the diverse and various radiographic
features of COVID-19 make it challenging, especially when considering each CXR
scan typically only generates one single image. Data scarcity is another issue
since collecting large-scale medical CXR data set could be difficult at
present. Therefore, how to extract more informative and relevant features from
the limited samples available becomes essential. To address these issues,
unlike traditional methods processing each CXR image from a single view, this
paper proposes triple-view convolutional neural networks for COVID-19 diagnosis
with CXR images. Specifically, the proposed networks extract individual
features from three views of each CXR image, i.e., the left lung view, the
right lung view and the overall view, in three streams and then integrate them
for joint diagnosis. The proposed network structure respects the anatomical
structure of human lungs and is well aligned with clinical diagnosis of
COVID-19 in practice. In addition, the labeling of the views does not require
experts' domain knowledge, which is needed by many existing methods. The
experimental results show that the proposed method achieves state-of-the-art
performance, especially in the more challenging three class classification
task, and admits wide generality and high flexibility.


  We compute the Selberg trace formula for Hecke operators (also called the
trace formula for modular correspondences) in the context of cocompact Kleinian
groups with finite-dimentional unitary representations. We give some
applications to the distribution of Hecke eigenvalues, and give an analogue of
Huber's theorem.


  The credit scoring industry has a long tradition of using statistical tools
for loan default probability prediction and domain specific standards have been
established long before the hype of machine learning. Although several
commercial software companies offer specific solutions for credit scorecard
modelling in R explicit packages for this purpose have been missing long time.
In the recent years this has changed and several packages have been developed
which are dedicated to credit scoring. The aim of this paper is to give a
structured overview on these packages. This may guide users to select the
appropriate functions for a desired purpose and further hopefully will
contribute to directing future development activities. The paper is guided by
the chain of subsequent modelling steps as they are forming the typical
scorecard development process.


  The paper presents two edge grouping algorithms for finding a closed contour
starting from a particular edge point and enclosing a fixation point. Both
algorithms search a shortest simple cycle in \textit{an angularly ordered
graph} derived from an edge image where a vertex is an end point of a contour
fragment and an undirected arc is drawn between a pair of end-points whose
visual angle from the fixation point is less than a threshold value, which is
set to $\pi/2$ in our experiments. The first algorithm restricts the search
space by disregarding arcs that cross the line extending from the fixation
point to the starting point. The second algorithm improves the solution of the
first algorithm in a greedy manner. The algorithms were tested with a large
number of natural images with manually placed fixation and starting points. The
results are promising.


  Recommender systems are important for providing personalized services to
users, but the vast amount of collected user data has raised concerns about
privacy (e.g., sensitive data), security (e.g., malicious data) and utility
(e.g., toxic data). To address these challenges, recommendation unlearning has
emerged as a promising approach, which allows specific data and models to be
forgotten, mitigating the risks of sensitive/malicious/toxic user data.
However, existing methods often struggle to balance completeness, utility, and
efficiency, i.e., compromising one for the other, leading to suboptimal
recommendation unlearning. In this paper, we propose an Interaction and Mapping
Matrices Correction (IMCorrect) method for recommendation unlearning. Firstly,
we reveal that many collaborative filtering (CF) algorithms can be formulated
as mapping-based approach, in which the recommendation results can be obtained
by multiplying the user-item interaction matrix with a mapping matrix. Then,
IMCorrect can achieve efficient recommendation unlearning by correcting the
interaction matrix and enhance the completeness and utility by correcting the
mapping matrix, all without costly model retraining. Unlike existing methods,
IMCorrect is a whitebox model that offers greater flexibility in handling
various recommendation unlearning scenarios. Additionally, it has the unique
capability of incrementally learning from new data, which further enhances its
practicality. We conducted comprehensive experiments to validate the
effectiveness of IMCorrect and the results demonstrate that IMCorrect is
superior in completeness, utility, and efficiency, and is applicable in many
recommendation unlearning scenarios.


  We investigate the possibility to study the charmed baryon $\Lambda_c(2940)$
by kaon-induced reaction on a proton target. By assuming the $\Lambda_c(2940)$
as a $pD^{*0}$ molecular state with spin-parity $J^{p}=1/2^{\pm}$, an effective
Lagrangian approach was adopted to calculate the cross section, the $D^0p$
invariant mass spectrum and Dalitz plot of the $\Lambda(2940)$ production. The
total cross section of the $K^{-}p\to\Lambda_c(2940)D_s^{-}$ reaction is found
at an order of magnitude about 10 $\mu$b. By considering the sub sequential
decay $\Lambda_c(2940)\to{}D^0p$ with contributions from the $\Lambda_c(2286)$
and the $\Sigma_c(2455)$ as background, the $K^{-}p\to{}D_{s}^{-}D^{0}p$
reaction are studied. It is found that the $\Lambda_c(2940)$ is produced mainly
at forward angles. The $\Lambda_c(2940)$ signal is predicted to be significant
in the $D^0p$ invariant mass spectrum and the Dalitz plot of the
$K^{-}p\to{}D_{s}^{-}D^{0}p$ reaction. The results suggest that it is promising
to study the $\Lambda_c(2940)$ with high-energy kaon beam on a proton target in
experiment.


  Let $u$ be a nilpotent endomorphism of a finite dimensional
$\mathbb{C}$-vector space. The set ${\mathcal F}_u$ of $u$-stable complete
flags is a projective algebraic variety called a Springer fiber. Its
irreducible components are parameterized by a set of standard tableaux. We
provide three characterizations of the singular components of ${\mathcal F}_u$
in the case $u^2=0$. First, we give the combinatorial description of standard
tableaux corresponding to singular components. Second, we prove that a
component is singular if and only if its Poincar\'e polynomial is not
palindromic. Third, we show that a component is singular when it has too many
intersections of codimension one with other components. Finally, relying on the
second criterion, we infer that, for $u$ general, whenever ${\mathcal F}_u$ has
a singular component, it admits a component whose Poincar\'e polynomial is not
palindromic. This work relies on a previous criterion of singularity for
components of ${\mathcal F}_u$ in the case $u^2=0$ by the first author and on
the description of the $B$-orbit decomposition of orbital varieties of
nilpotent order two by the second author.


  A theoretical many-body analysis is presented of the electron-electron
inelastic lifetimes of Shockley electrons and holes at the (111) surface of Cu.
For a description of the decay of Shockley states both below and above the
Fermi level, single-particle wave functions have been obtained by solving the
Schr\"odinger equation with the use of an approximate one-dimensional
pseudopotential fitted to reproduce the correct bulk energy bands and
surface-state dispersion. A comparison with previous calculations and
experiment indicates that inelastic lifetimes are very sensitive to the actual
shape of the surface-state single-particle orbitals beyond the $\bar\Gamma$
(${\bf k}_\parallel=0$) point, which controls the coupling between the Shockley
electrons and holes.


  Due to high mobility in multipath propagation environments,
vehicle-to-vehicle (V2V) channels are generally time and frequency variant.
Therefore, the criteria for wide-sense stationarity (WSS) and uncorrelated
scattering (US) are just satisfied over very limited intervals in the time and
frequency domains, respectively. We test the validity of these criteria in
measured vehicular 60 GHz millimeter wave (mmWave) channels, by estimating the
local scattering functions (LSFs) from the measured data. Based on the
variation of the LSFs, we define time-frequency stationarity regions, over
which the WSSUS assumption is assumed to be fulfilled approximately. We analyze
and compare both line-of-sight (LOS) and non-LOS (NLOS) V2V communication
conditions. We observe large stationarity regions for channels with a dominant
LOS connection, without relative movement between the transmitting and
receiving vehicle. In the same measured urban driving scenario, modified by
eliminating the LOS component in the post-processing, the channel is dominated
by specular components reflected from an overpassing vehicle with a relative
velocity of 56 km/h. Here, we observe a stationarity bandwidth of 270 MHz.
Furthermore, the NLOS channel, dominated by a single strong specular component,
shows a relatively large average stationarity time of 16 ms, while the
stationarity time for the channel with a rich multipath profile is much
shorter, in the order of 5 ms.


  Inertial particles in 2D driven by a Gaussian white noise forcing are
considered. For two examples of the forcing (compressible and incompressible)
upper and lower bounds are found for the mean number of caustics as a function
of Stokes number. Efficiency of the bounds is verified by numerical methods.


  A central vertex of a graph is a vertex whose eccentricity equals the radius.
The center of a graph is the set of all central vertices. The central ratio of
a graph is the ratio of the cardinality of its center to its order. In 1982,
Buckley proved that every positive rational number not exceeding one is the
central ratio of some graph. In this paper, we obtain more detailed information
by determining which cardinalities are possible for the center of a graph with
given order and radius. There are unexpected phenomena in the results. For
example, there exists a graph of order $14$ and radius $6$ whose center has
cardinality $s$ if and only if $s\in \{ 1, 2, 3, 4, 9,10,11,12,14\}.$ We also
prove a related uniqueness result.


  In this paper, we proposed a conceptual model to predict the chat experience
in a natural language generation dialog system. We evaluated the model with 120
participants with Partial Least Squares Structural Equation Modeling (PLS-SEM)
and obtained an R-square (R2) with 0.541. The model considers various factors,
including the prompts used for generation; coherence, sentiment, and similarity
in the conversation; and users' perceived dialog agents' favorability. We then
further explore the effectiveness of the subset of our proposed model. The
results showed that users' favorability and coherence, sentiment, and
similarity in the dialogue are positive predictors of users' chat experience.
Moreover, we found users may prefer dialog agents with characteristics of
Extroversion, Openness, Conscientiousness, Agreeableness, and Non-Neuroticism.
Through our research, an adaptive dialog system might use collected data to
infer factors in our model, predict the chat experience for users through these
factors, and optimize it by adjusting prompts.


  Despite raw driving videos contain richer information on facial expressions
than intermediate representations such as landmarks in the field of portrait
animation, they are seldom the subject of research. This is due to two
challenges inherent in portrait animation driven with raw videos: 1)
significant identity leakage; 2) Irrelevant background and facial details such
as wrinkles degrade performance. To harnesses the power of the raw videos for
vivid portrait animation, we proposed a pioneering conditional diffusion model
named as MegActor. First, we introduced a synthetic data generation framework
for creating videos with consistent motion and expressions but inconsistent IDs
to mitigate the issue of ID leakage. Second, we segmented the foreground and
background of the reference image and employed CLIP to encode the background
details. This encoded information is then integrated into the network via a
text embedding module, thereby ensuring the stability of the background.
Finally, we further style transfer the appearance of the reference image to the
driving video to eliminate the influence of facial details in the driving
videos. Our final model was trained solely on public datasets, achieving
results comparable to commercial models. We hope this will help the open-source
community.The code is available at
https://github.com/megvii-research/MegFaceAnimate.


  Interference mitigation is a major design challenge in wireless
systems,especially in the context of ultra-reliable low-latency communication
(URLLC) services. Conventional average-based interference management schemes
are not suitable for URLLC as they do not accurately capture the tail
information of the interference distribution. This letter proposes a novel
interference prediction algorithm that considers the entire interference
distribution instead of only the mean. The key idea is to model the
interference variation as a discrete state space discrete-time Markov chain.
The state transition probability matrix is then used to estimate the state
evolution in time, and allocate radio resources accordingly. The proposed
scheme is found to meet the target reliability requirements in a low-latency
single-shot transmission system considering realistic system assumptions, while
requiring only ~25% more resources than the optimum case with perfect
interference knowledge.


  What is the Broad Line Region (BLR) made of? What determines its location?
Why is it sometimes missing? What controls its properties? Some recent results
and new approaches which may shed light on these issues are briefly described.


  We present an investigation of the supernova remnant (SNR) G306.3$-$0.9 using
archival multi-wavelength data. The Suzaku spectra are well described by
two-component thermal plasma models: The soft component is in ionization
equilibrium and has a temperature $\sim$0.59 keV, while the hard component has
temperature $\sim$3.2 keV and ionization time-scale $\sim$$2.6\times10^{10}$
cm$^{-3}$ s. We clearly detected Fe K-shell line at energy of $\sim$6.5 keV
from this remnant. The overabundances of Si, S, Ar, Ca, and Fe confirm that the
X-ray emission has an ejecta origin. The centroid energy of the Fe-K line
supports that G306.3$-$0.9 is a remnant of a Type Ia supernova (SN) rather than
a core-collapse SN. The GeV gamma-ray emission from G306.3$-$0.9 and its
surrounding were analyzed using about 6 years of Fermi data. We report about
the non-detection of G306.3$-$0.9 and the detection of a new extended gamma-ray
source in the south-west of G306.3$-$0.9 with a significance of
$\sim$13$\sigma$. We discuss several scenarios for these results with the help
of data from other wavebands to understand the SNR and its neighborhood.


  Domain adaptation and covariate shift are big issues in deep learning and
they ultimately affect any causal inference algorithms that rely on deep neural
networks. Causal effect variational autoencoder (CEVAE) is trained to predict
the outcome given observational treatment data and it suffers from the
distribution shift at test time. In this paper, we introduce uniform treatment
variational autoencoders (UTVAE) that are trained with uniform treatment
distribution using importance sampling and show that using uniform treatment
over observational treatment distribution leads to better causal inference by
mitigating the distribution shift that occurs from training to test time. We
also explore the combination of uniform and observational treatment
distributions with inference and generative network training objectives to find
a better training procedure for inferring treatment effects. Experimentally, we
find that the proposed UTVAE yields better absolute average treatment effect
error and precision in the estimation of heterogeneous effect error than the
CEVAE on synthetic and IHDP datasets.


  The usual canonical Hamiltonian or Lagrangian formalism of classical
mechanics applied to macroscopic systems describes energy conserving adiabatic
motion. If irreversible diabatic processes are to be included, then the law of
increasing entropy must also be considered. The notion of entropy then enters
into the general classical mechanical formalism. The resulting general
formulation and its physical consequences are explored.


  Temperature determines the relative probability of observing a physical
system in an energy state when that system is energetically in equilibrium with
its environment. In this paper, we present a theory for engineering the
temperature of a quantum system different from its ambient temperature. We
define criteria for an engineered quantum bath that, when coupled to a quantum
system with Hamiltonian $H$, drives the system to the equilibrium state
$\frac{e^{-H/T}}{{{\rm{Tr}}}(e^{-H/T})}$ with a tunable parameter $T$. This is
basically an analog counterpart of the digital quantum metropolis algorithm.
For a system of superconducting qubits, we propose a circuit-QED approximate
realization of such an engineered thermal bath consisting of driven lossy
resonators. Our proposal opens the path to simulate thermodynamical properties
of many-body quantum systems of size not accessible to classical simulations.
Also we discuss how an artificial thermal bath can serve as a temperature knob
for a hybrid quantum-thermal annealer.


  The problem of quality of service (QoS) and jamming-aware communications is
considered in an adversarial wireless network subject to external eavesdropping
and jamming attacks. To ensure robust communication against jamming, an
interference-aware routing protocol is developed that allows nodes to avoid
communication holes created by jamming attacks. Then, a distributed cooperation
framework, based on deep reinforcement learning, is proposed that allows nodes
to assess network conditions and make deep learning-driven, distributed, and
real-time decisions on whether to participate in data communications, defend
the network against jamming and eavesdropping attacks, or jam other
transmissions. The objective is to maximize the network performance that
incorporates throughput, energy efficiency, delay, and security metrics.
Simulation results show that the proposed jamming-aware routing approach is
robust against jamming and when throughput is prioritized, the proposed deep
reinforcement learning approach can achieve significant (measured as
three-fold) increase in throughput, compared to a benchmark policy with fixed
roles assigned to nodes.


  We present work in progress on the temporal progression of compositionality
in noun-noun compounds. Previous work has proposed computational methods for
determining the compositionality of compounds. These methods try to
automatically determine how transparent the meaning of the compound as a whole
is with respect to the meaning of its parts. We hypothesize that such a
property might change over time. We use the time-stamped Google Books corpus
for our diachronic investigations, and first examine whether the vector-based
semantic spaces extracted from this corpus are able to predict compositionality
ratings, despite their inherent limitations. We find that using temporal
information helps predicting the ratings, although correlation with the ratings
is lower than reported for other corpora. Finally, we show changes in
compositionality over time for a selection of compounds.


  In this paper,we design a formation control systrm for multi-unmanned ground
vehicles(UGV) from the prospective of path planning and path tracking.The
master-slave control is adopted by electing out a main vehicle to address the
problem of possible accumulation,tranmission and amplification of errors.In the
process of formation transformation,we first generate an expected path by
combing the methods of dynamic window and potential energy field.Then a path
tracking algorithm based on Hermite curve is adopted to make the formation
transformation process more stable and accurate.Finally,the evaluation system
of the formation control system is constructed,which combines the expected
position,the actual position,the expected speed, the actual speed and the
actual acceleration,giving an evalutaion on the performance of the formation
transformation,response of the formation driving process and the performance of
the formation stability.


  We describe the challenges and pathways when probing inflaton as dark matter
with the stochastic gravitational waves (GWs) signal generated during the
(p)reheating. Such scenarios are of utmost interest when no other interaction
between the visible and dark sectors is present, therefore having no other
detectability prospects. We consider the remnant energy in the coherently
oscillating inflaton's zeroth mode to contribute to the observed relic dark
matter density in the Universe. To fully capture the nonlinear dynamics and the
effects of back-reactions during the oscillation, we resort to full nonlinear
lattice simulation with pseudo-spectral methods to eliminate the differencing
noises. We investigate for models whose behavior during the reheating era is of
$m_{\Phi}^2\Phi^2$ type and find the typical primordial stochastic GWs
backgrounds spectrum from scatterings among highly populated inflaton modes
behaving like matter. We comment on the challenges of constructing such viable
inflationary models such that the inflaton will account for the total dark
matter of the universe while the produced GWs are within the future GWs
detectors such as BBO, DECIGO, PTA, AION-MAGIS, and CE. We also describe the
necessary modifications to the standard perturbative reheating scenario to
prevent the depletion of residual inflaton energy via perturbative decay.


  We show that all groups in a very large class of Coxeter groups are locally
quasiconvex and have uniform membership problem solvable in quadratic time. If
a group in the class satisfies a further hypothesis it is subgroup separable
and relevant homomorphisms are also calculable in quadratic time.
  The algorithm also decides if a finitely generated subgroup has finite index.


  Quadratic unconstrained binary optimization (QUBO) has become the standard
format for optimization using quantum computers, i.e., for both the quantum
approximate optimization algorithm (QAOA) and quantum annealing (QA). We
present a toolkit of methods to transform almost arbitrary problems to QUBO by
(i) approximating them as a polynomial and then (ii) translating any polynomial
to QUBO. We showcase the usage of our approaches on two example problems (ratio
cut and logistic regression).


  We introduce MinimalRNN, a new recurrent neural network architecture that
achieves comparable performance as the popular gated RNNs with a simplified
structure. It employs minimal updates within RNN, which not only leads to
efficient learning and testing but more importantly better interpretability and
trainability. We demonstrate that by endorsing the more restrictive update
rule, MinimalRNN learns disentangled RNN states. We further examine the
learning dynamics of different RNN structures using input-output Jacobians, and
show that MinimalRNN is able to capture longer range dependencies than existing
RNN architectures.


  Bleher and Kuijlaars recently showed that the eigenvalue correlations from
matrix ensembles with external source can be expressed by means of a kernel
built out of special multiple orthogonal polynomials. We derive a
Christoffel-Darboux formula for this kernel for general multiple orthogonal
polynomials. In addition, we show that the formula can be written in terms of
the solution of the Riemann-Hilbert problem for multiple orthogonal
polynomials, which will be useful for asymptotic analysis.


  The weak-field and slow-motion limit of $f(R,\mathcal{G})$ gravity is
developed up to $(v/c)^{4}$ order in a spherically symmetric background.
Considering the Taylor expansion of a general function $f$ around vanishing
values of $R$ and $\mathcal{G}$, we present general vacuum solutions up to
$(v/c)^{4}$ order for the gravitational field generated by a ball-like source.
The spatial behaviors at $(v/c)^{2}$ order are the same for $f(R,\mathcal{G})$
gravity and $f(R)$ gravity, and their corresponding real valued static
behaviors are presented and compared with the one in general relativity. The
static Yukawa-like behavior is proved to be compatible with the previous result
of the most general fourth-order theory. At $(v/c)^{4}$ order, the static
corrections to the Yukawa-like behavior for $f(R,\mathcal{G})$ gravity, $f(R)$
gravity, and the Starobinsky gravity are presented and compared with the one in
general relativity.


  Topological graphic passwords (Topsnut-gpws) are one of graph-type passwords,
but differ from the existing graphical passwords, since Topsnut-gpws are saved
in computer by algebraic matrices. We focus on the transformation between
text-based passwords (TB-paws) and Topsnut-gpws in this article. Several
methods for generating TB-paws from Topsnut-gpws are introduced; these methods
are based on topological structures and graph coloring/labellings, such that
authentications must have two steps: one is topological structure
authentication, and another is text-based authentication. Four basic
topological structure authentications are introduced and many text-based
authentications follow Topsnut-gpws. Our methods are based on algebraic, number
theory and graph theory, many of them can be transformed into polynomial
algorithms. A new type of matrices for describing Topsnut-gpws is created here,
and such matrices can produce TB-paws in complex forms and longer bytes.
Estimating the space of TB-paws made by Topsnut-gpws is very important for
application. We propose to encrypt dynamic networks and try to face: (1)
thousands of nodes and links of dynamic networks; (2) large numbers of
Topsnut-gpws generated by machines rather than human's hands. As a try, we
apply spanning trees of dynamic networks and graphic groups (Topsnut-groups) to
approximate the solutions of these two problems. We present some unknown
problems in the end of the article for further research.


  In this paper we introduce a realcompactification for any metric space (X,
d), defined by means of the family of all its real-valued uniformly continuous
functions. We call it the Samuel realcompactification, according to the well
known Samuel compactification associated to the family of all the bounded
real-valued uniformly continuous functions. Among many other things, we study
the corresponding problem of the Samuel realcompactness for metric spaces. At
this respect, we prove that a result of Kat\v{e}tov-Shirota type occurs in this
context, where the completeness property is replaced by Bourbaki-completeness
(a notion recently introduced by the authors) and the closed discrete subspaces
are replaced by the uniformly discrete ones. More precisely, we see that a
metric space (X, d) is Samuel realcompact iff it is Bourbaki-complete and every
uniformly discrete subspace of X has non-measurable cardinal. As a consequence,
we derive that a normed space is Samuel realcompact iff it has finite
dimension. And this means in particular that realcompactness and Samuel
realcompactness can be very far apart. The paper also contains results relating
this realcompactification with the so-called Lipschitz realcompactification
(also studied here), with the classical Hewitt-Nachbin realcompactification and
with the completion of the initial metric space.


  In this work, the issue of obtaining consistent parameter estimators for
nonlinear regression models where the regressors are second-order modulus
functions is explored. It is shown that consistent instrumental variable
estimators can be obtained by estimating first and second-order moments of
non-additive environmental disturbances' probability distributions as nuisance
parameters in parallel to the sought-after model parameters, conducting
experiments with a static excitation offset of sufficient amplitude and forcing
the instruments to have zero mean. The proposed method is evaluated in a
simulation example with a model of a marine surface vessel.


  The asymptotic decay of passive scalar fields is solved analytically for the
Kraichnan model, where the velocity has a short correlation time. At long
times, two universality classes are found, both characterized by a distribution
of the scalar -- generally non-Gaussian -- with global self-similar evolution
in time. Analogous behavior is found numerically with a more realistic flow
resulting from an inverse energy cascade.


  The axis for Figure 2 was wrong. It has been fixed and the postscript file
replaced (The file was called comp.ps).


  The iPTF detection of the most recent outburst of the recurrent nova system
RX J0045.4+4154 in the Andromeda Galaxy has enabled the unprecedented study of
a massive ($M>1.3\ M_\odot$) accreting white dwarf (WD). We detected this nova
as part of the near daily iPTF monitoring of M31 to a depth of $R\approx
21$\,mag and triggered optical photometry, spectroscopy and soft X-ray
monitoring of the outburst. Peaking at an absolute magnitude of $M_R=-6.6$ mag,
and with a decay time of 1 mag per day, it is a faint and very fast nova. It
shows optical emission lines of He/N and expansion velocities of 1900 to 2600
km s$^{-1}$ 1--4 days after the optical peak. The {\it Swift} monitoring of the
X-ray evolution revealed a supersoft source (SSS) with $kT_{\rm eff}\approx
90-110\ {\rm eV}$ that appeared within 5 days after the optical peak, and
lasted only 12 days. Most remarkably, this is not the first event from this
system, rather it is a recurrent nova with a time between outbursts of
approximately 1 year, the shortest known. Recurrent X-ray emission from this
binary was detected by ROSAT in 1992 and 1993, and the source was well
characterized as a $M>1.3\ M_\odot$ WD SSS. Based on the observed recurrence
time between different outbursts, the duration and effective temperature of the
SS phase, MESA models of accreting WDs allow us to constrain the accretion rate
to $\dot M>1.7\times10^{-7}\ {M_{\odot}\ {\rm yr}}^{-1}$ and WD mass $>1.30\
M_{\odot}$. If the WD keeps $30\%$ of the accreted material, it will take less
than a Myr to reach core densities high enough for carbon ignition (if made of
C/O) or electron capture (if made of O/Ne) to end the binary evolution.


  Consider the following skew-symmetric Chern-Simons system
\begin{equation*}\left \{ \begin{split} &\Delta u_{1}+\frac{1}{\varepsilon^2}
e^{u_{2}}(1-e^{u_{1}})=4\pi \sum^{N_1}_{j=1}\delta_{p_{j,1}}\\ &\Delta
u_{2}+\frac{1}{\varepsilon^2} e^{u_{1}}(1-e^{u_{2}})=4\pi
\sum^{N_2}_{j=1}\delta_{p_{j,2}} \end{split}\right.\quad\text{ in }\quad\Omega,
\end{equation*} where $\Omega$ is a flat 2-dimensional torus $\mathbb{T}^2$ or
$\mathbb{R}^2$, $\varepsilon> 0$ is a coupling parameter, and $\delta_p$
denotes the Dirac measure concentrated at $p$. In this paper, we prove that,
when the coupling parameter $\varepsilon$ is small, the topological type
solutions to the above system are uniquely determined by the location of their
vortex points. This result follows by the bubbling analysis and the non-degency
of linearized equations.


  In the projective planes $\mathrm{PG}(2,q)$, we collect the smallest known
sizes of complete arcs for the regions \begin{align*} &\mbox{all }
q\le160001,~~ q \mbox{ prime power};\\ &Q_{4}=\{34 \mbox{ sporadic }q'\mbox{s
in the interval }[160801\ldots430007], \mbox{ see Table 3}\}. \end{align*}
  For $q\le160001$, the collection of arc sizes is complete in the sense that
arcs for all prime powers are considered. This proves new upper bounds on the
smallest size $t_{2}(2,q)$ of a complete arc in $\mathrm{PG}(2,q)$, in
particular \begin{align*} t_{2}(2,q)&<0.998\sqrt{3q\ln q}<1.729\sqrt{q\ln
q}&\mbox{ for }&&7&\le q\le160001;~~(1) \\
t_{2}(2,q)&<\sqrt{q}\ln^{0.7295}q&\mbox{ for }&&109&\le q\le160001;~~(2)\\
t_{2}(2,q)&<\sqrt{q}\ln^{c_{up}(q)}q,~~c_{up}(q)=\frac{0.27}{\ln q}+0.7,&\mbox{
for }&&19&\le q\le160001;~~(3)\\
t_{2}(2,q)&<0.6\sqrt{q}\ln^{\varphi_{up}(q;0.6)}
q,~~\varphi_{up}(q;0.6)=\frac{1.5}{\ln q}+0.802,&\mbox{ for }&&19&\le
q\le160001.~~(4) \end{align*} Moreover, the bounds (2) -- (4) hold also for
$q\in Q_{4}$. Also, \begin{align*} t_{2}(2,q)&<1.006\sqrt{3q\ln
q}<1.743\sqrt{q\ln q}&\mbox{ for }&&q\in Q_{4}.~~(5) \end{align*} Our
investigations and results allow to conjecture that the bounds (2) -- (5) hold
for all $q\geq109$.


  In YBa2Cu3Ox, distinct features are found in the pressure dependence of the
transition temperature, dTc/dp, and in DeltaCp*Tc, where DeltaCp is the jump in
the specific heat at Tc: dTc/dp becomes zero when DeltaCp*Tc is maximal,
whereas dTc/dp has a peak at lower oxygen contents where DeltaCp*Tc vanishes.
Substituting Nd for Y and doping with Ca leads to a shift of these specific
oxygen contents, since oxygen order and hole doping by Ca influences the hole
content nh in the CuO2 planes. Calculating nh from the parabolic Tc(nh)
behavior, the features coalesce for all samples at nh=0.11 and nh=0.175,
irrespective of substitution and doping. Hence, this behavior seems to reflect
an intrinsic property of the CuO2 planes. Analyzing our results we obtain
different mechanisms in three doping regions: Tc changes in the optimally doped
and overdoped region are mainly caused by charge transfer. In the slightly
underdoped region an increasing contribution to dTc/dp is obtained when well
ordered CuO chain fragments serve as pinning centers for stripes. This behavior
is supported by our results on Zn doped NdBa2Cu3Ox and is responsible for the
well known dTc/dp peak observed in YBa2Cu3Ox at x=6.7. Going to a hole content
below nh=0.11 our results point to a crossover from an underdoped
superconductor to a doped antiferromagnet, changing completely the physics of
these materials.


  Let U be an open subset of R^n. Let L^2=L^2(U,dx) and H^1_0=H^1_0(U) be the
standard Lebesgue and Sobolev spaces of complex-valued functions. The aim of
this paper is to study the group G of invertible operators on H^1_0 which
preserve the L^2-inner product. When U is bounded and the border $\partial U$
is smooth, this group acts as the intertwiner of the H^1_0 solutions of the
non-homogeneous Helmholtz equation $u-\Delta u=f$, $u|_{\partial U}=0$. We show
that G is a real Banach-Lie group, whose Lie algebra is (i times) the space of
symmetrizable operators. We discuss the spectrum of operators belonging to G by
means of examples. In particular, we give an example of an operator in G whose
spectrum is not contained in the unit circle. We also study the one parameter
subgroups of G. Curves of minimal length in G are considered. We introduce the
subgroups G_p:=G \cap (I - B_p(H^1_0)), where B_p(H_0^1) is a Schatten ideal of
operators on H_0^1. An invariant (weak) Finsler metric is defined by the p-norm
of the Schatten ideal of operators of L^2. We prove that any pair of operators
g_1,g_2 in G_p can be joined by a minimal curve of the form $a(t)=g_1 e^{itX}$,
where X is a symmetrizable operator in B_p(H^1_0).


  Its is a well known fact that Turbulence exhibits non-locality, however,
modeling has largely received local treatment following the work of Prandl over
mixing-length model. Thus, in this article we report our findings by
formulating a non-local closure model for Reynolds-averaged Navier-Stokes
(RANS) equation using Fractional Calculus. Two model formulations are studied,
namely one- and two-sided for Channel, Pipe and Couette flow, where the results
shown have less 1% error. The motivation of two-sided model lies in recognising
the fact that non-locality at a given spatial location is an aggregate of all
directions. Furthermore, scaling laws and asymptotic relationship for Couette,
Channel and Pipe flow is reported. It is to be noted that modeling in wall
units, no additional coefficient appears, thus there models could be applied to
complex flows with ease.


  This paper develops mixed-normal approximations for probabilities that
vectors of multiple Skorohod integrals belong to random convex polytopes when
the dimensions of the vectors possibly diverge to infinity. We apply the
developed theory to establish the asymptotic mixed normality of the realized
covariance matrix of a high-dimensional continuous semimartingale observed at a
high-frequency, where the dimension can be much larger than the sample size. We
also present an application of this result to testing the residual sparsity of
a high-dimensional continuous-time factor model.


  Mental health conversational agents (a.k.a. chatbots) are widely studied for
their potential to offer accessible support to those experiencing mental health
challenges. Previous surveys on the topic primarily consider papers published
in either computer science or medicine, leading to a divide in understanding
and hindering the sharing of beneficial knowledge between both domains. To
bridge this gap, we conduct a comprehensive literature review using the PRISMA
framework, reviewing 534 papers published in both computer science and
medicine. Our systematic review reveals 136 key papers on building mental
health-related conversational agents with diverse characteristics of modeling
and experimental design techniques. We find that computer science papers focus
on LLM techniques and evaluating response quality using automated metrics with
little attention to the application while medical papers use rule-based
conversational agents and outcome metrics to measure the health outcomes of
participants. Based on our findings on transparency, ethics, and cultural
heterogeneity in this review, we provide a few recommendations to help bridge
the disciplinary divide and enable the cross-disciplinary development of mental
health conversational agents.


  Resource theory is a widely-applicable framework for analyzing the physical
resources required for given tasks, such as computation, communication, and
energy extraction. In this paper, we propose a general scheme for analyzing
resource theories based on resource destroying maps, which leave resource-free
states unchanged but erase the resource stored in all other states. We
introduce a group of general conditions that determine whether a quantum
operation exhibits typical resource-free properties in relation to a given
resource destroying map. Our theory reveals fundamental connections among basic
elements of resource theories, in particular, free states, free operations, and
resource measures. In particular, we define a class of simple resource measures
that can be calculated without optimization, and that are monotone
nonincreasing under operations that commute with the resource destroying map.
We apply our theory to the resources of coherence and quantum correlations
(e.g., discord), two prominent features of nonclassicality.


  We present a framework which unifies classical phenomenological $J_2$ and
crystal plasticity theories with quantitative dislocation mechanics. The theory
allows the computation of stress fields of arbitrary dislocation distributions
and, coupled with minimally modified classical ($J_2$ and crystal plasticity)
models for the plastic strain rate of statistical dislocations, results in a
versatile model of finite deformation mesoscale plasticity. We demonstrate some
capabilities of the framework by solving two outstanding challenge problems in
mesoscale plasticity: 1) recover the experimentally observed power-law scaling
of stress-strain behavior in constrained simple shear of thin metallic films
inferred from micropillar experiments which all strain gradient plasticity
models overestimate and fail to predict; 2) predict the finite deformation
stress and energy density fields of a sequence of dislocation distributions
representing a progressively dense dislocation wall in a finite body, as might
arise in the process of polygonization when viewed macroscopically, with one
consequence being the demonstration of the inapplicability of current
mathematical results based on $\mathrm{\Gamma}$-convergence for this physically
relevant situation. Our calculations in this case expose a possible `phase
transition' - like behavior for further theoretical study. We also provide a
quantitative solution to the fundamental question of the volume change induced
by dislocations in a finite deformation theory, as well as show the massive
non-uniqueness in the solution for the (inverse) deformation map of a body
inherent in a model of finite strain dislocation mechanics, when approached as
a problem in classical finite elasticity.


  Two-dimensional conformal field theories with Virasoro symmetry generically
contain a Schwarzian sector. This sector is related to the near-horizon region
of the near-extremal BTZ black hole in the holographic dual. In this work we
generalize this picture to CFTs with higher spin conserved currents. It is
shown that the partition function in the near-extremal limit agrees with that
of BF higher spin gravity in AdS$_2$ which is described by a generalized
Schwarzian theory. We also provide a spectral decomposition of Schwarzian
partition functions via the $\mathcal{W}_N$ fusion kernel and consider
supersymmetric generalizations.


  3-dimensional Harvey Lawson submanifolds were introduced in an earlier paper
by Akbulut-Salur, as examples of Lagrangian-type manifolds inside G2 manifold.
In this paper, we first show that the space of deformations of a smooth,
compact, orientable Harvey-Lawson submanifold HL in a G2 manifold M can be
identified with the direct sum of the space of smooth functions and closed
2-forms on HL. We then introduce a new class of Lagrangian-type 4-dimensional
submanifolds inside G2, call them RS submanifolds and prove that the space of
deformations of a smooth, compact, orientable RS submanifold in a G2 manifold M
can be identified with closed 3-forms on RS.