  We present a simple quantum theory for the pulsed light generated by a
synchronously pumped optical parametric oscillator (SPOPO) in the degenerate
case where the signal and idler trains of pulses coincide, below threshold and
neglecting all dispersion effects. Our main goal is to precise in the obtained
quantum effects, which ones are identical to the c.w. case and which ones are
specific to the SPOPO. We demonstrate in particular that the temporal
correlations have interesting peculiarities: the quantum fluctuations at
different times within the same pulse turn out to be totally not correlated,
whereas they are correlated between nearby pulses at times that are placed in
the same position relative to the centre of the pulses. The number of
significantly correlated pulses is of the order of cavity finesse. We show also
that there is perfect squeezing at noise frequencies multiple of the pulse
repetition frequency when one approaches the threshold from below on the signal
field quadrature measured by a balanced homodyne detection with a local
oscillator of very short duration compared to the SPOPO pulse length.


  Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in
$G$, let $U$ be an open subset of $X$, and let $\{g_t\}$ be a one-parameter
subgroup of $G$. Consider the set of points in $X$ whose $g_t$-orbit misses
$U$; it has measure zero if the flow is ergodic. It has been conjectured that
this set has Hausdorff dimension strictly smaller than the dimension of $X$.
This conjecture has been proved when $X$ is compact or when $G$ is a simple Lie
group of real rank $1$. In this paper we prove this conjecture for the case
$G=\textrm{SL}_{m+n}(\mathbb{R})$, $\Gamma=\textrm{SL}_{m+n}(\mathbb{Z})$ and
$g_t=\textrm{diag} (e^{nt}, \dots, e^{nt},e^{-mt}, \dots, e^{-mt})$, in fact
providing an effective estimate for the codimension. The proof uses exponential
mixing of the flow together with the method of integral inequalities for height
functions on $\textrm{SL}_{m+n}(\mathbb{R})/\textrm{SL}_{m+n}(\mathbb{Z})$. We
also discuss an application to the problem of improving Dirichlet's theorem in
simultaneous Diophantine approximation.


  The ongoing COVID-19 pandemic is challenging every part of society. From a
scientific point of view the first major task is to predict the dynamics of the
pandemic, allowing governments to allocate proper resources and measures to
fight it, as well as gauging the success of these measures by comparison with
the predictions in hindsight. The vast majority of pandemic models are based on
extensive models with large numbers of fit parameters, leading to individual
descriptions for every hot spot on the world. This makes predictions and
comparisons cumbersome, if not impossible. We here propose a different
approach, by moving away from a description over time, and instead choosing the
total number of infected people in an enclosed area as the independent
variable. Analyzing a few hot spots data, we derive an empirical formula for
the dynamics, dependent only on three variables. The final number of infections
is strictly connected to one fit parameter we call mitigation factor, which in
turn is mostly dependent only on the enclosed population. Despite its
simpleness, this description applies to every of the around 50 countries we
have analyzed, allows to separate different waves of the pandemic, provides a
figure of merit for the overall usefulness of government measures, and shows
when a pandemic is ending. Our model is robust against undetected cases, and
allows all nations, in particular those with fewer resources, to reasonably
predict the outcome of the pandemic in their country.


  Endoscopic surgery is currently an important treatment method in the field of
spinal surgery and avoiding damage to the spinal nerves through video guidance
is a key challenge. This paper presents the first real-time segmentation method
for spinal nerves in endoscopic surgery, which provides crucial navigational
information for surgeons. A finely annotated segmentation dataset of
approximately 10,000 consec-utive frames recorded during surgery is constructed
for the first time for this field, addressing the problem of semantic
segmentation. Based on this dataset, we propose FUnet (Frame-Unet), which
achieves state-of-the-art performance by utilizing inter-frame information and
self-attention mechanisms. We also conduct extended exper-iments on a similar
polyp endoscopy video dataset and show that the model has good generalization
ability with advantageous performance. The dataset and code of this work are
presented at: https://github.com/zzzzzzpc/FUnet .


  An accurate method to measure the abundance of high-redshift galaxies
consists in the observation of absorbers along the line of sight toward a
background quasar. Here, we present abundance measurements of 13 z>3 sub-Damped
Lyman-alpha Systems (quasar absorbers with HI column density 19 < log N(HI) <
20.3 cm^-2) based on the high resolution observations with VLT UVES
spectrograph. These observations more than double the metallicity information
for sub-DLAs previously available at z>3. This new data, combined with other
sub-DLA measurements from the literature, confirm the stronger metallicity
redshift evolution than for the classical Damped Lyman-alpha absorbers.
Besides, these observations are used to compute for the first time the fraction
of gas ionised from photo-ionisation modelling in a sample of sub-DLAs. Based
on these results, we calculate that sub-DLAs contribute no more than 6% of the
expected amount of metals at z~2.5. We therefore conclude that even if sub-DLAs
are found to be more metal-rich than classical DLAs, they are insufficient to
close the so-called ``missing metals problem''.


  The development of the Atacama Large Millimeter/submillimeter Array (ALMA)
phasing system (APS) has allowed ALMA to function as an extraordinarily
sensitive station for very long baseline interferometry (VLBI) at frequencies
of up to 230 GHz (~1.3 mm). Efforts are now underway to extend use of the APS
to 345 GHz (~0.87 mm). Here we report a characterization of APS performance at
345 GHz based on a series of tests carried out between 2015-2021, including a
successful global VLBI test campaign conducted in 2018 October in collaboration
with the Event Horizon Telescope (EHT).


  Although debris discs have been detected around a significant number of
main-sequence stars, only a few of them are known to harbour hot dust in their
inner part where terrestrial planets may have formed. Thanks to infrared
interferometric observations, it is possible to obtain a direct measurement of
these regions, which are of prime importance for preparing future exo-Earth
characterisation missions. In this context, we have resolved the exozodiacal
dust disc around Vega with the help of infrared stellar interferometry and
estimated the integrated H-band flux originating from the first few AUs of the
debris disc. Using precise H-band interferometric measurements obtained with
the 3-telescope IOTA/IONIC interferometer (Mount Hopkins, Arizona), thorough
modelling of both interferometric data (squared visibility and closure phase)
and spectral energy distribution was performed to constrain the nature of the
near-infrared excess emission. The most straightforward scenario consists in a
compact dust disc producing a thermal emission that is largely dominated by
small grains located between 0.1 and 0.3 AU from Vega and accounting for 1.23
+/- 0.45% of the near-infrared stellar flux for our best-fit model. This flux
ratio is shown to vary slightly with the geometry of the model used to fit our
interferometric data (variations within +/-0.19%). Initially revealed by K-band
CHARA/FLUOR observations, the presence of hot exozodiacal dust in the vicinity
of Vega is confirmed by our H-band IOTA/IONIC measurements at the 3-sigma
level. Whereas the origin of the dust is still uncertain, its presence and the
possible connection with the outer disc suggest that the Vega system is
currently undergoing major dynamical perturbations.


  The purpose of this article is to investigate relations between
W-superalgebras and integrable super-Hamiltonian systems. To this end, we
introduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Lie
superalgebra $g$ and its even nilpotent element $f$, and we find a new
definition of the classical affine W-superalgebra $W(g,f,k)$ via the D-S
reduction. This new construction allows us to find free generators of
$W(g,f,k)$, as a differential superalgebra, and two independent Lie brackets on
$W(g,f,k)/\partial W(g,f,k).$ Moreover, we describe super-Hamiltonian systems
with the Poisson vertex algebras theory. A W-superalgebra with certain
properties can be understood as an underlying differential superalgebra of a
series of integrable super-Hamiltonian systems.


  We present DiffXPBD, a novel and efficient analytical formulation for the
differentiable position-based simulation of compliant constrained dynamics
(XPBD). Our proposed method allows computation of gradients of numerous
parameters with respect to a goal function simultaneously leveraging a
performant simulation model. The method is efficient, thus enabling
differentiable simulations of high resolution geometries and degrees of freedom
(DoFs). Collisions are naturally included in the framework. Our differentiable
model allows a user to easily add additional optimization variables. Every
control variable gradient requires the computation of only a few partial
derivatives which can be computed using automatic differentiation code. We
demonstrate the efficacy of the method with examples such as elastic material
parameter estimation, initial value optimization, optimizing for underlying
body shape and pose by only observing the clothing, and optimizing a
time-varying external force sequence to match sparse keyframe shapes at
specific times. Our approach demonstrates excellent efficiency and we
demonstrate this on high resolution meshes with optimizations involving over 26
million degrees of freedom. Making an existing solver differentiable requires
only a few modifications and the model is compatible with both modern CPU and
GPU multi-core hardware.


  To provide system design insights for practical communication systems
equipped with the frequency diverse array (FDA), this paper investigates the
secrecy performance of FDA systems exploiting finite-alphabet inputs over
fluctuating two-ray (FTR) fading channels. More specifically, closed-form
expressions for the average secrecy rate (ASR) and the secrecy outage
probability (SOP) are derived, while their correctness is confirmed by
numerical simulations. In addition, we perform asymptotic analysis to quantify
the secrecy performance gap between Gaussian and finite-alphabet inputs, for a
sufficiently large average signal-to-noise ratio (SNR) of the main channel.
Compared with Gaussian inputs-based research, this letter focuses on practical
scenarios which sheds lights on properties of FDA systems.


  A detection of a core-collapse supernova (CCSN) gravitational-wave (GW)
signal with an Advanced LIGO and Virgo detector network may allow us to measure
astrophysical parameters of the dying massive star. GWs are emitted from deep
inside the core and, as such, they are direct probes of the CCSN explosion
mechanism. In this study we show how we can determine the CCSN explosion
mechanism from a GW supernova detection using a combination of principal
component analysis and Bayesian model selection. We use simulations of GW
signals from CCSN exploding via neutrino-driven convection and rapidly-rotating
core collapse. Previous studies have shown that the explosion mechanism can be
determined using one LIGO detector and simulated Gaussian noise. As real GW
detector noise is both non-stationary and non-Gaussian we use real detector
noise from a network of detectors with a sensitivity altered to match the
advanced detectors design sensitivity. For the first time we carry out a
careful selection of the number of principal components to enhance our model
selection capabilities. We show that with an advanced detector network we can
determine if the CCSN explosion mechanism is neutrino-driven convection for
sources in our Galaxy and rapidly-rotating core collapse for sources out to the
Large Magellanic Cloud.


  The disks of galaxies are primarily stellar systems, and fundamentally
dynamical entities. Thus, to fully understand galactic disks, we must study
their stellar kinematics as well as their morphologies. Observational
techniques have now advanced to a point where quite detailed stellar-kinematic
information can be extracted from spectral observations. This review presents
three illustrative examples of analyses that make use of such information to
study the formation and evolution of these systems: the derivation of the
pattern speed of the bar in NGC 936; the calculation of the complete velocity
ellipsoid of random motions in NGC 488; and the strange phenomenon of
counter-rotation seen in NGC 3593.


  We determine a necessary and sufficient condition for the infinitude of
primes $p$ such that none of the equations $a_i^x \equiv b_i \pmod{p}, 1 \le i
\le n,$ are solvable. We control the insolvability of $a^x \equiv b \pmod{p}$
by power residues for multiplicatively independent $a$ and $b$, and by
divisibilities and, most importantly, parities of orders in multiplicatively
dependent cases. We also consider a more general problem concerning
divisibilities of orders. The problems are motivated by Artin's primitive root
conjecture and its variants.


  Social networks are pivotal for learning. Yet, we still lack a full
understanding of the mechanisms connecting networks with learning outcomes.
Here, we present the results of a large scale study (946 elementary school
children from 45 different classrooms) designed to understand the social
strategies used by elementary school children. We mapped the social networks of
students using both, a non-anonymous version of a prisoner's dilemma and a
survey of nominated friendships, and compared the strategies played by students
with their GPAs. We found that higher GPA students invest more strategically in
their relationships, cooperating more generously with friends and less
generously with non-friends than lower GPA students. Our findings suggest that
the higher selectivity of social capital investments by high performing
students may be one of the mechanisms helping them reap the learning benefits
of their social networks.


  We present a lattice-QCD calculation of the light-quark connected
contribution to window observables associated with the leading-order hadronic
vacuum polarization contribution to the anomalous magnetic moment of the muon,
$a_\mu^{\mathrm{HVP,LO}}$. We employ the MILC Collaboration's isospin-symmetric
QCD gauge-field ensembles, which contain four flavors of dynamical
highly-improved-staggered quarks with four lattice spacings between $a\approx
0.06$-$0.15$~fm and close-to-physical quark masses. We consider several
effective-field-theory-based schemes for finite-volume and other lattice
corrections and combine the results via Bayesian model averaging to obtain
robust estimates of the associated systematic uncertainties. After unblinding,
our final results for the intermediate and ``W2'' windows are $a^{ll,{\mathrm
W}}_{\mu}(\mathrm{conn.})=206.6(1.0) \times 10^{-10}$ and $a^{ll,\mathrm
{W2}}_{\mu}(\mathrm{conn.}) = 100.7(3.2)\times 10^{-10}$, respectively.


  We study $n$ non-intersecting Brownian motions corresponding to initial
configurations which have a vanishing density in the large $n$ limit at an
interior point of the support. It is understood that the point of vanishing can
propagate up to a critical time, and we investigate the nature of the
microscopic space-time correlations near the critical point and critical time.
We show that they are described either by the Pearcey process or by the Airy
line ensemble, depending on whether a simple integral related to the initial
configuration vanishes or not. Since the Airy line ensemble typically arises
near edge points of the macroscopic density, its appearance in the interior of
the spectrum is surprising. We explain this phenomenon by showing that, even
though there is no gap of macroscopic size near the critical point, there is
with high probability a gap of mesoscopic size. Moreover, we identify a path
which follows the Airy$_2$ process.


  We simulate anisotropic thermal conduction between the intracluster medium
(ICM) and the hot coronal interstellar medium (ISM) gas in cluster galaxies. In
the earlier Paper I (Vijayaraghavan & Sarazin 2017a), we simulated the
evaporation of the hot ISM due to isotropic (possibly saturated) conduction
between the ISM and ICM. We found that hot coronae evaporate on $\sim 10^2$ Myr
timescales, significantly shorter than the $\sim 10^3$ Myr gas loss times due
to ram pressure stripping. No tails of stripped gas are formed. This is in
tension with the observed ubiquity and implied longevity of compact X-ray
coronae and stripped ISM tails, and requires the suppression of evaporation,
possibly due to magnetic fields and anisotropic conduction. We perform a series
of wind tunnel simulations similar to Paper I, now including ISM and ICM
magnetic fields. We simulate the effect of anisotropic conduction for a range
of extreme magnetic field configurations: parallel and perpendicular to the ICM
wind, and continuous and completely disjoint between the ISM and ICM. We find
that when conduction is anisotropic, gas loss due to evaporation is severely
reduced; the overall gas loss rates with and without anisotropic conduction do
not differ by more than $10 - 20\%$. Magnetic fields also prevent stripped
tails from evaporating in the ICM by shielding, and providing few pathways for
heat transport between the ICM and ISM. The morphology of stripped tails and
magnetic fields in the tails and wakes of galaxies are sensitive to the initial
magnetic field configuration.


  We find a new formula for the limit of the capacity of certain sequences of
multidimensional semiconstrained systems as the dimension tends to infinity. We
do so by generalizing the notion of independence entropy, originally studied in
the context of constrained systems, to the study of semiconstrained systems.
Using the independence entropy, we obtain new lower bounds on the capacity of
multidimensional semiconstrained systems in general, and $d$-dimensional
axial-product systems in particular. In the case of the latter, we prove our
bound is asymptotically tight, giving the exact limiting capacity in terms of
the independence entropy. We show the new bound improves upon the best-known
bound in a case study of $(0,k,p)$-RLL.


  High harmonics generation (HHG) of coherent extreme ultraviolet (EUV)
radiation enables ultrafast pump-probe spectroscopy with attosecond-scale
timing resolutions. Yet beam control of generated EUV radiation remains a major
challenge for handy implementation of ultrafast spectroscopy particularly for
nano-micro samples. Here, we demonstrate a solid-based HHG scheme that
incorporates non-collinear illumination to perform the propagation control of
EUV harmonics by wavefront phase manipulation via a spatial light modulator.
Further, our solid-based non-collinear HHG scheme converts EUV harmonics to
Bessel beams without extra optics for beam focusing, offering a useful tool for
diverse EUV applications of metrology and fabrication.


  A new method to construct quasicrystalline lattices is proposed. It is based
on Landau crystallization theory. Like well-known cut and projection methods
our approach deals with N dimensional crystallography, but we don't need any
conception similar to an acceptance domain or atomic surfaces. The selection of
nodes, included into the lattice, is based on simple rules provided their local
order in a real space.


  The prominent success of neural networks, mainly in computer vision tasks, is
increasingly shadowed by their sensitivity to small, barely perceivable
adversarial perturbations in image input.
  In this work, we aim at explaining this vulnerability through the framework
of sparsity.
  We show the connection between adversarial attacks and sparse
representations, with a focus on explaining the universality and
transferability of adversarial examples in neural networks.
  To this end, we show that sparse coding algorithms, and the neural
network-based learned iterative shrinkage thresholding algorithm (LISTA) among
them, suffer from this sensitivity, and that common attacks on neural networks
can be expressed as attacks on the sparse representation of the input image.
The phenomenon that we observe holds true also when the network is agnostic to
the sparse representation and dictionary, and thus can provide a possible
explanation for the universality and transferability of adversarial attacks.
  The code is available at
https://github.com/danawr/adversarial_attacks_and_sparse_representations.


  Understanding how galaxies maintain the inefficiency of star formation with
physically self-consistent models is a central problem for galaxy evolution.
Although numerous theoretical models have been proposed in recent decades, the
debate still exists. By means of high-resolution two-dimensional hydrodynamical
simulations, we study the three feedback effects (the stellar wind heating, SNe
feedback, and AGN feedback) in suppressing star formation activities on the
evolution of early-type galaxies with different stellar masses. AGN feedback
models are updated based on \citet{Yuan2018}. The gas sources comes exclusively
from the mass losses of dying low-mass stars for most of our models. We find
that SNe feedback can keep star formation at a significantly low level for low
mass elliptical galaxies for a cosmological evolution time. For the high mass
galaxies, AGN feedback can efficiently offset the radiative cooling and thus
regulate the star formation activities. Such a suppression of star formation is
extremely efficient in the inner region of the galaxies. AGB heating cannot
account for this suppression for low and high mass galaxies. The X-ray
temperature $T_{\rm X}$ and luminosity $L_{\rm X}$ of hot plasma can be in
agreement with the observed data with the inclusion of effective feedback
processes. These results thus suggest that we can use $T_{\rm X}$ and $L_{\rm
X}$ to probe the role of different feedback processes. The inclusion of
additional gas sources can make the mass scale between SNe and AGN feedback
dominating in suppressing star formation decrease to an observationally
inferred value of a few $10^{10}~M_{\odot}$.


  An essential cover of the vertices of the $n$-cube $\{0,1\}^n$ by hyperplanes
is a minimal covering where no hyperplane is redundant and every variable
appears in the equation of at least one hyperplane. Linial and Radhakrishnan
gave a construction of an essential cover with $\lceil \frac{n}{2} \rceil + 1$
hyperplanes and showed that $\Omega(\sqrt{n})$ hyperplanes are required.
Recently, Yehuda and Yehudayoff improved the lower bound by showing that any
essential cover of the $n$-cube contains at least $\Omega(n^{0.52})$
hyperplanes. In this paper, building on the method of Yehuda and Yehudayoff, we
prove that $\Omega \left( \frac{n^{5/9}}{(\log n)^{4/9}} \right)$ hyperplanes
are needed.


  We prove a number of property (T) permanence results for locally compact
quantum groups under exact sequences and the presence of invariant states,
analogous to their classical versions. Along the way we characterize the
existence of invariant weights on quantum homogeneous spaces of quotient type,
and relate invariant states for LCQG actions on von Neumann algebras to
invariant vectors in canonical unitary implementations, providing an
application to amenability. Finally, we introduce a notion of lattice in a
locally compact quantum group, noting examples provided by Drinfeld doubles of
compact quantum groups. We show that property (T) lifts from a lattice to the
ambient LCQG, just as it does classically, thus obtaining new examples of
non-classical, non-compact, non-discrete LCQGs with property (T).


  We perform population synthesis of massive binaries to study the mergers of
neutron stars (NSs) and black holes (BHs) with the cores of their giant
secondaries during common envelope evolution (CEE). We use different values of
the efficiency parameter $\alpha_{\rm CE}$ in the framework of the energy
formalism for traditional CEE ($\alpha_{\rm CE} \leq 1$) and including
additional energy sources to unbind the envelope ($\alpha_{\rm CE} > 1$). We
constrain the possible values of $\alpha_{\rm CE}$ by comparing the results of
our simulations with local rate densities of binary compact object mergers as
inferred from gravitational-wave observations. We find two main evolutionary
pathways of binary systems that result in NS-core mergers, while only one of
them can also lead to the merger of a BH with the core of the giant star. We
explore the zero age main sequence (ZAMS) statistical properties of systems
that result in NS/BH-core mergers and find that the two evolutionary channels
correspond to a bimodal distribution of orbital separations. We estimate the
percentage of the mergers' event rates relative to core collapse supernovae
(CCSNe). We include the effect of mass accreted by the NS/BH during CEE in a
separate set of simulations and find it does not affect the mergers' event
rates.


  This paper strives to localize the temporal extent of an action in a long
untrimmed video. Where existing work leverages many examples with their start,
their ending, and/or the class of the action during training time, we propose
few-shot common action localization. The start and end of an action in a long
untrimmed video is determined based on just a hand-full of trimmed video
examples containing the same action, without knowing their common class label.
To address this task, we introduce a new 3D convolutional network architecture
able to align representations from the support videos with the relevant query
video segments. The network contains: (\textit{i}) a mutual enhancement module
to simultaneously complement the representation of the few trimmed support
videos and the untrimmed query video; (\textit{ii}) a progressive alignment
module that iteratively fuses the support videos into the query branch; and
(\textit{iii}) a pairwise matching module to weigh the importance of different
support videos. Evaluation of few-shot common action localization in untrimmed
videos containing a single or multiple action instances demonstrates the
effectiveness and general applicability of our proposal.


  We give an implementation of a statistical model, which can be successfully
applied for compressing of a sequence of binary digits with behavior close to
random.


  Recent evidence for a CP violating asymmetry in the semileptonic decays of
B_s mesons cannot be accommodated within the Standard Model. Such an asymmetry
can be explained by new physics contributions to Delta B=2 components of either
the mass matrix or the decay matrix. We show that mixing with a hidden
pseudoscalar meson with a mass around 5 GeV can result in a new CP violating
contribution to the mixing and can resolve several anomalies in this system
including the width difference, the average width and the charge asymmetry. We
also discuss the effects of the hidden meson on other b physics observables,
and present viable decay modes for the hidden meson. We make predictions for
new decay channels of B hadrons, which can be tested at the Tevatron, the LHC
and B-factories.


  We consider qubit coupling resulting from the capacitive coupling between two
double quantum dot (DQD) single-triplet qubits. Calculations of the coupling
when the two DQDs are detuned symmetrically or asymmetrically are performed
using a full configuration interaction (CI). The full CI reveals behavior that
is not observed by more commonly used approximations such as Heitler London or
Hund Mulliken, particularly related to the operation of both DQDs in the (0,2)
charge sector. We find that there are multiple points in detuning-space where a
two-qubit entangling gate can be realized, and that trade-offs between coupling
magnitude and sensitivity to fluctuations in detuning make a case for operating
the gate in the (0,2) regime not commonly considered.


  For any virtual link $L = S \cup T$ that may be decomposed into a pair of
oriented $n$-tangles $S$ and $T$, an oriented local move of type $T \mapsto T'$
is a replacement of $T$ with the $n$-tangle $T'$ in a way that preserves the
orientation of $L$. After developing a general decomposition for the Jones
polynomial of the virtual link $L = S \cup T$ in terms of various (modified)
closures of $T$, we analyze the Jones polynomials of virtual links $L_1,L_2$
that differ via a local move of type $T \mapsto T'$. Succinct divisibility
conditions on $V(L_1)-V(L_2)$ are derived for broad classes of local moves that
include the $\Delta$-move and the double-$\Delta$-move as special cases. As a
consequence of our divisibility result for the double-$\Delta$-move, we
introduce a necessary condition for any pair of classical knots to be
$S$-equivalent.


  Over the last several years, end-to-end neural conversational agents have
vastly improved in their ability to carry a chit-chat conversation with humans.
However, these models are often trained on large datasets from the internet,
and as a result, may learn undesirable behaviors from this data, such as toxic
or otherwise harmful language. Researchers must thus wrestle with the issue of
how and when to release these models. In this paper, we survey the problem
landscape for safety for end-to-end conversational AI and discuss recent and
related work. We highlight tensions between values, potential positive impact
and potential harms, and provide a framework for making decisions about whether
and how to release these models, following the tenets of value-sensitive
design. We additionally provide a suite of tools to enable researchers to make
better-informed decisions about training and releasing end-to-end
conversational AI models.


  La2Zr2O7 (LZO) formation of bulk powders and of films by Chemical Solution
Deposition (CSD) process have been studied using propionates. The treatment
involved a one step cycle in the reducing forming gas (Ar-5%H2) to be
compatible with Ni-5at%W RABITS. Large amount of residual carbon was found in
LZO powders formed in these conditions (10 wt %). The volume fraction of the
cube texture in LZO films on Ni-5at%w RABITS was found to be a function of the
speed of the gas flown above sample. This phenomenon is discussed in
considering the C deposited from the carbon-containing gases emitted during the
pyrolysis of the precursor. Using proper conditions (950 ^\circC and the speed
of gas of 6.8\times10^{-2} m/s), LZO films with good surface crystallinity
could be obtained on Ni-5at%W RABITS as demonstrated by X-ray diffraction,
electron backscattered diffraction and RHEED. The existence of residual carbon
in oxide films is a common question to films deposited by CSD processes under
reducing condition.


  Modulating the stiffness of soft actuators is crucial for improving the
efficiency of interaction with the environment. However, current stiffness
modulation mechanisms are hard to achieve high lateral stiffness and a wide
range of bending stiffness simultaneously. Here, we draw inspiration from the
anatomical structure of the finger and propose a bi-directional tunable
stiffness actuator (BTSA). BTSA is a soft-rigid hybrid structure that combines
air-tendon hybrid actuation (ATA) and bone-like structures (BLS). We develop a
corresponding fabrication method and a stiffness analysis model to support the
design of BLS. The results show that the influence of the BLS on bending
deformation is negligible, with a distal point distance error of less than 1.5
mm. Moreover, the bi-directional tunable stiffness is proved to be functional.
The bending stiffness can be tuned by ATA from 0.23 N/mm to 0.70 N/mm, with a
magnification of 3 times. The addition of BLS improves lateral stiffness up to
4.2 times compared with the one without BLS, and the lateral stiffness can be
tuned decoupling within 1.2 to 2.1 times (e.g. from 0.35 N/mm to 0.46 N/mm when
the bending angle is 45 deg). Finally, a four-BTSA gripper is developed to
conduct horizontal lifting and grasping tasks to demonstrate the advantages of
BTSA.


  The spinless Salpeter equation represents the simplest and most
straightforward generalization of the Schroedinger equation of standard
nonrelativistic quantum theory towards the inclusion of relativistic
kinematics. Moreover, it can be also regarded as a well-defined approximation
to the Bethe-Salpeter formalism for descriptions of bound states in
relativistic quantum field theories. The corresponding Hamiltonian is, in
contrast to all Schroedinger operators, a nonlocal operator. Because of the
nonlocality, constructing analytical solutions for such kind of equation of
motion proves difficult. In view of this, different sophisticated techniques
have been developed in order to extract rigorous analytical information about
these solutions. This review introduces some of these methods and compares
their significance by application to interactions relevant in physics.


  We have studied the energy dependence of several first scattering phases with
multi-atomic object. As concrete examples representing the general trends
endohedrals Neon inside C60 and Argon inside C60 are considered. It appeared
that the presence of an inner atom, either Ne or Ar, qualitatively affects the
scattering phases, in spite of the fact that the fullerene consists of 60
carbon atoms, while the atom staffed inside is only one. Calculations are
performed in the one-electron Hartree-Fock (HF) and random phase approximation
with exchange (RPAE) for the inner atom while the fullerenes shell is
substituted by static potential without and with the polarization potential. It
appeared that the total endohedral scattering phase is simply a sum of atomic,
Ne or Ar, and fullerenes C60 phases, contrary to the intuitive assumption that
the total phases on C60 and Neon inside C60 or Ar inside C60 has to be the
same.


  Molecular dynamics simulation is used to model the self-assembly of
polyhedral shells containing 180 trapezoidal particles that correspond to the
T=3 virus capsid. Three kinds of particle, differing only slightly in shape,
are used to account for the effect of quasi-equivalence. Bond formation between
particles is reversible and an explicit atomistic solvent is included. Under
suitable conditions the simulations are able to produce complete shells, with
the majority of unused particles remaining as monomers, and practically no
other clusters. There are also no incorrectly assembled clusters. The
simulations reveal details of intermediate structures along the growth pathway,
information that is relevant for interpreting experiment.


  The empirical success of distributional reinforcement learning~(RL) highly
depends on the distribution representation and the choice of distribution
divergence. In this paper, we propose \textit{Sinkhorn distributional
RL~(SinkhornDRL)} that learns unrestricted statistics from return distributions
and leverages Sinkhorn divergence to minimize the difference between current
and target Bellman return distributions. Theoretically, we prove the
contraction properties of SinkhornDRL, consistent with the interpolation nature
of Sinkhorn divergence between Wasserstein distance and Maximum Mean
Discrepancy~(MMD). We also establish the equivalence between Sinkhorn
divergence and a regularized MMD with a regularized Moment Matching behavior,
contributing to explaining the superiority of SinkhornDRL. Empirically, we show
that SinkhornDRL is consistently better or comparable to existing algorithms on
the Atari games suite.


  The study of kiloparsec-scale dual active galactic nuclei (AGN) will provide
important clues to understand the co-evolution between the host galaxies and
their central supermassive black holes undergoing a merging process. We present
long-slit spectroscopy of the J0038$+$4128, a kiloparsec-scale dual AGN
candidate discovered by Huang et al. recently, using the Yunnan Faint Object
Spectrograph and Camera (YFOSC) mounted on Li-Jiang 2.4-m telescope at Yunnan
observatories. From the long-slit spectra, we find that the average relative
line-of-sight (LOS) velocity between the two nuclei (J0038$+$4128N and
J0038$+$4128S) is about 150 km s$^{-1}$. The LOS velocities of the emission
lines from the gas ionized by the nuclei activities and of the absorption lines
from stars governed by the host galaxies for different regions of the
J0038$+$4128 exhibit the same trend. The same velocities trend indicates that
the gaseous disks are co-rotating with the stellar disks in this ongoing merge
system. We also find several knots/giant HII regions scattered around the two
nuclei with strong star formation revealed by the observed line ratios from the
spectra. Those regions are also detected clearly in HST $F336W/U$-band and HST
$F555W/V$-band images.


  The resonant mode approximation of the scattering matrix is considered for
calculating the optical properties of multilayered periodic structures within
the formalism of the Fourier-modal method for two diffraction thresholds in
close proximity of the spectral-angular range of interest. The developed
approximation opens up possibilities for the fast calculation of the scattering
matrix of these structures when describing the integral characteristics of
spectra and dispersion curves containing high-Q resonances, such as bound
states in the continuum.


  We summarize recent attempts to detect warm ionized gas at large
galactocentric distances. This includes searching for gas at the edges of
spirals, in between cluster galaxies, towards extragalactic HI clouds, and
towards high velocity clouds and the Magellanic Stream in the Galaxy. With the
exception of extragalactic HI clouds, all of these experiments have proved
successful. Within each class, we have only observed a handful of objects. It
is premature to assess what fraction of the missing baryonic mass fraction
might be in the form of ionized gas. But, in most cases, the detections provide
a useful constraint on the ambient ionizing flux, and in the case of spiral
edges, can even trace dark matter haloes out to radii beyond the reach of radio
telescopes.


  Common model selection criteria, such as $AIC$ and its variants, are based on
in-sample prediction error estimators. However, in many applications involving
predicting at interpolation and extrapolation points, in-sample error cannot be
used for estimating the prediction error. In this paper new prediction error
estimators, $tAI$ and $Loss(w_{t})$ are introduced. These estimators generalize
previous error estimators, however are also applicable for assessing prediction
error in cases involving interpolation and extrapolation. Based on the
prediction error estimators, two model selection criteria with the same spirit
as $AIC$ are suggested. The advantages of our suggested methods are
demonstrated in simulation and real data analysis of studies involving
interpolation and extrapolation in a Linear Mixed Model framework.


  Deep generative models (DGMs) are effective on learning multilayered
representations of complex data and performing inference of input data by
exploring the generative ability. However, little work has been done on
examining or empowering the discriminative ability of DGMs on making accurate
predictions. This paper presents max-margin deep generative models (mmDGMs),
which explore the strongly discriminative principle of max-margin learning to
improve the discriminative power of DGMs, while retaining the generative
capability. We develop an efficient doubly stochastic subgradient algorithm for
the piecewise linear objective. Empirical results on MNIST and SVHN datasets
demonstrate that (1) max-margin learning can significantly improve the
prediction performance of DGMs and meanwhile retain the generative ability; and
(2) mmDGMs are competitive to the state-of-the-art fully discriminative
networks by employing deep convolutional neural networks (CNNs) as both
recognition and generative models.


  A dessin is a 2-cell embedding of a connected bipartite graph into an
orientable closed surface. An automorphism of a dessin is a permutation of the
edges of the underlying graph which preserves the colouring of the vertices and
extends to an orientation-preserving self-homeomorphism of the supporting
surface. A dessin is regular if its automorphism group is transitive on the
edges, and a regular dessin is totally symmetric if it is invariant under all
dessin operations. Thus totally symmetric dessins possesses the highest level
of external symmetry. In this paper we present a classification of totally
symmetric dessins with a nilpotent automorphism group of class three


  In the HARP experiment the large-angle spectrometer is using a cylindrical
TPC as main tracking and particle identification detector. The momentum scale
of reconstructed tracks in the TPC is the most important systematic error for
the majority of kinematic bins used for the HARP measurements of the
double-differential production cross-section of charged pions in proton
interactions on nuclear targets at large angle. The HARP TPC operated with a
number of hardware shortfalls and operational mistakes. Thus it was important
to control and characterize its momentum calibration. While it was not possible
to enter a direct particle beam into the sensitive volume of the TPC to
calibrate the detector, a set of physical processes and detector properties
were exploited to achieve a precise calibration of the apparatus. In the
following we recall the main issues concerning the momentum measurement in the
HARP TPC, and describe the cross-checks made to validate the momentum scale. As
a conclusion, this analysis demonstrates that the measurement of momentum is
correct within the published precision of 3%.


  We studied the statistical properties of the HI-to-H$_2$ transition observed
in absorption in the local diffuse and multiphase ISM to identify the physical
processes controlling the probability of occurrence of any line of sight. The
turbulent diffuse ISM is modeled using the RAMSES code, which includes detailed
treatments of the magnetohydrodynamics, the thermal evolution of the gas, and
the chemistry of H$_2$. The impacts of the UV radiation field, the mean
density, the turbulent forcing, the integral scale, the magnetic field, and the
gravity on the molecular content of the gas are explored through a parametric
study covering a wide range of physical conditions. The statistics of the
HI-to-H$_2$ transition are interpreted through analytical prescriptions and
compared with the observations using a modified and robust version of the
Kolmogorov-Smirnov test. The results of one simulation, convolved with the
distribution of distances of the observational sample, are able to explain most
of the statistical properties of the HI-to-H$_2$ transition observed in the
local ISM. The tightest agreement is obtained for a neutral diffuse gas modeled
over ~200 pc, with a mean density of $1-2$ cm$^{-3}$, illuminated by the
standard interstellar UV radiation field, and stirred up by a large-scale
compressive turbulent forcing. Within this configuration, the 2D probability
histogram of the column densities of H and H$_2$ is remarkably stable and is
almost unaltered by gravity, the strength of the turbulent forcing, the
resolution of the simulation, or the strength of the magnetic field $B_x$. The
weak effect of the resolution and our analytical prescription suggest that the
column densities of HI are likely built up in large-scale WNM and CNM
structures correlated in density over ~20 pc and ~10 pc, respectively, while
those of H$_2$ are built up in CNM structures between ~3 pc and ~10 pc.


  We set up a framework for discussing `$q$-analogues' of the usual covariant
differential operators for hermitian symmetric spaces. This turns out to be
directly related to the deformation quantization associated to quadratic
algebras satisfying certain conditions introduced by Procesi and De Concini.


  We study the escort probability distribution function of work done during an
interaction quantum quench of Luttinger liquids. It crosses over from the
thermodynamic to the small system limit with increasing $a$, the order of the
escort distribution, and depends on the universal combination
$(|K_i-K_f|/(K_i+K_F))^a$ with $K_i$, $K_f$ the initial and final Luttinger
liquid parameters, respectively. From its characteristic function, the diagonal
R\'enyi entropies and the many body inverse participation ratio (IPR) are
determined to evaluate the information content of the time evolved wavefunction
in terms of the eigenstates of the final Hamiltonian. The hierarchy of overlaps
is dominated by that of the ground states. The IPR exhibits a crossover from
Gaussian to power law decay with increasing interaction quench parameter.


  Loss function are an essential part in modern data-driven approach, such as
bi-level training scheme and machine learnings. In this paper we propose a loss
function consisting of a $r$-order (an)-isotropic total variation semi-norms
$TV^r$, $r\in \mathbb{R}^+$, defined via the Riemann-Liouville (R-L) fractional
derivative. We focus on studying key theoretical properties, such as the lower
semi-continuity and compactness with respect to both the function and the order
of derivative $r$, of such loss functions.


  Ever since the pioneering work of Bardeen, Cooper and Schrieffer in the
1950s, exploring novel pairing mechanisms for fermion superfluids has become
one of the central tasks in modern physics. Here, we investigate a new type of
fermion superfluid with hybridized $s$- and $p$-wave pairings in an ultracold
spin-1/2 Fermi gas. Its occurrence is facilitated by the co-existence of
comparable $s$- and $p$-wave interactions, which is realizable in a
two-component $^{40}$K Fermi gas with close-by $s$- and $p$-wave Feshbach
resonances. The hybridized superfluid state is stable over a considerable
parameter region on the phase diagram, and can lead to intriguing patterns of
spin densities and pairing fields in momentum space. In particular, it can
induce a phase-locked $p$-wave pairing in the fermion species that has no
$p$-wave interactions. The hybridized nature of this novel superfluid can also
be confirmed by measuring the $s$-wave and $p$-wave contacts, which can be
extracted from the high-momentum tail of the momentum distribution of each spin
component. These results enrich our knowledge of pairing superfluidity in Fermi
systems, and open the avenue for achieving novel fermion superfluids with
multiple partial-wave scatterings in cold atomic gases.


  This study presents methane-air counterflow simulations, in computationally
efficient similar form, allowing combustible mixtures to flow from one or both
directions in order to learn more about multi-branched propagating flame
structures (e.g., a triple flame). These structures with both premixed and
non-premixed flames are commonly seen in more practical combustion analyses. A
range of realistic mass mixture fractions and asymmetric chemical rate laws are
examined while avoiding the commonly forced unreal symmetric behavior with
one-step second-order kinetics. Moreover, a survey of critical parameters is
performed varying pressure and normal strain rate to define the flame structure
and detect different characters. Three flames can co-exist if the strain rate
is low enough and the pressure is high enough. However, at higher strain rate
and/or lower pressure, only one or two flames might be obtained. Negative
regions of heat release rate are observed and linked to potential endothermic
reactions. With a rich premixed mixture at low strain rates and pressures, high
exothermic reactions producing CO$_2$ and H$_2$O, and consuming CO and H$_2$
causes a heat-release-rate peak. Unexpected character of the lean and rich
premixed flames is observed, leading to the conclusion that these flames are
diffusion-controlled.


  In the context of f(R)=R + alpha R^2 gravity, we study the existence of
neutron and quark stars with no intermediate approximations in the generalised
system of Tolman-Oppenheimer-Volkov equations. Analysis shows that for positive
alpha's the scalar curvature does not drop to zero at the star surface (as in
General Relativity) but exponentially decreases with distance. Also the stellar
mass bounded by star surface decreases when the value alpha increases.
Nonetheless distant observers would observe a gravitational mass due to
appearance of a so-called gravitational sphere around the star. The non-zero
curvature contribution to the gravitational mass eventually is shown to
compensate the stellar mass decrease for growing alpha's. We perform our
analysis for several equations of state including purely hadronic
configurations as well as hyperons and quark stars. In all cases, we assess
that the relation between the parameter $\alpha$ and the gravitational mass
weakly depend upon the chosen equation of state. Another interesting feature is
the increase of the star radius in comparison to General Relativity for stars
with masses close to maximal, whereas for intermediate masses around 1.4-1.6
solar masses, the radius of star depends upon alpha very weakly. Also the
decrease in the mass bounded by star surface may cause the surface redshift to
decrease in R^2-gravity when compared to Einsteinian predictions. This effect
is shown to hardly depend upon the observed gravitational mass. Finally, for
negative values of alpha our analysis shows that outside the star the scalar
curvature has damped oscillations but the contribution of the gravitational
sphere into the gravitational mass increases indefinitely with radial distance
putting into question the very existence of such relativistic stars.


  Motivated by the evidence for a finite neutrino mass we examine anew the
interaction of neutrinos in a magnetic field. We present the rate for radiative
scattering for both massless and massive neutrinos in the standard model and
give the corresponding numerical estimates. We also consider the effects
arising from a possible neutrino magnetic moment.


  Reconstructing a gene network from high-throughput molecular data is often a
challenging task, as the number of parameters to estimate easily is much larger
than the sample size. A conventional remedy is to regularize or penalize the
model likelihood. In network models, this is often done locally in the
neighbourhood of each node or gene. However, estimation of the many
regularization parameters is often difficult and can result in large
statistical uncertainties. In this paper we propose to combine local
regularization with global shrinkage of the regularization parameters to borrow
strength between genes and improve inference. We employ a simple Bayesian model
with non-sparse, conjugate priors to facilitate the use of fast variational
approximations to posteriors. We discuss empirical Bayes estimation of
hyper-parameters of the priors, and propose a novel approach to rank-based
posterior thresholding. Using extensive model- and data-based simulations, we
demonstrate that the proposed inference strategy outperforms popular (sparse)
methods, yields more stable edges, and is more reproducible.


  The ProAm effort in modern astronomy and astrophysics is now a reality. The
achievements of amateur astronomers throughout the early history of astronomy
are well known. However, during the 20th century, the high specialisation and
the technology required for dealing with the astronomical issues of that epoch,
forced a natural separation of the professional activities from the amateur
ones. Nowadays, technology has become much cheaper. Amateur astronomers have
equipment capable of producing scientific results within their reach. Good
equipment pushes some amateur astronomers to learn more, recovering their
dialog with professionals. ProAm activities may be fruitful in data mining, in
database feeding, in long-term campaigns and even in casual observations.


  We study online robust matrix completion on graphs. At each iteration a
vector with some entries missing is revealed and our goal is to reconstruct it
by identifying the underlying low-dimensional subspace from which the vectors
are drawn. We assume there is an underlying graph structure to the data, that
is, the components of each vector correspond to nodes of a certain (known)
graph, and their values are related accordingly. We give algorithms that
exploit the graph to reconstruct the incomplete data, even in the presence of
outlier noise. The theoretical properties of the algorithms are studied and
numerical experiments using both synthetic and real world datasets verify the
improved performance of the proposed technique compared to other state of the
art algorithms.


  We define a local homomorphism $(Q,k)\to (R,\ell)$ to be Koszul if its
derived fiber $R \otimes^{\mathsf{L}}_Q k$ is formal, and if
$\operatorname{Tor}^Q(R,k)$ is Koszul in the classical sense. This recovers the
classical definition when $Q$ is a field, and more generally includes all flat
deformations of Koszul algebras. The non-flat case is significantly more
interesting, and there is no need for examples to be quadratic: all complete
intersection and all Golod quotients are Koszul homomorphisms. We show that the
class of Koszul homomorphisms enjoys excellent homological properties, and we
give many more examples, especially various monomial and Gorenstein examples.
We then study Koszul homomorphisms from the perspective of
$\mathrm{A}_\infty$-structures on resolutions. We use this machinery to
construct universal free resolutions of $R$-modules by generalizing a classical
construction of Priddy. The resulting (infinite) free resolution of an
$R$-module $M$ is often minimal, and can be described by a finite amount of
data whenever $M$ and $R$ have finite projective dimension over $Q$. Our
construction simultaneously recovers the resolutions of Shamash and Eisenbud
over a complete intersection ring, and the bar resolutions of Iyengar and Burke
over a Golod ring, and produces analogous resolutions for various other classes
of local rings.


  The investigation of W-pair production offers unique precision tests of the
electroweak theory at future e+e- colliders, including precise determinations
of cross sections, the W-boson mass, and gauge-boson self-couplings. The
state-of-the-art and future requirements in the theoretical prediction for the
reaction e+e- -> WW -> 4f(+gamma) are briefly reviewed.


  The Randall-Sundrum model is studied in 6 dimension with AdS$_4$ or dS$_4$
metric in the physical 4 dimensional space. Two solutions are found, one with
induced 5-dimensional gravity terms added to the induced cosmological constant
terms. We study the graviton modes in both solutions by transforming the mass
eigenvalue equation to a Schrodinger equation with a volcano potential. The
spectrum of gravitational excitations depends on the input parameters of the
theory, the six dimensional and the effective four-dimensional cosmological
constants. The model gives a physically acceptable spectrum if the 4
dimensional cosmological constant is sufficiently small.


  A stabilized polydisc is a product of a symplectic polydisc and several
copies of the complex plane. This paper gives a complete characterization of
symplectic embeddings of stabilized polydiscs into other stabilized polydiscs.


  We construct a theoretical framework to match the formulas for forward
inclusive hadron productions in pA collisions in the small-x saturation
formalism and collinear factorization. The small-x calculation can be viewed as
a power series in $Q_s^2/k_\perp^2$, in which the collinear factorization
result corresponds to the leading term. At high transverse momentum, the
subleading correction terms are insignficant, whereas at low $p_\perp$, the
power corrections become important and the small-x resummation is essential to
describe the differential cross section. We show that the familiar collinear
factorization calculation can smoothly match the results from small-x
factorization at next-to-leading order in $\alpha_s$ when we use exact
kinematics, as opposed to the approximate kinematics in previous work. With
this matching, we can describe the experimental data from RHIC very well at
high $p_\perp$.


  EUV imaging observations from several space missions (SOHO/EIT, TRACE, and
SDO/AIA) have revealed a presence of propagating intensity disturbances in
solar coronal loops. These disturbances are typically interpreted as slow
magnetoacoustic waves. Recent spectroscopic observations with Hinode/EIS of
active region loops, however, revealed that the propagating intensity
disturbances are associated with intermittent plasma upflows (or jets) at the
footpoints which are presumably generated by magnetic reconnection. For this
reason, whether these disturbances are waves or periodic flows is still being
studied. This study is aimed at understanding the physical properties of
observed disturbances by investigating the excitation of waves by hot plasma
injections from below and the evolution of flows and wave propagation along the
loop. We expand our previous studies based on isothermal 3D MHD models of
active region to a more realistic model that includes full energy equation
accounting for effects of radiative losses. Computations are initialized with
an equilibrium state of a model active region using potential (dipole) magnetic
field, gravitationally stratified density and temperature obtained from
polytropic equation of state. We model an impulsive injection of hot plasma
into the steady plasma outflow along the loops of different temperature, warm
($\sim$1 MK) and hot ($\sim$6 MK). The simulations show that hot jets launched
at the coronal base excite slow magnetoacoustic waves that propagate along the
loops to the high corona, while the injected hot flows decelerates rapidly with
heights. The simulated results support that the observed coronal disturbances
are mainly the wave features. We also find that the effect of radiative cooling
on the damping of slow-mode waves in 1-6 MK coronal loops is small, in
agreement with the previous conclusion based on 1D MHD models.


  Score-based diffusion models (SBDMs) have achieved the SOTA FID results in
unpaired image-to-image translation (I2I). However, we notice that existing
methods totally ignore the training data in the source domain, leading to
sub-optimal solutions for unpaired I2I. To this end, we propose energy-guided
stochastic differential equations (EGSDE) that employs an energy function
pretrained on both the source and target domains to guide the inference process
of a pretrained SDE for realistic and faithful unpaired I2I. Building upon two
feature extractors, we carefully design the energy function such that it
encourages the transferred image to preserve the domain-independent features
and discard domain-specific ones. Further, we provide an alternative
explanation of the EGSDE as a product of experts, where each of the three
experts (corresponding to the SDE and two feature extractors) solely
contributes to faithfulness or realism. Empirically, we compare EGSDE to a
large family of baselines on three widely-adopted unpaired I2I tasks under four
metrics. EGSDE not only consistently outperforms existing SBDMs-based methods
in almost all settings but also achieves the SOTA realism results without
harming the faithful performance. Furthermore, EGSDE allows for flexible
trade-offs between realism and faithfulness and we improve the realism results
further (e.g., FID of 51.04 in Cat to Dog and FID of 50.43 in Wild to Dog on
AFHQ) by tuning hyper-parameters. The code is available at
https://github.com/ML-GSAI/EGSDE.


  We study the $L^p$ regularity of the Bergman projection $P$ over the
symmetrized polydisc in $\mathbb C^n$. We give a decomposition of the Bergman
projection on the polydisc and obtain an operator equivalent to the Bergman
projection over anti-symmetric function spaces. Using it, we obtain the $L^p$
irregularity of $P$ for $p=\frac{2n}{n-1}$ which also implies that $P$ is $L^p$
bounded if and only if $p\in (\frac{2n}{n+1},\frac{2n}{n-1})$.


  Based on recent developments in physics-informed deep learning and deep
hidden physics models, we put forth a framework for discovering turbulence
models from scattered and potentially noisy spatio-temporal measurements of the
probability density function (PDF). The models are for the conditional expected
diffusion and the conditional expected dissipation of a Fickian scalar
described by its transported single-point PDF equation. The discovered model
are appraised against exact solution derived by the amplitude mapping closure
(AMC)/ Johnsohn-Edgeworth translation (JET) model of binary scalar mixing in
homogeneous turbulence.


  The addition of magnetic impurities in topological insulators can drive
ferromagnetic order that leads to novel quantum anomalous Hall transport well
below the Curie temperature. The fragility of the quantized regime has been
ascribed to the random nature of the magnetic moment distribution. Here, we
refine this hypothesis by using inelastic neutron scattering and
density-functional theory calculations to show that two antagonistic components
define the magnetism in Mn-substituted SnTe, thereby limiting the effectiveness
of dilute magnetic TIs. One component is strongly bound antiferromagnetic
dimers that compete with ferromagnetic order. The other component consists of
undimerized moments where ferromagnetic order develops via long-range
interactions.


  This study addresses limited attention allocation in a stochastic linear
quadratic system with multiplicative noise. Our approach enables strategic
resource allocation to enhance noise estimation and improve control decisions.
We provide analytical optimal control and propose a numerical method for
optimal attention allocation. Additionally, we apply our ffndings to dynamic
mean-variance portfolio selection, showing effective resource allocation across
time periods and factors, providing valuable insights for investors.


  We use a power expansion representation of plane elasticity complex
potentials due to Kolossov and Muskhelishvili, to compute the elastic fields
induced by a localized plastic deformation event. Far from its center, the
dominant contributions correspond to first order singularities of quadrupolar
and dipolar symmetry which can be associated respectively to pure deviatoric
and pure volumetric plastic strain of an equivalent circular inclusion.
Constructing holomorphic functions from the displacement field and its
derivatives, it is possible to define path independent Cauchy integrals which
capture the amplitudes of these singularities. Analytical expressions and
numerical tests on simple finite element data are presented. The development of
such numerical tools is of direct interest for the identification of local
structural reorganizations which are believed to be the key mechanisms for
plasticity of amorphous materials.


  Velocity relaxation of an elastic sphere immersed in a viscous incompressible
fluid is studied on the basis of the equations of linear elasticity and the
linearized Navier-Stokes equations. It is found that both translational motion
after a sudden impulse and rotational motion after a sudden twist show jittery
behavior in the long-time regime, with many reversals of velocity if the sphere
is sufficiently flexible. In the extreme long-time regime the translational and
rotational velocity relaxation functions each decay with a universal algebraic
long-time tail. The added mass and the added moment of inertia of the sphere
are found to vanish.


  This study provides an in-depth analysis of the model architecture and key
technologies of generative artificial intelligence, combined with specific
application cases, and uses conditional generative adversarial networks ( cGAN
) and time series analysis methods to simulate and predict dynamic changes in
financial markets. The research results show that the cGAN model can
effectively capture the complexity of financial market data, and the deviation
between the prediction results and the actual market performance is minimal,
showing a high degree of accuracy.


  A novel interferometric method - SLIVER (Super Localization by Image
inVERsion interferometry) - is proposed for estimating the separation of two
incoherent point sources with a mean squared error that does not deteriorate as
the sources are brought closer. The essential component of the interferometer
is an image inversion device that inverts the field in the transverse plane
about the optical axis, assumed to pass through the centroid of the sources.
The performance of the device is analyzed using the Cram\'er-Rao bound applied
to the statistics of spatially-unresolved photon counting using photon
number-resolving and on-off detectors. The analysis is supported by Monte-Carlo
simulations of the maximum likelihood estimator for the source separation,
demonstrating the superlocalization effect for separations well below that set
by the Rayleigh criterion. Simulations indicating the robustness of SLIVER to
mismatch between the optical axis and the centroid are also presented. The
results are valid for any imaging system with a circularly symmetric
point-spread function.


  The growing capacity of neural networks has strongly contributed to their
success at complex machine learning tasks and the computational demand of such
large models has, in turn, stimulated a significant improvement in the hardware
necessary to accelerate their computations. However, models with high latency
aren't suitable for limited-resource environments such as hand-held and IoT
devices. Hence, many deep learning techniques aim to address this problem by
developing models with reasonable accuracy without violating the
limited-resource constraint. In this work, we use a one-shot neural
architecture search model to implicitly evaluate the performance of an
intractable number of multipath neural networks. Combining this architecture
search with a pruning technique and architecture sample evaluation, we can
model the relation between the accuracy and the latency of a spectrum of models
with graded complexity. We show that our method can accurately model the
relative performance between models with different latencies and predict the
performance of unseen models with good precision across different datasets.


  Asteroid (7) Iris is an ideal target for disk-resolved imaging owing to its
brightness (V$\sim$7-8) and large angular size of 0.33 arcsec during its
apparitions. Iris is believed to belong to the category of large unfragmented
asteroids that avoided internal differentiation, implying that its current
shape and topography may record the first few 100 Myr of the solar system's
collisional evolution. We recovered information about the shape and surface
topography of Iris from disk-resolved VLT/SPHERE/ZIMPOL images acquired in the
frame of our ESO large program. We used the All-Data Asteroid Modeling (ADAM)
shape reconstruction algorithm to model the 3D shape of Iris, using optical
disk-integrated data and disk-resolved images from SPHERE as inputs. We
analyzed the SPHERE images to infer the asteroid's global shape and the
morphology of its main craters. We present the volume-equivalent diameter
D$_{{\rm eq}}$=214$\pm$5 km, and bulk density $\rho$=2.7$\pm$0.3 g cm$^{-3}$ of
Iris. Its shape appears to be consistent with that of an oblate spheroid with a
large equatorial excavation. We identified eight putative surface features
20--40 km in diameter detected at several epochs, which we interpret as impact
craters. Craters on Iris have depth-to-diameter ratios that are similar to
those of analogous 10 km craters on Vesta. The bulk density of Iris is
consistent with that of its meteoritic analog, namely LL ordinary chondrites.
Considering the absence of a collisional family related to Iris and the number
of large craters on its surface, we suggest that its equatorial depression may
be the remnant of an ancient (at least 3 Gyr) impact. Iris's shape further
opens the possibility that large planetesimals formed as almost perfect oblate
spheroids. Finally, we attribute the difference in crater morphology between
Iris and Vesta to their different surface gravities.


  We study the dynamics of two kinds of entanglement, and there interplay. On
one hand, the intrinsic entanglement within a central system composed by three
two level atoms, and measured by multipartite concurrence, on the other, the
entanglement between the central system and a cavity, acting as an environment,
and measured with purity. Using dipole-dipole and Ising interactions between
atoms we propose two Hamiltonians, a homogeneous and a quasi-homogeneous one.
We find an upper bound for concurrence as a function of purity, associated to
the evolution of the $W$ state. A lower bound is also observed for the
homogeneous case. In both situations, we show the existence of critical values
of the interaction, for which the dynamics of entanglement seem complex.


  Nekrashevych algebras of self-similar group actions are natural
generalizations of the classical Leavitt algebras. They are discrete analogues
of the corresponding Nekrashevych $C^\ast$-algebras. In particular,
Nekrashevych, Clark, Exel, Pardo, Sims and Starling have studied the question
of simplicity of Nekrashevych algebras, in part, because non-simplicity of the
complex algebra implies non-simplicity of the $C^\ast$-algebra.
  In this paper we give necessary and sufficient conditions for the
Nekrashevych algebra of a contracting group to be simple. Nekrashevych algebras
of contracting groups are finitely presented. We give an algorithm which on
input the nucleus of the contracting group, outputs all characteristics of
fields over which the corresponding Nekrashevych algebra is simple. Using our
methods, we determine the fields over which the Nekrashevych algebras of a
number of well-known contracting groups are simple including the Basilica
group, Gupta-Sidki groups, GGS-groups, multi-edge spinal groups, \v{S}uni\'{c}
groups associated to polynomials (this latter family includes the Grigorchuk
group, Grigorchuk-Erschler group and Fabrykowski-Gupta group) and
self-replicating spinal automaton groups.


  We study semiclassical approximations to the time evolution of coherent
states for general spin-orbit coupling problems in two different semiclassical
scenarios: The limit \hbar to zero is first taken with fixed spin quantum
number s and then with \hbar*s held constant. In these two cases different
classical spin-orbit dynamics emerge. We prove that a coherent state propagated
with a suitable classical dynamics approximates the quantum time evolution up
to an error of size \sqrt{\hbar} and identify an Ehrenfest time scale.
Subsequently an improvement of the semiclassical error to an arbitray order
\hbar^{N/2} is achieved by a suitable deformation of the state that is
propagated classically.


  A novel approach for creating ER conceptual models and an algorithm for
transforming them to the relational model has been developed by modifying and
extending the existing methods. A part of the new algorithm has previously been
presented. This paper presents the rest of the algorithm. One of the objectives
of this paper is to use it as a supportive document for ongoing empirical
evaluations of the new approach being conducted using the cognitive engagement
method and with the participation of different segments of the field as
respondents.


  Let $\ell$ be a prime and let $q$ be a prime power not divisible by $\ell$.
Put $G=\mathrm{GL}_n(\mathrm{F}_q)$ and fix an irreducible cuspidal
representation, $\bar{\pi}$, of $G$ over a sufficiently large finite field,
$k$, of characteristic $\ell$ such that $\bar{\pi}$ is not supercuspidal. We
compute the $\mathrm{W}(k)[G]$-endomorphism ring of the projective envelope of
$\bar{\pi}$ under the assumption that $\ell>n$. Our computations provide
evidence for a conjecture of Helm relating the Bernstein center to the
deformation theory of Galois representations.


  Previous studies of the stock price response to trades focused on the
dynamics of single stocks, i.e. they addressed the self-response. We
empirically investigate the price response of one stock to the trades of other
stocks in a correlated market, i.e. the cross-responses. How large is the
impact of one stock on others and vice versa? -- This impact of trades on the
price change across stocks appears to be transient instead of permanent as we
discuss from the viewpoint of market efficiency. Furthermore, we compare the
self-responses on different scales and the self- and cross-responses on the
same scale. We also find that the cross-correlation of the trade signs turns
out to be a short-memory process.


  We explore the phenomenology of the recently proposed "+-+" brane model which
has a characteristic anomalously light first Kaluza-Klein mode. We consider the
processes e^+ e^- to mu^+ mu^- and the Kaluza-Klein production e^+ e^- to gamma
KK giving missing visible energy. These in combination with the latest
Cavendish experiments place severe bounds on the parameter space of the model.
We also discuss how forthcoming experiments can test the model for ``natural''
range of the parameters.


  Using its Conformal Field Theory description, the Luttinger liquid is coupled
to the quantum electromagnetic field. We compute the decoherence properties of
a superposition of two states obtained by creating the same elementary
excitation at different places in the system.


  We prove a qualitative and a quantitative stability of the following rigidity
theorem: an anisotropic totally umbilical closed hypersurface is the Wulff
shape. Consider $n \geq 2$, $p\in (1, \, +\infty)$ and $\Sigma$ an
$n$-dimensional, closed hypersurface in $\mathbb{R}^{n+1}$, boundary of a
convex, open set. We show that if the $L^p$ norm of the trace-free part of the
anisotropic second fundamental form is small, then $\Sigma$ must be $W^{2, \,
p}$-close to the Wulff shape, with a quantitative estimate.


  Relativistic quantum field theory offers, in form of the homogeneous
Bethe-Salpeter framework, a (Poincar\'e-covariant) description of bound states
in terms of their underlying theory's fundamental degrees of freedom. In view
of the intrinsic complexity of this approach, simplifications have been sought
and abundantly found. The significance of these latter approximations may be
estimated by comparing their predictions with (easily inferable) rigorous
constraints on the bound-state spectra, such as existence, number and location
of discrete eigenstates. The application of these techniques to selected
proposed bound-state equations is exemplified for a large class of
generalizations of the Hellmann potential frequently employed in several areas
of science such as physics and chemistry.


  In this work, we tackle the problems of efficiency and scalability for
predictive coding networks in machine learning. To do so, we first propose a
library called PCX, whose focus lies on performance and simplicity, and
provides a user-friendly, deep-learning oriented interface. Second, we use PCX
to implement a large set of benchmarks for the community to use for their
experiments. As most works propose their own tasks and architectures, do not
compare one against each other, and focus on small-scale tasks, a simple and
fast open-source library adopted by the whole community would address all of
these concerns. Third, we perform extensive benchmarks using multiple
algorithms, setting new state-of-the-art results in multiple tasks and
datasets, as well as highlighting limitations inherent to PC that should be
addressed. Thanks to the efficiency of PCX, we are able to analyze larger
architectures than commonly used, providing baselines to galvanize community
efforts towards one of the main open problems in the field: scalability. The
code for PCX is available at \textit{https://github.com/liukidar/pcax}.


  We introduce the delayed Mittag-Leffler type matrix functions, delayed
fractional cosine, delayed fractional sine and use the Laplace transform to
obtain an analytical solution to the IVP for a Hilfer type fractional linear
time-delay system $D_{0,t}^{\mu,\nu}z\left( t\right) +Az\left( t\right) +\Omega
z\left( t-h\right) =f\left( t\right) $ of order $1<\mu<2$ and type
$0\leq\nu\leq1,$ with nonpermutable matrices $A$ and $\Omega$. Moreover, we
study Ulam-Hyers stability of the Hilfer type fractional linear time-delay
system. Obtained results extend those for Caputo and Riemann-Liouville type
fractional linear time-delay systems and new even for these fractional delay
systems.


  The physical situation of the collision and subsequent interaction of plane
gravitational waves in a Minkowski background gives rise to a well-posed
characteristic initial value problem in which initial data are specified on the
two null characteristics that define the wavefronts. In this paper, we analyse
how the Abel transform method can be used in practice to solve this problem for
the linear case in which the polarization of the two gravitational waves is
constant and aligned. We show how the method works for some known solutions,
where problems arise in other cases, and how the problem can always be solved
in terms of an infinite series if the spectral functions for the initial data
can be evaluated explicitly.


  In this paper we present simple example of propositional logic which has one
modal operator and is based on intuitionistic core. This system is very weak in
modal sense - e.g. rules of regularity or monotonicity do not hold. It has
complete semantics composed of possible worlds equipped with neighborhoods and
pre-order relation. We discuss certain restrictions imposed on those
structures. Also, we present characterization of axiom 4 known from logic S4.


  Recognizing the activities causing distraction in real-world driving
scenarios is critical for ensuring the safety and reliability of both drivers
and pedestrians on the roadways. Conventional computer vision techniques are
typically data-intensive and require a large volume of annotated training data
to detect and classify various distracted driving behaviors, thereby limiting
their efficiency and scalability. We aim to develop a generalized framework
that showcases robust performance with access to limited or no annotated
training data. Recently, vision-language models have offered large-scale
visual-textual pretraining that can be adapted to task-specific learning like
distracted driving activity recognition. Vision-language pretraining models,
such as CLIP, have shown significant promise in learning natural
language-guided visual representations. This paper proposes a CLIP-based driver
activity recognition approach that identifies driver distraction from
naturalistic driving images and videos. CLIP's vision embedding offers
zero-shot transfer and task-based finetuning, which can classify distracted
activities from driving video data. Our results show that this framework offers
state-of-the-art performance on zero-shot transfer and video-based CLIP for
predicting the driver's state on two public datasets. We propose both
frame-based and video-based frameworks developed on top of the CLIP's visual
representation for distracted driving detection and classification tasks and
report the results.


  All-optical switching networks have been considered a promising candidate for
the next generation data center networks thanks to its scalability in data
bandwidth and power efficiency. However, the bufferless nature and the nonzero
recon- figuration delay of optical switches remain great challenges in
deploying all-optical networks. This paper considers the end-to- end scheduling
for all-optical data center networks with no in- network buffer and nonzero
reconfiguration delay. A framework is proposed to deal with the nonzero
reconfiguration delay. The proposed approach constructs an adaptive variant of
any given scheduling policy. It is shown that if a scheduling policy guarantees
its schedules to have schedule weights close to the MaxWeight schedule (and
thus is throughput optimal in the zero reconfiguration regime), then the
throughput optimality is inherited by its adaptive variant (in any nonzero
reconfiguration delay regime). As a corollary, a class of adaptive variants of
the well known MaxWeight policy is shown to achieve throughput optimality
without prior knowledge of the traffic load. Further- more, through numerical
simulations, the simplest such policy, namely the Adaptive MaxWeight (AMW), is
shown to exhibit better delay performance than all prior work.


  We describe the Lorentzian version of the Kapovitch-Millson phase space for
polyhedra with $N$ faces. Starting with the Schwinger representation of the
$\mathfrak{su}(1,1)$ Lie algebra in terms of a pair of complex variables (or
spinor), we define the phase space for a space-like vectors in the
three-dimensional Minkowski space $\mathbb{R}^{1,2}$. Considering $N$ copies of
this space, quotiented by a closure constraint forcing the sum of those
3-vectors to vanish, we obtain the phase space for Lorentzian polyhedra with
$N$ faces whose normal vectors are space-like, up to Lorentz transformations.
We identify a generating set of $SU(1,1)$-invariant observables, whose flow by
the Poisson bracket generate both area-preserving and area-changing
deformations. We further show that the area-preserving observables form a
$\mathfrak{gl}_{N}(\mathbb{R})$ Lie algebra and that they generate a
$GL_{N}(\mathbb{R})$ action on Lorentzian polyhedra at fixed total area. That
action is cyclic and all Lorentzian polyhedra can be obtained from a totally
squashed polyhedron (with only two non-trivial faces) by a $GL_{N}(\mathbb{R})$
transformation. All those features carry on to the quantum level, where quantum
Lorentzian polyhedra are defined as $SU(1,1)$ intertwiners between unitary
$SU(1,1)$-representations from the principal continuous series. Those
$SU(1,1)$-intertwiners are the building blocks of spin network states in loop
quantum gravity in 3+1 dimensions for time-like slicing and the present
analysis applies to deformations of the quantum geometry of time-like
boundaries in quantum gravity, which is especially relevant to the study of
quasi-local observables and holographic duality.


  In the last decade, deep learning has achieved great success in machine
learning tasks where the input data is represented with different levels of
abstractions. Driven by the recent research in reinforcement learning using
deep neural networks, we explore the feasibility of designing a learning model
based on expert behaviour for complex, multidimensional tasks where reward
function is not available. We propose a novel method for apprenticeship
learning based on the previous research on supervised learning techniques in
reinforcement learning. Our method is applied to video frames from Atari games
in order to teach an artificial agent to play those games. Even though the
reported results are not comparable with the state-of-the-art results in
reinforcement learning, we demonstrate that such an approach has the potential
to achieve strong performance in the future and is worthwhile for further
research.


  Singular equations with rank-deficient Jacobians arise frequently in
algebraic computing applications. As shown in case studies in this paper,
direct and intuitive modeling of algebraic problems often results in
nonisolated singular solutions. The challenges become formidable when the
problems need to be solved from empirical data of limited accuracy. A newly
discovered low-rank Newton's iteration emerges as an effective regularization
mechanism that enables solving singular equations accurately with an error
bound in the same order as the data error. This paper elaborates applications
of new methods on solving singular algebraic equations such as singular linear
systems, polynomial GCD and factorizations as well as matrix defective
eigenvalue problems.


  The Koebe problem for univalent polynomials with real coefficients is fully
solved only for trinomials, which means that in this case the Koebe radius and
the extremal polynomial (extremizer) have been found. The general case remains
open, but conjectures have been formulated. The corresponding conjectures have
also been hypothesized for univalent polynomials with real coefficients and
$T$-fold rotational symmetry. This paper provides confirmation of these
hypotheses for trinomials $z + az^{T + 1} + bz^{2T + 1}$. Namely, the Koebe
radius is $r=4\cos^2 \frac{\pi(1+T)}{2+3T}$, and the only extremizer of the
Koebe problem is the trinomial \begin{gather*}
B^{(T)}(z)=z+\frac2{2+3T}\left(-T+(2+2T)\cos\frac{\pi T}{2+3T}\right)z^{1+T}+\\
+\frac1{2+3T}\left(2+T-2T\cos\frac{\pi T}{2+3T}\right)z^{1+2T}. \end{gather*}
  Key words and phrases: Koebe one-quarter theorem, Koebe radius, univalent
polynomial, trinomials with fold symmetry.


  Programming question and answer (Q & A) websites, such as Quora, Stack
Overflow, and Yahoo! Answer etc. helps us to understand the programming
concepts easily and quickly in a way that has been tested and applied by many
software developers. Stack Overflow is one of the most frequently used
programming Q\&A website where the questions and answers posted are presently
analyzed manually, which requires a huge amount of time and resource. To save
the effort, we present a topic modeling based technique to analyze the words of
the original texts to discover the themes that run through them. We also
propose a method to automate the process of reviewing the quality of questions
on Stack Overflow dataset in order to avoid ballooning the stack overflow with
insignificant questions. The proposed method also recommends the appropriate
tags for the new post, which averts the creation of unnecessary tags on Stack
Overflow.


  Human visual scene understanding is so remarkable that we are able to
recognize a revisited place when entering it from the opposite direction it was
first visited, even in the presence of extreme variations in appearance. This
capability is especially apparent during driving: a human driver can recognize
where they are when travelling in the reverse direction along a route for the
first time, without having to turn back and look. The difficulty of this
problem exceeds any addressed in past appearance- and viewpoint-invariant
visual place recognition (VPR) research, in part because large parts of the
scene are not commonly observable from opposite directions. Consequently, as
shown in this paper, the precision-recall performance of current
state-of-the-art viewpoint- and appearance-invariant VPR techniques is orders
of magnitude below what would be usable in a closed-loop system. Current
engineered solutions predominantly rely on panoramic camera or LIDAR sensing
setups; an eminently suitable engineering solution but one that is clearly very
different to how humans navigate, which also has implications for how naturally
humans could interact and communicate with the navigation system. In this paper
we develop a suite of novel semantic- and appearance-based techniques to enable
for the first time high performance place recognition in this challenging
scenario. We first propose a novel Local Semantic Tensor (LoST) descriptor of
images using the convolutional feature maps from a state-of-the-art dense
semantic segmentation network. Then, to verify the spatial semantic arrangement
of the top matching candidates, we develop a novel approach for mining
semantically-salient keypoint correspondences.


  A transversal of a hypergraph is a set of vertices intersecting each
hyperedge. We design and analyze new exponential-time algorithms to enumerate
all inclusion-minimal transversals of a hypergraph. For each fixed k>2, our
algorithms for hypergraphs of rank k, where the rank is the maximum size of a
hyperedge, outperform the previous best. This also implies improved upper
bounds on the maximum number of minimal transversals in n-vertex hypergraphs of
rank k>2. Our main algorithm is a branching algorithm whose running time is
analyzed with Measure and Conquer. It enumerates all minimal transversals of
hypergraphs of rank 3 on n vertices in time O(1.6755^n). Our algorithm for
hypergraphs of rank 4 is based on iterative compression. Our enumeration
algorithms improve upon the best known algorithms for counting minimum
transversals in hypergraphs of rank k for k>2 and for computing a minimum
transversal in hypergraphs of rank k for k>5.


  We have studied the intensity correlations between two orthogonally linearly
polarized components of a laser field propagating through a resonant atomic
medium. These experiments have been performed in a Rubidium atomic vapor. We
observe that the correlations between the orthogonally polarized components of
the laser beam are maximal in the absence of a magnetic field. The magnitude of
the correlations depends on the applied magnetic field, and the magnitude first
decreases and then increases with increasing magnetic field. Minimal
correlations and maximal rotation angles are observed at the same magnetic
fields. The width of the correlation function is directly proportional to the
excited state lifetime and inversely proportional to the Rabi frequency of
laser field. These results can be useful for improving optical magnetometers
and for optical field or atomic spin squeezing.


  The use of large-scale antenna arrays can bring substantial improvements in
energy and/or spectral efficiency to wireless systems due to the greatly
improved spatial resolution and array gain. Recent works in the field of
massive multiple-input multiple-output (MIMO) show that the user channels
decorrelate when the number of antennas at the base stations (BSs) increases,
thus strong signal gains are achievable with little inter-user interference.
Since these results rely on asymptotics, it is important to investigate whether
the conventional system models are reasonable in this asymptotic regime. This
paper considers a new system model that incorporates general transceiver
hardware impairments at both the BSs (equipped with large antenna arrays) and
the single-antenna user equipments (UEs). As opposed to the conventional case
of ideal hardware, we show that hardware impairments create finite ceilings on
the channel estimation accuracy and on the downlink/uplink capacity of each UE.
Surprisingly, the capacity is mainly limited by the hardware at the UE, while
the impact of impairments in the large-scale arrays vanishes asymptotically and
inter-user interference (in particular, pilot contamination) becomes
negligible. Furthermore, we prove that the huge degrees of freedom offered by
massive MIMO can be used to reduce the transmit power and/or to tolerate larger
hardware impairments, which allows for the use of inexpensive and
energy-efficient antenna elements.


  The Probability Ranking Principle states that the document set with the
highest values of probability of relevance optimizes information retrieval
effectiveness given the probabilities are estimated as accurately as possible.
The key point of the principle is the separation of the document set into two
subsets with a given level of fallout and with the highest recall. The paper
introduces the separation between two vector subspaces and shows that the
separation yields a more effective performance than the optimal separation into
subsets with the same available evidence, the performance being measured with
recall and fallout. The result is proved mathematically and exemplified
experimentally.


  Virtualization enables the building of multiple virtual networks over a
shared substrate. One of the challenges to virtualisation is efficient resource
allocation. This problem has been found to be NP hard. Therefore, most
approaches to it have not only proposed static solutions, but have also made
many assumptions to simplify it. In this paper, we propose a distributed,
autonomic and artificial intelligence based solution to resource allocation.
Our aim is to obtain self-configuring, selfoptimizing, self-healing and context
aware virtual networks


  Unsupervised speech representations have taken off, with benchmarks (SUPERB,
ZeroSpeech) demonstrating major progress on semi-supervised speech recognition,
speech synthesis, and speech-only language modelling. Inspiration comes from
the promise of ``discovering the phonemes'' of a language or a similar
low-bitrate encoding. However, one of the critical properties of phoneme
transcriptions is context-invariance: the phonetic context of a speech sound
can have massive influence on the way it is pronounced, while the text remains
stable. This is what allows tokens of the same word to have the same
transcriptions -- key to language understanding. Current benchmarks do not
measure context-invariance. We develop a new version of the ZeroSpeech ABX
benchmark that measures context-invariance, and apply it to recent
self-supervised representations. We demonstrate that the context-independence
of representations is predictive of the stability of word-level
representations. We suggest research concentrate on improving
context-independence of self-supervised and unsupervised representations.


  Future astrophysical surveys such as J-PAS will produce very large datasets,
which will require the deployment of accurate and efficient Machine Learning
(ML) methods. In this work, we analyze the miniJPAS survey, which observed
about 1 deg2 of the AEGIS field with 56 narrow-band filters and 4 ugri
broad-band filters. We discuss the classification of miniJPAS sources into
extended (galaxies) and point-like (e.g. stars) objects, a necessary step for
the subsequent scientific analyses. We aim at developing an ML classifier that
is complementary to traditional tools based on explicit modeling. In order to
train and test our classifiers, we crossmatched the miniJPAS dataset with SDSS
and HSC-SSP data. We trained and tested 6 different ML algorithms on the two
crossmatched catalogs. As input for the ML algorithms we use the magnitudes
from the 60 filters together with their errors, with and without the
morphological parameters. We also use the mean PSF in the r detection band for
each pointing. We find that the RF and ERT algorithms perform best in all
scenarios. When analyzing the full magnitude range of 15<r<23.5 we find
AUC=0.957 with RF when using only photometric information, and AUC=0.986 with
ERT when using photometric and morphological information. Regarding feature
importance, when using morphological parameters, FWHM is the most important
feature. When using photometric information only, we observe that broad bands
are not necessarily more important than narrow bands, and errors are as
important as the measurements. ML algorithms can compete with traditional
star/galaxy classifiers, outperforming the latter at fainter magnitudes (r>21).
We use our best classifiers, with and without morphology, in order to produce a
value added catalog available at https://j-pas.org/datareleases .


  We describe a quantum-assisted machine learning (QAML) method in which
multivariate data is encoded into quantum states in a Hilbert space whose
dimension is exponentially large in the length of the data vector. Learning in
this space occurs through applying a low-depth quantum circuit with a tree
tensor network (TTN) topology, which acts as an unsupervised feature extractor
to identify the most relevant quantum states in a data-driven fashion. This
unsupervised feature extractor then feeds a supervised linear classifier and
encodes the output in a small-dimensional quantum register. In contrast to
previous work on \emph{quantum-inspired} TTN classifiers, in which the
embedding map and class decision weights did not map the data to well-defined
quantum states, we present an approach that can be implemented on gate-based
quantum computing devices. In particular, we identify an embedding map with
accuracy similar to exponential machines (Novikov \emph{et al.},
arXiv:1605.03795), but which produces valid quantum states from classical data
vectors, and utilize manifold-based gradient optimization schemes to produce
isometric operations mapping quantum states to a register of qubits defining a
class decision. We detail methods for efficiently obtaining one- and two-point
correlation functions of the decision boundary vectors of the quantum model,
which can be used for model interpretability, as well as methods for obtaining
classifications from partial data vectors. Further, we show that the use of
isometric tensors can significantly aid in the human interpretability of the
correlation functions extracted from the decision weights, and may produce
models that are less susceptible to adversarial perturbations. We demonstrate
our methodologies in applications utilizing the MNIST handwritten digit dataset
and a multivariate timeseries dataset of human activity recognition.


  We study canonical filtrations of finite-dimensional associative algebras and
Lie algebras. These filtrations are defined via optimal destabilizing
one-parameter subgroups in the sense of geometric invariant theory (GIT), and
appear to be a new invariant of finite-dimensional algebras. We establish some
fundamental properties of these filtrations, and show that an algebra is
semisimple if and only if it is GIT semistable. We give a method to compute
canonical filtrations of algebras whose automorphism group or module of
derivations is sufficiently rich, and use this to compute these filtrations in
examples when the automorphism group contains a sufficiently large torus. We
also obtain some results on the structure of the associated graded algebra of
the canonical filtration of an associative algebra.


  Fractional partial differential equations (FDEs) are used to describe
phenomena that involve a "non-local" or "long-range" interaction of some kind.
Accurate and practical numerical approximation of their solutions is
challenging due to the dense matrices arising from standard discretization
procedures. In this paper, we begin to extend the well-established
computational toolkit of Discrete Exterior Calculus (DEC) to the fractional
setting, focusing on proper discretization of the fractional derivative. We
define a Caputo-like fractional discrete derivative, in terms of the standard
discrete exterior derivative operator from DEC, weighted by a measure of
distance between $p$-simplices in a simplicial complex. We discuss key
theoretical properties of the fractional discrete derivative and compare it to
the continuous fractional derivative via a series of numerical experiments.