  Low temperature specific heat has been investigated in a novel ternary
superconductor La_{3}Pd_{4}Ge_{4} with an U_{3}Ni_{4}Si_{4}-type structure
consisting of the alternating BaAl_{4} (ThCr_{2}Si_{2})- and AlB$_{2}$-type
layers. A comparative study with the related ThCr_{2}Si_{2}-type superconductor
LaPd_{2}Ge_{2}, one of the layers in La_{3}Pd_{4}Ge_{4}, is also presented.
  From the normal state specific heat, the Sommerfeld coefficient $\gamma_{n} =
27.0$ mJ/mol K^2 and the Debye temperature $\Theta_{\rm D}$ = 256 K are derived
for the La_{3}Pd_{4}Ge_{4}, while those for the LaPd_{2}Ge_{2} are $\gamma_{n}
=8.26$ mJ/mol K^2 and $\Theta_{\rm D}$ = 291 K. The La_{3}Pd_{4}Ge_{4} has
moderately high electronic density of state at the Fermi level. Electronic
contribution on the specific heat, $C_{\rm el}$, in each compound is well
described by the BCS behavior, suggesting that both of the La_{3}Pd_{4}Ge_{4}
and the LaPd_{2}Ge_{2} have fully opened isotropic gap in the superconducting
state.


  In sequential machine teaching, a teacher's objective is to provide the
optimal sequence of inputs to sequential learners in order to guide them
towards the best model. In this paper we extend this setting from current
static one-data-set analyses to learners which change their learning algorithm
or latent state to improve during learning, and to generalize to new datasets.
We introduce a multi-agent formulation in which learners' inner state may
change with the teaching interaction, which affects the learning performance in
future tasks. In order to teach such learners, we propose an optimal control
approach that takes the future performance of the learner after teaching into
account. This provides tools for modelling learners having inner states, and
machine teaching of meta-learning algorithms. Furthermore, we distinguish
manipulative teaching, which can be done by effectively hiding data and also
used for indoctrination, from more general education which aims to help the
learner become better at generalization and learning in new datasets in the
absence of a teacher.


  The set of core imputations of the assignment game forms a (non-finite)
distributive lattice. So far, efficient algorithms were known for computing
only its two extreme imputations; however, each of them maximally favors one
side and disfavors the other side of the bipartition, leading to inequitable
profit sharing. Another issue is that a sub-coalition consisting of one player
(or a set of players from the same side of the bipartition) can make zero
profit, therefore a core imputation is not obliged to give them any profit.
Hence core imputations make no fairness guarantee at the level of individual
agents. This raises the question of computing {\em more equitable core
imputations}.
  In this paper, we give combinatorial (i.e., the mechanism does not invoke an
LP-solver) polynomial time mechanisms for computing the leximin and leximax
core imputations for the assignment game. These imputations achieve
``fairness'' in different ways: whereas leximin tries to make poor agents more
rich, leximax tries to make rich agents less rich. In general, the two
imputations are different.
  Our mechanisms were derived by a suitable adaptation of the classical
primal-dual paradigm from combinatorial optimization. The ``engine'' driving
them involves recent insights, obtained via complementarity, into core
imputations \cite{Va.New-characterizations} and the pristine combinatorial
structure of matching. We have identified other natural games which could
benefit from our approach.


  In previous work we proved that for a SU(2,C) valued loop having the critical
degree of smoothness (one half of a derivative in the L^2 Sobolev sense), the
following are equivalent: (1) the Toeplitz and shifted Toeplitz operators
associated to the loop are invertible, (2) the loop has a triangular
factorization, and (3) the loop has a root subgroup factorization. For a loop g
satisfying these conditions, the Toeplitz determinant det(A(g)A(g^{-1})) and
shifted Toeplitz determinant det(A_1(g)A_1(g^{-1})) factor as products in root
subgroup coordinates. In this paper we observe that, at least in broad outline,
there is a relatively simple generalization to loops having values in SL(2,C).
The main novel features are that (1) root subgroup coordinates are now rational
functions, i.e. there is an exceptional set, and (2) the non-compactness of
SL(2,C) entails that loops are no longer automatically bounded, and this
(together with the exceptional set) complicates the analysis at the critical
exponent.


  Time resolved photometry of the long-period intermediate polar V1062 Tau
confirmed the presence of the previously reported orbital and spin periods, and
revealed the presence of a third one, corresponding to the beat of the two.
While the orbital periodicity was present throughout our data, only one of the
shorter periods was detectable at any given time. On a time-scale of ~90 days,
the short-period modulation in the light curve of the star changed three times
between the spin period and the beat. On longer time-scales, we report two
outbursts of V1062 Tau (the first to be recorded for this object) - both of
which were probably short, low-amplitude ones (dm ~1.2 mag). Our data also
suggest a brief low state phase in 2002 Jan. Thus, this system joins two
exclusive groups of intermediate polars: those undergoing short outbursts, and
those having low states. We propose that the alternations between the short
periods that modulate the light curve were caused by changes in the accretion
mode, from disc-fed accretion, to disc-overflow accretion. We further suggest
that these changes may have been triggered by changes in mass-transfer rate,
which were manifested by the low-state/outburst activity of the system.


  Let $(M,g)$ be a compact, boundaryless manifold of dimension $n$ with the
property that either (i) $n=2$ and $(M,g)$ has no conjugate points, or (ii) the
sectional curvatures of $(M,g)$ are nonpositive. Let $\Delta$ be the positive
Laplacian on $M$ determined by $g$. We study the $L^{2}\to{}L^{p}$ mapping
properties of a spectral cluster of $\sqrt{\Delta}$ of width $1/\log\lambda$.
Under the geometric assumptions above, \cite{berard77} B\'{e}rard obtained a
logarithmic improvement for the remainder term of the eigenvalue counting
function which directly leads to a $(\log\lambda)^{1/2}$ improvement for
H\"ormander's estimate on the $L^{\infty}$ norms of eigenfunctions. In this
paper we extend this improvement to the $L^p$ estimates for all
$p>\frac{2(n+1)}{n-1}$.


  In these notes we want, in addition to presenting some new results, to both
clean up and refine some reflections on a couple of articles published on paper
a few years ago, 2019-20. These papers concerned integral sufficient conditions
on $u\,,$ $\n u\,,$ and mixed, to guarantee the equality of the energy, EE in
the sequel, for solutions of the Navier-Stokes equations under the classical
non-slip boundary condition. Concerning the $\n u$ case a crucial role was
enjoyed by a previous well known Berselli and Chiodaroli's pioneering 2019 work
on the subject. The above three papers are the main sources of these notes.
References will be mostly concentrated on their direct relation to the above
papers at the time of pubblication. More recent results will be not stated
throughout the article. However, in the last section, the reader will be
suitably sent to the more recent bibliography. Below, we also turn back to the
innovative interpretation of some main parameters which allowed to overcome
their apparent incongruence. Non-Newtonian fluids were also considered in our
2019 paper, maybe for the first time in the above Berselli-Chiodaroli's
particular $\n u\,$ context. However we will stick mostly to the Newtonian case
since in the end we come to the conclusion that there are not particular
additional obstacles to extend the present results from Newtonian to
non-Newtonian fluids. Hence we avoid to go further in this direction.


  We reconsider our former determination of the chiral quark condensate
$\langle \bar q q \rangle$ from the related QCD spectral density of the
Euclidean Dirac operator, using our Renormalization Group Optimized
Perturbation (RGOPT) approach. Thanks to the recently available {\em complete}
five-loop QCD RG coefficients, and some other related four-loop results, we can
extend our calculations exactly to $N^4LO$ (five-loops) RGOPT, and partially to
$N^5LO$ (six-loops), the latter within a well-defined approximation accounting
for all six-loop contents exactly predictable from five-loops RG properties.
The RGOPT results overall show a very good stability and convergence, giving
primarily the RG invariant condensate, $\langle \bar q
q\rangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) \bar\Lambda_0 $,
$\langle\bar q q\rangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019})
\bar\Lambda_2 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=3) =
-(0.751_{-.010}^{+0.019}) \bar\Lambda_3 $, where $\bar\Lambda_{n_f}$ is the
basic QCD scale in the \overline{MS} scheme for $n_f$ quark flavors, and the
range spanned is our rather conservative estimated theoretical error. This
leads {\it e.g.} to $ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) =
-(273^{+7}_{-4}\pm 13)$ MeV, using the latest $\bar\Lambda_3$ values giving the
second uncertainties. We compare our results with some other recent
determinations. As a by-product of our analysis we also provide complete
five-loop and partial six-loop expressions of the perturbative QCD spectral
density, that may be useful for other purposes.


  A steady fluid flow, called microstreaming, can be generated in the vicinity
of a micro-bubble excited by ultrasound. In this article, we use this
phenomenon to assemble and power a microfabricated rotor at rotation speeds as
high as 625 rpm. The extractible power is estimated to be on the order of a few
femtowatts. A first series of experiments with uncontrolled rotor shapes is
presented, demonstrating the possibility of this novel actuation scheme. A
second series of experiments with 65 micron rotors micromanufactured in SU-8
resin are presented. Variables controlling the rotation speed and rotor
stability are investigated, such as the bubble diameter, the acoustic
excitation frequency and amplitude, and the rotor geometry. Finally, an outlook
is provided on developing this micro-rotor into a MEMS-based motor capable of
delivering tunable, infinitesimal rotary power at the microscale.


  Within a multiphase transport model, medium modifications of differential jet
shapes are investigated in Pb+Pb collisions at $\sqrt{s_{_{\rm NN}}}$ = 2.76
TeV. The differential jet shapes are significantly modified by the strong
interactions between jets and a partonic medium in Pb+Pb collisions relative to
that in p+p collisions. The modifications are slightly weakened by the
hadronization of coalescence, but strengthened by resonance decays in hadronic
rescatterings. Subleading jets display larger medium modifications than leading
jets, especially in central Pb+Pb collisions with large dijet asymmetries.
These behaviors of medium modifications of differential jet shapes reflect a
dynamical evolution of redistribution of jet energy inside a quenched jet cone
in high-energy heavy-ion collisions.


  The policy gradient theorem is defined based on an objective with respect to
the initial distribution over states. In the discounted case, this results in
policies that are optimal for one distribution over initial states, but may not
be uniformly optimal for others, no matter where the agent starts from.
Furthermore, to obtain unbiased gradient estimates, the starting point of the
policy gradient estimator requires sampling states from a normalized discounted
weighting of states. However, the difficulty of estimating the normalized
discounted weighting of states, or the stationary state distribution, is quite
well-known. Additionally, the large sample complexity of policy gradient
methods is often attributed to insufficient exploration, and to remedy this, it
is often assumed that the restart distribution provides sufficient exploration
in these algorithms. In this work, we propose exploration in policy gradient
methods based on maximizing entropy of the discounted future state
distribution. The key contribution of our work includes providing a practically
feasible algorithm to estimate the normalized discounted weighting of states,
i.e, the \textit{discounted future state distribution}. We propose that
exploration can be achieved by entropy regularization with the discounted state
distribution in policy gradients, where a metric for maximal coverage of the
state space can be based on the entropy of the induced state distribution. The
proposed approach can be considered as a three time-scale algorithm and under
some mild technical conditions, we prove its convergence to a locally optimal
policy. Experimentally, we demonstrate usefulness of regularization with the
discounted future state distribution in terms of increased state space coverage
and faster learning on a range of complex tasks.


  From classical mechanics to quantum field theory, the physical facts at one
point in space are held to be independent of those at other points in space. I
propose that we can usefully challenge this orthodoxy in order to explain
otherwise puzzling correlations at both cosmological and microscopic scales.


  Machine learning has celebrated a lot of achievements on computer vision
tasks such as object detection, but the traditionally used models work with
relatively low resolution images. The resolution of recording devices is
gradually increasing and there is a rising need for new methods of processing
high resolution data. We propose an attention pipeline method which uses two
staged evaluation of each image or video frame under rough and refined
resolution to limit the total number of necessary evaluations. For both stages,
we make use of the fast object detection model YOLO v2. We have implemented our
model in code, which distributes the work across GPUs. We maintain high
accuracy while reaching the average performance of 3-6 fps on 4K video and 2
fps on 8K video.


  We present a continuum theory of self-propelled particles, without alignment
interactions, in a momentum-conserving solvent. To address phase separation we
introduce a scalar concentration field $\phi$ with advective-diffusive
dynamics. Activity creates a contribution
$\Sigma_{ij}=-\zeta((\partial_i\phi)(\partial_j\phi)-(\nabla\phi)^{2}\delta_{ij}/d)$
to the deviatoric stress, where $\zeta$ is odd under time reversal and $d$ is
the number of spatial dimensions; this causes an effective interfacial tension
contribution that is negative for contractile swimmers. We predict that domain
growth then ceases at a length scale where diffusive coarsening is balanced by
active stretching of interfaces, and confirm this numerically. Thus the
interplay of activity and hydrodynamics is highly nontrivial, even without
alignment interactions.


  A brief historical synopsis of the connection between gauge theories and
string theory is given. Meson configurations known as k-strings are examined
from string theory via the gauge/gravity correspondence. Backgrounds dual to
k-strings in both 2+1 and 3+1 are discussed. The energy of k-strings to lowest
order consists of a tension term, proportional to the length, L, of the
k-string, i.e., the size of the mesons in the configuration. The first quantum
correction is a Coulombic 1/L correction, known as a Luscher term, plus a
constant. Acquiring tensions and Luscher terms via the gauge/gravity
correspondence is discussed.


  We extend the construction of Calabi-Yau manifolds to hypersurfaces in
non-Fano toric varieties, requiring the use of certain Laurent defining
polynomials, and explore the phases of the corresponding gauged linear sigma
models. The associated non-reflexive and non-convex polytopes provide a
generalization of Batyrev's original work, allowing us to construct novel pairs
of mirror models. We showcase our proposal for this generalization by examining
Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences,
and outline the more general class of so-defined geometries.


  Based on the amplitude behavior of quantum Rabi oscillation driven by a
coherent field we show that there exists an upper bound to the number of
logical operation performed on any single qubit within one error-correction
period of a quantum computation. We introduce a parameter to depict the maximum
of this number and estimate its decoherence limit. The analysis shows that a
generally accepted error-rate threshold of quantum logic gates limits the
parameter to so small a number that even a double of fault-tolerant Toffoli
gates can hardly be implemented reliably within one error-correction period.
This result suggests that the design of feasible fault-tolerant quantum
circuits is still an arduous task.


  Quadrature amplitude modulation (QAM) and a complementary representation of a
causal waveform have been used to develop a sidelobe-free pulse-compression
technique. Envelopes of radio-frequency (RF) pulses under study include both
unimodal (Laplacian, Gaussian, rectangular) and bimodal (Hermite-Gaussian)
shapes. Although the achievable compression gain is small (~2), the generation
and phase-invariant correlation processing of such created compressible pulses
can be accomplished with the use of low-complexity systems.


  Nonlinear and low-frequency solitary waves are investigated in the framework
of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor
effects and a double adiabatic model for plasma pressures. The organization of
these localized structures in terms of the propagation angle with respect to
the ambient magnetic field $\theta$ and the propagation velocity $C$ is
discussed. There are three types of regions in the $\theta-C$ plane that
correspond to domains where either solitary waves cannot exist, are organized
in branches, or have a continuous spectrum. A numerical method valid for the
two latter cases, that rigorously proves the existence of the waves, is
presented and used to locate many waves, including bright and dark structures.
Some of them belong to parametric domains where solitary waves were not found
in previous works. The stability of the structures has been investigated by
first performing a linear analysis of the background plasma state and second by
means of numerical simulations. They show that the cores of some waves can be
robust but, for the parameters considered in the analysis, the tails are
unstable. The substitution of the double adiabatic model by evolution equations
for the plasma pressures appears to suppress the instability in some cases and
to allow the propagation of the solitary waves during long times.


  Interacting with humans is one of the main challenges for mobile robots in a
human inhabited environment. To enable adaptive behavior, a robot needs to
recognize touch gestures and/or the proximity to interacting individuals.
Moreover, a robot interacting with two or more humans usually needs to
distinguish between them. However, this remains both a configuration and cost
intensive task. In this paper we utilize inexpensive Bluetooth Low Energy (BLE)
devices and propose an easy and configurable technique to enhance the robot's
capabilities to interact with surrounding people. In a noisy laboratory
setting, a mobile spherical robot is utilized in three proof-of-concept
experiments of the proposed system architecture. Firstly, we enhance the robot
with proximity information about the individuals in the surrounding
environment. Secondly, we exploit BLE to utilize it as a touch sensor. And
lastly, we use BLE to distinguish between interacting individuals. Results show
that observing the raw received signal strength (RSS) between BLE devices
already enhances the robot's interaction capabilities and that the provided
infrastructure can be facilitated to enable adaptive behavior in the future. We
show one and the same sensor system can be used to detect different types of
information relevant in human-robot interaction (HRI) experiments.


  KOI-227, KOI-319 and KOI-884 are identified here as (at least) two planet
systems. For KOI-319 and KOI-884, the observed Transit Timing Variations (TTVs)
of the inner transiting planet are used to detect an outer non-transiting
planet. The outer planet in KOI-884 is 2.6 Jupiter masses and has the orbital
period just narrow of the 3:1 resonance with the inner planet (orbital period
ratio 2.93). The distribution of parameters inferred from KOI-319.01's TTVs is
bimodal with either a 1.6 Neptune-mass (M_N) planet wide of the 5:3 resonance
(period 80.1 d) or a 1 Saturn-mass planet wide of the 7:3 resonance (period
109.2 d). The radial velocity measurements can be used in this case to
determine which of these parameter modes is correct. KOI-227.01's TTVs with
large 10 hour amplitude can be obtained for planetary-mass companions in
various major resonances. Based on the Bayesian evidence, the current TTV data
favor the outer 2:1 resonance with a companion mass 1.5 M_N, but this solution
implies a very large density of KOI-227.01. The inner and outer 3:2 resonance
solutions with sub-Neptune-mass companions are physically more plausible, but
will need to be verified.


  The aim of this note is to consider different notions for the Banach-Saks
property in locally solid vector lattices as an extension for the known
concepts of the Banach-Saks property in Banach lattices. We investigate
relations between them; in particular, we shall characterize spaces in which,
these notions agree.


  We present the orbital analysis of four response models, that succeed in
reproducing morphological features of NGC 1300. Two of them assume a planar
(2D) geometry with $\Omega_p$=22 and 16 \ksk respectively. The two others
assume a cylindrical (thick) disc and rotate with the same pattern speeds as
the 2D models. These response models reproduce most successfully main
morphological features of NGC 1300 among a large number of models, as became
evident in a previous study. Our main result is the discovery of three new
dynamical mechanisms that can support structures in a barred-spiral grand
design system. These mechanisms are presented in characteristic cases, where
these dynamical phenomena take place. They refer firstly to the support of a
strong bar, of ansae type, almost solely by chaotic orbits, then to the support
of spirals by chaotic orbits that for a certain number of pat tern revolutions
follow an n:1 (n=7,8) morphology, and finally to the support of spiral arms by
a combination of orbits trapped around L$_{4,5}$ and sticky chaotic orbits with
the same Jacobi constant. We have encountered these dynamical phenomena in a
large fraction of the cases we studied as we varied the parameters of our
general models, without forcing in some way their appearance. This suggests
that they could be responsible for the observed morphologies of many
barred-spiral galaxies. Comparing our response models among themselves we find
that the NGC 130 0 morphology is best described by a thick disc model for the
bar region and a 2D disc model for the spirals, with both components rotating
with the same pattern speed $\Omega_p$=16 \ksk !. In such a case, the whole
structure is included inside the corotation of the system. The bar is supported
mainly by regular orbits, while the spirals are supported by chaotic orbits.


  We study the phase dynamics and IV--characteristics of DC--SQUIDs consisting
of Josephson junctions with topologically nontrivial barriers, which cause the
appearance of Majorana bound state. Its comparative analysis with the trivial
case is performed. The influence of external electromagnetic radiation is
considered and the analysis of the amplitude dependence of the Shapiro step
widths is performed. We have shown that in nontrivial case the width of even
harmonic of Shapiro step is larger than width of odd harmonic. In the presence
of external dc magnetic field a beating state is realized in the DC--SQUID,
which leads to a resonance branch in the IV--curve. We show that in the
presence of resonance branch the maximum width of Shapiro step and periods of
its amplitude dependence are decreased in comparison of situation without
resonance in both trivial and nontrivial cases. We demonstrate that in the
presence of the resonance branch the chaotic behavior of IV--curve is reduced.


  We introduce the entanglement gauge describing the combined effects of local
operations and nonlocal unitary transformations on bipartite quantum systems.
The entanglement gauge exploits the invariance of nonlocal properties for
bipartite systems under local (gauge) transformations. This new formalism
yields observable effects arising from the gauge geometry of the bipartite
system. In particular, we propose a non-Abelian gauge theory realized via two
separated spatial modes of the quantized electromagnetic field manipulated by
linear optics. In this linear optical realization, a bi-partite state of two
separated spatial modes can acquire a non-Abelian geometric phase.


  A deep imaging survey covering the entire $23\arcmin$ diameter of the old
open cluster M67 to $V = 25$ has been carried out using the mosaic imager
(UHCam) on the Canada-France-Hawaii Telescope. The cluster color-magnitude
diagram (CMD) can be traced from stars on its giant branch at $M_{V} = +1$ down
through main sequence stars at least as faint as $M_{V} = 13.5$. Stars this low
in luminosity have masses below $0.15 M_{\odot}$. A modest white dwarf (WD)
cooling sequence is also observed commencing slightly fainter than $M_V = 10$
and, after correction for background galaxy and stellar field contamination,
terminating near $M_V = 14.6$. The observed WDs follow quite closely a
theoretical cooling sequence for $0.7 M_{\odot}$ pure carbon core WDs with
hydrogen-rich atmospheres (DA WDs). The cooling time to an $M_V$ of 14.6 for
such WDs is 4.3 Gyr which we take as the WD cooling age of the cluster. A fit
of a set of isochrones to the cluster CMD indicates a turnoff age of 4.0 Gyr.
The excellent agreement between these results suggests that ages derived from
white dwarf cooling should be considered as reliable as those from other dating
techniques. The WDs currently contribute about 9% of the total cluster mass but
the number seen appears to be somewhat low when compared with the number of
giants observed in the cluster.


  Graph neural networks are promising architecture for learning and inference
with graph-structured data. Yet difficulties in modelling the ``parts'' and
their ``interactions'' still persist in terms of graph classification, where
graph-level representations are usually obtained by squeezing the whole graph
into a single vector through graph pooling. From complex systems point of view,
mixing all the parts of a system together can affect both model
interpretability and predictive performance, because properties of a complex
system arise largely from the interaction among its components. We analyze the
intrinsic difficulty in graph classification under the unified concept of
``resolution dilemmas'' with learning theoretic recovery guarantees, and
propose ``SLIM'', an inductive neural network model for Structural Landmarking
and Interaction Modelling. It turns out, that by solving the resolution
dilemmas, and leveraging explicit interacting relation between component parts
of a graph to explain its complexity, SLIM is more interpretable, accurate, and
offers new insight in graph representation learning.


  The backreaction of inhomogeneities describes the effect of inhomogeneous
structure on average properties of the Universe. We investigate this approach
by testing the consistency of cosmological $N$-body simulations as non-linear
structure evolves. Using the Delaunay Tessellation Field Estimator (DTFE), we
calculate the kinematical backreaction $Q$ from simulations on different scales
in order to measure how much $N$-body simulations should be corrected for this
effect. This is the first step towards creating fully relativistic and
inhomogeneous $N$-body simulations. In this paper we compare the interpolation
techniques available in DTFE and illustrate the statistical dependence of $Q$
as a function of length scale.


  Reliably measuring the collinearity of bivariate data is crucial in
statistics, particularly for time-series analysis or ongoing studies in which
incoming observations can significantly impact current collinearity estimates.
Leveraging identities from Welford's online algorithm for sample variance, we
develop a rigorous theoretical framework for analyzing the maximal change to
the Pearson correlation coefficient and its p-value that can be induced by
additional data. Further, we show that the resulting optimization problems
yield elegant closed-form solutions that can be accurately computed by linear-
and constant-time algorithms. Our work not only creates new theoretical avenues
for robust correlation measures, but also has broad practical implications for
disciplines that span econometrics, operations research, clinical trials,
climatology, differential privacy, and bioinformatics. Software implementations
of our algorithms in Cython-wrapped C are made available at
https://github.com/marc-harary/sensitivity for reproducibility, practical
deployment, and future theoretical development.


  This paper builds a model of interactive belief hierarchies to derive the
conditions under which judging an arbitrage opportunity requires Bayesian
market participants to exercise their higher-order beliefs. As a Bayesian, an
agent must carry a complete recursion of priors over the uncertainty about
future asset payouts, the strategies employed by other market participants that
are aggregated in the price, other market participants' beliefs about the
agent's strategy, other market participants beliefs about what the agent
believes their strategies to be, and so on ad infinitum. Defining this infinite
recursion of priors -- the belief hierarchy so to speak -- along with how they
update gives the Bayesian decision problem equivalent to the standard asset
pricing formulation of the question. The main results of the paper show that an
arbitrage trade arises only when an agent updates his recursion of priors about
the strategies and beliefs employed by other market participants. The paper
thus connects the foundations of finance to the foundations of game theory by
identifying a bridge from market arbitrage to market participant belief
hierarchies.


  We extend our previous demonstration of the first on-sky primary mirror
segment closed-loop control on Keck using a vector-Zernike wavefront sensor
(vZWFS), which improved the Strehl ratio on the NIRC2 science camera by up to
10 percentage points. Segment co-phasing errors contribute to Keck contrast
limits and will be necessary to correct for the segmented Extremely Large
Telescopes and future space missions. The goal of the post-AO vZWFS on Keck is
to monitor and correct segment co-phasing errors in parallel with science
observations. The ZWFS is ideal for measuring phase discontinuities and is one
of the most sensitive WFSs, but has limited dynamic range. The Keck vZWFS
consists of a metasurface mask imposing two different phase shifts to
orthogonal polarizations, split into two pupil images, extending its dynamic
range. We report on the vZWFS closed-loop co-phasing performance and early work
towards understanding the interactions between the AO system and segment
phasing. We discuss a comparison of the AO performance when co-phasing by
aligning segment edges, as is currently done at Keck, compared with aligning to
the average phase over the segments, as is done by the vZWFS.


  We analyse the properties of the HI gas distribution in the Auriga project, a
set of magnetohydrodynamic cosmological simulations performed with the
moving-mesh code AREPO and a physics model for galaxy formation that succeeds
in forming realistic late-type galaxies in the 30 Milky Way-sized haloes
simulated in this project. We use a simple approach to estimate the neutral
hydrogen fraction in our simulation set, which treats low-density and
star-forming gas separately, and we explore two different prescriptions to
subtract the contribution of molecular hydrogen from the total HI content. The
HI gas in the vast majority of the systems forms extended discs although more
disturbed morphologies are present. Notwithstanding the general good agreement
with observed HI properties -- such as radial profiles and the mass-diameter
relation -- the Auriga galaxies are systematically larger and more gas-rich
than typical nearby galaxies. Interestingly, the amount of HI gas outside the
disc plane correlates with the star formation rate, consistent with a picture
where most of this extra-planar HI gas originates from a fountain-like flow.
Our findings are robust with respect to the different assumptions adopted for
computing the molecular hydrogen fraction and do not vary significantly over a
wide range of numerical resolution. The HI modelling introduced in this paper
can be used in future work to build artificial interferometric HI data cubes,
allowing an even closer comparison of the gas dynamics in simulated galaxies
with observations.


  We extend the construction of the Alcubierre-Natario class of warp drives to
an infinite class of spacetimes with similar properties. This is achieved by
utilising the Martel-Poisson charts which closely resemble the Weak
Painleve-Gullstrand form for various background metrics (Mink, AdS, dS). The
highlight of this construction is the non-flat intrinsic metric which in
three-dimensional spacetimes introduces conical singularities at the origin and
in higher dimensions generates a non-zero Ricci scalar for the spatial
hypersurfaces away from the origin. We analyse the expansion/contraction of
space and negative energy densities associated with this class of warp drives
and find interesting deviations due to the global imprints of the conical
defects. Several generalizations are also discussed.


  The finite-time control problem of quantum systems is investigated in this
paper. We first define finite-time stability and present a finite-time Lyapunov
stability criterion for finite-dimensional quantum systems in coherence vector
representation. Then, for two-level quantum systems, we design a continuous
non-smooth control law with a state-dependent fractional power and prove the
uniqueness of solutions of the system dynamics with the controller via the
concept of transversality. By combining the finite-time Lyapunov stability
criterion with the homogeneity theory, the finite-time convergence of the
system to an eigenstate of its internal Hamiltonian is proved. Numerical
results on a spin-1/2 system demonstrate the effectiveness of the proposed
finite-time stabilization control scheme.


  The energy bands of non-Hermitian systems exhibit nontrivial topological
features that arise from the complex nature of the energy spectrum. Under
periodic boundary conditions (PBC), the energy spectrum describes rather
generally closed loops in complex plane, characterized by integer nonzero
winding numbers. Such nontrivial winding provides the topological signature of
the non-Hermitian skin effect (NHSE), i.e. the macroscopic condensation of bulk
states at the lattice edges under open boundary conditions (OBC). In spite of
the great relevance of band winding in the non-Hermitian topological band
theory and the related NHSE, most of current results rely on tight-binding
models of non-Hermitian systems, while exact Bloch wave function analysis of
the NHSE and related topological band theory is still lacking. While
tight-binding models can correctly describe narrow-band electronic states with
a relatively weak degree non-Hermiticity, they are not suited to describe
high-energy wide-band electronic states and/or regimes corresponding to strong
non-Hermiticity. Here we consider the single-particle continuous Schr\"odinger
equation in a periodic potential, in which non-Hermiticity is introduced by an
imaginary vector potential in the equation, and show that the NHSE is
ubiquitous under OBC and characterized by a non-vanishing integer winding
number, even thought the energy spectrum under PBC always comprises an open
curve, corresponding to high-energy electronic states. We also show that the
interior of the PBC energy spectrum corresponds to the complex eigenenergies
sustaining localized (edge) states under semi-infinite boundary conditions.


  We present SN 2019tsf (ZTF19ackjszs) and SN 2019oys (ZTF19abucwzt). These two
stripped envelope Type Ib supernovae suddenly showed a (re-)brightening in
their late light curves. We investigate this in the context of circumstellar
material (CSM) interaction with previously ejected material, a phenomenon that
is unusual among SE SNe. We analyse observational data, consisting of optical
light curves and spectra. For SN 2019oys we also have detections in radio as
well as limits from UV and X-rays. Both light curves show spectacular
re-brightening after about 100 days. In the case of SN 2019tsf, the
re-brightening is followed by a new period of decline, and the spectra never
show signs of narrow emission lines that would indicate CSM interaction. On the
contrary, SN 2019oys made a spectral makeover from a Type Ib to a spectrum
clearly dominated by CSM interaction at the light curve brightening phase. Deep
spectra reveal a plethora of narrow high ionization lines, including coronal
lines, and the radio observations show strong emission. The rather similar
light curve behaviour indicate CSM interaction as the powering source. For SN
2019oys the evidence for a phase where the ejecta hit H-rich material, likely
ejected from the progenitor star, is conspicuous. We observe strong narrow
lines of H and He, but also a plethora of high ionization lines, including
coronal lines, revealing shock interaction. Spectral simulations of SN 2019oys
show two distinct density components, one with density > 1e9/cm3, dominated by
somewhat broader, low ionization lines of H I, He I, Na I and Ca II, and one
with narrow, high ionization lines at a density about 1e6 /cm3. The former is
strongly affected by electron scattering. The evidence for CSM interaction in
SN 2019oys is corroborated by detections in radio. On the contrary, for SN
2019tsf, we find little evidence in the spectra for any CSM interaction.


  In recent years, over-the-air aggregation has been widely considered in
large-scale distributed learning, optimization, and sensing. In this paper, we
propose the over-the-air federated policy gradient algorithm, where all agents
simultaneously broadcast an analog signal carrying local information to a
common wireless channel, and a central controller uses the received aggregated
waveform to update the policy parameters. We investigate the effect of noise
and channel distortion on the convergence of the proposed algorithm, and
establish the complexities of communication and sampling for finding an
$\epsilon$-approximate stationary point. Finally, we present some simulation
results to show the effectiveness of the algorithm.


  Due to technology advancements and circuits miniaturization, the study of
logic systems that can be applied to nanotechnology has been progressing
steadily. Among the creation of nanoeletronic circuits reversible and majority
logic stand out. This paper proposes the MPC (Majority Primitives Combination)
algorithm, used for majority logic synthesis. The algorithm receives a truth
table as input and returns a majority function that covers the same set of
minterms. The formulation of a valid output function is made with the
combination of previously optimized functions. As cost criteria the algorithm
searches for a function with the least number of levels, followed by the least
number of gates, inverters, and gate inputs. In this paper it's also presented
a comparison between the MPC and the exact_mig, currently considered the best
algorithm for majority synthesis. The exact_mig encode the exact synthesis of
majority functions using the number of levels and gates as cost criteria. The
MPC considers two additional cost criteria, the number of inverters and the
number of gate inputs, with the goal to further improve exact_mig results.
Tests have shown that both algorithms return optimal solutions for all
functions with 3 input variables. For functions with 4 inputs, the MPC is able
to further improve 42,987 (66%) functions and achieves equal results for 7,198
(11%). For functions with 5 input variables, out of a sample of 1,000 randomly
generated functions, the MPC further improved 477 (48%) functions and achieved
equal results for 112 (11%).


  A new implementation for the time evolution of the magnetic vector potential
is obtained for smoothed particle magnetohydrodynamics by considering the
induction equation in integral form. Galilean invariance is achieved through
proper gauge choice. This new discretisation is tested using the Orszag-Tang
MHD vortex in a 3D configuration. The corresponding conservative equations of
motion are derived, but are not found to solve the MHD equations in the
continuum limit. Tests are performed using a hybrid approach instead, whereby
the equations of motion based on the magnetic field instead of vector potential
are used. Test results experience the same numerical instability as with the
Price (2010) formulation. We conclude that this new formulation is non-viable.


  We study some spectral properties of a simple two-dimensional model for small
angle defects in crystals and alloys. Starting from a periodic potential $V
\colon \R^2 \to \R$, we let $V_\theta(x,y) = V(x,y)$ in the right half-plane
$\{x \ge 0\}$ and $V_\theta = V \circ M_{-\theta}$ in the left half-plane $\{x
< 0\}$, where $M_\theta \in \R^{2 \times 2}$ is the usual matrix describing
rotation of the coordinates in $\R^2$ by an angle $\theta$. As a main result,
it is shown that spectral gaps of the periodic Schr\"odinger operator $H_0 =
-\Delta + V$ fill with spectrum of $R_\theta = -\Delta + V_\theta$ as $0 \ne
\theta \to 0$. Moreover, we obtain upper and lower bounds for a quantity
pertaining to an integrated density of states measure for the surface states.


  We develop a general energy method for proving the optimal time decay rates
of the solutions to the dissipative equations in the whole space. Our method is
applied to classical examples such as the heat equation, the compressible
Navier-Stokes equations and the Boltzmann equation. In particular, the optimal
decay rates of the higher-order spatial derivatives of solutions are obtained.
The negative Sobolev norms are shown to be preserved along time evolution and
enhance the decay rates. We use a family of scaled energy estimates with
minimum derivative counts and interpolations among them without linear decay
analysis.


  We analyze the charmless two-body $B\to VP$ decays in the
soft-collinear-effective-theory (SCET), where $V(P)$ denotes a light vector
(pseudoscalar) meson. Using the current experimental data, we find two
solutions in $\chi^2$ fit for the 16 non-perturbative inputs responsible for
the 87 $B\to PP$ and $B\to VP$ decay channels in SU(3) symmetry. Chirally
enhanced penguins can only change several charming penguins sizably, since they
share the same topology. The (S-P)(S+P) annihilation penguins in the
perturbative QCD approach have the same topology with charming penguins in
SCET, which play an important role in direct CP asymmetries.


  A locally decodable code (LDC) C:{0,1}^k -> {0,1}^n is an error correcting
code wherein individual bits of the message can be recovered by only querying a
few bits of a noisy codeword. LDCs found a myriad of applications both in
theory and in practice, ranging from probabilistically checkable proofs to
distributed storage. However, despite nearly two decades of extensive study,
the best known constructions of O(1)-query LDCs have super-polynomial
blocklength.
  The notion of relaxed LDCs is a natural relaxation of LDCs, which aims to
bypass the foregoing barrier by requiring local decoding of nearly all
individual message bits, yet allowing decoding failure (but not error) on the
rest. State of the art constructions of O(1)-query relaxed LDCs achieve
blocklength n = O(k^{1+ \gamma}) for an arbitrarily small constant \gamma.
  We prove a lower bound which shows that O(1)-query relaxed LDCs cannot
achieve blocklength n = k^{1+ o(1)}. This resolves an open problem raised by
Goldreich in 2004.


  In this paper, we establish Pogorelov type $C^2$ estimates for semi-convex
admissible solutions to the Dirichlet problem of $k$-Hessian equation with
general right hand side. Under some sufficient conditions, we apply such
estimates to obtain rigidity theorems for semi-convex admissible solutions of
$k$-Hessian equation, which can be seen as a improvement of Li-Ren-Wang and
Chu-Dinew's rigidity theorem for $k$-Hessian equation. When $2k>n$, we also
obtain Pogorelov type $C^2$ estimates for admissible solutions to the Dirichlet
problem of $k$-Hessian equation based on a concavity inequality, which is
inspired by the Ren-Wang's work on the global curvature estimates for the $n-1$
and $n-2$ curvature equation.


  The spins of the low-spin Ir4+ (S = 1/2, d5) ions at the octahedral sites of
the oxides Sr3NiIrO6, Sr2IrO4 and Na2IrO3 exhibit preferred orientations with
respect to their IrO6 octahedra. We evaluated the magnetic anisotropies of
these S = 1/2 ions on the basis of DFT calculations including spin-orbit
coupling (SOC), and probed their origin by performing perturbation theory
analyses with SOC as perturbation within the LS coupling scheme. The observed
spin orientations of Sr3NiIrO6 and Sr2IrO4 are correctly predicted by DFT
calculations, and are accounted for by the perturbation theory analysis. As for
the spin orientation of Na2IrO3, both experimental studies and DFT calculations
have not been unequivocal. Our analysis reveals that the Ir4+ spin orientation
of Na2IrO3 should have nonzero components along the c- and a-axes directions.
The spin orientations determined by DFT calculations are sensitive to the
accuracy of the crystal structures employed, which is explained by perturbation
theory analyses when interactions between adjacent Ir4+ ions are taken into
consideration. There are indications implying that the 5d electrons of Na2IrO3
are less strongly localized compared with those of Sr3NiIrO6 and Sr2IrO4. This
implication was confirmed by showing that the Madelung potentials of the Ir4+
ions are less negative in Na2IrO3 than in Sr3NiIrO6, Sr2IrO4. Most
transition-metal S = 1/2 ions do have magnetic anisotropies because the SOC
induces interactions among their crystal-field split d-states, and the
associated mixing of the states modifies only the orbital parts of the states.
This finding cannot be mimicked by a spin Hamiltonian because this model
Hamiltonian lacks the orbital degree of freedom, thereby leading to the
spin-half syndrome. The spin-orbital entanglement for the 5d spin-half ions
Ir4+ is not as strong as has been assumed lately.


  Dictionary learning is a key tool for representation learning, that explains
the data as linear combination of few basic elements. Yet, this analysis is not
amenable in the context of graph learning, as graphs usually belong to
different metric spaces. We fill this gap by proposing a new online Graph
Dictionary Learning approach, which uses the Gromov Wasserstein divergence for
the data fitting term. In our work, graphs are encoded through their nodes'
pairwise relations and modeled as convex combination of graph atoms, i.e.
dictionary elements, estimated thanks to an online stochastic algorithm, which
operates on a dataset of unregistered graphs with potentially different number
of nodes. Our approach naturally extends to labeled graphs, and is completed by
a novel upper bound that can be used as a fast approximation of Gromov
Wasserstein in the embedding space. We provide numerical evidences showing the
interest of our approach for unsupervised embedding of graph datasets and for
online graph subspace estimation and tracking.


  Rapidly scaling screening, testing and quarantine has shown to be an
effective strategy to combat the COVID-19 pandemic. We consider the application
of deep learning techniques to distinguish individuals with COVID from
non-COVID by using data acquirable from a phone. Using cough and context
(symptoms and meta-data) represent such a promising approach. Several
independent works in this direction have shown promising results. However, none
of them report performance across clinically relevant data splits.
Specifically, the performance where the development and test sets are split in
time (retrospective validation) and across sites (broad validation). Although
there is meaningful generalization across these splits the performance
significantly varies (up to 0.1 AUC score). In addition, we study the
performance of symptomatic and asymptomatic individuals across these three
splits. Finally, we show that our model focuses on meaningful features of the
input, cough bouts for cough and relevant symptoms for context. The code and
checkpoints are available at https://github.com/WadhwaniAI/cough-against-covid


  Improving the speed and fidelity of quantum logic gates is essential to reach
quantum advantage with future quantum computers. However, fast logic gates lead
to increased leakage errors in superconducting quantum processors based on
qubits with low anharmonicity, such as transmons. To reduce leakage errors, we
propose and experimentally demonstrate two new analytical methods, Fourier
ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and
higher-derivative (HD) DRAG, both of which enable shaping single-qubit control
pulses in the frequency domain to achieve stronger suppression of leakage
transitions compared to previously demonstrated pulse shapes. Using the new
methods to suppress the $ef$-transition of a transmon qubit with an
anharmonicity of -212 MHz, we implement $R_X(\pi/2)$-gates with a leakage error
below $3.0 \times 10^{-5}$ down to a gate duration of 6.25 ns, which
corresponds to a 20-fold reduction in leakage compared to a conventional Cosine
DRAG pulse. Employing the FAST DRAG method, we further achieve an error per
gate of $(1.56 \pm 0.07)\times 10^{-4}$ at a 7.9-ns gate duration,
outperforming conventional pulse shapes both in terms of error and gate speed.
Furthermore, we study error-amplifying measurements for the characterization of
temporal microwave control pulse distortions, and demonstrate that
non-Markovian coherent errors caused by such distortions may be a significant
source of error for sub-10-ns single-qubit gates unless corrected using
predistortion.


  We have shown theoretically that a combination of cross-section modulation
and acoustic mismatch in the core-shell Si/Ge nanowires can lead to a drastic
reduction of the thermal conductivity. Our calculations, which utilized two
different models - five-parameter Born-von Karman and six-parameter
valence-force field - for the lattice vibrations, indicate that the room
temperature thermal conductivity of Si/Ge cross-section modulated nanowires is
almost three orders of magnitude lower than that of bulk Si. Thermal flux in
the modulated nanowires is suppressed by an order of magnitude in comparison
with generic Si nanowires. The effect is explained by modification of the
phonon spectra in modulated nanowires leading to decrease of the phonon group
velocities and localization of certain phonon modes in narrow or wide nanowire
segments. The thermal conductivity inhibition is achieved in nanowires without
additional surface roughness and, thus, potentially reducing degradation of the
electron transport. Our results suggest that the acoustically mismatched
cross-section modulated nanowires are promising candidates for thermoelectric
applications.


  We study the recently reported excess in the diphoton resonance search by
ATLAS and CMS. We investigate the available parameter space in the combined
run-1 and run-2 diphoton data and study its interpretation in terms of a
singlet scalar field which possibly mixes with the Standard Model Higgs boson.
We show that the mixing angle is already strongly constrained by high-mass
Higgs searches in the diboson channel, and by Higgs coupling measurements.
While a broad resonance is slightly favored, we argue that the signal is
consistent with a narrow-width singlet which couples to colored and
electromagnetically-charged vector-like fermions. Dijet signals are predicted
and may be visible in upcoming analyses. Allowing for additional decay modes
could explain a broader resonance, however, we show that monojet searches
disfavor a large invisible width. Finally, we comment on the possible relation
of this scenario to the naturalness problem.


  In this work we prove the existence of an autonomous Hamiltonian vector field
in W^{1,r}(T^d;R^d) with r< d-1and d>=4 for which the associated transport
equation has non-unique positive solutions. As a consequence of Ambrosio
superposition principle, we show that this vector field has non-unique integral
curves with a positive Lebesgue measure set of initial data and moreover we
show that the Hamiltonian is not constant along these integral curves.


  We give a sufficient and necessary condition for a p-adic integer to have
p-th root in the ring of p-adic integers. The same condition holds clearly for
residues modulo p^k. We give a proof that Fermat's last theorem is false for
p-adic integers and for residues mod p^k.


  We study the quantum dynamics of polygonal rare-earth molecular clusters with
Ising-type ion magnetization. It is shown that the ground state of such systems
is a non-magnetic quasi-doublet of states with oppositely twisted ion spins.
The states differ in sign of toroidal moment, which is a natural physical
quantity to characterize the spin chirality of the clusters. The possibility of
macroscopic quantum tunneling of toroidal moment between the states is
predicted. The effects of an external current is considered, both in
equilibrium and in the frames of the Landau-Zener-St\"uckelberg tunneling
model. The special treatment is given for the most important case of triangular
rare-earth clusters.


  Lattice relaxation in twistronic bilayers with close lattice parameters and
almost perfect crystallographic alignment of the layers results in the
transformation of moir\'e pattern into a sequence of preferential stacking
domains and domain wall networks. Here, we show that reconstructed moir\'e
superlattices of the perfectly aligned heterobilayers of same-chalcogen
transition metal dichalcogenides have broken-symmetry structures featuring
twisted nodes ('twirls') of domain wall networks. Analysing
twist-angle-dependences of strain characteristics for the broken-symmetry
structures we show that the formation of twirl reduces amount of hydrostatic
strain around the nodes, potentially, reducing their infuence on the band edge
energies of electrons and holes.


  We consider a rank one group $G = \langle A,B \rangle $ which acts cubically
on a module $V$, this means $[V,A,A,A] =0$ but $[V,G,G,G] \ne 0$. We have to
distinguish whether the group $A_0 :=C_A([V,A]) \cap C_A(V/C_V(A))$ is trivial
or not. We show that if $A_0$ is trivial, $G$ is a rank one group associated to
a quadratic Jordan division algebra. If $A_0$ is not trivial (which is always
the case if $A$ is not abelian), then $A_0$ defines a subgroup $G_0$ of $G$
which acts quadratically on $V$. We will call $G_0$ the \textit{quadratic
kernel} of $G$. By a result of Timmesfeld we have $G_0 \cong \SL_2(J,R)$ for a
ring $R$ and a special quadratic Jordan division algebra $J \subseteq R$. We
show that $J$ is either a Jordan algebra contained in a commutative field or a
hermitian Jordan algebra. In the second case $G$ is the special unitary group
of a pseudo-quadratic form $\pi$ of Witt index $1$, in the first case $G$ is
the rank one group for a Freudenthal triple system. These results imply that if
$(V,G)$ is a quadratic pair such that no two distinct root groups commute and
$\characteristic V\ne 2,3$, then $G$ is a unitary group or an exceptional
algebraic group.


  Whereas much work in the mathematical literature on quantum chaos has focused
on phenomena such as quantum ergodicity and scarring, relatively little is
known at the rigorous level about the existence of eigenfunctions whose
morphology is more complex. Quantum systems whose dynamics is intermediate
between certain regimes - for example, at the transition between Anderson
localized and delocalized eigenfunctions, or in systems whose classical
dynamics is intermediate between integrability and chaos - have been
conjectured in the physics literature to have eigenfunctions exhibiting
multifractal, self-similar structure. To-date, no rigorous mathematical results
have been obtained about systems of this kind in the context of quantum chaos.
We give here the first rigorous proof of the existence of multifractal
eigenfunctions for a widely studied class of intermediate quantum systems.
Specifically, we derive an analytical formula for the Renyi entropy associated
with the eigenfunctions of arithmetic Seba billiards, in the semiclassical
limit, as the associated eigenvalues tend to infinity. We also prove
multifractality of the ground state for more general, non-arithmetic billiards
and show that the fractal exponent in this regime satisfies a symmetry
relation, similar to the one predicted in the physics literature, by
establishing a connection with the functional equation for Epstein's zeta
function.


  The long-time behavior of solutions to the initial value problem for the
Korteweg-de Vries equation on the whole line, with general initial conditions
has been described uniformly using five different asymptotic forms. Four of
these asymptotic forms were expected: the quiescent behavior (for |x| very
large), a soliton region (in which the solution behaves as a collection of
isolated solitary waves), a self-similar region (in which the solution is
described via a Painlev\'e transcendent), and a similarity region (where the
solution behaves as a simple trigonometric function of the quantities t and
x/t). A fifth asymptotic form, lying between the self-similar (Painlev\'e) and
the similarity one, has been described in terms of classical elliptic
functions. An integral of elliptic type, giving an explicit representation of
the phase, has appeared in this context. The same integral has appeared in the
table of integrals by Gradshteyn and Ryzhik. Our goal here is to confirm the
validity of this entry.


  In this paper, we study the existence and uniqueness of weak solution of a
nonlinear poroelasticity model. To better describe the proccess of deformation
and diffusion underlying in the original model, we firstly reformulate the
nonlinear poroelasticity by a multiphysics approach. Then, we adopt the similar
technique of proving the well-posedness of nonlinear Stokes equations to prove
the existence and uniqueness of weak solution of a nonlinear poroelasticity
model. And we strictly prove the growth, coercivity and monotonicity of the
nonlinear stress-strain relation, give the energy estimates and use Schauder's
fixed point theorem to show the existence and uniqueness of weak solution of
the nonlinear poroelasticity model.


  Motivated by the residual type neural networks (ResNet), this paper studies
optimal control problems constrained by a non-smooth integral equation. Such
non-smooth equations, for instance, arise in the continuous representation of
fractional deep neural networks (DNNs). Here the underlying non-differentiable
function
  is the ReLU or max function. The control enters in a nonlinear and
multiplicative manner and we additionally impose control constraints. Because
of the presence of the non-differentiable mapping, the application of standard
adjoint calculus is excluded. We derive strong stationary conditions by relying
on the limited differentiability properties of the non-smooth map. While
traditional approaches smoothen the non-differentiable function, no such
smoothness is retained in our final strong stationarity system. Thus, this work
also closes a gap which currently exists in continuous neural networks with
ReLU type activation function.


  The purpose of this short problem paper is to raise an extremal question on
set systems which seems to be natural and appealing. Our question is: which set
systems of a given size maximise the number of $(n+1)$-element chains in the
power set $\mathcal{P}(\{1,2,\dots,n\})$? We will show that for each fixed
$\alpha>0$ there is a family of $\alpha 2^n$ sets containing $(\alpha+o(1))n!$
such chains, and that this is asymptotically best possible. For smaller set
systems we are unable to answer the question. We conjecture that a `tower of
cubes' construction is extremal. We finish by mentioning briefly a connection
to an extremal problem on posets and a variant of our question for the grid
graph.


  We investigate the remarkable role of position dependent damping in
determining the parametric regions of symmetry breaking in nonlinear
$\cal{PT}$-symmetric systems. We illustrate the nature of $\cal{PT}$-symmetry
preservation and breaking with reference to a remarkable integrable scalar
nonlinear system. In the two dimensional cases of such position dependent
damped systems, we unveil the existence of a class of novel
bi-$\cal{PT}$-symmetric systems which have two fold $\cal{PT}$ symmetries. We
analyze the dynamics of these systems and show how symmetry breaking occurs,
that is whether the symmetry breaking of the two $\cal{PT}$ symmetries occurs
in pair or occurs one by one. The addition of linear damping in these
nonlinearly damped systems induces competition between the two types of
damping. This competition results in a $\cal{PT}$ phase transition in which the
$\cal{PT}$ symmetry is broken for lower loss/gain strength and is restored by
increasing the loss/gain strength. We also show that by properly designing the
form of the position dependent damping, we can tailor the $\cal{PT}$-symmetric
regions of the system.


  We analyze the distinguishability norm on the states of a multi-partite
system, defined by local measurements. Concretely, we show that the norm
associated to a tensor product of sufficiently symmetric measurements is
essentially equivalent to a multi-partite generalisation of the non-commutative
2-norm (aka Hilbert-Schmidt norm): in comparing the two, the constants of
domination depend only on the number of parties but not on the Hilbert spaces
dimensions.
  We discuss implications of this result on the corresponding norms for the
class of all measurements implementable by local operations and classical
communication (LOCC), and in particular on the leading order optimality of
multi-party data hiding schemes.


  Topological spin structures with transformable shapes may have potential
implications on data storage and computation. Here, we demonstrate that a
square cellular skyrmion on an artificial grid pinning pattern can be
manipulated by programmed current pulses. We find that parallel short pulses
could result in the elongation of the skyrmion mainly in the current direction,
while parallel long pulses are able to induce the elongation in the direction
perpendicular to the current due to the intrinsic skyrmion Hall effect.
Consequently, a programmed sequence of parallel pulses could lead to the
transformation of the skyrmion to I-, L-, and Z-shaped polyomino-like
structures without affecting the topological charge. In addition, we find that
orthogonal pulses could lead to the transformation to more complex
polyomino-like structures, including the T-shaped and irregular ones.
Particularly, when a small T-shaped structure is formed, the topological charge
of the system is found to be non-integer due to incomplete compensation of
local topological charge densities; however, the T-shaped structure is stable
on the attractive pinning pattern. Our results offer an effective way to create
polyomino-like spin structures toward functional applications.


  With the rise of social networks, information on the internet is no longer
solely organized by web pages. Rather, content is generated and shared among
users and organized around their social relations on social networks. This
presents new challenges to information retrieval systems. On a social network
search system, the generation of result sets not only needs to consider keyword
matches, like a traditional web search engine does, but it also needs to take
into account the searcher's social connections and the content's visibility
settings. Besides, search ranking should be able to handle both textual
relevance and the rich social interaction signals from the social network. In
this paper, we present our solution to these two challenges by first
introducing a social retrieval mechanism, and then investigate novel deep
neural networks for the ranking problem. The retrieval system treats social
connections as indexing terms, and generates meaningful results sets by biasing
towards close social connections in a constrained optimization fashion. The
result set is then ranked by a deep neural network that handles textual and
social relevance in a two-tower approach, in which personalization and textual
relevance are addressed jointly. The retrieval mechanism is deployed on
Facebook and is helping billions of users finding postings from their
connections efficiently. Based on the postings being retrieved, we evaluate our
two-tower neutral network, and examine the importance of personalization and
textual signals in the ranking problem.


  We introduce a model of the growth of a single microorganism in a
self-cycling fermentor in which an arbitrary number of resources are limiting,
and impulses are triggered when the concentration of one specific substrate
reaches a predetermined level. The model is in the form of a system of
impulsive differential equations. We consider the operation of the reactor to
be successful if it cycles indefinitely without human intervention and derive
conditions for this to occur. In this case, the system of impulsive
differential equations has a periodic solution. We show that success is
equivalent to the convergence of solutions to this periodic solution. We
provide conditions that ensure that a periodic solution exists. When it exists,
it is unique and attracting. However, we also show that whether a solution
converges to this periodic solution, and hence whether the model predicts that
the reactor operates successfully, is initial condition dependent. The analysis
is illustrated with numerical examples.


  We show that in the presence of sufficiently strong tau neutrino
annihilations into majorons, the primordial nucleosynthesis constraints can not
rule out tau neutrino masses in the MeV range.


  Motivated by an observational study of the effect of hospital ward versus
intensive care unit admission on severe sepsis mortality, we develop methods to
address two common problems in observational studies: (1) when there is a lack
of covariate overlap between the treated and control groups, how to define an
interpretable study population wherein inference can be conducted without
extrapolating with respect to important variables; and (2) how to use
randomization inference to form confidence intervals for the average treatment
effect with binary outcomes. Our solution to problem (1) incorporates existing
suggestions in the literature while yielding a study population that is easily
understood in terms of the covariates themselves, and can be solved using an
efficient branch-and-bound algorithm. We address problem (2) by solving a
linear integer program to utilize the worst case variance of the average
treatment effect among values for unobserved potential outcomes that are
compatible with the null hypothesis. Our analysis finds no evidence for a
difference between the sixty day mortality rates if all individuals were
admitted to the ICU and if all patients were admitted to the hospital ward
among less severely ill patients and among patients with cryptic septic shock.
We implement our methodology in R, providing scripts in the supplementary
material.


  Leveraging advanced reasoning capabilities and extensive world knowledge of
large language models (LLMs) to construct generative agents for solving complex
real-world problems is a major trend. However, LLMs inherently lack embodiment
as humans, resulting in suboptimal performance in many embodied decision-making
tasks. In this paper, we introduce a framework for building human-like
generative driving agents using post-driving self-report driving-thinking data
from human drivers as both demonstration and feedback. To capture high-quality,
natural language data from drivers, we conducted urban driving experiments,
recording drivers' verbalized thoughts under various conditions to serve as
chain-of-thought prompts and demonstration examples for the LLM-Agent. The
framework's effectiveness was evaluated through simulations and human
assessments. Results indicate that incorporating expert demonstration data
significantly reduced collision rates by 81.04\% and increased human likeness
by 50\% compared to a baseline LLM-based agent. Our study provides insights
into using natural language-based human demonstration data for embodied tasks.
The driving-thinking dataset is available at
\url{https://github.com/AIR-DISCOVER/Driving-Thinking-Dataset}.


  We consider an adaptive finite element method with arbitrary but fixed
polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based
residual error estimator. Based on the modified maximum criterion from [Diening
et al, Found. Comput. Math. 16, 2016], we propose a goal-oriented adaptive
algorithm and prove that it is instance optimal. More precisely, the goal-error
is bounded by the product of the total errors (being the sum of energy error
plus data oscillations) of the primal and the dual problem, and the proposed
algorithm is instance optimal with respect to this upper bound. Numerical
experiments underline our theoretical findings.


  We present a novel method to compute the relative pose of multi-camera
systems using two affine correspondences (ACs). Existing solutions to the
multi-camera relative pose estimation are either restricted to special cases of
motion, have too high computational complexity, or require too many point
correspondences (PCs). Thus, these solvers impede an efficient or accurate
relative pose estimation when applying RANSAC as a robust estimator. This paper
shows that the 6DOF relative pose estimation problem using ACs permits a
feasible minimal solution, when exploiting the geometric constraints between
ACs and multi-camera systems using a special parameterization. We present a
problem formulation based on two ACs that encompass two common types of ACs
across two views, i.e., inter-camera and intra-camera. Moreover, the framework
for generating the minimal solvers can be extended to solve various relative
pose estimation problems, e.g., 5DOF relative pose estimation with known
rotation angle prior. Experiments on both virtual and real multi-camera systems
prove that the proposed solvers are more efficient than the state-of-the-art
algorithms, while resulting in a better relative pose accuracy. Source code is
available at https://github.com/jizhaox/relpose-mcs-depth.


  In this paper, we derive the first order approximate symmetries for the Harry
Dym equation by the method of approximate transformation groups proposed by
Baikov, Gaszizov and Ibragimov. Moreover, we investigate the structure of the
Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the
one-dimensional optimal system of subalgebras as well as point out some
approximately differential invariants with respect to the generators of Lie
algebra and optimal system.


  We present an alternative method for reconstructing a velocity-delay map in
reverberation mapping (RM) based on the pixon algorithm initially proposed for
image reconstruction by Pina & Puetter (1993). The pixon algorithm allows for a
variable pixon basis to adjust resolution of each image pixel according the
information content in that pixel, which therefore enables the algorithm to
make the best possible use of measured data. The final optimal pixon basis
functions would be those that minimize the number of pixons while still
providing acceptable descriptions to data within the accuracy allowed by
noises. We adapt the pixon algorithm to RM analysis and develop a generic
framework to implement the algorithm. Simulation tests and comparisons with the
widely used maximum entropy method demonstrate the feasibility and high
performance of our pixon-based RM analysis. This paper serves as an
introduction to the framework and the application to velocity-unresolved RM. An
extension to velocity-resolved cases will be presented in a companion paper.


  We use spatial spin separation by a magnetic focusing technique to probe the
polarization of quantum point contacts. The point contacts are fabricated from
p-type GaAs/AlGaAs heterostructures. A finite polarization is measured in the
low-density regime, when the conductance of a point contact is tuned to
<2e^2/h. Polarization is stronger in samples with a well defined ``0.7
structure''


  For any $n$-partite state $\rho_{A_{1}A_{2}\cdot\cdot\cdot A_{n}}$, we define
its quantum mutual information matrix as an $n$ by $n$ matrix whose
$(i,j)$-entry is given by quantum mutual information $I(\rho_{A_{i}A_{j}})$.
Although each entry of quantum mutual information matrix, like its classical
counterpart, is also used to measure bipartite correlations, the similarity
ends here: quantum mutual information matrices are not always positive
semidefinite even for collections of up to 3-partite states. In this work, we
obtain necessary and sufficient conditions for the positive semidefinite
quantum mutual information matrix. We further define the \emph{genuine}
$n$-partite mutual information which can be easily calculated. This definition
is symmetric, nonnegative, bounded and more accurate for measuring multipartite
states.


  S. Artstein, K. Ball, F. Barthe, and A. Naor have shown that if (X_j) are
i.i.d. random variables, then the entropy of n^{-1/2}(X_1+....+X_n) increases
as n increases. The free analogue was recently proven by D. Shlyakhtenko. That
is, if (x_j) are freely independent, identically distributed, self-adjoint
elements in a noncommutative probability space, then the free entropy of
n^{-1/2}(x_1+....+x_n) increases as n increases. In this paper we prove that if
X_1 (x_1, resp.) has finite entropy (free entropy, resp.), and if the entropy
(the free entropy, resp.) is not a strictly increasing function of n, then X_1
(x_1, resp.) must be Gaussian (semicircular, resp.).


  It is generally taken for granted that our Universe is free of antimatter
objects and domains. This certitude has recently been challenged by the
possible detection of anti-helium nuclei by AMS-02. Should the observation be
confirmed, the existence of nearby antistars would make a plausible hypothesis
to explain the origin of the antinuclei. In this paper we use the 10-years
Fermi Large Area Telescope (LAT) gamma-ray source catalog to set constraints on
the abundance of antistars around the Sun. We identify in the catalog 14
antistar candidates not associated with any objects belonging to established
gamma-ray source classes and with a spectrum compatible with baryon-antibaryon
annihilation. We use them along with an estimate of the LAT sensitivity to
antistars to set upper limits on the local antistar fraction $f_{\bar{\ast}}$
with respect to normal stars. We provide parametric limits as a function of the
closest antistar mass, velocity, and surrounding matter density. We also employ
a novel Monte~Carlo method to set limits for a few hypotheses about the
antistar population. For a population with properties equivalent to those of
regular stars concentrated in the Galactic disk we obtain $f_{\bar{\ast}} < 2.5
\times 10^{-6}$ at 95\% confidence level, which is 20 times more constraining
than limits previously available. For a primordial population of antistars
distributed in the Galactic halo we obtain new local upper limits which
decrease as a function of antistar mass $M$ from $f_{\bar{\ast}} < 0.2$ at 95\%
confidence level for $M = 1 \; M_\odot$ to $f_{\bar{\ast}} < 1.6 \times
10^{-4}$ at 95\% confidence level for $M = 10 \; M_\odot$. By combining these
limits with existing microlensing constraints for lighter objects in the
Magellanic clouds, we infer that a primordial population of halo antistars must
have a density lower than $\mathcal{O}(10^{-5}\;\text{pc}^{-3})$ to
$\mathcal{O}(10^{-2}\;\text{pc}^{-3})$ depending on their masses. Our limits
can constrain models for the origin and propagation of antinuclei in cosmic
rays.


  This paper develops an optimal data aggregation policy for learning-based
traffic control systems based on imagery collected from Road Side Units (RSUs)
under imperfect communications. Our focus is optimizing semantic information
flow from RSUs to a nearby edge server or cloud-based processing units by
maximizing data diversity based on the target machine learning application
while taking into account heterogeneous channel conditions (e.g., delay, error
rate) and constrained total transmission rate. As a proof-of-concept, we
enforce fairness among class labels to increase data diversity for
classification problems. The developed constrained optimization problem is
non-convex. Hence it does not admit a closed-form solution, and the exhaustive
search is NP-hard in the number of RSUs. To this end, we propose an approximate
algorithm that applies a greedy interval-by-interval scheduling policy by
selecting RSUs to transmit. We use coalition game formulation to maximize the
overall added fairness by the selected RSUs in each transmission interval.
Once, RSUs are selected, we employ a maximum uncertainty method to handpick
data samples that contribute the most to the learning performance. Our method
outperforms random selection, uniform selection, and pure network-based
optimization methods (e.g., FedCS) in terms of the ultimate accuracy of the
target learning application.


  From the beginning of quantum mechanics, there has been a discussion about
the concept of reality, as exemplified by the EPR paradox. To many, the idea of
the paradox and the possibility of local hidden variables was dismissed by the
Bell inequality. Yet, there remains considerable evidence that this inequality
can be violated even by classical systems, so that experiments showing quantum
behavior and the violation of the inequality must be questioned. Here, we
demonstrate that classical optical polarization experiments based upon noise in
the system can be shown to violate the Bell inequality.


  In this paper we propose a novel second-order accurate well balanced scheme
for shallow water equations in general covariant coordinates over manifolds. In
our approach, once the gravitational field is defined for the specific case,
one equipotential surface is detected and parametrized by a frame of general
covariant coordinates. This surface is the manifold whose covariant
parametrization induces a metric tensor. The model is then re-written in a
hyperbolic form with a tuple of conserved variables composed both of the
evolving physical quantities and the metric coefficients. This formulation
allows the numerical scheme to automatically compute the curvature of the
manifold as long as the physical variables are evolved.


  Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We give a description
of characters of irreducible Whittaker modules for $\mathfrak{g}$ with any
infinitesimal character, along with a Kazhdan-Lusztig algorithm for computing
them. This generalizes Milicic-Soergel's and Romanov's results for integral
infinitesimal characters. As a special case, we recover the non-integral
Kazhdan-Lusztig conjecture for Verma modules.


  Sound event detection (SED) entails identifying the type of sound and
estimating its temporal boundaries from acoustic signals. These events are
uniquely characterized by their spatio-temporal features, which are determined
by the way they are produced. In this study, we leverage some distinctive
high-level acoustic characteristics of various sound events to assist the SED
model training, without requiring additional labeled data. Specifically, we use
the DCASE Task 4 2022 dataset and categorize the 10 classes into four
subcategories based on their high-level acoustic characteristics. We then
introduce a novel multi-task learning framework that jointly trains the SED and
high-level acoustic characteristics classification tasks, using shared layers
and weighted loss. Our method significantly improves the performance of the SED
system, achieving a 36.3% improvement in terms of the polyphonic sound event
detection score compared to the baseline on the DCASE 2022 Task 4 validation
set.


  The main aim of this article is to calculate explicit formula for S-curvature
in homogeneous generalized m-Kropina metric. Further, we also deduce mean
Berwald curvature for homogeneous generalized m-Kropina metric from
S-curvature.


  We develop efficient algorithms to construct utility maximizing mechanisms in
the presence of risk averse players (buyers and sellers) in Bayesian settings.
We model risk aversion by a concave utility function, and players play
strategically to maximize their expected utility. Bayesian mechanism design has
usually focused on maximizing expected revenue in a {\em risk neutral}
environment, and no succinct characterization of expected utility maximizing
mechanisms is known even for single-parameter multi-unit auctions.
  We first consider the problem of designing optimal DSIC mechanism for a risk
averse seller in the case of multi-unit auctions, and we give a poly-time
computable SPM that is $(1-1/e-\eps)$-approximation to the expected utility of
the seller in an optimal DSIC mechanism. Our result is based on a novel
application of a correlation gap bound, along with {\em splitting} and {\em
merging} of random variables to redistribute probability mass across buyers.
This allows us to reduce our problem to that of checking feasibility of a small
number of distinct configurations, each of which corresponds to a covering LP.
A feasible solution to the LP gives us the distribution on prices for each
buyer to use in a randomized SPM.
  We next consider the setting when buyers as well as the seller are risk
averse, and the objective is to maximize the seller's expected utility. We
design a truthful-in-expectation mechanism whose utility is a $(1-1/e
-\eps)^3$-approximation to the optimal BIC mechanism under two mild
assumptions. Our mechanism consists of multiple rounds that processes each
buyer in a round with small probability. Lastly, we consider the problem of
revenue maximization for a risk neutral seller in presence of risk averse
buyers, and give a poly-time algorithm to design an optimal mechanism for the
seller.


  In this paper we study an abstract framework for computing shape derivatives
of functionals subject to PDE constraints. We revisit the Lagrangian approach
using the implicit function theorem in an abstract setting tailored for
applications to shape optimization. This abstract framework yields practical
formulae to compute the derivative of a shape functional, the material
derivative of the state, and the adjoint state. Furthermore, it allows to gain
insight on the duality between the material derivative of the state and the
adjoint state. We show several applications of our main result to the
computation of distributed shape derivatives for problems involving linear
elliptic, nonlinear elliptic, parabolic PDEs and distributions. We compare our
approach with other techniques for computing shape derivatives including the
material derivative method and the averaged adjoint method.


  We study the joint mixing of colloids and salt released together in a
stagnation point or in a globally chaotic flow. In the presence of salt
inhomogeneities, the mixing time is strongly modified depending on the sign of
the diffusiophoretic coefficient $D_\mathrm{dp}$. Mixing is delayed when
$D_\mathrm{dp}>0$ (salt-attracting configuration), or faster when
$D_\mathrm{dp}<0$ (salt-repelling configuration). In both configurations, as
for molecular diffusion alone, large scales are barely affected in the dilating
direction while the Batchelor scale for the colloids, $\ell_{c,\mathrm{diff}}$,
is strongly modified by diffusiophoresis. We propose here to measure a global
effect of diffusiophoresis in the mixing process through an effective P\'eclet
number built on this modified Batchelor scale. Whilst this small scale is
obtained analytically for the stagnation point, in the case of chaotic
advection, we derive it using the equation of gradients of concentration,
following Raynal \& Gence (\textit{Intl J. Heat Mass Transfer}, vol. 40 (14),
1997, pp. 3267--3273). Comparing to numerical simulations, we show that the
mixing time can be predicted by using the same function as in absence of salt,
but as a function of the effective P\'eclet numbers computed for each
configuration. The approach is shown to be valid when the ratio
$D_\mathrm{dp}^2/D_s D_c \gg 1$, where $D_c$ and $D_s$ are the diffusivities of
the colloids and salt.


  In this work, we study multi-source test-time model adaptation from user
feedback, where K distinct models are established for adaptation. To allow
efficient adaptation, we cast the problem as a stochastic decision-making
process, aiming to determine the best adapted model after adaptation. We
discuss two frameworks: multi-armed bandit learning and multi-armed dueling
bandits. Compared to multi-armed bandit learning, the dueling framework allows
pairwise collaboration among K models, which is solved by a novel method named
Co-UCB proposed in this work. Experiments on six datasets of extractive
question answering (QA) show that the dueling framework using Co-UCB is more
effective than other strong baselines for our studied problem.


  In this paper, we revisit the question of how the dynamic optimality of
search trees should be defined in external memory. A defining characteristic of
external-memory data structures is that there is a stark asymmetry between
queries and inserts/updates/deletes: by making the former slightly
asymptotically slower, one can make the latter significantly asymptotically
faster (even allowing for operations with sub-constant amortized I/Os). This
asymmetry makes it so that rotation-based search trees are not optimal (or even
close to optimal) in insert/update/delete-heavy external-memory workloads. To
study dynamic optimality for such workloads, one must consider a different
class of data structures.
  The natural class of data structures to consider are what we call
buffered-propagation trees. Such trees can adapt dynamically to the locality
properties of an input sequence in order to optimize the interactions between
different inserts/updates/deletes and queries. We also present a new form of
beyond-worst-case analysis that allows for us to formally study a continuum
between static and dynamic optimality. Finally, we give a novel data structure,
called the \jellotree, that is statically optimal and that achieves dynamic
optimality for a large natural class of inputs defined by our beyond-worst-case
analysis.


  We present the results of a BeppoSAX observation of the fastest rotating
pulsar known: PSR B1937+21. The ~200 ks observation (78.5 ks MECS/34 ks LECS
on-source time) allowed us to investigate with high statistical significance
both the spectral properties and the pulse profile shape. The pulse profile is
clearly double peaked at energies > ~4 keV. Peak widths are compatible with the
instrumental time resolution and the second pulse lags the main pulse 0.52 in
phase, like is the case in the radio. In the 1.3-4 keV band we detect a ~45% DC
component; conversely the 4-10 keV pulsed fraction is consistent with 100%. The
on-pulse spectrum is fitted with an absorbed power-law of spectral index ~1.2,
harder than that of the total flux which is ~1.9. The total unabsorbed (2-10
keV) flux is F_{2-10} = 4.1 10^-13 cgs, implying a luminosity of L_X = 5.0
10^31 \Theta (d/3.6 kpc)^2 erg s^-1 and a X-ray efficiency of \eta = 4.5 10^-5
\Theta, where \Theta is the solid angle spanned by the emission beam. These
results are in agreement with those obtained by ASCA and a more recent
Rossi-XTE observation. The hydrogen column density N_H ~2 10^22 cm^-2 is ~10
times higher than expected from the radio dispersion measure and average
Galactic density of e-. Though it is compatible (within 2\sigma) with the
Galactic (HI derived) value of ~1 10^22 cm^-2, inspection of dust extinction
maps reveal that the pulsar falls in a highly absorbed region. In addition, 1.4
GHz radio map shows that the nearby (likely unrelated) HII source 4C21.53W is
part of a circular emission region ~4' across.


  Purpose - To characterise and assess the quality of published research
evaluating artificial intelligence (AI) methods for ovarian cancer diagnosis or
prognosis using histopathology data. Methods - A search of PubMed, Scopus, Web
of Science, CENTRAL, and WHO-ICTRP was conducted up to 19/05/2023. The
inclusion criteria required that research evaluated AI on histopathology images
for diagnostic or prognostic inferences in ovarian cancer. The risk of bias was
assessed using PROBAST. Information about each model of interest was tabulated
and summary statistics were reported. PRISMA 2020 reporting guidelines were
followed. Results - 1573 records were identified, of which 45 were eligible for
inclusion. There were 80 models of interest, including 37 diagnostic models, 22
prognostic models, and 21 models with other diagnostically relevant outcomes.
Models were developed using 1-1375 slides from 1-776 ovarian cancer patients.
Model outcomes included treatment response (11/80), malignancy status (10/80),
stain quantity (9/80), and histological subtype (7/80). All models were found
to be at high or unclear risk of bias overall, with most research having a high
risk of bias in the analysis and a lack of clarity regarding participants and
predictors in the study. Research frequently suffered from insufficient
reporting and limited validation using small sample sizes. Conclusion - Limited
research has been conducted on the application of AI to histopathology images
for diagnostic or prognostic purposes in ovarian cancer, and none of the
associated models have been demonstrated to be ready for real-world
implementation. Key aspects to help ensure clinical translation include more
transparent and comprehensive reporting of data provenance and modelling
approaches, as well as improved quantitative performance evaluation using
cross-validation and external validations.


  Modern malware evolves various detection avoidance techniques to bypass the
state-of-the-art detection methods. An emerging trend to deal with this issue
is the combination of image transformation and machine learning techniques to
classify and detect malware. However, existing works in this field only perform
simple image transformation methods that limit the accuracy of the detection.
In this paper, we introduce a novel approach to classify malware by using a
deep network on images transformed from binary samples. In particular, we first
develop a novel hybrid image transformation method to convert binaries into
color images that convey the binary semantics. The images are trained by a deep
convolutional neural network that later classifies the test inputs into benign
or malicious categories. Through the extensive experiments, our proposed method
surpasses all baselines and achieves 99.14% in terms of accuracy on the testing
set.


  Multi-source domain adaptation (MDA) aims to transfer knowledge from multiple
source domains to an unlabeled target domain. MDA is a challenging task due to
the severe domain shift, which not only exists between target and source but
also exists among diverse sources. Prior studies on MDA either estimate a mixed
distribution of source domains or combine multiple single-source models, but
few of them delve into the relevant information among diverse source domains.
For this reason, we propose a novel MDA approach, termed Pseudo Target for MDA
(PTMDA). Specifically, PTMDA maps each group of source and target domains into
a group-specific subspace using adversarial learning with a metric constraint,
and constructs a series of pseudo target domains correspondingly. Then we align
the remainder source domains with the pseudo target domain in the subspace
efficiently, which allows to exploit additional structured source information
through the training on pseudo target domain and improves the performance on
the real target domain. Besides, to improve the transferability of deep neural
networks (DNNs), we replace the traditional batch normalization layer with an
effective matching normalization layer, which enforces alignments in latent
layers of DNNs and thus gains further promotion. We give theoretical analysis
showing that PTMDA as a whole can reduce the target error bound and leads to a
better approximation of the target risk in MDA settings. Extensive experiments
demonstrate PTMDA's effectiveness on MDA tasks, as it outperforms
state-of-the-art methods in most experimental settings.


  Community microgrids offer many advantages for power distribution systems.
When there is an extreme event happening, distribution systems can be
seamlessly partitioned into several community microgrids for uninterrupted
supply to the end-users. In order to guarantee the system reliability,
distributed energy resources (DERs) should be sized for ensuring generation
adequacy to cover unexpected events. This paper presents a comprehensive
methodology for DERs selection in community microgrids, and an economic
approach to meet the system reliability requirements. Algorithms of discrete
time Fourier transform (DTFT) and particle swarm optimization (PSO) are
employed to find the optimal solution. Uncertainties of load demand and
renewable generation are taken into consideration. As part of the case study, a
sensitivity analysis is carried out to show the renewable generation impact on
DERs' capacity planning.


  Backdoor attack is a new AI security risk that has emerged in recent years.
Drawing on the previous research of adversarial attack, we argue that the
backdoor attack has the potential to tap into the model learning process and
improve model performance. Based on Clean Accuracy Drop (CAD) in backdoor
attack, we found that CAD came out of the effect of pseudo-deletion of data. We
provided a preliminary explanation of this phenomenon from the perspective of
model classification boundaries and observed that this pseudo-deletion had
advantages over direct deletion in the data debiasing problem. Based on the
above findings, we proposed Debiasing Backdoor Attack (DBA). It achieves SOTA
in the debiasing task and has a broader application scenario than
undersampling.


  A scaling analysis is undertaken for the load balance in sliding friction in
the hydrodynamic lubrication regime, with a particular emphasis on power-law
shear-thinning typical of a structured liquid. It is argued that the
shear-thinning regime is mechanically unstable if the power-law index n < 1/2,
where n is the exponent that relates the shear stress to the shear rate.
Consequently the Stribeck (friction) curve should be discontinuous, with
possible hysteresis. Further analysis suggests that normal stress and flow
transience (stress overshoot) do not destroy this basic picture, although they
may provide stabilising mechanisms at higher shear rates. Extensional viscosity
is also expected to be insignificant unless the Trouton ratio is large. A
possible application to shear thickening in non-Brownian particulate
suspensions is indicated.


  Recently, Colomo and Sportiello introduced a powerful method, known as the
\emph{Tangent Method}, for computing the arctic curve in statistical models
which have a (non- or weakly-) intersecting lattice path formulation. We apply
the Tangent Method to compute arctic curves in various models: the domino
tiling of the Aztec diamond for which we recover the celebrated arctic circle;
a model of Dyck paths equivalent to the rhombus tiling of a half-hexagon for
which we find an arctic half-ellipse; another rhombus tiling model with an
arctic parabola; the vertically symmetric alternating sign matrices, where we
find the same arctic curve as for unconstrained alternating sign matrices. The
latter case involves lattice paths that are non-intersecting but that are
allowed to have osculating contact points, for which the Tangent Method was
argued to still apply. For each problem we estimate the large size asymptotics
of a certain one-point function using LU decomposition of the corresponding
Gessel-Viennot matrices, and a reformulation of the result amenable to
asymptotic analysis.


  This paper studies joint models for selecting correct answer sentences among
the top $k$ provided by answer sentence selection (AS2) modules, which are core
components of retrieval-based Question Answering (QA) systems. Our work shows
that a critical step to effectively exploit an answer set regards modeling the
interrelated information between pair of answers. For this purpose, we build a
three-way multi-classifier, which decides if an answer supports, refutes, or is
neutral with respect to another one. More specifically, our neural architecture
integrates a state-of-the-art AS2 model with the multi-classifier, and a joint
layer connecting all components. We tested our models on WikiQA, TREC-QA, and a
real-world dataset. The results show that our models obtain the new state of
the art in AS2.


  Mondino and Naber recently proved that finite dimensional $\sf RCD$ spaces
are rectifiable. Here we show that the push-forward of the reference measure
under the charts built by them is absolutely continuous with respect to the
Lebesgue measure. This result, read in conjunction with another recent work of
us, has relevant implications on the structure of tangent spaces to $\sf RCD$
spaces. A key tool that we use is a recent paper by De Philippis-Rindler about
the structure of measures on the Euclidean space.


  We evaluate one-loop open-string amplitudes at finite $\alpha'$ for the first
time. Our method involves a deformation of the integration contour over the
modular parameter $\tau$ to a fractal contour introduced by Rademacher in the
context of analytic number theory. This procedure leads to explicit and
practical formulas for the one-loop four-point amplitudes in type-I superstring
theory, amenable to numerical evaluation. We plot the amplitudes as a function
of the Mandelstam invariants $s$ and $t$ and directly verify long-standing
conjectures about their behaviour at high energies.