  Morphogenetic dynamics of tissue sheets require coordinated cell shape
changes regulated by global patterning of mechanical forces. Inspired by such
biological phenomena, we propose a minimal mechanochemical model based on the
notion that cell shape changes are induced by diffusible biomolecules that
influence tissue contractility in a concentration-dependent manner -- and whose
concentration is in turn affected by the macroscopic tissue shape. We perform
computational simulations of thin shell elastic dynamics to reveal propagating
chemical and three-dimensional deformation patterns arising due to a sequence
of buckling instabilities. Depending on the concentration threshold that
actuates cell shape change, we find qualitatively different patterns. The
mechanochemically coupled patterning dynamics are distinct from those driven by
purely mechanical or purely chemical factors. Using numerical simulations and
theoretical arguments, we analyze the elastic instabilities that result from
our model and provide simple scaling laws to identify wrinkling morphologies.


  We consider particle dynamics in singular gravitational field. In 2d
spacetime the system splits into two independent gravitational systems without
singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but
the corresponding symmetry transformations are not defined globally.
Quantization leads to ambiguity. By including singularity one can get the
global $SO(2.1)$ symmetry. Quantization in this case leads to unique quantum
theory.


  To any quiver with relations we associate a consistent scattering diagram
taking values in the motivic Hall algebra of its category of representations.
We show that the chamber structure of this scattering diagram coincides with
the natural chamber structure in an open subset of the space of stability
conditions on the associated triangulated category. In the three-dimensional
Calabi-Yau situation, when the relations arise from a potential, we can apply
an integration map to give a consistent scattering diagram taking values in a
tropical vertex group.


  The current experimental values of anomalous magnetic moments of muon and
electron deviate from the Standard Model predictions by few standard
deviations, which might be a hint of new physics. The sizes and signs of these
deviations are different and opposite between the electron and muon, which
makes it difficult to explain both of these anomalies in a consistent model
without introducing large flavour-violating effects. It is shown that they can
be simultaneously explained in the Minimal Supersymmetric Standard Model (MSSM)
by arranging the sizes of bino-slepton and chargino-sneutrino contributions
differently between the electron and muon sectors. The MSSM spectrum features
very light selectrons and wino-like chargino, while they can evade LHC
constraints due to degenerate spectra.


  In the derivation of the Born-Infeld action for the case with a nontrivial
boundary of the string world sheet the appearance of a new term changes the
conformal anomaly. This may have many consequences, especially also in the
study of generalized interacting brane systems.


  In this paper, we apply the Boole discrete line integral to solve the Lorentz
force system which is written as a non-canonical Hamiltonian system. The method
is exactly energy-conserving for polynomial Hamiltonians of degree $\nu \leq
4$. In any other case, the energy can also be conserved approximatively. With
comparison to well-used Boris method, numerical experiments are presented to
demonstrate the energy-preserving property of the method.


  We calculate the joint period-spindown (P-Pdot) distributions of millisecond
radio pulsars (MSRP) for the standard evolutionary model in order to test
whether the observed MSRPs are the unequivocal descendants of millisecond X-ray
pulsars (MSXP). The P-Pdot densities implied by the standard evolutionary model
compared with observations suggest that there is a statistically significant
overabundance of young/high magnetic field MSRPs. Taking biases due to
observational selection effects into account, it is unlikely that MSRPs have
evolved from a single coherent progenitor population that loses energy via
magnetic dipole radiation after the onset of radio emission. By producing the
P-Pdot probability map, we show with more than 95% confidence that the fastest
spinning millisecond pulsars with high magnetic fields, e.g. PSR B1937+21,
cannot be produced by the observed MSXPs within the framework of the standard
model.


  In this work we propose a nonconvex two-stage \underline{s}tochastic
\underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase
retrieval. The proposed algorithm is guaranteed to have an exact recovery from
$O(s\log n)$ samples if provided the initial guess is in a local neighbour of
the ground truth. Thus, the proposed algorithm is two-stage, first we estimate
a desired initial guess (e.g. via a spectral method), and then we introduce a
randomized alternating minimization strategy for local refinement. Also, the
hard-thresholding pursuit algorithm is employed to solve the sparse constraint
least square subproblems. We give the theoretical justifications that SAM find
the underlying signal exactly in a finite number of iterations (no more than
$O(\log m)$ steps) with high probability. Further, numerical experiments
illustrates that SAM requires less measurements than state-of-the-art
algorithms for sparse phase retrieval problem.


  We demonstrate a modularity bug in the interface system of Java 8 on the
practical example of a textbook design of a modular interface for vector
spaces. Our example originates in our teaching of modular object-oriented
design in Java 8 to undergraduate students, simply following standard
programming practices and mathematical definitions. The bug shows up as a
compilation error and should be fixed with a language extension due to the
importance of best practices (design fidelity).


  Liquid helium 4 had been the only bosonic superfluid available in experiments
for a long time. This situation was changed in 1995, when a new superfluid was
born with the realization of the Bose-Einstein condensation in ultracold atomic
gases. The liquid helium 4 is strongly interacting and has no spin; there is
almost no way to change its parameters, such as interaction strength and
density. The new superfluid, Bose-Einstein condensate (BEC), offers various
aspects of advantages over liquid helium. On the one hand, BEC is weakly
interacting and has spin degrees of freedom. On the other hand, it is
convenient to tune almost all the parameters of a BEC, for example, the kinetic
energy by spin-orbit coupling, the density by the external potential, and the
interaction by Feshbach resonance. Great efforts have been devoted to studying
these new aspects of superfluidity, and the results have greatly enriched our
understanding of superfluidity. Here we review these developments by focusing
on the stability and critical velocity of various superfluids. The BEC systems
considered include a uniform superfluid in free space, a superfluid with its
density periodically modulated, a superfluid with artificially engineered
spin-orbit coupling, and a superfluid of pure spin current. Due to the weak
interaction, these BEC systems can be well described by the mean field
Gross-Pitaevskii theory and their superfluidity, in particular critical
velocities, can be examined with Landau's theory of superfluid. Experimental
proposals to observe these new aspects of superfluidity are discussed.


  We present here a re-calibration of the photometric systems used in the
Pantheon+ sample of Type Ia supernovae (SNe Ia) including those used for the
SH0ES distance-ladder measurement of H$_0$. We utilize the large and uniform
sky coverage of the public Pan-STARRS stellar photometry catalog to
cross-calibrate against tertiary standards released by individual SN Ia
surveys. The most significant updates over the `SuperCal' cross-calibration
used for the previous Pantheon and SH0ES analyses are: 1) expansion of the
number of photometric systems (now 25) and filters (now 105), 2) solving for
all filter offsets in all systems simultaneously in order to produce a
calibration uncertainty covariance matrix that can be used in
cosmological-model constraints, and 3) accounting for the change in the
fundamental flux calibration of the HST CALSPEC standards from previous
versions on the order of $1.5\%$ over a $\Delta \lambda$ of 4000~\AA. The
re-calibration of samples used for light-curve fitting has historically been
decoupled from the retraining of the light-curve model. Here, we are able to
retrain the SALT2 model using this new calibration and find the change in the
model coupled with the change to the calibration of the light-curves themselves
causes a net distance modulus change ($d\mu/dz$) of 0.04 mag over the redshift
range $0<z<1$. We introduce a new formalism to determine the systematic impact
on cosmological inference by propagating the covariance in fitted calibration
offsets through retraining simultaneously with light-curve fitting and find a
total calibration uncertainty impact of $\sigma_w=0.013$, which is roughly half
the size of the sample statistical uncertainty. Similarly, we find a systematic
SN calibration contribution to the SH0ES H$_0$ uncertainty is less than
0.2~km/s/Mpc, suggesting that SN Ia calibration cannot resolve the current
level of the `Hubble Tension'.


  ThreadTone is an NPR representation of an input image by half-toning using
threads on a circle. Current approaches to create ThreadTone paintings greedily
draw the chords on the circle. We introduce the concept of chord space, and
design a new algorithm to improve the quality of the thread painting. We use an
optimization process that estimates the fitness of every chord in the chord
space, and an error-diffusion based sampling process that selects a moderate
number of chords to produce the output painting. We used an image similarity
measure to evaluate the quality of our thread painting and also conducted a
user study. Our approach can produce high quality results on portraits,
sketches as well as cartoon pictures.


  To interact with humans, artificial intelligence (AI) systems must understand
our social world. Within this world norms play an important role in motivating
and guiding agents. However, very few computational theories for learning
social norms have been proposed. There also exists a long history of debate on
the distinction between what is normal (is) and what is normative (ought). Many
have argued that being capable of learning both concepts and recognizing the
difference is necessary for all social agents. This paper introduces and
demonstrates a computational approach to learning norms from natural language
text that accounts for both what is normal and what is normative. It provides a
foundation for everyday people to train AI systems about social norms.


  We investigate the long-time evolution of branching diffusion processes
(starting with a single particle) in inhomogeneous media. The qualitative
behavior of the processes depends on the intensity of the branching. We analyze
the super-critical case, when the total number of particles growing
exponentially with positive probability. We study the asymptotics of the number
of particles in different regions of space and describe the growth of the
region occupied by the particles.


  We study group graded extensions of fusion 2-categories. As an application,
we obtain a homotopy theoretic classification of fermionic strongly fusion
2-categories. We examine various examples in detail.


  We present a study of the B spectrum performed in the framework of Heavy
Quark Effective Theory expanded to next-to-leading order in 1/m and
non-perturbative in the strong coupling. Our analyses have been performed on
Nf=2 lattice gauge field ensembles corresponding to three different lattice
spacings and a wide range of pion masses. We obtain the Bs-meson mass and
hyperfine splittings of the B- and Bs-mesons that are in good agreement with
the experimental values and examine the mass difference m_{Bs}-m_B as a further
cross-check of our previous estimate of the b-quark mass. We also report on the
mass splitting between the first excited state and the ground state in the B
and Bs systems.


  A new, self-contained, proof of a coherence result for categories equipped
with two symmetric monoidal structures bridged by a natural transformation is
given. It is shown that this coherence result is sufficient for
$\omega\times\omega$-indexed family of iterated reduced bar constructions based
on such a category.


  Multimodal MRIs play a crucial role in clinical diagnosis and treatment.
Feature disentanglement (FD)-based methods, aiming at learning superior feature
representations for multimodal data analysis, have achieved significant success
in multimodal learning (MML). Typically, existing FD-based methods separate
multimodal data into modality-shared and modality-specific features, and employ
concatenation or attention mechanisms to integrate these features. However, our
preliminary experiments indicate that these methods could lead to a loss of
shared information among subsets of modalities when the inputs contain more
than two modalities, and such information is critical for prediction accuracy.
Furthermore, these methods do not adequately interpret the relationships
between the decoupled features at the fusion stage. To address these
limitations, we propose a novel Complete Feature Disentanglement (CFD) strategy
that recovers the lost information during feature decoupling. Specifically, the
CFD strategy not only identifies modality-shared and modality-specific
features, but also decouples shared features among subsets of multimodal
inputs, termed as modality-partial-shared features. We further introduce a new
Dynamic Mixture-of-Experts Fusion (DMF) module that dynamically integrates
these decoupled features, by explicitly learning the local-global relationships
among the features. The effectiveness of our approach is validated through
classification tasks on three multimodal MRI datasets. Extensive experimental
results demonstrate that our approach outperforms other state-of-the-art MML
methods with obvious margins, showcasing its superior performance.


  We show that the integrable Lindblad superoperators found recently can be
used to build integrable nonunitary quantum circuits with two-site gates by
demonstrating that the $\check{R}$-matrices are completely positive and trace
preserving. Using the bond-site transformation, we obtain the corresponding
integrable nonunitary quantum circuits with three-site gates. When restricted
to the diagonals of the density matrix, these quantum models reduce to
integrable classical cellular automata. This approach may pave the way for a
systematic construction of integrable nonunitary quantum circuits.


  Existing gradient-based optimization methods update parameters locally, in a
direction that minimizes the loss function. We study a different approach,
symmetry teleportation, that allows parameters to travel a large distance on
the loss level set, in order to improve the convergence speed in subsequent
steps. Teleportation exploits symmetries in the loss landscape of optimization
problems. We derive loss-invariant group actions for test functions in
optimization and multi-layer neural networks, and prove a necessary condition
for teleportation to improve convergence rate. We also show that our algorithm
is closely related to second order methods. Experimentally, we show that
teleportation improves the convergence speed of gradient descent and AdaGrad
for several optimization problems including test functions, multi-layer
regressions, and MNIST classification.


  The object of this paper is to present a computable solution of a fractional
partial differential equation associated with a Riemann-Liouville derivative of
fractional order as the time-derivative and Riesz-Feller fractional derivative
as the space derivative. The method followed in deriving the solution is that
of joint Laplace and Fourier transforms. The solution is derived in a closed
and computable form in terms of the H-function. It provides an elegant
extension of the results given earlier by Debnath, Chen et al., Haubold et al.,
Mainardi et al., Saxena et al., and Pagnini et al. The results obtained are
presented in the form of four theorems. Some results associated with fractional
Schroeodinger equation and fractional diffusion-wave equation are also derived
as special cases of the findings.


  We study symmetric random walks on finitely generated groups of
orientation-preserving homeomorphisms of the real line. We establish an
oscillation property for the induced Markov chain on the line that implies a
weak form of recurrence. Except for a few special cases, which can be treated
separately, we prove a property of "global stability at a finite distance":
roughly speaking, there exists a compact interval such that any two
trajectories get closer and closer whenever one of them returns to the compact
interval. The probabilistic techniques employed here lead to interesting
results for the study of group actions on the line. For instance, we show that
under a suitable change of the coordinates, the drift of every point becomes
zero provided that the action is minimal. As a byproduct, we recover the fact
that every finitely generated group of homeomorphisms of the real line is
topologically conjugate to a group of (globally) Lipschitz homeomorphisms.
Moreover, we show that such a conjugacy may be chosen in such a way that the
displacement of each element is uniformly bounded.


  A microscopic theory of the dynamic spin susceptibility (DSS) in the
superconducting state within the t-J model is presented. It is based on an
exact representation for the DSS obtained by applying the Mori-type projection
technique for the relaxation function in terms of Hubbard operators. The static
spin susceptibility is evaluated by a sum-rule-conserving generalized
mean-field approximation, while the self-energy is calculated in the
mode-coupling approximation. The spectrum of spin excitations is studied in the
underdoped and optimally doped regions. The DSS reveals a resonance mode (RM)
at the antiferromagnetic wave vector Q = \pi(1,1) at low temperatures due to a
strong suppression of the damping of spin excitations. This is explained by an
involvement of spin excitations in the decay process besides the particle-hole
continuum usually considered in random-phase-type approximations. The spin gap
in the spin-excitation spectrum at Q plays a dominant role in limiting the
decay in comparison with the superconducting gap which results in the
observation of the RM even above $T_c$ in the underdoped region. A good
agreement with inelastic neutron-scattering experiments on the RM in YBCO
compounds is found.


  Weakly-supervised action localization aims to recognize and localize action
instancese in untrimmed videos with only video-level labels. Most existing
models rely on multiple instance learning(MIL), where the predictions of
unlabeled instances are supervised by classifying labeled bags. The MIL-based
methods are relatively well studied with cogent performance achieved on
classification but not on localization. Generally, they locate temporal regions
by the video-level classification but overlook the temporal variations of
feature semantics. To address this problem, we propose a novel attention-based
hierarchically-structured latent model to learn the temporal variations of
feature semantics. Specifically, our model entails two components, the first is
an unsupervised change-points detection module that detects change-points by
learning the latent representations of video features in a temporal hierarchy
based on their rates of change, and the second is an attention-based
classification model that selects the change-points of the foreground as the
boundaries. To evaluate the effectiveness of our model, we conduct extensive
experiments on two benchmark datasets, THUMOS-14 and ActivityNet-v1.3. The
experiments show that our method outperforms current state-of-the-art methods,
and even achieves comparable performance with fully-supervised methods.


  The basic principles of General Theory of Relativity historically have been
tested in gedanken experiments in rotating frame of references. One of the key
issues, which still evokes a lot of controversy, is the centrifugal
acceleration. Machabeli & Rogava (1994) argued that centrifugal acceleration
reverse direction for particles moving radially with relativistic velocities
within a "bead on a wire" approximation. We show that this result is
frame-dependent and reflects a special relativistic dilution of time (as
correctly argued by de Felice (1995)) and is analogous to freezing of motion on
the black hole horizon as seen by a remote observer. It is a reversal of
coordinate acceleration; there is no such effect as measured by a defined set
of observers, e.g., proper and/or comoving. Frame-independent velocity of a
"bead" with respect to stationary rotating observers increases and formally
reaches the speed of light on the light cylinder. In general relativity,
centrifugal force does reverse its direction at photon circular orbit, r=3M in
Schwarzschild metric, as argued by Abramowicz (1990).


  Belief propagation is known to perform extremely well in many practical
statistical inference and learning problems using graphical models, even in the
presence of multiple loops. The iterative use of belief propagation algorithm
on loopy graphs is referred to as Loopy Belief Propagation (LBP). Various
sufficient conditions for convergence of LBP have been presented; however,
general necessary conditions for its convergence to a unique fixed point remain
unknown. Because the approximation of beliefs to true marginal probabilities
has been shown to relate to the convergence of LBP, several methods have been
explored whose aim is to obtain distance bounds on beliefs when LBP fails to
converge. In this paper, we derive uniform and non-uniform error bounds on
messages, which are tighter than existing ones in literature, and use these
bounds to derive sufficient conditions for the convergence of LBP in terms of
the sum-product algorithm. We subsequently use these bounds to study the
dynamic behavior of the sum-product algorithm, and analyze the relation between
convergence of LBP and sparsity and walk-summability of graphical models. We
finally use the bounds derived to investigate the accuracy of LBP, as well as
the scheduling priority in asynchronous LBP.


  We provide strong evidence that the asymptotically free (1+1)-dimensional
non-linear O(3) sigma model can be regularized using a quantum lattice
Hamiltonian, referred to as the "Heisenberg-comb", that acts on a Hilbert space
with only two qubits per spatial lattice site. The Heisenberg-comb consists of
a spin-half anti-ferromagnetic Heisenberg-chain coupled anti-ferromagnetically
to a second local spin-half particle at every lattice site. Using a world-line
Monte Carlo method we show that the model reproduces the universal step-scaling
function of the traditional model up to correlation lengths of 200,000 in
lattice units and argue how the continuum limit could emerge. We provide a
quantum circuit description of time-evolution of the model and argue that
near-term quantum computers may suffice to demonstrate asymptotic freedom.


  Optical intrinsic angular momentum can be regarded as derivation from spatial
superposition of optical vector fields embodied by spinning or and spiraling
the electric field vector. We employ vectorial formulation derivation to
comprehensively study all angular momentum contents of optical vector fields in
arbitrary superposition states, including the longitudinal and transverse, spin
and orbital (SAM and OAM) components. As for the orthogonal superposition
fields, there inherently exists spin-orbit shift from longitudinal SAM to OAM,
and the whole local spin flow manifests local multiple fold helical
trajectories. Especially, both the spin-orbit shift and transverse SAM could
become considerable in the non-paraxial condition. Our studies here provide an
explicit insight into the derivation and evolution, intrinsic correlations and
salient features of various types of angular momentum components.


  We relate the gerbe of sheaves of chiral differential operators (CDO) on a
algebraic variety X, studied by Gorbounov, Malikov and Schechtman, to the
determinantal gerbe of the formal loop space LX introduced in our earlier
paper. The liens of the two gerbes are related by a version of the symplectic
action homomorphism. The determinantal gerbe of LX has a factorization
structure in the spirit of Beilinson and Drinfeld. In our identification,
sheaves of CDO correspond to factorizing objects of this factorization gerbe.


  The aim of this note is to exploit a new relationship between additive
combinatorics and the geometry of monomial projective curves. We associate to a
finite set of non-negative integers $A=\{a_1,\cdots, a_n\}$ a monomial
projective curve $C_A\subset \mathbb P^{n-1}_{k}$ such that the Hilbert
function of $C_A$ and the cardinalities of $sA:=\{a_{i_1}+\cdots+a_{i_s}\mid
1\le i_1\le \cdots \le i_s\le n\}$ agree. The singularities of $C_A$ determines
the asymptotic behaviour of $|sA|$, equivalently the Hilbert polynomial of
$C_A$, and the asymptotic structure of $sA$. We show that some additive inverse
problems can be translate to the rigidity of Hilbert polynomials and we improve
an upper bound of the Castelnuovo-Mumford regularity of monomial projective
curves by using results of additive combinatorics.


  This work presents a novel dense RGB-D SLAM approach for dynamic planar
environments that enables simultaneous multi-object tracking, camera
localisation and background reconstruction. Previous dynamic SLAM methods
either rely on semantic segmentation to directly detect dynamic objects; or
assume that dynamic objects occupy a smaller proportion of the camera view than
the static background and can, therefore, be removed as outliers. Our approach,
however, enables dense SLAM when the camera view is largely occluded by
multiple dynamic objects with the aid of camera motion prior. The dynamic
planar objects are separated by their different rigid motions and tracked
independently. The remaining dynamic non-planar areas are removed as outliers
and not mapped into the background. The evaluation demonstrates that our
approach outperforms the state-of-the-art methods in terms of localisation,
mapping, dynamic segmentation and object tracking. We also demonstrate its
robustness to large drift in the camera motion prior.


  Parikh-Wilczek tunnelling framework is investigated again. We argue that
Parikh-Wilczek's treatment, which satisfies the first law of black hole
thermodynamics and consists with an underlying unitary theory, is only suitable
for a reversible process. Because of the negative heat capacity, an evaporating
black hole is a highly unstable system. That is, the factual emission process
is irreversible, the unitary theory will not be satisfied and the information
loss is possible.


  The experimental data on p, Lambda, Xi-, Omega-, baryons and the
corresponding antibaryons spectra obtained by different collaborations are
compared with the results of the calculations performed into the frame of the
Quark-Gluon String Model. The contribution of String Junction diffusion and the
inelastic screening corrections are accounted for in the theoretical
calculations. The predictions of the Quark-Gluon String Model both for pp and
pA collisions are extended up to the LHC energies.


  Two general models with hierarchical and almost degenerate neutrino masses,
which are able to explain the solar and atmospheric anomalies are investigated.
We show how neutrinoless double beta decay experiments discern Dirac and
Majorana natures of neutrinos. The strongest result is, that almost degenerate
neutrinos with masses above 0.22 eV combined with the SMA MSW must be Dirac
particles. In the general case, the same bound is true for specific parity
assignments. In the near future (GENIUS experiment), one of the hierarchical
schemes, and the VO mechanism for almost degenerate neutrinos and specific
mixing matrix elements and parity assignments will be tested.


  Calculating opacities for a wide range of plasma conditions (i.e.
temperature, density, element) requires detailed knowledge of the plasma
configuration space and electronic structure. For plasmas composed of heavier
elements, relativistic effects are important in both the electronic structure
and the details of opacity spectra. We extend our previously described
superconfiguration and super transition array capabilities [N. M. Gill et al.,
JPB, 56, 015001 (2023)] to include a fully relativistic formalism. The use of
hybrid bound-continuum supershells in our superconfigurations demonstrates the
importance of a consistent treatment of bound and continuum electrons in dense
plasma opacities, and we expand the discussion of these consequences to include
issues associated with equation of state and electron correlations between
bound and continuum electrons.


  The growing share of proactive actors in the electricity markets calls for
more attention on prosumers and more support for their decision-making under
decentralized electricity markets. In view of the changing paradigm, it is
crucial to study the long-term planning under the decentralized and
prosumer-centric markets to unravel the effects of such markets on the planning
decisions. In the first part of the two-part paper, we propose a
prosumer-centric framework for concurrent generation and transmission planning.
Here, three planning models are presented where a peer-to-peer market with
product differentiation, a pool market and a mixed bilateral/pool market and
their associated trading costs are explicitly modeled, respectively. To fully
reveal the individual costs and benefits, we start by formulating the
optimization problems of various actors, i.e. prosumers, transmission system
operator, energy market operator and carbon market operator. Moreover, to
enable decentralized planning where the privacy of the prosumers is preserved,
distributed optimization algorithms are presented based on the corresponding
centralized optimization problems.


  We show that every interval in the homomorphism order of finite undirected
graphs is either universal or a gap. Together with density and universality
this "fractal" property contributes to the spectacular properties of the
homomorphism order.
  We first show the fractal property by using Sparse Incomparability Lemma and
then by more involved elementary argument.


  We construct N=1 supersymmetric theories on worldvolumes of D5 branes wrapped
around 2-cycles of threefolds which are A-D-E fibrations over a plane. We
propose large N duals as geometric transitions involving blowdowns of two
cycles and blowups of three-cycles. This yields exact predictions for a large
class of N=1 supersymmetric gauge systems including U(N) gauge theories with
two adjoint matter fields deformed by superpotential terms, which arise in
A-D-E fibered geometries with non-trivial monodromies.


  We give a simple proof of a nice formula for the means and covariances of the
diagonal sums of a uniformly random boxed plane parition.


  We present a spectroscopic investigation of the Be+sdO binary system HR 2142
that is based upon large sets of ultraviolet observations from the
International Ultraviolet Explorer and ground-based H-alpha observations. We
measured radial velocities for the Be star component from these spectra, and
computed a revised orbit. In order to search for the spectral signature of the
hot subdwarf, we cross-correlated the short wavelength end of each IUE spectrum
with a model hot star spectrum, and then we used the predicted Doppler shifts
of the subdwarf to shift-and-add all the cross-correlation functions to the
frame of the subdwarf. This merged function shows the weak signal from the
spectral lines of the hot star, and a best fit is obtained with a mass ratio
M_2/M_1 = 0.07 +/- 0.02, companion temperature T_{eff} > 43 +/- 5 kK, projected
rotational velocity V sin i < 30 km/s, and a monochromatic flux ratio near 1170
Angstroms of f_2/f_1 > 0.009 +/- 0.001. This hot subdwarf creates a one-armed
spiral, tidal wake in the disk of the Be star, and we present a circumbinary
disk model that can explain the occurrence of shell absorption lines by gas
enhancements that occur where gas crossing the gap created by the subdwarf
strikes the disk boundaries. The faint companion of HR 2142 may be
representative of a significant fraction of Be stars with undetected former
mass donor companion stars.


  Given an open subset $\Omega$ of a Banach space and a Lipschitz function
$u_0: \overline{\Omega} \to \mathbb{R},$ we study whether it is possible to
approximate $u_0$ uniformly on $\Omega$ by $C^k$-smooth Lipschitz functions
which coincide with $u_0$ on the boundary $\partial \Omega$ of $\Omega$ and
have the same Lipschitz constant as $u_0.$ As a consequence, we show that every
$1$-Lipschitz function $u_0: \overline{\Omega} \to \mathbb{R},$ defined on the
closure $\overline{\Omega}$ of an open subset $\Omega$ of a finite dimensional
normed space of dimension $n \geq 2$, and such that the Lipschitz constant of
the restriction of $u_0$ to the boundary of $\Omega$ is less than $1$, can be
uniformly approximated by differentiable $1$-Lipschitz functions $w$ which
coincide with $u_0$ on $\partial \Omega$ and satisfy the equation $\| D w\|_*
=1$ almost everywhere on $\Omega.$ This result does not hold in general without
assumption on the restriction of $u_0$ to the boundary of $\Omega$.


  Database de-anonymization typically involves matching an anonymized database
with correlated publicly available data. Existing research focuses either on
practical aspects without requiring knowledge of the data distribution yet
provides limited guarantees, or on theoretical aspects assuming known
distributions. This paper aims to bridge these two approaches, offering
theoretical guarantees for database de-anonymization under synchronization
errors and obfuscation without prior knowledge of data distribution. Using a
modified replica detection algorithm and a new seeded deletion detection
algorithm, we establish sufficient conditions on the database growth rate for
successful matching, demonstrating a double-logarithmic seed size relative to
row size is sufficient for detecting deletions in the database. Importantly,
our findings indicate that these sufficient de-anonymization conditions are
tight and are the same as in the distribution-aware setting, avoiding
asymptotic performance loss due to unknown distributions. Finally, we evaluate
the performance of our proposed algorithms through simulations, confirming
their effectiveness in more practical, non-asymptotic, scenarios.


  We study the ability of neural networks to calculate feedback control signals
that steer trajectories of continuous time non-linear dynamical systems on
graphs, which we represent with neural ordinary differential equations (neural
ODEs). To do so, we present a neural-ODE control (NODEC) framework and find
that it can learn feedback control signals that drive graph dynamical systems
into desired target states. While we use loss functions that do not constrain
the control energy, our results show, in accordance with related work, that
NODEC produces low energy control signals. Finally, we evaluate the performance
and versatility of NODEC against well-known feedback controllers and deep
reinforcement learning. We use NODEC to generate feedback controls for systems
of more than one thousand coupled, non-linear ODEs that represent epidemic
processes and coupled oscillators.


  When visualizing a high-dimensional dataset, dimension reduction techniques
are commonly employed which provide a single 2-dimensional view of the data. We
describe ENS-t-SNE: an algorithm for Embedding Neighborhoods Simultaneously
that generalizes the t-Stochastic Neighborhood Embedding approach. By using
different viewpoints in ENS-t-SNE's 3D embedding, one can visualize different
types of clusters within the same high-dimensional dataset. This enables the
viewer to see and keep track of the different types of clusters, which is
harder to do when providing multiple 2D embeddings, where corresponding points
cannot be easily identified. We illustrate the utility of ENS-t-SNE with
real-world applications and provide an extensive quantitative evaluation with
datasets of different types and sizes.


  We study the convergence of $Z$-estimators $\widehat \theta(\eta)\in \mathbb
R^p$ for which the objective function depends on a parameter $\eta$ that
belongs to a Banach space $\mathcal H$. Our results include the uniform
consistency over $\mathcal H$ and the weak convergence in the space of bounded
$\mathbb R^p$-valued functions defined on $\mathcal H$. Furthermore when $\eta$
is a tuning parameter optimally selected at $\eta_0$, we provide conditions
under which an estimated $\widehat \eta$ can be replaced by $\eta_0$ without
affecting the asymptotic variance. Interestingly, these conditions are free
from any rate of convergence of $\widehat \eta$ to $\eta_0$ but they require
the space described by $\widehat \eta$ to be not too large. We highlight
several applications of our results and we study in detail the case where
$\eta$ is the weight function in weighted regression.


  Huge image data sets are the fundament for the development of the perception
of automated driving systems. A large number of images is necessary to train
robust neural networks that can cope with diverse situations. A sufficiently
large data set contains challenging situations and objects. For testing the
resulting functions, it is necessary that these situations and objects can be
found and extracted from the data set. While it is relatively easy to record a
large amount of unlabeled data, it is far more difficult to find demanding
situations and objects. However, during the development of perception systems,
it must be possible to access challenging data without having to perform
lengthy and time-consuming annotations. A developer must therefore be able to
search dynamically for specific situations and objects in a data set. Thus, we
designed a method which is based on state-of-the-art neural networks to search
for objects with certain properties within an image. For the ease of use, the
query of this search is described using natural language. To determine the time
savings and performance gains, we evaluated our method qualitatively and
quantitatively on automotive data sets.


  We study source-to-sink excitation transport on carbon nanotubes using the
concept of quantum walks. In particular, we focus on transport properties of
Grover coined quantum walks on ideal and percolation perturbed nanotubes with
zig-zag and armchair chiralities. Using analytic and numerical methods we
identify how geometric properties of nanotubes and different types of a sink
altogether control the structure of trapped states and, as a result, the
overall source-to-sink transport efficiency. It is shown that chirality of
nanotubes splits behavior of the transport efficiency into a few typically well
separated quantitative branches. Based on that we uncover interesting quantum
transport phenomena, e.g. increasing the length of the tube can enhance the
transport and the highest transport efficiency is achieved for the thinnest
tube. We also demonstrate, that the transport efficiency of the quantum walk on
ideal nanotubes may exhibit even oscillatory behavior dependent on length and
chirality.


  Call a directed partially ordered cancellative divisibility monoid $M$ a
Riesz monoid if for all $x,y_{1},y_{2}\geq 0$ in $M,$ $x\leq
y_{1}+y_{2}\Rightarrow x=x_{1}+x_{2}$ where $0\leq x_{i}\leq y_{i}$. We explore
the necessary and sufficient conditions under which a Riesz monoid $% M $ with
$M^{+}=\{x\geq 0|x\in M\}=M$ generates a Riesz group and indicate some
applications. We call a directed p.o. monoid $M$ $\Pi $-pre-Riesz if $%
M^{+}=M$ and for all $x_{1},x_{2},...,x_{n}\in M$, $%
glb(x_{1},x_{2},...,x_{n})=0$ or there is $r\in \Pi $ such that $0<r\leq
x_{1},x_{2},...,x_{n},$ for some subset $\Pi $ of $M.$ We explore examples of
$\Pi $-pre-Riesz monoids of $\star $-ideals of different types. We show for
instance that if $M$ is the monoid of nonzero (integral) ideals of a Noetherian
domain $D$ and $\Pi $ the set of invertible ideals, $M$ is $\Pi $ -pre-Riesz if
and only $D$ is a Dedekind domain. We also study factorization in pre-Riesz
monoids of a certain type and link it with factorization theory of ideals in an
integral domain.


  We report the experimental demonstration of a magnetologic gate built on
graphene at room temperature. This magnetologic gate consists of three
ferromagnetic electrodes contacting a single layer graphene spin channel and
relies on spin injection and spin transport in the graphene. We utilize
electrical bias tuning of spin injection to balance the inputs and achieve
"exclusive or" (XOR) logic operation. Furthermore, simulation of the device
performance shows that substantial improvement towards spintronic applications
can be achieved by optimizing device parameters such as device dimensions. This
advance holds promise as a basic building block for spin-based information
processing.


  Despite significant success of deep learning in object detection tasks, the
standard training of deep neural networks requires access to a substantial
quantity of annotated images across all classes. Data annotation is an arduous
and time-consuming endeavor, particularly when dealing with infrequent objects.
Few-shot object detection (FSOD) methods have emerged as a solution to the
limitations of classic object detection approaches based on deep learning. FSOD
methods demonstrate remarkable performance by achieving robust object detection
using a significantly smaller amount of training data. A challenge for FSOD is
that instances from novel classes that do not belong to the fixed set of
training classes appear in the background and the base model may pick them up
as potential objects. These objects behave similarly to label noise because
they are classified as one of the training dataset classes, leading to FSOD
performance degradation. We develop a semi-supervised algorithm to detect and
then utilize these unlabeled novel objects as positive samples during the FSOD
training stage to improve FSOD performance. Specifically, we develop a
hierarchical ternary classification region proposal network (HTRPN) to localize
the potential unlabeled novel objects and assign them new objectness labels to
distinguish these objects from the base training dataset classes. Our improved
hierarchical sampling strategy for the region proposal network (RPN) also
boosts the perception ability of the object detection model for large objects.
We test our approach and COCO and PASCAL VOC baselines that are commonly used
in FSOD literature. Our experimental results indicate that our method is
effective and outperforms the existing state-of-the-art (SOTA) FSOD methods.
Our implementation is provided as a supplement to support reproducibility of
the results.


  Identification of non-amplified DNA sequences and single-base mutations is
essential for molecular biology and genetic diagnostics. This paper reports a
novel sensor consisting of electrochemically-gated graphene coplanar waveguides
coupled with a microfluidic channel. Upon exposure to analytes, propagation of
electromagnetic waves in the waveguides is modified as a result of interactions
with the fringing field and modulation of graphene dynamic conductivity
resulting from electrostatic gating. Probe DNA sequences are immobilised on the
graphene surface, and the sensor is exposed to DNA sequences which either
perfectly match the probe, contain a singlebase mismatch or are unrelated. By
monitoring the scattering parameters at frequencies between 50 MHz and 50 GHz,
unambiguous and reproducible discrimination of the different strands is
achieved at concentrations as low as 1 attomole per litre (1 aM). By
controlling and synchronising frequency sweeps, electrochemical gating, and
liquid flow in the microfluidic channel, the sensor generates multidimensional
datasets. Advanced data analysis techniques are utilised to take full advantage
of the richness of the dataset. A classification accuracy > 97% between all
three sequences is achieved using different Machine Learning models, even in
the presence of simulated noise and low signal-to-noise ratios. The sensor
exceeds state-of-the-art sensitivity of field-effect transistors and microwave
sensors for the identification of single-base mismatches.


  We present here two detailed examples of additive categorifications of the
cluster algebra structure of a coordinate ring of a maximal unipotent subgroup
of a simple Lie group. The first one is of simply-laced type ($A_3$) and relies
on an article by Gei\ss, Leclerc and Schr\"oer. The second is of non
simply-laced type ($C_2$) and relies on an article by the author of this note.
This is aimed to be accessible, specially for people who are not familiar with
this subject.


  We study the dynamics of the family $f_c(x, y)= (xy+c, x)$ of endomorphisms
of $\mathbb{R}^2$ and $\mathbb{C}^2$, where $c$ is a real or complex parameter.
Such maps can be seen as perturbations of the map $f_0(x,y)=(xy,x)$, which is a
complexification of the Anosov torus map $(u,v) \mapsto (u+v,u)$.


  We study Maxwell's equations on a 4-manifold where the electromagnetic medium
is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting,
the Tamm-Rubilar tensor density determines a polynomial surface of fourth order
in each cotangent space. This surface is called the Fresnel surface and acts as
a generalisation of the light-cone determined by a Lorentz metric; the Fresnel
surface parameterises electromagnetic wave-speed as a function of direction.
Favaro and Bergamin have recently proven that if $\kappa$ has only a principal
part and if the Fresnel surface of $\kappa$ coincides with the light cone for a
Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of
$g$. That is, under additional assumptions, the Fresnel surface of $\kappa$
determines the conformal class of $\kappa$. The purpose of this paper is
twofold. First, we provide a new proof of this result using Gr\"obner bases.
Second, we describe a number of cases where the Fresnel surface does not
determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For
example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have
the same Fresnel surfaces.


  In order to obtain the information about flow field, traditional
computational fluid dynamics methods need to solve the Navier-Stokes equations
on the mesh with boundary conditions, which is a time-consuming task. In this
work, a data-driven method based on convolutional neural network and multi-head
perceptron is used to predict the incompressible laminar steady sparse flow
field around the airfoils. Firstly, we use convolutional neural network to
extract the geometry parameters of the airfoil from the input gray scale image.
Secondly, the extracted geometric parameters together with Reynolds number,
angle of attack and flow field coordinates are used as the input of the
multi-layer perceptron and the multi-head perceptron. The proposed multi-head
neural network architecture can predict the aerodynamic coefficients of the
airfoil in seconds. Furthermore, the experimental results show that for sparse
flow field, multi-head perceptron can achieve better prediction results than
multi-layer perceptron.


  The basic mathematical assumptions for autonomous linear kinetic equations
for a classical system are formulated, leading to the conclusion that if they
are differential equations on its phase space $M$, they are at most of the 2nd
order. For open systems interacting with a bath at canonical equilibrium they
have a particular form of an equation of a generalized Fokker-Planck type. We
show that it is possible to obtain them as Liouville equations of Hamiltonian
dynamics on $M$ with a particular non-commutative differential structure,
provided certain geometric in character, conditions are fulfilled. To this end,
symplectic geometry on $M$ is developped in this context, and an outline of the
required tensor analysis and differential geometry is given. Certain questions
for the possible mathematical interpretation of this structure are also
discussed.


  The goal of the SIMBA collaboration is to provide a global fit to the
available data in inclusive B -> X_s gamma and B -> X_u l nu decays. By
performing a global fit one is able to simultaneously determine the relevant
normalizations, i.e. the total B -> X_s gamma rate and the CKM-matrix element
|Vub|, together with the required input parameters, most importantly the
b-quark mass and the b-quark distribution function in the B-meson, called the
shape function. This strategy is analogous to the determination of |Vcb| from
global fits to inclusive B -> X_c l nu decays. In this talk, we present
preliminary results for the shape function and |C_7^incl Vtb Vts^*|, which
parametrizes the total B -> X_s gamma rate, from a global fit to the available
B -> X_s gamma measurements from BABAR and Belle.


  We present the first detailed spatio-kinematical analysis and modelling of
the planetary nebula HaTr 4, one of few known to contain a post-common-envelope
central star system. Common envelope evolution is believed to play an important
role in the shaping of planetary nebulae, but the exact nature of this role is
yet to be understood. High spatial- and spectral- resolution spectroscopy of
the [OIII]5007 nebular line obtained with VLT-UVES are presented alongside deep
narrowband Ha+[NII]6584 imagery obtained using EMMI-NTT, and together the two
are used to derive the three-dimensional morphology of HaTr 4. The nebula is
found to display an extended ovoid morphology with an enhanced equatorial
region consistent with a toroidal waist - a feature believed to be typical
amongst planetary nebulae with post-common-envelope central stars. The nebular
symmetry axis is found to lie perpendicular to the orbital plane of the central
binary, concordant with the idea that the formation and evolution of HaTr 4 has
been strongly influenced by its central binary.


  We have studied the electrical conductivity of nanoring-based, transparent
conductive films, these being promising elements for flexible electronic
devices. Both the wire resistance and the junction resistance were taken into
account. We have calculated the dependency of the electrical conductivity on
the number density of the rings. We have proposed a mean-field approach to
estimate the dependency of the electrical conductivity on the main parameters.
Comparison of direct computations of the electrical conductivity and the
estimates provided by the mean-field approach evidenced the applicability of
this approach for those cases where the wire resistance dominates over the
junction resistance and where both resistances are of the same order. For these
two cases, both the direct computations and the mean-field approach evidenced a
linear dependence of the electrical conductivity of the films on the number
density of the conductive rings. By contrast, the dependence of the electrical
conductivity on the number density of the conductive rings is a quadratic when
the junction resistance dominates over the wire resistance. In this case, the
mean-field approach significantly overestimates the electrical conductivity,
since the main assumptions underlying this approach are no longer fulfilled.


  Weak supervision has emerged as a promising approach for rapid and
large-scale dataset creation in response to the increasing demand for
accelerated NLP development. By leveraging labeling functions, weak supervision
allows practitioners to generate datasets quickly by creating learned label
models that produce soft-labeled datasets. This paper aims to show how such an
approach can be utilized to build an Indonesian NLP dataset from conservation
news text. We construct two types of datasets: multi-class classification and
sentiment classification. We then provide baseline experiments using various
pretrained language models. These baseline results demonstrate test
performances of 59.79% accuracy and 55.72% F1-score for sentiment
classification, 66.87% F1-score-macro, 71.5% F1-score-micro, and 83.67% ROC-AUC
for multi-class classification. Additionally, we release the datasets and
labeling functions used in this work for further research and exploration.


  We describe a class of theories of dielectric polarization and a species of
solitons in these theories. The solitons, made entirely out of the polarization
field, have quantized values of the electric charge and can be interpreted as
electrons and holes. A soliton-antisoliton pair is an exciton. We present
numerical evidence that the elementary soliton is stable.


  Results obtained recently in Phys. Rev. Lett. 108, 120603 (2012) by Cleuren
et al. apparently contradict to the third law of thermodynamics. We discuss a
scenario for resolving this contradiction, and show that this scenario is
pertinent for clarifying the general message of the third law.


  Td-WTe2 is a topological Weyl semimetal. WTe2 in the orthorhombic structure
is stable at room temperature. Elastic, electronic, bonding, and optoelectronic
properties of WTe2 have been investigated in detail in this work using the
density functional theory. Elastic behaviour together with anisotropy indices
of WTe2 have been investigated for the first time. Bonding nature among the
constituent atoms and electric field polarization dependent optical constants
have also been explored for the first time. WTe2 is elastically anisotropic;
optical anisotropy on the other hand is low. The electronic band structure
reveals quasi-linear dispersions along certain direction in the Brillouin zone
with semi-metallic features. The Fermi level is located at a pseudogap
separating bonding and anti-bonding density of states. The electronic effective
mass tensor is predicted to be highly direction dependent. The energy
dispersion is significantly weaker in the c-direction. The bonding in WTe2 is
an admixture of covalent and metallic bonds. Optoelectronic properties show
strongly reflecting character over a wide band of photon energies. The compound
is a strong absorber of ultraviolet radiation. The Debye temperature has been
calculated from the elastic constants. We have compared all the calculated
physical properties of WTe2 with those of isostructural MoTe2 Weyl semimetals.
The properties of WTe2 and MoTe2 have been compared and contrasted. The
calculated parameters of WTe2 have also been compared with those already
available in the literature. Very good agreements have been found.


  Suppose the ground field $\mathbb{F}$ is an algebraically closed field
characteristic of $p>2$. In this paper, we investigate the restricted
cohomology theory of restricted Lie superalgebras. Algebraic interpretations of
low dimensional restricted cohomology of restricted Lie superalgebra are given.
We show that there is a family of restricted model filiform Lie superalgebra
$L_{p,p}^{\lambda}$ structures parameterized by elements $\lambda\in
\mathbb{F}^{p}.$ We explicitly describe both the $1$-dimensional ordinary and
restricted cohomology superspaces of $L_{p,p}^{\lambda}$ with coefficients in
the $1$-dimensional trivial module and show that these superspaces are equal.
We also describe the $2$-dimensional ordinary and restricted cohomology
superspaces of $L_{p,p}^{\lambda}$ with coefficients in the $1$-dimensional
trivial module and show that these superspaces are unequal.


  In this paper, we study the average case complexity of the Unique Games
problem. We propose a natural semi-random model, in which a unique game
instance is generated in several steps. First an adversary selects a completely
satisfiable instance of Unique Games, then she chooses an epsilon-fraction of
all edges, and finally replaces ("corrupts") the constraints corresponding to
these edges with new constraints. If all steps are adversarial, the adversary
can obtain any (1-epsilon) satisfiable instance, so then the problem is as hard
as in the worst case. In our semi-random model, one of the steps is random, and
all other steps are adversarial. We show that known algorithms for unique games
(in particular, all algorithms that use the standard SDP relaxation) fail to
solve semi-random instances of Unique Games.
  We present an algorithm that with high probability finds a solution
satisfying a (1-delta) fraction of all constraints in semi-random instances (we
require that the average degree of the graph is Omega(log k). To this end, we
consider a new non-standard SDP program for Unique Games, which is not a
relaxation for the problem, and show how to analyze it. We present a new
rounding scheme that simultaneously uses SDP and LP solutions, which we believe
is of independent interest.
  Our result holds only for epsilon less than some absolute constant. We prove
that if epsilon > 1/2, then the problem is hard in one of the models, the
result assumes the 2-to-2 conjecture.
  Finally, we study semi-random instances of Unique Games that are at most
(1-epsilon) satisfiable. We present an algorithm that with high probability,
distinguishes between the case when the instance is a semi-random instance and
the case when the instance is an (arbitrary) (1-delta) satisfiable instance if
epsilon > c delta.


  A locally correctable code (LCC) is an error correcting code that allows
correction of any arbitrary coordinate of a corrupted codeword by querying only
a few coordinates. We show that any {\em zero-error} $2$-query locally
correctable code $\mathcal{C}: \{0,1\}^k \to \Sigma^n$ that can correct a
constant fraction of corrupted symbols must have $n \geq \exp(k/\log|\Sigma|)$.
We say that an LCC is zero-error if there exists a non-adaptive corrector
algorithm that succeeds with probability $1$ when the input is an uncorrupted
codeword. All known constructions of LCCs are zero-error.
  Our result is tight upto constant factors in the exponent. The only previous
lower bound on the length of 2-query LCCs over large alphabet was
$\Omega\left((k/\log|\Sigma|)^2\right)$ due to Katz and Trevisan (STOC 2000).
Our bound implies that zero-error LCCs cannot yield $2$-server private
information retrieval (PIR) schemes with sub-polynomial communication. Since
there exists a $2$-server PIR scheme with sub-polynomial communication (STOC
2015) based on a zero-error $2$-query locally decodable code (LDC), we also
obtain a separation between LDCs and LCCs over large alphabet.
  For our proof of the result, we need a new decomposition lemma for directed
graphs that may be of independent interest. Given a dense directed graph $G$,
our decomposition uses the directed version of Szemer\'edi regularity lemma due
to Alon and Shapira (STOC 2003) to partition almost all of $G$ into a constant
number of subgraphs which are either edge-expanding or empty.


  Surface properties of Co-doped BaFe2As2 epitaxial superconducting thin films
were inspected by X-ray photoelectron spectroscopy, scanning spreading
resistance microscopy (SSRM), and point contact spectroscopy (PCS). It has been
shown that surface of Fe-based superconductors degrades rapidly if being
exposed to air, what results in suppression of gap-like structure on PCS
spectra. Moreover, SSRM measurements revealed inhomogeneous surface
conductivity, what is consistent with strong dependence of PCS spectra on
contact position. Presented results suggest that fresh surface and small
probing area should be assured for surface sensitive measurements like PCS to
obtain intrinsic properties of Fe-based superconductors.


  The feasibility of a model-independent extraction of the forward strong
amplitude from elastic nuclear cross section data in the Coulomb-nuclear
interference region is assessed for $\pi$ and $K^+$ scattering at intermediate
energies. Theoretically-generated "data" are analyzed to provide criteria for
optimally designing experiments to measure these amplitudes, whose energy
dependence (particularly that of the real parts) is needed for disentangling
various sources of medium modifications of the projectile-nucleon interaction.
The issues considered include determining the angular region over which to make
the measurements, the role of the most forward angles measured, and the effects
of statistical and systematic errors. We find that there is a region near the
forward direction where Coulomb-nuclear interference allows reliable extraction
of the strong forward amplitude for both pions and the $K^+$ from .3 to 1
GeV/c.


  The local atomic and magnetic structures of the compounds $A$MnO$_2$ ($A$ =
Na, Cu), which realize a geometrically frustrated, spatially anisotropic
triangular lattice of Mn spins, have been investigated by atomic and magnetic
pair distribution function analysis of neutron total scattering data. Relief of
frustration in CuMnO$_2$ is accompanied by a conventional cooperative
symmetry-lowering lattice distortion driven by N\'eel order. In NaMnO$_2$,
however, the distortion has a short-range nature. A cooperative interaction
between the locally broken symmetry and short-range magnetic correlations lifts
the magnetic degeneracy on a nanometer length scale, enabling long-range
magnetic order in the Na-derivative. The degree of frustration, mediated by
residual disorder, contributes to the rather differing pathways to a single,
stable magnetic ground state in these two related compounds. This study
demonstrates how nanoscale structural distortions that cause local-scale
perturbations can lift the ground state degeneracy and trigger macroscopic
magnetic order.


  The number of earthquakes as a function of magnitude decays as a power law.
This trend is usually justified using spring-block models, where slips with the
appropriate global statistics have been numerically observed. However,
prominent spatial and temporal clustering features of earthquakes are not
reproduced by this kind of modeling. We show that when a spring-block model is
complemented with a mechanism allowing for structural relaxation, realistic
earthquake patterns are obtained. The proposed model does not need to include a
phenomenological velocity weakening friction law, as traditional spring-block
models do, since this behavior is effectively induced by the relaxational
mechanism as well. In this way, the model provides also a simple microscopic
basis for the widely used phenomenological rate-and-state equations of rock
friction.


  A problem with Convolutional Neural Networks (CNNs) is that they require
large datasets to obtain adequate robustness; on small datasets, they are prone
to overfitting. Many methods have been proposed to overcome this shortcoming
with CNNs. In cases where additional samples cannot easily be collected, a
common approach is to generate more data points from existing data using an
augmentation technique. In image classification, many augmentation approaches
utilize simple image manipulation algorithms. In this work, we build ensembles
on the data level by adding images generated by combining fourteen augmentation
approaches, three of which are proposed here for the first time. These novel
methods are based on the Fourier Transform (FT), the Radon Transform (RT) and
the Discrete Cosine Transform (DCT). Pretrained ResNet50 networks are finetuned
on training sets that include images derived from each augmentation method.
These networks and several fusions are evaluated and compared across eleven
benchmarks. Results show that building ensembles on the data level by combining
different data augmentation methods produce classifiers that not only compete
competitively against the state-of-the-art but often surpass the best
approaches reported in the literature.


  In the conventional picture, the temperature of a liquid bath in the
quiescent state is uniform down to thermal fluctuation length scales. Here we
examine the impact of a low frequency shear mechanical field (Hz) on the
thermal equilibrium of liquids (Polypropylene glycol and pentadecane away from
any phase transition) confined between high energy surfaces. We show the
emergence of both cooling and heating shear waves of several tens microns
widths varying synchronously with the applied shear strain wave. The thermal
wave is stable at low strain amplitude and low frequency while thermal
harmonics develop by slightly increasing the frequency or the strain amplitude.
The liquid layer behaves as a thermoelastic medium. This view is in agreement
with recent theoretical models predicting that liquids support shear elastic
waves up to finite propagation length scale of the order the thermal wave.


  We aim to present a generalized Bayesian inference method for constraining
interiors of super Earths and sub-Neptunes. Our methodology succeeds in
quantifying the degeneracy and correlation of structural parameters for high
dimensional parameter spaces. Specifically, we identify what constraints can be
placed on composition and thickness of core, mantle, ice, ocean, and
atmospheric layers given observations of mass, radius, and bulk refractory
abundance constraints (Fe, Mg, Si) from observations of the host star's
photospheric composition. We employed a full probabilistic Bayesian inference
analysis that formally accounts for observational and model uncertainties.
Using a Markov chain Monte Carlo technique, we computed joint and marginal
posterior probability distributions for all structural parameters of interest.
We included state-of-the-art structural models based on self-consistent
thermodynamics of core, mantle, high-pressure ice, and liquid water.
Furthermore, we tested and compared two different atmospheric models that are
tailored for modeling thick and thin atmospheres, respectively. First, we
validate our method against Neptune. Second, we apply it to synthetic
exoplanets of fixed mass and determine the effect on interior structure and
composition when (1) radius, (2) atmospheric model, (3) data uncertainties, (4)
semi-major axes, (5) atmospheric composition (i.e., a priori assumption of
enriched envelopes versus pure H/He envelopes), and (6) prior distributions are
varied. Our main conclusions are: [...]


  Let G be a semisimple quasi-split group defined over a global function field.
We express the relative Tamagawa number of G in terms of local data including
the number of types of special vertices in one orbit of the Bruhat-Tits
building over some completion with respect to a place and the class number of G
at that place.


  Context. Current constraints on distributed matter in the innermost Galactic
Centre (such as a cluster of faint stars and stellar remnants, Dark Matter or a
combination thereof) based on the orbital dynamics of the visible stars closest
to the central black hole, typically assume simple functional forms for the
distributions. Aims. We take instead a general model agnostic approach in which
the form of the distribution is not constrained by prior assumptions on the
physical composition of the matter. This approach yields unbiased - entirely
observation driven - fits for the matter distribution and places constraints on
our ability to discriminate between different density profiles (and
consequently between physical compositions) of the distributed matter. Methods.
We construct a spherical shell model with the flexibility to fit a wide variety
of physically reasonable density profiles by modelling the distribution as a
series of concentric mass shells. We test this approach in an analysis of mock
observations of the star S2. Results. For a sufficiently large and precise data
set, we find that it is possible to discriminate between several physically
motivated density profiles. However, for data coming from current and expected
next generation observational instruments, the potential for profile
distinction will remain limited by the precision of the instruments. Future
observations will still be able to constrain the overall enclosed distributed
mass within the apocentre of the probing orbit in an unbiased manner. We
interpret this in the theoretical context of constraining the secular versus
non-secular orbital dynamics.


  We derive an upper limit on the neutrino mass from the WMAP three-year data
alone by employing a deterministic minimisation method based on a grid search
in multi-parameter space. Assuming the flat LCDM model with power-law adiabatic
perturbations, we find the sum of m_nu < 2.0 eV in agreement with the result of
the WMAP team. This result, the limit being nearly the same as that from the
WMAP first-year data, means that the fundamental limit on the neutrino mass
obtainable from the cosmic microwave background alone is already nearly met, as
anticipated from the previous analysis. We also clarify the role of the
polarisation data in deriving the limit on the neutrino mass.


  Rich empirical evidence has shown that visual object recognition in the brain
is fast and effortless, with relevant brain signals reported to start as early
as 80 ms. Here we study the time trajectory of the recognition process at the
level of minimal recognizable images (termed MIRC). These are images that can
be recognized reliably, but in which a minute change of the image (reduction by
either size or resolution) has a drastic effect on recognition. Subjects were
assigned to one of nine exposure conditions: 200, 500, 1000, 2000 ms with or
without masking, as well as unlimited time. The subjects were not limited in
time to respond after presentation. The results show that in the masked
conditions, recognition rates develop gradually over an extended period, e.g.
average of 18% for 200 ms exposure and 45% for 500 ms, increasing significantly
with longer exposure even above 2 secs. When presented for unlimited time
(until response), MIRC recognition rates were equivalent to the rates of
full-object images presented for 50 ms followed by masking. What takes the
brain so long to recognize such images? We discuss why processes involving
eye-movements, perceptual decision-making and pattern completion are unlikely
explanations. Alternatively, we hypothesize that MIRC recognition requires an
extended top-down process complementing the feed-forward phase.


  We find a transformation which relates a new third-order integrable nonlinear
evolution equation, introduced recently by Qiao, with the well-known modified
Korteweg - de Vries equation. Then we use this transformation to derive smooth
soliton solutions of the new equation from the known rational and soliton
solutions of the old one.


  Heavy-quark spin symmetry is explicitly broken by the mass splitting between
a heavy-light pseudoscalar meson and its vector partner. This fact plays a
pivotal role in the physics of states whose mass lies close to the threshold of
an open-flavor meson pair, like $X(3872)$. We show that this source of
heavy-quark spin symmetry breaking can be systematically included within the
diabatic representation of the Born-Oppenheimer approximation. We verify that
including all the appropriate coupled channels guarantees conservation of total
angular momentum, parity, and charge-conjugation parity. This marks a
fundamental step towards a unified, first-principles study of quarkonia and
meson molecules with hidden flavor.


  This paper discusses how to crawl the data of financial forums such as stock
bar, and conduct emotional analysis combined with the in-depth learning model.
This paper will use the Bert model to train the financial corpus and predict
the Shenzhen stock index. Through the comparative study of the maximal
information coefficient (MIC), it is found that the emotional characteristics
obtained by applying the BERT model to the financial corpus can be reflected in
the fluctuation of the stock market, which is conducive to effectively improve
the prediction accuracy. At the same time, this paper combines in-depth
learning with financial texts to further explore the impact mechanism of
investor sentiment on the stock market through in-depth learning, which will
help the national regulatory authorities and policy departments to formulate
more reasonable policies and guidelines for maintaining the stability of the
stock market.


  We present results from combining a grid-based radiative transfer code with a
Smoothed Particle Hydrodynamics code to produce a flexible system for modelling
radiation hydrodynamics. We use a benchmark model of a circumstellar disc to
determine a robust method for constructing a gridded density distribution from
SPH particles. The benchmark disc is then used to determine the accuracy of the
radiative transfer results. We find that the SED and the temperature
distribution within the disc are sensitive to the representation of the disc
inner edge, which depends critically on both the grid and SPH resolution. The
code is then used to model a circumstellar disc around a T-Tauri star. As the
disc adjusts towards equilibrium vertical motions in the disc are induced
resulting in scale height enhancements which intercept radiation from the
central star. Vertical transport of radiation enables these perturbations to
influence the mid-plane temperature of the disc. The vertical motions decay
over time and the disc ultimately reaches a state of simultaneous hydrostatic
and radiative equilibrium.


  Unsupervised 3D keypoints estimation from Point Cloud Data (PCD) is a complex
task, even more challenging when an object shape is deforming. As keypoints
should be semantically and geometrically consistent across all the 3D frames -
each keypoint should be anchored to a specific part of the deforming shape
irrespective of intrinsic and extrinsic motion. This paper presents, "SelfGeo",
a self-supervised method that computes persistent 3D keypoints of non-rigid
objects from arbitrary PCDs without the need of human annotations. The gist of
SelfGeo is to estimate keypoints between frames that respect invariant
properties of deforming bodies. Our main contribution is to enforce that
keypoints deform along with the shape while keeping constant geodesic distances
among them. This principle is then propagated to the design of a set of losses
which minimization let emerge repeatable keypoints in specific semantic
locations of the non-rigid shape. We show experimentally that the use of
geodesic has a clear advantage in challenging dynamic scenes and with different
classes of deforming shapes (humans and animals). Code and data are available
at: https://github.com/IIT-PAVIS/SelfGeo


  It is shown that in the greatly simplified model of the mutually interacting
electron-positron pairs and the electric field time-crystal structures can
spontaneously form. For a special choice of parameters we find a periodic
modulation of the pair number and the electric field.


  A scheme for optimal and deterministic linear optical purification of mixed
squeezed Gaussian states is proposed and experimentally demonstrated. The
scheme requires only linear optical elements and homodyne detectors, and allows
the balance between purification efficacy and squeezing degradation to be
controlled. One particular choice of parameters gave a ten-fold reduction of
the thermal noise with a corresponding squeezing degradation of only 11%. We
prove optimality of the protocol, and show that it can be used to enhance the
performance of quantum informational protocols such as dense coding and
entanglement generation.


  We present ShapeFlow, a flow-based model for learning a deformation space for
entire classes of 3D shapes with large intra-class variations. ShapeFlow allows
learning a multi-template deformation space that is agnostic to shape topology,
yet preserves fine geometric details. Different from a generative space where a
latent vector is directly decoded into a shape, a deformation space decodes a
vector into a continuous flow that can advect a source shape towards a target.
Such a space naturally allows the disentanglement of geometric style (coming
from the source) and structural pose (conforming to the target). We parametrize
the deformation between geometries as a learned continuous flow field via a
neural network and show that such deformations can be guaranteed to have
desirable properties, such as be bijectivity, freedom from self-intersections,
or volume preservation. We illustrate the effectiveness of this learned
deformation space for various downstream applications, including shape
generation via deformation, geometric style transfer, unsupervised learning of
a consistent parameterization for entire classes of shapes, and shape
interpolation.


  We derive general and complete expressions for N-point tree-level amplitudes
in Type II string models with matter fields localised at D-brane intersections.


  In this work we propose to simulate many-body thermodynamics of infinite-size
quantum lattice models in one, two, and three dimensions, in terms of few-body
models of only O(10) sites, which we coin as quantum entanglement simulators
(QES's). The QES is described by a temperature-independent Hamiltonian, with
the boundary interactions optimized by the tensor network methods to mimic the
entanglement between the bulk and environment in a finite-size canonical
ensemble. The reduced density matrix of the physical bulk then gives that of
the infinite-size canonical ensemble under interest. We show that the QES can,
for instance, accurately simulate varieties of many-body phenomena, including
finite-temperature crossover and algebraic excitations of the one-dimensional
spin liquid, the phase transitions and low-temperature physics of the two- and
three-dimensional antiferromagnets, and the crossovers of the two-dimensional
topological system. Our work provides an efficient way to explore the
thermodynamics of intractable quantum many-body systems with easily accessible
systems.


  The widespread prevalence of close-in, nearly coplanar super-Earth- and
sub-Neptune-sized planets in multiple-planet systems was one of the most
surprising results from the Kepler mission. By studying a uniform sample of
Kepler "multis" with mass measurements from transit timing variations (TTVs),
we show that a given planetary system tends to harbor a characteristic type of
planet. That is, planets in a system have both masses and radii that are far
more similar than if the system were assembled randomly from planets in the
population. This finding has two important ramifications. First, the large
intrinsic compositional scatter in the planet mass-radius relation is dominated
by system-to-system variance rather than intra-system variance. Second, if
provided enough properties of the star and primordial protoplanetary disk,
there may be a substantial degree of predictability in the outcome of the
planet formation process. We show that stellar mass and metallicity account for
of order $20\%$ of the variation in outcomes; the remainder is as-yet unknown.


  A number of interesting physical phenomena have been discovered in
magic-angle twisted bilayer graphene (MATBG), such as superconductivity,
correlated gapped and gapless phases, etc. The gapped phases are believed to be
symmetry-breaking states described by mean-field theories, whereas gapless
phases exhibit features beyond mean field. This work, combining poor man's
scaling, numerical renormalization group, and dynamic mean-field theory,
demonstrates that the gapless phases are the heavy Fermi liquid state with some
symmetries broken and the others preserved. We adopt the recently proposed
topological heavy fermion model for MATBG with effective local orbitals around
AA-stacking regions and Dirac fermions surrounding them. At zero temperature
and most non-integer fillings, the ground states are found to be heavy Fermi
liquids and exhibit Kondo resonance peaks. The Kondo temperature $T_K$ is found
at the order of 1meV. A higher temperature than $T_K$ will drive the system
into a metallic LM phase where disordered LM's and a Fermi liquid coexist. At
integer fillings $\pm1,\pm2$, $T_K$ is suppressed to zero or a value weaker
than RKKY interaction, leading to Mott insulators or symmetry-breaking states.
This theory offers a unified explanation for several experimental observations,
such as zero-energy peaks and quantum-dot-like behaviors in STM, the
Pomeranchuk effect, and the saw-tooth feature of inverse compressibility, etc.
For future experimental verification, we predict that the Fermi surface in the
gapless phase will shrink upon heating - as a characteristic of the heavy Fermi
liquid. We also conjecture that the heavy Fermi liquid is the parent state of
the observed unconventional superconductivity because the Kondo screening
reduces the overwhelming Coulomb interaction (~60meV) to a rather small
effective interaction (~1meV) comparable to possible weak attractive
interactions.


  A suitable NMR experiment in a one-dimensional dipolar coupled spin system
allows one to reduce the natural many-body dynamics into effective one-body
dynamics. We verify this in a polycrystalline sample of hydroxyapatite (HAp) by
monitoring the excitation of NMR many-body superposition states: the
multiple-quantum coherences. The observed effective one-dimensionality of HAp
relies on the quasi 1d structure of the dipolar coupled network that, as we
show here, is dynamically enhanced by the quantum Zeno effect. Decoherence is
also probed through a Loschmidt echo experiment, where the time reversal is
implemented on the double-quantum Hamiltonian, I_{i,+}I_{j,+} + I_{i,-}I_{j,-}.
We contrast the decoherence of adamantane, a standard 3d system, with that of
HAp. While the first shows an abrupt Fermi-type decay, HAp presents a smooth
exponential law.


  Researchers and journalists have repeatedly shown that algorithms commonly
used in domains such as credit, employment, healthcare, or criminal justice can
have discriminatory effects. Some organizations have tried to mitigate these
effects by simply removing sensitive features from an algorithm's inputs. In
this paper, we explore the limits of this approach using a unique opportunity.
In 2019, Facebook agreed to settle a lawsuit by removing certain sensitive
features from inputs of an algorithm that identifies users similar to those
provided by an advertiser for ad targeting, making both the modified and
unmodified versions of the algorithm available to advertisers. We develop
methodologies to measure biases along the lines of gender, age, and race in the
audiences created by this modified algorithm, relative to the unmodified one.
Our results provide experimental proof that merely removing demographic
features from a real-world algorithmic system's inputs can fail to prevent
biased outputs. As a result, organizations using algorithms to help mediate
access to important life opportunities should consider other approaches to
mitigating discriminatory effects.


  The structure function of the vortex lattice of layered superconductor is
calculated to one-loop order. Based on a phenomenological melting criterion
concerning the Debye-Waller factor, we calculate the melting line of the vortex
lattice, and compare our results to Monte Carlo simulation and experiment. We
find that our results are quantitatively in good agreement with the Monte Carlo
results. Moreover, our analytic calculation of the melting line of BSCCO fits
the experiment reasonably well in a temperature range not far from Tc.


  In the race towards high-performance ultra-scaled devices, two-dimensional
materials offer an alternative paradigm thanks to their atomic thickness
suppressing short-channel effects. It is thus urgent to study the most
promising candidates in realistic configurations, and here we present detailed
multiscale simulations of field-effect transistors based on arsenene and
antimonene monolayers as channels. The accuracy of first-principles approaches
in describing electronic properties is combined with the efficiency of
tight-binding Hamiltonians based on maximally-localised Wannier functions to
compute the transport properties of the devices. These simulations provide for
the first time estimates on the upper limits for the electron and hole
mobilities in the Takagi's approximation, including spin-orbit and multi-valley
effects, and demonstrate that ultra-scaled devices in the sub-10 nm scale show
a performance that is compliant with industry requirements.


  Large Language Models (LLMs) have achieved remarkable performance in
objective tasks such as open-domain question answering and mathematical
reasoning, which can often be solved through recalling learned factual
knowledge or chain-of-thought style reasoning. However, we find that the
performance of LLMs in subjective tasks is still unsatisfactory, such as
metaphor recognition, dark humor detection, etc. Compared to objective tasks,
subjective tasks focus more on interpretation or emotional response rather than
a universally accepted reasoning pathway. Based on the characteristics of the
tasks and the strong dialogue-generation capabilities of LLMs, we propose RiC
(Reasoning in Conversation), a method that focuses on solving subjective tasks
through dialogue simulation. The motivation of RiC is to mine useful contextual
information by simulating dialogues instead of supplying chain-of-thought style
rationales, thereby offering potential useful knowledge behind dialogues for
giving the final answers. We evaluate both API-based and open-source LLMs
including GPT-4, ChatGPT, and OpenChat across twelve tasks. Experimental
results show that RiC can yield significant improvement compared with various
baselines.


  Accurate and precise stellar ages are best determined for stars which are
strongly observationally constrained, that is which are intrinsically
oscillating. We review here the seismic diagnostics which are sensitive to
stellar ages and provide some illustrating examples of seismically age-dated
stars.


  We numerically investigate quantum rings in graphene and find that their
electronic properties may be strongly influenced by the geometry, the edge
symmetries and the structure of the corners. Energy spectra are calculated for
different geometries (triangular, hexagonal and rhombus-shaped graphene rings)
and edge terminations (zigzag, armchair, as well as the disordered edge of a
round geometry). The states localized at the inner edges of the graphene rings
describe different evolution as a function of magnetic field when compared to
those localized at the outer edges. We show that these different evolutions are
the reason for the formation of sub-bands of edge states energy levels,
separated by gaps (anticrossings). It is evident from mapping the charge
densities that the anticrossings occur due to the coupling between inner and
outer edge states.


  Whereas low-temperature ferroelectrics have a well understood ordered spatial
dipole arrangement, the fate of these dipoles in paraelectric phases remains
poorly understood. Using density functional theory (DFT), we find that unlike
the case in conventional non-polar ABO$_3$ compounds illustrated here for cubic
BaZrO$_3$, the origin of the distribution of the B site off-centering in cubic
paraelectric such as BaTiO$_3$ is an intrinsic, energy stabilizing symmetry
breaking. Minimizing the internal energy E of a constrained cubic phase already
reveals the formation of a distribution of intrinsic local displacements that
(i) mimic the symmetries of the low temperature phases, while (ii) being the
precursors of what finite temperature DFT Molecular Dynamics finds as thermal
motifs. The implications of such symmetry breaking on the microscopic
structures and anomalous properties in these kinds of PE materials are
discussed.


  We give a new construction of free distributive p-algebras. Our construction
relies on a detailed description of completely meet-irreducible congruences, so
it is purely universal algebraic. It yields a normal form theorem for p-algebra
terms, simpler proofs of several existing results, as well as a complete
characterisation of structurally complete varieties of p-algebras.


  Censored survival data are common in clinical trial studies. We propose a
unified framework for sensitivity analysis to censoring at random in survival
data using multiple imputation and martingale, called SMIM. The proposed
framework adopts the \delta-adjusted and control-based models, indexed by the
sensitivity parameter, entailing censoring at random and a wide collection of
censoring not at random assumptions. Also, it targets for a broad class of
treatment effect estimands defined as functionals of treatment-specific
survival functions, taking into account of missing data due to censoring.
Multiple imputation facilitates the use of simple full-sample estimation;
however, the standard Rubin's combining rule may overestimate the variance for
inference in the sensitivity analysis framework. We decompose the multiple
imputation estimator into a martingale series based on the sequential
construction of the estimator and propose the wild bootstrap inference by
resampling the martingale series. The new bootstrap inference has a theoretical
guarantee for consistency and is computationally efficient compared to the
non-parametric bootstrap counterpart. We evaluate the finite-sample performance
of the proposed SMIM through simulation and an application on a HIV clinical
trial.


  The FLARE code is a magnetic mesh generator that is integrated within a suite
of tools for the analysis of the magnetic geometry in toroidal fusion devices.
A magnetic mesh is constructed from field line segments and permits fast
reconstruction of field lines in 3D plasma boundary codes such as EMC3-EIRENE.
Both intrinsically non-axisymmetric configurations (stellarators) and those
with symmetry breaking perturbations of an axisymmetric equilibrium (tokamaks)
are supported. The code itself is written in Modern Fortran with MPI support
for parallel computing, and it incorporates object-oriented programming for the
definition of the magnetic field and the material surface geometry. Extended
derived types for a number of different magnetohydrodynamic (MHD) equilibrium
and plasma response models are implemented. The core element of FLARE is a
field line tracer with adaptive step-size control, and this is integrated into
tools for the construction of Poincar\'e maps and invariant manifolds of
X-points. A collection of high-level procedures that generate output files for
visualization is build on top of that. The analysis modules are build with
Python frontends that facilitate customization of tasks and/or scripting of
parameter scans.


  The aim of this paper is to use a selection process and a careful study of
the interaction of bubbling solutions to show a classification result for the
blow-up values of the elliptic sinh-Gordon equation $$\Delta
u+h_1e^u-h_2e^{-u}=0 \quad \mathrm{in}~B_1\subset\mathbb{R}^2.$$ In particular
we get that the blow-up values are multiple of $8\pi.$ It generalizes the
result of Jost, Wang, Ye and Zhou \cite{jwyz} where the extra assumption $h_1 =
h_2$ is crucially used.


  In many robot control problems, factors such as stiffness and damping
matrices and manipulability ellipsoids are naturally represented as symmetric
positive definite (SPD) matrices, which capture the specific geometric
characteristics of those factors. Typical learned skill models such as dynamic
movement primitives (DMPs) can not, however, be directly employed with
quantities expressed as SPD matrices as they are limited to data in Euclidean
space.
  In this paper, we propose a novel and mathematically principled framework
that uses Riemannian metrics to reformulate DMPs such that the resulting
formulation can operate with SPD data in the SPD manifold. Evaluation of the
approach demonstrates that beneficial properties of DMPs such as change of the
goal during operation apply also to the proposed formulation.


  Investigation of the magnetism of Cu$_3$Mo$_2$O$_9$ single crystal, which has
antiferromagnetic (AF) linear chains interacting with AF dimers, reveals an AF
second-order phase transition at $T_{\rm N} = 7.9$ K. Although weak
ferromagnetic-like behavior appears at lower temperatures in low magnetic
fields, complete remanent magnetization cannot be detected down to 0.5 K.
However, a jump is observed in the magnetization below weak ferromagnetic (WF)
phase transition at $T_{\rm c} \simeq 2.5$ K when a tiny magnetic field along
the a axis is reversed, suggesting that the coercive force is very weak. A
component of magnetic moment parallel to the chain forms AF long-range order
(LRO) below $T_{\rm N}$, while a perpendicular component is disordered above
$T_{\rm c}$ at zero magnetic field and forms WF-LRO below $T_{\rm c}$.
Moreover, the WF-LRO is also realized with applying magnetic fields even
between $T_{\rm c}$ and $T_{\rm N}$. These results are explainable by both
magnetic frustration among symmetric exchange interactions and competition
between symmetric and asymmetric Dzyaloshinskii-Moriya exchange interactions.


  We propose a novel current-induced thermoelectric phenomenon, the nonlinear
anomalous Ettingshausen effect (AEE), at zero magnetic field in
inversion-asymmetric conductors. As an example, we discuss the weak charge
ordering state in a layered organic conductor alpha-(BEDT-TTF)2I3, which is a
two-dimensional massive Dirac fermion system with a pair of tilted Dirac cones.
The nonlinear AEE is a thermoelectric analogue of the nonlinear anomalous Hall
effect, which is recently observed in alpha-(BEDT-TTF)2I3, and these two
effects generally appear simultaneously. The nonlinear AEE generates a
transverse heat current, which exhibits rectifying characteristics, namely
unidirectionality even under an AC current.


  A central goal in algorithmic game theory is to analyze the performance of
decentralized multiagent systems, like communication and information networks.
In the absence of a central planner who can enforce how these systems are
utilized, the users can strategically interact with the system, aiming to
maximize their own utility, possibly leading to very inefficient outcomes, and
thus a high price of anarchy. To alleviate this issue, the system designer can
use decentralized mechanisms that regulate the use of each resource (e.g.,
using local queuing protocols or scheduling mechanisms), but with only limited
information regarding the state of the system. These information limitations
have a severe impact on what such decentralized mechanisms can achieve, so most
of the success stories in this literature have had to make restrictive
assumptions (e.g., by either restricting the structure of the networks or the
types of cost functions).
  In this paper, we overcome some of the obstacles that the literature has
imposed on decentralized mechanisms, by designing mechanisms that are enhanced
with predictions regarding the missing information. Specifically, inspired by
the big success of the literature on "algorithms with predictions", we design
decentralized mechanisms with predictions and evaluate their price of anarchy
as a function of the prediction error, focusing on two very well-studied
classes of games: scheduling games and multicast network formation games.


  The population-attributable fraction (PAF) expresses the proportion of events
that can be ascribed to a certain exposure in a certain population. It can be
strongly time-dependent because either exposure incidence or excess risk may
change over time. Competing events may moreover hinder the outcome of interest
from being observed. Occurrence of either of these events may, in turn, prevent
the exposure of interest. Estimation approaches therefore need to carefully
account for the timing of events in such highly dynamic settings. The use of
multistate models has been widely encouraged to eliminate preventable yet
common types of time-dependent bias. Even so, it has been pointed out that
proposed multistate modeling approaches for PAF estimation fail to fully
eliminate such bias. In addition, assessing whether patients die from rather
than with a certain exposure not only requires adequate modeling of the timing
of events but also of their confounding factors. While proposed multistate
modeling approaches for confounding adjustment may adequately accommodate
baseline imbalances, unlike g-methods, these proposals are not generally
equipped to handle time-dependent confounding. However, the connection between
multistate modeling and g-methods (e.g. inverse probability of censoring
weighting) for PAF estimation is not readily apparent. In this paper, we
provide a weighting-based characterization of both approaches to illustrate
this connection, to pinpoint current shortcomings of multistate modeling, and
to enhance intuition into simple modifications to overcome these. R code is
made available to foster the uptake of g-methods for PAF estimation.


  For the special linear group $\mathrm{SL}_2(\mathbb{C})$ and for the singular
quadratic Danielewski surface $x y = z^2$ we give explicitly a finite number of
complete polynomial vector fields that generate the Lie algebra of all
polynomial vector fields on them. Moreover, we give three unipotent
one-parameter subgroups that generate a subgroup of algebraic automorphisms
acting infinitely transitively on $x y = z^2$.


  We compute exterior Green functions for equipotential, grounded hyperspheres
in N-dimensional electrostatics by squashing Riemannian wormholes, where an
image charge is placed in the branch of the wormhole opposite the branch
containing the source charge, thereby providing a vivid geometrical approach to
a method first suggested in 1897 by Sommerfeld. We compare and contrast the
strength and location of the image charge in the wormhole approach with that of
the conventional Euclidean solution where an image charge of reduced magnitude
is located inside the hypersphere. While the two approaches give mathematically
equivalent Green functions, we believe they provide strikingly different
physics perspectives.


  In this study, we present a stabilized finite element analysis for completely
unified Stokes-Brinkman problems fully coupled with variable coefficient
transient Advection-Diffusion-Reaction equation(VADR). As well we have carried
out the stabilized finite element analysis for Stokes-Brinkman model with
interface conditions fully coupled with VADR. The viscosity of the fluid,
involved in flow problem, depends on the concentration of the solute, whose
transport is described by VADR equation. The algebraic subgrid multiscale
approach has been employed to arrive at the stabilized coupled variational
formulation. For the time discretization the fully implicit Euler scheme has
been used. A detailed derivation of both the apriori and aposteriori estimates
for the stabilized subgrid multiscale finite element scheme have been
presented. Few numerical experiments have been carried out to verify the
credibility of the method.