  We are concerned with relating derived categories of all modules of two dual
Koszul algebras defined by a locally bounded quiver. We first generalize the
well known Acyclic Assembly Lemma and formalize an old method of extending a
functor from an additive category into a complex category to its complex
category. Applying this to the Koszul functor associated with a Koszul algebra
defined by a gradable quiver, we obtain a Koszul complex functor, that descends
to an equivalence of a continuous family of pairs of triangulated subcategories
of doubly unbounded complexes of the respective derived categories of all
modules of the Koszul algebra and its Koszul dual. Under this special setting,
this extends Beilinson, Ginzburg and Soegel's Koszul duality. In case the
Koszul algebra is right or left locally bounded and its Koszul dual is left or
right locally bounded respectively (for instance, the quiver has no right
infinite path or no left infinite path), our Koszul duality restricts to an
equivalence of the bounded derived categories of finitely supported modules,
and an equivalence of the bounded derived categories of finite dimensional
modules.


  We study the merit of transfer learning for two sound recognition problems,
i.e., audio tagging and sound event detection. Employing feature fusion, we
adapt a baseline system utilizing only spectral acoustic inputs to also make
use of pretrained auditory and visual features, extracted from networks built
for different tasks and trained with external data. We perform experiments with
these modified models on an audiovisual multi-label data set, of which the
training partition contains a large number of unlabeled samples and a smaller
amount of clips with weak annotations, indicating the clip-level presence of 10
sound categories without specifying the temporal boundaries of the active
auditory events. For clip-based audio tagging, this transfer learning method
grants marked improvements. Addition of the visual modality on top of audio
also proves to be advantageous in this context. When it comes to generating
transcriptions of audio recordings, the benefit of pretrained features depends
on the requested temporal resolution: for coarse-grained sound event detection,
their utility remains notable. But when more fine-grained predictions are
required, performance gains are strongly reduced due to a mismatch between the
problem at hand and the goals of the models from which the pretrained vectors
were obtained.


  Surgery risk assessment is an effective tool for physicians to manage the
treatment of patients, but most current research projects fall short in
providing a comprehensive platform to evaluate the patients' surgery risk in
terms of different complications. The recent evolution of big data analysis
techniques makes it possible to develop a real-time platform to dynamically
analyze the surgery risk from large-scale patients information. In this paper,
we propose the Intelligent Perioperative System (IPS), a real-time system that
assesses the risk of postoperative complications (PC) and dynamically interacts
with physicians to improve the predictive results. In order to process large
volume patients data in real-time, we design the system by integrating several
big data computing and storage frameworks with the high through-output
streaming data processing components. We also implement a system prototype
along with the visualization results to show the feasibility of system design.


  The Einstein equation is derived from the proportionality of entropy and
horizon area together with the fundamental relation $\delta Q=TdS$ connecting
heat, entropy, and temperature. The key idea is to demand that this relation
hold for all the local Rindler causal horizons through each spacetime point,
with $\delta Q$ and $T$ interpreted as the energy flux and Unruh temperature
seen by an accelerated observer just inside the horizon. This requires that
gravitational lensing by matter energy distorts the causal structure of
spacetime in just such a way that the Einstein equation holds. Viewed in this
way, the Einstein equation is an equation of state. This perspective suggests
that it may be no more appropriate to canonically quantize the Einstein
equation than it would be to quantize the wave equation for sound in air.


  Parameter-space regularization in neural network optimization is a
fundamental tool for improving generalization. However, standard
parameter-space regularization methods make it challenging to encode explicit
preferences about desired predictive functions into neural network training. In
this work, we approach regularization in neural networks from a probabilistic
perspective and show that by viewing parameter-space regularization as
specifying an empirical prior distribution over the model parameters, we can
derive a probabilistically well-motivated regularization technique that allows
explicitly encoding information about desired predictive functions into neural
network training. This method -- which we refer to as function-space empirical
Bayes (FSEB) -- includes both parameter- and function-space regularization, is
mathematically simple, easy to implement, and incurs only minimal computational
overhead compared to standard regularization techniques. We evaluate the
utility of this regularization technique empirically and demonstrate that the
proposed method leads to near-perfect semantic shift detection,
highly-calibrated predictive uncertainty estimates, successful task adaption
from pre-trained models, and improved generalization under covariate shift.


  In the present Note we have presented some documents to reveal the
longstanding relationship of Indian amateur astronomer R. G. Chandra with
British Astronomical Association.


  We study the spectrum of the Toeplitz matrix with a sine kernel, which
corresponds to the single-particle reduced density matrix for free fermions on
the one-dimensional lattice. For the spectral determinant of this matrix, a
Fisher--Hartwig expansion in the inverse matrix size has been recently
conjectured. This expansion can be verified order by order, away from the line
of accumulation of zeros, using the recurrence relation known from the theory
of discrete Painleve equations. We perform such a verification to the tenth
order and calculate the corresponding coefficients in the Fisher-Hartwig
expansion. Under the assumption of the validity of the Fisher-Hartwig expansion
in the whole range of the spectral parameter, we further derive expansions for
an equation on the eigenvalues of this matrix and for the von Neumann
entanglement entropy in the corresponding fermion problem. These analytical
results are supported by a numerical example.


  In this paper, we investigate the two-hop full-duplex (FD) relay channel with
self-interference and fading, which is comprised of a source, an FD relay, and
a destination, where a direct source-destination link does not exist and the FD
relay is impaired by self-interference. For this channel, we propose three
buffer-aided relaying schemes with adaptive reception-transmission at the FD
relay for the cases when the source and the relay both perform adaptive-power
allocation, fixed-power allocation, and fixed-rate transmission, respectively.
The proposed buffer-aided relaying schemes significantly improve the achievable
rate and the throughput of the considered relay channel by enabling the FD
relay to adaptively select to either receive, transmit, or simultaneously
receive and transmit in a given time slot based on the qualities of the
receiving, transmitting, and self-interference channels. Our numerical results
show that significant performance gains are achieved using the proposed
buffer-aided relaying schemes compared to conventional FD relaying, where the
FD relay is forced to always simultaneously receive and transmit, and to
buffer-aided half-duplex relaying, where the half-duplex relay cannot
simultaneously receive and transmit.


  We show that the boundary behaviour of solutions to nonlocal fractional
equations posed in bounded domains strongly differs from the one of solutions
to elliptic problems modelled upon the Laplace-Poisson equation with zero
boundary data. In this classical case it is known that, at least in a suitable
weak sense, solutions of non-homogeneous Dirichlet problem are unique and tend
to zero at the boundary. Limits of these solutions then produce solutions of
some non-homogeneous Dirichlet problem as the interior data concentrate
suitably to the boundary. Here, we show that such results are false for
equations driven by a wide class of nonlocal fractional operators, extending
previous findings for some models of the fractional Laplacian operator.
Actually, different blow-up phenomena may occur at the boundary of the domain.
We describe such explosive behaviours and obtain precise quantitative estimates
depending on simple parameters of the nonlocal pperators. Our unifying
technique is based on a careful study of the inverse operator in terms of the
corresponding Green function.


  In this paper, the homotopy analysis method (HAM) is successfully applied to
solve the Von Karman's plate equations in the integral form for a circular
plate with the clamped boundary under an arbitrary uniform external pressure.
Two HAM-based approaches are proposed. One is for a given external load Q, the
other for a given central deflection. Both of them are valid for an arbitrary
uniform external pressure by means of choosing a proper value of the so-called
convergence-control parameters c_1 and c_2 in the frame of the HAM. Besides, it
is found that iteration can greatly accelerate the convergence of solution
series. In addition, we prove that the interpolation iterative method is a
special case of the HAM-based 1st-order iteration approach for a given external
load Q when c_1=-theta and c_2=-1, where theta denotes the interpolation
parameter of the interpolation iterative method. Therefore, like Zheng and
Zhou}, one can similarly prove that the HAM-based approaches are valid for an
arbitrary uniform external pressure, at least in some special cases such as
c_1=-theta and c_2=-1. Furthermore, it is found that the HAM-based iteration
approaches converge much faster than the interpolation iterative method. All of
these illustrate the validity and potential of the HAM for the famous Von
Karman's plate equations, and show the superiority of the HAM over perturbation
methods.


  Linear statistics, a random variable build out of the sum of the evaluation
of functions at the eigenvalues of a N times N random matrix,sum[j=1 to N]f(xj)
or tr f(M), is an ubiquitous statistical characteristics in random matrix
theory. Hermitian random matrix ensembles, under the eigenvalue-eigenvector
decomposition give rise to the joint probability density functions of N random
variables. We show that if f(.) is a polynomial of degree K, then the variance
of trf(M), is of the form,sum[n=1 to K] n(d[n])square, and d[n] is related to
the expansion coefficients c[n] of the polynomial f(x) =sum[n=0 to K] c[n] b
Pn(x), where Pn(x) are polynomials of degree n, orthogonal with respect to the
weights 1/[(b-x)(x-a)]^(1/2), [(b -x)(x -a)]^(1/2), [(b-x)(x-a)]^(1/2)/x; (0 <
a < x < b), [(b-x)(x-a)]^(1/2)/[x(1-x)] ; (0 < a < x < b < 1), respectively.


  Previous research has shown that computation of convolution in the frequency
domain provides a significant speedup versus traditional convolution network
implementations. However, this performance increase comes at the expense of
repeatedly computing the transform and its inverse in order to apply other
network operations such as activation, pooling, and dropout. We show,
mathematically, how convolution and activation can both be implemented in the
frequency domain using either the Fourier or Laplace transformation. The main
contributions are a description of spectral activation under the Fourier
transform and a further description of an efficient algorithm for computing
both convolution and activation under the Laplace transform. By computing both
the convolution and activation functions in the frequency domain, we can reduce
the number of transforms required, as well as reducing overall complexity. Our
description of a spectral activation function, together with existing spectral
analogs of other network functions may then be used to compose a fully spectral
implementation of a convolution network.


  One of the most intriguing topological features of open systems is exhibiting
exceptional point (EP) singularities. Apart from the widely explored
second-order EPs (EP2s), the explorations of higher-order EPs in any system
requires more complex topology, which is still a challenge. Here, we encounter
a third-order EP (EP3) for the first time in a simple fabrication feasible
gain-loss assisted optical microcavity. Using scattering-matrix formalism, we
study the simultaneous interactions between three successive coupled states
around two EP2s, which yield an EP3. Following an adiabatic parametric
variation around the identified EP3, we present a robust
successive-state-conversion mechanism among three coupled states. The proposed
scheme indeed opens a unique platform to manipulate light in integrated
devices.


  Using the effective conformal field theory for the quantum Hall edge states
we propose a compact and convenient scheme for the computation of the periods,
amplitudes and temperature behavior of the chiral persistent currents and the
magnetic susceptibilities in the mesoscopic disk version of the Z_k parafermion
quantum Hall states in the second Landau level. Our numerical calculations show
that the persistent currents are periodic in the Aharonov-Bohm flux with period
exactly one flux quantum and have a diamagnetic nature. In the high-temperature
regime their amplitudes decay exponentially with increasing the temperature and
the corresponding exponents are universal characteristics of non-Fermi liquids.
Our theoretical results for these exponents are in perfect agreement with those
extracted from the numerical data and demonstrate that there is in general a
non-trivial contribution coming from the neutral sector. We emphasize the
crucial role of the non-holomorphic factors, first proposed by Cappelli and
Zemba in the context of the conformal field theory partition functions for the
quantum Hall states, which ensure the invariance of the annulus partition
function under the Laughlin spectral flow.


  Deriving co-speech 3D gestures has seen tremendous progress in virtual avatar
animation. Yet, the existing methods often produce stiff and unreasonable
gestures with unseen human speech inputs due to the limited 3D speech-gesture
data. In this paper, we propose CoCoGesture, a novel framework enabling vivid
and diverse gesture synthesis from unseen human speech prompts. Our key insight
is built upon the custom-designed pretrain-fintune training paradigm. At the
pretraining stage, we aim to formulate a large generalizable gesture diffusion
model by learning the abundant postures manifold. Therefore, to alleviate the
scarcity of 3D data, we first construct a large-scale co-speech 3D gesture
dataset containing more than 40M meshed posture instances across 4.3K speakers,
dubbed GES-X. Then, we scale up the large unconditional diffusion model to 1B
parameters and pre-train it to be our gesture experts. At the finetune stage,
we present the audio ControlNet that incorporates the human voice as condition
prompts to guide the gesture generation. Here, we construct the audio
ControlNet through a trainable copy of our pre-trained diffusion model.
Moreover, we design a novel Mixture-of-Gesture-Experts (MoGE) block to
adaptively fuse the audio embedding from the human speech and the gesture
features from the pre-trained gesture experts with a routing mechanism. Such an
effective manner ensures audio embedding is temporal coordinated with motion
features while preserving the vivid and diverse gesture generation. Extensive
experiments demonstrate that our proposed CoCoGesture outperforms the
state-of-the-art methods on the zero-shot speech-to-gesture generation. The
dataset will be publicly available at: https://mattie-e.github.io/GES-X/


  We construct a series of examples of non--flat non--homogeneous parabolic
geometries that carry a symmetry of the parabolic geometry at each point.


  Inelastic neutron scattering measurements are reported that show a new
longitudinal mode in the antiferromagnetically ordered phase of the spin-1/2
quasi-one-dimensional antiferromagnet KCuF3. This mode signals the cross-over
from one-dimensional to three-dimensional behavior and indicates a reduction in
the ordered spin moment of a spin-1/2 antiferromagnet. The measurements are
compared with recent quantum field theory results and are found to be in
excellent agreement. A feature of the data not predicted by theory is a damping
of the mode by decay processes to the transverse spin-wave branches.


  MULTEXT-East language resources, a multilingual dataset for language
engineering research, focused on the morphosyntactic level of linguistic
description. The MULTEXT-East dataset includes the EAGLES-based morphosyntactic
specifications, morphosyntactic lexicons, and an annotated multilingual
corpora. The parallel corpus, the novel "1984" by George Orwell, is sentence
aligned and contains hand-validated morphosyntactic descriptions and lemmas.
The resources are uniformly encoded in XML, using the Text Encoding Initiative
Guidelines, TEI P5, and cover 16 languages: Bulgarian, Croatian, Czech,
English, Estonian, Hungarian, Macedonian, Persian, Polish, Resian, Romanian,
Russian, Serbian, Slovak, Slovene, and Ukrainian. This dataset is extensively
documented, and freely available for research purposes. This case study gives a
history of the development of the MULTEXT-East resources, presents their
encoding and components, discusses related work and gives some conclusions.


  The rate region of the task-encoding problem for two correlated sources is
characterized using a novel parametric family of dependence measures. The
converse uses a new expression for the $\rho$-th moment of the list size, which
is derived using the relative $\alpha$-entropy.


  In this paper, we propose and experimentally validate a scheduling and
control framework for distributed energy resources (DERs) that achieves to
track a day-ahead dispatch plan of a distribution network hosting controllable
and stochastic heterogeneous resources while respecting the local grid
constraints on nodal voltages and lines ampacities. The framework consists of
two algorithmic layers. In the first one (day-ahead scheduling), we determine
an aggregated dispatch plan. In the second layer (real-time control), a
distributed model predictive control (MPC) determines the active and reactive
power set-points of the DERs so that their aggregated contribution tracks the
dispatch plan while obeying to DERs operational constraints as well as the
grids ones. The proposed framework is experimentally validated on a real-scale
microgrid that reproduces the network specifications of the CIGRE microgrid
benchmark system.


  A diverse range of phenomena is possible when a black hole experiences very
rapid accretion from a disk due to the incomplete explosion of a massive
presupernova star endowed with rotation. In the most extreme case, the outgoing
shock fails promptly in a rotating helium star, a black hole and an accretion
disk form, and a strong gamma-ray burst (GRB) results. However, there may also
be more frequently realized cases where the black hole forms after a delay of
from several tens of seconds to several hours as approximately 0.1 to 5 solar
masses falls back into the collapsed remnant following a mildly successful
supernova explosion. There, the same MHD mechanisms frequently invoked to
produce GRBs would also produce jets in stars already in the process of
exploding. The presupernova star could be a Wolf-Rayet star or a red or blue
supergiant. Depending upon its initial pressure, the collimation of the jet may
also vary since ``hot'' jets will tend to diverge and share their energy with
the rest of the star. From these situations, one expects diverse outcomes
ranging from GRBs with a large range of energies and durations, to asymmetric,
energetic supernovae with weak GRBs. SN 1998bw may have been the explosion of a
star in which fall back produced a black hole and a less collimated jet than in
the case of prompt black hole formation.


  Douglas-Rachford splitting and the alternating direction method of
multipliers (ADMM) can be used to solve convex optimization problems that
consist of a sum of two functions. Convergence rate estimates for these
algorithms have received much attention lately. In particular, linear
convergence rates have been shown by several authors under various assumptions.
One such set of assumptions is strong convexity and smoothness of one of the
functions in the minimization problem. The authors recently provided a linear
convergence rate bound for such problems. In this paper, we show that this rate
bound is tight for many algorithm parameter choices.


  We improve the estimate of the axion CDM energy density by considering the
new values of current quark masses, the QCD phase transition effect and a
possible anharmonic effect.


  The transverse momentum technique is used to analyse charged-particle
exclusive data in the central C-Ne and C-Cu interactions at energy of 3.7 Gev
per nucleon. The clear evidence of in-plane and out-of-plane (squeeze-out) flow
effects for protons and $\pi^{-}$ mesons have been obtained. In C-Ne
interactions the $\pi^{-}$ mesons in-plane flow is in the same direction to the
protons, while in C-Cu collisions pions show antiflow behaviour. From the
transverse momentum and azimuthal distributions of protons and pi^{-} mesons
with respect to the reaction plane the flow F (the measure of the amount of
collective transverse momentum transfer in the reaction plane) and the
parameter a_{2} (the measure of the strength of the anisotropic emission) have
been extracted. The flow effects increase with the mass of the particle and
atomic number of target A_{T}. The comparison of our in-plane flow results with
flow data of various projectile/target configurations had been done by a scaled
flow F_{S}=F/(A_{P}^{1/3}+A_{T}^{1/3}). F_{S} demonstrates a common scaling
behaviour among flow values from different systems.


  Recent studies have shown the fluid of hard right triangles to possess
fourfold and quasi-eightfold (octatic) orientational symmetries. However, the
standard density-functional theory for two-dimensional anisotropic fluids,
based on two-body correlations, and an extension to incorporate three-body
correlations, fail to describe these symmetries. To explain the origin of
octatic symmetry we postulate strong particle clustering as a crucial
ingredient. We use Scaled Particle Theory to analyze four binary mixtures of
hard right triangles and squares, three of them being extreme models for a
one-component fluid, where right triangles can exist as monomeric entities
together with triangular dimers, square dimers or square tetramers. Phase
diagrams exhibit a rich phenomenology, with demixing and three-phase
coexistences. More important, under some circumstances the orientational
distribution function of triangles has equally high peaks at relative particle
angles 0, $\pi/2,$ and $\pi$, signalling fourfold, tetratic order, but also
secondary peaks located at $\pi/4$ and $3\pi/4$, a feature of eightfold,
octatic order. Also, we extend the binary mixture model to a quaternary mixture
consisting of four types of clusters: monomers, triangular and square dimers,
and square tetramers. This mixture is analyzed using Scaled Particle Theory
under the restriction of fixed cluster fractions. Apart from the obvious
tetratic phase promoted by tetramers, we found that, for certain cluster
compositions, the total orientational distribution function of monomers can
exhibit quasi-eightfold (octatic) symmetry. The study gives evidence on the
importance of clustering to explain the peculiar orientational properties of
liquid-crystal phases in some two dimensional fluids.


  The paper presents four distinct new ideas and results for communication
networks:
  1) We show that relay-networks (i.e. communication networks where different
nodes use the same coding functions) can be used to model dynamic networks.
  2) We introduce {\em the term model}, which is a simple, graph-free symbolic
approach to communication networks.
  3) We state and prove variants of a theorem concerning the dispersion of
information in single-receiver communications.
  4) We show that the solvability of an abstract multi-user communication
problem is equivalent to the solvability of a single-target communication in a
suitable relay network.
  In the paper, we develop a number of technical ramifications of these ideas
and results. One technical result is a max-flow min-cut theorem for the R\'enyi
entropy with order less than one, given that the sources are equiprobably
distributed; conversely, we show that the max-flow min-cut theorem fails for
the R\'enyi entropy with order greater than one. We leave the status of the
theorem with regards to the ordinary Shannon Entropy measure (R\'enyi entropy
of order one and the limit case between validity or failure of the theorem) as
an open question. In non-dynamic static communication networks with a single
receiver, a simple application of Menger's theorem shows that the optimal
throughput can be achieved without proper use of network coding i.e. just by
using ordinary packet-switching. This fails dramatically in relay networks with
a single receiver. We show that even a powerful method like linear network
coding fails miserably for relay networks. With that in mind, it is noticeable
that our rather weak form of network coding (routing with dynamic headers) is
asymptotically sufficient to reach capacity.


  Hecke has shown that the different of an extension of number fields is a
square in the class group. We prove an analog for branched covers of closed
$3$-manifolds saying that the branch divisor is a square in the first homology
group.


  A coprime commutator in a profinite group $G$ is an element of the form
$[x,y]$, where $x$ and $y$ have coprime order and an anti-coprime commutator is
a commutator $[x,y]$ such that the orders of $x$ and $y$ are divisible by the
same primes. In the present paper we establish that a profinite group $G$ is
finite-by-pronilpotent if the cardinality of the set of coprime commutators in
$G$ is less than $2^{\aleph_0}$. Moreover, a profinite group $G$ has finite
commutator subgroup $G'$ if the cardinality of the set of anti-coprime
commutators in $G$ is less than $2^{\aleph_0}$.


  We measure the spin splitting in a magnetic field $B$ of localized states in
single-electron transistors using a new method, inelastic spin-flip
cotunneling. Because it involves only internal excitations, this technique
gives the most precise value of the Zeeman energy $\Delta = \ZeemanE$. In the
same devices we also measure the splitting with $B$ of the Kondo peak in
differential conductance. The Kondo splitting appears only above a threshold
field as predicted by theory. However, the magnitude of the Kondo splitting at
high fields exceeds $2 \ZeemanE$ in disagreement with theory.


  Gowers introduced, for d\geq 1, the notion of dimension-d uniformity U^d(f)
of a function f: G -> \C, where G is a finite abelian group and \C are the
complex numbers. Roughly speaking, if U^d(f) is small, then f has certain
"pseudorandomness" properties.
  We prove the following property of functions with large U^d(f). Write G=G_1 x
>... x G_n as a product of groups. If a bounded balanced function f:G_1 x ... x
G_n -> \C is such that U^{d} (f) > epsilon, then one of the coordinates of f
has influence at least epsilon/2^{O(d)}.
  The Gowers inner product of a collection of functions is a related notion of
pseudorandomness. We prove that if a collection of bounded functions has large
Gowers inner product, and at least one function in the collection is balanced,
then there is a variable that has high influence for at least four of the
functions in the collection.
  Finally, we relate the acceptance probability of the "hypergraph long-code
test" proposed by Samorodnitsky and Trevisan to the Gowers inner product of the
functions being tested and we deduce applications to the construction of
Probabilistically Checkable Proofs and to hardness of approximation.


  We present a new method for determining time delays among the light curves of
various images in a gravitational lens. The method is based on constructing a
simple model for the source variation and forming a chi squared measure of the
agreement of this same variation with all of the lightcurves. While inspired by
Press et al. (1992a, b) our approach is different since we do not assume a
Gaussian process for the source variation. We apply our method to the light
curves of the quadruple gravitational lens PG1115+080 measured by Schechter et
al. (1997). Unlike Schechter et al. we include correlated measurement errors in
the analysis, as well as the possibility that microlensing may cause different
images to vary by different factors in flux. We find a value of 25.0
(+3.3,-3.8) days (95% confidence) for the delay between components B and C
(close to the 24 day value of Schechter et al). However, the ratio t_AC/t_BA of
the two intermediate delays is poorly determined at 1.13 (+.18,-.17) (68%
confidence), close to the value predicted by lens models (1.4) unlike the
Schechter et al. value (0.7). The variation ratios of C with respect to A and
of A with respect to B are both different from 1, 1.39 (+.16,-.20) and .79
(+.10,-.12) (95% confidence), respectively. This is an indication of a
microlensing gradient, and this type of microlensing may allow us to conclude
that the size of the quasar optical emission region is about 1000 AU.


  Achieving resource efficiency while preserving end-user experience is
non-trivial for cloud application operators. As cloud applications
progressively adopt microservices, resource managers are faced with two
distinct levels of system behavior: end-to-end application latency and
per-service resource usage. Translating between the two levels, however, is
challenging because user requests traverse heterogeneous services that
collectively (but unevenly) contribute to the end-to-end latency. We present
Autothrottle, a bi-level resource management framework for microservices with
latency SLOs (service-level objectives). It architecturally decouples
application SLO feedback from service resource control, and bridges them
through the notion of performance targets. Specifically, an application-wide
learning-based controller is employed to periodically set performance targets
-- expressed as CPU throttle ratios -- for per-service heuristic controllers to
attain. We evaluate Autothrottle on three microservice applications, with
workload traces from production scenarios. Results show superior CPU savings,
up to 26.21% over the best-performing baseline and up to 93.84% over all
baselines.


  In this manuscript, we address the issue of the loss of SU(2) internal
symmetry in Loop Quantum Cosmology and its relationship with Loop Quantum
Gravity. Drawing inspiration from Yang-Mills theory and employing the framework
of fiber bundle theory, we successfully identify a cosmological sector for
General Relativity in Ashtekar variables, which preserves the SU(2) structure
of the theory and the diffeomorphism gauge symmetry. Additionally, we proceed
to quantize it using the machinery of Loop Quantum Gravity, uncovering that the
resulting spin-network states exhibit distinctive symmetry properties and
encompass the usual states of Loop Quantum Cosmology.


  A La0.75Ca0.25MnO3-film grown by metalorganic aerosol deposition technique
was investigated by scanning tunnelling microscopy and spectroscopy. A small
spot was found on the surface which exhibits the expected magnetic field
dependence of the tunnelling conductivity giving the opportunity for a local
spectroscopic study of the intrinsic colossal magnetoresistance (CMR) behavior.
The tunnelling conductivity is strongly enhanced in an external magnetic field
of 4 T and the CMR behavior can be interpreted in terms of a redistribution of
occupied electronic states torwards the Fermi energy.


  We show that the volume of the inner $r$-neighborhood of a polytope in the
$d$-dimensional Euclidean space is a pluri-phase Steiner-like function, i.e. a
continuous piecewise polynomial function of degree $d$, proving thus a
conjecture of Lapidus and Pearse. In the case when the polytope is
dimension-wise equiangular we determine the coefficients of the initial
polynomial as functions of the dihedral angles and the skeletal volumes of the
polytope. We discuss also the degree of differentiability of this function and
give a lower bound in terms of the set of normal vectors of the hyperplanes
defining the polytope. We give also sufficient conditions for the highest
differentiability degree to be attained.


  We examine run and tumble disks in two-dimensional systems where the
particles also have a Magnus component to their dynamics. For increased
activity, we find that the system forms a motility-induced phase-separated
(MIPS) state with chiral edge flow around the clusters, where the direction of
the current is correlated with the sign of the Magnus term. The stability of
the MIPS state is non-monotonic as a function of increasing Magnus term
amplitude, with the MIPS region first extending down to lower activities
followed by a break up of MIPS at large Magnus amplitudes into a gel-like
state. We examine the dynamics in the presence of quenched disorder and a
uniform drive, and find that the bulk flow exhibits a drive-dependent Hall
angle. This is a result of the side jump effect produced by scattering from the
pinning sites, and is similar to the behavior found for skyrmions in chiral
magnets with quenched disorder.


  Automated machine learning (AutoML) seeks to build ML models with minimal
human effort. While considerable research has been conducted in the area of
AutoML in general, aiming to take humans out of the loop when building
artificial intelligence (AI) applications, scant literature has focused on how
AutoML works well in open-environment scenarios such as the process of training
and updating large models, industrial supply chains or the industrial
metaverse, where people often face open-loop problems during the search
process: they must continuously collect data, update data and models, satisfy
the requirements of the development and deployment environment, support massive
devices, modify evaluation metrics, etc. Addressing the open-environment issue
with pure data-driven approaches requires considerable data, computing
resources, and effort from dedicated data engineers, making current AutoML
systems and platforms inefficient and computationally intractable.
Human-computer interaction is a practical and feasible way to tackle the
problem of open-environment AI. In this paper, we introduce OmniForce, a
human-centered AutoML (HAML) system that yields both human-assisted ML and
ML-assisted human techniques, to put an AutoML system into practice and build
adaptive AI in open-environment scenarios. Specifically, we present OmniForce
in terms of ML version management; pipeline-driven development and deployment
collaborations; a flexible search strategy framework; and widely provisioned
and crowdsourced application algorithms, including large models. Furthermore,
the (large) models constructed by OmniForce can be automatically turned into
remote services in a few minutes; this process is dubbed model as a service
(MaaS). Experimental results obtained in multiple search spaces and real-world
use cases demonstrate the efficacy and efficiency of OmniForce.


  Katz and Sarnak conjectured a correspondence between the $n$-level density
statistics of zeros from families of $L$-functions with eigenvalues from random
matrix ensembles. In many cases the sums of smooth test functions, whose
Fourier transforms are finitely supported, over scaled zeros in a family
converge to an integral of the test function against a density $W_{n, G}$
depending on the symmetry $G$ of the family (unitary, symplectic or
orthogonal). This integral bounds the average order of vanishing at the central
point of the corresponding family of $L$-functions. We can obtain better
estimates on this vanishing by finding better test functions to minimize the
integral. We pursue this problem when $n=2$, minimizing \[ \frac{1}{\Phi(0, 0)}
\int_{{\mathbb R}^2} W_{2,G} (x, y) \Phi(x, y) dx dy \] over test functions
$\Phi \colon {\mathbb R}^2 \to [0, \infty)$ with compactly supported Fourier
transform. We study a restricted version of this optimization problem, imposing
that our test functions take the form $\phi(x) \psi(y)$ for some fixed
admissible $\psi(y)$ and $\mathrm{supp}({\hat \phi}) \subseteq [-1, 1]$.
Extending results from the $1$-level case, namely the functional analytic
arguments of Iwaniec, Luo and Sarnak and the differential equations method
introduced by Freeman and Miller, we explicitly solve for the optimal $\phi$
for appropriately chosen fixed test function $\psi$. The solution allows us to
deduce strong estimates for the proportion of newforms of rank $0$ or $2$ in
the case of $\mathrm{SO}(\mathrm{even})$, rank $1$ or $3$ in the case of
$\mathrm{SO}(\mathrm{odd})$, and rank at most $2$ for $\mathrm{O}$,
$\mathrm{Sp}$, and $\mathrm{U}$; our estimates are a significant strengthening
of the best known estimates obtained with the $1$-level density. We conclude by
discussing further improvements on estimates by the method of iteration.


  We study spherically-symmetric solutions in Massive Gravity generated by
matter sources with polytropic equation of state. We concentrate in the
non-perturbative regime where the mass term non-linearities are important, and
present the main features of the solutions.


  We introduce a neural relighting algorithm for captured indoors scenes, that
allows interactive free-viewpoint navigation. Our method allows illumination to
be changed synthetically, while coherently rendering cast shadows and complex
glossy materials. We start with multiple images of the scene and a 3D mesh
obtained by multi-view stereo (MVS) reconstruction. We assume that lighting is
well-explained as the sum of a view-independent diffuse component and a
view-dependent glossy term concentrated around the mirror reflection direction.
We design a convolutional network around input feature maps that facilitate
learning of an implicit representation of scene materials and illumination,
enabling both relighting and free-viewpoint navigation. We generate these input
maps by exploiting the best elements of both image-based and physically-based
rendering. We sample the input views to estimate diffuse scene irradiance, and
compute the new illumination caused by user-specified light sources using path
tracing. To facilitate the network's understanding of materials and synthesize
plausible glossy reflections, we reproject the views and compute mirror images.
We train the network on a synthetic dataset where each scene is also
reconstructed with MVS. We show results of our algorithm relighting real indoor
scenes and performing free-viewpoint navigation with complex and realistic
glossy reflections, which so far remained out of reach for view-synthesis
techniques.


  In this paper, we consider the initial-boundary value problem of the 3D
primitive equations for planetary oceanic and atmospheric dynamics with only
horizontal eddy viscosity in the horizontal momentum equations and only
horizontal diffusion in the temperature equation. Global well-posedness of
strong solution is established for any $H^2$ initial data. An $N$-dimensional
logarithmic Sobolev embedding inequality, which bounds the $L^\infty$ norm in
terms of the $L^q$ norms up to a logarithm of the $L^p$-norm, for $p>N$, of the
first order derivatives, and a system version of the classic Gronwall
inequality are exploited to establish the required a priori $H^2$ estimates for
the global regularity.


  Federated learning is a promising privacy-preserving paradigm for distributed
machine learning. In this context, there is sometimes a need for a specialized
process called machine unlearning, which is required when the effect of some
specific training samples needs to be removed from a learning model due to
privacy, security, usability, and/or legislative factors. However, problems
arise when current centralized unlearning methods are applied to existing
federated learning, in which the server aims to remove all information about a
class from the global model. Centralized unlearning usually focuses on simple
models or is premised on the ability to access all training data at a central
node. However, training data cannot be accessed on the server under the
federated learning paradigm, conflicting with the requirements of the
centralized unlearning process. Additionally, there are high computation and
communication costs associated with accessing clients' data, especially in
scenarios involving numerous clients or complex global models. To address these
concerns, we propose a more effective and efficient federated unlearning scheme
based on the concept of model explanation. Model explanation involves
understanding deep networks and individual channel importance, so that this
understanding can be used to determine which model channels are critical for
classes that need to be unlearned. We select the most influential channels
within an already-trained model for the data that need to be unlearned and
fine-tune only influential channels to remove the contribution made by those
data. In this way, we can simultaneously avoid huge consumption costs and
ensure that the unlearned model maintains good performance. Experiments with
different training models on various datasets demonstrate the effectiveness of
the proposed approach.


  The concentration-mass relations proposed by Prada et al. (2012) and by Duffy
et al. (2008) on the scales of galaxy clusters show some of the largest
discrepancies among all the works present in literature. This is surprising
because they are both derived from the analysis of dark-matter halos forming in
LCDM simulations with similar set-ups. With the help of analytic models and
numerical simulations we investigate the origin of this discrepancy focusing on
the procedures used to derive the concentrations (circular velocity ratios
versus density profile fitting) and on the selection criteria used to bin the
halos (binning in maximum circular velocity versus binning in mass). We find
that both steps of the analysis have a large impact on the resulting c-M
relation. In particular, we show that the two c-M relations can be entirely
reconciled, if we account for these methodological differences. Our analysis
demonstrates that the concentration estimates are sensitive to the largely
different radial scales probed by a particular measurement method. This implies
that concentrations derived with different techniques (both in observations and
in simulations) must be compared over the same radial range.


  Image understanding is an important research domain in the computer vision
due to its wide real-world applications. For an image understanding framework
that uses the Bag-of-Words model representation, the visual codebook is an
essential part. Random forest (RF) as a tree-structure discriminative codebook
has been a popular choice. However, the performance of the RF can be degraded
if the local patch labels are poorly assigned. In this paper, we tackle this
problem by a novel way to update the RF codebook learning for a more
discriminative codebook with the introduction of the soft class labels,
estimated from the pLSA model based on a feedback scheme. The feedback scheme
is performed on both the image and patch levels respectively, which is in
contrast to the state- of-the-art RF codebook learning that focused on either
image or patch level only. Experiments on 15-Scene and C-Pascal datasets had
shown the effectiveness of the proposed method in image understanding task.


  A "statistician" takes an action on behalf of an agent, based on the agent's
self-reported personal data and a sample involving other people. The action
that he takes is an estimated function of the agent's report. The estimation
procedure involves model selection. We ask the following question: Is
truth-telling optimal for the agent given the statistician's procedure? We
analyze this question in the context of a simple example that highlights the
role of model selection. We suggest that our simple exercise may have
implications for the broader issue of human interaction with "machine learning"
algorithms.


  In this paper we develop an a posteriori error analysis for the stationary
Stokes-Darcy coupled problem approximated by conforming finite element method
on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a
new robust stabilized fully mixed discretization developed by Jiaping Yu et al.
(Advances in Difference Equations, SpringerOpen Journal, 2018). The a
posteriori error estimate is based on a suitable evaluation on the residual of
the finite element solution plus the stabilization terms. It is proven that the
a posteriori error estimate provided in this paper is both reliable and
efficient.


  In multispecies electrolyte solutions, even in the absence of an external
electric field, differences in ion diffusivities induce an electric potential
and generate additional fluxes for each species. This electro-diffusion process
is well-described by the advection-Nernst-Planck equation. This study aims to
analyze the long-time behavior of the governing equation under
electroneutrality and zero current conditions and investigate how the
diffusion-induced electric potential and shear flow enhance the effective
diffusion coefficients of each species in channel domains. The some exact
solutions of the effective equation and the asymptotic analyses for ions with
large diffusivity discrepancies are presented. Furthermore, there are several
interesting properties of the effective equation. First, it is a generalization
of the Taylor dispersion, with a nonlinear diffusion tensor replacing the
scalar diffusion coefficient. Second, the effective equation exhibits a scaling
relation, revealing that the system with a weak flow is equivalent to the
system with a strong flow under scaled physical parameters. Third, in the case
of injecting a lower-concentration electrolyte solution into a pre-existing
solution with the same ion species, the effective equation simplifies to a
multidimensional diffusion equation. However, when introducing the electrolyte
solution into a channel filled with deionized water, the ion-electric
interaction results in several phenomena do not present in the
advection-diffusion equation, including upstream migration of some species,
spontaneous separation of ions, and non-monotonic dependence of the effective
diffusivity on P\'eclet numbers. Last, the dependence of effective diffusivity
on concentration and ion diffusivity suggests a method to infer the
concentration ratio of each component and ion diffusivity by measuring the
effective diffusivity.


  We develop a probabilistic framework for deep learning based on the Deep
Rendering Mixture Model (DRMM), a new generative probabilistic model that
explicitly capture variations in data due to latent task nuisance variables. We
demonstrate that max-sum inference in the DRMM yields an algorithm that exactly
reproduces the operations in deep convolutional neural networks (DCNs),
providing a first principles derivation. Our framework provides new insights
into the successes and shortcomings of DCNs as well as a principled route to
their improvement. DRMM training via the Expectation-Maximization (EM)
algorithm is a powerful alternative to DCN back-propagation, and initial
training results are promising. Classification based on the DRMM and other
variants outperforms DCNs in supervised digit classification, training 2-3x
faster while achieving similar accuracy. Moreover, the DRMM is applicable to
semi-supervised and unsupervised learning tasks, achieving results that are
state-of-the-art in several categories on the MNIST benchmark and comparable to
state of the art on the CIFAR10 benchmark.


  This paper concerns the numerical study for the generalized
Rosenau-Kawahara-RLW equation obtained by coupling the generalized Rosenau-RLW
equation and the generalized Rosenau-Kawahara equation. We first derive the
energy conservation law of the equation, and then develop a three-level
linearly implicit difference scheme for solving the equation. We prove that the
proposed scheme is energy-conserved, unconditionally stable and second-order
accurate both in time and space variables. Finally, numerical experiments are
carried out to confirm the energy conservation, the convergence rates of the
scheme and effectiveness for long-time simulation.


  Magnetic permeabilities derived for infinite, periodic media are used in the
Fresnel equation to calculate the reflection from corresponding semi-infinite
media. By comparison to finite-difference-time-domain (FDTD) simulations, we
find that the Fresnel equation gives accurate results for 2D metamaterials
which mimic natural magnetism, in a frequency range where the magnetic moment
density dominates the $\mathcal O(k^2)$ part of the total Landau--Lifshitz
permittivity. For a 1D layered structure, or for large frequencies, the
correspondence is poor. We also demonstrate that even if a medium is described
accurately by a local permittivity and permeability, the Fresnel equation is
not necessarily valid.


  We investigate the consequences of a generalized
$\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry on a scaling neutrino Majorana mass
matrix. It enables us to determine definite analytical relations between the
mixing angles $\theta_{12}$ and $\theta_{13}$, maximal CP violation for the
Dirac type and vanishing for the Majorana type. Beside the other testable
predictions on the low energy neutrino parameters such as $\beta\beta_{0\nu}$
decay matrix element $|M_{ee}|$ and the light neutrino masses $m_{1,2,3}$, the
model also has intriguing consequences from the perspective of leptogenesis.
With the assumption that the required CP violation for leptogenesis is created
by the decay of lightest ($N_1$) of the heavy Majorana neutrinos, only
$\tau$-flavored leptogenesis scenario is found to be allowed in this model. For
a normal (inverted) ordering of light neutrino masses, $\theta_{23}$ is found
be less (greater) than its maximal value, for the final baryon asymmetry $Y_B$
to be in the observed range. Besides, an upper and a lower bound on the mass of
$N_1$ have also been estimated. Effect of the heavier neutrinos $N_{2,3}$ on
final $Y_B$ has been worked out subsequently. The predictions of this model
will be tested in the experiments such as nEXO, LEGEND, GERDA-II, T2K,
NO$\nu$A, DUNE etc.


  GERDA is an experiment searching for the neutrinoless {\beta}{\beta} decay of
Ge-76. The experiment uses an array of high-purity germanium detectors,
enriched in Ge-76, directly immersed in liquid argon. GERDA recently started
the physics data taking using eight enriched coaxial detectors. The status of
the experiment has to be closely monitored in order to promptly identify
possible instabilities or problems. The on-line slow control system is
complemented by a regular off-line monitoring of data quality. This ensures
that data are qualified to be used in the physics analysis and allows to reject
data sets which do not meet the minimum quality standards. The off-line data
monitoring is entirely performed within the software framework GELATIO. In
addition, a relational database, complemented by a web-based interface, was
developed to support the off-line monitoring and to automatically provide
information to daily assess data quality. The concept and the performance of
the off-line monitoring tools were tested and validated during the one-year
commissioning phase.


  A standard practice in developing image recognition models is to train a
model on a specific image resolution and then deploy it. However, in real-world
inference, models often encounter images different from the training sets in
resolution and/or subject to natural variations such as weather changes, noise
types and compression artifacts. While traditional solutions involve training
multiple models for different resolutions or input variations, these methods
are computationally expensive and thus do not scale in practice. To this end,
we propose a novel neural network model, parallel-structured and all-component
Fourier neural operator (PAC-FNO), that addresses the problem. Unlike
conventional feed-forward neural networks, PAC-FNO operates in the frequency
domain, allowing it to handle images of varying resolutions within a single
model. We also propose a two-stage algorithm for training PAC-FNO with a
minimal modification to the original, downstream model. Moreover, the proposed
PAC-FNO is ready to work with existing image recognition models. Extensively
evaluating methods with seven image recognition benchmarks, we show that the
proposed PAC-FNO improves the performance of existing baseline models on images
with various resolutions by up to 77.1% and various types of natural variations
in the images at inference.


  We examine the evolution of the relation between stellar mass surface
density, velocity dispersion and half-light radius$-$the stellar mass
fundamental plane$-$for quiescent galaxies at $z<0.6$. We measure the local
relation from galaxies in the Sloan Digital Sky Survey and the intermediate
redshift relation from $\sim500$ quiescent galaxies with stellar masses $10
\lesssim \mathrm{log}(M_\ast/M_\odot) \lesssim 11.5$. Nearly half of the
quiescent galaxies in our intermediate redshift sample are compact. After
accounting for important selection and systematic effects, the velocity
dispersion distribution of galaxies at intermediate redshifts is similar to
galaxies in the local universe. Galaxies at $z<0.6$ appear to be smaller
($\lesssim0.1$ dex) than galaxies in the local sample. The orientation of the
stellar mass fundamental plane is independent of redshift for massive quiescent
galaxies at $z<0.6$ and the zero-point evolves by $\sim 0.04$ dex. Compact
quiescent galaxies fall on the same relation as the extended objects. We
confirm that compact quiescent galaxies are the tail of the size and mass
distribution of the normal quiescent galaxy population.


  In this paper, we investigate the employment of reconfigurable intelligent
surfaces (RISs) into vehicle platoons, functioning in tandem with a base
station (BS) in support of the high-precision location tracking. In particular,
the use of a RIS imposes additional structured sparsity that, when paired with
the initial sparse line-of-sight (LoS) channels of the BS, facilitates
beneficial group sparsity. The resultant group sparsity significantly enriches
the energies of the original direct-only channel, enabling a greater
concentration of the LoS channel energies emanated from the same vehicle
location index. Furthermore, the burst sparsity is exposed by representing the
non-line-of-sight (NLoS) channels as their sparse copies. This thus constitutes
the philosophy of the diverse sparsities of interest. Then, a diverse dynamic
layered structured sparsity (DiLuS) framework is customized for capturing
different priors for this pair of sparsities, based upon which the location
tracking problem is formulated as a maximum a posterior (MAP) estimate of the
location. Nevertheless, the tracking issue is highly intractable due to the
ill-conditioned sensing matrix, intricately coupled latent variables associated
with the BS and RIS, and the spatialtemporal correlations among the vehicle
platoon. To circumvent these hurdles, we propose an efficient algorithm, namely
DiLuS enabled spatial-temporal platoon localization (DiLuS-STPL), which
incorporates both variational Bayesian inference (VBI) and message passing
techniques for recursively achieving parameter updates in a turbo-like way.
Finally, we demonstrate through extensive simulation results that the
localization relying exclusively upon a BS and a RIS may achieve the comparable
precision performance obtained by the two individual BSs, along with the
robustness and superiority of our proposed algorithm as compared to various
benchmark schemes.


  Multi-model fitting has been extensively studied from the random sampling and
clustering perspectives. Most assume that only a single type/class of model is
present and their generalizations to fitting multiple types of
models/structures simultaneously are non-trivial. The inherent challenges
include choice of types and numbers of models, sampling imbalance and parameter
tuning, all of which render conventional approaches ineffective. In this work,
we formulate the multi-model multi-type fitting problem as one of learning deep
feature embedding that is clustering-friendly. In other words, points of the
same clusters are embedded closer together through the network. For inference,
we apply K-means to cluster the data in the embedded feature space and model
selection is enabled by analyzing the K-means residuals. Experiments are
carried out on both synthetic and real world multi-type fitting datasets,
producing state-of-the-art results. Comparisons are also made on single-type
multi-model fitting tasks with promising results as well.


  Comparing isotropic solids and fluids at either imposed volume or pressure we
investigate various correlations of the instantaneous pressure and its ideal
and excess contributions. Focusing on the compression modulus K it is
emphasized that the stress fluctuation representation of the elastic moduli may
be obtained directly (without a microscopic displacement field) by comparing
the stress fluctuations in conjugated ensembles. This is made manifest by
computing the Rowlinson stress fluctuation expression K_row of the compression
modulus for NPT-ensembles. It is shown theoretically and numerically that
K_row|P = P_id (2 - P_id/K) with P_id being the ideal pressure contribution.


  ATP-driven proton pumps, which are critical to the operation of a cell,
maintain cytosolic and organellar pH levels within a narrow functional range.
These pumps employ two very different mechanisms: an elaborate rotary mechanism
used by V-ATPase H+ pumps, and a simpler alternating access mechanism used by
P-ATPase H+ pumps. Why are two different mechanisms used to perform the same
function? Systematic analysis, without parameter fitting, of kinetic models of
the rotary, alternating access and other possible mechanisms suggest that, when
the ratio of protons transported per ATP hydrolyzed exceeds one, the
one-at-a-time proton transport by the rotary mechanism is faster than other
possible mechanisms across a wide range of driving conditions. When the ratio
is one, there is no intrinsic difference in the free energy landscape between
mechanisms, and therefore all mechanisms can exhibit the same kinetic
performance. To our knowledge all known rotary pumps have an H+:ATP ratio
greater than one, and all known alternating access ATP-driven proton pumps have
a ratio of one. Our analysis suggests a possible explanation for this apparent
relationship between coupling ratio and mechanism. When the conditions under
which the pump must operate permit a coupling ratio greater than one, the
rotary mechanism may have been selected for its kinetic advantage. On the other
hand, when conditions require a coupling ratio of one or less, the alternating
access mechanism may have been selected for other possible advantages resulting
from its structural and functional simplicity.


  We investigate large deviations properties for centered stationary AR(1) and
MA(1) processes with independent Gaussian innovations, by giving the explicit
bivariate rate functions for the sequence of random vectors
$(\boldsymbol{S}_n)_{n \in \N} = \left(n^{-1}(\sum_{k=1}^n X_k, \sum_{k=1}^n
X_k^2)\right)_{n \in \N}$. In the AR(1) case, we also give the explicit rate
function for the bivariate random sequence $(\W_n)_{n \geq 2} =
\left(n^{-1}(\sum_{k=1}^n X_k^2, \sum_{k=2}^n X_k X_{k+1})\right)_{n \geq
  2}$. Via Contraction Principle, we provide explicit rate functions for the
sequences $(n^{-1} \sum_{k=1}^n X_k)_{n \in \N}$, $(n^{-1} \sum_{k=1}^n
X_k^2)_{n \geq 2}$ and $(n^{-1} \sum_{k=2}^n X_k X_{k+1})_{n \geq 2}$, as well.
In the AR(1) case, we present a new proof for an already known result on the
explicit deviation function for the Yule-Walker estimator.


  We study the existence of nonnegative solutions (and ground states) to the
nonlinear Schr\"{o}dinger equation in $\mathbb{R}^N$ with radial potentials and
super-linear or sub-linear nonlinearities. The potentials satisfy power type
estimates at the origin and at infinity, but no compatibility condition is
required on their growth (or decay) rates at zero and infinity. In this respect
our results extend some well known results in the literature and we also
believe that they can highlight the role of the sum of Lebesgue spaces in
studying nonlinear equations with weights.


  The emergence of in-context learning (ICL) is potentially attributed to two
major abilities: task recognition (TR) for recognizing the task from
demonstrations and utilizing pre-trained priors, and task learning (TL) for
learning from demonstrations. However, relationships between the two abilities
and how such relationships affect the emergence of ICL is unclear. In this
paper, we take the first step by examining the pre-training dynamics of the
emergence of ICL. With carefully designed metrics, we find that these two
abilities are, in fact, competitive during pre-training. Moreover, we observe a
strong negative correlation between the competition and ICL performance.
Further analysis of common pre-training factors (i.e., model size, dataset
size, and data curriculum) demonstrates possible ways to manage the
competition. Based on these insights, we propose a simple yet effective method
to better integrate these two abilities for ICL at inference time. Through
adaptive ensemble learning, the performance of ICL can be significantly
boosted, enabling two small models to outperform a larger one with more than
twice the parameters. The code is available at
https://github.com/RUCAIBox/Competitive-ICL.


  The risk of cascading blackouts greatly relies on failure probabilities of
individual components in power grids. To quantify how component failure
probabilities (CFP) influences blackout risk (BR), this paper proposes a
sample-induced semi-analytic approach to characterize the relationship between
CFP and BR. To this end, we first give a generic component failure probability
function (CoFPF) to describe CFP with varying parameters or forms. Then the
exact relationship between BR and CoFPFs is built on the abstract
Markov-sequence model of cascading outages. Leveraging a set of samples
generated by blackout simulations, we further establish a sample-induced
semi-analytic mapping between the unbiased estimation of BR and CoFPFs.
Finally, we derive an efficient algorithm that can directly calculate the
unbiased estimation of BR when the CoFPFs change. Since no additional
simulations are required, the algorithm is computationally scalable and
efficient. Numerical experiments well confirm the theory and the algorithm.


  Recent advances in 3D object detection (3DOD) have obtained remarkably strong
results for LiDAR-based models. In contrast, surround-view 3DOD models based on
multiple camera images underperform due to the necessary view transformation of
features from perspective view (PV) to a 3D world representation which is
ambiguous due to missing depth information. This paper introduces X$^3$KD, a
comprehensive knowledge distillation framework across different modalities,
tasks, and stages for multi-camera 3DOD. Specifically, we propose cross-task
distillation from an instance segmentation teacher (X-IS) in the PV feature
extraction stage providing supervision without ambiguous error backpropagation
through the view transformation. After the transformation, we apply cross-modal
feature distillation (X-FD) and adversarial training (X-AT) to improve the 3D
world representation of multi-camera features through the information contained
in a LiDAR-based 3DOD teacher. Finally, we also employ this teacher for
cross-modal output distillation (X-OD), providing dense supervision at the
prediction stage. We perform extensive ablations of knowledge distillation at
different stages of multi-camera 3DOD. Our final X$^3$KD model outperforms
previous state-of-the-art approaches on the nuScenes and Waymo datasets and
generalizes to RADAR-based 3DOD. Qualitative results video at
https://youtu.be/1do9DPFmr38.


  Many excited states in the hadron spectrum have large branching ratios to the
three-hadron final states. Understanding such particles from first principles
QCD requires input from lattice QCD with one-, two-, and three-meson
interpolators as well as a reliable three-body formalism relating finite-volume
spectra at unphysical pion masses to the scattering amplitudes at the physical
point. In this work, we provide the first-ever calculation of the resonance
parameters of the $\omega$-meson from lattice QCD to the physical point,
including an update of the formalism through matching to effective field
theories. The main result of this pioneering study, the pole position of the
$\omega$-meson at $\sqrt{s_\omega}= (778.0(11.2)-i\,3.0(5) )\,\mathrm{MeV}$,
agrees reasonably well with experiment providing a pathway to study heavier
three-hadron resonances. In addition we provide an estimate of the
$\omega-\rho$ mass difference as $29(15)\,\mathrm{MeV}$.


  We calculate solar models including dark matter (DM) weakly-interacting
massive particles (WIMPs) of mass 5-50 GeV and test these models against
helioseismic constraints on sound speed, convection zone depth, convection zone
helium abundance, and small separations of low-degree p-modes. Our main
conclusion is that both direct detection experiments and particle accelerators
may be complemented by using the Sun as a probe for WIMP DM particles in the
5-50 GeV mass range. The DM most sensitive to this probe has suppressed
annihilations and a large spin-dependent elastic scattering cross section. For
the WIMP cross-section parameters explored here, the lightest WIMP masses <10
GeV are ruled out by constraints on core sound speed and low-degree frequency
spacings. For WIMP masses 30-50 GeV, the changes to the solar structure are
confined to the inner 4% of the solar radius and so do not significantly affect
the solar p-modes. Future helioseismology observations, most notably involving
g-modes, and future solar neutrino experiments may be able to constrain the
allowable DM parameter space in a mass range that is of current interest for
direct detection.


  In this expository paper we present proofs of Grothendieck-Serre Formula for
multi-graded algebras and Rees algebras for admissible multi-graded
filtrations. As applications, we derive formulas of Sally for postulation
number of admissible filtrations and Hilbert coefficients. We also discuss a
partial solution of Itoh's conjecture by Kummini and Masuti. We present an
alternate proof of Huneke-Ooishi Theorem and a generalisation for multi-graded
filtrations.


  One aim of data mining is the identification of interesting structures in
data. For better analytical results, the basic properties of an empirical
distribution, such as skewness and eventual clipping, i.e. hard limits in value
ranges, need to be assessed. Of particular interest is the question of whether
the data originate from one process or contain subsets related to different
states of the data producing process. Data visualization tools should deliver a
clear picture of the univariate probability density distribution (PDF) for each
feature. Visualization tools for PDFs typically use kernel density estimates
and include both the classical histogram, as well as the modern tools like
ridgeline plots, bean plots and violin plots. If density estimation parameters
remain in a default setting, conventional methods pose several problems when
visualizing the PDF of uniform, multimodal, skewed distributions and
distributions with clipped data, For that reason, a new visualization tool
called the mirrored density plot (MD plot), which is specifically designed to
discover interesting structures in continuous features, is proposed. The MD
plot does not require adjusting any parameters of density estimation, which is
what may make the use of this plot compelling particularly to non-experts. The
visualization tools in question are evaluated against statistical tests with
regard to typical challenges of explorative distribution analysis. The results
of the evaluation are presented using bimodal Gaussian, skewed distributions
and several features with already published PDFs. In an exploratory data
analysis of 12 features describing quarterly financial statements, when
statistical testing poses a great difficulty, only the MD plots can identify
the structure of their PDFs. In sum, the MD plot outperforms the above
mentioned methods.


  A command-following robot that serves people in everyday life must
continually improve itself in deployment domains with minimal help from its end
users, instead of engineers. Previous methods are either difficult to
continuously improve after the deployment or require a large number of new
labels during fine-tuning. Motivated by (self-)supervised contrastive learning,
we propose a novel representation that generates an intrinsic reward function
for command-following robot tasks by associating images with sound commands.
After the robot is deployed in a new domain, the representation can be updated
intuitively and data-efficiently by non-experts without any hand-crafted reward
functions. We demonstrate our approach on various sound types and robotic
tasks, including navigation and manipulation with raw sensor inputs. In
simulated and real-world experiments, we show that our system can continually
self-improve in previously unseen scenarios given fewer new labeled data, while
still achieving better performance over previous methods.


  We investigate the chiral electronic modes at the interface between two
regions of a threefold topological semimetal, which is illuminated by left and
right handed elliptically polarized waves. The radiation effects on the band
structure of semimetal is analyzed by using Floquet theory. Two distinct
solutions of the interface modes are found with the chirality depending on the
phase of the irradiation. We also consider the anomalous Hall response which is
attributed to the transition between dispersionless flat band and conic bands.


  We have developed an efficient scheme for the calculation of transition
properties within the four-component relativistic equation-of-motion
coupled-cluster (EOM-CC) method using the expectation value approach. The
calculation of transition properties within the relativistic EOM-CC framework
requires the solution of both right and left eigenvectors using Davidson's
iterative diagonalization scheme. The accuracy of the approach has been
investigated by calculating low-lying transitions of Xe atom, HI molecule and
spin forbidden 1S0 to 3P1 and spin allowed 1S0 to 1P1 transitions in a few
closed shell cations. Additionally, applications aimed at evaluating the L-edge
X-ray absorption spectrum (XAS) of Ar atom is studied. The calculated results
show good agreement with the earlier theoretical studies and experimental
values.


  We report on the low-energy electron and fast neutron irradiated 4H-SiC
studied by deep-level transient spectroscopy (DLTS) and Laplace DLTS.
Irradiations introduced two defects, Ec-0.4eV and Ec-0.7eV. They were
previously assigned to carbon interstitial (Ci) labeled as EH1/3 and
silicon-vacancy (VSi) labeled as S1/2, for the low-energy electron and fast
neutron irradiation, respectively. This work demonstrates how Laplace DLTS can
be used as a useful tool for distinguishing the EH1 and S1 defects. We show
that EH1 consists of a single emission line arising from the Ci(h), while S1
has two emission lines arising from the VSi(h) and VSi(k) lattice sites.


  This paper studies the structure of special preenvelopes and envelopes with
respect to maximal Cohen-Macaulay modules. We investigate the structure of them
in terms of their kernels and cokernels. Moreover, using this result, we also
study the structure of special proper coresolutions with respect to maximal
Cohen-Macaulay modules over a Henselian Cohen-Macaulay local ring.


  Photo-real digital human avatars are of enormous importance in graphics, as
they enable immersive communication over the globe, improve gaming and
entertainment experiences, and can be particularly beneficial for AR and VR
settings. However, current avatar generation approaches either fall short in
high-fidelity novel view synthesis, generalization to novel motions,
reproduction of loose clothing, or they cannot render characters at the high
resolution offered by modern displays. To this end, we propose HDHumans, which
is the first method for HD human character synthesis that jointly produces an
accurate and temporally coherent 3D deforming surface and highly
photo-realistic images of arbitrary novel views and of motions not seen at
training time. At the technical core, our method tightly integrates a classical
deforming character template with neural radiance fields (NeRF). Our method is
carefully designed to achieve a synergy between classical surface deformation
and NeRF. First, the template guides the NeRF, which allows synthesizing novel
views of a highly dynamic and articulated character and even enables the
synthesis of novel motions. Second, we also leverage the dense pointclouds
resulting from NeRF to further improve the deforming surface via 3D-to-3D
supervision. We outperform the state of the art quantitatively and
qualitatively in terms of synthesis quality and resolution, as well as the
quality of 3D surface reconstruction.


  Users of decentralized finance (DeFi) applications face significant risks
from adversarial actions that manipulate the order of transactions to extract
value from users. Such actions -- an adversarial form of what is called
maximal-extractable value (MEV) -- impact both individual outcomes and the
stability of the DeFi ecosystem. MEV exploitation, moreover, is being
institutionalized through an architectural paradigm known Proposer-Builder
Separation (PBS).
  This work introduces a system called PROF (PRotected Order Flow) that is
designed to limit harmful forms of MEV in existing PBS systems. PROF aims at
this goal using two ideas. First, PROF imposes an ordering on a set ("bundle")
of privately input transactions and enforces that ordering all the way through
to block production -- preventing transaction-order manipulation. Second, PROF
creates bundles whose inclusion is profitable to block producers, thereby
ensuring that bundles see timely inclusion in blocks.
  PROF is backward-compatible, meaning that it works with existing and future
PBS designs. PROF is also compatible with any desired algorithm for ordering
transactions within a PROF bundle (e.g., first-come, first-serve, fee-based,
etc.). It executes efficiently, i.e., with low latency, and requires no
additional trust assumptions among PBS entities. We quantitatively and
qualitatively analyze incentive structure of PROF, and its utility to users
compared with existing solutions. We also report on inclusion likelihood of
PROF transactions, and concrete latency numbers through our end-to-end
implementation.


  We discuss the thermodynamics of an array of collinear black holes which may
be accelerating. We prove a general First Law, including variations in the
tensions of strings linking and accelerating the black holes. We analyse the
implications of the First Law in a number of instructive cases, including that
of the C-metric, and relate our findings to the previously obtained
thermodynamics of slowly accelerating black holes in anti-de Sitter spacetime.
The concept of thermodynamic length is found to be robust and a
Christoudoulou-Ruffini formula for the C-metric is shown.


  In this thesis new objects to the existing set of invariants of Lie algebras
are added. These invariant characteristics are capable of describing the
nilpotent parametric continuum of Lie algebras. The properties of these
invariants, in view of possible alternative classifications of Lie algebras,
are formulated and their behaviour on known lower--dimensional Lie algebras
investigated. It is demonstrated that these invariants, in view of their
application on graded contractions of sl(3,C), are also effective in higher
dimensions. A necessary contraction criterion involving these invariants is
derived and applied to lower--dimensional cases. Possible application of these
invariant characteristics to Jordan algebras is investigated.


  Many computer vision tasks involve processing large amounts of data
contaminated by outliers, which need to be detected and rejected. While outlier
detection methods based on robust statistics have existed for decades, only
recently have methods based on sparse and low-rank representation been
developed along with guarantees of correct outlier detection when the inliers
lie in one or more low-dimensional subspaces. This paper proposes a new outlier
detection method that combines tools from sparse representation with random
walks on a graph. By exploiting the property that data points can be expressed
as sparse linear combinations of each other, we obtain an asymmetric affinity
matrix among data points, which we use to construct a weighted directed graph.
By defining a suitable Markov Chain from this graph, we establish a connection
between inliers/outliers and essential/inessential states of the Markov chain,
which allows us to detect outliers by using random walks. We provide a
theoretical analysis that justifies the correctness of our method under
geometric and connectivity assumptions. Experimental results on image databases
demonstrate its superiority with respect to state-of-the-art sparse and
low-rank outlier detection methods.


  In this paper, we propose a model predictive control (MPC) that accomplishes
interactive robotic tasks, in which multiple contacts may occur at unknown
locations. To address such scenarios, we made an explicit contact feedback loop
in the MPC framework. An algorithm called Multi-Contact Particle Filter with
Exploration Particle (MCP-EP) is employed to establish real-time feedback of
multi-contact information. Then the interaction locations and forces are
accommodated in the MPC framework via a spring contact model. Moreover, we
achieved real-time control for a 7 degrees of freedom robot without any
simplifying assumptions by employing a Differential-Dynamic-Programming
algorithm. We achieved 6.8kHz, 1.9kHz, and 1.8kHz update rates of the MPC for
0, 1, and 2 contacts, respectively. This allows the robot to handle unexpected
contacts in real time. Real-world experiments show the effectiveness of the
proposed method in various scenarios.


  Numerical simulations of the supernova (SN) neutrino self-induced flavor
conversions, associated with the neutrino-neutrino interactions in the deepest
stellar regions, have been typically carried out assuming the "bulb-model". In
this approximation, neutrinos are taken to be emitted half-isotropically by a
common neutrinosphere. In the recent Ref. \cite{Mirizzi:2011tu} we have removed
this assumption by introducing flavor-dependent angular distributions for SN
neutrinos, as suggested by core-collapse simulations. We have found that in
this case a novel multi-angle instability in the self-induced flavor
transitions can arise. In this work we perform an extensive study of this
effect, carrying out a linearized flavor stability analysis for different SN
neutrino energy fluxes and angular distributions, in both normal and inverted
neutrino mass hierarchy. We confirm that spectra of different nu species which
cross in angular space (where F_{\nu_e}=F_{\nu_x} and
F_{\bar\nu_e}=F_{\bar\nu_x}) present a significant enhancement of the flavor
instability, and a shift of the onset of the flavor conversions at smaller
radii with respect to the case of an isotropic neutrino emission. We also
illustrate how a qualitative (and sometimes quantitative) understanding of the
dynamics of these systems follows from a stability analysis.


  Starting from parametrization of scalar perturbations generated during
inflation in terms of $e$--fold $N$ and using an approach recently developed by
Starobinsky, dubbed "direct smooth reconstruction", we show that, in the
slow--roll approximation, it is possible to reconstruct the inflation potential
in the Einstein frame and its corresponding Lagrangian $f(R)$ model


  Automated detection of surgical errors can improve robotic-assisted surgery.
Despite promising progress, existing methods still face challenges in capturing
rich temporal context to establish long-term dependencies while maintaining
computational efficiency. In this paper, we propose a novel hierarchical model
named SEDMamba, which incorporates the selective state space model (SSM) into
surgical error detection, facilitating efficient long sequence modelling with
linear complexity. SEDMamba enhances selective SSM with bottleneck mechanism
and fine-to-coarse temporal fusion (FCTF) to detect and temporally localize
surgical errors in long videos. The bottleneck mechanism compresses and
restores features within their spatial dimension, thereby reducing
computational complexity. FCTF utilizes multiple dilated 1D convolutional
layers to merge temporal information across diverse scale ranges, accommodating
errors of varying durations. Besides, we deploy an established observational
clinical human reliability assessment tool (OCHRA) to annotate the errors of
suturing tasks in an open-source radical prostatectomy dataset (SAR-RARP50),
constructing the first frame-level in-vivo surgical error detection dataset to
support error detection in real-world scenarios. Experimental results
demonstrate that our SEDMamba outperforms state-of-the-art methods with at
least 1.82% AUC and 3.80% AP performance gain with significantly reduced
computational complexity.


  Evolutionary Algorithms (EAs) and Deep Reinforcement Learning (DRL) have
recently been integrated to take the advantage of the both methods for better
exploration and exploitation.The evolutionary part in these hybrid methods
maintains a population of policy networks.However, existing methods focus on
optimizing the parameters of policy network, which is usually high-dimensional
and tricky for EA.In this paper, we shift the target of evolution from
high-dimensional parameter space to low-dimensional action space.We propose
Evolutionary Action Selection-Twin Delayed Deep Deterministic Policy Gradient
(EAS-TD3), a novel hybrid method of EA and DRL.In EAS, we focus on optimizing
the action chosen by the policy network and attempt to obtain high-quality
actions to promote policy learning through an evolutionary algorithm. We
conduct several experiments on challenging continuous control tasks.The result
shows that EAS-TD3 shows superior performance over other state-of-art methods.


  Determining gas content and star formation rate has known remarkable progress
in field galaxies, but has been much less investigated in galaxies inside
clusters. We present the first CO observations of luminous infrared galaxies
(LIRGs) inside the virial radii of two intermediate redshift clusters,
CL1416+4446 (z=0.397) and CL0926+1242 (z=0.489). We detect three galaxies at
high significance (5 to 10 sigma), and provide robust estimates of their CO
luminosities, L'CO. In order to put our results into a general context, we
revisit the relation between cold and hot gas and stellar mass in nearby field
and cluster galaxies. We find evidence that at fixed LIR (or fixed stellar
mass), the frequency of high L'CO galaxies is lower in clusters than in the
field, suggesting environmental depletion of the reservoir of cold gas. The
level of star formation activity in a galaxy is primarily linked to the amount
of cold gas, rather than to the galaxy mass or the lookback time. In clusters,
just as in the field, the conversion between gas and stars seems universal. The
relation between LIR and L'CO for distant cluster galaxies extends the relation
of nearby galaxies to higher IR luminosities. Nevertheless, the intermediate
redshift galaxies fall well within the dispersion of the trend defined by local
systems. Considering that L'CO is generally derived from the CO(1-0) line and
sensitive to the vast majority of the molecular gas in the cold interstellar
medium of galaxies, but less to the part which will actually be used to form
stars, we suggest that molecular gas can be stripped before the star formation
rate is affected. Combining the sample of Geach et al. (2009, 2011) and ours,
we find evidence for a decrease in CO towards the cluster centers. This is the
first hint of an environmental impact on cold gas at intermediate redshift.


  The multivariate conditional probability distribution models the effects of a
set of variables onto the statistical properties of another set of variables.
In the study of systemic risk in a financial system, the multivariate
conditional probability distribution can be used for stress-testing by
quantifying the propagation of losses from a set of `stressing' variables to
another set of `stressed' variables. In this paper I describe how to compute
such conditional probability distributions for the vast family of multivariate
elliptical distributions, and in particular for the multivariate Student-t and
the multivariate Normal distributions. Measures of stress impact and systemic
risk are proposed. An application to the US equity market illustrates the
potentials of this approach.


  In this paper, inspired by the spectral sequences constructed by signature
operators with respect to the composition of fibrations, we define the
"spectral sequences" for fiberwise Dirac operators and prove the equivariant
family version of the adiabatic limit formula of eta invariants using the heat
kernel method and the analytic localization techniques established by
Bismut-Lebeau. In our formula, the remainder terms are constructed by "spectral
sequences" and completely extend those of Dai and Bunke-Ma.


  We propose a simple and efficient multi-hop dense retrieval approach for
answering complex open-domain questions, which achieves state-of-the-art
performance on two multi-hop datasets, HotpotQA and multi-evidence FEVER.
Contrary to previous work, our method does not require access to any
corpus-specific information, such as inter-document hyperlinks or
human-annotated entity markers, and can be applied to any unstructured text
corpus. Our system also yields a much better efficiency-accuracy trade-off,
matching the best published accuracy on HotpotQA while being 10 times faster at
inference time.


  Within the algebraic framework of Hopf algebras, random walks and associated
diffusion equations (master equations) are constructed and studied for two
basic operator algebras of Quantum Mechanics i.e the Heisenberg-Weyl algebra
(hw) and its q-deformed version hw_q. This is done by means of functionals
determined by the associated coherent state density operators. The ensuing
master equations admit solutions given by hw and hw_q-valued Appell systems.


  The inherent nature of patient data poses several challenges. Prevalent cases
amass substantial longitudinal data owing to their patient volume and
consistent follow-ups, however, longitudinal laboratory data are renowned for
their irregularity, temporality, absenteeism, and sparsity; In contrast,
recruitment for rare or specific cases is often constrained due to their
limited patient size and episodic observations. This study employed
self-supervised learning (SSL) to pretrain a generalized laboratory progress
(GLP) model that captures the overall progression of six common laboratory
markers in prevalent cardiovascular cases, with the intention of transferring
this knowledge to aid in the detection of specific cardiovascular event. GLP
implemented a two-stage training approach, leveraging the information embedded
within interpolated data and amplify the performance of SSL. After GLP
pretraining, it is transferred for TVR detection. The proposed two-stage
training improved the performance of pure SSL, and the transferability of GLP
exhibited distinctiveness. After GLP processing, the classification exhibited a
notable enhancement, with averaged accuracy rising from 0.63 to 0.90. All
evaluated metrics demonstrated substantial superiority (p < 0.01) compared to
prior GLP processing. Our study effectively engages in translational
engineering by transferring patient progression of cardiovascular laboratory
parameters from one patient group to another, transcending the limitations of
data availability. The transferability of disease progression optimized the
strategies of examinations and treatments, and improves patient prognosis while
using commonly available laboratory parameters. The potential for expanding
this approach to encompass other diseases holds great promise.


  Mobile phones have been closed environments until recent years. The change
brought by open platform technologies such as the Symbian operating system and
Java technologies has opened up a significant business opportunity for anyone
to develop application software such as games for mobile terminals. However,
developing mobile applications is currently a challenging task due to the
specific demands and technical constraints of mobile development. Furthermore,
at the moment very little is known about the suitability of the different
development processes for mobile application development. Due to these issues,
we have developed an agile development approach called Mobile-D. The Mobile-D
approach is briefly outlined here and the experiences gained from four case
studies are discussed.


  We carry out a first-principles investigation on magnetism, electronic
structure, magneto-optical effects and topological property of newly grown
cubic double perovskite Ba2NiOsO6 and its (111) (Ba2NiOsO6)/(BaTiO3)10
superlattice, based on the density functional theory with the generalized
gradient approximation (GGA) plus onsite Couloumb interactions. Interestingly,
we find that both structures are rare ferromagnetic (FM) semiconductors with
estimated Curie temperatures of ~150 and 70 K, respectively. The calculated
near-neighbor exchange coupling parameters reveal that the ferromagnetism is
driven by exotic FM coupling between Ni and Os atoms, which is due to the FM
superexchange interaction caused by the abnormally strong hybridization between
the half-filled Nieg and unoccupied Os eg orbitals. The strong spin-orbit
coupling (SOC) on the Os atom is found to not only open the semiconducting gap
but also produce a large antiparallel orbital magnetic moment on the Os atom,
thus reducing the total magnetization from 4.0 uB/f.u.,


  Micropaleontology in geosciences focuses on studying the evolution of
microfossils (e.g., foraminifera) through geological records to reconstruct
past environmental and climatic conditions. This field heavily relies on visual
recognition of microfossil features, making it suitable for computer vision
technology, specifically deep convolutional neural networks (CNNs), to automate
and optimize microfossil identification and classification. However, the
application of deep learning in micropaleontology is hindered by limited
availability of high-quality, high-resolution labeled fossil images and the
significant manual labeling effort required by experts. To address these
challenges, we propose a novel deep learning workflow combining hierarchical
vision transformers with style-based generative adversarial network algorithms
to efficiently acquire and synthetically generate realistic high-resolution
labeled datasets of micropaleontology in large volumes. Our study shows that
this workflow can generate high-resolution images with a high signal-to-noise
ratio (39.1 dB) and realistic synthetic images with a Frechet inception
distance similarity score of 14.88. Additionally, our workflow provides a large
volume of self-labeled datasets for model benchmarking and various downstream
visual tasks, including fossil classification and segmentation. For the first
time, we performed few-shot semantic segmentation of different foraminifera
chambers on both generated and synthetic images with high accuracy. This novel
meta-learning approach is only possible with the availability of
high-resolution, high-volume labeled datasets. Our deep learning-based workflow
shows promise in advancing and optimizing micropaleontological research and
other visual-dependent geological analyses.


  We study correlated phases occurring in the flat lowest band of the dice
lattice model at flux density one half. We discuss how to realize the dice
lattice model, also referred to as the T_3 lattice, in cold atomic gases. We
construct the projection of the model to the lowest dice band, which yields a
Hubbard-Hamiltonian with interaction-assisted hopping processes. We solve this
model for bosons in two limits. In the limit of large density, we use
Gross-Pitaevskii mean-field theory to reveal time-reversal symmetry breaking
vortex lattice phases. At low density, we use exact diagonalization to identify
three stable phases at fractional filling factors \nu of the lowest band,
including a classical crystal at \nu=1/3, a supersolid state at \nu=1/2 and a
Mott insulator at \nu=1.


  Two-dimensional van der Waals single crystals DyOBr and SmOCl have been grown
by flux method and their anisotropic magnetic properties are reported. DyOBr
orders antiferromagnetically at T$_{N}$=9.5 K with magnetic moments lying along
$a$-axis, similar as DyOCl. Its magnetic susceptibility shows an anomaly at
T$^{*}$=30 K possibly due to the crystal field effect. Furthermore a 1/3
magnetization plateau is clearly observed under H$\parallel$a and
H$\parallel$[110], which might be a field-induced spin-flop phase or some
exotic quantum magnetic state. On the other hand, isostructural SmOCl undergoes
an antiferromagnetic transition at T$_{N}$=7.1 K and exhibits a contrasting
Ising-like perpendicular $c$-axis magnetic anisotropy, which could be well
explained by our crystal field calculations. Both DyOBr and SmOCl are
insulators with band gap of $\sim$5 eV, our results suggest they are promising
in building van der Waals heterostructures and applications in multifunctional
devices.


  We investigate the large-scale structure of Lyman-alpha emission intensity in
the Universe at redshifts z=2-3.5 using cross-correlation techniques. Our Lya
emission samples are spectra of BOSS Luminous Red Galaxies from Data Release 12
with the best fit model galaxies subtracted. We cross-correlate the residual
flux in these spectra with BOSS quasars, and detect a positive signal on scales
1-15 Mpc/h. We identify and remove a source of contamination not previously
accounted for, due to the effects of quasar clustering on cross-fibre light.
Corrected, our quasar-Lya emission cross-correlation is 50 % lower than that
seen by Croft et al. for DR10, but still significant. Because only 3% of space
is within 15 Mpc/h of a quasar, the result does not fully explore the global
large-scale structure of Lya emission. To do this, we cross-correlate with the
Lya forest. We find no signal in this case. The 95% upper limit on the global
Lya mean surface brightness from Lya emission-Lya forest cross-correlation is
mu < 1.2x10^-22 erg/s/cm^2/A/arcsec^2 This null result rules out the scenario
where the observed quasar-Lya emission cross-correlation is primarily due to
the large scale structure of star forming galaxies, Taken in combination, our
results suggest that Lya emitting galaxies contribute, but quasars dominate
within 15 Mpc/h. A simple model for Lya emission from quasars based on
hydrodynamic simulations reproduces both the observed forest-Lya emission and
quasar-Lya emission signals. The latter is also consistent with extrapolation
of observations of fluorescent emission from smaller scales r < 1 Mpc.


  Current solar and atmospheric neutrino oscillation data seem to favor a
bimaximal pattern for neutrino mixings where the matrix elements U_{e2} and
U_{\mu 3} are of order one, while U_{e3} is much smaller. We show that such a
pattern can be obtained quite easily in theories with ``lopsided'' mass
matrices for the charged leptons and the down type quarks. A relation
connecting the solar and atmospheric neutrino mixing angles is derived,
\tan^2\theta_{atm} \simeq 1+ \tan^2\theta_{sol}, which predicts \sin^2
2\theta_{atm} \simeq 0.97 corresponding to the best fit LMA solution for solar
neutrinos. Predictive schemes in SO(10) realizing these ideas are presented. A
new class of SO(10) models with lopsided mass matrices is found which makes use
of an adjoint VEV along the I_{3R} direction, rather than the traditional B-L
direction.


  We discuss the sharp interface limit, leading to a mean curvature flow
energy, for the rate function of the large deviation principle of a
Glauber+Kawasaki process with speed change. We provide an explicit formula of
the limiting functional given by the mobility and the transport coefficient.


  The noncommutative (or mixed) trace algebra $T_{nd}$ is generated by $d$
generic $n\times n$ matrices and by the algebra $C_{nd}$ generated by all
traces of products of generic matrices, $n,d\geq 2$. It is known that over a
field of characteristic 0 this algebra is a finitely generated free module over
a polynomial subalgebra $S$ of the center $C_{nd}$. For $n=3$ and $d=2$ we have
found explicitly such a subalgebra $S$ and a set of free generators of the
$S$-module $T_{32}$. We give also a set of defining relations of $T_{32}$ as an
algebra and a Groebner basis of the corresponding ideal. The proofs are based
on easy computer calculations with standard functions of Maple, the explicit
presentation of $C_{32}$ in terms of generators and relations, and methods of
representation theory of the general linear group.