  In this paper, we consider a quasi-orthogonal (QO) space-time block code
(STBC) with minimum decoding complexity (MDC-QO-STBC). We formulate its
algebraic structure and propose a systematic method for its construction. We
show that a maximum-likelihood (ML) decoder for this MDC-QOSTBC, for any number
of transmit antennas, only requires the joint detection of two real symbols.
Assuming the use of a square or rectangular quadratic-amplitude modulation
(QAM) or multiple phase-shift keying (MPSK) modulation for this MDC-QOSTBC, we
also obtain the optimum constellation rotation angle, in order to achieve full
diversity and optimum coding gain. We show that the maximum achievable code
rate of these MDC-QOSTBC is 1 for three and four antennas and 3/4 for five to
eight antennas. We also show that the proposed MDC-QOSTBC has several desirable
properties, such as a more even power distribution among antennas and better
scalability in adjusting the number of transmit antennas, compared with the
coordinate interleaved orthogonal design (CIOD) and asymmetric CIOD (ACIOD)
codes. For the case of an odd number of transmit antennas, MDC-QO-STBC also has
better decoding performance than CIOD.


  A detailed low-energy electronic structure of a Kondo insulator YbB$_{12}$
was revealed by a synergetic combination of ultrahigh-resolution laser
photoemission spectroscopy (PES) and time-resolved PES. The former confirmed a
25-meV pseudogap corresponding to the Kondo temperature of this material, and
more importantly, it revealed that a 15-meV gap and a Kondo-peak feature
developed below a crossover temperature $T^\ast \sim 110$ K. In harmony with
this, the latter discovered a very long recombination time exceeding 100 ps
below $\sim$$T^\ast$. This is a clear manifestation of photoexcited carriers
due to the bottleneck in the recovery dynamics, which is interpreted as a
developing hybridization gap of a hard gap.


  Geometric feature learning for 3D surfaces is critical for many applications
in computer graphics and 3D vision. However, deep learning currently lags in
hierarchical modeling of 3D surfaces due to the lack of required operations
and/or their efficient implementations. In this paper, we propose a series of
modular operations for effective geometric feature learning from 3D triangle
meshes. These operations include novel mesh convolutions, efficient mesh
decimation and associated mesh (un)poolings. Our mesh convolutions exploit
spherical harmonics as orthonormal bases to create continuous convolutional
filters. The mesh decimation module is GPU-accelerated and able to process
batched meshes on-the-fly, while the (un)pooling operations compute features
for up/down-sampled meshes. We provide open-source implementation of these
operations, collectively termed Picasso. Picasso supports heterogeneous mesh
batching and processing. Leveraging its modular operations, we further
contribute a novel hierarchical neural network for perceptual parsing of 3D
surfaces, named PicassoNet++. It achieves highly competitive performance for
shape analysis and scene segmentation on prominent 3D benchmarks. The code,
data and trained models are available at
https://github.com/EnyaHermite/Picasso.


  We analyze a divergence based first order system least squares method applied
to a second order elliptic model problem with homogeneous boundary conditions.
We prove optimal convergence in the $L^2(\Omega)$ norm for the scalar variable.
Numerical results confirm our findings.


  In the present Letter we show that the concept of the generalized
synchronization regime in discrete maps needs refining in the same way as it
has been done for the flow systems [PRE, 84 (2011) 037201]. We have shown
that\alkor{, in the general case, when the relationship between state vectors
of the interacting chaotic maps are considered,} the prehistory must be taken
into account. We extend the phase tube approach to the systems with a discrete
time coupled both unidirectionally and mutually and analyze the essence of the
generalized synchronization by means of this technique. Obtained results show
that the division of the generalized synchronization into the weak and the
strong ones also must be reconsidered. Unidirectionally coupled logistic maps
and H\'enon maps coupled mutually are used as sample systems.


  We consider the one-loop effective action due to a spinor loop coupled to an
abelian vector and axial vector field background. After rewriting this
effective action in terms of an auxiliary non-abelian gauge connection, we use
the De Witt expansion to analyze both its anomalous and non-anomalous content.
The same transformation allows us to obtain a novel worldline path integral
representation for this effective action which avoids the usual separation into
the real and imaginary parts of the Euclidean effective action, as well as the
introduction of auxiliary dimensions.


  In the upcoming LHC run we will be able to probe the structure ofthe
loop--induced Higgs--gluon coupling through kinematics. First, we establish
state-of-the-art simulations with up to two jets to next-to-leading order
including top mass effects. They allow us to search for deviations from the
low-energy limits in boosted Higgs production. In addition, the size of the top
mass effects suggests that they should generally be included in Higgs studies
at the LHC. Next, we show how off-shell Higgs production with a decay to four
leptons is sensitive to the same top mass effects. We compare the potential of
both methods based on the same top--Higgs Lagrangian. Finally, we comment on
related model assumptions required for a Higgs width measurement.


  Bulow and Klemperer's well-known result states that, in a single-item auction
where the $n$ bidders' values are independently and identically drawn from a
regular distribution, the Vickrey auction with one additional bidder (a
duplicate) extracts at least as much revenue as the optimal auction without the
duplicate. Hartline and Roughgarden, in their influential 2009 paper, removed
the requirement that the distributions be identical, at the cost of allowing
the Vickrey auction to recruit $n$ duplicates, one from each distribution, and
relaxing its revenue advantage to a $2$-approximation.
  In this work we restore Bulow and Klemperer's number of duplicates in
Hartline and Roughgarden's more general setting with a worse approximation
ratio. We show that recruiting a duplicate from one of the distributions
suffices for the Vickrey auction to $10$-approximate the optimal revenue. We
also show that in a $k$-items unit demand auction, recruiting $k$ duplicates
suffices for the VCG auction to $O(1)$-approximate the optimal revenue.
  As another result, we tighten the analysis for Hartline and Roughgarden's
Vickrey auction with $n$ duplicates for the case with two bidders in the
auction. We show that in this case the Vickrey auction with two duplicates
obtains at least $3/4$ of the optimal revenue. This is tight by meeting a lower
bound by Hartline and Roughgarden. En route, we obtain a transparent analysis
of their $2$-approximation for $n$~bidders, via a natural connection to Ronen's
lookahead auction.


  Prompting has become one of the main approaches to leverage emergent
capabilities of Large Language Models [Brown et al. NeurIPS 2020, Wei et al.
TMLR 2022, Wei et al. NeurIPS 2022]. During the last year, researchers and
practitioners have been playing with prompts to see how to make the most of
LLMs. By homogeneously dissecting 80 papers, we investigate in deep how
software testing and verification research communities have been abstractly
architecting their LLM-enabled solutions. More precisely, first, we want to
validate whether downstream tasks are an adequate concept to convey the
blueprint of prompt-based solutions. We also aim at identifying number and
nature of such tasks in solutions. For such goal, we develop a novel downstream
task taxonomy that enables pinpointing some engineering patterns in a rather
varied spectrum of Software Engineering problems that encompasses testing,
fuzzing, debugging, vulnerability detection, static analysis and program
verification approaches.


  We present analytic expressions of all integrals required to complete the
explicit evaluation of the real-virtual integrated counterterms needed to
define a recently proposed subtraction scheme for jet cross sections at
next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation
of these integrals in $4-2\epsilon$ dimensions to obtain the coefficients of
their Laurent expansions around $\epsilon=0$. These coefficients are given by
linear combinations of multidimensional Mellin-Barnes integrals. We compute the
coefficients of such expansions in $\epsilon$ both numerically and analytically
by complex integration over the Mellin-Barnes contours.


  Magnetic skyrmions are nano-scale magnetic states that could be used in
various spintronics devices. A central issue is the mechanism and rate of
various possible annihilation processes and the lifetime of metastable
skyrmions. While most studies have focused on classical over-the-barrier
mechanism for annihilation, it is also possible that quantum mechanical
tunneling through the energy barrier takes place. Calculations of the lifetime
of magnetic skyrmions in a two-dimensional lattice are presented and the rate
of tunneling compared with the classical annihilation rate. A remarkably strong
variation in the crossover temperature and the lifetime of the skyrmion is
found as a function of the values of parameters in the extended Heisenberg
Hamiltonian, i.e. the out-of-plane anisotropy, Dzyaloshinskii-Moriya
interaction (DMI) and applied magnetic field. Materials parameters and
conditions are identified where the onset of tunneling could be observed on a
laboratory time scale. In particular, it is predicted that skyrmion tunneling
could be observed in the PdFe/Ir(111) system when an external magnetic field on
the order of 6 T is applied.


  The proton's gluon structure function at small x is larger than nowadays is
commonly believed


  We present 3-5 micron spectroscopy of the interacting system NGC 6240,
showing the presence of two active galactic nuclei. The brightest (southern)
nucleus shows up with a starburst-like emission, with a prominent 3.3 micron
emission feature. However, the presence of an AGN is revealed by the detection
of a broad Br alpha emission line, with a width of ~1,800 km/s. The spectrum of
the faintest (northern) nucleus shows typical AGN features, such as a steep
continuum and broad absorption features in the M-band. We discuss the physical
properties of the dusty absorbers/emitters, and show that in both nuclei the
AGN is dominant in the 3-5 micron band, but its contribution to the total
luminosity is small (a few percent of the starburst emission).


  We investigate quantum entanglement in an analogue black hole realized in the
flow of a Bose-Einstein condensate. The system is described by a three-mode
Gaussian state and we construct the corresponding covariance matrix at zero and
finite temperature. We study associated bipartite and tripartite entanglement
measures and discuss their experimental observation. We identify a simple
optical setup equivalent to the analogue Bose-Einstein black hole which
suggests a new way of determining the Hawking temperature and grey-body factor
of the system.


  We make use of multiplicative degree-based topological indices $X_\Pi(G)$ to
perform a detailed analytical and statistical study of random networks
$G=(V(G),E(G))$. We consider two classes of indices: $X_\Pi(G) = \prod_{u \in
V(G)} F_V(d_u)$ and $X_\Pi(G) = \prod_{uv \in E(G)} F_E(d_u,d_v)$, where $uv$
denotes the edge of $G$ connecting the vertices $u$ and $v$, $d_u$ is the
degree of the vertex $u$, and $F_V(x)$ and $F_E(x,y)$ are functions of the
vertex degrees. Specifically, we find analytical inequalities involving these
multiplicative indices. Also, we apply $X_\Pi(G)$ on three models of random
networks: Erd\"os-R\'enyi networks, random geometric graphs, and bipartite
random networks. We show that $\left< \ln X_\Pi(G) \right>$, normalized to the
order of the network, scale with the corresponding average degree; here $\left<
\cdot \right>$ denotes the average over an ensemble of random networks.


  Using stickers in online chatting is very prevalent on social media
platforms, where the stickers used in the conversation can express someone's
intention/emotion/attitude in a vivid, tactful, and intuitive way. Existing
sticker retrieval research typically retrieves stickers based on context and
the current utterance delivered by the user. That is, the stickers serve as a
supplement to the current utterance. However, in the real-world scenario, using
stickers to express what we want to say rather than as a supplement to our
words only is also important. Therefore, in this paper, we create a new dataset
for sticker retrieval in conversation, called \textbf{StickerInt}, where
stickers are used to reply to previous conversations or supplement our
words\footnote{We believe that the release of this dataset will provide a more
complete paradigm than existing work for the research of sticker retrieval in
the open-domain online conversation.}. Based on the created dataset, we present
a simple yet effective framework for sticker retrieval in conversation based on
the learning of intention and the cross-modal relationships between
conversation context and stickers, coined as \textbf{Int-RA}. Specifically, we
first devise a knowledge-enhanced intention predictor to introduce the
intention information into the conversation representations. Subsequently, a
relation-aware sticker selector is devised to retrieve the response sticker via
cross-modal relationships. Extensive experiments on the created dataset show
that the proposed model achieves state-of-the-art performance in sticker
retrieval\footnote{The dataset and source code of this work are released at
\url{https://github.com/HITSZ-HLT/Int-RA}.}.


  A toric domain is a subset of $(\mathbb{C}^n,\omega_{\text{std}})$ which is
invariant under the standard rotation action of $\mathbb{T}^n$ on
$\mathbb{C}^n$. For a toric domain $U$ from a certain large class for which
this action is not free, we find a corresponding toric domain $V$ where the
standard action is free, and for which $c(U)=c(V)$ for any symplectic capacity
$c$. Michael Hutchings gives a combinatorial formula for calculating his
embedded contact homology symplectic capacities for certain toric
four-manifolds on which the $\mathbb{T}^2$-action is free. Our theorem allows
one to extend this formula to a class of toric domains where the action is not
free. We apply our theorem to compute ECH capacities for certain intersections
of ellipsoids, and find that these capacities give sharp obstructions to
symplectically embedding these ellipsoid intersections into balls.


  We present hydrodynamic simulations of a major merger of disk galaxies, and
study the ISM dynamics and star formation properties. High spatial and mass
resolutions of 12pc and 4x10^4 M_sol allow to resolve cold and turbulent gas
clouds embedded in a warmer diffuse phase. We compare to lower resolution
models, where the multiphase ISM is not resolved and is modeled as a relatively
homogeneous and stable medium. While merger-driven bursts of star formation are
generally attributed to large-scale gas inflows towards the nuclear regions, we
show that once a realistic ISM is resolved, the dominant process is actually
gas fragmentation into massive and dense clouds and rapid star formation
therein. As a consequence, star formation is more efficient by a factor of up
to 10 and is also somewhat more extended, while the gas density probability
distribution function (PDF) rapidly evolves towards very high densities. We
thus propose that the actual mechanism of starburst triggering in galaxy
collisions can only be captured at high spatial resolution and when the cooling
of gas is modeled down to less than 10^3 K. Not only does our model reproduce
the properties of the Antennae system, but it also explains the ``starburst
mode'' revealed recently in high-redshift mergers compared to quiescent disks.


  Detection of differential item functioning by use of the logistic modelling
approach has a long tradition. One big advantage of the approach is that it can
be used to investigate non-uniform DIF as well as uniform DIF. The classical
approach allows to detect DIF by distinguishing between multiple groups. We
propose an alternative method that is a combination of recursive partitioning
methods (or trees) and logistic regression methodology to detect uniform and
non-uniform DIF in a nonparametric way. The output of the method are trees that
visualize in a simple way the structure of DIF in an item showing which
variables are interacting in which way when generating DIF. In addition we
consider a logistic regression method in which DIF can by induced by a vector
of covariates, which may include categorical but also continuous covariates.
The methods are investigated in simulation studies and illustrated by two
applications.


  Current state of the art devices for detecting and manipulating Majorana
fermions commonly consist of networks of Majorana wires and tunnel junctions.
We study a key ingredient of these networks - a topological Josephson junction
with charging energy - and pinpoint crucial features for device implementation.
The phase dependent tunneling term contains both the usual 2pi-periodic
Josephson term and a 4pi-periodic Majorana tunneling term representing the
coupling between Majoranas on both sides of the junction. In non-topological
junctions when the charging energy is small compared to the Josephson tunneling
scale the low energy physics is described by 2pi phase slips. By contrast, in a
topological junction, due to the 4pi periodicity of the tunneling term it is
usually expected that only 4pi phase slips are possible while 2pi phase slips
are suppressed. However, we find that if the ratio between the strengths of the
Majorana assisted tunneling and the Josephson tunneling is small, as is likely
to be the case for many setups, 2pi phase slips occur and may even dominate the
low energy physics. In this limit one can view the 4pi phase slips as a pair of
2pi phase slips with arbitrarily large separation. We provide an effective
descriptions of the system in terms of 2pi and 4pi phase slips valid for all
values of the tunneling ratio. Comparing the spectrum of the effective models
with numerical simulations we determine the cross-over between the 4pi phase
slip regime to 2pi phase slip dominated regime. We also discuss the role of the
charging energy as well as the implications of our results on the dissipative
phase transitions expected in such a system.


  Based on parity violation in the weak interaction and evidences from neutrino
oscillation, a natural choice is that neutrinos may be spacelike particles with
a tiny mass. To keep causality for spacelike particles, a kinematic time under
a non-standard form of the Lorentz transformation is introduced, which is
related to a preferred frame. A Dirac-type equation for spacelike neutrinos is
further investigated and its solutions are discussed. This equation can be
written in two spinor equations coupled together via nonzero mass while
respecting maximum parity violation. As a consequence, parity violation implies
that the principle of relativity is violated in the weak interaction.


  The metallic interface between two oxide insulators, such as LaAlO3/SrTiO3
(LAO/STO), provides new opportunities for electronics and spintronics. However,
due to the presence of multiple orbital populations, tailoring the interfacial
properties such as the ground state and metal-insulator transitions remains
challenging. Here, we report an unforeseen tunability of the phase diagram of
LAO/STO by alloying LAO with a ferromagnetic LaMnO3 insulator without forming
lattice disorder and at the same time without changing the polarity of the
system. By increasing the Mn-doping level, x, of LaAl1-xMnxO3/STO, the
interface undergoes a Lifshitz transition at x = 0.225 across a critical
carrier density of nc= 2.8E13 cm-2, where a peak TSC =255 mK of superconducting
transition temperature is observed. Moreover, the LaAl1-xMnxO3 turns
ferromagnetic at x >=0.25. Remarkably, at x = 0.3, where the metallic interface
is populated by only dxy electrons and just before it becomes insulating, we
achieve reproducibly a same device with both signatures of superconductivity
and clear anomalous Hall effect. This provides a unique and effective way to
tailor oxide interfaces for designing on-demand electronic and spintronic
devices.


  Semiconductor lasers, one of the key components for optical communication
systems, have been rapidly evolving to meet the requirements of next generation
optical networks with respect to high speed, low power consumption, small form
factor etc. However, these demands have brought severe challenges to the
semiconductor laser reliability. Therefore, a great deal of attention has been
devoted to improving it and thereby ensuring reliable transmission. In this
paper, a predictive maintenance framework using machine learning techniques is
proposed for real-time heath monitoring and prognosis of semiconductor laser
and thus enhancing its reliability. The proposed approach is composed of three
stages: i) real-time performance degradation prediction, ii) degradation
detection, and iii) remaining useful life (RUL) prediction. First of all, an
attention based gated recurrent unit (GRU) model is adopted for real-time
prediction of performance degradation. Then, a convolutional autoencoder is
used to detect the degradation or abnormal behavior of a laser, given the
predicted degradation performance values. Once an abnormal state is detected, a
RUL prediction model based on attention-based deep learning is utilized.
Afterwards, the estimated RUL is input for decision making and maintenance
planning. The proposed framework is validated using experimental data derived
from accelerated aging tests conducted for semiconductor tunable lasers. The
proposed approach achieves a very good degradation performance prediction
capability with a small root mean square error (RMSE) of 0.01, a good anomaly
detection accuracy of 94.24% and a better RUL estimation capability compared to
the existing ML-based laser RUL prediction models.


  We highlight a fundamental ill-posedness issue for nonlinear stochastic wave
equations driven by a fractional noise. Namely, if the noise becomes too rough
(i.e., the sum of its Hurst indexes becomes too small), then there is
essentially no hope to provide an interpretation of the model, whether directly
or through a Wick-type renormalization procedure. This phenomenon can be
compared with the situation of a general SDE driven by a two-dimensional
fractional noise of index $H\leq \frac{1}{4}$. Our results clarify and extend
previous similar properties exhibited in [3] or in [14].


  Employing an effective formalism for decaying system we are able to
investigate Heisenberg's uncertainty relation for observables measured at
accelerator facilities. In particular we investigate the neutral K--meson
system and show that, firstly, due to the time evolution an uncertainty between
strangeness measurements at different times is introduced and, secondly, due to
the imbalance of matter and antimatter (CP violation) an uncertainty in the
evolution of the eigenstates of the effective Hamiltonian of the system.
Consequently, the existence of CP violation is linked to uncertainties of
observables, i.e. the outcomes cannot be predicted even in principle to
arbitrary precisions.


  In this paper, we determine the descriptive complexity of subsets of the
Polish space of marked groups defined by various group theoretic properties. In
particular, using Grigorchuk groups, we establish that the sets of solvable
groups, groups of exponential growth and groups with decidable word problem are
$\mathbf{\Sigma}^0_2$-complete and that the sets of periodic groups and groups
of intermediate growth are $\mathbf{\Pi}^0_2$-complete. We also provide bounds
for the descriptive complexity of simplicity, amenability, residually
finiteness, Hopficity and co-Hopficity. This paper is intended to serve as a
compilation of results on this theme.


  This paper introduces a comprehensive formalism for decomposing the state
space of a quantum field into several entangled subobjects, i.e., fields
generating a subspace of states. Projecting some of the subobjects onto
degenerate background states reduces the system to an effective field theory
depending on parameters representing the degeneracies. Notably, these
parameters are not exogenous. The entanglement among subobjects in the initial
system manifests as an interrelation between parameters and non-projected
subobjects. Untangling this dependency necessitates imposing linear first-order
equations on the effective field. The geometric characteristics of the
parameter spaces depend on both the effective field and the background of the
projected subobjects. The system, governed by arbitrary variables, has no
dynamics, but the projection of some subobjects can be interpreted as slicing
the original state space according to the lowest eigenvalues of a
parameter-dependent family of operators. The slices can be endowed with
amplitudes similar to some transitions between each other, contingent upon
these eigenvalues. Averaging over all possible transitions shows that the
amplitudes are higher for maps with increased eigenvalue than for maps with
decreasing eigenvalue.


  We explore the consequences of the so-called intertwinings between gradients
and Markov diffusion operators on $R^d$ in terms of second-order Brascamp-Lieb
inequalities for log-concave distributions and beyond, extending our
inequalities established in a previous paper. As a result, we derive some
convenient lower bounds on the $(d+1)^{th}$ positive eigenvalue depending on
the spectral gap of the dual Markov diffusion operator given by the
intertwining. To see the relevance of our approach, we apply our spectral
results in the case of perturbed product measures, freeing us from Helffer's
classical method based on uniform spectral estimates for the one-dimensional
conditional distributions.


  It was recently reported that there exists a population of "glitch
candidates" and "anti-glitch candidates" which are effectively small spin-ups
and spin-downs of a neutron star with magnitudes smaller than those seen in
typical glitches. The physical origin of these small events is not yet
understood. In this paper, we outline a model that can account for the changes
in spin, and crucially, is independently testable with gravitational wave
observations. In brief, the model posits that small spin-up/spin-down events
are caused by the excitation and decay of non-axisymmetric $f$-modes which
radiate angular momentum away in a burst-like way as gravitational waves. The
model takes the change in spin frequency as an input and outputs the initial
mode amplitude and the signal-to-noise ratio achievable from gravitational wave
detectors. We find that the model presented here will become falsifiable once
3rd generation gravitational wave detectors, like the Einstein Telescope and
Cosmic Explorer, begin taking data.


  We present a complete and consistent quantum theory of generalised X waves
with orbital angular momentum (OAM) in dispersive media. We show that the
resulting quantised light pulses are affected by neither dispersion nor
diffraction and are therefore resilient against external perturbations. The
nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear
media is also presented and studied in detail.


  In this letter, we introduce two hybrid transmission schemes combining a
passive reconfigurable intelligent surface (RIS) with decode-and-forward
relaying in a synergistic manner. The proposed schemes offer a flexible as well
as cost- and power-efficient solution for coverage extension in future
generation wireless networks. We present closed-form expressions for the
end-to-end signal-to-noise ratio of both schemes and a sequential optimization
algorithm for the power allocation and the RIS phase configurations. Our
computer simulations and theoretical analysis demonstrate that the RIS and
relaying technologies enhance the achievable rate and error performance
remarkably when working complementary to each other, rather than being
considered as competing technologies.


  We present BIMA two-field mosaic CO(1-0) images of the Taffy galaxies (UGC
12914/15), which show the distinct taffy-like radio continuum emission bridging
the two spiral disks. Large amounts of molecular gas (1.4 x 10^{10} Msun, using
the standard Galactic CO-to-H$_2$ conversion applicable to Galactic disk giant
molecular clouds [GMCs]) were clearly detected throughout the taffy bridge
between the two galaxies, which, as in the more extreme case of HI, presumably
results from a head-on collision between the two galaxies. The highest CO
concentration between the two galaxies corresponds to the H_alpha source in the
taffy bridge near the intruder galaxy UGC 12915. This HII region is also
associated with the strongest source of radio continuum in the bridge, and
shows both morphological and kinematic connections to UGC 12915. The overall CO
distribution of the entire system agrees well with that of the radio continuum
emission, particularly in the taffy bridge. This argues for the star formation
origin of a significant portion of the radio continuum emission. Compared to
the HI morphology and kinematics, which are strongly distorted owing to the
high-speed collision, CO better defines the orbital geometry and impact
parameter of the interaction, as well as the disk properties (e.g., rotation,
orientation) of the progenitor galaxies. Based on the 20cm-to-CO ratio maps, we
conclude that the starburst sites are primarily located in UGC 12915 and the
H_alpha source in the bridge and show that the molecular gas in the taffy
bridge is forming into stars with star formation efficiency comparable to that
of the target galaxy UGC 12914 and similar to that in the Galactic disk.


  The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was
based on an inverse-free algorithm to compute the regularized pseudo-inverse,
which was deduced from an inverse-free recursive algorithm to update the
inverse of a Hermitian matrix. Before that recursive algorithm was applied in
[4], its improved version had been utilized in previous literatures [9], [10].
Accordingly from the improved recursive algorithm [9], [10], several efficient
inverse-free algorithms for ELM were proposed in [13] to reduce the
computational complexity. In this paper, we propose two inverse-free algorithms
for ELM with Tikhonov regularization, which can increase multiple hidden nodes
in an iteration. On the other hand, we also propose two efficient decremental
learning algorithms for ELM with Tikhonov regularization, which can remove
multiple redundant nodes in an iteration.


  Using the initial-value formulation, a dynamic theory for systems evolving
according to a Generalized Langevin Equation is developed, providing more
restrictive conditions on the existence of equilibrium behavior and its
fluctuation-dissipation implications. For systems fulfilling the property of
local realizability,
  that for all the practical purposes corresponds to the postulate of the
existence of a Markovian embedding, physical constraints, expressed in the form
of dissipative stability and stochastic realizability are derived. If these two
properties are met, Kubo theory is constructively recovered, while if one of
these conditions is violated a thermodynamic equilibrium behavior does not
exist (and this occurs also for `` well-behaved dissipative systems'' according
to the classical Kubo theory), with significant implications in the linear
response theory.


  We present InstantStyleGaussian, an innovative 3D style transfer method based
on the 3D Gaussian Splatting (3DGS) scene representation. By inputting a target
style image, it quickly generates new 3D GS scenes. Our approach operates on
pre-reconstructed GS scenes, combining diffusion models with an improved
iterative dataset update strategy. It utilizes diffusion models to generate
target style images, adds these new images to the training dataset, and uses
this dataset to iteratively update and optimize the GS scenes. Extensive
experimental results demonstrate that our method ensures high-quality stylized
scenes while offering significant advantages in style transfer speed and
consistency.


  The probability simplex is the set of all probability distributions on a
finite set and is the most fundamental object in the finite probability theory.
In this paper we give a characterization of statistical models on finite sets
which are statistically equivalent to probability simplexes in terms of
$\alpha$-families including exponential families and mixture families. The
subject has a close relation to some fundamental aspects of information
geometry such as $\alpha$-connections and autoparallelity.


  We describe a framework in which is possible to develop and implement
algorithms for the approximation of invariant measures of dynamical systems
with a given bound on the error of the approximation.
  Our approach is based on a general statement on the approximation of fixed
points for operators between normed vector spaces, allowing an explicit
estimation of the error.
  We show the flexibility of our approach by applying it to piecewise expanding
maps and to maps with indifferent fixed points. We show how the required
estimations can be implemented to compute invariant densities up to a given
error in the $L^{1}$ or $L^\infty $ distance. We also show how to use this to
compute an estimation with certified error for the entropy of those systems.
  We show how several related computational and numerical issues can be solved
to obtain working implementations, and experimental results on some one
dimensional maps.


  We imagine that large neutrino telescopes will be built and that distant
neutrino sources of high energies and fluxes exist. Some possible, if
difficult, uses to which they might be put are described; including (i)
detecting neutrino mass-mixing possibly upto delta m^2 of 10^{-16}eV^2; (ii)
measuring neutrino cross-sections at PeV energies; (iii) detecting relic
neutrinos; (iv) doing cosmology with neutrinos and (v) SETI with neutrinos.


  Many reduced order models are neither robust with respect to the parameter
changes nor cost-effective enough for handling the nonlinear dependence of
complex dynamical systems. In this study, we put forth a robust machine
learning framework for projection based reduced order modeling of such
nonlinear and nonstationary systems. As a demonstration, we focus on a
nonlinear advection-diffusion system given by the viscous Burgers equation,
which is a prototype setting of more realistic fluid dynamics applications with
the same quadratic nonlinearity. In our proposed methodology the effects of
truncated modes are modeled using a singe layer feed-forward neural network
architecture. The neural network architecture is trained by utilizing both the
Bayesian regularization and extreme learning machine approaches, where the
latter one is found to be computationally more efficient. A particular effort
is devoted to the selection of basis functions considering the proper
orthogonal decomposition and Fourier bases. It is shown that the proposed
models yield significant improvements in the accuracy over the standard
Galerkin projection models with a negligibly small computational overhead and
provide reliable predictions with respect to the parameter changes.


  Ratio control for two interacting processes is proposed with a PID
feedforward design based on model predictive control (MPC) scheme. At each
sampling instant, the MPC control action minimizes a state-dependent
performance index associated with a PID-type state vector, thus yielding a
PID-type control structure. Compared to the standard MPC formulations with
separated single-variable control, such a control action allows one to take
into account the non-uniformity of the two process outputs. After reformulating
the MPC control law as a PID control law, we provide conditions for prediction
horizon and weighting matrices so that the closed-loop control is
asymptotically stable, and show the effectiveness of the approach with
simulation and experiment results.


  Many questions in Data Science are fundamentally causal in that our objective
is to learn the effect of some exposure, randomized or not, on an outcome
interest. Even studies that are seemingly non-causal, such as those with the
goal of prediction or prevalence estimation, have causal elements, including
differential censoring or measurement. As a result, we, as Data Scientists,
need to consider the underlying causal mechanisms that gave rise to the data,
rather than simply the pattern or association observed in those data. In this
work, we review the 'Causal Roadmap' of Petersen and van der Laan (2014) to
provide an introduction to some key concepts in causal inference. Similar to
other causal frameworks, the steps of the Roadmap include clearly stating the
scientific question, defining of the causal model, translating the scientific
question into a causal parameter, assessing the assumptions needed to express
the causal parameter as a statistical estimand, implementation of statistical
estimators including parametric and semi-parametric methods, and interpretation
of our findings. We believe that using such a framework in Data Science will
help to ensure that our statistical analyses are guided by the scientific
question driving our research, while avoiding over-interpreting our results. We
focus on the effect of an exposure occurring at a single time point and
highlight the use of targeted maximum likelihood estimation (TMLE) with Super
Learner.


  Understanding and explaining the mistakes made by trained models is critical
to many machine learning objectives, such as improving robustness, addressing
concept drift, and mitigating biases. However, this is often an ad hoc process
that involves manually looking at the model's mistakes on many test samples and
guessing at the underlying reasons for those incorrect predictions. In this
paper, we propose a systematic approach, conceptual counterfactual explanations
(CCE), that explains why a classifier makes a mistake on a particular test
sample(s) in terms of human-understandable concepts (e.g. this zebra is
misclassified as a dog because of faint stripes). We base CCE on two prior
ideas: counterfactual explanations and concept activation vectors, and validate
our approach on well-known pretrained models, showing that it explains the
models' mistakes meaningfully. In addition, for new models trained on data with
spurious correlations, CCE accurately identifies the spurious correlation as
the cause of model mistakes from a single misclassified test sample. On two
challenging medical applications, CCE generated useful insights, confirmed by
clinicians, into biases and mistakes the model makes in real-world settings.


  An Equation of State (\textit{EoS}) closes the set of fluid equations.
Although an ideal EoS with a constant \textit{adiabatic index} $\Gamma$ is the
preferred choice due to its simplistic implementation, many astrophysical fluid
simulations may benefit from a more sophisticated treatment that can account
for diverse chemical processes. Here, we first review the basic thermodynamic
principles of a gas mixture in terms of its thermal and caloric EoS by
including effects like ionization, dissociation as well as temperature
dependent degrees of freedom such as molecular vibrations and rotations. The
formulation is revisited in the context of plasmas that are either in
equilibrium conditions (local thermodynamic- or collisional excitation-
equilibria) or described by non-equilibrium chemistry coupled to optically thin
radiative cooling. We then present a numerical implementation of thermally
ideal gases obeying a more general caloric EoS with non-constant adiabatic
index in Godunov-type numerical schemes.We discuss the necessary modifications
to the Riemann solver and to the conversion between total energy and pressure
(or vice-versa) routinely invoked in Godunov-type schemes. We then present two
different approaches for computing the EoS.The first one employs root-finder
methods and it is best suited for EoS in analytical form. The second one leans
on lookup table and interpolation and results in a more computationally
efficient approach although care must be taken to ensure thermodynamic
consistency. A number of selected benchmarks demonstrate that the employment of
a non-ideal EoS can lead to important differences in the solution when the
temperature range is $500-10^4$ K where dissociation and ionization occur. The
implementation of selected EoS introduces additional computational costs
although using lookup table methods can significantly reduce the overhead by a
factor $3\sim 4$.


  A pair of giant gamma-ray bubbles have been revealed by the {\it Fermi} LAT.
In this paper we investigate their formation mechanism. Observations have
indicated that the activity of the supermassive black hole located at the
Galactic center, Sgr A*, was much stronger than the present time. Specifically,
one possibility is that while Sgr A* was also in the hot accretion regime, the
accretion rate should be $10^3-10^4$ times higher during the past $\sim 10^7$
yr. On the other hand, recent MHD numerical simulations of hot accretion flows
have unambiguously shown the existence of strong winds and obtained their
properties. Based on these knowledge, by performing three-dimensional
hydrodynamical simulations, we show in this paper that the Fermi bubbles could
be inflated by winds launched from the ``past' hot accretion flow in Sgr A*. In
our model, the active phase of Sgr A* is required to last for about 10 million
years and it was quenched no more than 0.2 million years ago. The Central
Molecular Zone (CMZ) is included and it collimates the wind orientation towards
the Galactic poles. Viscosity suppresses the Rayleigh-Taylor and
Kelvin-Helmholtz instabilities and results in the smoothness of the bubble
edge. The main observational features of the bubbles can be well explained.
Specifically, the {\it ROSAT} X-ray features are interpreted by the shocked
interstellar medium and the interaction region between winds and CMZ gas. The
thermal pressure and temperature obtained in our model are in good consistency
with the recent {\it Suzaku} observations.


  We consider stochastically modeled chemical reaction systems with mass-action
kinetics and prove that a product-form stationary distribution exists for each
closed, irreducible subset of the state space if an analogous deterministically
modeled system with mass-action kinetics admits a complex balanced equilibrium.
Feinberg's deficiency zero theorem then implies that such a distribution exists
so long as the corresponding chemical network is weakly reversible and has a
deficiency of zero. The main parameter of the stationary distribution for the
stochastically modeled system is a complex balanced equilibrium value for the
corresponding deterministically modeled system. We also generalize our main
result to some non-mass-action kinetics.


  Dusty Star-Forming Galaxies (DSFGs) are amongst the most massive and active
star-forming galaxies during the cosmic noon. Theoretical studies have proposed
various formation mechanisms of DSFGs, including major merger-driven starbursts
and secular star-forming disks. Here, we report J0107a, a bright ($\sim8$ mJy
at observed-frame 888 $\mu$m) DSFG at $z=2.467$ that appears to be a gas-rich
massive disk and might be an extreme case of the secular disk scenario. J0107a
has a stellar mass $M_\star\sim5\times10^{11}M_\odot$, molecular gas mass
$M_\mathrm{mol}\sim(1\textendash6)\times10^{11}M_\odot$, and a star formation
rate (SFR) of $\sim500M_\odot$ yr$^{-1}$. J0107a does not have a gas-rich
companion. The rest-frame 1.28 $\mu$m JWST NIRCam image of J0107a shows a
grand-design spiral with a prominent stellar bar extending $\sim15$ kpc. ALMA
band 7 continuum map reveals that the dust emission originates from both the
central starburst and the stellar bar. 3D disk modeling of the CO(4-3) emission
line indicates a dynamically cold disk with rotation-to-dispersion ratio
$V_\mathrm{max}/\sigma\sim8$. The results suggest a bright DSFG may have a
non-merger origin, and its vigorous star formation may be triggered by bar
and/or rapid gas inflow.


  We introduce fusion bialgebras and their duals and systematically study their
Fourier analysis. As an application, we discover new efficient analytic
obstructions on the unitary categorification of fusion rings. We prove the
Hausdorff-Young inequality, uncertainty principles for fusion bialgebras and
their duals. We show that the Schur product property, Young's inequality and
the sum-set estimate hold for fusion bialgebras, but not always on their duals.
If the fusion ring is the Grothendieck ring of a unitary fusion category, then
these inequalities hold on the duals. Therefore, these inequalities are
analytic obstructions of categorification. We classify simple integral fusion
rings of Frobenius type up to rank 8 and of Frobenius-Perron dimension less
than 4080. We find 34 ones, 4 of which are group-like and 28 of which can be
eliminated by applying the Schur product property on the dual. In general,
these inequalities are obstructions to subfactorize fusion bialgebras.


  We consider quantum integrable models solvable by the algebraic Bethe ansatz
and possessing $\mathfrak{gl}(2)$-invariant $R$-matrix. We study the models of
both periodic boundary conditions and boundary conditions based on reflection
algebra. We present a new method to calculate the scalar products based on
formula of an action of transfer matrix of a model onto Bethe vector. Using
this method we identify some coefficient in the multiple action of the transfer
matrix with the scalar product between on-shell and off-shell Bethe vectors.
This allows us to find determinant representation of the scalar products in
both types of boundary conditions.


  Decreasing thermal conductivity of a thermoelectric material is always a
prerequisite for its potential application. Using first-principle calculations,
we examine the magnetism induced change in lattice thermal transport in bismuth
telluride. The source of magnetic moment, Cr in the doped system, weakly
magnetizes the coordinated Te atoms to make the latter's phonon softer than
that in the pure compound. Though the transition metal dopants do not
participate directly in the heat conduction process, the anharmonicity induced
by them favor in reducing the lattice thermal conductivity. Large anharmonicity
in $(Bi_{0.67}Cr_{0.33})_2Te_3$ reduces the in-plane room temperature lattice
thermal conductivity by $\sim 79\%$. The thermal conductivity, strictly, does
not vary monotonically with doping concentration. Even, for any particular
doping level, the thermal conductivity is different for different
configurations which is related to the internal energy of the system. We found
that the internal energy variance of 0.03 $eV$ would reduce the in-plane
thermal conductivity of the room temperature lattice by at least 60$\%$ for
50$\%$ doping.


  Active learning is a learning strategy whereby the machine learning algorithm
actively identifies and labels data points to optimize its learning. This
strategy is particularly effective in domains where an abundance of unlabeled
data exists, but the cost of labeling these data points is prohibitively
expensive. In this paper, we consider cases of binary classification, where
acquiring a positive instance incurs a significantly higher cost compared to
that of negative instances. For example, in the financial industry, such as in
money-lending businesses, a defaulted loan constitutes a positive event leading
to substantial financial loss. To address this issue, we propose a shifted
normal distribution sampling function that samples from a wider range than
typical uncertainty sampling. Our simulation underscores that our proposed
sampling function limits both noisy and positive label selection, delivering
between 20% and 32% improved cost efficiency over different test datasets.


  The field theoretic renormalization group is applied to Kraichnan's model of
a passive scalar quantity advected by the Gaussian velocity field with the pair
correlation function $\propto\delta(t-t')/k^{d+\epsilon}$. Inertial-range
anomalous scaling for the structure functions and various pair correlators is
established as a consequence of the existence in the corresponding operator
product expansions of ``dangerous'' composite operators (powers of the local
dissipation rate), whose {\it negative} critical dimensions determine anomalous
exponents. The latter are calculated to order $\epsilon^3$ of the $\epsilon$
expansion (three-loop approximation).


  Search query classification, as an effective way to understand user intents,
is of great importance in real-world online ads systems. To ensure a lower
latency, a shallow model (e.g. FastText) is widely used for efficient online
inference. However, the representation ability of the FastText model is
insufficient, resulting in poor classification performance, especially on some
low-frequency queries and tailed categories. Using a deeper and more complex
model (e.g. BERT) is an effective solution, but it will cause a higher online
inference latency and more expensive computing costs. Thus, how to juggle both
inference efficiency and classification performance is obviously of great
practical importance. To overcome this challenge, in this paper, we propose
knowledge condensation (KC), a simple yet effective knowledge distillation
framework to boost the classification performance of the online FastText model
under strict low latency constraints. Specifically, we propose to train an
offline BERT model to retrieve more potentially relevant data. Benefiting from
its powerful semantic representation, more relevant labels not exposed in the
historical data will be added into the training set for better FastText model
training. Moreover, a novel distribution-diverse multi-expert learning strategy
is proposed to further improve the mining ability of relevant data. By training
multiple BERT models from different data distributions, it can respectively
perform better at high, middle, and low-frequency search queries. The model
ensemble from multi-distribution makes its retrieval ability more powerful. We
have deployed two versions of this framework in JD search, and both offline
experiments and online A/B testing from multiple datasets have validated the
effectiveness of the proposed approach.


  We introduce a class of Banach algebras that we call anti-C*-algebras. We
show that the normed standard embedding of a C*-ternary ring is the direct sum
of a C*-algebra and an anti-C*-algebra. We prove that C*-ternary rings and
anti-C*-algebras are semisimple. We give two new characterizations of
C*-ternary rings which are isomorphic to a TRO (ternary ring of operators),
providing answers to a query raised by Zettl in 1983, and we propose some
problems for further study.


  Despite the rapid progress of end-to-end (E2E) automatic speech recognition
(ASR), it has been shown that incorporating external language models (LMs) into
the decoding can further improve the recognition performance of E2E ASR
systems. To align with the modeling units adopted in E2E ASR systems,
subword-level (e.g., characters, BPE) LMs are usually used to cooperate with
current E2E ASR systems. However, the use of subword-level LMs will ignore the
word-level information, which may limit the strength of the external LMs in E2E
ASR. Although several methods have been proposed to incorporate word-level
external LMs in E2E ASR, these methods are mainly designed for languages with
clear word boundaries such as English and cannot be directly applied to
languages like Mandarin, in which each character sequence can have multiple
corresponding word sequences. To this end, we propose a novel decoding
algorithm where a word-level lattice is constructed on-the-fly to consider all
possible word sequences for each partial hypothesis. Then, the LM score of the
hypothesis is obtained by intersecting the generated lattice with an external
word N-gram LM. The proposed method is examined on both Attention-based
Encoder-Decoder (AED) and Neural Transducer (NT) frameworks. Experiments
suggest that our method consistently outperforms subword-level LMs, including
N-gram LM and neural network LM. We achieve state-of-the-art results on both
Aishell-1 (CER 4.18%) and Aishell-2 (CER 5.06%) datasets and reduce CER by
14.8% relatively on a 21K-hour Mandarin dataset.


  In this paper, we study the Ma-Trudinger-Wang (MTW) conditions for cost
functions $c$ which are of the form $c=l\circ d$, where $d$ is a Riemannian
distance function with constant sectional curvature. In this case, the MTW
conditions are equivalent to some computable conditions on the function $l$. As
a corollary, we give some new costs on Riemannian manifolds of constant
negative curvature for which the MTW conditions are satisfied.


  We consider smooth codimension two subcanonical subvarieties in
$\mathbb{P}^n$ with $n \geq 5$, lying on a hypersurface of degree $s$ having a
linear subspace of multiplicity $(s-2)$. We prove that such varieties are
complete intersections. We also give a little improvement to some earlier
results on the non existence of rank two vector bundles on $\mathbb{P}^4$ with
small Chern classes.


  In a recent experiment on the Trident laser facility, a laser-driven beam of
quasi-monoenergetic aluminum ions was used to heat solid gold and diamond foils
isochorically to 5.5 eV and 1.7 eV, respectively. Here theoretical calculations
are presented that suggest the gold and diamond were heated uniformly by these
laser-driven ion beams. According to calculations and SESAME equation-of-state
tables, laser-driven aluminum ion beams achievable on Trident, with a finite
energy spread of (delta E)/E ~ 20%, are expected to heat the targets more
uniformly than a beam of 140 MeV aluminum ions with zero energy spread. The
robustness of the expected heating uniformity relative to the changes in the
incident ion energy spectra is evaluated, and expected plasma temperatures of
various target materials achievable with the current experimental platform are
presented.


  This research proposes a machine learning-based attack detection model for
power systems, specifically targeting smart grids. By utilizing data and logs
collected from Phasor Measuring Devices (PMUs), the model aims to learn system
behaviors and effectively identify potential security boundaries. The proposed
approach involves crucial stages including dataset pre-processing, feature
selection, model creation, and evaluation. To validate our approach, we used a
dataset used, consist of 15 separate datasets obtained from different PMUs,
relay snort alarms and logs. Three machine learning models: Random Forest,
Logistic Regression, and K-Nearest Neighbour were built and evaluated using
various performance metrics. The findings indicate that the Random Forest model
achieves the highest performance with an accuracy of 90.56% in detecting power
system disturbances and has the potential in assisting operators in
decision-making processes.


  As Moore's Law continues to increase the complexity of electronic systems,
Electronic Design Automation (EDA) must advance to meet global demand. An
important example of an EDA technology is SKILL, a scripting language used to
customize and extend EDA software. Recently, code generation models using the
transformer architecture have achieved impressive results in academic settings
and have even been used in commercial developer tools to improve developer
productivity. To the best of our knowledge, this study is the first to apply
transformers to SKILL code autocompletion towards improving the productivity of
hardware design engineers. In this study, a novel, data-efficient methodology
for generating SKILL code is proposed and experimentally validated. More
specifically, we propose a novel methodology for (i) creating a high-quality
SKILL dataset with both unlabeled and labeled data, (ii) a training strategy
where T5 models pre-trained on general programming language code are fine-tuned
on our custom SKILL dataset using unsupervised and supervised learning, and
(iii) evaluating synthesized SKILL code. We show that models trained using the
proposed methodology outperform baselines in terms of human-judgment score and
BLEU score. A major challenge faced was the extremely small amount of available
SKILL code data that can be used to train a transformer model to generate SKILL
code. Despite our validated improvements, the extremely small dataset available
to us was still not enough to train a model that can reliably autocomplete
SKILL code. We discuss this and other limitations as well as future work that
could address these limitations.


  The nucleus 49Cr has been studied analysing gamma-gamma coincidences in the
reaction 46Ti(alpha,n)49Cr at the bombarding energy of 12 MeV. The level scheme
has been greatly extended at low excitation energy and several new lifetimes
have been determined by means of the Doppler Shift Attenuation Method.
  Shell model calculations in the full pf configuration space reproduce well
negative-parity levels. Satisfactory agreement is obtained for positive parity
levels by extending the configuration space to include a nucleon-hole either in
the 1d3/2 or in the 2s1/2 orbitals.
  A nearly one-to-one correspondence is found between experimental and
theoretical levels up to an excitation energy of 4 MeV.
  Experimental data and shell model calculations are interpreted in terms of
the Nilsson diagram and the particle-rotor model, showing the strongly coupled
nature of the bands in this prolate nucleus. Nine values of K(pi) are proposed
for the levels observed in this experiment.
  As a by-result it is shown that the values of the experimental magnetic
moments in 1f7/2 nuclei are well reproduced without quenching the nucleon
g-factors.


  We derive bounds from oblique parameters on the dimension-6 operators of an
effective field theory of electroweak gauge bosons and the Higgs doublet. The
loop- induced contributions to the S, T, and U oblique parameters are sensitive
to these contributions and we pay particular attention to the role of
renormalization when computing loop corrections in the effective theory. Limits
on the coefficients of the effective theory from loop contributions to oblique
parameters yield complementary information to direct Higgs production
measurements.


  We develop monitoring procedures for cointegrating regressions, testing the
null of no breaks against the alternatives that there is either a change in the
slope, or a change to non-cointegration. After observing the regression for a
calibration sample m, we study a CUSUM-type statistic to detect the presence of
change during a monitoring horizon m+1,...,T. Our procedures use a class of
boundary functions which depend on a parameter whose value affects the delay in
detecting the possible break. Technically, these procedures are based on almost
sure limiting theorems whose derivation is not straightforward. We therefore
define a monitoring function which - at every point in time - diverges to
infinity under the null, and drifts to zero under alternatives. We cast this
sequence in a randomised procedure to construct an i.i.d. sequence, which we
then employ to define the detector function. Our monitoring procedure rejects
the null of no break (when correct) with a small probability, whilst it rejects
with probability one over the monitoring horizon in the presence of breaks.


  We show how the quantum trace map of Bonahon and Wong can be constructed in a
natural way using the skein algebra of Muller, which is an extension of the
Kauffman bracket skein algebra of surfaces. We also show that the quantum
Teichm\"uller space of a marked surface, defined by Chekhov-Fock (and Kashaev)
in an abstract way, can be realized as a concrete subalgebra of the skew field
of the skein algebra.


  Accretion disk outbursts, and their subsequent decline, offer a unique
opportunity to constrain the physics of angular momentum transport in hot
accretion disks. Recent work has centered on the claim by Cannizzo et al. that
the exponential decay of luminosity following an outburst in black hole
accretion disk systems is only consistent with a particular form for the
dimensionless viscosity, $\alpha=35(c_s/r\Omega)^{3/2}$. This result can be
understood in terms of a simple model of the evolution of cooling fronts in
accretion disks. In particular, the cooling front speed during decline is $\sim
\alpha_F c_{s,F}(c_{s,F}/r\Omega)^{n}$, where $F$ denotes the position of the
cooling front, and the exact value of $n$ depends on the hot state opacity,
(although generally $n\approx 1/2$). Setting this speed proportional to $r$
constrains the functional form of $\alpha$ in the hot phase of the disk, which
sets it apart from previous arguments based on the relative durations of
outburst and quiescence. However, it remains uncertain how well we know the
exponent $n$. In addition, more work is needed to clarify the role of
irradiation in these systems and its effect on the cooling front evolution.


  We propose a method for learning embeddings for few-shot learning that is
suitable for use with any number of ways and any number of shots (shot-free).
Rather than fixing the class prototypes to be the Euclidean average of sample
embeddings, we allow them to live in a higher-dimensional space (embedded class
models) and learn the prototypes along with the model parameters. The class
representation function is defined implicitly, which allows us to deal with a
variable number of shots per each class with a simple constant-size
architecture. The class embedding encompasses metric learning, that facilitates
adding new classes without crowding the class representation space. Despite
being general and not tuned to the benchmark, our approach achieves
state-of-the-art performance on the standard few-shot benchmark datasets.


  This short note gives an overview of how a few conjectures and theorems of
the author and collaborators fit together. It was prepared for Oberwolfach's
workshop Differentialgeometrie im Gro{\ss}en, 28 June - 4 July 2015, and
contains no new results.


  We prove that a subshift $(X,T)$ is linearly recurrent if and only if it is a
primitive and proper $S$-adic subshift. This corrects Proposition 6 in F.
Durand ({\it Ergod. Th. & Dynam. Sys. {\bf 20}} (2000), 1061--1078).


  We report on a lattice QCD calculation of the flavor-singlet axial coupling
constant $g_A$ of the proton from the axial-vector current. The simulation is
carried out at $\beta = 6$ on a quenched $16^3 \times 24$ lattice. An
extrapolation to the chiral limit shows that the connected insertion (valence
and cloud parts) is $0.62 \pm 0.09$, which is close to $g_A^8$. The
disconnected insertion (vacuum polarization from the sea quark) for the $u$ or
$d$ quark is $- 0.12\pm 0.01 $ and the $s$ quark also contributes $-0.12\pm
0.01$. The total $g_A^1$ is thus $0.25 \pm 0.12$ which is in agreement with
experiments. In addition, we find $g_A^3 = 1.20 \pm 0.11$, $g_A^8 = 0.61 \pm
0.13$ and $F_A/D_A = 0.60 \pm 0.02$, also in agreement with experiments.


  Automotive-Industry 5.0 will use beyond fifth-generation (B5G) technologies
to provide robust, computationally intelligent, and energy-efficient data
sharing among various onboard sensors, vehicles, and other devices. Recently,
ambient backscatter communications (AmBC) have gained significant interest in
the research community for providing battery-free communications. AmBC can
modulate useful data and reflect it towards near devices using the energy and
frequency of existing RF signals. However, obtaining channel state information
(CSI) for AmBC systems would be very challenging due to no pilot sequences and
limited power. As one of the latest members of multiple access technology,
non-orthogonal multiple access (NOMA) has emerged as a promising solution for
connecting large-scale devices over the same spectral resources in B5G wireless
networks. Under imperfect CSI, this paper provides a new optimization framework
for energy-efficient transmission in AmBC enhanced NOMA cooperative
vehicle-to-everything (V2X) networks. We simultaneously minimize the total
transmit power of the V2X network by optimizing the power allocation at BS and
reflection coefficient at backscatter sensors while guaranteeing the individual
quality of services. The problem of total power minimization is formulated as
non-convex optimization and coupled on multiple variables, making it complex
and challenging. Therefore, we first decouple the original problem into two
sub-problems and convert the nonlinear rate constraints into linear
constraints. Then, we adopt the iterative sub-gradient method to obtain an
efficient solution. For comparison, we also present a conventional NOMA
cooperative V2X network without AmBC. Simulation results show the benefits of
our proposed AmBC enhanced NOMA cooperative V2X network in terms of total
achievable energy efficiency.


  This paper is devoted to the study of large time bounds for the Sobolev norms
of the solutions of the following fractional cubic Schr{\"o}dinger equation on
the torus :$$i \partial\_t u = |D|^\alpha u+|u|^2 u, \quad u(0,
\cdot)=u\_0,$$where $\alpha$ is a real parameter. We show that, apart from the
case $\alpha = 1$, which corresponds to a half-wave equation with no dispersive
property at all, solutions of this equation grow at a polynomial rate at most.
We also address the case of the cubic and quadratic half-wave equations.


  A reliable estimate of the molecular gas content in galaxies plays a crucial
role in determining their dynamical and star-forming properties. However, H2,
the dominant molecular species, is difficult to observe directly, particularly
in the regions where most molecular gas is thought to reside. Its mass is
therefore commonly inferred by assuming a direct proportionality with the
integrated intensity of the CO(J=1-0) emission line, using a CO-to-H2
conversion factor, X. Although a canonical value for X is used extensively in
such estimates, there is increasing evidence, both theoretical and
observational, that the conversion factor may vary by over an order of
magnitude under conditions different to those of the local neighbourhood. In an
effort to understand the influence of changing environmental conditions on the
conversion factor, we derive theoretical estimates of X for a wide range of
physical parameters using a photon-dominated region (PDR) time-dependent
chemical model, benchmarking key results against those of an independent PDR
code to ensure reliability. Based on these results, the sensitivity of the X
factor to change in each physical parameter is interpreted in terms of the
chemistry and physical processes within the cloud. In addition to confirming
previous observationally derived trends, we find that the time-dependence of
the chemistry, often neglected in such models, has a considerable influence on
the value of the conversion factor.


  Using a sensitive DC torque magnetometer we measure the orbital magnetization
by sweeping the density at fixed magnetic fields on GaAs-AlGaAs
heterostructures. At low temperatures strong nonequilibrium magnetization
signals dominate the data. In literature the observation of nonequilibrium
signals are often associated with eddy currents generated by sweeping the
magnetic field. The elimination of a changing magnetic field then poses a
question regarding the origin of these signals. Our data suggests another
source of nonequilibrium magnetization potentially due to the change of area
occupied by compressible and incompressible states as one sweeps the Fermi
energy from one Landau level to the next.


  A disk wind can cause perturbations that propagate throughout the disk via
diffusive processes. On reaching the inner disk, these perturbations can change
the disk luminosity, which in turn, can change the wind mass loss rate,
$\dot{M}_w$. It has been argued that this so-called "wind driven relaxation
cycle" might explain the observed variability in some disk accreting objects.
Here, we study the response of the innermost mass accretion rate $\dot{M}_a$ to
the loss of matter at different rates and radii. We allow the wind launching
radius, $R_L$, to scale with $\dot{M}_a$. We computed a grid of time-dependent
models for various $\dot{M}_w$-$\dot{M}_a$ and $R_{L}$-$\dot{M}_a$
dependencies. We find that the disk behaviour significantly differs for the
'variable $R_L$' case compared to the 'fixed $R_L$' case. In particular, much
stronger winds are required to destabilize the disk in the former than the
latter case. However, the $\dot{M}_a$ amplitude does not grow significantly
even for unstable cases because the oscillations saturate at a low level either
due to disk depletion or due to the wind being launched at very small radii, or
both. This result implies that disk winds are unlikely to be responsible for
state transitions as those require large changes in the inner disk. Despite
modest changes at the inner disk regions, the disk surface density at large
radii can vary with a large amplitude, i.e., from 0 to a few factors of the
steady state value. This dramatic variation of the outer disk could have
observable consequences.


  In the presence of an electric dipole coupling of the top quark to a photon,
and an analogous "weak" dipole coupling to the Z, CP violation in the process
e+e- -> t tbar leads to the polarization of the top and anti-top. This
polarization can be analyzed by studying the angular distributions of decay
charged leptons when the top or anti-top decays leptonically. We have obtained
analytic expressions for these distributions when either t or tbar decays
leptonically, including O(alpha_s) QCD corrections in the soft-gluon
approximation. The angular distributions are insensitive to anomalous
interactions in top decay. We study two types of simple CP-violating
polar-angle asymmetries and two azimuthal asymmetries which do not need the
full reconstruction of the t or tbar. We have evaluated independent 90% CL
limits that may be obtained on the real and imaginary parts of the electric and
weak dipole couplings at a linear collider operating at centre-of-mass energy
500 GeV with integrated luminosity 200 inverse fb and also at 1000 GeV with
integrated luminosity 1000 inverse fb. The effect of longitudinal beam
polarization has been included.


  We establish a more precise description of those surjective or bijective
continuous linear operators preserving orthogonality between C$^*$-algebras.
The new description is applied to determine all uniformly continuous
one-parameter semigroups of orthogonality preserving operators on an arbitrary
C$^*$-algebra. We prove that given a family $\{T_t: t\in \mathbb{R}_0^{+}\}$ of
orthogonality preserving bounded linear bijections on a general C$^*$-algebra
$A$ with $T_0=Id$, if for each $t\geq 0,$ we set $h_t = T_t^{**} (1)$ and we
write $r_t$ for the range partial isometry of $h_t$ in $A^{**},$ and $S_t$
stands for the triple isomorphism on $A$ associated with $T_t$ satisfying
$h_t^* S_t(x)$ $= S_t(x^*)^* h_t$, $h_t S_t(x^*)^* =$ $ S_t(x) h_t^*$, $h_t
r_t^* S_t(x) =$ $S_t(x) r_t^* h_t$, and $T_t(x) = h_t r_t^* S_t(x) = S_t(x)
r_t^* h_t, \hbox{ for all } x\in A,$ the following statements are equivalent:
  $(a)$ $\{T_t: t\in \mathbb{R}_0^{+}\}$ is a uniformly continuous
one-parameter semigroup of orthogonality preserving operators on $A$;
  $(b)$ $\{S_t: t\in \mathbb{R}_0^{+}\}$ is a uniformly continuous
one-parameter semigroup of surjective linear isometries (i.e. triple
isomorphisms) on $A$ (and hence there exists a triple derivation $\delta$ on
$A$ such that $S_t = e^{t \delta}$ for all $t\in \mathbb{R}$), the mapping
$t\mapsto h_t $ is continuous at zero, and the identity $ h_{t+s} = h_t r_t^*
S_t^{**} (h_s),$ holds for all $s,t\in \mathbb{R}.$


  In this paper we prove that, for any $n\ge 3$, there exist infinitely many
$r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such
that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme
$\hilb(\P^r)$. This is proven by reducing the problem to an analogous statement
for the moduli of surfaces of general type.


  In the paper a generalization of the (1+1)-dimensional model by Chodos et al
[Phys. Rev. D61, 045011 (2000)] has been performed to the case of
(2+1)-dimensional spacetime. The model includes four-fermion interaction both
in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting)
channels. We study temperature $T$ and chemical potential $\mu$ induced phase
transitions in the leading order of large-$N$ expansion technique, where $N$ is
a number of fermion fields. It is shown that at sufficiently large values of
$\mu$ and arbitrary relations between coupling constants, superconducting phase
appears in the system both at T=0 and $T>0$. In particular, at T=0 and
sufficiently weak attractive interaction in the chiral channel, the Cooper
pairing occurs for arbitrary couplings in the superconducting channel even at
infinitesimal values of $\mu$.


  At asymptotically late times ultrametricity can emerge from the persistent
slow aging dynamics of the glass phase. We show that this suffices to recover
the breaking of replica symmetry in mean-field spin glasses from the late time
limit of the time evolution using the Keldysh path integral. This provides an
alternative approach to replica symmetry breaking by connecting it rigorously
to the dynamic formulation. Stationary spin glasses are thereby understood to
spontaneously break thermal symmetry, or the Kubo-Martin-Schwinger relation of
a state in global thermal equilibrium. We demonstrate our general statements
for the spherical quantum $p$-spin model and the quantum
Sherrington-Kirkpatrick model in the presence of transverse and longitudinal
fields. In doing so, we also derive their dynamical Ginzburg-Landau effective
Keldysh actions starting from microscopic quantum models.


  We study a chain of alternating hot and cold electronic nanocavities --
connected to one another via resonant-tunneling quantum dots -- with the intent
of achieving precise thermal control across the chain. This is accomplished by
positioning the dots' energy levels such that a predetermined distribution of
heat currents is realized across the chain in the steady state. The number of
electrons in each cavity is conserved in the steady state which constrains the
cavities' chemical potentials. We determine these chemical potentials
analytically in the linear response regime where the energy differences between
the dots' resonant levels and the neighboring chemical potentials are much
smaller than the thermal energy. In this regime, the thermal control problem
can be solved exactly, while, in the general case, thermal control can only be
achieved in a relative sense, that is, when one only preassigns the ratios
between different heat currents. We apply our results to two different cases:
We first demonstrate that a "heat switch" can be easily realized with three
coupled cavities, then we show that our linear response results can provide
accurate results in situations with a large number of cavities.


  We have performed white-light reflectivity measurements on GaAs/AlAs
micropillar cavities with diameters ranging from 1 {\mu}m up to 20 {\mu}m. We
are able to resolve the spatial field distribution of each cavity mode in real
space by scanning a small-sized beam across the top facet of each micropillar.
We spectrally resolve distinct transverse optical cavity modes in reflectivity.
Using this procedure we can selectively address a single mode in the multimode
micropillar cavity. Calculations for the coupling efficiency of a
small-diameter beam to each mode are in very good agreement with our
reflectivity measurements.


  Large language models (LLMs) have gained significant attention in various
fields but prone to hallucination, especially in knowledge-intensive (KI)
tasks. To address this, retrieval-augmented generation (RAG) has emerged as a
popular solution to enhance factual accuracy. However, traditional retrieval
modules often rely on large document index and disconnect with generative
tasks. With the advent of generative retrieval (GR), language models can
retrieve by directly generating document identifiers (DocIDs), offering
superior performance in retrieval tasks. However, the potential relationship
between GR and downstream tasks remains unexplored. In this paper, we propose
\textbf{CorpusLM}, a unified language model that leverages external corpus to
tackle various knowledge-intensive tasks by integrating generative retrieval,
closed-book generation, and RAG through a unified greedy decoding process. We
design the following mechanisms to facilitate effective retrieval and
generation, and improve the end-to-end effectiveness of KI tasks: (1) We
develop a ranking-oriented DocID list generation strategy, which refines GR by
directly learning from a DocID ranking list, to improve retrieval quality. (2)
We design a continuous DocIDs-References-Answer generation strategy, which
facilitates effective and efficient RAG. (3) We employ well-designed
unsupervised DocID understanding tasks, to comprehend DocID semantics and their
relevance to downstream tasks. We evaluate our approach on the widely used KILT
benchmark with two variants of backbone models, i.e., T5 and Llama2.
Experimental results demonstrate the superior performance of our models in both
retrieval and downstream tasks.


  In this work, we study the geometric properties of spacelike foliations by
hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves
being stable, totally geodesic or totally umbilical. We consider that
$\overline{M}^{n+1}$ is equipped with a timelike closed conformal vector field
$\xi$. If the foliation has constant mean curvature, we show that the leaves
are stable. When the leaves are compact spacelike hypersurfaces we show that,
under certain conditions, its are totally umbilic hypersurfaces. In the case of
foliations by complete noncompact hypersurfaces, we using a Maximum Principle
at infinity to conclude that the foliation is totally geodesic.


  We consider here probabilistic models of transportation flows. The main goal
of this introduction is rather not to present various techniques for problem
solving but to present some intuition to invent adequate and natural models
having visual simplicity and simple (but rigorous) formulation, the main
objects being cars not abstract flows. The papers consists of three parts.
First part considers mainly linear flows on short time scale - dynamics of the
flow due to changing driver behavior. Second part studies linear flow on longer
time scales - individual car trajectory from entry to exit from the road. Part
three considers collective car movement in complex transport networks.


  Solar flares - which are the most prominent manifestation of the solar
activity - typically manifest themselves as a single or a set of luminous arcs
(magnetic flux tubes) rooted in regions of opposite polarity in the
photosphere. However, a careful analysis of the archival data by Hinode
satellite sometimes reveals surprising cases of flaring arcs whose footpoints
belong to regions of the same polarity or to areas without any appreciable
magnetic field. Despite the counterintuitive nature of this phenomenon, it can
be reasonably interpreted in the framework of the so-called 'topological model'
of magnetic reconnection, where a magnetic null point is formed due to specific
superposition of influences from remote sources rather than by local current
systems. As a result, the energy release propagates along a separator of the
flipping two-dome structure rather than along a fixed magnetic field line.
Therefore, the luminous arc needs not to be associated anymore immediately with
the magnetic sources. Here, we report both observational cases of the
above-mentioned type as well as provide their theoretical model and numerical
simulations.


  We study a special case at which the analytical solution of the
Lippmann-Schwinger integral equation for the partial wave two-body Coulomb
transition matrix for likely charged particles at negative energy is possible.
With the use of the Fock's method of the stereographic projection of the
momentum space onto the four-dimensional unit sphere, the analytical
expressions for s-, p- and d-wave partial Coulomb transition matrices for
repulsively interacting particles at bound-state energy have been derived.


  A comprehensive understanding of the physical origin of the unique magnetic
and transport properties of A_(1-x)A'^xMnO_3 manganites (A = trivalent
rare-earth and A' = divalent alkali-earth metal) is still far from being
achieved. The complexity of these systems arises from the interplay among
several competing interactions of comparable strength. Recently the
electron-phonon coupling, triggered by a Jahn-Teller distortion of the MnO_6
octahedra, has been recognised to play an essential role in the insulator to
metal transition and in the closely related colossal magneto-resistance. The
pressure tuning of the octahedral distortion gives a unique possibility to
separate the basic interactions and, at least in principle, to follow the
progressive transformation of a manganite from an intermediate towards a weak
electron-phonon coupling regime. Using a diamond anvil cell, temperature and
pressure-dependent infrared absorption spectra of La_(0.75)Ca_(0.25)MnO_3 have
been collected and, from the spectral weight analysis, the pressure dependence
of the insulator to metal transition temperature T_IM has been determined for
the first time up to 11.2 GPa. The T_IM(P) curve we proposed to model the
present data revealed a universality character in accounting for the whole
class of intermediate coupling compounds. This property can be exploited to
distinguish the intermediate from the weak coupling compounds pointing out the
fundamental differences between the two coupling regimes.


  We study the connections between the notions of combinatorial discrepancy and
graph degeneracy. In particular, we prove that the maximum discrepancy over all
subgraphs $H$ of a graph $G$ of the neighborhood set system of $H$ is
sandwiched between $\Omega(\log\mathrm{deg}(G))$ and
$\mathcal{O}(\mathrm{deg}(G))$, where $\mathrm{deg}(G)$ denotes the degeneracy
of $G$. We extend this result to inequalities relating weak coloring numbers
and discrepancy of graph powers and deduce a new characterization of bounded
expansion classes.
  Then, we switch to a model theoretical point of view, introduce pointer
structures, and study their relations to graph classes with bounded expansion.
We deduce that a monotone class of graphs has bounded expansion if and only if
all the set systems definable in this class have bounded hereditary
discrepancy.
  Using known bounds on the VC-density of set systems definable in nowhere
dense classes we also give a characterization of nowhere dense classes in terms
of discrepancy. As consequences of our results, we obtain a corollary on the
discrepancy of neighborhood set systems of edge colored graphs, a
polynomial-time algorithm to compute $\varepsilon$-approximations of size
$\mathcal{O}(1/\varepsilon)$ for set systems definable in bounded expansion
classes, an application to clique coloring, and even the non-existence of a
quantifier elimination scheme for nowhere dense classes.


  The vast majority of sampling systems operate in a standard way: at each tick
of a fixed-frequency master clock a digitizer reads out a voltage that
corresponds to the value of some physical quantity and translates it into a bit
pattern that is either transmitted, stored, or processed right away. Thus
signal sampling at evenly spaced time intervals is the rule: however this is
not always the case, and uneven sampling is sometimes unavoidable.
  While periodic or quasi-periodic uneven sampling of a deterministic signal
can reasonably be expected to produce artifacts, it is much less obvious that
the same happens with noise: here I show that this is indeed the case only for
long-memory noise processes, i.e., power-law noises $1/f^\alpha$ with $\alpha >
2$. The resulting artifacts are usually a nuisance although they can be
eliminated with a proper processing of the signal samples, but they could also
be turned to advantage and used to encode information.


  We analytically compute the thermoelectric conductivities at zero frequency
(DC) in the holographic dual of a four dimensional
Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically
hyperscaling violating Lifshitz backgrounds with a dynamical exponent $z$ and
hyperscaling violating parameter $\theta$. We show that the heat current in the
dual Lifshitz theory involves the energy flux, which is an irrelevant operator
for $z>1$. The linearized fluctuations relevant for computing the
thermoelectric conductivities turn on a source for this irrelevant operator,
leading to several novel and non-trivial aspects in the holographic
renormalization procedure and the identification of the physical observables in
the dual theory. Moreover, imposing Dirichlet or Neumann boundary conditions on
the spatial components of one of the two Maxwell fields present leads to
different thermoelectric conductivities. Dirichlet boundary conditions
reproduce the thermoelectric DC conductivities obtained from the near horizon
analysis of Donos and Gauntlett, while Neumann boundary conditions result in a
new set of DC conductivities. We make preliminary analytical estimates for the
temperature behavior of the thermoelectric matrix in appropriate regions of
parameter space. In particular, at large temperatures we find that the only
case which could lead to a linear resistivity $\rho \sim T$ corresponds to
$z=4/3$.


  In the quantum regime information can be copied with only a finite fidelity.
This fidelity gradually increases to 1 as the system becomes classical. In this
article we show how this fact can be used to directly measure the amount of
radiated power. We demonstrate how these principles could be used to build a
practical primary standard.


  The numerical renormalization group is employed to study a double quantum
(DQD) dot system consisting of two equivalent single-level dots, each coupled
to its own lead and with a mutual capacitive coupling embodied in an interdot
interaction U', in addition to the intradot Coulomb interaction U. We focus on
the regime with two electrons on the DQD, and the evolution of the system on
increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is
found to persist robustly with increasing U'/U, before a rapid but continuous
crossover to (a) the SU(4) point U'=U where charge and spin degrees of freedom
are entangled and the Kondo scale strongly enhanced; and then (b) a
charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the
leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless
type then occurs from this Fermi liquid, strong coupling (SC) phase, to a
broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c.
Our emphasis in this paper is on the structure, stability and flows between the
underlying RG fixed points, on the overall phase diagram in the (U,U')-plane
and evolution of the characteristic low-energy Kondo scale inherent to the SC
phase; and on static physical properties such as spin- and
charge-susceptibilities (staggered and uniform), including universality and
scaling behaviour in the strongly correlated regime. Some exact results for
associated Wilson ratios are also obtained.


  Today's mobile robots are expected to operate in complex environments they
share with humans. To allow intuitive human-robot collaboration, robots require
a human-like understanding of their surroundings in terms of semantically
classified instances. In this paper, we propose a new approach for deriving
such instance-based semantic maps purely from occupancy grids. We employ a
combination of deep learning techniques to detect, segment and extract door
hypotheses from a random-sized map. The extraction is followed by a
post-processing chain to further increase the accuracy of our approach, as well
as place categorization for the three classes room, door and corridor. All
detected and classified entities are described as instances specified in a
common coordinate system, while a topological map is derived to capture their
spatial links. To train our two neural networks used for detection and map
segmentation, we contribute a simulator that automatically creates and
annotates the required training data. We further provide insight into which
features are learned to detect doorways, and how the simulated training data
can be augmented to train networks for the direct application on real-world
grid maps. We evaluate our approach on several publicly available real-world
data sets. Even though the used networks are solely trained on simulated data,
our approach demonstrates high robustness and effectiveness in various
real-world indoor environments.


  We investigate the phase structure of an asymmetric fermion superfluid with
inter- and intra-species pairings. The introduction of the intra-species
pairing mechanism in canonical ensemble changes significantly the phase diagram
and brings in a new state with coexisting inter- and intra-species pairings.
Different from the case with only inter-species pairing, all the fermion
excitations are fully gapped in the region with intra-species pairing.


  Exceptional points are spectral degeneracies of non-Hermitian systems where
eigenvalues and eigenvectors coalesce, inducing unique topological phases that
have no counterpart in the Hermitian realm. Here we consider a non-Hermitian
system by coupling a two-dimensional semiconductor with Rashba spin-orbit
coupling to a ferromagnet lead and show the emergence of highly tunable
exceptional points along rings in momentum space. Interestingly, these
exceptional degeneracies are the endpoints of lines formed by the eigenvalue
coalescence at finite real energy, resembling the bulk Fermi arcs commonly
defined at zero real energy. We then show that an in-plane Zeeman field
provides a way to control these exceptional degeneracies although higher values
of non-Hermiticity are required in contrast to the zero Zeeman field regime.
Furthermore, we find that the spin projections also coalescence at the
exceptional degeneracies and can acquire larger values than in the Hermitian
regime. Finally, we demonstrate that the exceptional degeneracies induce large
spectral weights, which can be used as a signature for their detection. Our
results thus reveal the potential of systems with Rashba spin-orbit coupling
for realizing non-Hermitian bulk phenomena.


  Cavity QED is a versatile tool to explore small scale quantum information
processing. Within this setting, we describe a particular protocol for
implementing a Toffoli gate with Rydberg atoms and a cavity field. Our scheme
uses both resonant and non resonant interactions, and in particular a cavity
assisted atomic collision. The experimental feasibility of the protocol is
carefully analyzed with the help of numerical simulations and takes into
account the decoherence process. Moreover, we show that our protocol is optimal
within the constraints imposed by the experimental setting.


  The Permuted Kernel Problem (PKP) is a problem in linear algebra that was
first introduced by Shamir in 1989. Roughly speaking, given an $\ell \times m$
matrix $\mathbf{A}$ and an $m \times 1$ vector $\mathbf{b}$ over a finite field
of $q$ elements $\mathbb{F}_q$, the PKP asks to find an $m \times m$
permutation matrix $\mathbf{\pi}$ such that $\mathbf{\pi} \mathbf{b}$ belongs
to the kernel of $\mathbf{A}$. In recent years, several post-quantum digital
signature schemes whose security can be provably reduced to the hardness of
solving random instances of the PKP have been proposed. In this regard, it is
important to know the expected number of solutions to a random instance of the
PKP in terms of the parameters $q,\ell,m$. Previous works have heuristically
estimated the expected number of solutions to be $m! / q^\ell$.
  We provide, and rigorously prove, exact formulas for the expected number of
solutions to a random instance of the PKP and the related Inhomogeneous
Permuted Kernel Problem (IPKP), considering two natural ways of generating
random instances.


  When a metal undergoes a transition to an insulator it will lose its
electronic Fermi surface. Interestingly in some situations a `ghost' Fermi
surface of electrically neutral spin carrying fermions may survive into the
insulator. Such a novel ghost Fermi surface has been proposed to underlie the
properties of a few different materials but its direct detection has proven
elusive. In this paper we show that the ghost Fermi surface leads to slowly
decaying spatial oscillations of the electron density near impurities or other
defects. These and related oscillations stem from the sharpness of the ghost
Fermi surface and are direct analogs of the familiar Friedel oscillations in
metals. The oscillation period contains geometric information about the shape
of the ghost Fermi surface which can be potentially exploited to detect its
existence.


  What is the right way to reason about human activities? What directions
forward are most promising? In this work, we analyze the current state of human
activity understanding in videos. The goal of this paper is to examine
datasets, evaluation metrics, algorithms, and potential future directions. We
look at the qualitative attributes that define activities such as pose
variability, brevity, and density. The experiments consider multiple
state-of-the-art algorithms and multiple datasets. The results demonstrate that
while there is inherent ambiguity in the temporal extent of activities, current
datasets still permit effective benchmarking. We discover that fine-grained
understanding of objects and pose when combined with temporal reasoning is
likely to yield substantial improvements in algorithmic accuracy. We present
the many kinds of information that will be needed to achieve substantial gains
in activity understanding: objects, verbs, intent, and sequential reasoning.
The software and additional information will be made available to provide other
researchers detailed diagnostics to understand their own algorithms.


  We estimate the number of zeros of a polynomial in $\mathbb{C}[z]$ within any
small circular disc centered on the unit circle, which improves and
comprehensively extends a result established by Borwein, Erd{\'e}lyi, and
Littmann~\cite{BE1} in 2008. Furthermore, by combining this result with
Euclidean geometry, we derive an upper bound on the number of zeros of such a
polynomial within a region resembling a gear wheel. Additionally, we obtain a
sharp upper bound on the annular discrepancy of such zeros near the unit
circle. Our approach builds upon a modified version of the method described in
\cite{BE1}, combined with the refined version of the best-known upper bound for
angular discrepancy of zeros of polynomials.


  Some basic quantum neural networks were analyzed and constructed in the
recent work of the author \cite{dndiep3}, published in International Journal of
Theoretical Physics (2020). In particular the Least Quare Problem (LSP) and the
Linear Regression Problem (LRP) was discussed. In this second paper we continue
to analyze and construct the least square quantum neural network (LS-QNN), the
polynomial interpolation quantum neural network (PI-QNN), the polynomial
regression quantum neural network (PR-QNN) and chi-squared quantum neural
network ($\chi^2$-QNN). We use the corresponding solution or tests as the
threshold for the corresponding training rules.


  It is shown that a spontaneously-broken gauge theory of the Lorentz group
contains Ashtekar's chiral formulation of General Relativity accompanied by
dust. From this perspective, gravity is described entirely by a connection
$\omega$ valued in the Lie algebra of the complexified Lorentz group and a
Lorentz-charged scalar field $\tau$. The model is "pre-geometric" in the sense
that the spacetime metric may be constructed only in the symmetry-broken
regime. We speculate on the extent to which this dust may account for dark
matter and on the behaviour of the theory in regimes where the symmetry is not
broken.


  We study the evolution of linear cosmological perturbations in f(R) models of
accelerated expansion in the physical frame where the gravitational dynamics
are fourth order and the matter is minimally coupled. These models predict a
rich and testable set of linear phenomena. For each expansion history, fixed
empirically by cosmological distance measures, there exists two branches of
f(R) solutions that are parameterized by B propto d^2 f/dR^2. For B<0, which
include most of the models previously considered, there is a short-timescale
instability at high curvature that spoils agreement with high redshift
cosmological observables. For the stable B>0 branch, f(R) models can reduce the
large-angle CMB anisotropy, alter the shape of the linear matter power
spectrum, and qualitatively change the correlations between the CMB and galaxy
surveys. All of these phenomena are accessible with current and future data and
provide stringent tests of general relativity on cosmological scales.


  Cross-resonance interactions are a promising way to implement all-microwave
two-qubit gates with fixed-frequency qubits. In this work, we study the
dependence of the cross-resonance interaction rate on qubit-qubit detuning and
compare with a model that includes the higher levels of a transmon system. To
carry out this study we employ two transmon qubits--one fixed frequency and the
other flux tunable--to allow us to vary the detuning between qubits. We find
that the interaction closely follows a three-level model of the transmon, thus
confirming the presence of an optimal regime for cross-resonance gates.