  Let $f$ be a map with bounded set of singular values for which periodic
dynamic rays exist and land. We prove that each non-repelling cycle is
associated to a singular orbit which cannot accumulate on any other
non-repelling cycle. When $f$ has finitely many singular values this implies a
refinement of the Fatou-Shishikura inequality. Our approach is combinatorial in
the spirit of the approach used by [Ki00], [BCL+16] for polynomials.


  In this paper, we address the inverse problem, or the statistical machine
learning problem, in Markov random fields with a non-parametric pair-wise
energy function with continuous variables. The inverse problem is formulated by
maximum likelihood estimation. The exact treatment of maximum likelihood
estimation is intractable because of two problems: (1) it includes the
evaluation of the partition function and (2) it is formulated in the form of
functional optimization. We avoid Problem (1) by using Bethe approximation.
Bethe approximation is an approximation technique equivalent to the loopy
belief propagation. Problem (2) can be solved by using orthonormal function
expansion. Orthonormal function expansion can reduce a functional optimization
problem to a function optimization problem. Our method can provide an analytic
form of the solution of the inverse problem within the framework of Bethe
approximation.


  We investigate conditions for when the $t$-structure of
Happel-Reiten-Smal{\o} associated to a torsion pair is a compactly generated
$t$-structure. The concept of a $t$CG torsion pair is introduced and for any
ring $R$, we prove that $\mathbf{t}=(\mathcal{T},\mathcal{F})$ is a $t$CG
torsion pair in $R\text{-Mod}$ if, and only if, there exists, $\{T_{\lambda}\}$
a set of finitely presented $R$-modules in $\mathcal{T}$, such that
$\mathcal{F}=\bigcap \text{Ker}({\text{Hom}}_{R}(T_{\lambda},?))$. We also show
that every $t$CG torsion pair is of finite type, and show that the reciprocal
is not true. Finally, we give a precise description of the $t$CG torsion pairs
over Noetherian rings and von Neumman regular rings.


  With the development of the Internet, natural language processing (NLP), in
which sentiment analysis is an important task, became vital in information
processing.Sentiment analysis includes aspect sentiment classification. Aspect
sentiment can provide complete and in-depth results with increased attention on
aspect-level. Different context words in a sentence influence the sentiment
polarity of a sentence variably, and polarity varies based on the different
aspects in a sentence. Take the sentence, 'I bought a new camera. The picture
quality is amazing but the battery life is too short.'as an example. If the
aspect is picture quality, then the expected sentiment polarity is 'positive',
if the battery life aspect is considered, then the sentiment polarity should be
'negative'; therefore, aspect is important to consider when we explore aspect
sentiment in the sentence. Recurrent neural network (RNN) is regarded as a good
model to deal with natural language processing, and RNNs has get good
performance on aspect sentiment classification including Target-Dependent LSTM
(TD-LSTM) ,Target-Connection LSTM (TC-LSTM) (Tang, 2015a, b), AE-LSTM, AT-LSTM,
AEAT-LSTM (Wang et al., 2016).There are also extensive literatures on sentiment
classification utilizing convolutional neural network, but there is little
literature on aspect sentiment classification using convolutional neural
network. In our paper, we develop attention-based input layers in which aspect
information is considered by input layer. We then incorporate attention-based
input layers into convolutional neural network (CNN) to introduce context words
information. In our experiment, incorporating aspect information into CNN
improves the latter's aspect sentiment classification performance without using
syntactic parser or external sentiment lexicons in a benchmark dataset from
Twitter but get better performance compared with other models.


  A sufficient condition for the linear stability of three dimensional
equilibria with incompressible flows parallel to the magnetic field is derived.
The condition involves physically interpretable terms related to the magnetic
shear and the flow shear.


  We analyze whether preferential attachment in scientific coauthorship
networks is different for authors with different forms of centrality. Using a
complete database for the scientific specialty of research about "steel
structures," we show that betweenness centrality of an existing node is a
significantly better predictor of preferential attachment by new entrants than
degree or closeness centrality. During the growth of a network, preferential
attachment shifts from (local) degree centrality to betweenness centrality as a
global measure. An interpretation is that supervisors of PhD projects and
postdocs broker between new entrants and the already existing network, and thus
become focal to preferential attachment. Because of this mediation, scholarly
networks can be expected to develop differently from networks which are
predicated on preferential attachment to nodes with high degree centrality.


  We consider information-theoretic bounds on expected generalization error for
statistical learning problems in a networked setting. In this setting, there
are $K$ nodes, each with its own independent dataset, and the models from each
node have to be aggregated into a final centralized model. We consider both
simple averaging of the models as well as more complicated multi-round
algorithms. We give upper bounds on the expected generalization error for a
variety of problems, such as those with Bregman divergence or Lipschitz
continuous losses, that demonstrate an improved dependence of $1/K$ on the
number of nodes. These "per node" bounds are in terms of the mutual information
between the training dataset and the trained weights at each node, and are
therefore useful in describing the generalization properties inherent to having
communication or privacy constraints at each node.


  We study a model for the evolution of chemical species under a combination of
population dynamics on a short time scale and a selection mechanism on a longer
time scale. Least fit nodes are replaced by new nodes whose links are attached
to the nodes of the given network via preferential attachment. In contrast to a
random attachment of newly incoming nodes that was used in previous work, this
preferential attachment mechanism accelerates the generation of a so-called
autocatalytic set after a start from a random geometry and the growth of this
structure until it saturates in a stationary phase in which the whole system is
an autocatalytic set. Moreover, the system in the stationary phase becomes much
more stable against crashes in the population size as compared to random
attachment. We explain in detail in terms of graph theoretical notions which
structure of the resulting network is responsible for this stability.
Essentially it is a very dense core with many loops and less nodes playing the
role of a keystone that prevents the system against crashes almost completely.


  An \emph{$\alpha$-approximate vertex fault-tolerant distance sensitivity
oracle} (\emph{$\alpha$-VSDO}) for a weighted input graph $G=(V, E, w)$ and a
source vertex $s \in V$ is the data structure answering an $\alpha$-approximate
distance from $s$ to $t$ in $G-x$ for any given query $(x, t) \in V \times V$.
It is a data structure version of the so-called single-source replacement path
problem (SSRP). In this paper, we present a new \emph{nearly linear-time}
algorithm of constructing a $(1 + \epsilon)$-VSDO for any directed input graph
with polynomially bounded integer edge weights. More precisely, the presented
oracle attains $\tilde{O}(m \log (nW)/ \epsilon + n \log^2 (nW)/\epsilon^2)$
construction time, $\tilde{O}(n \log (nW) / \epsilon)$ size, and
$\tilde{O}(1/\epsilon)$ query time, where $n$ is the number of vertices, $m$ is
the number of edges, and $W$ is the maximum edge weight. These bounds are all
optimal up to polylogarithmic factors. To the best of our knowledge, this is
the first non-trivial algorithm for SSRP/VSDO beating $\tilde{O}(mn)$
computation time for directed graphs with general edge weight functions, and
also the first nearly linear-time construction breaking approximation factor 3.
Such a construction has been unknown even for undirected and unweighted graphs.
In addition, our result implies that the known conditional lower bounds for the
exact SSRP computation does not apply to the case of approximation.


  Deep neural networks are susceptible to backdoor attacks, where adversaries
manipulate model predictions by inserting malicious samples into the training
data. Currently, there is still a lack of direct filtering methods for
identifying suspicious training data to unveil potential backdoor samples. In
this paper, we propose a novel method, Prediction Shift Backdoor Detection
(PSBD), leveraging an uncertainty-based approach requiring minimal unlabeled
clean validation data. PSBD is motivated by an intriguing Prediction Shift (PS)
phenomenon, where poisoned models' predictions on clean data often shift away
from true labels towards certain other labels with dropout applied during
inference, while backdoor samples exhibit less PS. We hypothesize PS results
from neuron bias effect, making neurons favor features of certain classes. PSBD
identifies backdoor training samples by computing the Prediction Shift
Uncertainty (PSU), the variance in probability values when dropout layers are
toggled on and off during model inference. Extensive experiments have been
conducted to verify the effectiveness and efficiency of PSBD, which achieves
state-of-the-art results among mainstream detection methods.


  Finite mixture distributions arise in sampling a heterogeneous population.
Data drawn from such a population will exhibit extra variability relative to
any single subpopulation. Statistical models based on finite mixtures can
assist in the analysis of categorical and count outcomes when standard
generalized linear models (GLMs) cannot adequately account for variability
observed in the data. We propose an extension of GLM where the response is
assumed to follow a finite mixture distribution, while the regression of
interest is linked to the mixture's mean. This approach may be preferred over a
finite mixture of regressions when the population mean is the quantity of
interest; here, only a single regression function must be specified and
interpreted in the analysis. A technical challenge is that the mean of a finite
mixture is a composite parameter which does not appear explicitly in the
density. The proposed model is completely likelihood-based and maintains the
link to the regression through a certain random effects structure. We consider
typical GLM cases where means are either real-valued, constrained to be
positive, or constrained to be on the unit interval. The resulting model is
applied to two example datasets through a Bayesian analysis: one with
success/failure outcomes and one with count outcomes. Supporting the extra
variation is seen to improve residual plots and to appropriately widen
prediction intervals.


  This paper aims to explore processes and their identity with a focus on the
upper ontology Basic Formal Ontology (BFO). We begin with a classification
based on two basic classes of changes of independent continuants: changes with
respect to a single specifically dependent continuant thereof or with respect
to the spatial region that its parts occupy. We accordingly distinguish two
kinds of simple processes: specifically dependent continuant changes and
spatial changes. Next, we investigate a compositional approach to the identity
of processes: the identity of any process is determined by the identity of the
simple processes that compose them. Then, we consider a causal approach to the
identity of processes with recourse to a dispositional view of processes
according to which any process is a realization of some disposition. We also
examine assumptions on which these two approaches to the identity of processes
are based.


  Carbon Dioxide is an important tracer of the chemistry and physics in the
terrestrial planet forming zone. Using a thermo-chemical model that has been
tested against the mid-infrared water emission we re-interpret the CO2 emission
as observed with Spitzer. We find that both water UV-shielding and extra
chemical heating significantly reduce the total CO2 column in the emitting
layer. Water UV-shielding is the more efficient effect, reducing the CO2 column
by $\sim$ 2 orders of magnitude. These lower CO2 abundances lead to CO2-to-H2O
flux ratios that are closer to the observed values, but CO2 emission is still
too bright, especially in relative terms. Invoking the depletion of elemental
oxygen outside of the water mid-plane iceline more strongly impacts the CO2
emission than it does the H2O emission, bringing the CO2-to-H2O emission in
line with the observed values. We conclude that the CO2 emission observed with
Spitzer-IRS is coming from a thin layer in the photo-sphere of the disk,
similar to the strong water lines. Below this layer, we expect CO2 not to be
present except when replenished by a physical process. This would be visible in
the $^{13}$CO2 spectrum as well as certain $^{12}$CO2 features that can be
observed by JWST-MIRI.


  We combine ionized gas ([N II] 6583) and stellar central velocity dispersions
for a sample of 345 galaxies, with and without active galactic nuclei (AGNs),
to study the dynamical state of the nuclear gas and its physical origin. The
gas dispersions strongly correlate with the stellar dispersions over the
velocity range of 30-350 km/s such that sigma_g/sigma_* ~ 0.6-1.4, with an
average value of 0.80. These results are independent of Hubble type (for
galaxies from E to Sbc), presence or absence of a bar, or local galaxy
environment. For galaxies of type Sc and later and that have sigma_* < 40 km/s,
the gas seems to have a minimum threshold of sigma_g ~ 30 km/s, such that
sigma_g/sigma_* always exceeds 1. Within the sample of AGNs, sigma_g/sigma_*
increases with nuclear luminosity or Eddington ratio, a possible manifestation
of AGN feedback associated with accretion disk winds or outflows. This extra
source of nongravitational line broadening should be removed when trying to use
sigma_g to estimate sigma_*. We show that the mass budget of the narrow-line
region can be accounted for by mass loss from evolved stars. The kinematics of
the gas, dominated by random motions, largely reflect the velocity field of the
hot gas in the bulge. Lastly, we offer a simple explanation for the correlation
between line width and line luminosity observed in the narrow-line region of
AGNs.


  Battery-limited devices and time-sensitive applications are considered as key
players in the forthcoming wireless sensor network. Therefore, the main goal of
the network is two-fold; Charge battery-limited devices, and provide status
updates to users where information-freshness matters. In this paper, a
multi-antenna base station (BS) in assistance of
simultaneously-transmitting-and-reflecting reconfigurable intelligent surface
(STAR-RIS) transmits power to energy-harvesting devices while controlling
status update performance at information-users by analyzing age of information
(AoI) metric. Therefore, we derive a scheduling policy at BS, and analyze joint
transmit beamforming and amplitude-phase optimization at BS and STAR-RIS,
respectively, to reduce average sum-AoI for the time-sensitive
information-users while satisfying minimum required energy at energy-harvesting
users. Moreover, two different energy-splitting and mode switching policies at
STAR-RIS are studied. Then, by use of an alternating optimization algorithm,
the optimization problem is studied and non-convexity of the problem is tackled
by using the successive convex approximation technique. Through numerical
results, AoI-metric and energy harvesting requirements of the network are
analyzed versus different parameters such as number of antennas at BS, size of
STAR-RIS, and transmitted power to highlight how we can improve two fold
performance of the system by utilizing STAR-RIS compared to the conventional
RIS structure.


  Objective To assess the price elasticity of branded imatinib in chronic
myeloid leukemia (CML) patients on Medicare Part D to determine if high
out-of-pocket payments (OOP) are driving the substantial levels of
non-adherence observed in this population.
  Data sources and study setting We use data from the TriNetX Diamond Network
(TDN) United States database for the period from first availability in 2011
through the end of patent exclusivity following the introduction of generic
imatinib in early 2016.
  Study design We implement a fuzzy regression discontinuity design to
separately estimate the effect of Medicare Part D enrollment at age 65 on
adherence and OOP in newly-diagnosed CML patients initiating branded imatinib.
The corresponding price elasticity of demand (PED) is estimated and results are
assessed across a variety of specifications and robustness checks.
  Data collection/extraction methods Data from eligible patients following the
application of inclusion and exclusion criteria were analyzed.
  Principal findings Our analysis suggests that there is a significant increase
in initial OOP of $232 (95% Confidence interval (CI): $102 to $362) for
individuals that enrolled in Part D due to expanded eligibility at age 65. The
relatively smaller and non-significant decrease in adherence of only 6
percentage points (95% CI: -0.21 to 0.08) led to a PED of -0.02 (95% CI:
-0.056, 0.015).
  Conclusion This study provides evidence regarding the financial impact of
coinsurance-based benefit designs on Medicare-age patients with CML initiating
branded imatinib. Results indicate that factors besides high OOP are driving
the substantial non-adherence observed in this population and add to the
growing literature on PED for specialty drugs.


  We show that intersection homology extends Poincare duality to manifold
homotopically stratified spaces (satisfying mild restrictions). This includes
showing that, on such spaces, the sheaf of singular intersection chains is
quasi-isomorphic to the Deligne sheaf.


  High-density and nanosized deformation twins in face-centered cubic
(fcc)materials can effectively improve the combination of strength and
ductility. However, the microscopic dislocation mechanisms enabling a high
twinnability remain elusive. Twinning usually occurs via continuous nucleation
and gliding of twinning partial dislocations on consecutive close-packed atomic
planes. Here we unveil a completely different twinning mechanism being active
in metastable fcc materials. The transformation-mediated twinning (TMT) is
featured by a preceding displacive transformation from the fcc phase to the
hexagonal close-packed (hcp) one, followed by a second-step transformation from
the hcp phase to the fcc twin. The nucleation of the intermediate hcp phase is
driven by the thermodynamic instability and the negative stacking fault energy
of the metastable fcc phase. The intermediate hcp structure is characterized by
the easy slips of Shockley partial dislocations on the basal planes, which
leads to both fcc and fcc twin platelets during deformation, creating more twin
boundaries and further enhancing the prosperity of twins. The disclosed
fundamental understanding of the complex dislocation mechanism of deformation
twinning in metastable alloys paves the road to design novel materials with
outstanding mechanical properties.


  Elucidating the impact of strong electronic interactions on the collective
excitations of metallic systems has been of longstanding interest, mainly due
to the inadequacy of the random phase approximation (RPA) in the strongly
correlated regime. Here, we adopt our newly developed radial Kotliar and
Ruckenstein slave boson representation to analyze the charge excitation
spectrum of a Hubbard model, extended with long range interactions. Working on
the face centered cubic lattice, at half filling, and in different coupling
regimes ranging from uncorrelated to the metal-to-insulator transition, we
compare our results to conventional RPA as a benchmark. We focus on the
influence of the local and long range couplings on the particle-hole excitation
continuum and the plasmon and upper Hubbard band collective modes. Beyond the
weak coupling regime, we find numerous quantitative and even qualitative
discrepancies between our method and standard RPA. Our work thus deepens our
understanding of charge collective modes in correlated systems, and lays the
foundations for future studies of realistic materials.


  Recommender systems play an increasingly important role in online
applications to help users find what they need or prefer. Collaborative
filtering algorithms that generate predictions by analyzing the user-item
rating matrix perform poorly when the matrix is sparse. To alleviate this
problem, this paper proposes a simple recommendation algorithm that fully
exploits the similarity information among users and items and intrinsic
structural information of the user-item matrix. The proposed method constructs
a new representation which preserves affinity and structure information in the
user-item rating matrix and then performs recommendation task. To capture
proximity information about users and items, two graphs are constructed.
Manifold learning idea is used to constrain the new representation to be smooth
on these graphs, so as to enforce users and item proximities. Our model is
formulated as a convex optimization problem, for which we need to solve the
well-known Sylvester equation only. We carry out extensive empirical
evaluations on six benchmark datasets to show the effectiveness of this
approach.


  Models such as latent semantic analysis and those based on neural embeddings
learn distributed representations of text, and match the query against the
document in the latent semantic space. In traditional information retrieval
models, on the other hand, terms have discrete or local representations, and
the relevance of a document is determined by the exact matches of query terms
in the body text. We hypothesize that matching with distributed representations
complements matching with traditional local representations, and that a
combination of the two is favorable. We propose a novel document ranking model
composed of two separate deep neural networks, one that matches the query and
the document using a local representation, and another that matches the query
and the document using learned distributed representations. The two networks
are jointly trained as part of a single neural network. We show that this
combination or `duet' performs significantly better than either neural network
individually on a Web page ranking task, and also significantly outperforms
traditional baselines and other recently proposed models based on neural
networks.


  A recent paper by James et al. finds that mutualistic interactions decrease
the biodiversity of model ecosystems. However, this result can be reverted if
we consider ecological trade-offs and choose parameters suitable for sparse
mutualistic networks instead of fully connected networks.


  With the increasing amount of information on the Internet, recommender
systems are becoming increasingly crucial in supporting people to find and
explore relevant content. This is also true in the online recruitment space,
with websites such as LinkedIn, Indeed.com, and Monster.com all using
recommender systems. In online recruitment, it can often be challenging for
companies to find suitable candidates with appropriate skills because of the
huge volume of user profiles available. Identifying users which satisfy a range
of different employer needs is also a difficult task. Thus, effective matching
of user-profiles and jobs is becoming crucial for companies. This research
project applies a wide range of recommendation techniques to the task of user
profile recommendation. Extensive experiments are conducted on a large-scale
real-world LinkedIn dataset to evaluate their performance, with the aim of
identifying the most suitable approach in this particular recommendation
scenario.


  Iris restoration from complexly degraded iris images, aiming to improve iris
recognition performance, is a challenging problem. Due to the complex
degradation, directly training a convolutional neural network (CNN) without
prior cannot yield satisfactory results. In this work, we propose a generative
iris prior embedded Transformer model (Gformer), in which we build a
hierarchical encoder-decoder network employing Transformer block and generative
iris prior. First, we tame Transformer blocks to model long-range dependencies
in target images. Second, we pretrain an iris generative adversarial network
(GAN) to obtain the rich iris prior, and incorporate it into the iris
restoration process with our iris feature modulator. Our experiments
demonstrate that the proposed Gformer outperforms state-of-the-art methods.
Besides, iris recognition performance has been significantly improved after
applying Gformer.


  Within systems biology there is an increasing interest in the stochastic
behavior of genetic and biochemical reaction networks. An appropriate
stochastic description is provided by the chemical master equation, which
represents a continuous time Markov chain (CTMC). In this paper we consider the
stochastic properties of a biochemical circuit, known to control eukaryotic
cell cycle and possibly involved in oncogenesis, recently proposed in the
literature within a deterministic framework. Due to the inherent stochasticity
of biochemical processes and the small number of molecules involved, the
stochastic approach should be more correct in describing the real system: we
study the agreement between the two approaches by exploring the system
parameter space. We address the problem by proposing a simplified version of
the model that allows analytical treatment, and by performing numerical
simulations for the full model. We observed optimal agreement between the
stochastic and the deterministic description of the circuit in a large range of
parameters, but some substantial differences arise in at least two cases: 1)
when the deterministic system is in the proximity of a transition from a
monostable to a bistable configuration, and 2) when bistability (in the
deterministic system) is "masked" in the stochastic system by the distribution
tails. The approach provides interesting estimates of the optimal number of
molecules involved in the toggle. Our discussion of the points of strengths,
potentiality and weakness of the chemical master equation in systems biology
and the differences with respect to deterministic modeling are leveraged in
order to provide useful advice for both the bioinformatician practitioner and
the theoretical scientist.


  We present a new analytic approach to the disk-planet interaction that is
especially useful for planets with eccentricity larger than the disk aspect
ratio. We make use of the dynamical friction formula to calculate the force
exerted on the planet by the disk, and the force is averaged over the period of
the planet. The resulting migration and eccentricity damping timescale agrees
very well with the previous works in which the planet eccentricity is
moderately larger than the disk aspect ratio. The advantage of this approach is
that it is possible to apply this formulation to arbitrary large eccentricity.
We have found that the timescale of the orbital evolution depends largely on
the adopted disk model in the case of highly eccentric planets. We discuss the
possible implication of our results to the theory of planet formation.


  In the present paper, we theoretically study the effect of density of state
variation on the phenomena in the discontinuous magnetic field. Special
attention is paid to the transient processes when the magnetic field is
switched on (off). The difference in the density of states for the free 2D
electron gas and the electron gas on under the magnetic field can lead to the
occurrence of the electrostatic potential. Considering the transient phenomena
of magnetic field switching, we obtain oscillating behavior of the
electrostatic potential. The analysis includes two limit cases when the
oscillation frequency of the electrostatic potential is low relative to the
cyclotron frequency and when they are of the same order.


  Motion trajectories offer reliable references for physics-based motion
learning but suffer from sparsity, particularly in regions that lack sufficient
data coverage. To address this challenge, we introduce a self-supervised,
structured representation and generation method that extracts spatial-temporal
relationships in periodic or quasi-periodic motions. The motion dynamics in a
continuously parameterized latent space enable our method to enhance the
interpolation and generalization capabilities of motion learning algorithms.
The motion learning controller, informed by the motion parameterization,
operates online tracking of a wide range of motions, including targets unseen
during training. With a fallback mechanism, the controller dynamically adapts
its tracking strategy and automatically resorts to safe action execution when a
potentially risky target is proposed. By leveraging the identified
spatial-temporal structure, our work opens new possibilities for future
advancements in general motion representation and learning algorithms.


  Isospin-mixing corrections for superallowed Fermi transitions in {\it
fp}-shell nuclei are computed within the framework of the shell model. The
study includes three nuclei that are part of the set of nine accurately
measured transitions as well as five cases that are expected to be measured in
the future at radioactive-beam facilities. We also include some new
calculations for $^{10}$C. With the isospin-mixing corrections applied to the
nine accurately measured $ft$ values, the conserved-vector-current hypothesis
and the unitarity condition of the Cabbibo-Kobayashi-Maskawa (CKM) matrix are
tested.


  The Sylow graph $\Gamma(G)$ of a finite group $G$ originated from recent
investigations on the so--called $\mathbf{N}$--closed classes of groups. The
connectivity of $\Gamma(G)$ was proved only few years ago, involving the
classification of finite simple groups, and the structure of $G$ may be
strongly restricted, once information on $\Gamma(G)$ are given. The first
result of the present paper deals with a condition on $\mathbf{N}$--closed
classes of groups. The second result deals with a computational criterion,
related to the connectivity of $\Gamma(G)$.


  We study representations of the locally unital and locally finite dimensional
algebra $B$ associated to the Brauer category $\mathcal B(\delta_0)$ with
defining parameter $\delta_0$ over an algebraically closed field $K$ with
characteristic $p\neq 2$. The Grothendieck group $K_0(B\text{-mod}^\Delta)$
will be used to categorify the integrable highest weight $\mathfrak
{sl}_{K}$-module $ V(\varpi_{\frac{\delta_0-1}{2}})$ with the fundamental
weight $\varpi_{\frac{\delta_0-1}{2}}$ as its highest weight, where
$B$-mod$^\Delta$ is a subcategory of $B$-lfdmod in which each object has a
finite $\Delta$-flag, and $\mathfrak {sl}_{K}$ is either $\mathfrak{sl}_\infty$
or $\hat{\mathfrak{sl}}_p$ depending on whether $p=0$ or $2\nmid p$. As
$\mathfrak g$-modules, $\mathbb C\otimes_{\mathbb Z} K_0(B\text{-mod}^\Delta)$
is isomorphic to $ V(\varpi_{\frac{\delta_0-1}{2}})$, where $\mathfrak g$ is a
Lie subalgebra of $\mathfrak {sl}_{K}$ (see Definition~4.2). When $p=0$,
standard $B$-modules and projective covers of simple $B$-modules correspond to
monomial basis and so-called quasi-canonical basis of
$V(\varpi_{\frac{\delta_0-1}{2}}) $, respectively.


  Classification of AS-regular algebras is one of the main interests in
noncommutative algebraic geometry. We say that a $3$-dimensional quadratic
AS-regular algebra is of Type EC if its point scheme is an elliptic curve in
$\mathbb{P}^{2}$. In this paper, we give a complete list of geometric pairs and
a complete list of twisted superpotentials corresponding to such algebras. As
an application, we show that there are only two exceptions up to isomorphism
among all $3$-dimensional quadratic AS-regular algebras which cannot be written
as a twist of a Calabi-Yau AS-regular algebra by a graded algebra automorphism.


  We improve upon the recent keystone result of Dasgupta-Kakde on the $\Bbb
Z[G(H/F)]^-$-Fitting ideals of certain Selmer modules $Sel_S^T(H)^-$ associated
to an abelian, CM extension $H/F$ of a totally real number field $F$ and use
this to compute the $\Bbb Z_p[[G(H_\infty/F)]]^-$-Fitting ideal of the Iwasawa
module analogues $Sel_S^T(H_\infty)_p^-$ of these Selmer modules, where
$H_\infty$ is the cyclotomic $\Bbb Z_p$-extension of $H$, for an odd prime $p$.
Our main Iwasawa theoretic result states that the $\Bbb
Z_p[[G(H_\infty/F]]^-$-module $Sel_S^T(H_\infty)_p^-$ is of projective
dimension $1$, is quadratically presented, and that its Fitting ideal is
principal, generated by an equivariant $p$-adic $L$-function
$\Theta_S^T(H_\infty/F)$. Further, we establish a perfect duality pairing
between $Sel_S^T(H_\infty)_p^-$ and a certain $\Bbb
Z_p[[G(H_\infty/F)]]^-$-module $\mathcal M_S^T(H_\infty)^-$, essentially
introduced earlier by Greither-Popescu. As a consequence, we recover the
Equivariant Main Conjecture for the Tate module $T_p(\mathcal
M_S^T(H_\infty))^-$, proved by Greither-Popescu under the hypothesis that the
classical Iwasawa $\mu$-invariant associated to $H$ and $p$ vanishes. As a
further consequence, we give an unconditional proof of the refined
Coates-Sinnott Conjecture, proved by Greither-Popescu under the same $\mu=0$
hypothesis, and also recently proved unconditionally but with different methods
by Johnston-Nickel, regarding the $\Bbb Z[G(H/F)]$-Fitting ideals of the higher
Quillen $K$-groups $K_{2n-2}(\mathcal O_{H,S})$, for all $n\geq 2$. Finally, we
combine the techniques developed in the process with the method of
''Taylor-Wiles primes'' to strengthen further the keystone result of
Dasgupta-Kakde and prove, as a consequence, a conjecture of Burns-Kurihara-Sano
on Fitting ideals of Selmer groups of CM number fields.


  In the ultra-cold regime Van der Waals forces between neutral atoms can be
represented by short range effective interactions. We show that universal low
energy scaling features of the underlying vdW long range force stemming from
two photon exchange impose restrictions on an Effective Field Theory without
explicit photons. The role of naively redundant operators, relevant to the
definition of three body forces, is also analyzed.


  Motivated by the study of branes in curved backgrounds, we investigate the
construction of non-perturbative extensions of the super-isometry algebra
osp*(8|4) of the AdS_7xS^4 background of M-theory. This algebra is not a
subalgebra of osp(1|32) and its non-perturbative extension can therefore not be
obtained by embedding in this simple superalgebra. We show how, instead, it is
possible to construct an extension directly by solving the Jacobi identities.
This requires, in addition to the expected non-perturbative charges, the
introduction of new charges which appear in the {Q,Q} bracket only via a linear
combination with the bosonic generators of the isometry algebra. The resulting
extended algebra has the correct flat-space limit, but it is not simple and the
non-perturbative charges do not commute with the super-isometry generators. We
comment on the consequences of this structure for the representation theory and
on possible alternatives to our construction.


  MSr2Y1.5Ce0.5Cu2Oz (M-1222) compounds, with M = Fe and Co, have been
synthesized through a solid-state reaction route. Both compounds crystallize in
a tetragonal structure (space group I4/mmm). A Rietveld structural refinement
of room-temperature neutron diffraction data for Fe-1222 reveals that nearly
half the Fe remains at the M site, while the other half goes to the Cu site in
the CuO2 planes. Existence of Fe at two different lattice sites, is also
confirmed by 57Fe Mossbauer spectroscopy from which it is inferred that nearly
50% of the total Fe occupies the Cu site in the CuO2 planes as Fe3+, whereas
the other 50 % is located at the M site with nearly 40 % as Fe4+ and around 10%
as Fe3+. For the M = Co compound, nearly 84 % of Co remains at its designated M
site, while the rest occupies the Cu site in the CuO2 planes. The oxygen
content, z, based on oxygen occupancies refined from the neutron diffraction
data, comes close to 9.0 for both the samples The ZFC and FC magnetization
curves as a function of temperature show a complex behavior for both Fe-1222
and Co-1222 compounds.


  Artificial intelligence (AI) models are increasingly finding applications in
the field of medicine. Concerns have been raised about the explainability of
the decisions that are made by these AI models. In this article, we give a
systematic analysis of explainable artificial intelligence (XAI), with a
primary focus on models that are currently being used in the field of
healthcare. The literature search is conducted following the preferred
reporting items for systematic reviews and meta-analyses (PRISMA) standards for
relevant work published from 1 January 2012 to 02 February 2022. The review
analyzes the prevailing trends in XAI and lays out the major directions in
which research is headed. We investigate the why, how, and when of the uses of
these XAI models and their implications. We present a comprehensive examination
of XAI methodologies as well as an explanation of how a trustworthy AI can be
derived from describing AI models for healthcare fields. The discussion of this
work will contribute to the formalization of the XAI field.


  In this work we present 3D numerical relativity simulations of thick
accretion disks around tilted Kerr BH. We investigate the evolution of three
different initial disk models with a range of initial black hole spin
magnitudes and tilt angles. For all the disk-to-black hole mass ratios
considered (0.044-0.16) we observe significant black hole precession and
nutation during the evolution. This indicates that for such mass ratios,
neglecting the self-gravity of the disks by evolving them in a fixed background
black hole spacetime is not justified. We find that the two more massive models
are unstable against the Papaloizou-Pringle (PP) instability and that those
PP-unstable models remain unstable for all initial spins and tilt angles
considered, showing that the development of the instability is a very robust
feature of such PP-unstable disks. Our lightest model, which is the most
astrophysically favorable outcome of mergers of binary compact objects, is
stable. The tilt between the black hole spin and the disk is strongly modulated
during the growth of the PP instability, causing a partial global realignment
of black hole spin and disk angular momentum in the most massive model with
constant specific angular momentum l. For the model with non-constant l-profile
we observe a long-lived m=1 non-axisymmetric structure which shows strong
oscillations of the tilt angle in the inner regions of the disk. This effect
might be connected to the development of Kozai-Lidov oscillations. Our
simulations also confirm earlier findings that the development of the PP
instability causes the long-term emission of large amplitude gravitational
waves, predominantly for the l=m=2 multipole mode. The imprint of the BH
precession on the gravitational waves from tilted BH-torus systems remains an
interesting open issue that would require significantly longer simulations than
those presented in this work.


  We present some limit theorems for the normalized laws (with respect to
functionals involving last passage times at a given level up to time t) of a
large class of null recurrent diffusions. Our results rely on hypotheses on the
L\'evy measure of the diffusion inverse local time at 0. As a special case, we
recover some of the penalization results obtained by Najnudel, Roynette and Yor
in the (reflected) Brownian setting.


  Musical source separation methods exploit source-specific spectral
characteristics to facilitate the decomposition process. Kernel Additive
Modelling (KAM) models a source applying robust statistics to time-frequency
bins as specified by a source-specific kernel, a function defining similarity
between bins. Kernels in existing approaches are typically defined using
metrics between single time frames. In the presence of noise and other sound
sources information from a single-frame, however, turns out to be unreliable
and often incorrect frames are selected as similar. In this paper, we
incorporate a temporal context into the kernel to provide additional
information stabilizing the similarity search. Evaluated in the context of
vocal separation, our simple extension led to a considerable improvement in
separation quality compared to previous kernels.


  We make an estimate of the possible range of $\Delta T_c$ induced by
high-pressure effects in post-metallic superconductors by using the theory of
{\it extended irreversible/reversible thermodynamics} and Pippard's length
scale. The relationship between the increment of the superconducting
temperature and the increase of the pressure is parabolic.


  For highly perforated domains the paper addresses a novel approach to study
mixed boundary value problems for the equations of linear elasticity in the
framework of meso-scale approximations. There are no assumptions of periodicity
involved in the description of the geometry of the domain. The size of the
perforations is small compared to the minimal separation between neighbouring
defects and here we discuss a class of problems in perforated domains, which
are not covered by the homogenisation approximations. The meso-scale
approximations presented here are uniform. Explicit asymptotic formulae are
supplied with the remainder estimates.


  We consider a head-on collision of two massive particles that move in the
equatorial plane of an extremal Kerr black hole, which results in the
production of two massless particles. Focusing on a typical case, where both of
the colliding particles have zero angular momenta, we show that a massless
particle produced in such a collision can escape to infinity with arbitrarily
large energy in the near-horizon limit of the collision point. Furthermore, if
we assume that the emission of the produced massless particles is isotropic in
the center-of-mass frame but confined to the equatorial plane, the escape
probability of the produced massless particle approaches $5/12$ and almost all
escaping massless particles have arbitrarily large energy at infinity and an
impact parameter approaching $2GM/c^2$, where $M$ is the mass of the black
hole.


  To reduce technical debt and make code more maintainable, it is important to
be able to warn programmers about code smells. State-of-the-art code small
detectors use deep learners, without much exploration of alternatives within
that technology.
  One promising alternative for software analytics and deep learning is GHOST
(from TSE'21) that relies on a combination of hyper-parameter optimization of
feedforward neural networks and a novel oversampling technique to deal with
class imbalance.
  The prior study from TSE'21 proposing this novel "fuzzy sampling" was
somewhat limited in that the method was tested on defect prediction, but
nothing else. Like defect prediction, code smell detection datasets have a
class imbalance (which motivated "fuzzy sampling"). Hence, in this work we test
if fuzzy sampling is useful for code smell detection.
  The results of this paper show that we can achieve better than
state-of-the-art results on code smell detection with fuzzy oversampling. For
example, for "feature envy", we were able to achieve 99+\% AUC across all our
datasets, and on 8/10 datasets for "misplaced class". While our specific
results refer to code smell detection, they do suggest other lessons for other
kinds of analytics. For example: (a) try better preprocessing before trying
complex learners (b) include simpler learners as a baseline in software
analytics (c) try "fuzzy sampling" as one such baseline.


  We derive two formulae for (A + B)^n, where A and B are elements in a
non-commutative, associative algebra with identity.


  Let $\Omega$ be a tiling space and let $G$ be the maximal group of rotations
which fixes $\Omega$. Then the cohomology of $\Omega$ and $\Omega/G$ are both
invariants which give useful geometric information about the tilings in
$\Omega$. The noncommutative analog of the cohomology of $\Omega$ is the
K-theory of a C*-algebra associated to $\Omega$, and for translationally finite
tilings of dimension 2 or less the K-theory is isomorphic to the direct sum of
cohomology groups. In this paper we give a prescription for calculating the
noncommutative analog of the cohomology of $\Omega/G$, that is, the K-theory of
the crossed product of the tiling C*-algebra by $G$. We also provide a table
with some calculated K-groups for many common examples, including the Penrose
and pinwheel tilings.


  Tables of the currently known parameters of symmetric configurations are
given. Formulas for parameters of the known infinite families of symmetric
configurations are presented as well. The results of the recent paper [18] are
used. This work can be viewed as an appendix to [18], in the sense that the
tables given here cover a much larger set of parameters.


  We investigate the ground states of 1D continuum models having short-range
ferromagnetic type interactions and a wide class of competing longer-range
antiferromagnetic type interactions. The model is defined in terms of an energy
functional, which can be thought of as the Hamiltonian of a coarse-grained
microscopic system or as a mesoscopic free energy functional describing various
materials. We prove that the ground state is simple periodic whatever the
prescribed total magnetization might be. Previous studies of this model of
frustrated systems assumed this simple periodicity but, as in many examples in
condensed matter physics, it is neither obvious nor always true that ground
states do not have a more complicated, or even chaotic structure.


  In this paper, we develop a novel efficient and robust nonparametric
regression estimator under a framework of feedforward neural network. There are
several interesting characteristics for the proposed estimator. First, the loss
function is built upon an estimated maximum likelihood function, who integrates
the information from observed data, as well as the information from data
structure. Consequently, the resulting estimator has desirable optimal
properties, such as efficiency. Second, different from the traditional maximum
likelihood estimation (MLE), the proposed method avoid the specification of the
distribution, hence is flexible to any kind of distribution, such as heavy
tails, multimodal or heterogeneous distribution. Third, the proposed loss
function relies on probabilities rather than direct observations as in least
squares, contributing the robustness in the proposed estimator. Finally, the
proposed loss function involves nonparametric regression function only. This
enables a direct application of existing packages, simplifying the computation
and programming. We establish the large sample property of the proposed
estimator in terms of its excess risk and minimax near-optimal rate. The
theoretical results demonstrate that the proposed estimator is equivalent to
the true MLE in which the density function is known. Our simulation studies
show that the proposed estimator outperforms the existing methods in terms of
prediction accuracy, efficiency and robustness. Particularly, it is comparable
to the true MLE, and even gets better as the sample size increases. This
implies that the adaptive and data-driven loss function from the estimated
density may offer an additional avenue for capturing valuable information. We
further apply the proposed method to four real data examples, resulting in
significantly reduced out-of-sample prediction errors compared to existing
methods.


  By developing and leveraging an explicit molecular realisation of a
measurement-and-feedback-powered Szilard engine, we investigate the extraction
of work from complex environments by minimal machines with finite capacity for
memory and decision-making. Living systems perform inference to exploit complex
structure, or correlations, in their environment, but the physical limits and
underlying cost/benefit trade-offs involved in doing so remain unclear. To
probe these questions, we consider a minimal model for a structured environment
- a correlated sequence of molecules - and explore mechanisms based on extended
Szilard engines for extracting the work stored in these non-equilibrium
correlations. We consider systems limited to a single bit of memory making
binary 'choices' at each step. We demonstrate that increasingly complex
environments allow increasingly sophisticated inference strategies to extract
more energy than simpler alternatives, and argue that optimal design of such
machines should also consider the energy reserves required to ensure robustness
against fluctuations due to mistakes.


  We prove the differentiability of Lipschitz maps X-->V, where X is a complete
metric measure space satisfying a doubling condition and a Poincar\'e
inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The
proof depends on a new characterization of the differentiable structure on such
metric measure spaces, in terms of directional derivatives in the direction of
tangent vectors to suitable rectifiable curves.


  In [C. Xue, C. Yerger: Optimal Pebbling on Grids, Graphs and Combinatorics]
the authors conjecture that if every vertex of an infinite square grid is
reachable from a pebble distribution, then the covering ratio of this
distribution is at most $3.25$. First we present such a distribution with
covering ratio $3.5$, disproving the conjecture. The authors in the above paper
also claim to prove that the covering ratio of any pebble distribution is at
most $6.75$. The proof contains some errors. We present a few interesting
pebble distributions that this proof does not seem to cover and highlight some
other difficulties of this topic.


  We construct for the first time an energy-momentum tensor for the
electromagnetic field of a p-brane in arbitrary dimensions, entailing finite
energy-momentum integrals. The construction relies on distribution theory and
is based on a Lorentz-invariant regularization, followed by the subtraction of
divergent and finite counterterms supported on the brane. The resulting
energy-momentum tensor turns out to be uniquely determined. We perform the
construction explicitly for a generic flat brane. For a brane in arbitrary
motion our approach provides a new paradigm for the derivation of the,
otherwise divergent, self-force of the brane. The so derived self-force is
automatically finite and guarantees, by construction, energy-momentum
conservation.


  Nonlinearly constrained nonconvex and nonsmooth optimization models play an
increasingly important role in machine learning, statistics and data analytics.
In this paper, based on the augmented Lagrangian function we introduce a
flexible first-order primal-dual method, to be called nonconvex auxiliary
problem principle of augmented Lagrangian (NAPP-AL), for solving a class of
nonlinearly constrained nonconvex and nonsmooth optimization problems. We
demonstrate that NAPP-AL converges to a stationary solution at the rate of
o(1/\sqrt{k}), where k is the number of iterations. Moreover, under an
additional error bound condition (to be called VP-EB in the paper), we further
show that the convergence rate is in fact linear. Finally, we show that the
famous Kurdyka- Lojasiewicz property and the metric subregularity imply the
afore-mentioned VP-EB condition.


  We introduce a design for an electronic device capable of superposing 8 bias
voltages up to $\pm$48V on a voltage of up to 1.5~kV. Such a device has been
implemented to provide biasing of a beam steerer-shifter system for use in
aligning an ion beam with the optical axis of a multi-reflection time-of-flight
mass spectrograph. The device features a 16-bit digital interface both to set
and to monitor the applied voltages, and can be built for less than \$500~USD.
By selection of higher isolation components, the design could allow operation
up to 10~kV or more.


  We prove that the Hilbert-Kunz function of the ideal $(I,It)$ of the Rees
algebra $\mathcal{R}(I)$, where $I$ is an $\mathfrak{m}$-primary ideal of a
$1$-dimensional local ring $(R,\mathfrak{m})$, is a quasi-polynomial in $e$,
for large $e.$ For $s \in \mathbb{N}$, we calculate the Hilbert-Samuel function
of the $R$-module $I^{[s]}$ and obtain an explicit description of the
generalized Hilbert-Kunz function of the ideal $(I,It)\mathcal{R}(I)$ when $I$
is a parameter ideal in a Cohen-Macaulay local ring of dimension $d \geq 2$,
proving that the generalized Hilbert-Kunz function is a piecewise polynomial in
this case.


  We report results of quantum chemical calculations for the neutral and
anionic species of (4,4{'})-bipyridine (44BPY), a prototypical molecule with a
floppy degree of freedom, placed in vacuo and in solvents. In addition to
equilibrium geometries and vibrational frequencies and spectra, we present
adiabatic energy curves for the vibrational modes with significant
intramolecular reorganization upon charge transfer. Special attention is paid
to the floppy strongly anharmonic degree of freedom of 44BPY, which is related
to the most salient structural feature, namely the twist angle $\theta$ between
the two pyridine rings. The relevance of the present results for molecular
transport will be emphasized. We show that the solvent acts as an effective
gate electrode and propose a scissor operator to account for solvent effects on
molecular transport. Our result on the conductance $G$ vs. $\cos^2\theta$ is
consistent with a significant transmission in perpendicular conformation
indicated by previous microscopic analysis.


  XTE J1810-189 is a Low-Mass X-ray Binary transient system hosting a neutron
star, which underwent a three-month-long outburst in 2020. In order to study
its spectral evolution during this outburst, we analysed all the available
observations performed by NICER, in the 1-10 keV energy band. Firstly, we
fitted the spectra with a thermal Comptonisation model. Our analysis revealed
the lack of a significant direct emission from a black-body-like component,
therefore we calculated the optical depth of the Comptonising region, deriving
an upper limit of 4.5, which suggests the presence of a moderately thick
corona. We also attempted to fit the spectrum with an alternative model, i.e. a
cold Comptonised emission from a disc and a direct thermal component from the
neutron star, finding a similarly good fit. The source did not enter a full
high luminosity/soft state throughout the outburst, with a photon index ranging
from 1.7 to 2.2, and an average unabsorbed flux in the 1-10 keV band of
3.6x10^(-10) erg cm^(-2) s^(-1). We searched for the presence of Fe K-shell
emission lines in the range 6.4-7 keV, significantly detecting a broad
component only in a couple of observations. Finally, we conducted a
time-resolved spectral analysis of the detected type-I X-ray burst, observed
during the outburst, finding no evidence of a photospheric radius expansion.
The type-I burst duration suggests a mix of H/He fuel.


  Using interpolators with different SU(2)_L \times SU(2)_R transformation
properties we study the chiral symmetry and spin contents of the rho- and
rho'-mesons in lattice simulations with dynamical quarks. A ratio of couplings
of the $\qbar\gamma^i{\tau}q$ and $\qbar\sigma^{0i}{\tau}q$ interpolators to a
given meson state at different resolution scales tells one about the degree of
chiral symmetry breaking in the meson wave function at these scales. Using a
Gaussian gauge invariant smearing of the quark fields in the interpolators, we
are able to extract the chiral content of mesons up to the infrared resolution
of ~1 fm. In the ground state rho meson the chiral symmetry is strongly broken
with comparable contributions of both the (0,1) + (1,0) and (1/2,1/2)_b chiral
representations with the former being the leading contribution. In contrast, in
the rho' meson the degree of chiral symmetry breaking is manifestly smaller and
the leading representation is (1/2,1/2)_b. Using a unitary transformation from
the chiral basis to the {2S +1}L_J basis, we are able to define and measure the
angular momentum content of mesons in the rest frame. This definition is
different from the traditional one which uses parton distributions in the
infinite momentum frame. The rho meson is practically a 3S_1 state with no
obvious trace of a "spin crisis". The rho' meson has a sizeable contribution of
the 3D_1 wave, which implies that the rho' meson cannot be considered as a pure
radial excitation of the rho meson.


  High-resolution imaging and long-slit spectroscopy obtained with HST,
combined with ground-based integral-field spectroscopy, provides the kinematics
of stars and gas in nearby galactic nuclei with sufficient accuracy to derive
the intrinsic dynamical structure, and to measure the mass of the central black
hole. This has revealed that many nuclei contain decoupled kinematic components
and asymmetric structures, and that nuclear and global properties of galaxies
are correlated. Higher spatial resolution and significantly increased
sensitivity are required to cover the full range of galaxy properties and
types, including the nearest powerful active radio galaxies, and to study the
evolution of galactic nuclei as a function of redshift. The prospects in this
area are discussed.


  Linear-assignment Gel'fand-Pinsker coding (LA-GPC) is a coding technique for
channels with interference known only at the transmitter, where the known
interference is treated as side-information (SI). As a special case of LA-GPC,
dirty paper coding has been shown to be able to achieve the optimal
interference-free rate for interference channels with perfect channel state
information at the transmitter (CSIT). In the cases where only the channel
distribution information at the transmitter (CDIT) is available, LA-GPC also
has good (sometimes optimal) performance in a variety of fast and slow fading
SI channels. In this paper, we design the filters in nested-lattice based
coding to make it achieve the same rate performance as LA-GPC in multiple-input
multiple-output (MIMO) channels. Compared with the random Gaussian codebooks
used in previous works, our resultant coding schemes have an algebraic
structure and can be implemented in practical systems. A simulation in a
slow-fading channel is also provided, and near interference-free error
performance is obtained. The proposed coding schemes can serve as the
fundamental building blocks to achieve the promised rate performance of MIMO
Gaussian broadcast channels with CDIT or perfect CSIT


  We consider the smooth, compactly supported solutions of the steady 3D Euler
equations of incompressible fluids constructed by Gavrilov in 2019, and we
study the corresponding fluid particle dynamics. This is an ode analysis, which
contributes to the description of Gavrilov's vector field.


  The beam coupling impedances of small discontinuities of an accelerator
vacuum chamber have been calculated [e.g., S.S. Kurennoy, R.L. Gluckstern, and
G.V. Stupakov, Phys. Rev. E 52, 4354 (1995)] for ultrarelativistic beams using
the Bethe diffraction theory. Here we extend the results to an arbitrary beam
velocity. The vacuum chamber is assumed to have an arbitrary, but uniform along
the beam path, cross section. The longitudinal and transverse coupling
impedances are derived in terms of series over cross-section eigenfunctions,
while the discontinuity shape enters via its polarizabilities. Simple explicit
formulas for two important particular cases - circular and rectangular chamber
cross sections - are presented. The impedance dependence on the beam velocity
exhibits some unusual features: for example, the reactive impedance, which
dominates in the ultrarelativistic limit, can vanish at a certain beam
velocity, or its magnitude can exceed the ultrarelativistic value many times.
In addition, we demonstrate that the same technique, the field expansion into a
series of cross-section eigenfunctions, is convenient for calculating the
space-charge impedance of uniform beam pipes with arbitrary cross section.


  We study the diffractive production of $q\bar{q}g$ jets with large transverse
momenta in the region of large diffractive masses (small $\beta$). Cross
sections for transverse and longitudinal photons are obtained in the leading
log $1/x_{\fP}$ and log $1/\beta$ approximation, keeping all powers in log
$k_t^2/Q^2$. We perform a numerical study and illustrate the angular
distribution of the three jets. We also estimate the integrated diffractive
three jet cross section and compare with the dijet cross section obtained
before.


  Compact groups of galaxies provide conditions similar to those experienced by
galaxies in the earlier universe. Recent work on compact groups has led to the
discovery of a dearth of mid-infrared transition galaxies (MIRTGs) in IRAC (3.6
- 8.0 micron) color space (Johnson et al. 2007; Walker et al. 2012) as well as
at intermediate specific star formation rates (Tzanavaris et al. 2010).
However, we find that in compact groups these mid-infrared (mid-IR) transition
galaxies in the mid-infrared dearth have already transitioned to the optical
([g-r]) red sequence. We investigate the optical color-magnitude diagram (CMD)
of 99 compact groups containing 348 galaxies and compare the optical CMD with
mid-IR color space for compact group galaxies. Utilizing redshifts available
from SDSS, we identified new galaxy members for 6 groups. By combining optical
and mid-IR data, we obtain information on both the dust and the stellar
populations in compact group galaxies. We also compare with more isolated
galaxies and galaxies in the Coma cluster, which reveals that, similar to
clusters, compact groups are dominated by optically red galaxies. While we find
that compact group transition galaxies lie on the optical red sequence,
LVL+SINGS mid-IR transition galaxies span the range of optical colors. The
dearth of mid-IR transition galaxies in compact groups may be due to a lack of
moderately star forming low mass galaxies; the relative lack of these galaxies
could be due to their relatively small gravitational potential wells. This
makes them more susceptible to this dynamic environment, thus causing them to
more easily lose gas or be accreted by larger members.


  Noisy Intermediate-Scale Quantum Computing (NISQ) has dominated headlines in
recent years, with the longer-term vision of Fault-Tolerant Quantum Computation
(FTQC) offering significant potential albeit at currently intractable resource
costs and quantum error correction (QEC) overheads. For problems of interest,
FTQC will require millions of physical qubits with long coherence times,
high-fidelity gates, and compact sizes to surpass classical systems. Just as
heterogeneous specialization has offered scaling benefits in classical
computing, it is likewise gaining interest in FTQC. However, systematic use of
heterogeneity in either hardware or software elements of FTQC systems remains a
serious challenge due to the vast design space and variable physical
constraints.
  This paper meets the challenge of making heterogeneous FTQC design practical
by introducing HetArch, a toolbox for designing heterogeneous quantum systems,
and using it to explore heterogeneous design scenarios. Using a hierarchical
approach, we successively break quantum algorithms into smaller operations
(akin to classical application kernels), thus greatly simplifying the design
space and resulting tradeoffs. Specializing to superconducting systems, we then
design optimized heterogeneous hardware composed of varied superconducting
devices, abstracting physical constraints into design rules that enable devices
to be assembled into standard cells optimized for specific operations. Finally,
we provide a heterogeneous design space exploration framework which reduces the
simulation burden by a factor of 10^4 or more and allows us to characterize
optimal design points. We use these techniques to design superconducting
quantum modules for entanglement distillation, error correction, and code
teleportation, reducing error rates by 2.6x, 10.7x, and 3.0x compared to
homogeneous systems.


  We consider a possibility to describe spin one-half and higher spins of
massive relativistic particles by means of commuting spinors. We present two
classical gauge models with the variables $x^\mu,\xi_\alpha,\chi_\alpha$, where
$\xi,\chi$ are commuting Majorana spinors. In course of quantization both
models reproduce Dirac equation. We analyze the possibility to introduce an
interaction with an external electromagnetic background into the models and to
generalize them to higher spin description. The first model admits a minimal
interaction with the external electromagnetic field, but leads to reducible
representations of the Poincare group being generalized for higher spins. The
second model turns out to be appropriate for description of the massive higher
spins. However, it seams to be difficult to introduce a minimal interaction
with an external electromagnetic field into this model. We compare our approach
with one, which uses Grassman variables, and establish a relation between them.


  We investigate the causal temperature profiles in a recent model of a
radiating star undergoing dissipative gravitational collapse without the
formation of an horizon. It is shown that this simple exact model provides a
physically reasonable behaviour for the temperature profile within the
framework of extended irreversible thermodynamics.


  We examine the mechanism of moduli stabilization by fluxes in the limit of a
large number of moduli. We conjecture that one cannot stabilize all
complex-structure moduli in F-theory at a generic point in moduli space (away
from singularities) by fluxes that satisfy the bound imposed by the tadpole
cancelation condition. More precisely, while the tadpole bound in the limit of
a large number of complex-structure moduli goes like 1/4 of the number of
moduli, we conjecture that the amount of charge induced by fluxes stabilizing
all moduli grows faster than this, and is therefore larger than the allowed
amount. Our conjecture is supported by two examples: K3 x K3 compactifications,
where by using evolutionary algorithms we find that moduli stabilization needs
fluxes whose induced charge is 44% of the number of moduli, and Type IIB
compactifications on CP^3, where the induced charge of the fluxes needed to
stabilize the D7-brane moduli is also 44% of the number of these moduli.
Proving our conjecture would rule out de Sitter vacua obtained via antibrane
uplift in long warped throats with a hierarchically small supersymmetry
breaking scale, which require a large tadpole.


  Jumps between neighboring minima in the energy landscape of both
homopolymeric and heteropolymeric chains are numerically investigated by
determining the average escape time from different valleys. The numerical
results are compared to the theoretical expression derived by Langer [J.S.
Langer, Ann. Phys. 54 (1969) 258] with reference to a 2N-dimensional space. Our
simulations indicate that the dynamics within the native valley is well
described by a sequence of thermally activated process up to temperatures well
above the folding temperature. At larger temperatures, systematic deviations
from the Langer's estimate are instead observed. Several sources for such
discrepancies are thoroughly discussed.


  Holographic dark energy (HDE), presents a dynamical view of dark energy which
is consistent with the observational data and has a solid theoretical
background. Its definition follows from the entropy-area relation $S(A)$, where
$S$ and $A$ are entropy and area respectively. In the framework of loop quantum
gravity, a modified definition of HDE called "entropy-corrected holographic
dark energy" (ECHDE) has been proposed recently to explain dark energy with the
help of quantum corrections to the entropy-area relation. Using this new
definition, we establish a correspondence between modified variable Chaplygin
gas, new modified Chaplygin gas and the viscous generalized Chaplygin gas with
the entropy corrected holographic dark energy and reconstruct the corresponding
scalar potentials which describe the dynamics of the scalar field.


  Simulations are performed of a small quantum system interacting with a
quantum environment. The system consists of various initial states of two
harmonic oscillators coupled to give normal modes. The environment is
"designed" by its level pattern to have a thermodynamic temperature. A random
coupling causes the system and environment to become entangled in the course of
time evolution. The approach to a Boltzmann distribution is observed, and
effective fitted temperatures close to the designed temperature are obtained.
All initial pure states of the system are driven to equilibrium at very similar
rates, with quick loss of memory of the initial state. The time evolution of
the von Neumann entropy is calculated as a measure of equilibration and of
quantum coherence. It is argued, contrary to common understanding, that quantum
interference and coherence are eliminated only with maximal entropy, which
corresponds thermally to infinite temperature. Implications of our results for
the notion of "classicalizing" behavior in the approach to thermal equilibrium
are briefly considered.


  We present a discrete model theory similar in structure to ordinary quantum
mechanics, but based on a finite field instead of complex amplitudes. The
interpretation of this theory involves only the "modal" concepts of possibility
and necessity rather than quantitative probability measures. Despite its
simplicity, our model theory includes entangled states and has versions of both
Bell's theorem and the no cloning theorem.


  With the increasing demands for privacy protection, privacy-preserving
machine learning has been drawing much attention in both academia and industry.
However, most existing methods have their limitations in practical
applications. On the one hand, although most cryptographic methods are provable
secure, they bring heavy computation and communication. On the other hand, the
security of many relatively efficient private methods (e.g., federated learning
and split learning) is being questioned, since they are non-provable secure.
Inspired by previous work on privacy-preserving machine learning, we build a
privacy-preserving machine learning framework by combining random permutation
and arithmetic secret sharing via our compute-after-permutation technique.
Since our method reduces the cost for element-wise function computation, it is
more efficient than existing cryptographic methods. Moreover, by adopting
distance correlation as a metric for privacy leakage, we demonstrate that our
method is more secure than previous non-provable secure methods. Overall, our
proposal achieves a good balance between security and efficiency. Experimental
results show that our method not only is up to 6x faster and reduces up to 85%
network traffic compared with state-of-the-art cryptographic methods, but also
leaks less privacy during the training process compared with non-provable
secure methods.


  Quandle Coloring Quivers are directed graph-valued invariants of classical
and virtual knots and links associated to finite quandles. Quandle action
quivers are subquivers of the full quandle coloring quiver associated to
quandle actions by elements of the coloring quandle. These quivers provide a
categorification of the quandle counting invariant associated to each element
of the quandle. We obtain new polynomial invariants called quandle action
polynomials from these quivers as decategorifications.


  The individualization-refinement paradigm provides a strong toolbox for
testing isomorphism of two graphs and indeed, the currently fastest
implementations of isomorphism solvers all follow this approach. While these
solvers are fast in practice, from a theoretical point of view, no general
lower bounds concerning the worst case complexity of these tools are known. In
fact, it is an open question whether individualization-refinement algorithms
can achieve upper bounds on the running time similar to the more theoretical
techniques based on a group theoretic approach.
  In this work we give a negative answer to this question and construct a
family of graphs on which algorithms based on the individualization-refinement
paradigm require exponential time. Contrary to a previous construction of
Miyazaki, that only applies to a specific implementation within the
individualization-refinement framework, our construction is immune to changing
the cell selector, or adding various heuristic invariants to the algorithm.
Furthermore, our graphs also provide exponential lower bounds in the case when
the $k$-dimensional Weisfeiler-Leman algorithm is used to replace the standard
color refinement operator and the arguments even work when the entire
automorphism group of the inputs is initially provided to the algorithm.


  We study the collapse of an axisymmetric liquid filament both analytically
and by means of a numerical model. The liquid filament, also known as ligament,
may either collapse stably into a single droplet or break up into multiple
droplets. The dynamics of the filament are governed by the viscosity and the
aspect ratio, and the initial perturbations of its surface. We find that the
instability of long viscous filaments can be completely explained by the
Rayleigh-Plateau instability, whereas a low viscous filament can also break up
due to end pinching. We analytically derive the transition between stable
collapse and breakup in the Ohnesorge number versus aspect ratio phase space.
Our result is confirmed by numerical simulations based on the slender jet
approximation and explains recent experimental findings by Castrejon-Pita et
al., PRL 108, 074506 (2012).


  The first large-scale deployment of private federated learning uses
differentially private counting in the continual release model as a subroutine
(Google AI blog titled "Federated Learning with Formal Differential Privacy
Guarantees"). In this case, a concrete bound on the error is very relevant to
reduce the privacy parameter. The standard mechanism for continual counting is
the binary mechanism. We present a novel mechanism and show that its mean
squared error is both asymptotically optimal and a factor 10 smaller than the
error of the binary mechanism. We also show that the constants in our analysis
are almost tight by giving non-asymptotic lower and upper bounds that differ
only in the constants of lower-order terms. Our algorithm is a matrix mechanism
for the counting matrix and takes constant time per release. We also use our
explicit factorization of the counting matrix to give an upper bound on the
excess risk of the private learning algorithm of Denisov et al. (NeurIPS 2022).
Our lower bound for any continual counting mechanism is the first tight lower
bound on continual counting under approximate differential privacy. It is
achieved using a new lower bound on a certain factorization norm, denoted by
$\gamma_F(\cdot)$, in terms of the singular values of the matrix. In
particular, we show that for any complex matrix, $A \in \mathbb{C}^{m \times
n}$, \[ \gamma_F(A) \geq \frac{1}{\sqrt{m}}\|A\|_1, \] where $\|\cdot \|$
denotes the Schatten-1 norm.
  We believe this technique will be useful in proving lower bounds for a larger
class of linear queries. To illustrate the power of this technique, we show the
first lower bound on the mean squared error for answering parity queries.


  Chemical modelling of AGB outflows is typically focused on either
non-thermodynamic equilibrium chemistry in the inner region or photon-driven
chemistry in the outer region. We include, for the first time, a comprehensive
dust-gas chemistry in our AGB outflow chemical kinetics model, including both
dust-gas interactions and grain-surface chemistry. The dust is assumed to have
formed in the inner region, and follows an interstellar-like dust-size
distribution. Using radiative transfer modelling, we obtain dust temperature
profiles for different dust types in an O-rich and a C-rich outflow. We
calculate a grid of models, sampling different outflow densities, drift
velocities between the dust and gas, and dust types. Dust-gas chemistry can
significantly affect the gas-phase composition, depleting parent and daughter
species and increasing the abundance of certain daughter species via
grain-surface formation followed by desorption/sputtering. Its influence
depends on four factors: outflow density, dust temperature, initial
composition, and drift velocity. The largest effects are for higher density
outflows with cold dust and O-rich parent species, as these species generally
have a larger binding energy. At drift velocities larger than $\sim 10$ km
s$^{-1}$, ice mantles undergo sputtering; however, they are not fully
destroyed. Models with dust-gas chemistry can better reproduce the observed
depletion of species in O-rich outflows. When including colder dust in the
C-rich outflows and adjusting the binding energy of CS, the depletion in C-rich
outflows is also better reproduced. To best interpret high-resolution molecular
line observations from AGB outflows, dust-gas interactions are needed in
chemical kinetics models.


  In this work, the authors develop regression approaches based on deep
learning to perform thread density estimation for plain weave canvas analysis.
Previous approaches were based on Fourier analysis, which is quite robust for
some scenarios but fails in some others, in machine learning tools, that
involve pre-labeling of the painting at hand, or the segmentation of thread
crossing points, that provides good estimations in all scenarios with no need
of pre-labeling. The segmentation approach is time-consuming as the estimation
of the densities is performed after locating the crossing points. In this novel
proposal, we avoid this step by computing the density of threads directly from
the image with a regression deep learning model. We also incorporate some
improvements in the initial preprocessing of the input image with an impact on
the final error. Several models are proposed and analyzed to retain the best
one. Furthermore, we further reduce the density estimation error by introducing
a semi-supervised approach. The performance of our novel algorithm is analyzed
with works by Ribera, Vel\'azquez, and Poussin where we compare our results to
the ones of previous approaches. Finally, the method is put into practice to
support the change of authorship or a masterpiece at the Museo del Prado.


  The properties of molecular gas, the fuel that forms stars, inside the cavity
of the circumnuclear disk (CND) are not well constrained. We present results of
a velocity-resolved submillimeter scan (~480 to 1250 GHz}) and [CII]158um line
observations carried out with Herschel/HIFI toward Sgr A*; these results are
complemented by a ~2'x2' CO (J=3-2) map taken with the IRAM 30 m telescope at
~7'' resolution. We report the presence of high positive-velocity emission (up
to about +300 km/s) detected in the wings of CO J=5-4 to 10-9 lines. This wing
component is also seen in H2O (1_{1,0}-1_{0,1}) a tracer of hot molecular gas;
in [CII]158um, an unambiguous tracer of UV radiation; but not in [CI]492,806
GHz. This first measurement of the high-velocity CO rotational ladder toward
Sgr A* adds more evidence that hot molecular gas exists inside the cavity of
the CND, relatively close to the supermassive black hole (< 1 pc). Observed by
ALMA, this velocity range appears as a collection of CO (J=3-2) cloudlets lying
in a very harsh environment that is pervaded by intense UV radiation fields,
shocks, and affected by strong gravitational shears. We constrain the physical
conditions of the high positive-velocity CO gas component by comparing with
non-LTE excitation and radiative transfer models. We infer T_k~400 K to 2000 K
for n_H~(0.2-1.0)x10^5 cm^-3. These results point toward the important role of
stellar UV radiation, but we show that radiative heating alone cannot explain
the excitation of this ~10-60 M_Sun component of hot molecular gas inside the
central cavity. Instead, strongly irradiated shocks are promising candidates.


  We study the density perturbation by a curvaton with a double well potential
and estimate the nonlinear parameters for non-Gaussianity and the amplitude of
gravitational wave background generated during inflation. The predicted
nonlinear parameters strongly depend on the size of a curvaton self-coupling
constant as well as the reheating temperature after inflation for a given
initial amplitude of the curvaton. The difference from usual massive
self-interacting curvaton is also emphasized.


  Research on Brain-Computer Interface (BCI) began in the 1970s and has
increased in volume and diversified significantly since then. Today BCI is
widely used for applications like assistive devices for physically challenged
users, mental state monitoring, input devices for hands-free applications,
marketing, education, security, games and entertainment. This article explores
the advantages and disadvantages of invasive and non-invasive BCI technologies
and focuses on use cases of several non-invasive technologies, namely
electroencephalogram (EEG), functional Magnetic Resonance Imaging (fMRI), Near
Infrared Spectroscopy (NIRs) and hybrid systems.


  We consider 2D Dirac fermions in the presence of three types of disorder:
random scalar potential, random gauge potential and random mass with long-range
correlations decaying as a power law. Using various methods such as the
self-consistent Born approximation (SCBA), renormalization group (RG), the
matrix Green function formalism and bosonisation we calculate the density of
states and study the full counting statistics of fermionic transport at lower
energy. The SCBA and RG show that the random correlated scalar potentials
generate an algebraically small energy scale below which the density of states
saturates to a constant value. For correlated random gauge potential, RG and
bosonisation calculations provide consistent behavior of the density of states
which diverges at zero energy in an integrable way. In the case of correlated
random mass disorder the RG flow has a nontrivial infrared stable fixed point
leading to a universal power-law behavior of the density of states and also to
universal transport properties. In contrast to uncorrelated case the correlated
scalar potential and random mass disorders give rise to deviation from the
pseudodiffusive transport already to lowest order in disorder strength.


  We examined the reliability of estimates of pseudoisothermal, Burkert and NFW
dark halo parameters for the methods based on the mass-modelling of the
rotation curves.To do it we constructed the $\chi^2$ maps for the grid of the
dark matter halo parameters for a sample of 14 disc galaxies with high quality
rotation curves from THINGS. We considered two variants of models in which: a)
the mass-to-light ratios of disc and bulge were taken as free parameters, b)
the mass-to-light ratios were fixed in a narrow range according to the models
of stellar populations.
  To reproduce the possible observational features of the real galaxies we made
tests showing that the parameters of the three halo types change critically in
the cases of a lack of kinematic data in the central or peripheral areas and
for different spatial resolutions.
  We showed that due to the degeneracy between the central densities and the
radial scales of the dark haloes there are considerable uncertainties of their
concentrations estimates. Due to this reason it is also impossible to draw any
firm conclusion about universality of the dark halo column density based on
mass-modelling of even a high quality rotation curve. The problem is not solved
by fixing the density of baryonic matter.
  In contrast, the estimates of dark halo mass within optical radius are much
more reliable. We demonstrated that one can evaluate successfully the halo mass
using the pure best-fitting method without any restrictions on the
mass-to-light ratios.


  Optomechanical systems have been shown both theoretically and experimentally
to exhibit an analogon to atomic electromagnetically induced transparency, with
sharp transmission features that are controlled by a second laser beam. Here we
investigate these effects in the regime where the fundamental nonlinear nature
of the optomechanical interaction becomes important. We demonstrate that pulsed
transistor-like switching of transmission still works even in this regime. We
also show that optomechanically induced transparency at the second mechanical
sideband could be a sensitive tool to see first indications of the nonlinear
quantum nature of the optomechanical interaction even for single-photon
coupling strengths significantly smaller than the cavity linewidth.


  We give a new proof of a theorem of Zudilin that equates a very-well-poised
hypergeometric series and a particular multiple integral. This integral
generalizes integrals of Vasilenko and Vasilyev which were proposed as tools in
the study of the arithmetic behaviour of values of the Riemann zeta function at
integers. Our proof is based on limiting cases of a basic hypergeometric
identity of Andrews.


  According to the strange quark matter hypothesis, pulsars may actually be
strange stars composed of self-bound strange quark matter. The normal matter
crust of a strange star, unlike that of a normal neutron star, is supported by
a strong electric field. A gap is then presented between the crust and the
strange quark core. Therefore, peculiar core-crust oscillation may occur in a
strange star, which can produce distinctive gravitational waves. In this paper,
the waveforms of such gravitational waves are derived using a rigid model. We
find that the gravitational waves are extremely weak and undetectable, even for
the next-generation detectors. Therefore, the seismology of a strange star is
not affected by the core-crust oscillation. Observers will have to search for
other effects to diagnose the existence of the crust.


  We derive new Bell's inequalities for entangled K0 anti-K0 pairs. This
requires 1) mutually exclusive setups allowing either K0 vs anti-K0 or KS vs KL
detection and 2) the use of kaon regenerators. The inequalities turn out to be
significantly violated by Quantum Mechanics, resulting in interesting tests of
Local Realism at phi-factories and p anti-p machines.


  Online Continual Learning (OCL) studies learning over a continuous data
stream without observing any single example more than once, a setting that is
closer to the experience of humans and systems that must learn "on-the-wild".
Yet, commonly available benchmarks are far from these real-world conditions,
because they explicitly signal different tasks, lack latent similarity
structure or assume temporal independence between different examples. Here, we
propose a new benchmark for OCL based on language modelling in which input
alternates between different languages and domains without any explicit
delimitation. Additionally, we propose new metrics to study catastrophic
forgetting in this setting and evaluate multiple baseline models based on
compositions of experts. Finally, we introduce a simple gating technique that
learns the latent similarities between different inputs, improving the
performance of a Products of Experts model.


  We address the problem of novel view synthesis (NVS) from a few sparse source
view images. Conventional image-based rendering methods estimate scene geometry
and synthesize novel views in two separate steps. However, erroneous geometry
estimation will decrease NVS performance as view synthesis highly depends on
the quality of estimated scene geometry. In this paper, we propose an
end-to-end NVS framework to eliminate the error propagation issue. To be
specific, we construct a volume under the target view and design a source-view
visibility estimation (SVE) module to determine the visibility of the
target-view voxels in each source view. Next, we aggregate the visibility of
all source views to achieve a consensus volume. Each voxel in the consensus
volume indicates a surface existence probability. Then, we present a soft
ray-casting (SRC) mechanism to find the most front surface in the target view
(i.e. depth). Specifically, our SRC traverses the consensus volume along
viewing rays and then estimates a depth probability distribution. We then warp
and aggregate source view pixels to synthesize a novel view based on the
estimated source-view visibility and target-view depth. At last, our network is
trained in an end-to-end self-supervised fashion, thus significantly
alleviating error accumulation in view synthesis. Experimental results
demonstrate that our method generates novel views in higher quality compared to
the state-of-the-art.


  We present the result of a calculation for the third and fourth moments of
the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in
QCD with full color and flavour structures. We discuss also a general
expressions for some contributions to the full four-loop anomalous dimension
obtained with the help of the method, based on LLL-algorithm, which was
proposed earlier by us for the reconstruction of a general form of the
anomalous dimension from a fixed values.


  Quantum materials are driving a technology revolution in sensing,
communication, and computing, while simultaneously testing many core theories
of the past century. Materials such as topological insulators, complex oxides,
quantum dots, color center hosting semiconductors, and other types of strongly
correlated materials can exhibit exotic properties such as edge conductivity,
multiferroicity, magnetoresistance, single photon emission, and optical-spin
locking. These emergent properties arise and depend strongly on the materials
detailed atomic scale structure, including atomic defects, dopants, and lattice
stacking. In this review, after introduction of different classes of quantum
materials and quantum excitations, we describe how progress in the field of
electron microscopy, including in situ and in operando EM, can accelerate
advances in quantum materials. Our review describes EM methods including: i)
principles and operation modes of EM, ii) EM spectroscopies, such as electron
energy loss spectroscopy, cathodoluminescence, and electron energy gain
spectroscopy, iii) 4D scanning transmission electron microscopy, iv) dynamic
and ultrafast EM, v) complimentary ultrafast spectroscopies, and vi) atomic
electron tomography. We discuss how these methods inform structure function
relations in quantum materials down to the picometer scale and femtosecond time
resolution, and how they enable high resolution manipulation of quantum
materials. Among numerous results, our review highlights how EM has enabled
identification of the 3D structure of quantum defects, measuring reversible and
metastable dynamics of quantum excitations, mapping exciton states and single
photon emission, measuring nanoscale thermal transport and coupled excitation
dynamics, and measuring the internal electric field of quantum
heterointerfaces, all at the quantum materials intrinsic atomic and near
atomic-length scale.


  In this paper we develop a 3D Lattice-Boltzmann model that recovers in the
continuous limit the two-fluids theory for plasmas, and consecuently includes
the generalizated Ohm's law. The model reproduces the magnetic reconnection
process just by given the right initial equlibrium conditions in the
magnetotail, without any assumption on the resistivity in the diffusive region.
In this model, the plasma is handled like two fluids with an interaction term,
each one with distribution functions associated to a cubic lattice with 19
velocities (D3Q19). The electromagnetic fields are considered like a third
fluid with an external force on a cubic lattice with 13 velocities (D3Q13). The
model can simulate either viscous fluids in the incompressible limit or
non-viscous compressible fluids, and sucessfully reproduces both the Hartmann
flow and the magnetic reconnection in the magnetotail. The reconnection rate
obtained with this model is R=0.109, which is in excellent agreement with the
observations.


  The DWF formulation becomes increasingly problematic at gauge couplings for
which $a^{-1}<2$ GeV, where the roughness of the gauge field leads to increased
explicit chiral symmetry breaking ($\mres$). This problem becomes especially
severe for sufficiently strong coupling where the underlying 4-dimensional
Wilson theory is in the Aoki phase. We review our attempts to find a suitable
modification of the gauge and/or the fermion action which would allow the DWF
method to work reliably at stronger coupling.


  A search for a neutrino flux difference between weekdays and weekend days was
undertaken for the average week of the Super-Kamiokande-I (SK-I) Experiment,
using the 5-day period version of the SK-I data taken from May 31st, 1996 to
July 15th, 2001. Arbitrarily uneven distributions of live time during the run
time periods were considered before rejecting the null hypothesis. Such live
time distributions were built into a robust method that calculated
time-weighted neutrino flux means. The purpose was to show that the calculated
results were unaffected by any distribution of live time, and thus that live
time had no role in rejecting the null hypothesis. A significant (p << 0.001)
difference was found and the most obvious neutrino flux change from weekdays to
weekend days can be summarized as follows: "Some neutrinos took the weekend
off, especially on Saturday".


  We present predictions for the interactions of energetic neutrinos with
matter as they propagate through Earth towards large-volume detectors. Our
results are based on state-of-the-art calculations of the high-energy
neutrino-matter interaction cross-sections, which we have implemented in the
HEDIS module of GENIE. In addition to the dominant interaction process, deep
inelastic scattering off quarks and gluons, we include the relevant subdominant
channels: (in)elastic scattering off the photon field of nucleons, coherent
scattering off the photon field of nuclei, as well as the scattering on atomic
electrons via the Glashow resonance. Our predictions for the neutrino
attenuation rates are provided by a new software package, NuPropEarth. We
quantify the dependence of our results on the cross-section model, including
nuclear corrections, the incidence angle, and the spectral index, and compare
them with other publicly available tools.


  Spin relaxation in a site-disordered Ising model within master equation
approach is studied. The $\vec{q},\omega$-dependent susceptibility of the model
is calculated and investigated. Effects described by the two-site cluster
approximation and lost by the mean field approximation are discussed.
Comparison of obtained results with dielectric measurements in
$Cs(H_{1-x}D_x)_2PO_4$ is presented.


  The various entropy bounds that exist in the literature suggest that
spacetime is fundamentally discrete, and hint at an underlying relationship
between geometry and "information". The foundation of this relationship is yet
to be uncovered, but should manifest itself in a theory of quantum gravity. We
present a measure for the maximal entropy of spherically symmetric spacelike
regions within the causal set approach to quantum gravity. In terms of the
proposal, a bound for the entropy contained in this region can be derived from
a counting of potential "degrees of freedom" associated to the Cauchy horizon
of its future domain of dependence. For different spherically symmetric
spacelike regions in Minkowski spacetime of arbitrary dimension, we show that
this proposal leads, in the continuum approximation, to Susskind's well-known
spherical entropy bound.


  Applying deep learning (DL) techniques in the electronic design automation
(EDA) field has become a trending topic. Most solutions apply well-developed DL
models to solve specific EDA problems. While demonstrating promising results,
they require careful model tuning for every problem. The fundamental question
on "How to obtain a general and effective neural representation of circuits?"
has not been answered yet. In this work, we take the first step towards solving
this problem. We propose DeepGate, a novel representation learning solution
that effectively embeds both logic function and structural information of a
circuit as vectors on each gate. Specifically, we propose transforming circuits
into unified and-inverter graph format for learning and using signal
probabilities as the supervision task in DeepGate. We then introduce a novel
graph neural network that uses strong inductive biases in practical circuits as
learning priors for signal probability prediction. Our experimental results
show the efficacy and generalization capability of DeepGate.


  The spatial positioning of chromosomes relative to functional nuclear bodies
is intertwined with genome functions such as transcription. However, the
sequence patterns and epigenomic features that collectively influence chromatin
spatial positioning in a genome-wide manner are not well understood. Here, we
develop a new transformer-based deep learning model called UNADON, which
predicts the genome-wide cytological distance to a specific type of nuclear
body, as measured by TSA-seq, using both sequence features and epigenomic
signals. Evaluations of UNADON in four cell lines (K562, H1, HFFc6, HCT116)
show high accuracy in predicting chromatin spatial positioning to nuclear
bodies when trained on a single cell line. UNADON also performed well in an
unseen cell type. Importantly, we reveal potential sequence and epigenomic
factors that affect large-scale chromatin compartmentalization to nuclear
bodies. Together, UNADON provides new insights into the principles between
sequence features and large-scale chromatin spatial localization, which has
important implications for understanding nuclear structure and function.