  Average trapping time (ATT) is central in the trapping problem since it is a
key indicator characterizing the efficiency of the problem. Previous research
has provided the scaling of a lower bound of the ATT for random walks in
general networks with a deep trap. However, it is still not well understood in
which networks this minimal scaling can be reached. Particularly, explicit
quantitative results for ATT in such networks, even in a specific network, are
lacking, in spite that such networks shed light on the design for optimal
networks with the highest trapping efficiency. In this paper, we study the
trapping problem taking place on a hierarchical scale-free network with a
perfect trap. We focus on four representative cases with the immobile trap
located at the root, a peripheral node, a neighbor of the root with a single
connectivity, and a farthest node from the root, respectively. For all the four
cases, we obtain the closed-form formulas for the ATT, as well as its leading
scalings. We show that for all the four cases of trapping problems, the
dominating scalings of ATT can reach the predicted minimum scalings. This work
deepens the understanding of behavior of trapping in scale-free networks, and
is helpful for designing networks with the most efficient transport process.


  This review compiles results of experimental and theoretical studies on thin
films and quantum structures of semiconductors with randomly distributed Mn
ions, which exhibit spintronic functionalities associated with collective
ferromagnetic spin ordering. Properties of p-type Mn-containing III-V as well
as II-VI, V_2-VI_3, IV-VI, I-II-V, and elemental group IV semiconductors are
described paying particular attention to the most thoroughly investigated
system (Ga,Mn)As that supports the hole-mediated ferromagnetic order up to 190
K for the net concentration of Mn spins below 10%. Multilayer structures
showing efficient spin injection and spin-related magnetotransport properties
as well as enabling magnetization manipulation by strain, light, electric
fields, and spin currents are presented together with their impact on metal
spintronics. The challenging interplay between magnetic and electronic
properties in topologically trivial and non-trivial systems is described,
emphasizing the entangled roles of disorder and correlation at the carrier
localization boundary. Finally, the case of dilute magnetic insulators is
considered, such as (Ga,Mn)N, where low temperature spin ordering is driven by
short-ranged superexchange that is ferromagnetic for certain charge states of
magnetic impurities.


  Building on Bosca's method, we extend to tame ray class groups the results on
capitulation of ideals of a number field by composition with abelian extensions
of a subfield first studied by Gras. More precisely, for every extension of
number fields K/k, where at least one infinite place splits completely, and
every squarefree divisor m of K, we prove that there exist infinitely many
abelian extensions F/k such that the ray class group mod m of K capitulates in
KF. As a consequence we generalize to tame ray class groups the results of
Kurihara on triviality of class groups for maximal abelian pro-extensions of
totally real number fields.


  This paper discusses the possible observation of an integrated gear tooth
crack analysis procedure that employs the combined approach of variable mode
decomposition (VMD) and time synchronous averaging (TSA) based on the coupled
electromechanical gearbox (CEMG) system. This paper also incorporates the
modified Lagrangian formulation to model the CEMG system by considering
Rayleigh's dissipative potential. An analytical improved time-varying mesh
stiffness (IAM-TVMS) with different levels of gear tooth crack depts is also
incorporated into the CEMG system to inspect the influence of cracks on the
system's dynamic behavior. Dynamic responses of the CEMG system with different
tooth crack levels have been used for further investigations. For the first
time, the integrated approach of variable mode decomposition (VMD) and
time-synchronous averaging (TSA) has been presented to analyze the dynamic
behaviour of CEMG systems at the different gear tooth cracks have been
experienced as non-stationary and complex vibration signals with noise. Based
on the integrated approach of VMD-TSA, two types of nonlinear features, i.e.,
Lyapunov Exponent (LE) and Correlation Dimension (CD), were calculated to
predict the level of chaotic vibration and complexity of the CEMG system at the
different levels of gear tooth cracks. Also, the LE and CD are used as chaotic
behaviour features to predict the gear tooth crack propagation level. The
results of the proposed approach show significant improvements in the gear
tooth crack analysis based on the chaotic features. Also, this is one of the
first attempts to study the CEMG system using chaotic features based on the
combined approach of VMD-TSA.


  Using traditional morphological classifications of galaxies in 10
intermediate-redshift (z~0.5) clusters observed with WFPC-2 on the Hubble Space
Telescope, we derive relations between morphology and local galaxy density
similar to that found by Dressler for low-redshift clusters. Taken
collectively, the `morphology-density' relationship, M-D, for these more
distant, presumably younger clusters is qualitatively similar to that found for
the local sample, but a detailed comparison shows two substantial differences:
(1) For the clusters in our sample, the M-D relation is strong in centrally
concentrated ``regular'' clusters, those with a strong correlation of radius
and surface density, but nearly absent for clusters that are less concentrated
and irregular, in contrast to the situation for low redshift clusters where a
strong relation has been found for both. (2) In every cluster the fraction of
elliptical galaxies is as large or larger than in low-redshift clusters, but
the S0 fraction is 2-3 times smaller, with a proportional increase of the
spiral fraction. Straightforward, though probably not unique, interpretations
of these observations are (1) morphological segregation proceeds
hierarchically, affecting richer, denser groups of galaxies earlier, and (2)
the formation of elliptical galaxies predates the formation of rich clusters,
and occurs instead in the loose-group phase or even earlier, but S0's are
generated in large numbers only after cluster virialization.


  This paper proposes a Robust One-Step Estimator(ROSE) to solve the Byzantine
failure problem in distributed M-estimation when a moderate fraction of node
machines experience Byzantine failures. To define ROSE, the algorithms use the
robust Variance Reduced Median Of the Local(VRMOL) estimator to determine the
initial parameter value for iteration, and communicate between the node
machines and the central processor in the Newton-Raphson iteration procedure to
derive the robust VRMOL estimator of the gradient, and the Hessian matrix so as
to obtain the final estimator. ROSE has higher asymptotic relative efficiency
than general median estimators without increasing the order of computational
complexity. Moreover, this estimator can also cope with the problems involving
anomalous or missing samples on the central processor. We prove the asymptotic
normality when the parameter dimension p diverges as the sample size goes to
infinity, and under weaker assumptions, derive the convergence rate. Numerical
simulations and a real data application are conducted to evidence the
effectiveness and robustness of ROSE.


  Let $(G,K)$ be one of the following classical irreducible Hermitian symmetric
pairs of noncompact type: $(SU(p,q), S(U(p) \times U(q))),(Sp(n,R), U(n))$, or
$(SO*(2n), U(n))$. Let $G_{\mathbb C}$ and $K_{\mathbb C}$ be complexifications
of $G$ and $K$, respectively, and let $P$ be a maximal parabolic subgroup of
$G_{\mathbb C}$ whose Levi subgroup is $K_{\mathbb C}$. Let $V$ be the
holomorphic part of the complexifiaction of the tangent space at the origin of
$G/K$. It is well known that the ring of $K_{\mathbb C}$-invariant differential
operators on $V$ has a generating system $\{\varGamma_k \}$ given in terms of
determinant or Pfaffian that plays an essential role in the Capelli identities.
Our main result of this paper is that determinant or Pfaffian of the ``moment
map'' on the holomorphic cotangent bundle of $G_{\mathbb C}/P$ provides a
generating function for the principal symbols of $\varGamma_k$'s.


  In this paper we show that embedded and compact $C^1$ manifolds have finite
integral Menger curvature if and only if they are locally graphs of certain
Sobolev-Slobodeckij spaces. Furthermore, we prove that for some intermediate
energies of integral Menger type a similar characterization of objects with
finite energy can be given.


  Recently, time-dependent current-density functional theory has been extended
to include the dynamical interaction of quantum systems with external
environments [Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. Here we show that such
a theory allows us to study a fundamentally important class of phenomena
previously inaccessible by standard density-functional methods: the decay of
excited systems. As an example we study the decay of an ensemble of excited He
atoms, and discuss these results in the context of quantum measurement theory.


  The Ti$_2$Ni and the related $\eta$-carbide structure are known to exhibit
various intriguing physical properties. The Ti$_2$Ni structure with the cubic
space group $Fd\bar{3}m$ is surprisingly complex, consisting of a unit cell
with 96 metal atoms. The related $\eta$-carbide compounds correspond to a
filled version of the Ti$_2$Ni structure. Here, we report on the structure and
superconductivity in the $\eta$-carbide type suboxides Ti$_4$M$_2$O with M =
Co, Rh, Ir. We have successfully synthesized all three compounds in single
phase form. We find all three compounds to be type-II bulk superconductors with
transition temperatures of $T_{\rm c}$ = 2.7, 2.8, and 5.4 K, and with
normalized specific heat jumps of $\Delta C/\gamma T_{\rm c}$ = 1.65, 1.28, and
1.80 for Ti$_4$Co$_2$O, Ti$_4$Rh$_2$O, and Ti$_4$Ir$_2$O, respectively. We find
that all three superconductors, exhibit high upper-critical fields.
Particularly noteworthy is Ti$_4$Ir$_2$O with an upper critical field of $\mu_0
H_{\rm c2}{\rm (0)}$ =~16.06~T, which exceeds by far the weak-coupling Pauli
limit of 9.86~T. The role of the void filling light atom X has so far been
uncertain for the overall physical properties of these materials. Herein, we
have successfully grown single crystals of Ti$_2$Co. In contrast to the
metallic $\eta$-carbide type suboxides Ti$_4$M$_2$O, we find that Ti$_2$Co
displays a semimetallic behavior. Hence, the octahedral void-filling oxygen
plays a crucial role for the overall physical properties, even though its
effect on the crystal structure is small. Our results indicate that the design
of new superconductors by incorporation of electron-acceptor atoms may in the
Ti$_2$Ni-type structures and other materials with crystallographic void
position be a promising future approach. The remarkably high upper critical
fields, in this family of compounds, may furthermore spark significant future
interest.


  In this paper we show that the solution of the discrete Double Bubble problem
over $\mathbb{Z}^2$ is at most the ceiling function plus two of the continuous
solution to the Double Bubble problem, with respect to the $\ell^1$ norm, found
in \cite{morgan1998wulff} and \cite{duncan2020elementary}.


  In this paper we perform a comprehensive study of the main sources of random
and systematic errors in stellar mass measurement for galaxies using their
Spectral Energy Distributions (SEDs). We use mock galaxy catalogs with
simulated multi-waveband photometry (from U-band to mid-infrared) and known
redshift, stellar mass, age and extinction for individual galaxies. Given
different parameters affecting stellar mass measurement (photometric S/N
ratios, SED fitting errors, systematic effects, the inherent degeneracies and
correlated errors), we formulated different simulated galaxy catalogs to
quantify these effects individually. We studied the sensitivity of stellar mass
estimates to the codes/methods used, population synthesis models, star
formation histories, nebular emission line contributions, photometric
uncertainties, extinction and age. For each simulated galaxy, the difference
between the input stellar masses and those estimated using different simulation
catalogs, $\Delta\log(M)$, was calculated and used to identify the most
fundamental parameters affecting stellar masses. We measured different
components of the error budget, with the results listed as follows: (1). no
significant bias was found among different codes/methods, with all having
comparable scatter; (2). A source of error is found to be due to photometric
uncertainties and low resolution in age and extinction grids; (3). The median
of stellar masses among different methods provides a stable measure of the mass
associated with any given galaxy; (4). The deviations in stellar mass strongly
correlate with those in age, with a weaker correlation with extinction; (5).
the scatter in the stellar masses due to free parameters are quantified, with
the sensitivity of the stellar mass to both the population synthesis codes and
inclusion of nebular emission lines studied.


  We present new large field-of-view ($\sim$1\deg$\times$1\deg) Ca-CN
photometry of the prototypical metal-rich globular cluster 47 Tucanae (NGC
104). Our results are the following. (1) The populational number ratios of the
red giant branch (RGB) and red horizontal branch (RHB) are in excellent
agreement: n(CN-w):n(CN-s) = 30:70 ($\pm$1--2), where the CN-w and CN-s stand
for the CN-weak and CN-strong populations, respectively. Both the CN-s RGB and
RHB populations are more centrally concentrated than those of CN-w populations
are. (2) Our photometric metallicities of individual RGB stars in each
population can be well described by bimodal distributions with two metallicity
peaks, [Fe/H] $\sim$ $-$0.72 and $-$0.92 dex, where the metal-poor components
occupy $\sim$ 13% of the total RGB stars. The metal-poor populations are more
significantly centrally concentrated than the metal-rich populations, showing a
similar result that we found in M3. (3) The RGB bump $V$ magnitudes of
individual populations indicate that there is no difference in the helium
abundance between the two metal-poor populations, while the helium enhancement
of $\Delta Y$ $\sim$ 0.02--0.03 is required between the the two metal-rich
populations. (4) The RHB morphology of 47 Tuc appears to support our idea of
the bimodal metallicity distribution of the cluster. We suggest that 47 Tuc
could be another example of merger remnants of two globular clusters, similar
to M3 and M22.


  We investigate structural implications arising from the condition that a
given directed graph does not interpret, in the sense of primitive positive
interpretation with parameters or orbits, every finite structure. Our results
generalize several theorems from the literature and yield further algebraic
invariance properties that must be satisfied in every such graph. Algebraic
properties of this kind are tightly connected to the tractability of constraint
satisfaction problems, and we obtain new such properties even for infinite
countably categorical graphs. We balance these positive results by showing the
existence of a countably categorical hypergraph that fails to interpret some
finite structure, while still lacking some of the most essential algebraic
invariance properties known to hold for finite structures.


  We derive the criterion for the Bose-Einstein condensation (BEC) of a
Gaussian field $\phi$ (real or complex) in the thermodynamic limit. The field
is characterized by its covariance function and the control parameter is the
intensity $u=\|\phi\|_2^2/V$, where $V$ is the volume of the box containing the
field. We show that for any dimension $d$ (including $d=1$), there is a class
of covariance functions for which $\phi$ exhibits a BEC as $u$ is increased
through a critical value $u_c$. In this case, we investigate the probability
distribution of the part of $u$ contained in the condensate. We show that
depending on the parameters characterizing the covariance function and the
dimension $d$, there can be two distinct types of condensate: a Gaussian
distributed "normal" condensate with fluctuations scaling as $1/\sqrt{V}$, and
a non Gaussian distributed "anomalous" condensate. A detailed analysis of the
anomalous condensate is performed for a one-dimensional system ($d=1$).
Extending this one-dimensional analysis to exactly the point of transition
between normal and anomalous condensations, we find that the condensate at the
transition point is still Gaussian distributed but with anomalously large
fluctuations scaling as $\sqrt{\ln(L)/L}$, where $L$ is the system length. The
conditional spectral density of $\phi$, knowing $u$, is given for all the
regimes (with and without BEC).


  Majorana zero modes are non-Abelian quasiparticles that emerge on the edges
of topological phases of superconductors. Evidence of their presence has been
reported in transport measurements on engineered superconducting-based
nanostructures. In this manuscript we identify signatures of a topologically
protected dynamical manipulation of Majorana zero modes via continuous
transport measurement during the manipulation. Specifically, we show that, in a
two-terminal geometry, the heat pumped across the terminals at low temperature
and voltage bias is characterized by a universal value. We show that this
feature is inherent to the presence of Majorana zero modes and discuss its
robustness against temperature, voltage bias and the detailed coupling to the
contacts.


  Imitation learning trains a policy by mimicking expert demonstrations.
Various imitation methods were proposed and empirically evaluated, meanwhile,
their theoretical understanding needs further studies. In this paper, we
firstly analyze the value gap between the expert policy and imitated policies
by two imitation methods, behavioral cloning and generative adversarial
imitation. The results support that generative adversarial imitation can reduce
the compounding errors compared to behavioral cloning, and thus has a better
sample complexity. Noticed that by considering the environment transition model
as a dual agent, imitation learning can also be used to learn the environment
model. Therefore, based on the bounds of imitating policies, we further analyze
the performance of imitating environments. The results show that environment
models can be more effectively imitated by generative adversarial imitation
than behavioral cloning, suggesting a novel application of adversarial
imitation for model-based reinforcement learning. We hope these results could
inspire future advances in imitation learning and model-based reinforcement
learning.


  Supersymmetric probe branes satisfy the kappa-symmetry condition which
ensures that the action is minimized with respect to both variations of the
embedding and of the world-volume gauge field. We observe that the
kappa-symmetry condition for a D7-brane in an imaginary self-dual (ISD)
background can be generalized yielding minimization of the action with respect
to variations of the gauge field only but not of the embedding. This provides a
new way to construct non-BPS solutions for D7-branes once the embedding
extremizes the geometrical volume of the brane. We then apply this method to
the Klebanov-Strassler background and find a new D7-anti D7-brane configuration
that realizes the spontaneous breaking of flavor chiral symmetry as evidenced
by the Goldstone boson identified in the spectrum. This result generalizes our
previous construction for the Klebanov-Witten model. We compare our setup with
the Sakai-Sugimoto model and discuss possible applications to QCD-like physics.


  We characterize the selection function of RAVE using 2MASS as our underlying
population, which we assume represents all stars which could have potentially
been observed. We evaluate the completeness fraction as a function of position,
magnitude, and color in two ways: first, on a field-by-field basis, and second,
in equal-size areas on the sky. Then, we consider the effect of the RAVE
stellar parameter pipeline on the final resulting catalogue, which in principle
limits the parameter space over which our selection function is valid. Our
final selection function is the product of the completeness fraction and the
selection function of the pipeline. We then test if the application of the
selection function introduces biases in the derived parameters. To do this, we
compare a parent mock catalogue generated using Galaxia with a mock-RAVE
catalogue where the selection function of RAVE has been applied. We conclude
that for stars brighter than I = 12, between $4000 \rm K < T_{\rm eff} < 8000
\rm K$ and $0.5 < \rm{log}\,g < 5.0$, RAVE is kinematically and chemically
unbiased with respect to expectations from Galaxia.


  We consider the problem of counting matchings in planar graphs. While perfect
matchings in planar graphs can be counted by a classical polynomial-time
algorithm, the problem of counting all matchings (possibly containing unmatched
vertices, also known as defects) is known to be #P-complete on planar graphs.
To interpolate between the hard case of counting matchings and the easy case of
counting perfect matchings, we study the parameterized problem of counting
matchings with exactly k unmatched vertices in a planar graph G, on input G and
k. This setting has a natural interpretation in statistical physics, and it is
a special case of counting perfect matchings in k-apex graphs (graphs that can
be turned planar by removing at most k vertices).
  Starting from a recent #W[1]-hardness proof for counting perfect matchings on
k-apex graphs, we obtain that counting matchings with k unmatched vertices in
planar graphs is #W[1]-hard. In contrast, given a plane graph G with s
distinguished faces, there is an $O(2^s \cdot n^3)$ time algorithm for counting
those matchings with k unmatched vertices such that all unmatched vertices lie
on the distinguished faces. This implies an $f(k,s)\cdot n^{O(1)}$ time
algorithm for counting perfect matchings in k-apex graphs whose apex
neighborhood is covered by s faces.


  Providing reliable and surreptitious communications is difficult in the
presence of adaptive and resourceful state level censors. In this paper we
introduce Tithonus, a framework that builds on the Bitcoin blockchain and
network to provide censorship-resistant communication mechanisms. In contrast
to previous approaches, we do not rely solely on the slow and expensive
blockchain consensus mechanism but instead fully exploit Bitcoin's peer-to-peer
gossip protocol. We develop adaptive, fast and cost effective data
communication solutions that camouflage client requests into inconspicuous
Bitcoin transactions. We propose solutions to securely request and transfer
content, with unobservability and censorship resistance, and free,
pay-per-access and subscription based payment options. When compared to
state-of-the-art Bitcoin writing solutions, Tithonus reduces the cost of
transferring data to censored clients by 2 orders of magnitude and increases
the goodput by 3 to 5 orders of magnitude. We show that Tithonus client
initiated transactions are hard to detect, while server initiated transactions
cannot be censored without creating split world problems to the Bitcoin
blockchain.


  The confinement-induced resonances for trapped bosons in the cigar-shaped and
pancake geometries are studied within the generalized Gross-Pitaevskii
equations, which are a simplified version of the Hartree-Fock-Bogoliubov
approximation. Although the Hartree-Fock-Bogoliubov method is considered
applicable only for small interparticle interactions, the resonance
denominators for the chemical potential are obtained in both quasi-one and
quasi-two dimensions. A useful integral representation of the one-particle
Green's function are found for the cylindrical confinement. We find the
position of a smoothed resonance for the chemical potential in the pancake
geometry at positive scattering length.


  We consider a nonlinear area preserving Anosov map M on the torus phase
space, which is the simplest example of a fully chaotic dynamics. We are
interested in the quantum dynamics for long time, generated by the unitary
quantum propagator Mq. The usual semi-classical Trace formula expresses
Tr(Mq^t) for finite time t, in the limit hbar->0, in terms of periodic orbits
of M of period t. Recent work reach time t<< tE/6 where tE=log(1/hbar)/lambda
is the Ehrenfest time, and lambda is the Lyapounov coefficient. Using a
semi-classical normal form description of the dynamics uniformly over phase
space, we show how to extend the trace formula for longer time of the form t=
C.tE where C is any constant, with an arbitrary small error.


  We investigate asymmetry of information in the context of robust approach to
pricing and hedging of financial derivatives. We consider two agents, one who
only observes the stock prices and another with some additional information,
and investigate when the pricing--hedging duality for the former extends to the
latter. We introduce a general framework to express the superhedging and market
model prices for an informed agent. Our key insight is that an informed agent
can be seen as a regular agent who can restrict her attention to a certain
subset of possible paths. We use results of Hou & Ob\l\'oj on robust approach
with beliefs to establish the pricing--hedging duality for an informed agent.
Our results cover number of scenarios, including information arriving before
trading starts, arriving after static position in European options is formed
but before dynamic trading starts or arriving at some point before the
maturity. For the latter we show that the superhedging value satisfies a
suitable dynamic programming principle, which is of independent interest.


  Memristive systems were proposed in 1976 by Leon Chua and Sung Mo Kang as a
model for 2-terminal passive nonlinear dynamical systems which exhibit memory
effects. Such systems were originally shown to be relevant to the modeling of
action potentials in neurons in regards to the Hodgkin-Huxley model and, more
recently, to the modeling of thin film materials such as TiO2-x proposed for
non-volatile resistive memory. However, over the past 50 years a variety of
3-terminal non-passive dynamical devices have also been shown to exhibit memory
effects similar to that predicted by the memristive system model. This article
extends the original memristive systems framework to incorporate 3-terminal,
non-passive devices and explains the applicability of such dynamic systems
models to 1) the Widrow-Hoff memistor, 2) floating gate memory cells, and 3)
nano-ionic FETs.
  Keywords-memristive systems, memistor, transconductance, synaptic transistor,
non-linear dynamic systems


  Proteins perform their functions usually by interacting with other proteins.
Predicting which proteins interact is a fundamental problem. Experimental
methods are slow, expensive, and have a high rate of error. Many computational
methods have been proposed among which sequence-based ones are very promising.
However, so far no such method is able to predict effectively the entire human
interactome: they require too much time or memory. We present SPRINT (Scoring
PRotein INTeractions), a new sequence-based algorithm and tool for predicting
protein-protein interactions. We comprehensively compare SPRINT with
state-of-the-art programs on seven most reliable human PPI datasets and show
that it is more accurate while running orders of magnitude faster and using
very little memory. SPRINT is the only program that can predict the entire
human interactome. Our goal is to transform the very challenging problem of
predicting the entire human interactome into a routine task. The source code of
SPRINT is freely available from github.com/lucian-ilie/SPRINT/ and the datasets
and predicted PPIs from www.csd.uwo.ca/faculty/ilie/SPRINT/.


  Nailing down the unknown neutrino mixing angle theta_13 is one of the most
important goals in current lepton physics. In this context, we perform a global
analysis of neutrino oscillation data, focusing on theta_13, and including
recent results [Neutrino 2008, Proceedings of the XXIII International
Conference on Neutrino Physics and Astrophysics, Christchurch, New Zealand,
2008 (unpublished)]. We discuss two converging hints of theta_13>0, each at the
level of ~1sigma: an older one coming from atmospheric neutrino data, and a
newer one coming from the combination of solar and long-baseline reactor
neutrino data. Their combination provides the global estimate sin^2(theta_13) =
0.016 +- 0.010 (1sigma), implying a preference for \theta_13>0 with
non-negligible statistical significance (~90% C.L.). We discuss possible
refinements of the experimental data analyses, which might sharpen such
intriguing indication.


  The interaction between an intense laser and a relativistic dense electron
beam propagating in the same direction could down-shift the laser frequency.
This process, which can be used to generate a coherent THz radiation, is
theoretically analyzed. With a set of practically relevant parameters, it is
suggested that the radiation energy could reach the order of 1 mJ per shot in
the duration of 100 pico-second, or the temporal radiation power of 10 MW.


  Quantum physics is a long established content in high school curricula. More
recently, alternative approaches based on information-theoretical formulations
of quantum theory have been discussed, in which conceptual emphases change in
comparison to established didactical approaches. In particular, the notions of
"superposition" and "entanglement" are brought into the center of discussion in
these approaches. Likewise, there is a broad public interest in the new
applications of quantum physics such as quantum computing, which has led to a
variety of popular depictions. In this paper we identify common inaccuracies
and errors in these representations, explain the technical background and make
first recommendations to avoid misunderstandings. Our initial focus is on the
notion of "superposition".
  --
  Die Quantenphysik ist seit vielen Jahren ein etablierter Inhalt der
Oberstufenphysik. In j\"ungerer Zeit werden alternative Zug\"ange \"uber die
informationstheoretische Formulierung der Quantentheorie diskutiert, bei denen
sich konzeptionelle und begriffliche Schwerpunkte im Vergleich zu etablierten
Elementarisierungen ver\"andern. Im Besonderen die Begriffe "Superposition" und
"Verschr\"ankung" werden bei diesen Zug\"angen in das Zentrum der Diskussion
ger\"uckt. Ebenfalls besteht ein breites \"offentliches Interesse an den neuen
Anwendungen der Quantenphysik wie dem Quanten-computer, das zu einer Vielzahl
popul\"arer Darstellungen gef\"uhrt hat. In dieser Arbeit identifizieren wir
verbreitete Ungenauigkeiten und Fehler in diesen Darstellungen, erl\"autern den
fachlichen Hintergrund und machen erste Empfehlungen, um Missverst\"andnisse zu
vermeiden. Unser Schwerpunkt liegt dabei zun\"achst auf dem Begriff der
"Superposition".


  Recently, a novel framework for semi-device-independent quantum
prepare-and-measure protocols has been proposed, based on the assumption of a
limited distinguishability between the prepared quantum states. Here, we
discuss the problem of characterizing an unknown quantum measurement device in
this setting. We present several methods to attack this problem. Considering
the simplest scenario of two preparations with lower bounded overlap, we show
that genuine 3-outcome POVMs can be certified, even in the presence of noise.
Moreover, we show that the optimal POVM for performing unambiguous state
discrimination can be self-tested.


  For a compact connected Riemannian manifold with smooth boundary, by
computing the full symbol of the elastic Dirichlet-to-Neumann map, we prove
that the elastic Dirichlet-to-Neumann map can uniquely determine the partial
derivatives of all orders of the Riemannian metric on the boundary of the
manifold.


  The evaluation of Fock exchange is often the computationally most expensive
part of hybrid functional density functional theory calculations in a
systematically improvable, complete basis. In this work, we employ a Tucker
tensor based approach that substantially accelerates the evaluation of the
action of Fock exchange by transforming 3-dimensional convolutional integrals
into a tensor product of 1-dimensional convolution integrals. Our numerical
implementation uses a parallelization strategy that balances the memory and
communication bottlenecks, alongside overalapping compute and communication
operations to enhance computational efficiency and parallel scalability. The
accuracy and computational efficiency is demonstrated on various systems,
including Pt clusters of various sizes and a $\text{TiO}_{\text{2}}$ cluster
with 3,684 electrons.


  This article is divided in two parts. In the first part we endow a certain
ring of ``Drinfeld quasi-modular forms'' for $\GL_2(\FF_q[T])$ (where $q$ is a
power of a prime) with a system of "divided derivatives" (or hyperderivations).
This ring contains Drinfeld modular forms as defined by Gekeler in \cite{Ge},
and the hyperdifferential ring obtained should be considered as a close
analogue in positive characteristic of famous Ramanujan's differential system
relating to the first derivatives of the classical Eisenstein series of weights
2, 4 and 6. In the second part of this article we prove that, when $q\not=2,3$,
if ${\cal P}$ is a non-zero hyperdifferential prime ideal, then it contains the
Poincar\'e series $h=P_{q+1,1}$ of \cite{Ge}. This last result is the analogue
of a crucial property proved by Nesterenko \cite{Nes} in characteristic zero in
order to establish a multiplicity estimate.


  Cascaded stimulated Brillouin scattering (SBS) is a complex nonlinear optical
process that results in the generation of several optical waves that are
frequency shifted by an acoustic resonance frequency. Four-wave mixing (FWM)
between these Brillouin shifted optical waves can create an equally spaced
optical frequency comb with a stable spectral phase, i.e. a Brillouin frequency
comb (BFC). Here, we investigate phase-locking of the spectral components of
BFCs, considering FWM interactions arising from the Kerr-nonlinearity as well
as from coupling by the acoustic field. Deriving for the first time the
coupled-mode equations that include all relevant nonlinear interactions, we
examine the contribution of the various nonlinear processes to phase-locking,
and show that different regimes can be obtained that depend on the length scale
on which the field amplitudes vary.


  Noninformative uniform priors are staples of Bayesian inference, especially
in Bayesian machine learning. This study challenges the assumption that they
are optimal and their use in Bayesian inference yields optimal outcomes.
Instead of using arbitrary noninformative uniform priors, we propose a machine
learning based alternative method, learning optimal priors from data by
maximizing a target function of interest. Applying na\"ive Bayes text
classification methodology and a search algorithm developed for this study, our
system learned priors from data using the positive predictive value metric as
the target function. The task was to find Wikipedia articles that had not (but
should have) been categorized under certain Wikipedia categories. We conducted
five sets of experiments using separate Wikipedia categories. While the
baseline models used the popular Bayes-Laplace priors, the study models learned
the optimal priors for each set of experiments separately before using them.
The results showed that the study models consistently outperformed the baseline
models with a wide margin of statistical significance (p < 0.001). The measured
performance improvement of the study model over the baseline was as high as
443% with the mean value of 193% over five Wikipedia categories.


  We study the problem of empirical minimization for variance-type functionals
over functional classes. Sharp non-asymptotic bounds for the excess variance
are derived under mild conditions. In particular, it is shown that under some
restrictions imposed on the functional class fast convergence rates can be
achieved including the optimal non-parametric rates for expressive classes in
the non-Donsker regime under some additional assumptions. Our main applications
include variance reduction and optimal control.


  The study of the ethical impact of AI and the design of trustworthy systems
needs the analysis of the scenarios where AI systems are used, which is related
to the software engineering concept of "use case" and the "intended purpose"
legal term. However, there is no standard methodology for use case
documentation covering the context of use, scope, functional requirements and
risks of an AI system. In this work, we propose a novel documentation
methodology for AI use cases, with a special focus on the affective computing
domain. Our approach builds upon an assessment of use case information needs
documented in the research literature and the recently proposed European
regulatory framework for AI. From this assessment, we adopt and adapt the
Unified Modeling Language (UML), which has been used in the last two decades
mostly by software engineers. Each use case is then represented by an UML
diagram and a structured table, and we provide a set of examples illustrating
its application to several affective computing scenarios.


  We address the problem of stability of one-dimensional non-periodic
ground-state configurations with respect to finite-range perturbations of
interactions in classical lattice-gas models. We show that a relevant property
of non-periodic ground-state configurations in this context is their
homogeneity. The so-called strict boundary condition says that the number of
finite patterns of a configuration have bounded fluctuations on any finite
subsets of the lattice. We show that if the strict boundary condition is not
satisfied, then in order for non-periodic ground-state configurations to be
stable, interactions between particles should not decay faster than
$1/r^{\alpha}$ with $\alpha>2$. In the Thue-Morse ground state, number of
finite patterns may fluctuate as much as the logarithm of the lenght of a
lattice subset. We show that the Thue-Morse ground state is unstable for any
$\alpha >1$ with respect to arbitrarily small two-body interactions favoring
the presence of molecules consisting of two spins up or down. We also
investigate Sturmian systems defined by irrational rotations on the circle.
They satisfy the strict boundary condition but nevertheless they are unstable
for $\alpha>3$.


  We study how active-region-scale flux tubes rise buoyantly from the base of
the convection zone to near the solar surface by embedding a thin flux tube
model in a rotating spherical shell of solar-like turbulent convection. These
toroidal flux tubes that we simulate range in magnetic field strength from 15
kG to 100 kG at initial latitudes of 1 degree to 40 degrees in both
hemispheres. This article expands upon Weber, Fan, and Miesch (Astrophys. J.,
741, 11, 2011) (Article 1) with the inclusion of tubes with magnetic flux of
10^20 Mx and 10^21 Mx, and more simulations of the previously investigated case
of 10^22 Mx, sampling more convective flows than the previous article, greatly
improving statistics. Observed properties of active regions are compared to
properties of the simulated emerging flux tubes, including: the tilt of active
regions in accordance with Joy's Law as in Article 1, and in addition the
scatter of tilt angles about the Joy's Law trend, the most commonly occurring
tilt angle, the rotation rate of the emerging loops with respect to the
surrounding plasma, and the nature of the magnetic field at the flux tube apex.
We discuss how these diagnostic properties constrain the initial field strength
of the active region flux tubes at the bottom of the solar convection zone, and
suggest that flux tubes of initial magnetic field strengths of \geq 40 kG are
good candidates for the progenitors of large (10^21 Mx to 10^22 Mx) solar
active regions, which agrees with the results from Article 1 for flux tubes of
10^22 Mx. With the addition of more magnetic flux values and more simulations,
we find that for all magnetic field strengths, the emerging tubes show a
positive Joy's Law trend, and that this trend does not show a statistically
significant dependence on the magnetic flux.


  A simple and transparent example of a non-autonomous flow system, with
hyperbolic strange attractor is suggested. The system is constructed on a basis
of two coupled van der Pol oscillators, the characteristic frequencies differ
twice, and the parameters controlling generation in both oscillators undergo a
slow periodic counter-phase variation in time. In terms of stroboscopic
Poincar\'{e} section, the respective four-dimensional mapping has a hyperbolic
strange attractor of Smale - Williams type. Qualitative reasoning and
quantitative data of numerical computations are presented and discussed, e.g.
Lyapunov exponents and their parameter dependencies. A special test for
hyperbolicity based on statistical analysis of distributions of angles between
stable and unstable subspaces of a chaotic trajectory has been performed.
Perspectives of further comparative studies of hyperbolic and non-hyperbolic
chaotic dynamics in physical aspect are outlined.


  The nucleosynthesis of Be and B by spallation processes provides unique
insight into the origin of cosmic rays. Namely, different spallation schemes
predict sharply different trends for the growth of LiBeB abundances with
respect to oxygen. ``Primary'' mechanisms predict BeB $\propto$ O, and are well
motivated by the data if O/Fe is constant at low metallicity. In contrast,
``secondary'' mechanisms predict BeB $\propto$ O$^2$ and are consistent with
the data if O/Fe increases towards low metallicity as some recent data suggest.
Clearly, any primary mechanism, if operative, will dominate early in the
history of the Galaxy. In this paper, we fit the BeB data to a two-component
scheme which includes both primary and secondary trends. In this way, the data
can be used to probe the period in which primary mechanisms are effective. We
analyze the data using consistent stellar atmospheric parameters based on
Balmer line data and the continuum infrared flux. Results depend sensitively on
Pop II O abundances and, unfortunately, on the choice of stellar parameters.
When using recent results which show O/Fe increasing toward lower metallicity,
a two-component Be-O fits indicates that primary and secondary components
contribute equally at [O/H]$_{eq}$ = -1.8 for Balmer line data; and
[O/H]$_{eq}$ = -1.4 to -1.8 for IRFM. We apply these constraints to recent
models for LiBeB origin. The Balmer line data does not show any evidence for
primary production. On the other hand, the IRFM data does indicate a preference
for a two-component model, such as a combination of standard GCR and
metal-enriched particles accelerated in superbubbles. These conclusions rely on
a detailed understanding of the abundance data including systematic effects
which may alter the derived O-Fe and BeB-Fe relations.


  A new method is described for constructing initial data for a binary
neutron-star (BNS) system in quasi-equilibrium circular orbit. Two formulations
for non-conformally flat data, waveless (WL) and near-zone helically symmetric
(NHS), are introduced; in each formulation, the Einstein-Euler system, written
in 3+1 form on an asymptotically flat spacelike hypersurface, is exactly solved
for all metric components, including the spatially non-conformally flat
potentials, and for irrotational flow. A numerical method applicable to both
formulations is explained with an emphasis on the imposition of a spatial gauge
condition. Results are shown for solution sequences of irrotational BNS with
matter approximated by parametrized equations of state that use a few segments
of polytropic equations of state. The binding energy and total angular momentum
of solution sequences computed within the conformally flat --
Isenberg-Wilson-Mathews (IWM) -- formulation are closer to those of the third
post-Newtonian (3PN) two point particles up to the closest orbits, for the more
compact stars, whereas sequences resulting from the WL/NHS formulations deviate
from the 3PN curve even more for the sequences with larger compactness. We
think it likely that this correction reflects an overestimation in the IWM
formulation as well as in the 3PN formula, by $\sim 1$ cycle in the
gravitational wave phase during the last several orbits. The work suggests that
imposing spatial conformal flatness results in an underestimate of the
quadrupole deformation of the components of binary neutron-star systems in the
last few orbits prior to merger.


  Next location prediction is of great importance for many location-based
applications and provides essential intelligence to business and governments.
In existing studies, a common approach to next location prediction is to learn
the sequential transitions with massive historical trajectories based on
conditional probability. Unfortunately, due to the time and space complexity,
these methods (e.g., Markov models) only use the just passed locations to
predict next locations, without considering all the passed locations in the
trajectory. In this paper, we seek to enhance the prediction performance by
considering the travel time from all the passed locations in the query
trajectory to a candidate next location. In particular, we propose a novel
method, called Travel Time Difference Model (TTDM), which exploits the
difference between the shortest travel time and the actual travel time to
predict next locations. Further, we integrate the TTDM with a Markov model via
a linear interpolation to yield a joint model, which computes the probability
of reaching each possible next location and returns the top-rankings as
results. We have conducted extensive experiments on two real datasets: the
vehicle passage record (VPR) data and the taxi trajectory data. The
experimental results demonstrate significant improvements in prediction
accuracy over existing solutions. For example, compared with the Markov model,
the top-1 accuracy improves by 40% on the VPR data and by 15.6% on the Taxi
data.


  Weyl semimetals are expected to open up new horizons in physics and materials
science because they provide the first realization of Weyl fermions and exhibit
protected Fermi arc surface states. However, they had been found to be
extremely rare in nature. Recently, a family of compounds, consisting of TaAs,
TaP, NbAs and NbP was predicted as Weyl semimetal candidates. Here, we
experimentally realize a Weyl semimetal state in TaP. Using photoemission
spectroscopy, we directly observe the Weyl fermion cones and nodes in the bulk
and the Fermi arcs on the surface. Moreover, we find that the surface states
show an unexpectedly rich structure, including both topological Fermi arcs and
several topologically-trivial closed contours in the vicinity of the Weyl
points, which provides a promising platform to study the interplay between
topological and trivial surface states on a Weyl semimetal's surface. We
directly demonstrate the bulk-boundary correspondence and hence establish the
topologically nontrivial nature of the Weyl semimetal state in TaP, by
resolving the net number of chiral edge modes on a closed path that encloses
the Weyl node. This also provides, for the first time, an experimentally
practical approach to demonstrating a bulk Weyl fermion from a surface state
dispersion measured in photoemission.


  Spectral and transport properties of electrons in confined phosphorene
systems are investigated in a five hopping parameter tight-binding model, using
analytical and numerical techniques. The main emphasis is on the properties of
the topological edge states accommodated by the quasi-flat band that
characterizes the phosphorene energy spectrum. We show, in the particular case
of phosphorene, how the breaking of the bipartite lattice structure gives rise
to the electron-hole asymmetry of the energy spectrum. The properties of the
topological edge states in the zig-zag nanoribbons are analyzed under different
aspects: degeneracy, localization, extension in the Brillouin zone, dispersion
of the quasi-flat band in magnetic field. The finite-size phosphorene plaquette
exhibits a Hofstadter-type spectrum made up of two unequal butterflies
separated by a gap, where a quasi-flat band composed of zig-zag edge states is
located. The transport properties are investigated by simulating a four-lead
Hall device (importantly, all leads are attached on the same zig-zag side), and
using the Landauer-Buttiker formalism. We find out that the chiral edge states
due to the magnetic field yield quantum Hall plateaus, but the topological edge
states in the gap do not support the quantum Hall effect and prove a
dissipative behavior. By calculating the complex eigenenergies of the
non-Hermitian effective Hamiltonian that describes the open system
(plaquette+leads), we prove the superradiance effect in the energy range of the
quasi-flat band, with consequences for the density of states and electron
transmission properties.


  A discrete spherical harmonics method is developed for the radiative transfer
problem in inhomogeneous polarized planar atmosphere illuminated at the top by
a collimated sunlight while the bottom reflects the radiation. The method
expands both the Stokes vector and the phase matrix in a finite series of
generalized spherical functions and the resulting vector radiative transfer
equation is expressed in a set of polar directions. Hence, the polarized
characteristics of the radiance within the atmosphere at any polar direction
and azimuthal angle can be determined without linearization and/or
interpolations. The spatial dependent of the problem is solved using the
spectral Chebyshev method. The emergent and transmitted radiative intensity and
the degree of polarization are predicted for both Rayleigh and Mie scattering.
The discrete spherical harmonics method predictions using 36 streams are found
in good agreement with benchmark literature results. The maximum deviation
between the proposed method and literature results and for absolue value of the
polar directions greater than 0.1 is less than 0.5% and 0.9% for the Rayleigh
and Mie scattering, respectively. These deviations for directions close to zero
are about 3% and 10 % for Rayleigh and Mie scattering, respectively.


  We study the conformational freedom of a protein made by two rigid domains
connected by a flexible linker. The conformational freedom is represented as an
unknown probability distribution on the space of allowed states. A new
algorithm for the calculation of the Maximum Allowable Probability is proposed,
which can be extended to any type of measurements. In this paper we use Pseudo
Contact Shifts and Residual Dipolar Coupling. We reconstruct a single central
tendency in the distribution and discuss in depth the results.


  We show the existence of canonical heights of subvarieties for bounded
sequences of morphisms and give some applications.


  Distributed Complex Event Processing (DCEP) is a commonly used paradigm to
detect and act on situational changes of many applications, including the
Internet of Things (IoT). DCEP achieves this using a simple specification of
analytical tasks on data streams called operators and their distributed
execution on a set of infrastructure. The adaptivity of DCEP to the dynamics of
IoT applications is essential and very challenging in the face of changing
demands concerning Quality of Service. In our previous work, we addressed this
issue by enabling transitions, which allow for the adaptive use of multiple
operator placement mechanisms. In this article, we extend the transition
methodology by optimizing the costs of transition and analyzing the behaviour
using multiple operator placement mechanisms. Furthermore, we provide an
extensive evaluation on the costs of transition imposed by operator migrations
and learning, as it can inflict overhead on the performance if operated
uncoordinatedly.


  Based on density functional theory calculations, we elucidated the origin of
multifunctional properties for cubic antiperovskites with noncollinear magnetic
ground states, which can be attributed to strong isotropic and anisotropic
magnetostructural coupling. 16 out of 54 stable magnetic antiperovskites
M$_3$XZ (M = Cr, Mn, Fe, Co, and Ni; X = selected elements from Li to Bi except
for noble gases and 4f rare-earth metals; and Z = C and N) are found to exhibit
the $\Gamma_{4g}$/$\Gamma_{5g}$ (i.e., characterized by irreducible
representations) antiferromagnetic magnetic configurations driven by frustrated
exchange coupling and strong magnetocrystalline anisotropy. Using the magnetic
deformation as an effective proxy, the isotropic magnetostructural coupling is
characterized, and it is observed that the paramagnetic state is critical to
understand the experimentally observed negative thermal expansion and to
predict the magnetocaloric performance. Moreover, the piezomagnetic and
piezospintronic effects induced by biaxial strain are investigated. It is
revealed that there is not a strong correlation between the induced
magnetization and anomalous Hall conductivities by the imposed strain.
Interestingly, the anomalous Hall/Nernst conductivities can be significantly
tailored by the applied strain due to the fine-tuning of the Weyl points
energies, leading to promising spintronic applications.


  This work introduces EUvsDisinfo, a multilingual dataset of trustworthy and
disinformation articles related to pro-Kremlin themes. It is sourced directly
from the debunk articles written by experts leading the EUvsDisinfo project.
Our dataset is the largest to-date resource in terms of the overall number of
articles and distinct languages. It also provides the largest topical and
temporal coverage. Using this dataset, we investigate the dissemination of
pro-Kremlin disinformation across different languages, uncovering
language-specific patterns targeting specific disinformation topics. We further
analyse the evolution of topic distribution over an eight-year period, noting a
significant surge in disinformation content before the full-scale invasion of
Ukraine in 2022. Lastly, we demonstrate the dataset's applicability in training
models to effectively distinguish between disinformation and trustworthy
content in multilingual settings.


  We show that a dissipative two-dimensional Raman lattice can be engineered in
a two-component ultracold atomic gas, where the interplay of the
two-dimensional spin-orbit coupling and lightinduced atom loss gives rise to a
density flow diagonal to the underlying square lattice. The flow is driven by
the non-Hermitian corner skin effect, under which eigenstates localize toward
one corner of the system. We illustrate that the topological edge states of the
system can only be accounted for by the non-Bloch band theory where the
deformation of the bulk eigenstates are explicitly considered. The directional
flow can be detected through the dynamic evolution of an initially localized
condensate in the lattice, or by introducing an immobile impurity species that
interact spin-selectively with a condensate in the ground state of the Raman
lattice.


  In this paper we relate the cohomology of $J$-invariant forms to the
Dolbeault cohomology of an almost complex manifold. We find necessary and
sufficient condition for the inclusion of the former into the latter to be true
up to isomorphism. We also extend some results obtained by J. Cirici and S.O.
Wilson about the computation of the left-invariant cohomology of nilmanifolds
to the setting of solvmanifolds. Several examples are given.


  As is well known, quantum mechanical behavior cannot, in general, be
simulated by a local hidden variables model. Most -if not all- the proofs of
this incompatibility refer to the correlations which arise when each of two (or
more) systems separated in space is subjected to a single ideal measurement.
This setting is good enough to show contradictions between local hidden
variables models and quantum mechanics in the case of pure states. However, as
shown here, it is not powerful enough in the case of mixtures. This is
illustrated by an example. In this example, the correlations which arise when
each of two systems separated in space is subjected to a single ideal
measurement are classical; only when each system is subjected to a {\it
sequence} of ideal measurements non-classical correlations are obtained. We
also ask whether there are situations for which even this last procedure is not
powerful enough and non-ideal measurements have to be considered as well.


  Explicit extensions representing cocycles $x \in Ext_{A}^{s,t}(F_2,F_2)$ are
useful in calculating Steenrod operations $Sq^i : Ext_{A}^{s,t}(F_2,F_2)
\longrightarrow Ext_{A}^{s+i,2t}(F_2,F_2)$ by a method devised by the second
author. This can be used to identify explicit cocycles in the minimal
resolutions produced by the first author's computer programs, and this
information is useful in determining differentials in the Adams spectral
sequence.


  ENN Science and Technology Development Co., Ltd. (ENN) is committed to
generating fusion energy in an environmentally friendly and cost-effective
manner, which requires abundant aneutronic fuel. Proton-boron ( p-$^{11}$B or
p-B) fusion is considered an ideal choice for this purpose. Recent studies have
suggested that p-B fusion, although challenging, is feasible based on new
cross-section data, provided that a hot ion mode and high wall reflection can
be achieved to reduce electron radiation loss. The high beta and good
confinement of the spherical torus (ST) make it an ideal candidate for p-B
fusion. By utilizing the new spherical torus energy confinement scaling law, a
reactor with a major radius $R_0=4$ m, central magnetic field $B_0=6$ T,
central temperature $T_{i0}=150$ keV, plasma current $I_p=30$ MA, and hot ion
mode $T_i/T_e=4$ can yield p-B fusion with $Q>10$. A roadmap for p-B fusion has
been developed, with the next-generation device named EHL-2. EHL stands for ENN
He-Long, which literally means ``peaceful Chinese Loong". The main target
parameters include $R_0\simeq1.05$ m, $A\simeq1.85$, $B_0\simeq3$ T,
$T_{i0}\simeq30$ keV, $I_p\simeq3$ MA, and $T_i/T_e\geq2$. The existing ST
device EXL-50 was simultaneously upgraded to provide experimental support for
the new roadmap, involving the installation and upgrading of the central
solenoid, vacuum chamber, and magnetic systems. The construction of the
upgraded ST fusion device, EXL-50U, was completed at the end of 2023, and it
achieved its first plasma in January 2024. The construction of EHL-2 is
estimated to be completed by 2026.


  We study the steady-state characteristics and the transient behavior of the
nonequilibrium double-dot Aharonov-Bohm interferometer using analytical tools
and numerical simulations. Our simple setup includes noninteracting degenerate
quantum dots that are coupled to two biased metallic leads at the same
strength. A magnetic flux $\Phi$ is piercing the setup perpendicularly. As we
tune the degenerate dots energies away from the symmetric point we observe four
nontrivial magnetic flux control effects: (i) flux dependency of the dots
occupation, (ii) magnetic flux induced occupation difference between the dots,
at degeneracy, (iii) the effect of "phase-localization" of the dots coherence
holds only at the symmetric point, while in general both real and imaginary
parts of the coherence are nonzero, and (iv) coherent evolution survives even
when the dephasing strength, introduced into our model using B\"uttiker probe,
is large and comparable to the dots energies and the bias voltage. Moreover,
not only finite dephasing strength does not destroy the coherence features, it
can provide new type of coherent oscillations. These four phenomena take place
when the dots energies are gated, to be positioned away from the symmetric
point, demonstrating that the combination of bias voltage, magnetic flux and
gating field, can provide delicate controllability over the occupation of each
of the quantum dots, and their coherence.


  We argue that contemporary jet substructure techniques might facilitate a
more direct measurement of hard medium-induced gluon bremsstrahlung in
heavy-ion collisions, and focus specifically on the "soft drop declustering"
procedure that singles out the two leading jet substructures. Assuming coherent
jet energy loss, we find an enhancement of the distribution of the energy
fractions shared by the two substructures at small subjet energy caused by hard
medium-induced gluon radiation. Departures from this approximation are
discussed, in particular, the effects of colour decoherence and the
contamination of the grooming procedure by soft background. Finally, we propose
a complementary observable, that is the ratio of the two-pronged probability in
Pb-Pb to proton-proton collisions and discuss its sensitivity to various energy
loss mechanisms.


  In this paper, based on the principles of gauge/gravity duality and
considering the so called \textit{hydrodynamic} limit we compute various charge
transport properties for a class of strongly coupled non relativistic CFTs
corresponding to $ z=2 $ fixed point whose dual gravitational counter part
could be realized as the consistent truncation of certain non relativistic $ Dp
$ branes in the non extremal limit. From our analysis we note that unlike the
case for the AdS black branes, the charge diffusion constant in the non
relativistic background scales differently with the temperature. This shows a
possible violation of the universal bound on the charge conductivity to
susceptibility ratio in the context of non relativistic holography.


  Large language model (LLM) platforms, such as ChatGPT, have recently begun
offering an app ecosystem to interface with third-party services on the
internet. While these apps extend the capabilities of LLM platforms, they are
developed by arbitrary third parties and thus cannot be implicitly trusted.
Apps also interface with LLM platforms and users using natural language, which
can have imprecise interpretations. In this paper, we propose a framework that
lays a foundation for LLM platform designers to analyze and improve the
security, privacy, and safety of current and future third-party integrated LLM
platforms. Our framework is a formulation of an attack taxonomy that is
developed by iteratively exploring how LLM platform stakeholders could leverage
their capabilities and responsibilities to mount attacks against each other. As
part of our iterative process, we apply our framework in the context of
OpenAI's plugin (apps) ecosystem. We uncover plugins that concretely
demonstrate the potential for the types of issues that we outline in our attack
taxonomy. We conclude by discussing novel challenges and by providing
recommendations to improve the security, privacy, and safety of present and
future LLM-based computing platforms.


  Fault tolerance is achieved through multiply redundant hardware systems in
large civil aircraft. This means of achieving fault tolerance is infeasible for
small compact unmanned aerial vehicles. In this paper we apply a fault tolerant
control system which exploits analytical redundancy rather than hardware
redundancy to an actual UAV model currently in operation via model-in-the-loop
simulation. The fault tolerant control system comprises a nonlinear model
predictive controller integrated with an unscented Kalman filter for fault
detection and identification. The results show that our fault tolerant control
system design is able to identify engine failure within seconds of fault
occurrence and distribute control authority to the healthy actuators to
maintain safe flight.


  Non-experts have long made important contributions to machine learning (ML)
by contributing training data, and recent work has shown that non-experts can
also help with feature engineering by suggesting novel predictive features.
However, non-experts have only contributed features to prediction tasks already
posed by experienced ML practitioners. Here we study how non-experts can design
prediction tasks themselves, what types of tasks non-experts will design, and
whether predictive models can be automatically trained on data sourced for
their tasks. We use a crowdsourcing platform where non-experts design
predictive tasks that are then categorized and ranked by the crowd.
Crowdsourced data are collected for top-ranked tasks and predictive models are
then trained and evaluated automatically using those data. We show that
individuals without ML experience can collectively construct useful datasets
and that predictive models can be learned on these datasets, but challenges
remain. The prediction tasks designed by non-experts covered a broad range of
domains, from politics and current events to health behavior, demographics, and
more. Proper instructions are crucial for non-experts, so we also conducted a
randomized trial to understand how different instructions may influence the
types of prediction tasks being proposed. In general, understanding better how
non-experts can contribute to ML can further leverage advances in Automatic ML
and has important implications as ML continues to drive workplace automation.


  The rapid nuetron-capture process (r process) produces roughly half of the
elements heavier than iron. The path and abundances produced are uncertain,
however, because of the lack of nuclear strucure information on important
neutron-rich nuclei. We are studying nuclei on or near the r-process path via
single-nucleon transfer reactions on neutron-rich radioactive beams at ORNL's
Holifield Radioactive Ion Beam Facility (HRIBF). Owing to the difficulties in
studying these reactions in inverse kinematics, a variety of experimental
approaches are being developed. We present the experimental methods and initial
results.


  Thin surfaces, such as the leaves of a plant, pose a significant challenge
for implicit surface reconstruction techniques, which typically assume a
closed, orientable surface. We show that by approximately interpolating a point
cloud of the surface (augmented with off-surface points) and restricting the
evaluation of the interpolant to a tight domain around the point cloud, we need
only require an orientable surface for the reconstruction. We use polyharmonic
smoothing splines to fit approximate interpolants to noisy data, and a
partition of unity method with an octree-like strategy for choosing subdomains.
This method enables us to interpolate an N-point dataset in O(N) operations. We
present results for point clouds of capsicum and tomato plants, scanned with a
handheld device. An important outcome of the work is that sufficiently smooth
leaf surfaces are generated that are amenable for droplet spreading
simulations.


  In this paper, we give the general forms of the minimal $L$ matrix (the
elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann
weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal
representation of the $A_{n-1}$ series elliptic quantum group given by Felder
and Varchenko. The explicit dependence of elements of $L$-matrices on spectral
parameter $z$ are given. They are of five different forms (A(1-4) and B). The
algebra for the coefficients (which do not depend on $z$) are given. The
algebra of form A is proved to be trivial, while that of form B obey
Yang-Baxter equation (YBE). We also give the PBW base and the centers for the
algebra of form B.


  Existing generative retrieval (GR) approaches rely on training-based
indexing, i.e., fine-tuning a model to memorise the associations between a
query and the document identifier (docid) of a relevant document.
Training-based indexing has three limitations: high training overhead,
under-utilization of the pre-trained knowledge of large language models (LLMs),
and challenges in adapting to a dynamic document corpus. To address the above
issues, we propose a novel few-shot indexing-based GR framework (Few-Shot GR).
It has a novel few-shot indexing process, where we prompt an LLM to generate
docids for all documents in a corpus, ultimately creating a docid bank for the
entire corpus. During retrieval, we feed a query to the same LLM and constrain
it to generate a docid within the docid bank created during indexing, and then
map the generated docid back to its corresponding document. Few-Shot GR relies
solely on prompting an LLM without requiring any training, making it more
efficient. Moreover, we devise few-shot indexing with one-to-many mapping to
further enhance Few-Shot GR. Experiments show that Few-Shot GR achieves
superior performance to state-of-the-art GR methods that require heavy
training.


  We propose a combination of the Eulerian Lagrangian Localised Adjoint Method
(ELLAM) and the Modified Method of Characteristics (MMOC) for time-dependent
advection-domina\-ted PDEs. The combined scheme, so-called GEM scheme, takes
advantages of both ELLAM scheme (mass conservation) and MMOC scheme (easier
computations), while at the same time avoids their disadvantages (respectively,
harder tracking around the injection regions, and loss of mass).
  We present a precise analysis of mass conservation properties for these three
schemes, and after achieving global mass balance, an adjustment yielding local
volume conservation is then proposed. Numerical results for all three schemes
are then compared, illustrating the advantages of the GEM scheme.
  A convergence result of the MMOC scheme, motivated by our previous work on
the convergence of ELLAM schemes, is provided, which can be extended to obtain
the convergence of GEM scheme.


  We give a complete combinatorial characterization of homogeneous quadratic
relations of "universal character" valid for minors of quantum matrices (more
precisely, for minors in the quantized coordinate ring $O_q(M_{m,n}(K))$ of
$m\times n$ matrices over a field $K$, where $q\in K^\ast$). This is obtained
as a consequence of a study of quantized minors of matrices generated by paths
in certain planar graphs, called SE-graphs, generalizing the ones associated
with Cauchon diagrams. Our efficient method of verifying universal quadratic
identities for minors of quantum matrices is illustrated with many appealing
examples.


  We investigate the quasinormal modes of a massless scalar field in a
Schwarzschild black hole, which is deformed due to noncommutative corrections.
We introduce the deformed Schwarzschild black hole solution, which depends on
the noncommutative parameter $\Theta$. We then extract the master equation as a
Schr\"odinger-like equation, giving the explicit expression of the effective
potential which is modified due to the noncommutative corrections. After that,
we solve the master equation numerically. The significance of these results is
twofold. Firstly, our results can be related to the detection of gravitational
waves by the near future gravitational wave detectors, such as LISA, which will
have a significantly increased accuracy. In particular, these observed
gravitational waves produced by binary strong gravitational systems have
oscillating modes which can provide valuable information. Secondly, our results
can serve as an additional tool to test the predictions of GR, as well as to
examine the possible detection of this kind of gravitational corrections.


  This article extends recent results on log-Coulomb gases in a $p$-field $K$
(i.e., a nonarchimedean local field) to those in its projective line
$\mathbb{P}^1(K)$, where the latter is endowed with the $PGL_2$-invariant Borel
probability measure and spherical metric. Our first main result is an explicit
combinatorial formula for the canonical partition function of log-Coulomb gases
in $\mathbb{P}^1(K)$ with arbitrary charge values. Our second main result is
called the "$(q+1)$th Power Law", which relates the grand canonical partition
functions for one-component gases in $\mathbb{P}^1(K)$ (where all particles
have charge 1) to those in the open and closed unit balls of $K$ in a simple
way. The final result is a quadratic recurrence for the canonical partition
functions for one-component gases in both unit balls of $K$ and in
$\mathbb{P}^1(K)$. In addition to efficient computation of the canonical
partition functions, the recurrence provides their "$q\to 1$" limits and
"$q\mapsto q^{-1}$" functional equations.


  A well-known conjecture asserts that smooth threefolds $X\subset\{\mathbb
P}^5$ are quadratically normal with the only exception of the Palatini scroll.
As a corollary of a more general statement we obtain the following result,
which is related to the previous conjecture: If $X\subset\{\mathbb P}^5$ is not
quadratically normal, then its triple curve is reducible. Similar results are
also given for higher dimensional varieties.


  The mode III fracture problem for a hexagonal lattice is discussed and
compared with square and triangular lattices.


  In this note, we give an alternative proof of the following result. Let p, q
>= 2 be two multiplicatively independent integers. If an infinite set of
integers is both p- and q-recognizable, then it is syndetic. Notice that this
result is needed in the classical proof of the celebrated Cobham?s theorem.
Therefore the aim of this paper is to complete [13] and [1] to obtain an
accessible proof of Cobham?s theorem.


  Realistic predictions are made for lepton flavour violating and flavour
changing neutral current decays in the large tan beta regime of a SUSY-seesaw
model. Lepton flavour violating neutral Higgs decays are discussed within this
framework along with the highly constraining charged lepton decays l_i --> l_j
+ gamma. In the b-s system the important constraint from b --> s + gamma is
studied in conjunction with the rare FCNC Bs --> mu mu (tau mu) decays and the
recently measured Delta Ms.


  We revisit Walds analysis in the context of spin-one fields in three
dimensions. A key technical difference from Walds is the role played by the
three dimensional completely antisymmetric tensor. We show how this changes the
analysis as well as the result.


  In Ciuperca (2012) (Ciuperca. Model selection by LASSO methods in a
change-point model, Stat. Papers, 2012; (in press)), the author considered a
linear regression model with multiple change-points occurring at unknown times.
In particular, the author studied the asymptotic properties of the LASSO-type
and of the adaptive LASSO estimators. While the established results seem
interesting, we point out some major errors in proof of the most important
result of the quoted paper. Further, we present a corrected result and proof.


  This paper investigates the geometric properties of a special case of the
two-sided system given by $2 \times 2$ tropical commuting constraints. Given a
finite matrix $A \in \mathbb{R}^{2\times 2}$, the paper studies the extremals
of the tropical polyhedral cone generated by the entries of matrices $B$ such
that $A \otimes B = B \otimes A$ and proposes a criterion to test whether two
$2\times 2$ matrices commute in max linear algebra.


  In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we
study randomly driven $(1+1)$ dimensional conformal field theories (CFTs), a
family of quantum many-body systems with soluble non-equilibrium quantum
dynamics. The sequence of driving Hamiltonians is drawn from an independent and
identically distributed random ensemble. At each driving step, the deformed
Hamiltonian only involves the energy-momentum density spatially modulated at a
single wavelength and therefore induces a M\"obius transformation on the
complex coordinates. The non-equilibrium dynamics is then determined by the
corresponding sequence of M\"obius transformations, from which the Lyapunov
exponent $\lambda_L$ is defined. We use Furstenberg's theorem to classify the
dynamical phases and show that except for a few \emph{exceptional points} that
do not satisfy Furstenberg's criteria, the random drivings always lead to a
heating phase with the total energy growing exponentially in the number of
driving steps $n$ and the subsystem entanglement entropy growing linearly in
$n$ with a slope proportional to central charge $c$ and the Lyapunov exponent
$\lambda_L$. On the contrary, the subsystem entanglement entropy at an
exceptional point could grow as $\sqrt{n}$ while the total energy remains to
grow exponentially. In addition, we show that the distributions of the operator
evolution and the energy density peaks are also useful characterizations to
distinguish the heating phase from the exceptional points: the heating phase
has both distributions to be continuous, while the exceptional points could
support finite convex combinations of Dirac measures depending on their
specific type. In the end, we compare the field theory results with the lattice
model calculations for both the entanglement and energy evolution and find
remarkably good agreement.


  We present a comprehensive study of Magnetospheric Multiscale (MMS)
spacecraft encounter with KHI during a geomagnetic storm, focusing on
elucidating key turbulence properties and reconnection signatures observed at
the edges of KH vortices. The spectral slope for electric field stays
approximately constant for frequencies below the ion cyclotron frequency and
exhibits a break around the lower hybrid frequency, indicating wave activity.
Furthermore, MMS observes a current sheet accompanied by intense electron jets
and features consistent with strong guide-field asymmetric reconnection across
the magnetopause. Substantial agyrotropy (by a factor of 10) in electron
distribution functions is observed in the reconnecting current sheet and at the
edges of KH. Our observation presents a multi-scale view into KH turbulence
under strongly driven conditions and into the dynamics occurring at electron
dissipation scales.


  The cross section value of doubly charmonium production in e+e- annihilations
have been estimated at interaction energy 10.6 GeV. The quarkonium wave
function shape, as well as the nonzero value of charm quark have been taken
into account.


  We present a study of exclusion processes on networks as models for complex
transport phenomena and in particular for active transport of motor proteins
along the cytoskeleton. We argue that active transport processes on networks
spontaneously develop density heterogeneities at various scales. These
heterogeneities can be regulated through a variety of multi-scale factors, such
as the interplay of exclusion interactions, the non-equilibrium nature of the
transport process and the network topology.
  We show how an effective rate approach allows to develop an understanding of
the stationary state of transport processes through complex networks from the
phase diagram of one single segment. For exclusion processes we rationalize
that the stationary state can be classified in three qualitatively different
regimes: a homogeneous phase as well as inhomogeneous network and segment
phases.
  In particular, we present here a study of the stationary state on networks of
three paradigmatic models from non-equilibrium statistical physics: the totally
asymmetric simple exclusion process, the partially asymmetric simple exclusion
process and the totally asymmetric simple exclusion process with Langmuir
kinetics. With these models we can interpolate between equilibrium (due to
bi-directional motion along a network or infinite diffusion) and
out-of-equilibrium active directed motion along a network. The study of these
models sheds further light on the emergence of density heterogeneities in
active phenomena.


  Considering viscous friction that varies spatially and temporally, the
general expressions for entropy production, free energy, and entropy extraction
rates are derived to a Brownian particle that walks in an overdamped and
underdamped media. Via the well known stochastic approaches to underdamped and
overdamped media, the thermodynamic expressions first derived at trajectory
level then generalized to an ensemble level. To study the non-equilibrium
thermodynamic features of a Brownian particle that hops in a medium where its
viscosity varies on time, a Brownian particle that walks on a periodic
isothermal medium (in the presence or absence of load) is considered. The exact
analytical results depict that in the absence of load $f=0$, the entropy
production rate ${\dot e}_{p}$ approaches the entropy extraction rate ${\dot
h}_{d}=0$. This is reasonable since any system which is in contact with a
uniform temperature should obey the detail balance condition in a long time
limit. In the presence of load and when the viscous friction decreases either
spatially or temporally, the entropy $S(t)$ monotonously increases with time
and saturates to a constant value as $t$ further steps up. The entropy
production rate ${\dot e}_{p}$ decreases in time and at steady state (in the
presence of load), ${\dot e}_{p}={\dot h}_{d}>0$. On the contrary, when the
viscous friction increases either spatially or temporally, the rate of entropy
production as well as the rate of entropy extraction monotonously steps up
showing that such systems are inherently irreversible.


  We introduce the task of open-vocabulary visual instance search (OVIS). Given
an arbitrary textual search query, Open-vocabulary Visual Instance Search
(OVIS) aims to return a ranked list of visual instances, i.e., image patches,
that satisfies the search intent from an image database. The term "open
vocabulary" means that there are neither restrictions to the visual instance to
be searched nor restrictions to the word that can be used to compose the
textual search query. We propose to address such a search challenge via
visual-semantic aligned representation learning (ViSA). ViSA leverages massive
image-caption pairs as weak image-level (not instance-level) supervision to
learn a rich cross-modal semantic space where the representations of visual
instances (not images) and those of textual queries are aligned, thus allowing
us to measure the similarities between any visual instance and an arbitrary
textual query. To evaluate the performance of ViSA, we build two datasets named
OVIS40 and OVIS1600 and also introduce a pipeline for error analysis. Through
extensive experiments on the two datasets, we demonstrate ViSA's ability to
search for visual instances in images not available during training given a
wide range of textual queries including those composed of uncommon words.
Experimental results show that ViSA achieves an mAP@50 of 21.9% on OVIS40 under
the most challenging setting and achieves an mAP@6 of 14.9% on OVIS1600
dataset.


  Visual Language Tracking (VLT) enhances single object tracking (SOT) by
integrating natural language descriptions from a video, for the precise
tracking of a specified object. By leveraging high-level semantic information,
VLT guides object tracking, alleviating the constraints associated with relying
on a visual modality. Nevertheless, most VLT benchmarks are annotated in a
single granularity and lack a coherent semantic framework to provide scientific
guidance. Moreover, coordinating human annotators for high-quality annotations
is laborious and time-consuming. To address these challenges, we introduce
DTLLM-VLT, which automatically generates extensive and multi-granularity text
to enhance environmental diversity. (1) DTLLM-VLT generates scientific and
multi-granularity text descriptions using a cohesive prompt framework. Its
succinct and highly adaptable design allows seamless integration into various
visual tracking benchmarks. (2) We select three prominent benchmarks to deploy
our approach: short-term tracking, long-term tracking, and global instance
tracking. We offer four granularity combinations for these benchmarks,
considering the extent and density of semantic information, thereby showcasing
the practicality and versatility of DTLLM-VLT. (3) We conduct comparative
experiments on VLT benchmarks with different text granularities, evaluating and
analyzing the impact of diverse text on tracking performance. Conclusionally,
this work leverages LLM to provide multi-granularity semantic information for
VLT task from efficient and diverse perspectives, enabling fine-grained
evaluation of multi-modal trackers. In the future, we believe this work can be
extended to more datasets to support vision datasets understanding.


  The almost splitting theorem of Cheeger-Colding is established in the setting
of almost nonnegative generalized $m$-Bakry-\'{E}mery Ricci curvature, in which
$m$ is positive and the associated vector field is not necessarily required to
be the gradient of a function. In this context it is shown that with a diameter
upper bound and volume lower bound the fundamental group of such manifolds is
almost abelian. Furthermore, extensions of well-known results concerning Ricci
curvature lower bounds are given for generalized $m$-Bakry-\'{E}mery Ricci
curvature. These include: the first Betti number bound of Gromov and Gallot,
Anderson's finiteness of fundamental group isomorphism types, volume
comparison, the Abresch-Gromoll inequality, and a Cheng-Yau gradient estimate.
Finally, this analysis is applied to stationary vacuum black holes in higher
dimensions to find that low temperature horizons must have limited topology,
similar to the restrictions exhibited by (extreme) horizons of zero
temperature.


  When a measurement falls outside the quantization or measurable range, it
becomes saturated and cannot be used in classical reconstruction methods. For
example, in C-arm angiography systems, which provide projection radiography,
fluoroscopy, digital subtraction angiography, and are widely used for medical
diagnoses and interventions, the limited dynamic range of C-arm flat detectors
leads to overexposure in some projections during an acquisition, such as
imaging relatively thin body parts (e.g., the knee). Aiming at overexposure
correction for computed tomography (CT) reconstruction, we in this paper
propose a mixed one-bit compressive sensing (M1bit-CS) to acquire information
from both regular and saturated measurements. This method is inspired by the
recent progress on one-bit compressive sensing, which deals with only sign
observations. Its successful applications imply that information carried by
saturated measurements is useful to improve recovery quality. For the proposed
M1bit-CS model, alternating direction methods of multipliers is developed and
an iterative saturation detection scheme is established. Then we evaluate
M1bit-CS on one-dimensional signal recovery tasks. In some experiments, the
performance of the proposed algorithms on mixed measurements is almost the same
as recovery on unsaturated ones with the same amount of measurements. Finally,
we apply the proposed method to overexposure correction for CT reconstruction
on a phantom and a simulated clinical image. The results are promising, as the
typical streaking artifacts and capping artifacts introduced by saturated
projection data are effectively reduced, yielding significant error reduction
compared with existing algorithms based on extrapolation.


  Surgical planning for congenital heart diseases requires a collaborative
approach, traditionally involving the 3D-printing of physical heart models for
inspection by surgeons and cardiologists. Recent advancements in mobile
augmented reality (AR) technologies have offered a promising alternative, noted
for their ease-of-use and portability. Despite this progress, there remains a
gap in research exploring the use of multi-user mobile AR environments for
facilitating collaborative cardiovascular surgical planning. We are developing
ARCollab, an iOS AR application designed to allow multiple surgeons and
cardiologists to interact with patient-specific 3D heart models in a shared
environment. ARCollab allows surgeons and cardiologists to import heart models,
perform gestures to manipulate the heart, and collaborate with other users
without having to produce a physical heart model. We are excited by the
potential for ARCollab to make long-term real-world impact, thanks to the
ubiquity of iOS devices that will allow for ARCollab's easy distribution,
deployment and adoption.


  A brief summary of the emerging evidence for a new class of collective states
of two-dimensional electrons in partially occupied excited Landau levels is
presented. Among the most dramatic phenomena described are the large
anisotropies of the resistivity observed at very low temperatures near
half-filling of the third and higher Landau levels and the non-linear character
of the re-entrant integer quantized Hall states in the flanks of the same
levels. The degree to which these findings support recent theoretical
predictions of charge density wave ground states is discussed and a preliminary
comparison to recent transport theories is made.


  Given two square matrices $A$ and $B$, we propose a new approach for
computing the smallest value $\varepsilon \geq 0$ such that $A+E$ and $A+F$
share an eigenvalue, where $\|E\|=\|F\|=\varepsilon$. In 2006, Gu and Overton
proposed the first algorithm for computing this quantity, called
$\mathrm{sep}_\lambda(A,B)$ ("sep-lambda"), using ideas inspired from an
earlier algorithm of Gu for computing the distance to uncontrollability.
However, the algorithm of Gu and Overton is extremely expensive, which limits
it to the tiniest of problems, and until now, no other algorithms have been
known. Our new algorithm can be orders of magnitude faster and can solve
problems where $A$ and $B$ are of moderate size. Moreover, our method consists
of many "embarrassingly parallel" computations, and so it can be further
accelerated on multi-core hardware. Finally, we also propose the first
algorithm to compute an earlier version of sep-lambda where $\|E\| +
\|F\|=\varepsilon$.


  We perform large-scale shell model Monte Carlo (SMMC) calculations for many
nuclei in the mass range A=56-65 in the complete pfg_{9/2}d_{5/2} model space
using an effective quadrupole-quadrupole+pairing residual interaction. Our
calculations are performed at finite temperatures between T=0.33-2 MeV. Our
main focus is the temperature dependence of the symmetry energy which we
determine from the energy differences between various isobaric pairs with the
same pairing structure and at different temperatures. Our SMMC studies are
consistent with an increase of the symmetry energy with temperature. We also
investigate possible consequences for core-collapse supernovae events.


  Gaussian process (GP) models have received increasingly attentions in recent
years due to their superb prediction accuracy and modeling flexibility. To
address the computational burdens of GP models for large-scale datasets,
distributed learning for GPs are often adopted. Current aggregation models for
distributed GPs are not time-efficient when incorporating correlations between
GP experts. In this work, we propose a novel approach for aggregated prediction
in distributed GPs. The technique is suitable for both the exact and sparse
variational GPs. The proposed method incorporates correlations among experts,
leading to better prediction accuracy with manageable computational
requirements. As demonstrated by empirical studies, the proposed approach
results in more stable predictions in less time than state-of-the-art
consistent aggregation models.


  We explicitly derive collective field theory description for the system of
fermions in the harmonic potential. This field theory appears to be a coupled
system of free scalar and (modified) Liouville field. This theory should be
considered as an exact bosonization of the system of non-relativistic fermions
in the harmonic potential. Being surprisingly similar to the world-sheet
formulation of c=1 string theory, this theory has quite different physical
features and it is conjectured to give space-time description of the string
theory, dual to the fermions in the harmonic potential. A vertex operator in
this theory is shown to be a field theoretical representation of the local
fermion operator, thus describing a D0 brane in the string language. Possible
generalization of this result and its derivation for the case of c=1 string
theory (fermions in the inverse harmonic potential) is discussed.


  The X-ray and radio flares observed in X-ray binaries and active galactic
nuclei (AGN) are attributed to energetic electrons in the plasma ejecta from
the accretion flows near the black hole in these systems. It is argued that
magnetic reconnection could occur in the coronae above the accretion disk
around the black hole, and that this drives plasmoid outflows resembling the
solar coronal mass ejection (CME) phenomenon. The X-ray and radio flares are
emission from energetic electrons produced in the process. As the emission
region is located near the black hole event horizon, the flare emission would
be subject to special- and general-relativistic effects. We present
calculations of the flaring emission from plasmoids orbiting around a black
hole and plasmoid ejecta launched from the inner accretion disk when
general-relativistic effects are crucial in determining the observed
time-dependent properties of the emission. We consider fully
general-relativistic radiative transfer calculations of the emission from
evolving ejecta from black hole systems, with proper accounting for
differential arrival times of photons emitted from the plasmoids, and determine
the emission lightcurves of plasmoids when they are in orbit and when they
break free from their magnetic confinement. The implications for interpreting
time-dependent spectroscopic observations of flaring emission from accreting
black holes are discussed.


  Search for low-dimensional materials with unique electronic properties is
important for the development of electronic devices in nano scale. Through
systematic first-principles calculations, we found that the band gaps of the
two-dimensional honeycomb monolayers and one-dimensional single-walled
nanotubes of IIB-VI semiconductors (ZnO, CdO, ZnS and CdS) are nearly
chirality-independent and weakly diameter-dependent. Based on analysis of the
electronic structures, it was found that the conduction band minimum is
contributed by the spherically symmetric $s$ orbitals of cations and the
valence band maximum is dominated by the in-plane $(d_{xy}-p_y)$ and
$(d_{x^2-y^2}-p_x)$ hybridizations. These electronic states are robust against
radius curvature, resulting in the invariant feature of the band gaps for the
structures changing from honeycomb monolayer to single-walled nanotubes. The
band gaps of these materials range from 2.3 eV to 4.7 eV, which is of potential
applications in electronic devices and optoelectronic devices. Our studies show
that searching for and designing specific electronic structures can facilitate
the process of exploring novel nanomaterials for future applications.


  Let L be a lattice ordered effect algebra. We prove that the lattice
uniformities on L which make uniformly continuous the operations $\ominus$ and
$\oplus$ of L are uniquely determined by their system of neighbourhoods of 0
and form a distributive lattice. Moreover we prove that every such uniformity
is generated by a family of weakly subadditive $[0,+\infty]$-valued functions
on L.


  We present a complete microscopic Fermi-liquid description for
next-to-leading order transport through an Anderson impurity under a finite
bias voltage $V$. It is applicable to multilevel quantum dots without
particle-hole or time-reversal symmetry, and is constructed based on the
nonequilibrium Keldysh formalism, taking into account the current conservation
between electrons in the impurity levels and the conduction bands.
Specifically, we derive the formula for the current noise generated in the
steady flow up to terms of order $(eV)^3$ at zero temperature $T=0$. To this
end, we calculate the Keldysh vertex functions
$\Gamma_{\sigma\sigma';\sigma'\sigma}^{ \nu_1\nu_2;\nu_3\nu_4} (\omega,\omega';
\omega',\omega)$, which depend on branches $\nu_1, \nu_2, \nu_3$ and $\nu_4$ of
the time-loop contour and on spin degrees of freedom $\sigma$ and $\sigma'$, up
to linear-order terms with respect to $eV$, $T$, and frequencies $\omega$ and
$\omega'$. The coefficients of these linear-order terms are determined by a set
of the parameters, defined with respect to the equilibrium ground state: the
phase shift, static susceptibilities, and nonlinear three-body susceptibilities
of the impurity electrons. The low-energy expressions of the vertex components
are shown to satisfy the Ward identities with the Keldysh Green's functions
expanded up to terms of order $\omega^2$, $(eV)^2$, and $T^2$. We also find
that the imaginary part of the Ward identities can be described in terms of the
$eV$-dependent collision integrals for a single-quasiparticle excitation and
that for a single quasiparticle-quasihole pair excitation. These collision
integrals ensure the current conservation of the next-to-leading order
Fermi-liquid transport due to the quasiparticles with a finite damping rate.


  In this work, we investigate collisionless shocks propagating in a
relativistically hot unmagnetized electron-positron plasmas. We estimate the
dissipation fraction at shocks in the relativistically hot plasma, showing that
it is sufficiently large to explain the observation of gamma-ray bursts even
when the shock is not highly relativistic. It is shown by two-dimensional
particle in cell simulations that magnetic fields are generated around the
shock front by the Weibel instability, as in the cold upstream plasma. However,
in contrast to the cold upstream plasma, no particles are accelerated at the
shock in the simulation time of $t = 3600 \omega_p^{-1}$. The decay of the
magnetic field in the downstream region is slower for slower shock velocities
in the hot plasma cases. Applying the slow decay of the downstream magnetic
field, we propose a model that generate magnetic fields in large downstream
region, which is required from the standard model of the gamma-ray burst
afterglow.


  We show that the differential cross section d_sigma/d_t of gamma p --> \phi p
reaction at the threshold is finite and its value is crucial to the mechanism
of the phi meson photoproduction and for the models of phi-N interaction.