  Non-orthogonal multiple access (NOMA) emerges as a superior technology for
enhancing spectral efficiency compared to orthogonal multiple access. In NOMA
networks, successive interference cancellation (SIC) plays a crucial role in
decoding user signals sequentially. The challenge lies in the joint
optimization of SIC ordering and power allocation, due to the factorial nature
of ordering combinations. This study introduces an innovative solution, the
Attention-based SIC Ordering and Power Allocation (ASOPA) framework, targeting
an uplink NOMA network with dynamic SIC ordering. ASOPA aims to maximize
weighted proportional fairness by employing deep reinforcement learning,
strategically decomposing the problem into two manageable subproblems: SIC
ordering optimization and optimal power allocation. Our approach utilizes an
attention-based neural network, which processes instantaneous channel gains and
user weights to determine the SIC decoding sequence for each user. Once the SIC
ordering is established, the power allocation subproblem transforms into a
convex optimization problem, enabling efficient calculation. Extensive
simulations validate ASOPA's efficacy, demonstrating a performance closely
paralleling the exhaustive method, with over 97% confidence in normalized
network utility. Notably, ASOPA maintains a low execution latency of
approximately 50 milliseconds in a ten-user NOMA network, aligning with static
SIC ordering algorithms. Furthermore, ASOPA demonstrates superior performance
in various NOMA network configurations, including scenarios with imperfect
channel state information, multiple base stations, and multiple-antenna setups.
Such results underscore ASOPA's robustness and effectiveness, highlighting its
ability to excel across various NOMA network environments. The complete source
code for ASOPA is accessible at https://github.com/Jil-Menzerna/ASOPA.


  The paradigmatic view where information is seen as a more fundamental concept
than the laws of physics leads to a different understanding of spacetime where
the causal order of events emerges from correlations between random variables
representing physical quantities. In particular, such an information-theoretic
approach does not enforce a global spacetime structure. By following this path,
we conclude that perfect signaling correlations among three parties are
possible which do not obey the restrictions imposed by global spacetime. We
show this using a recent framework based on the sole assumptions that locally,
quantum theory is valid and random variables can be described by probability
distributions. Our result is of zero-error type and is an analog to a
tripartite appearance of quantum non-locality which manifests itself by
satisfying a condition with certainty whereas the same is impossible for any
local theory.


  We investigate one of the consequences of the twisted Poincare symmetry. We
derive the charge conservation law and show that the equivalence principle is
satisfied in the canonical noncommutative spacetime. We applied the twisted
Poincare symmetry to the Weinberg's analysis. To this end, we generalize our
earlier construction of the twisted S matrix \cite{Bu}, which apply the
noncommutativity to the fourier modes, to the massless fields of integer spins.
The transformation formula for the twisted S matrix for the massless fields of
integer spin has been obtained. For massless fields of spin 1, we obtain the
conservation of charge, and the universality of coupling constant for massless
fields of spin 2, which can be interpreted as the equality of gravitational
mass and inertial mass, i.e., the equivalence principle.


  The classical nu-metric introduced by Vinnicombe in robust control theory for
rational plants was extended to classes of nonrational transfer functions in
Ball and Sasane [Complex Analysis and Operator Theory; 2012]. In Sasane
[Mathematics of Control and Related Fields; 2012], an extension of the
classical nu-metric was given when the underlying ring of stable transfer
functions is the Hardy algebra, H^infty. However, this particular extension to
H^infty did not directly fit in the abstract framework given in Ball and Sasane
[CAOT 2012]. In this paper we show that the case of H^infty also fits into the
general abstract framework in [BS CAOT 2012] and that the nu-metric defined in
this setting is identical to the extension of the nu-metric defined in Sasane
[MCRF 2012]. This is done by introducing a particular Banach algebra, which is
the inductive limit of certain C*-algebras.


  Out-of-distribution (OOD) detection is critical when deploying machine
learning models in the real world. Outlier exposure methods, which incorporate
auxiliary outlier data in the training process, can drastically improve OOD
detection performance compared to approaches without advanced training
strategies. We introduce Hopfield Boosting, a boosting approach, which
leverages modern Hopfield energy (MHE) to sharpen the decision boundary between
the in-distribution and OOD data. Hopfield Boosting encourages the model to
concentrate on hard-to-distinguish auxiliary outlier examples that lie close to
the decision boundary between in-distribution and auxiliary outlier data. Our
method achieves a new state-of-the-art in OOD detection with outlier exposure,
improving the FPR95 metric from 2.28 to 0.92 on CIFAR-10 and from 11.76 to 7.94
on CIFAR-100.


  The aim of this paper is to provide another perspective on secant varieties
on algebraic curves by reformulating the problem in terms of refined de
Jonqui\`eres divisors, that is divisors on the curve with prescribed
multiplicities and dimensions of their spaces of global sections. We are able
to both recover some already known results and to obtain some new statements
concerning the dimension theory of secant varieties. We do this via the study
of the dimension theory of refined de Jonqui\`eres divisors in some relevant
cases and degeneration arguments.


  Cracking of suspensions during drying is a common problem. While additives,
e.g. binders and surfactants, can mitigate this problem, some applications,
such as printing conductive pastes or sintering green bodies, do not lend
themselves to the use of additives. Capillary suspensions provide an
alternative formulation without additives. In this work, we use simultaneous
stress and weight measurements to investigate the influence of formulation and
drying conditions. Capillary suspensions dry more homogeneously and with lower
peak stresses, leading to an increased robustness against cracking compared. An
increase in dry film porosity is not the key driver for the stress reduction.
Instead, the capillary bridges, which create strong particle networks, resist
the stress. Increasing the relative humidity enhances this effect, even for
pure suspensions. While lower boiling point secondary liquids, e.g. water,
persist for very long times during drying, higher boiling point liquids offer
further potential to tune the the drying process.


Comment withdrawn.


  Two recent theoretical works studied the role of Kitaev interactions in the
newly observed incommensurate magnetic order in the hyper-honeycomb
($\beta$-Li$_2$IrO$_3$) and stripy-honeycomb ($\gamma$-Li$_2$IrO$_3$) iridates.
Each of these works analyzed a different model ($JK\Gamma$ versus coupled
zigzag chain model) using a contrasting method (classical versus soft-spin
analysis). The lack of commonality between these works precludes meaningful
comparisons and a proper understanding of these unusual orderings. In this
study, we complete the unfinished picture initiated by these two works by
solving both models with both approaches for both 3D honeycomb iridates.
Through comparisons between all combinations of models, techniques, and
materials, we find that the bond-isotropic $JK\Gamma$ model consistently
predicts the experimental phase of $\beta$-Li$_2$IrO$_3$ regardless of the
method used, while the experimental phase of $\gamma$-Li$_2$IrO$_3$ can be
generated by the soft-spin approach with eigenmode mixing irrespective of the
model used. To gain further insights, we solve a 1D quantum spin-chain model
related to both 3D models using the density matrix renormalization group method
to form a benchmark. We discover that in the 1D model, incommensurate
correlations in the classical and soft-spin analysis survive in the quantum
limit only in the presence of the symmetric-off-diagonal exchange $\Gamma$
found in the $JK\Gamma$ model. The relevance of these results to the real
materials are also discussed.


  Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory
of normal forms based on continuous averaging. We concentrate on the case of
normal forms near an elliptic singular point, but unlike arXiv:2303.02992 we do
not assume that frequences of the linearized system are nonresonant. We study
analytic properties of the normalization procedure. In particular we show that
in the case of a codimension one resonance an analytic Hamiltonian function may
be reduced to a normal form up to an exponentially small reminder with explicit
estimates of the reminder and the analyticity domain.


  We investigate sl(n) conformal Toda theory with maximally symmetric
boundaries. There are two types of maximally symmetric boundary conditions, due
to the existence of an order two automorphism of the W(n>2) algebra. In one of
the two cases, we find that there exist D-branes of all possible dimensions 0
=< d =< n-1, which correspond to partly degenerate representations of the W(n)
algebra. We perform classical and conformal bootstrap analyses of such
D-branes, and relate these two approaches by using the semi-classical light
asymptotic limit. In particular we determine the bulk one-point functions. We
observe remarkably severe divergences in the annulus partition functions, and
attribute their origin to the existence of infinite multiplicities in the
fusion of representations of the W(n>2) algebra. We also comment on the issue
of the existence of a boundary action, using the calculus of constrained
functional forms, and derive the generating function of the B"acklund
transformation for sl(3) Toda classical mechanics, using the minisuperspace
limit of the bulk one-point function.


  This paper presents instruct-imagen, a model that tackles heterogeneous image
generation tasks and generalizes across unseen tasks. We introduce *multi-modal
instruction* for image generation, a task representation articulating a range
of generation intents with precision. It uses natural language to amalgamate
disparate modalities (e.g., text, edge, style, subject, etc.), such that
abundant generation intents can be standardized in a uniform format.
  We then build instruct-imagen by fine-tuning a pre-trained text-to-image
diffusion model with a two-stage framework. First, we adapt the model using the
retrieval-augmented training, to enhance model's capabilities to ground its
generation on external multimodal context. Subsequently, we fine-tune the
adapted model on diverse image generation tasks that requires vision-language
understanding (e.g., subject-driven generation, etc.), each paired with a
multi-modal instruction encapsulating the task's essence. Human evaluation on
various image generation datasets reveals that instruct-imagen matches or
surpasses prior task-specific models in-domain and demonstrates promising
generalization to unseen and more complex tasks.


  The MeerKAT Exploration of Relics, Giant Halos, and Extragalactic Radio
Sources (MERGHERS) survey is a planned project to study a large statistical
sample of galaxy clusters with the MeerKAT observatory. Here we present the
results of a 16--hour pilot project, observed in response to the 2019 MeerKAT
Shared Risk proposal call, to test the feasibility of using MeerKAT for a large
cluster study using short (0.2--2.1\,hour) integration times. The pilot focuses
on 1.28\,GHz observations of 13 massive, low-to-intermediate redshift ($0.22 <
z < 0.65$) clusters from the Sunyaev-Zel'dovich-selected Atacama Cosmology
Telescope (ACT) DR5 catalogue that show multiwavelength indications of
dynamical disturbance. With a 70 per cent detection rate (9/13 clusters), this
pilot study validates our proposed MERGHERS observing strategy and provides
twelve detections of diffuse emission, eleven of them new, indicating the
strength of MeerKAT for such types of studies. The detections (signal-to-noise
ratio $\gtrsim6$) are summarised as follows: two systems host both relic(s) and
a giant radio halo, five systems host radio halos, and two have candidate radio
halos. Power values, $k$-corrected to 1.4 GHz assuming a fiducial spectral
index of $\alpha = -1.3 \pm 0.4$, are consistent with known radio halo and
relic scaling relations.


  Spiking Neural Networks (SNNs) emulate the integrated-fire-leak mechanism
found in biological neurons, offering a compelling combination of biological
realism and energy efficiency. In recent years, they have gained considerable
research interest. However, existing SNNs predominantly rely on the Leaky
Integrate-and-Fire (LIF) model and are primarily suited for simple, static
tasks. They lack the ability to effectively model long-term temporal
dependencies and facilitate spatial information interaction, which is crucial
for tackling complex, dynamic spatio-temporal prediction tasks. To tackle these
challenges, this paper draws inspiration from the concept of autaptic synapses
in biology and proposes a novel Spatio-Temporal Circuit (STC) model. The STC
model integrates two learnable adaptive pathways, enhancing the spiking
neurons' temporal memory and spatial coordination. We conduct a theoretical
analysis of the dynamic parameters in the STC model, highlighting their
contribution in establishing long-term memory and mitigating the issue of
gradient vanishing. Through extensive experiments on multiple spatio-temporal
prediction datasets, we demonstrate that our model outperforms other adaptive
models. Furthermore, our model is compatible with existing spiking neuron
models, thereby augmenting their dynamic representations. In essence, our work
enriches the specificity and topological complexity of SNNs.


  Signal sampling and reconstruction is a fundamental engineering task at the
heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees
perfect signal reconstruction from uniform samples, obtained at a rate twice
the maximum frequency present in the signal. Unfortunately a large number of
signals of interest are far from being band-limited. This motivated research on
reconstruction from sub-Nyquist samples, which mainly hinges on the use of
random / incoherent sampling procedures. However, uniform or regular sampling
is more appealing in practice and from the system design point of view, as it
is far simpler to implement, and often necessary due to system constraints. In
this work, we study regular sampling and reconstruction of three- or
higher-dimensional signals (tensors). We show that reconstructing a tensor
signal from regular samples is feasible. Under the proposed framework, the
sample complexity is determined by the tensor rank---rather than the signal
bandwidth. This result offers new perspectives for designing practical regular
sampling patterns and systems for signals that are naturally tensors, e.g.,
images and video. For a concrete application, we show that functional magnetic
resonance imaging (fMRI) acceleration is a tensor sampling problem, and design
practical sampling schemes and an algorithmic framework to handle it. Numerical
results show that our tensor sampling strategy accelerates the fMRI sampling
process significantly without sacrificing reconstruction accuracy.


  This paper is devoted to the study of quantum dissipation in cluster decay
phenomena in the frame of the Lindblad approach to quantum open systems. The
tunneling of a metastable state across a piecewise quadratic potential is
envisaged for two cases : one and two harmonic wells smoothly joined to an
inverted parabola which simulates the barrier. The width and depth of the
second harmonic oscillator well was varied over a wide range of values in order
to encompass particular cases of tunneling such as the double well potential
and the cluster decay. The evolution of the averages and covariances of the
quantum sub-system is studied in both under- and overdamped regimes. For a
gaussian intial wave-packet we compute the tunneling probability for different
values of the friction coefficient and fixed values of the diffusion
coefficients.


  Two-dimensional numerical simulations with Eulerian-Lagrangian method and
detailed chemical mechanism are conducted to study the methane detonation
propagation across a water curtain with finite thickness. The critical length
of the water curtain with sprayed droplets is determined through parametric
simulations with different water mass loadings and droplet sizes. The influence
of water curtain length on the methane detonation is examined by the
trajectories of peak pressure and time history of average heat release rate.
The results indicate that the water curtain not only inhibit the incident
detonation wave, but also prevent the detonation re-ignition after the incident
wave is quenched. Moreover, unsteady response of gaseous methane detonation to
water curtain are analyzed. The detonation re-initiation process behind the
water curtain near the critical loading is also captured. In addition,
mechanism of detonation inhibition with fine water droplets are discussed. It
is found that energy and momentum exchanges start immediately when the
detonation wave enters the water curtain area, but the mass transfer starts
well behind the detonation wave due to the finitely long droplet heating
duration. It is shown that the convective heat transfer by water droplets plays
a significant role in quenching a detonation.


  Contact of a fluid with a solid or an elastic wall is investigated. The wall
exerts molecular forces on the fluid which is locally strongly nonhomogeneous.
The problem is approached with a fluid energy of the second gradient form and a
wall surface energy depending on the value of the fluid density at the contact.
>From the virtual work principle are obtained limit conditions taking into
account the fluid density, its normal derivative to the wall and the curvature
of the surface


  This article aims to classify diabetic retinopathy (DR) disease into five
different classes using an ensemble approach based on two popular pre-trained
convolutional neural networks: VGG16 and Inception V3. The proposed model aims
to leverage the strengths of the two individual nets to enhance the
classification performance for diabetic retinopathy. The ensemble model
architecture involves freezing a portion of the layers in each pre-trained
model to utilize their learned representations effectively. Global average
pooling layers are added to transform the output feature maps into fixed-length
vectors. These vectors are then concatenated to form a consolidated
representation of the input image. The ensemble model is trained using a
dataset of diabetic retinopathy images (APTOS), divided into training and
validation sets. During the training process, the model learns to classify the
retinal images into the corresponding diabetic retinopathy classes.
Experimental results on the test set demonstrate the efficacy of the proposed
ensemble model for DR classification achieving an accuracy of 96.4%.


  The ability to cool and manipulate levitated nano-particles in vacuum is a
promising new tool for exploring macroscopic quantum
mechanics\cite{WanPRL2016,Scala2013,Zhang2013}, precision measurements of
forces, \cite{GambhirPRA2016} and non-equilibrium thermodynamics
\cite{GieselerNatNano2014,MillenNat2014}. The extreme isolation afforded by
optical levitation offers a low noise, undamped environment that has to date
been used to measure zeptonewton forces \cite{GambhirPRA2016}, radiation
pressure shot noise,\cite{Jain2016} and to demonstrate the cooling of the
centre-of-mass motion \cite{LiNatPhys2011,Gieseler2012}. Ground state cooling,
and the creation and measurement of macroscopic quantum superpositions, are now
within reach, but control of both the center-of-mass and internal temperature
is required. While cooling the centre-of-mass motion to microKelvin
temperatures has now been achieved, the internal temperature has remained at or
well above room temperature. Here we demonstrate refrigeration of levitated
Yb$^{3+}$:YLF from room temperature to 130 K using anti-Stokes fluorescence
cooling, while simultaneously using the optical trapping field to align the
crystal to maximise cooling.


  Analyzing massive spatial datasets using Gaussian process model poses
computational challenges. This is a problem prevailing heavily in applications
such as environmental modeling, ecology, forestry and environmental heath. We
present a novel approximate inference methodology that uses profile likelihood
and Krylov subspace methods to estimate the spatial covariance parameters and
makes spatial predictions with uncertainty quantification. The proposed method,
Kryging, applies for both observations on regular grid and irregularly-spaced
observations, and for any Gaussian process with a stationary covariance
function, including the popular $\Matern$ covariance family. We make use of the
block Toeplitz structure with Toeplitz blocks of the covariance matrix and use
fast Fourier transform methods to alleviate the computational and memory
bottlenecks. We perform extensive simulation studies to show the effectiveness
of our model by varying sample sizes, spatial parameter values and sampling
designs. A real data application is also performed on a dataset consisting of
land surface temperature readings taken by the MODIS satellite. Compared to
existing methods, the proposed method performs satisfactorily with much less
computation time and better scalability.


  Non-Hermitian systems, which contain gain or loss, commonly host exceptional
point degeneracies rather than the diabolic points found in Hermitian systems.
We present a class of non-Hermitian lattice models with symmetry-stabilized
diabolic points, such as Dirac or Weyl points. They exhibit
non-Hermiticity-induced phenomena previously existing in the Hermitian regime,
including topological phase transitions, Landau levels induced by
pseudo-magnetic fields, and Fermi arc surface states. These behaviors are
controllable via gain and loss, with promising applications in tunable active
topological devices.


  In \cite{K-rig}, a map $\beta:\mathcal R\to\mathcal{B}el$ from the set
$\mathcal R$ of equivalence classes of rigid germs of finite morphisms branched
in germs of curves having $ADE$ singularity types onto the set $\mathcal{B}el$
of rational Belyi pairs $f:\mathbb P^1\to\mathbb P^1$ considered up to the
action of $PGL(2,\mathbb C)$ was defined. In this article, the inverse images
of this map are investigated in terms of monodromies of Belyi pairs.


  This paper discusses the concept of cyber defence exercises -CDX- that are
very important tool when it comes to enhancing the safety awareness of
cyberspace, testing an organization's ability to put up resistance and respond
to different cyber events to establish the secure environment, gathering
empirical data related to security, and looking at the practical training of
experts on this subject. The exercises can give ideas to the decision makers
about the precautions in the cybersecurity area and to the officials,
institutions, organizations, and staff who are responsible on the cyber tools,
techniques, and procedures that can be developed for this field. In the cyber
defense exercises, the scenarios that are simulated closest to reality which
provides very important contributions by bringing together the necessity of
making the best decisions and management capabilities under the cyber crisis by
handling stress and coordinated movement as a team. The objective of this paper
is to address the issue from a scientific point of view by setting out the
stages of planning, implementation, and evaluation of these exercises, taking
into account and comparing international firefighting exercises. Another aim of
the work is to be able to reveal the necessary processes that are required for
all kind of cyber exercises, regardless of the type, although the processes
involved vary according to the target mass of the planned exercise.


  More recently, we have proposed a set of noncommutative space that describes
the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303
(2020)]. The interesting significant result we found is that, the generalized
uncertainty principle induces a maximal measurable length of quantum gravity.
This measurement revealed strong quantum gravitational effects at this scale
and predicted a detection of gravity particles with low energies. In the
present paper, to make evidence this prediction, we study in this space, the
dynamics of a particle with position-dependent mass (PDM) trapped in an
infinite square well. We show that, by increasing the quantum gravitational
effect, the PDM of the particle increases and induces deformations of the
quantum energy levels. These deformations are more pronounced as one increases
the quantum levels allowing, the particle to jump from one state to another
with low energies and with high probability densities.


  Let $X,X_1,X_2,\ldots$ be i.i.d. mean zero random vectors with values in a
separable Banach space $B$, $S_n=X_1+\cdots+X_n$ for $n\ge1$, and assume
$\{c_n:n\ge1\}$ is a suitably regular sequence of constants. Furthermore, let
$S_{(n)}(t),0\le t\le1$ be the corresponding linearly interpolated partial sum
processes. We study the cluster sets $A=C(\{S_n/c_n\})$ and
$\mathcal{A}=C(\{S_{(n)}(\cdot)/c_n\})$. In particular, $A$ and $\mathcal{A}$
are shown to be nonrandom, and we derive criteria when elements in $B$ and
continuous functions $f:[0,1]\to B$ belong to $A$ and $\mathcal{A}$,
respectively. When $B=\mathbb{R}^d$ we refine our clustering criteria to show
both $A$ and $\mathcal{A}$ are compact, symmetric, and star-like, and also
obtain both upper and lower bound sets for $\mathcal{A}$. When the coordinates
of $X$ in $\mathbb{R}^d$ are independent random variables, we are able to
represent $\mathcal {A}$ in terms of $A$ and the classical Strassen set
$\mathcal{K}$, and, except for degenerate cases, show $\mathcal{A}$ is strictly
larger than the lower bound set whenever $d\ge2$. In addition, we show that for
any compact, symmetric, star-like subset $A$ of $\mathbb{R}^d$, there exists an
$X$ such that the corresponding functional cluster set $\mathcal{A}$ is always
the lower bound subset. If $d=2$, then additional refinements identify
$\mathcal{A}$ as a subset of $\{(x_1g_1,x_2g_2):(x_1,x_2)\in
A,g_1,g_2\in\mathcal{K}\}$, which is the functional cluster set obtained when
the coordinates are assumed to be independent.


  Motivated by a recent Comment by J. H\"oller and N. Read [Phys. Rev. B 93,
197401 (2016)], we revisit the problem of a chiral Luttinger liquid on a
boundary of a Galilean-invariant quantum Hall fluid. After correcting the
linear response calculation, the real part of the longitudinal conductivity
derived in the model constructed in our paper [Phys. Rev. B 91, 195409 (2015)]
agrees with the result found in the Comment for non-interacting fermions
confined by a linear potential. We also withdraw our previous conjecture that
the longitudinal conductivity contains a universal contribution determined by
the "shift" and provide arguments demonstrating its non-universal nature.


  The Bonnaf\'e-Rouquier equivalence can be seen as a modular analogue of
Lusztig's Jordan decomposition for groups of Lie type. In this paper, we show
that this equivalence can be lifted to include automorphisms of the finite
group of Lie type. Moreover, we prove the existence of a local version of this
equivalence which satisfies similar properties.


  {\it Ab initio} investigations of the full static dielectric response and
Born effective charge of BN nanotubes (BN-NTs) have been performed for the
first time using finite electric field method. It is found that the ionic
contribution to the static dielectric response of BN-NTs is substantial and
also that a pronounced chirality-dependent oscillation is superimposed on the
otherwise linear relation between the longitudinal electric polarizability and
the tube diameter ($D$), as for a thin dielectric cylinderical shell. In
contrast, the transverse dielectric response of the BN-NTs resemble the
behavior of a thin (non-ideal) conducting cylindrical shell of a diameter of
$D+4$\AA$ $, with a screening factor of 2 for the inner electric field. The
medium principal component $Z_y^*$ of the Born effective charge corresponding
to the transverse atomic displacement tangential to the BN-NT surface, has a
pronounced $D$-dependence (but independent of chirality), while the large
longitudinal component $Z_z^*$ exhibits a clear chirality dependence (but
nearly $D$-independent), suggesting a powerful way to characterize the diameter
and chirality of a BN-NT.


  Motivated by the mutation theory of quivers with potentials developed by
Derksen-Weyman-Zelevinsky, and the representation-theoretic approach to cluster
algebras it provides, we propose a mutation theory of species with potentials
for species that arise from skew-symmetrizable matrices that admit a
skew-symmetrizer with pairwise coprime diagonal entries. The class of
skew-symmetrizable matrices covered by the mutation theory proposed here
contains a class of matrices that do not admit global unfoldings, that is,
unfoldings compatible with all possible sequences of mutations.


  We propose a closed form for the statistical distribution of non-interacting
Majorana fermions at low temperature. Majorana particles often appear in the
contemporary many-body literature in the Kitaev, Fu-Kane, or Sachdev-Ye-Kitaev
models, where the Majorana condition of self-conjugacy immediately results in
nonconserved particle number, non-trivial braiding statistics, and the absence
of a noninteracting limit. We deviate from this description and instead
consider a gas of noninteracting, spin-1/2 Majorana fermions that obey the
spin-statistics theorem via imposing a condensed matter analog of momentum
conservation. This allows us to build a quantum statistical theory of the
Majorana system in the low temperature, low density limit without the need to
account for strong fluctuations in the particle number. A combinatorial
analysis leads to a configurational entropy which deviates from the fermionic
result with an increasing number of available microstates. A number-conserving
Majorana distribution function is derived which shows signatures of a
sharply-defined Fermi surface at finite temperatures. Such a distribution is
then re-derived from a microscopic model in the form of a modified Kitaev chain
with a bosonic pair interaction. The thermodynamics of this free Majorana
system is found to be nearly identical to that of a free Fermi gas, except now
distinguished by a two-fold ground state degeneracy and, subsequently, a
residual entropy at zero temperature. Despite clear differences with the
anyonic or Sachdev-Ye-Kitaev models, we nevertheless find surprising agreement
between our theory and experimental signatures of Majorana excitations in
several materials. Experimental realization of our exactly solvable model is
also discussed in the realm of astrophysical and high-energy phenomena.


  Let V_D be the Shimura curve over \Q attached to the indefinite rational
quaternion algebra of discriminant D. In this note we investigate the group of
automorphisms of V_D and prove that, in many cases, it is the Atkin-Lehner
group. Moreover, we determine the family of bielliptic Shimura curves over \bar
\Q and over \Q and we use it to study the set of rational points on V_D over
quadratic fields. Finally, we obtain explicit equations of elliptic
Atkin-Lehner quotients of V_D.


  Pretext training followed by task-specific fine-tuning has been a successful
approach in vision and language domains. This paper proposes a self-supervised
pretext training framework tailored to event sequence data. We introduce a
novel alignment verification task that is specialized to event sequences,
building on good practices in masked reconstruction and contrastive learning.
Our pretext tasks unlock foundational representations that are generalizable
across different down-stream tasks, including next-event prediction for
temporal point process models, event sequence classification, and missing event
interpolation. Experiments on popular public benchmarks demonstrate the
potential of the proposed method across different tasks and data domains.


  We propose a novel two-phase approach to functional network estimation of
multi-subject functional Magnetic Resonance Imaging (fMRI) data, which applies
model-based image segmentation to determine a group-representative connectivity
map. In our approach, we first improve clustering-based Independent Component
Analysis (ICA) to generate maps of components occurring consistently across
subjects, and then estimate the group-representative map through MAP-MRF
(Maximum a priori - Markov random field) labeling. For the latter, we provide a
novel and efficient variational Bayes algorithm. We study the performance of
the proposed method using synthesized data following a theoretical model, and
demonstrate its viability in blind extraction of group-representative
functional networks using simulated fMRI data. We anticipate the proposed
method will be applied in identifying common neuronal characteristics in a
population, and could be further extended to real-world clinical diagnosis.


  I review the most recent evolutions of the QCD codes on new architectures,
with a focus on the performances obtained by the different coding strategies as
presented during the Lattice2017 conference.


  We describe hard exclusive processes beyond the leading twist approximation
in a framework based on the Taylor expansion of the amplitude around the
dominant light-cone directions. This naturally introduces an appropriate set of
non-perturbative correlators whose number is minimalized after taking into
account QCD equations of motion and the invariance under rotation on the
light-cone.
  We examplify this method at the twist 3 level and show that the coordinate
and momentum space descriptions are fully equivalent.


  Context. Stars in transition phases, like those showing the B[e] phenomenon
and luminous blue variables (LBVs), undergo strong, often irregular mass
ejection events. The prediction of these phases in stellar evolution models is
therefore extremely difficult if not impossible. As a result, their effective
temperatures, their luminosities and even their true nature are not fully
known.
  Aims. A suitable procedure to derive the stellar parameters of these types of
objects is to use the BCD spectrophotometric classification system, based on
the analysis of the Balmer discontinuity. The BCD parameters ({\lambda}_1, D)
are independent of interstellar extinction and circumstellar contributions.
  Methods. We obtained low-resolution spectra for 14 stars with the B[e]
phenomenon and LBVs. Using the BCD method, we derived the stellar and physical
parameters. The study was complemented with the information provided by the JHK
colour-colour diagram.
  Results. For each star, the BCD system gives a complete set of fundamental
parameters and related quantities such as luminosity and distance. We confirmed
HK Ori, HD 323771 and HD 52721 as pre-main sequence HAe/B[e], AS 202 and HD
85567 as FS CMa-type, and HD 62623 as sgB[e] stars. We classified Hen 3-847,
CD-24 5721, and HD 53367 as young B[e] stars or FS CMa-type candidates, and HD
58647 as a slightly evolved B[e] star. In addition, Hen 3-1398 is an sgB[e] and
MWC 877, CPD-59 2854 and LHA 120-S 65 are LBV candidates. The stellar
parameters of the latter two LBVs are determined for the first time.
  Conclusions. Our results emphasise that the BCD system is a highly valuable
tool to derive stellar parameters and physical properties of B-type stars in
transition phases. This method can be combined with near-IR colour-colour
diagrams to determine or confirm the evolutionary stage of emission-line stars
with dust disks.


  We calculate the density matrix for the decay of a polarised top quark into a
polarised W boson and a massive b quark, for the most general Wtb vertex
arising from dimension-six gauge-invariant effective operators. We show that,
in addition to the well-known W helicity fractions, for polarised top decays it
is worth to define and study the transverse and normal W polarisation
fractions, that is, the W polarisation along two directions orthogonal to its
momentum. In particular, a rather simple forward-backward asymmetry in the
normal direction is found to be very sensitive to complex phases in one of the
Wtb anomalous couplings. This asymmetry, which indicates a normal W
polarisation, can be generated for example by a P-odd, T-odd transition
electric dipole moment. We also investigate the angular distribution of decay
products in the top quark rest frame, calculating the spin analysing powers for
a general Wtb vertex. Finally we show that, using a combined fit to top decay
observables and the tW cross section, at LHC it will be possible to obtain
model-independent measurements of all the (complex) Wtb couplings as well as
the single top polarisation. Implications for spin correlations in top pair
production are also discussed.


  In this paper, we propose a new dynamical model to study the two-stage
volatility evolution of stock market index after extreme events, and find that
the volatility after extreme events follows a stretched exponential decay in
the initial stage and becomes a power law decay at later times by using high
frequency minute data. Empirical study of the evolutionary behaviors of
volatility after endogenous and exogenous events further demonstrates the
descriptive power of our new model. To further explore the underlying
mechanisms of volatility evolution, we introduce the sequential arrival of
information hypothesis (SAIH) and the mixture of distribution hypothesis (MDH)
to test the two-stage assumption, and find that investors transform from the
uninformed state to the informed state in the first stage and informed
investors subsequently dominate in the second stage. The testing results offer
a supporting explanation for the validity of our new model and the fitted
values of relevant parameters.


  We consider the equation $\e^{2}\Delta u=(u-a(x))(u^2-1)$ in $\Omega$,
$\frac{\partial u}{\partial \nu} =0$ on $\partial \Omega$, where $\Omega$ is a
smooth and bounded domain in $\R^n$, $\nu$ the outer unit normal to
$\pa\Omega$, and $a$ a smooth function satisfying $-1<a(x)<1$ in $\ov{\Omega}$.
We set $K$, $\Omega_+$ and $\Omega_-$ to be respectively the zero-level set of
$a$, {a>0} and {a<0}. Assuming $\nabla a \neq 0$ on $K$ and $a\ne 0$ on
$\partial \Omega$, we show that there exists a sequence $\e_j \to 0$ such that
the above equation has a solution $u_{\e_j}$ which converges uniformly to $\pm
1$ on the compact sets of $\O_{\pm}$ as $j \to + \infty$.


  We demonstrate a novel technique for coupling XUV harmonic radiation out of a
femtosecond enhancement cavity. We use a small-period diffraction grating
etched directly into the surface of a dielectric mirror. For the fundamental
light, this element acts as a high reflector. For harmonic wavelengths, it acts
as a diffraction grating, coupling XUV radiation out of the cavity. Using this
method, we observed the 3rd through 21st odd harmonics with a dramatic increase
in usable power over previous results of high harmonic generation at high
repetition rates.


  New constraints on the large-scale wind structures responsible for discrete
absorption components are obtained from far-ultraviolet time-series
observations of O supergiants in the Large Magellanic Cloud.


  We consider two families of subgroups of a group. Each subgroup which belongs
to one family is contained in some subgroup which belongs to the other family.
We then discuss relations of relative hyperbolicity for the group with respect
to the two families, respectively. If the group is supposed to be hyperbolic
relative to the two families, respectively, then we consider relations of
relative quasiconvexity for a subgroup of the group with respect to the two
families, respectively.


  Although unstable, the Si(337) orientation has been known to appear in
diverse experimental situations such as the nanoscale faceting of Si(112), or
in the case of miscutting a Si(113) surface. Various models for Si(337) have
been proposed over time, which motivates a comprehensive study of the structure
of this orientation. Such a study is undertaken in this article, where we
report the results of a genetic algorithm optimization of the Si(337)-$(2\times
1)$ surface. The algorithm is coupled with a highly optimized empirical
potential for silicon, which is used as an efficient way to build a set of
possible Si(337) models; these structures are subsequently relaxed at the level
of ab initio density functional methods. Using this procedure, we retrieve most
of the (337) reconstructions proposed in previous works, as well as a number of
novel ones.


  Hurwitz numbers with completed cycles are standard Hurwitz numbers with
simple branch points replaced by completed cycles. In fact, simple branch
points correspond to completed $2$-cycles. Okounkov and Pandharipande have
established the remarkable GW/H correspondence, saying that the stationary
sectors of the Gromov--Witten theory relative to $r$ points equal Hurwitz
numbers with $r$ branch points besides the completed cycles. However, from the
viewpoint of computation, known results for Hurwitz numbers (standard or with
completed cycles) are mainly for $r\leq 2$. It is hard to obtain explicit
formulas and then discuss the structural properties for the cases $r>2$. In
this paper, we obtain explicit formulas for the case $r=3$ and uncover a number
of structural properties of these Hurwitz numbers. For instance, we discover a
piecewise polynomiality with respect to the orders of the completed cycles in
addition to the parts of the profiles of branch points as usual, we show that
certain hook-shape Hurwitz numbers are building blocks of all our Hurwitz
numbers, and we prove an analogue of the celebrated $\lambda_g$-conjecture.


  A marsupial robotics system comprises three components: an Unmanned Ground
Vehicle (UGV), an Unmanned Aerial Vehicle (UAV), and a tether connecting both
robots. Marsupial systems are highly beneficial in industry as they extend the
UAV's battery life during flight. This paper introduces a novel strategy for a
specific path planning problem in marsupial systems, where each of the
components must avoid collisions with ground and aerial obstacles modeled as 3D
cuboids. Given an initial configuration in which the UAV is positioned atop the
UGV, the goal is to reach an aerial target with the UAV. We assume that the UGV
first moves to a position from which the UAV can take off and fly through a
vertical plane to reach an aerial target. We propose an approach that
discretizes the space to approximate an optimal solution, minimizing the sum of
the lengths of the ground and air paths. First, we assume a taut tether and use
a novel algorithm that leverages the convexity of the tether and the geometry
of obstacles to efficiently determine the locus of feasible take-off points for
the UAV. We then apply this result to scenarios that involve loose tethers. The
simulation test results show that our approach can solve complex situations in
seconds, outperforming a baseline planning algorithm based on RRT* (Rapidly
exploring Random Trees).


  The neutrino-cooled accretion disk, which was proposed to work as the central
engine of gamma-ray bursts, encounters difficulty in interpreting the X-ray
flares after the prompt gamma-ray emission. In this paper, the magnetic
coupling between the inner disk and the central black hole is taken into
consideration. For mass accretion rates around $0.001 \sim 0.1 M_{\sun}
s^{-1}$, our results show that the luminosity of neutrino annihilation can be
significantly enhanced due to the coupling effects. As a consequence, after the
gamma-ray emission, a remnant disk with mass $M_{disk} \la 0.5 M_{\sun}$ may
power most of the observed X-ray flares with the rest frame duration less than
100 seconds. In addition, a comparison between the magnetic coupling process
and the Blandford-Znajek mechanism is shown on the extraction of black hole
rotational energy.


  Lectures at the 1998 Les Houches Summer School: Topological Aspects of Low
Dimensional Systems. These lectures contain an introduction to various aspects
of Chern-Simons gauge theory: (i) basics of planar field theory, (ii) canonical
quantization of Chern-Simons theory, (iii) Chern-Simons vortices, and (iv)
radiatively induced Chern-Simons terms.


  We model a 3D turbulent fluid, evolving toward a statistical equilibrium, by
adding to the equations for the mean field $(v, p)$ a term like $-\alpha
\nabla\cdot(\ell(x) D v_t)$. This is of the Kelvin-Voigt form, where the
Prandtl mixing length $\ell$ is not constant and vanishes at the solid walls.
We get estimates for velocity $v$ in $L^\infty_t H^1_x \cap W^{1,2}_t
H^{1/2}_x$, that allow us to prove the existence and uniqueness of a
regular-weak solutions $(v, p)$ to the resulting system, for a given fixed eddy
viscosity. We then prove a structural compactness result that highlights the
robustness of the model. This allows us to pass to the limit in the quadratic
source term in the equation for the turbulent kinetic energy $k$, which yields
the existence of a weak solution to the corresponding Reynolds Averaged
Navier-Stokes system satisfied by $(v, p, k)$.


  We investigate the statistical properties of an over-damped Brownian particle
that is trapped by a harmonic potential and simultaneously exposed to a linear
shear flow or to a plane Poiseuille flow. Its probability distribution is
determined via the corresponding Smoluchowski equation, which is solved
analytically for a linear shear flow. In the case of a plane Poiseuille flow,
analytical approximations for the distribution are obtained by a perturbation
analysis and they are substantiated by numerical results. There is a good
agreement between the two approaches for a wide range of parameters.


  The emerging field of quantum thermodynamics is contributing important
results and insights into archetypal many-body problems, including quantum
phase transitions. Still, the question whether out-of-equilibrium quantities,
such as fluctuations of work, exhibit critical scaling after a sudden quench in
a closed system has remained elusive. Here, we take a novel approach to the
problem by studying a quench across an impurity quantum critical point. By
performing density matrix renormalization group computations on the
two-impurity Kondo model, we are able to establish that the irreversible work
produced in a quench exhibits finite-size scaling at quantum criticality. This
scaling faithfully predicts the equilibrium critical exponents for the
crossover length and the order parameter of the model, and, moreover, implies a
new exponent for the rescaled irreversible work. By connecting the irreversible
work to the two-impurity spin correlation function, our findings can be tested
experimentally.


  Sequence-to-sequence models provide a viable new approach to generative
summarization, allowing models that are no longer limited to simply selecting
and recombining sentences from the original text. However, these models have
three drawbacks: their grasp of the details of the original text is often
inaccurate, and the text generated by such models often has repetitions, while
it is difficult to handle words that are beyond the word list. In this paper,
we propose a new architecture that combines reinforcement learning and
adversarial generative networks to enhance the sequence-to-sequence attention
model. First, we use a hybrid pointer-generator network that copies words
directly from the source text, contributing to accurate reproduction of
information without sacrificing the ability of generators to generate new
words. Second, we use both intra-temporal and intra-decoder attention to
penalize summarized content and thus discourage repetition. We apply our model
to our own proposed COVID-19 paper title summarization task and achieve close
approximations to the current model on ROUEG, while bringing better
readability.


  We present ionizing spectra estimated at 13.6--100 eV for ten dwarf galaxies
with strong high ionization lines of He {\sc {ii}}$\lambda$4686 and [Ne
{\sc{v}}]$\lambda$3426 ([Ne {\sc{iv}}]$\lambda$2424) at $z=0$ ($z=8$) that are
identified in our Keck/LRIS spectroscopy and the literature (the JWST ERO
program). With the flux ratios of these high ionization lines and $>10$
low-ionization lines of hydrogen, helium, oxygen, neon, and sulfur, we
determine ionizing spectra consisting of stellar and non-thermal power-law
radiation by photoionization modeling with free parameters of nebular
properties including metallicity and ionization parameter, cancelling out
abundance ratio differences. We find that all of the observed flux ratios are
well reproduced by the photoinization models with the power law index
$\alpha_{\rm EUV}$ of $\alpha_{\rm EUV}\sim (-1)-0$ and the luminosity $L_{\rm
EUV}$ of $L_{\rm EUV}\sim 10^{40}-10^{42}$ erg s$^{-1}$ at $\sim 55-100$ eV for
six galaxies, while four galaxies include large systematics in $\alpha_{\rm
EUV}$ caused by stellar radiation contamination. We then compare $\alpha_{\rm
EUV}$ and $L_{\rm EUV}$ of these six galaxies with those predicted by the black
hole (BH) accretion disk models, and find that $\alpha_{\rm EUV}$ and $L_{\rm
EUV}$ are similar to those of the intermediate mass black holes (IMBHs) in BH
accretion disk models {albeit with possibilities of the other scenarios.}
Confirming these results with a known IMBH having a mass $M_{\rm BH}$ of
$M_{\rm BH}=10^{5.75} \ M_\odot$, we find that four local galaxies and one
$z=7.665$ galaxy have ionizing spectra consistent with those of IMBHs with
$M_{\rm BH} \sim 10^3-10^5 \ M_\odot$.


  We establish a Large Deviations Principle for stochastic processes with
Lipschitz continuous oblique reflections on regular domains. The rate
functional is given as the value function of a control problem and is proved to
be good. The proof is based on an original viscosity solution approach. The
idea consists in interpreting the probabilities as the solutions of some PDEs,
make the logarithmic transform, pass to the limit, and then identify the action
functional as the solution of the limiting equation.


  Predicting the macroscopic chiral behaviour of cholesteric liquid crystals
from the microscopic chirality of the particles is highly non-trivial, even
when the chiral interactions are purely entropic in nature. Here we introduce a
novel chiral hard-particle model, namely particles with a twisted polyhedral
shape and obtain, for the first time, a stable fully-entropy-driven cholesteric
phase by computer simulations. By slightly modifying the triangular base of the
particle, we are able to switch from a left-handed prolate to a right-handed
oblate cholesteric using the same right-handed twisted particle model.
Furthermore, we find qualitative agreement with an Onsager-like theory,
suggesting that the latter can be used as a quick tool to scan the huge
parameter space associated to the microscopic chirality. Our results unveil how
the competition between particle biaxiality and chirality is reflected into the
nematic self-organization and new theoretical challenges on the self-assembly
of chiral particles can be undertaken.


  Matrix factorizations are among the most important building blocks of
scientific computing. State-of-the-art libraries, however, are not
communication-optimal, underutilizing current parallel architectures. We
present novel algorithms for Cholesky and LU factorizations that utilize an
asymptotically communication-optimal 2.5D decomposition. We first establish a
theoretical framework for deriving parallel I/O lower bounds for linear algebra
kernels, and then utilize its insights to derive Cholesky and LU schedules,
both communicating N^3/(P*sqrt(M)) elements per processor, where M is the local
memory size. The empirical results match our theoretical analysis: our
implementations communicate significantly less than Intel MKL, SLATE, and the
asymptotically communication-optimal CANDMC and CAPITAL libraries. Our code
outperforms these state-of-the-art libraries in almost all tested scenarios,
with matrix sizes ranging from 2,048 to 262,144 on up to 512 CPU nodes of the
Piz Daint supercomputer, decreasing the time-to-solution by up to three times.
Our code is ScaLAPACK-compatible and available as an open-source library.


  Deep learning has been wildly successful in practice and most
state-of-the-art machine learning methods are based on neural networks.
Lacking, however, is a rigorous mathematical theory that adequately explains
the amazing performance of deep neural networks. In this article, we present a
relatively new mathematical framework that provides the beginning of a deeper
understanding of deep learning. This framework precisely characterizes the
functional properties of neural networks that are trained to fit to data. The
key mathematical tools which support this framework include transform-domain
sparse regularization, the Radon transform of computed tomography, and
approximation theory, which are all techniques deeply rooted in signal
processing. This framework explains the effect of weight decay regularization
in neural network training, the use of skip connections and low-rank weight
matrices in network architectures, the role of sparsity in neural networks, and
explains why neural networks can perform well in high-dimensional problems.


  Inverse Kohn-Sham (iKS) problems are needed to fully understand the
one-to-one mapping between densities and potentials on which Density Functional
Theory is based. They are also important to advance computational schemes that
rely on density-to-potential inversions such as the Optimized Effective
Potential method and various techniques for density-based embedding. Unlike the
forward Kohn-Sham problems, numerical iKS problems are ill-posed and can be
unstable. We discuss some of the fundamental and practical difficulties of iKS
problems with constrained-optimization methods on finite basis sets. Various
factors that affect the performance are systematically compared and discussed,
both analytically and numerically, with a focus on two of the most practical
methods: the Wu-Yang method (WY) and partial-differential-equation
constrained-optimization (PDE-CO). Our analysis of the WY and PDE-CO highlights
the limitation of finite basis sets and the importance of regularization. We
introduce two new ideas that will hopefully contribute to making iKS problems
more tractable: (1) A correction to the WY method that utilizes the null space
of the relevant Hessian matrices; and (2) A finite potential basis-set
implementation of the PDE-CO method. We provide an overall strategy for
performing numerical density-to-potential inversions that can be directly
adopted in practice. We also provide an Appendix with several examples that can
be used for benchmarking.


  The multielectron LDA+GTB approach has been developed to calculate electronic
structure of strongly correlated cuprates. At low energies the effective
Hamiltonian of the $t - t' - t" - {t_ \bot } - {J^ * } - {J_ \bot }$-model has
been derived with parameters coming from the ab initio calculation for LSCO.
The electronic structure of LSCO has been calculated self-consistently with the
short-range antiferromagnetic order for various doping level. Two Lifshitz-type
quantum phase transitions with Fermi surface topology changes have been found
at dopings $x_{c1}=0.15$ and $x_{c2}=0.24$. Its effect on normal and
superconducting properties has been calculated. The interatomic exchange
parameter and its pressure dependence has been calculated within LDA+GTB
scheme. The magnetic mechanisms of d-wave pairing induced by static and
dynamical spin correlations are discussed. Simultaneous treatment of magnetic
and phonon pairing results in the conclusion that both contributions are of the
same order. For two layer cuprates like YBCO the interlayer hopping and
exchange effects on the electronic structure and doping dependence of $T_c$ is
discussed as well as the Coulomb interaction induced mechanism of pairing.


  We present a simple method based on the stability and duality of the
properties of sampling and interpolation, which allows one to substantially
simplify the proofs of some classical results.


  We study the growth rate of stars via stellar collisions in dense star
clusters, calibrating our analytic calculations with direct N-body simulations
of up to 65536 stars, performed on the GRAPE family of special-purpose
computers. We find that star clusters with initial half-mass relaxation times
of about 25 Myr are dominated by stellar collisions, the first collisions
occurring at or near the point of core collapse, which is driven by the
segregation of the most massive stars to the cluster center, where they end up
in hard binaries. The majority of collisions occur with the same star,
resulting in the runaway growth of a supermassive object. This object can grow
up to about 0.1% of the mass of the entire star cluster and could manifest
itself as an intermediate-mass black hole (IMBH). The phase of runaway growth
lasts until mass loss by stellar evolution arrests core collapse. Star clusters
older than about 5 Myr and with present-day half-mass relaxation times less
than 100 Myr are expected to contain an IMBH.


  Randomly coupled neural fields demonstrate chaotic variation of firing rates,
if the coupling is strong enough, as has been shown by Sompolinsky et. al
[Phys. Rev. Lett., v. 61, 259 (1988)]. We present a method for reconstruction
of the coupling matrix from the observations of the chaotic firing rates. The
approach is based on the particular property of the nonlinearity in the
coupling, as the latter is determined by a sigmoidal gain function. We
demonstrate that for a large enough data set, the method gives an accurate
estimation of the coupling matrix and of other parameters of the system,
including the gain function.


  We have used the high-resolution data of the Magnetospheric Multiscale (MMS)
mission dayside phase to identify twenty-one previously unreported encounters
with the electron diffusion region (EDR), as evidenced by electron agyrotropy,
ion jet reversals, and j dot E greater than 0. Three of the new EDR encounters,
which occurred within a one-minute-long interval on November 23rd, 2016, are
analyzed in detail. These events, which resulted from a relatively low and
oscillating magnetopause velocity, contained large electric fields (several
tens to hundreds of milliVolts per meter), crescent-shaped electron velocity
phase space densities, large currents (greater than 2 microAmperes per square
meter), and Ohmic heating of the plasma (near or exceeding 10 nanoWatts per
cubic meter). Because of the slow in-and-out motion of the magnetopause, two of
these events show the unprecedented mixture of perpendicular and parallel
crescents, indicating the first breaking and reconnecting of solar wind and
magnetospheric field lines. An extended list of thirty-two EDR or near-EDR
events is also included, and demonstrates a wide variety of observed plasma
behavior inside and surrounding the reconnection site.


  It is shown that the striking energy variation in the $p\, d \rightarrow
\mbox{$^{\, 3}{\rm He}$}\, \eta$ cross section near threshold is probably due
to a final state interaction associated with a large (complex) $\eta
-\mbox{$^{3}{\rm He}$}$ scattering length. The consequences of this hypothesis
are studied for the production of the meson in the $\eta -\mbox{$^{4}{\rm
He}$}$ and $\eta -\mbox{$^{7}{\rm Be}$}$ channels.


  We study Toeplitz operators on Hilbert spaces of holomorphic functions on
symmetric domains, and more generally on certain algebraic subvarieties,
determined by integration over boundary orbits of the underlying domain. The
main result classifies the irreducible representations of the Toeplitz
$C^*$-algebra generated by Toeplitz operators with continuous symbol. This
relies on the limit behavior of "hypergeometric" measures under certain peaking
functions.


  This paper is concerned with the computation of the local Lipschitz constant
of feedforward neural networks (FNNs) with activation functions being rectified
linear units (ReLUs). The local Lipschitz constant of an FNN for a target input
is a reasonable measure for its quantitative evaluation of the reliability. By
following a standard procedure using multipliers that capture the behavior of
ReLUs,we first reduce the upper bound computation problem of the local
Lipschitz constant into a semidefinite programming problem (SDP). Here we newly
introduce copositive multipliers to capture the ReLU behavior accurately. Then,
by considering the dual of the SDP for the upper bound computation, we second
derive a viable test to conclude the exactness of the computed upper bound.
However, these SDPs are intractable for practical FNNs with hundreds of ReLUs.
To address this issue, we further propose a method to construct a reduced order
model whose input-output property is identical to the original FNN over a
neighborhood of the target input. We finally illustrate the effectiveness of
the model reduction and exactness verification methods with numerical examples
of practical FNNs.


  We study homoclinic bifurcations in an interval map associated with a
saddle-focus of (2, 1)-type in $\mathbb{Z}_2$-symmetric systems. Our study of
this map reveals the homoclinic structure of the saddle-focus, with a
bifurcation unfolding guided by the codimension-two Belyakov bifurcation. We
consider three parameters of the map, corresponding to the saddle quantity,
splitting parameter, and focal frequency of the smooth saddle-focus in a
neighborhood of homoclinic bifurcations. We symbolically encode dynamics of the
map in order to find stability windows and locate homoclinic bifurcation sets
in a computationally efficient manner. The organization and possible shapes of
homoclinic bifurcation curves in the parameter space are examined, taking into
account the symmetry and discontinuity of the map. Sufficient conditions for
stability and local symbolic constancy of the map are presented. This study
furnishes insights into the structure of homoclinic bifurcations of the
saddle-focus map, furthering comprehension of low-dimensional chaotic systems.


  We propose a real-time image matching framework, which is hybrid in the sense
that it uses both hand-crafted features and deep features obtained from a
well-tuned deep convolutional network. The matching problem, which we
concentrate on, is specific to a certain application, that is, printing design
to product photo matching. Printing designs are any kind of template image
files, created using a design tool, thus are perfect image signals. However,
photographs of a printed product suffer many unwanted effects, such as
uncontrolled shooting angle, uncontrolled illumination, occlusions, printing
deficiencies in color, camera noise, optic blur, et cetera. For this purpose,
we create an image set that includes printing design and corresponding product
photo pairs with collaboration of an actual printing facility. Using this image
set, we benchmark various hand-crafted and deep features for matching
performance and propose a framework in which deep learning is utilized with
highest contribution, but without disabling real-time operation using an
ordinary desktop computer.


  In [arXiv:0911.4808] K. Karami commented on my publication
[arXiv:hep-th/0701242] and claimed that my result would be invalid. In fact he
found an error in calculation of the entropy of cold dark matter in section 3
of my article, which is, however, a rather trivial one. It is shown that my
discussion in section 3 of my paper works correctly if we take the value of
free parameter $b^2>0.264$.


  A discussion of polyhomogeneity (asymptotic expansions in terms of $1/r$ and
$\ln r$) for zero-rest-mass fields and gravity and its relation with the
Newman-Penrose (NP) constants is given. It is shown that for spin-$s$
zero-rest-mass fields propagating on Minkowski spacetime, the logarithmic terms
in the asymptotic expansion appear naturally if the field does not obey the
``Peeling theorem''. The terms that give rise to the slower fall-off admit a
natural interpretation in terms of advanced field. The connection between such
fields and the NP constants is also discussed. The case when the background
spacetime is curved and polyhomogeneous (in general) is considered. The free
fields have to be polyhomogeneous, but the logarithmic terms due to the
connection appear at higher powers of $1/r$. In the case of gravity, it is
shown that it is possible to define a new auxiliary field, regular at null
infinity, and containing some relevant information on the asymptotic behaviour
of the spacetime. This auxiliary zero-rest-mass field ``evaluated at future
infinity ($i^+$)'' yields the logarithmic NP constants.


  Multi-electron and multi-muon production at high transverse momentum is
measured in $ep$ scattering at HERA. Previous published analyses are extended,
combining new HERA II data taken in 2003-2004 with previous HERA I data sample.
In addition events with high $P_T$ electrons and muons are investigated here
for the first time. Yields of di-lepton and tri-lepton events are measured and
a general good agreement is found with the Standard Model prediction, dominated
by photon-photon interactions. Events are observed with leptons of high
transverse momenta in a domain where the Standard Model prediction is low.


  A variant of the Archimedean Positivstellensatz is proved which is based on
Archimedean semirings or quadratic modules of generating subalgebras. It allows
one to obtain representations of strictly positive polynomials on compact
semi-algebraic by means of smaller sets of squares or polynomials. A large
number of examples is developed in detail.


  Recently Nvidia has released a new GPU model: GTX Titan X (TX) in a linage of
the Maxwell architecture. We use our conjugate gradient code and
non-perturbative renormalization code to measure the performance of TX. The
results are compared with those of GTX Titan Black (TB) in a lineage of the
Kepler architecture. We observe a significant gain in the single and double
precision calculations much greater than the theoretical expectation.


  We consider an evolutionary problem with rapidly oscillating coefficients.
This causes the problem to change frequently between a parabolic and an
hyperbolic state. We prove convergence of the homogenisation process in the
unit square and present a numerical method to deal with approximations of the
resulting equations. A numerical study finalises the contribution.


  This paper proposes entitymetrics to measure the impact of knowledge units.
Entitymetrics highlight the importance of entities embedded in scientific
literature for further knowledge discovery. In this paper, we use Metformin, a
drug for diabetes, as an example to form an entity-entity citation network
based on literature related to Metformin. We then calculate the network
features and compare the centrality ranks of biological entities with results
from Comparative Toxicogenomics Database (CTD). The comparison demonstrates the
usefulness of entitymetrics to detect most of the outstanding interactions
manually curated in CTD.


  Our recent discoveries of magnetic fields in a small number of Herbig Ae/Be
(HAeBe) stars, the evolutionary progenitors of main sequence A/B stars, raise
new questions about the origin of magnetic fields in the intermediate mass
stars. The favoured fossil field hypothesis suggests that a few percent of
magnetic pre-main sequence A/B stars should exhibit similar magnetic strengths
and topologies to the magnetic Ap/Bp stars. In this talk I will present the
methods that we have used to characterise the magnetic fields of the Herbig
Ae/Be stars, as well as our first conclusions on the origin of magnetism in
intermediate-mass stars.


  In the present manuscript, we present a high-speed method to control,
manipulate and retrieve an intense vector soliton stored in the ground state
coherences of a four-level atomic system. Additionally, we show the importance
of the pulse area in determining the evolution of the system and present a
constant in the evolution defined as the three-pulse area, a surprising
extension to previously defined pulse areas.


  Matt Blum conjectured that the number of tilings of a hexagonal dungeon with
side-lengths $a,2a,b,a,2a,b$ (for $b\geq2a$) equals $13^{2a^2}14^{\lfloor
a^2/2\rfloor}$. Ciucu and the author of the present paper proved the conjecture
by using Kuo's graphical condensation method. In this paper, we investigate a
3-parameter refinement of the conjecture and its application to enumeration of
tilings of several new types of the hexagonal dungeons.


  Using a recently proposed classification for the primary translationally
shape invariant potentials, we show that the exact quantization rule formulated
by Ma and Xu is equivalent to the supersymmetric JWKB quantization condition.
The energy levels for the two considered categories of shaped invariant
potentials are also derived.


  Traditional global stability measure for sequences is hard to determine
because of large search space. We propose the $k$-error linear complexity with
a zone restriction for measuring the local stability of sequences. Accordingly,
we can efficiently determine the global stability by studying a local stability
for these sequences. For several classes of sequences, we demonstrate that the
$k$-error linear complexity is identical to the $k$-error linear complexity
within a zone, while the length of a zone is much smaller than the whole period
when the $k$-error linear complexity is large. These sequences have periods
$2^n$, or $2^v r$ ($r$ odd prime and $2$ is primitive modulo $r$), or $2^v
p_1^{s_1} \cdots p_n^{s_n}$ ($p_i$ is an odd prime and $2$ is primitive modulo
$p_i$ and $p_i^2$, where $1\leq i \leq n$) respectively. In particular, we
completely determine the spectrum of $1$-error linear complexity with any zone
length for an arbitrary $2^n$-periodic binary sequence.


  We present the 'simage' software suite for the simulation of artificial
extragalactic images, based empirically around real observations of the Hubble
Ultra Deep Field (UDF). The simulations reproduce galaxies with realistic and
complex morphologies via the modeling of UDF galaxies as shapelets. Images can
be created in the B, V, i and z bands for both space- and ground-based
telescopes and instruments. The simulated images can be produced for any
required field size, exposure time, Point Spread Function (PSF), telescope
mirror size, pixel resolution, field star density, and a variety of detector
noise sources. It has the capability to create images with both a
pre-determined number of galaxies or one calibrated to the number counts of
pre-existing data sets such as the HST COSMOS survey. In addition, simple
options are included to add a known weak gravitational lensing (both shear and
flexion) to the simulated images. The software is available in Interactive Data
Language (IDL) and can be freely downloaded for scientific, developmental and
teaching purposes.


  We propose autoencoding speaker conversion for training data augmentation in
automatic speech translation. This technique directly transforms an audio
sequence, resulting in audio synthesized to resemble another speaker's voice.
Our method compares favorably to SpecAugment on English$\to$French and
English$\to$Romanian automatic speech translation (AST) tasks as well as on a
low-resource English automatic speech recognition (ASR) task. Further, in
ablations, we show the benefits of both quantity and diversity in augmented
data. Finally, we show that we can combine our approach with augmentation by
machine-translated transcripts to obtain a competitive end-to-end AST model
that outperforms a very strong cascade model on an English$\to$French AST task.
Our method is sufficiently general that it can be applied to other speech
generation and analysis tasks.


  Can far-from-equilibrium material response under arbitrary loading be
inferred from equilibrium data and vice versa? Can the effect of element
transmutation on mechanical behavior be predicted? Remarkably, such
extrapolations are possible in principle for systems governed by stochastic
differential equations, thanks to a set of exact relations between probability
densities for trajectories derived from the path integral formalism [1, 2, 3].
In this article, we systematically investigate inferences (in the form of
ensemble-averages) drawn on system/process S based on stochastic trajectory
data of system/process S~, with quantified uncertainty, to directly address the
aforementioned questions. Interestingly, such inferences and their associated
uncertainty do not require any simulations or experiments of S. The results are
exemplified over two illustrative examples by means of numerical simulations: a
one-dimensional system as a prototype for polymers and biological
macromolecules, and a two-dimensional glassy system. In principle, the approach
can be pushed to the extreme case where S~ is simply comprised of Brownian
trajectories, i.e., equilibrium non-interacting particles, and S is a complex
interacting system driven far from equilibrium. In practice, however, the
"further" S~ is from S, the greater the uncertainty in the predictions, for a
fixed number of realizations of system S~.


  This paper develops a mathematical framework for the analysis of
continuous-time trading strategies which, in contrast to the classical setting
of continuous-time mathematical finance, does not rely on stochastic integrals
or other probabilistic notions. Our purely analytic framework allows for the
derivation of a pathwise self-financial condition for continuous-time trading
strategies, which is consistent with the classical definition in case a
probability model is introduced. Our first proposition provides us with a
pathwise definition of the gain process for a large class of continuous-time,
path-dependent, self-finacing trading strategies, including the important class
of 'delta-hedging' strategies, and is based on the recently developed
'non-anticipative functional calculus'. Two versions of the statement involve
respectively continuous and c\`adl\`ag price paths. The second proposition is a
pathwise replication result that generalizes the ones obtained in the classical
framework of diffusion models. Moreover, it gives an explicit and purely
pathwise formula for the hedging error of delta-hedging strategies for
path-dependent derivatives across a given set of scenarios. We also provide an
economic justification of our main assumption on price paths.


  We consider four-dimensional UV descriptions of composite Higgs models
without elementary scalars, in which four-fermion interactions are introduced
to an underlying gauge theory like in the gauged NJL model. When the anomalous
dimension of the fermion bilinear is large, these interactions drive the
spontaneous global symmetry breaking in the model, with the Higgs identified as
a Nambu-Goldstone boson. The UV descriptions support composite top partner
operators, also with large anomalous dimensions, thereby providing an explicit
realisation of the idea of partial compositeness. In particular, the composite
SO(6)/SO(5) model can be described by an Sp gauge theory with four flavours of
fermion, together with a vector-like pair of fermions transforming in the
antisymmetric representation and charged under SU(3) colour. These fermions
confine to produce both the Higgs and top partner bound states. Our methods can
also be applied to different coset groups, suggesting that four-fermion
operators can describe the underlying UV dynamics of other composite Higgs
models.


  We address the question of how to use a machine learned parameterization in a
general circulation model, and assess its performance both computationally and
physically. We take one particular machine learned parameterization
\cite{Guillaumin1&Zanna-JAMES21} and evaluate the online performance in a
different model from which it was previously tested. This parameterization is a
deep convolutional network that predicts parameters for a stochastic model of
subgrid momentum forcing by mesoscale eddies. We treat the parameterization as
we would a conventional parameterization once implemented in the numerical
model. This includes trying the parameterization in a different flow regime
from that in which it was trained, at different spatial resolutions, and with
other differences, all to test generalization. We assess whether tuning is
possible, which is a common practice in general circulation model development.
We find the parameterization, without modification or special treatment, to be
stable and that the action of the parameterization to be diminishing as spatial
resolution is refined. We also find some limitations of the machine learning
model in implementation: 1) tuning of the outputs from the parameterization at
various depths is necessary; 2) the forcing near boundaries is not predicted as
well as in the open ocean; 3) the cost of the parameterization is prohibitively
high on CPUs. We discuss these limitations, present some solutions to problems,
and conclude that this particular ML parameterization does inject energy, and
improve backscatter, as intended but it might need further refinement before we
can use it in production mode in contemporary climate models.


  Let $L/K$ be a finite Galois extension of $p$-adic fields with group $G$. It
is well-known that $\mathcal{O}_L$ contains a free $\mathcal{O}_K[G]$-submodule
of finite index. We study the minimal index of such a free submodule, and
determine it exactly in several cases, including for any cyclic extension of
degree $p$ of $p$-adic fields.


  We present a new mechanism for the creation of large rapidity gaps in DIS
events at HERA. Soft colour interactions between perturbatively produced
partons and colour-charges in the proton remnant, modifies the colour structure
for hadronization giving colour singlet systems that are well separated in
rapidity. An explicit model is presented that, although the detailed results
depend on the initial state parton emission, can describe both the observed
rapidity gaps and, in addition, the forward energy flow in an inclusive event
sample.


  Radio astronomical observations have very poor signal to noise ratios, unlike
in other disciplines. On the other hand, it is possible to observe the object
of interest for long time intervals as well as using a wider bandwidth.
Traditionally, by averaging in time and in frequency, it has been possible to
improve the signal to noise ratio of astronomical observations to improve the
dynamic range. This is possible due to the inherent assumption that the object
of interest in the sky is invariant over time and the frequency range of
observation. However, in reality this assumption does not hold, due to
intrinsic variation of the sky as well as due to errors generated by the
instrument. In this paper, we shall discuss an alternative to averaging of
images, without ignoring subtle changes in the observed data over time and
frequency, using subspace decomposition. By separation of data to signal and
noise subspaces, not only would this improve the quality of the data, but also
enable us to detect faint artifacts due to calibration errors, interference
etc.


  Computation of derivatives (gradient and Hessian) of a fidelity function is
one of the most crucial steps in many optimization algorithms. Having access to
accurate methods to calculate these derivatives is even more desired where the
optimization process requires propagation of these calculations over many
steps, which is in particular important in optimal control of spin systems.
Here we propose a novel numerical approach, ESCALADE (Efficient Spin Control
using Analytical Lie Algebraic Derivatives) that offers the exact first and
second derivatives of the fidelity function by taking advantage of the
properties of the Lie group of $2\times 2$ Hermitian matrices,
$\mathrm{SU}(2)$, and its Lie algebra, the Lie algebra of skew-Hermitian
matrices, $\mathfrak{su}(2)$. A full mathematical treatment of the proposed
method along with some numerical examples are presented.


  Modern design of complex optical systems relies heavily on computational
tools. These typically utilize geometrical optics as well as Fourier optics,
which enables the use of diffractive elements to manipulate light with features
on the scale of a wavelength. Fourier optics is typically used for designing
thin elements, placed in the system's aperture, generating a shift-invariant
Point Spread Function (PSF). A major bottleneck in applying Fourier Optics in
many cases of interest, e.g. when dealing with multiple, or out-of-aperture
elements, comes from numerical complexity. In this work, we propose and
implement an efficient and differentiable propagation model based on the
Collins integral, which enables the optimization of diffraction optical systems
with unprecedented design freedom using backpropagation. We demonstrate the
applicability of our method, numerically and experimentally, by engineering
shift-variant PSFs via thin plate elements placed in arbitrary planes inside
complex imaging systems, performing cascaded optimization of multiple planes,
and designing optimal machine-vision systems by deep learning.


  After shortly recalling the construction of the Khovanov-Kuperberg algebras,
we give a characterisation of indecomposable web-modules. It says that a
web-module is indecomposable if and only if one can deduce it directly from the
Kuperberg bracket (via a Schur lemma argument). The proofs relies on the
construction of idempotents given by explicit foams. These foams are encoded by
combinatorial data called red graphs. The key point is to show that when, for a
web $w$ the Schur lemma does not apply, one can find an appropriate red graph
for $w$.


  Within the hyperspherical harmonics approach the three-body problem is
reduced to a motion of one effective particle in a "strongly deformed" field,
which is described in coupled-channel formalism. This method is especially
suited to studies of phenomena characterized by genuine three-body dynamics,
e.g. Borromean haloes and true three-body decays. The reduction of the
hyperspherical equations set to a single-channel Schr\"odinger equation
provides the basis for the use of the standard quasiclassical expression for
calculations of widths for true three-body decays. We demonstrate that the
quasiclassical approach by itself is quite precise in application to typical
profiles of the three-body effective potentials. However, the reduction to
single-channel formalism leads to significant overestimation of the two-proton
width $\Gamma_{2p}$. This is demonstrated by the example of the $^{17}$Ne first
excited $3/2^-$ state decay, questioning, however, the applicability of such an
approximation in general.


  The most dramatic "Sommerfeld enhancements" of neutral-wino-pair annihilation
occur when the wino mass is tuned to near critical values where there is a
zero-energy S-wave resonance at the neutral-wino-pair threshold. If the wino
mass is larger than the critical value, the resonance is a wino-pair bound
state. If the wino mass is near a critical value, low-energy winos can be
described by a zero-range effective field theory in which the winos interact
nonperturbatively through a contact interaction. The parameters of the
zero-range effective field theory can be determined by matching wino scattering
amplitudes calculated by solving the Schr\"odinger equation for a
nonrelativistic effective field theory in which the winos interact through a
potential due to the exchange of electroweak gauge bosons. The utility of the
zero-range effective field theory is illustrated by calculating the rate for
formation of an S-wave bound state in the collision of two neutral winos
through the emission of two soft photons.


  Quantum critical states exhibit strong quantum fluctuations and are therefore
highly susceptible to perturbations. In this work we study the dynamical
stability against a sudden coupling to these strong fluctuations by quenching
the order parameter of the underlying transition. Such a quench can generate
superextensive energy fluctuations. This leads to a dynamical quantum phase
transition (DQPT) with nonanalytic real-time behavior in the resulting decay of
the initial state. By establishing a general connection between DQPTs and
quantum speed limits, this allows us to obtain a yet unrecognized quantum speed
limit with unconventional system size dependence. These findings are
illustrated for the one-dimensional and the infinitely-connected
transverse-field Ising model. The main concepts, however, are general and can
be applied also to other critical states. An outlook is given onto the
implications of the superextensive energy fluctuations on potential restricted
thermalization despite of nonintegrability.


  Most current works in Sim2Real learning for robotic manipulation tasks
leverage camera vision that may be significantly occluded by robot hands during
the manipulation. Tactile sensing offers complementary information to vision
and can compensate for the information loss caused by the occlusion. However,
the use of tactile sensing is restricted in the Sim2Real research due to no
simulated tactile sensors being available. To mitigate the gap, we introduce a
novel approach for simulating a GelSight tactile sensor in the commonly used
Gazebo simulator. Similar to the real GelSight sensor, the simulated sensor can
produce high-resolution images by an optical sensor from the interaction
between the touched object and an opaque soft membrane. It can indirectly sense
forces, geometry, texture and other properties of the object and enables
Sim2Real learning with tactile sensing. Preliminary experimental results have
shown that the simulated sensor could generate realistic outputs similar to the
ones captured by a real GelSight sensor. All the materials used in this paper
are available at https://danfergo.github.io/gelsight-simulation.


  The demand for keeping the information secure and confidential simultaneously
has been progressively increasing. Among various techniques- Audio
Steganography, a technique of embedding information transparently in a digital
media thereby restricting the access to such information has been prominently
developed. Imperceptibility, robustness, and payload or hiding capacity are the
main character for it. In earlier, LSB techniques increased payload capacity
would hamper robustness as well as imperceptibility of the cover media and vice
versa. The proposed technique overcomes the problem. It provides relatively
good improvement in the payload capacity by dividing the bytes of cover media
into ranges to hide the bits of secret message appropriately. As well as due to
the use of ranges of bytes the robustness of cover media has maintained and
imperceptibility preserved by using a pyramid structure.


  Ecological Cooperative and Adaptive Cruise Control (Eco-CACC) is widely
focused to enhance sustainability of CACC. However, state-of-the-art Eco-CACC
studies are still facing challenges in adopting on rolling terrain.
Furthermore, they cannot ensure both ecology optimality and computational
efficiency. Hence, this paper proposes a nonlinear optimal control based
Eco-CACC controller. It has the following features: i) enhancing performance
across rolling terrains by modeling in space domain; ii) enhancing fuel
efficiency via globally optimizing all vehicle's fuel consumptions; iii)
ensuring computational efficiency by developing a differential dynamic
programming-based solving method for the non-linear optimal control problem;
iv) ensuring string stability through theoretically proving and experimentally
validating. The performance of the proposed Eco-CACC controller was evaluated.
Results showed that the proposed Eco-CACC controller can improve average fuel
saving by 37.67% at collector road and about 17.30% at major arterial.


  In this paper, we build morphological chains for agglutinative languages by
using a log-linear model for the morphological segmentation task. The model is
based on the unsupervised morphological segmentation system called
MorphoChains. We extend MorphoChains log linear model by expanding the
candidate space recursively to cover more split points for agglutinative
languages such as Turkish, whereas in the original model candidates are
generated by considering only binary segmentation of each word. The results
show that we improve the state-of-art Turkish scores by 12% having a F-measure
of 72% and we improve the English scores by 3% having a F-measure of 74%.
Eventually, the system outperforms both MorphoChains and other well-known
unsupervised morphological segmentation systems. The results indicate that
candidate generation plays an important role in such an unsupervised log-linear
model that is learned using contrastive estimation with negative samples.


  In this note, we continue to highlight some applications of Theorem 1 of [3].
Here is a sample: Let $X$ be an open set in ${\bf C}^n$, $\Omega$ an open
convex set in ${\bf C}$ and $f, g : X\to {\bf C}$ two holomorphic functions
such that $f(X)\cap\Omega\neq\emptyset$, $f(X)\setminus\Omega\neq \emptyset$
and $g(X)\subseteq \Omega$. Then, there exists a set $A$ in $[0,1]$ with the
following properties:$(a)$ for each $x\in X$, there exists $\lambda\in A$ such
that $\lambda g(x)+(1-\lambda)f(x)\in\Omega$\ ; $(b)$ for each finite set $B$
in $A$, there exists $u\in X$ such that $\mu g(u)+(1-\mu)f(u)\in {\bf
C}\setminus\Omega$ for all $\mu\in B$.


  The widespread application of III-V colloidal quantum dots (QDs) as
non-toxic, highly tunable emitters is stymied by their high density of trap
states. Here, we utilize density functional theory (DFT) to investigate trap
state formation in a diverse set of realistically passivated core-only InP and
GaP QDs. Through orbital localization techniques, we deconvolute the dense
manifold of trap states to allow for detailed assignment of surface defects. We
find that the three-coordinate species dominate trapping in III-V QDs and
identify features in the geometry and charge environment of trap centers
capable of deepening, or sometimes passivating, traps. Furthermore, we observe
stark differences in surface reconstruction between InP and GaP, where the more
labile InP reconstructs to passivate three-coordinate indium at the cost of
distortion elsewhere. These results offer explanations for experimentally
observed trapping behavior and suggest new avenues for controlling trap states
in III-V QDs.


  In this short note we show the equivalence of Fourier expansion and Poisson
summation approaches for the series approximation of the exponential function
$\exp ({-{t^2}/4})$. The application of the Poisson summation formula is shown
to reduce to that of the Fourier expansion method.


  Software weaknesses that create attack surfaces for adversarial exploits,
such as lateral SQL injection (LSQLi) attacks, are usually introduced during
the design phase of software development. Security design patterns are
sometimes applied to tackle these weaknesses. However, due to the stealthy
nature of lateral-based attacks, employing traditional security patterns to
address these threats is insufficient. Hence, we present SEAL, a secure design
that extrapolates architectural, design, and implementation abstraction levels
to delegate security strategies toward tackling LSQLi attacks. We evaluated
SEAL using case study software, where we assumed the role of an adversary and
injected several attack vectors tasked with compromising the confidentiality
and integrity of its database. Our evaluation of SEAL demonstrated its capacity
to address LSQLi attacks.


  In this paper we study M-theory compactifications on manifolds of G2
structure. By computing the gravitino mass term in four dimensions we derive
the general form for the superpotential which appears in such compactifications
and show that beside the normal flux term there is a term which appears only
for non-minimal G2 structure. We further apply these results to
compactifications on manifolds with weak G2 holonomy and make a couple of
statements regarding the deformation space of such manifolds. Finally we show
that the superpotential derived from fermionic terms leads to the potential
that can be derived from the explicit compactification, thus strengthening the
conjectures we make about the space of deformations of manifolds with weak G2
holonomy.


  From first-principles approaches, we illustrate that the current-induced
forces and the selection rule for inelastic effects are highly relevant to the
current density in an asymmetric molecular junction. The curved flow of current
streamline around the asymmetric molecule may induce a net torque, which tends
to rotate the benzene molecule, similar to the way a stream of water rotates a
waterwheel. Thus, the Pt/benzene junction offers a practical system in the
exploration of the possibility of atomic-scale motors. We also enumerate
examples to show that the use of selection rule can lead to misjudgement of the
importance of normal modes in the inelastic profiles when the detailed
information about the current density is not considered.


  We give a simple and direct proof of the characterization of positivity
preserving semi-flows for ordinary differential systems. The same method
provides an abstract result on a class of evolution systems containing
reaction-diffusion systems in a bounded domain of $ \mathbb{R}^n$ with either
Neumann or Dirichlet homogeneous boundary conditions. The conditions are
exactly the same with or without diffusion. A similar approach gives the
optimal result for invariant rectangles in the case of Neumann conditions.


  Level statistics of systems that undergo many--body localization transition
are studied. An analysis of the gap ratio statistics from the perspective of
inter- and intra-sample randomness allows us to pin point differences between
transitions in random and quasi-random disorder, showing the effects due to
Griffiths rare events for the former case. It is argued that the transition in
the case of random disorder exhibits universal features that are identified by
constructing an appropriate model of intermediate spectral statistics which is
a generalization of the family of short-range plasma models. The considered
weighted short-range plasma model yields a very good agreement both for level
spacing distribution including its exponential tail and the number variance up
to tens of level spacings outperforming previously proposed models. In
particular, our model grasps the critical level statistics which arise at
disorder strength for which the inter-sample fluctuations are the strongest.
Going beyond the paradigmatic examples of many-body localization in spin
systems, we show that the considered model also grasps the level statistics of
disordered Bose- and Fermi-Hubbard models. The remaining deviations for
long-range spectral correlations are discussed and attributed mainly to the
intricacies of level unfolding.


  In this study, we investigate the real-time dynamics during the spontaneous
deformation of an unstable spherical black hole in asymptotically anti-de
Sitter (AdS) spacetime. For the initial value, the static solutions with
spherical symmetry are obtained numerically, revealing the presence of a
spinodal region in the phase diagram. From the linear stability analysis, we
find that only the central part of such a thermodynamically unstable spinodal
region leads to the emergence of a type of axial instability. To trigger the
dynamical instability, an axial perturbation is imposed on the scalar field. As
a result, by the fully nonlinear dynamical simulation, the spherical symmetry
of the gravitational system is broken spontaneously, leading to the formation
of an axisymmetric black hole.


  The Force Concept Inventory (FCI) is a well-established physics education
assessment tool used to evaluate students' comprehension of elementary
mechanics principles. While it can be used to analyse the effectiveness of
instruction if deployed as a pre- and post-test, we utilise the FCI here as
pre-test only, to extract insights into first-year students' (mis)conceptions
of Newtonian mechanics as they enter university. In this preliminary study, we
tested 353 students enrolled at the University of Johannesburg in 2021, across
six introductory physics courses. We focus on their responses to six
"polarising" questions, for which the presence of a correct and a
mostly-correct answer allows for a clear demonstration of persistent
misconceptions.


  The Arcanum mission is a proposed L-class spacecraft that highlights the
revolutionary approach which can now be taken to future space mission design.
Using the case of the SpaceX Starship vehicle and in particular the high mass
and volume characteristics of this launcher, the feasible large size of future
missions, even with high delta-V transfer requirements, are analysed. A
demonstrator vehicle, designed to support a large and capable science platform
with multiple components, is detailed, clearly showing the range and depth of
science goals that will be answerable thanks to the current revolution in super
heavy-lift launch vehicles.


  The purpose of this paper is to investigate the connection between
context-free grammars and normal ordering problem, and then to explore various
extensions of the Stirling grammar. We present grammatical characterizations of
several well known combinatorial sequences, including the generalized Stirling
numbers of the second kind related to the normal ordering problem and the
$r$-Dowling polynomials. Also, possible avenues for future research are
described.


  Penalty functions or regularization terms that promote structured solutions
to optimization problems are of great interest in many fields. Proposed in this
work is a nonconvex structured sparsity penalty that promotes one-sparsity
within arbitrary overlapping groups in a vector. This allows one to enforce
mutual exclusivity between components within solutions to optimization
problems. We show multiple example use cases (including a total variation
variant), demonstrate synergy between it and other regularizers, and propose an
algorithm to efficiently solve problems regularized or constrained by the
proposed penalty.