  Electric vehicle (EV) charging stations have become prominent in electricity
grids in the past years. Analysis of EV charging sessions is useful for
flexibility analysis, load balancing, offering incentives to customers, etc.
Yet, the limited availability of such EV sessions data hinders further
development in these fields. Addressing this need for publicly available and
realistic data, we develop a synthetic data generator (SDG) for EV charging
sessions. Our SDG assumes the EV inter-arrival time to follow an exponential
distribution. Departure times are modeled by defining a conditional probability
density function (pdf) for connection times. This pdf for connection time and
required energy is fitted by Gaussian mixture models. Since we train our SDG
using a large real-world dataset, its output is realistic.


  The Mellin-Barnes representation for the free energy of the genus-$g$ string
is constructed. It is shown that the interactions of the open bosonic string do
not modify the critical (Hagedorn) temperature. However,for the sectors having
a spinor structure, the critical temperature exists also for all $g$ and
depends on the windings. The appearance of a periodic structure is briefly
discussed.


  In this paper, we report the discovery of a binary composed of a brown dwarf
and a low-mass M dwarf from the observation of the microlensing event
OGLE-2014-BLG-0257. Resolution of the very short-lasting caustic crossing
combined with the detection of subtle continuous deviation in the lensing light
curve induced by the Earth's orbital motion enable us to precisely measure both
the Einstein radius \theta_E and the lens parallax pi_E, which are the two
quantities needed to unambiguously determine the mass and distance to the lens.
It is found that the companion is a substellar brown dwarf with a mass 0.036
+/- 0.005 Msun (37.7 +/- 5.2\ M_J) and it is orbiting an M dwarf with a mass
0.19 +/- 0.02 Msun. The binary is located at a distance 1.25 +/- 0.13 kpc
toward the Galactic bulge and the projected separation between the binary
components is 0.61 +/- 0.07 AU. The separation scaled by the mass of the host
is 3.2 AU/Msun. Under the assumption that separations scale with masses, then,
the discovered brown dwarf is located in the zone of the brown dwarf desert.
With the increasing sample of brown dwarfs existing in various environments,
microlensing will provide a powerful probe of brown dwarfs in the Galaxy.


  An analytical study of discrete and resonant impurity quasi-Coulomb states in
a narrow gaped armchair graphene nanoribbon (GNR) is performed. We employ the
adiabatic approximation assuming that the motions parallel ("slow") and
perpendicular ("fast") to the boundaries of the ribbon are separated
adiabatically. The energy spectrum comprises a sequence of series of
quasi-Rydberg levels relevant to the "slow" motion adjacent from the low
energies to the size-quantized levels associated with the "fast" motion. Only
the series attributed to the ground size-quantized sub-band is really discrete,
while others corresponding to the excited sub-bands consist of quasi-discrete
(Fano resonant) levels of non-zero energetic widths, caused by the coupling
with the states of the continuous spectrum branching from the low lying
sub-bands. In the two- and three-subband approximation the spectrum of the
complex energies of the impurity electron is derived in an explicit form.
Narrowing the GNR leads to an increase of the binding energy and the resonant
width both induced by the finite width of the ribbon. Displacing the impurity
centre from the mid-point of the GNR causes the binding energy to decrease
while the resonant width of the first excited Rydberg series increases. As for
the second excited series their widths become narrower with the shift of the
impurity. A successful comparison of our analytical results with those obtained
by other theoretical and experimental methods is presented. Estimates of the
binding energies and the resonant widths taken for the parameters of typical
GNRs show that not only the strictly discrete but also the some resonant states
are quite stable and could be studied experimentally in doped GNRs.


  We show if we use countable support iteration of forcing notions not adding
reals that satisfy additional conditions, then the limit forcing does not add
reals. As a result we prove that we can amalgamate two earlier methods and
prove the consistency with ZFC + GCH of two statements gotten separately
earlier: Souslin hypothesis and non-club guessing. We also answer a question of
Justin Moore by proving the consistency of one further case of "strong failure
of club guessing" with GCH.


  In many applications, linear models fit the data poorly. This article studies
an appealing alternative, the generalized regression model. This model only
assumes that there exists an unknown monotonically increasing link function
connecting the response $Y$ to a single index $X^T\beta^*$ of explanatory
variables $X\in\mathbb{R}^d$. The generalized regression model is flexible and
covers many widely used statistical models. It fits the data generating
mechanisms well in many real problems, which makes it useful in a variety of
applications where regression models are regularly employed. In low dimensions,
rank-based M-estimators are recommended to deal with the generalized regression
model, giving root-$n$ consistent estimators of $\beta^*$. Applications of
these estimators to high dimensional data, however, are questionable. This
article studies, both theoretically and practically, a simple yet powerful
smoothing approach to handle the high dimensional generalized regression model.
Theoretically, a family of smoothing functions is provided, and the amount of
smoothing necessary for efficient inference is carefully calculated.
Practically, our study is motivated by an important and challenging scientific
problem: decoding gene regulation by predicting transcription factors that bind
to cis-regulatory elements. Applying our proposed method to this problem shows
substantial improvement over the state-of-the-art alternative in real data.


  We combine recent measurements of Cosmic Microwave Background Anisotropies,
Supernovae luminosity distances and Baryonic Acoustic Oscillations to derive
constraints on the dark energy equation of state w in the redshift range 0<z<2,
using a principal components approach. We find no significant deviations from
the expectations of a cosmological constant. However, combining the datasets we
find slight indication for w<-1 at low redshift, thus highlighting how these
datasets prefer a non-constant w. Nevertheless the cosmological constant is
still in agreement with these observations, while we find that some classes of
alternative models may be in tension with the inferred w(z) behaviour.


  We provide a new description of Joyal's arithmetic universes through a
characterization of the exact and regular completions of pure existential
completions. We show that the regular and exact completions of the pure
existential completion of an elementary doctrine $P$ are equivalent to the
$\mathsf{reg}/\mathsf{lex}$ and $\mathsf{ex}/\mathsf{lex}$-completions,
respectively, of the category of predicates of $P$. This result generalizes a
previous one by the first author with F. Pasquali and G. Rosolini about
doctrines equipped with Hilbert's $\epsilon$-operators. Thanks to this
characterization, each arithmetic universe in the sense of Joyal can be seen as
the exact completion of the pure existential completion of the doctrine of
predicates of its Skolem theory. In particular, the initial arithmetic universe
in the standard category of ZFC-sets turns out to be the completion with exact
quotients of the doctrine of recursively enumerable predicates.


  Contributions of the present paper consist of two parts. In the first one, we
contribute to the theory of stochastic calculus for signed measures. For
instance, we provide some results permitting to characterize martingales and
Brownian motion both defined under a signed measure. We also prove that the
uniformly integrable martingales (defined with respect to a signed measure) can
be expressed as relative martingales and we provide some new results to the
study of the class $\Sigma(H)$ which appeared for the first time in \cite{f}
and studied in \cite{f,e,o}. The second part is devoted to the construction of
solutions for the \textbf{homogeneous skew Brownian motion equation} and for
the \textbf{inhomogeneous skew Brownian motion equation}. To do this, our
ingredients are the techniques and results developed in the first part that we
apply on some stochastic processes borrowed from the theory of stochastic
calculus for signed measures. Our methods are inspired by those used by
Bouhadou and Ouknine in \cite{siam}. Moreover, their solution of the
inhomogeneous skew Brownian motion equation is a particular case of those we
propose in this paper.


  In this paper, we present a novel distributed state estimation approach in
networked DC microgrids to detect the false data injection in the microgrid
control network. Each microgrid monitored by a distributed state estimator will
detect if there is manipulated data received from their neighboring microgrids
for control purposes. A dynamic model supporting the dynamic state estimation
will be constructed for the networked microgrids. The optimal distributed state
estimation, which is robust to load disturbances but sensitive to false data
injected from neighboring microgrids will be presented. To demonstrate the
effectiveness of the proposed approach, we simulate a 12kV three-bus networked
DC microgrids in MATLAB/Simulink. Residual information corresponding to the
false data injected from neighbors validates the efficacy of the proposed
approach in detecting compromised agents of neighboring microgrids.


  Results of a search for supersymmetry are presented using events with a
photon, an electron or muon, and large missing transverse momentum. The
analysis is based on a data sample corresponding to an integrated luminosity of
35.9 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} =$ 13 TeV, produced by
the LHC and collected with the CMS detector in 2016. Theoretical models with
gauge-mediated supersymmetry breaking predict events with photons in the final
state, as well as electroweak gauge bosons decaying to leptons. Searches for
events with a photon, a lepton, and missing transverse momentum are sensitive
probes of these models. No excess of events is observed beyond expectations
from standard model processes. The results of the search are interpreted in the
context of simplified models inspired by gauge-mediated supersymmetry breaking.
These models are used to derive upper limits on the production cross sections
and set lower bounds on masses of supersymmetric particles. Gaugino masses
below 930 GeV are excluded at the 95% confidence level in a simplified model
with electroweak production of a neutralino and chargino. For simplified models
of gluino and squark pair production, gluino masses up to 1.75 TeV and squark
masses up to 1.43 TeV are excluded at the 95% confidence level.


  We consider modified gravity cosmological models that can be transformed into
two-field chiral cosmological models by the conformal metric transformation.
For the $R^2$ gravity model with an additional scalar field and the
corresponding two-field model with the cosmological constant and nonstandard
kinetic part of the action, the general solutions have been obtained in the
spatially flat FLRW metric. We analyze the correspondence of the cosmic time
solutions obtained and different possible evolutions of the Hubble parameters
in the Einstein and Jordan frames.


  Conventional superstring amplitudes in flat space exhibits exponential fall
off at wide angle in contrast to the power law behavior found in QCD. It has
recently been argued by Polchinski and Strassler that this conflict can be
resolved via String/Gauge duality. They carried out their analysis in terms of
strings in a deformed $AdS^5$ background. On the other hand, an equally valid
approach to the String/Gauge duality for 4-d QCD is based on M-theory in a
specific Black Hole deformation of $AdS^7 \times S^4$. We show that a very
natural extension to this phenomenologically interesting M-theory background
also gives the correct hard scattering power laws. In the Regge limit we extend
the analysis to show the co-existence of both the hard BFKL-like Pomeron and
the soft Pomeron Regge pole.


  A \emph{matching} is a subset of edges in a graph $G$ that do not share an
endpoint. A matching $M$ is a \emph{$\mathcal{P}$-matching} if the subgraph of
$G$ induced by the endpoints of the edges of $M$ satisfies property
$\mathcal{P}$. For example, if the property $\mathcal{P}$ is that of being a
matching, being acyclic, or being disconnected, then we obtain an \emph{induced
matching}, an \emph{acyclic matching}, and a \emph{disconnected matching},
respectively. In this paper, we analyze the problems of the computation of
these matchings from the viewpoint of Parameterized Complexity with respect to
the parameter \emph{treewidth}.


  The growing popularity of autonomous systems creates a need for reliable and
efficient metric pose retrieval algorithms. Currently used approaches tend to
rely on nearest neighbor search of binary descriptors to perform the 2D-3D
matching and guarantee realtime capabilities on mobile platforms. These methods
struggle, however, with the growing size of the map, changes in viewpoint or
appearance, and visual aliasing present in the environment. The rigidly defined
descriptor patterns only capture a limited neighborhood of the keypoint and
completely ignore the overall visual context.
  We propose LandmarkBoost - an approach that, in contrast to the conventional
2D-3D matching methods, casts the search problem as a landmark classification
task. We use a boosted classifier to classify landmark observations and
directly obtain correspondences as classifier scores. We also introduce a
formulation of visual context that is flexible, efficient to compute, and can
capture relationships in the entire image plane. The original binary
descriptors are augmented with contextual information and informative features
are selected by the boosting framework. Through detailed experiments, we
evaluate the retrieval quality and performance of LandmarkBoost, demonstrating
that it outperforms common state-of-the-art descriptor matching methods.


  Text-Video Retrieval plays an important role in multi-modal understanding and
has attracted increasing attention in recent years. Most existing methods focus
on constructing contrastive pairs between whole videos and complete caption
sentences, while overlooking fine-grained cross-modal relationships, e.g.,
clip-phrase or frame-word. In this paper, we propose a novel method, named
Hierarchical Cross-Modal Interaction (HCMI), to explore multi-level cross-modal
relationships among video-sentence, clip-phrase, and frame-word for text-video
retrieval. Considering intrinsic semantic frame relations, HCMI performs
self-attention to explore frame-level correlations and adaptively cluster
correlated frames into clip-level and video-level representations. In this way,
HCMI constructs multi-level video representations for frame-clip-video
granularities to capture fine-grained video content, and multi-level text
representations at word-phrase-sentence granularities for the text modality.
With multi-level representations for video and text, hierarchical contrastive
learning is designed to explore fine-grained cross-modal relationships, i.e.,
frame-word, clip-phrase, and video-sentence, which enables HCMI to achieve a
comprehensive semantic comparison between video and text modalities. Further
boosted by adaptive label denoising and marginal sample enhancement, HCMI
achieves new state-of-the-art results on various benchmarks, e.g., Rank@1 of
55.0%, 58.2%, 29.7%, 52.1%, and 57.3% on MSR-VTT, MSVD, LSMDC, DiDemo, and
ActivityNet, respectively.


  Large Language Models (LLMs) like ChatGPT and GPT-4 are versatile and capable
of addressing a diverse range of tasks. However, general LLMs, which are
developed on open-domain data, may lack the domain-specific knowledge essential
for tasks in vertical domains, such as legal, medical, etc. To address this
issue, previous approaches either conduct continuous pre-training with
domain-specific data or employ retrieval augmentation to support general LLMs.
Unfortunately, these strategies are either cost-intensive or unreliable in
practical applications. To this end, we present a novel framework named BLADE,
which enhances Black-box LArge language models with small Domain-spEcific
models. BLADE consists of a black-box LLM and a small domain-specific LM. The
small LM preserves domain-specific knowledge and offers specialized insights,
while the general LLM contributes robust language comprehension and reasoning
capabilities. Specifically, our method involves three steps: 1) pre-training
the small LM with domain-specific data, 2) fine-tuning this model using
knowledge instruction data, and 3) joint Bayesian optimization of the general
LLM and the small LM. Extensive experiments conducted on public legal and
medical benchmarks reveal that BLADE significantly outperforms existing
approaches. This shows the potential of BLADE as an effective and
cost-efficient solution in adapting general LLMs for vertical domains.


  Pulsars can act as an excellent probe of the Milky Way magnetic field. The
average strength of the Galactic magnetic field component parallel to the line
of sight can be estimated as $\langle B_\parallel \rangle = 1.232 \,
\text{RM}/\text{DM}$, where $\text{RM}$ and $\text{DM}$ are the rotation and
dispersion measure of the pulsar. However, this assumes that the thermal
electron density and magnetic field of the interstellar medium are
uncorrelated. Using numerical simulations and observations, we test the
validity of this assumption. Based on magnetohydrodynamical simulations of
driven turbulence, we show that the correlation between the thermal electron
density and the small-scale magnetic field increases with increasing Mach
number of the turbulence. We find that the assumption of uncorrelated thermal
electron density and magnetic fields is valid only for subsonic and transsonic
flows, but for supersonic turbulence, the field strength can be severely
overestimated by using $1.232 \, \text{RM}/\text{DM}$. We then correlate
existing pulsar observations from the Australia Telescope National Facility
with regions of enhanced thermal electron density and magnetic fields probed by
${^{12} \mathrm {CO}}$ data of molecular clouds, magnetic fields from the
Zeeman splitting of the 21 cm line, neutral hydrogen column density, and
H$\alpha$ observations. Using these observational data, we show that the
thermal electron density and magnetic fields are largely uncorrelated over kpc
scales. Thus, we conclude that the relation $\langle B_\parallel \rangle =
1.232 \, \text{RM}/\text{DM}$ provides a good estimate of the magnetic field on
Galactic scales but might break down on sub - kpc scales.


  Given a connected Riemannian manifold $\mathcal{N}$, an \(m\)--dimensional
Riemannian manifold $\mathcal{M}$ which is either compact or the Euclidean
space, $p\in [1, +\infty)$ and $s\in (0,1]$, we establish, for the problems of
surjectivity of the trace, of weak-bounded approximation, of lifting and of
superposition, that qualitative properties satisfied by every map in a
nonlinear Sobolev space $W^{s,p}(\mathcal{M}, \mathcal{N})$ imply corresponding
uniform quantitative bounds. This result is a nonlinear counterpart of the
classical Banach--Steinhaus uniform boundedness principle in linear Banach
spaces.


  In this paper, we propose a mesh-free numerical method for solving elliptic
PDEs on unknown manifolds, identified with randomly sampled point cloud data.
The PDE solver is formulated as a spectral method where the test function space
is the span of the leading eigenfunctions of the Laplacian operator, which are
approximated from the point cloud data. While the framework is flexible for any
test functional space, we will consider the eigensolutions of a weighted
Laplacian obtained from a symmetric Radial Basis Function (RBF) method induced
by a weak approximation of a weighted Laplacian on an appropriate Hilbert
space. Especially, we consider a test function space that encodes the geometry
of the data yet does not require us to identify and use the sampling density of
the point cloud. To attain a more accurate approximation of the expansion
coefficients, we adopt a second-order tangent space estimation method to
improve the RBF interpolation accuracy in estimating the tangential
derivatives. This spectral framework allows us to efficiently solve the PDE
many times subjected to different parameters, which reduces the computational
cost in the related inverse problem applications. In a well-posed elliptic PDE
setting with randomly sampled point cloud data, we provide a theoretical
analysis to demonstrate the convergent of the proposed solver as the sample
size increases. We also report some numerical studies that show the convergence
of the spectral solver on simple manifolds and unknown, rough surfaces. Our
numerical results suggest that the proposed method is more accurate than a
graph Laplacian-based solver on smooth manifolds. On rough manifolds, these two
approaches are comparable. Due to the flexibility of the framework, we
empirically found improved accuracies in both smoothed and unsmoothed Stanford
bunny domains by blending the graph Laplacian eigensolutions and RBF
interpolator.


  TUS (Track Ultraviolet Setup) is the first space experiment aimed to check
the possibility of registering extreme energy cosmic rays (EECRs) at E>50 EeV
by measuring the fluorescence signal of extensive air showers in the
atmosphere. The detector operates as a part of the scientific payload of the
Lomonosov satellite for more than a year. We describe an algorithm of searching
for EECR events in the TUS data and briefly discuss a number of candidates
selected by formal criteria.


  The whole spectrum of high-energy cosmic ray (HECR) is, very likely,
influenced by tachyonic neutrinos. Especially, the appearance of two knees can
be fitted by the tachyon mass $m(\nu_e)=m(\nu_\mu)\simeq 0.51$ eV/$c^2$ as
predicted by a minimal three - flavor model for tachyonic neutrino with one
parameter $\delta=0.38$ eV only. Then the evasion of GZK cutoff could be
ascribed to $Z^0(W^\pm)$-burst model together with the same mechanism for knees
as well as a prediction of left-right polarization dependent lifetime
asymmetry. A further conclusive experiment might be whether the protons of HECR
detected on Earth are really right handed polarized?


  We address the problem of reaching consensus in the presence of Byzantine
faults. In particular, we are interested in investigating the impact of
messages relay on the network connectivity for a correct iterative approximate
Byzantine consensus algorithm to exist. The network is modeled by a simple
directed graph. We assume a node can send messages to another node that is up
to $l$ hops away via forwarding by the intermediate nodes on the routes, where
$l\in \mathbb{N}$ is a natural number. We characterize the necessary and
sufficient topological conditions on the network structure. The tight
conditions we found are consistent with the tight conditions identified for
$l=1$, where only local communication is allowed, and are strictly weaker for
$l>1$. Let $l^*$ denote the length of a longest path in the given network. For
$l\ge l^*$ and undirected graphs, our conditions hold if and only if $n\ge
3f+1$ and the node-connectivity of the given graph is at least $2f+1$ , where
$n$ is the total number of nodes and $f$ is the maximal number of Byzantine
nodes; and for $l\ge l^*$ and directed graphs, our conditions is equivalent to
the tight condition found for exact Byzantine consensus.
  Our sufficiency is shown by constructing a correct algorithm, wherein the
trim function is constructed based on investigating a newly introduced minimal
messages cover property. The trim function proposed also works over
multi-graphs.


  In the present paper we establish the necessary and sufficient conditions for
two generalized Abel differential equations to be locally equivalent under the
action of the pseudogroup of linear transformations of the form $\{x\mapsto
f(x),~ y\mapsto g(x)\cdot y + h(x)\}$. These conditions are formulated in terms
of differential invariants.


  The annotation of domain experts is important for some medical applications
where the objective ground truth is ambiguous to define, e.g., the
rehabilitation for some chronic diseases, and the prescreening of some
musculoskeletal abnormalities without further medical examinations. However,
improper uses of the annotations may hinder developing reliable models. On one
hand, forcing the use of a single ground truth generated from multiple
annotations is less informative for the modeling. On the other hand, feeding
the model with all the annotations without proper regularization is noisy given
existing disagreements. For such issues, we propose a novel Learning to
Agreement (Learn2Agree) framework to tackle the challenge of learning from
multiple annotators without objective ground truth. The framework has two
streams, with one stream fitting with the multiple annotators and the other
stream learning agreement information between annotators. In particular, the
agreement learning stream produces regularization information to the classifier
stream, tuning its decision to be better in line with the agreement between
annotators. The proposed method can be easily added to existing backbones, with
experiments on two medical datasets showed better agreement levels with
annotators.


  We define a new finite type invariant for stably homeomorphic class of curves
on compact oriented surfaces without boundaries and extend to a regular
homotopy invariant for spherical curves.


  Finite-temperature charge-ordering phase transition in quasi one-dimensional
(1D) molecular conductors is investigated theoretically, based on a quasi 1D
extended Hubbard model at quarter filling with interchain Coulomb repulsion
$V_\perp$. The interchain term is treated within mean-field approximation
whereas the 1D fluctuations in the chains are fully taken into account by the
bosonization theory. Three regions are found depending on how the charge
ordered state appears at finite temperature when $V_\perp$ is introduced:
  (i) weak-coupling region where the system transforms from a metal to a charge
ordered insulator with finite transition temperature at a finite critical value
of $V_\perp$,
  (ii) an intermediate region where this transition occurs by infinitesimal
$V_\perp$ due to the stability of inherent 1D fluctuation, and
  (iii) strong-coupling region where the charge ordered state is realized
already in the purely 1D case, of which the transition temperature becomes
finite with infinitesimal $V_\perp$. Analytical formula for the $V_\perp$
dependence of the transition temperature is derived for each region.


  Ray nil-affine geometries are defined on nilpotent spaces. They occur in
every parabolic geometry and in those cases, the nilpotent space is an open
dense subset of the corresponding flag manifold. We are interested in closed
manifolds having a ray nil-affine structure. We show that under a rank one
condition on the isotropy, closed manifolds are either complete or their
developing map is a cover onto the complement of a nil-affine subspace. We
prove that if additionally there is a parallel volume or if the automorphism
group acts non properly then closed manifolds are always complete.This paper is
a sequel to a previous work on ray manifolds in affine geometry.


  Electrons which are slowly moving through chiral magnetic textures can
effectively be described as if they where influenced by electromagnetic fields
emerging from the real-space topology. This adiabatic viewpoint has been very
successful in predicting physical properties of chiral magnets. Here, based on
a rigorous quantum-mechanical approach, we unravel the emergence of chiral and
topological orbital magnetism in one- and two-dimensional spin systems. We
uncover that the quantized orbital magnetism in the adiabatic limit can be
understood as a Landau-Peierls response to the emergent magnetic field. Our
central result is that the spin-orbit interaction in interfacial skyrmions and
domain walls can be used to tune the orbital magnetism over orders of magnitude
by merging the real-space topology with the topology in reciprocal space. Our
findings point out the route to experimental engineering of orbital properties
of chiral spin systems, thereby paving the way to the field of chiral
orbitronics.


  Quasi-conformal models are an appealing scenario that can offer naturally a
strongly supercooled phase transition and a period of thermal inflation in the
early Universe. A crucial aspect for the viability of these models is how the
Universe escapes from the supercooled state. One possibility is that thermal
inflation phase ends by nucleation and percolation of true vacuum bubbles. This
route is not, however, always efficient. In such case another escape mechanism,
based on the growth of quantum fluctuations of the scalar field that eventually
destabilize the false vacuum, becomes relevant. We study both of these cases in
detail in a simple yet representative model. We determine the duration of the
thermal inflation, the curvature power spectrum generated for the scales that
exit horizon during the thermal inflation, and the stochastic gravitational
wave background from the phase transition. We show that these gravitational
waves provide an observable signal from the thermal inflation in almost the
entire parameter space of interest. Furthermore, the shape of the gravitational
wave spectrum can be used to ascertain how the Universe escaped from
supercooling.


  The absolute calibration of an air fluorescence detector (FD) is an important
element in correctly determining the energy of detected cosmic rays. The
absolute calibration relates the flux of photons of a given wavelength at the
detector aperture to the electronic signal recorded by the FD data acquisition
system. For the Auger FDs, the primary absolute calibration method uses a
diffusive surface which is placed in front of a telescope aperture to uniformly
illuminate the telescope field of view with a known light signal. This
single-wavelength measurement (375 nm) will be made at intervals of several
months until the stability of the telescopes is determined. The relative
wavelength dependence of the calibration is determined through independent
measurements. The error in absolute calibration at a single wavelength is
estimated to be less than 10%. Two other absolute calibration methods are used
to provide an independent verification of the primary measurement. The
stability of the calibration with time is monitored nightly by a relative
calibration system. In this paper we will provide descriptions of the absolute
and relative calibration methods used by the Auger air fluorescence
observatory. Results from the calibration of the Auger Engineering Array
telescopes will also be presented.


  The Kurth solution is a particular non-isotropic steady state solution to the
gravitational Vlasov-Poisson system. It has the property that by means of a
suitable time-dependent transformation it can be turned into a family of
time-dependent solutions. Therefore, for a general steady state $Q(x,
v)=\tilde{Q}(e_Q, \beta)$, depending upon the particle energy $e_Q$ and
$\beta=\ell^2=|x\wedge v|^2$, the question arises if solutions $f$ could be
generated that are of the form \[ f(t)=\tilde{Q}\Big(e_Q(R(t), P(t), B(t)),
B(t)\Big) \] for suitable functions $R$, $P$ and $B$, all depending on $(t, r,
p_r, \beta)$ for $r=|x|$ and $p_r=\frac{x\cdot v}{|x|}$. We are going to show
that, under some mild assumptions, basically if $R$ and $P$ are independent of
$\beta$, and if $B=\beta$ is constant, then $Q$ already has to be the Kurth
solution.
  This paper is dedicated to the memory of Professor Robert Glassey.


  Designing a good reward function is essential to robot planning and
reinforcement learning, but it can also be challenging and frustrating. The
reward needs to work across multiple different environments, and that often
requires many iterations of tuning. We introduce a novel divide-and-conquer
approach that enables the designer to specify a reward separately for each
environment. By treating these separate reward functions as observations about
the underlying true reward, we derive an approach to infer a common reward
across all environments. We conduct user studies in an abstract grid world
domain and in a motion planning domain for a 7-DOF manipulator that measure
user effort and solution quality. We show that our method is faster, easier to
use, and produces a higher quality solution than the typical method of
designing a reward jointly across all environments. We additionally conduct a
series of experiments that measure the sensitivity of these results to
different properties of the reward design task, such as the number of
environments, the number of feasible solutions per environment, and the
fraction of the total features that vary within each environment. We find that
independent reward design outperforms the standard, joint, reward design
process but works best when the design problem can be divided into simpler
subproblems.


  We analyze subhalos in the Via Lactea II (VL2) cosmological simulation to
look for correlations among their infall times and z = 0 dynamical properties.
We find that the present day orbital energy is tightly correlated with the time
at which subhalos last crossed into the virial radius. This energy-infall
correlation provides a means to infer infall times for Milky Way satellite
galaxies. Assuming that the Milky Way's assembly can be modeled by VL2, we show
that the infall times of some satellites are well constrained given only their
Galactocentric positions and line-of-sight velocities. The constraints sharpen
for satellites with proper motion measurements. We find that Carina, Ursa
Minor, and Sculptor were all accreted early, more than 8 Gyr ago. Five other
dwarfs, including Sextans and Segue 1, are also probable early accreters,
though with larger uncertainties. On the other extreme, Leo T is just falling
into the Milky Way for the first time while Leo I fell in \sim 2 Gyr ago and is
now climbing out of the Milky Way's potential after its first perigalacticon.
The energies of several other dwarfs, including Fornax and Hercules, point to
intermediate infall times, 2 - 8 Gyr ago. We compare our infall time estimates
to published star formation histories and find hints of a dichotomy between
ultrafaint and classical dwarfs. The classical dwarfs appear to have quenched
star formation after infall but the ultrafaint dwarfs tend to be quenched long
before infall, at least for the cases in which our uncertainties allow us to
discern differences. Our analysis suggests that the Large Magellanic Cloud
crossed inside the Milky Way virial radius recently, within the last \sim 4
billion years.


  An order four automorphism of a Lie algebra gives rise to an integrable
system discussed by Terng. We show that solutions of this system may be
identified with certain vertically harmonic twistor lifts of conformal maps of
surfaces in a Riemannian symmetric space.
  Specialising to 4-dimensional target, we find that surfaces with holomorphic
mean curvature in 4-dimensional spaces with constant sectional or holomorphic
sectional curvatures constitute an integrable system as do Hamiltonian
stationary Lagrangian surfaces in a 4-dimensional Hermitian symmetric space
(this last being a result of Helein-Romon).


  We demonstrate an all-fiber cavity QED system with a trapped single atom in
the strong coupling regime. We use a nanofiber Fabry-Perot cavity, that is, an
optical nanofiber sandwiched by two fiber-Bragg-grating mirrors. Measurements
of the cavity transmission spectrum with a single atom in a state-insensitive
nanofiber trap clearly reveal the vacuum Rabi splitting.


  The harmonic sawtooth map w(x) of the unit interval onto itself is defined
where it is shown that its fixed points are enumerated by generating functions
involving the golden ratio in their parameters. The appropriately scaled Mellin
transform of w(x) is an analytic continuation of the Riemann zeta function
{\zeta}(s) valid for all -Re(s) not an integer. The series expansion of the
inverse scaling function which makes the Mellin transform of w(x) equal to the
zeta function has coefficients enumerating the Large Schroder Numbers S_n, the
number of perfect matchings in a triangular grid of n squares. A finite-sum
approximation to is examined and an associated function is found which solves a
reflection formula. The reflection function is singular at s = 0 and the
residue at this point changes sign from negative to positive between the values
of N = 176 and N = 177. The Gauss map h(x) is recalled so that its fixed points
and Mellin transform can be contrasted to those of w(x). The geometric counting
function of the fractal string associated to the lengths of the harmonic
sawtooth map components happens to coincide with the counting function for the
number of Pythagorean triangles of the form {(a,b,b+1):(b+1)<=x}. The volume of
the inner tubular neighborhood of the boundary of the map with radius
{\epsilon} is shown to have the particuarly simple closed-form. Also, the
Minkowski content is shown to be 2 and the Minkowski dimension to be 1/2 and
thus not invertible. Some definitions from the theory of fractal strings and
membranes are also recalled.


  We study the dynamical instability in spherical gravitating systems with core
using the Ricci curvature criterion. By means of numerical estimations of the
Ricci curvature for static N-body systems, it is shown that the core can both,
increase and decrease the degree of instability in the system. This behavior is
determined by the radius of the core and differs from the role of a central
mass.


  The incompressible Navier-Stokes equations coupled to the Maxwell-Stefan
relations for the molar fluxes are analyzed in bounded domains with no-flux
boundary conditions. The system models the dynamics of a multicomponent gaseous
mixture under isothermal conditions. The global-in-time existence of bounded
weak solutions to the strongly coupled model and their exponential decay to the
homogeneous steady state are proved. The mathematical difficulties are due to
the singular Maxwell-Stefan diffusion matrix, the cross-diffusion terms, and
the Navier-Stokes coupling. The key idea of the proof is the use of a new
entropy functional and entropy variables, which allows for a proof of positive
lower and upper bounds of the mass densities without the use of a maximum
principle.


  We study a modified notion of Ollivier's coarse Ricci curvature on graphs
introduced by Lin, Lu, and Yau in [11]. We establish a rigidity theorem for
complete graphs that shows a connected finite simple graph is complete if and
only if the Ricci curvature is strictly greater than one. We then derive
explicit Ricci curvature formulas for strongly regular graphs in terms of the
graph parameters and the size of a maximal matching in the core neighborhood.
As a consequence we are able to derive exact Ricci curvature formulas for
strongly regular graphs of girth 4 and 5 using elementary methods. An example
is provided that shows there is no exact formula for the Ricci curvature for
strongly regular graphs of girth $3$ that is purely in terms of graph
parameters.


  Interference is traditionally viewed as a performance limiting factor in
wireless communication systems, which is to be minimized or mitigated.
Nevertheless, a recent line of work has shown that by manipulating the
interfering signals such that they add up constructively at the receiver side,
known interference can be made beneficial and further improve the system
performance in a variety of wireless scenarios, achieved by symbol-level
precoding (SLP). This paper aims to provide a tutorial on interference
exploitation techniques from the perspective of precoding design in a
multi-antenna wireless communication system, by beginning with the
classification of constructive interference (CI) and destructive interference
(DI). The definition for CI is presented and the corresponding mathematical
characterization is formulated for popular modulation types, based on which
optimization-based precoding techniques are discussed. In addition, the
extension of CI precoding to other application scenarios as well as for
hardware efficiency is also described. Proof-of-concept testbeds are
demonstrated for the potential practical implementation of CI precoding, and
finally a list of open problems and practical challenges are presented to
inspire and motivate further research directions in this area.


  Quantitative phase imaging (QPI) recovers the exact wavefront of light from
the intensity measured by a camera. Topographical maps of translucent
microscopic bodies can be extracted from these quantified phase shifts. We
demonstrate quantitative phase imaging at the tip of an optical fiber endoscope
with a chromatic silicon nitride metalens. Our method leverages spectral
multiplexing to recover phase from multiple defocus planes in a single capture.
The half millimeter wide metalens shows phase imaging capability with a 280
field of view and 0.1{\lambda} sensitivity in experiments with an endoscopic
fiber bundle. Since the spectral functionality is encoded directly in the
imaging lens, no additional filters are needed. Key limitations in the scaling
of a phase imaging system, such as multiple acquisition, interferometric
alignment or mechanical scanning are completely mitigated in the proposed
scheme


  We report measurements of radiative B decays with K eta gamma final states,
using a data sample of 140 /fb recorded at the Upsilon(4S) resonance with the
Belle detector at the KEKB e+e- asymmetric energy collider. We observe B -> K
eta gamma for the first time with a branching fraction of (6.9 +1.7-1.6 (stat)
+1.3-1.0 (syst)) X 10^{-6} for M(Keta) < 2.4 GeV/c2. We also set an upper limit
on B -> K3*(1780) gamma.


  Video denoising aims at removing noise from videos to recover clean ones.
Some existing works show that optical flow can help the denoising by exploiting
the additional spatial-temporal clues from nearby frames. However, the flow
estimation itself is also sensitive to noise, and can be unusable under large
noise levels. To this end, we propose a new multi-scale refined optical
flow-guided video denoising method, which is more robust to different noise
levels. Our method mainly consists of a denoising-oriented flow refinement
(DFR) module and a flow-guided mutual denoising propagation (FMDP) module.
Unlike previous works that directly use off-the-shelf flow solutions, DFR first
learns robust multi-scale optical flows, and FMDP makes use of the flow
guidance by progressively introducing and refining more flow information from
low resolution to high resolution. Together with real noise degradation
synthesis, the proposed multi-scale flow-guided denoising network achieves
state-of-the-art performance on both synthetic Gaussian denoising and real
video denoising. The codes will be made publicly available.


  Understanding 3D scenes from multi-view inputs has been proven to alleviate
the view discrepancy issue in 3D visual grounding. However, existing methods
normally neglect the view cues embedded in the text modality and fail to weigh
the relative importance of different views. In this paper, we propose
ViewRefer, a multi-view framework for 3D visual grounding exploring how to
grasp the view knowledge from both text and 3D modalities. For the text branch,
ViewRefer leverages the diverse linguistic knowledge of large-scale language
models, e.g., GPT, to expand a single grounding text to multiple
geometry-consistent descriptions. Meanwhile, in the 3D modality, a transformer
fusion module with inter-view attention is introduced to boost the interaction
of objects across views. On top of that, we further present a set of learnable
multi-view prototypes, which memorize scene-agnostic knowledge for different
views, and enhance the framework from two perspectives: a view-guided attention
module for more robust text features, and a view-guided scoring strategy during
the final prediction. With our designed paradigm, ViewRefer achieves superior
performance on three benchmarks and surpasses the second-best by +2.8%, +1.5%,
and +1.35% on Sr3D, Nr3D, and ScanRefer. Code is released at
https://github.com/Ivan-Tang-3D/ViewRefer3D.


  We use the shell model Monte Carlo method to calculate complete 0f1p-shell
response functions for Gamow-Teller (GT) operators and obtain the corresponding
strength distributions using a Maximum Entropy technique. The approach is
validated against direct diagonalization for 48Ti. Calculated GT strength
distributions agree well with data from (n,p) and (p,n) reactions for nuclei
with A=48-64. We also calculate the temperature evolution of the GT+
distributions for representative nuclei and find that the GT+ distributions
broaden and the centroids shift to lower energies with increasing temperature.


  The wide-field CCD camera at the CFH telescope was used to survey the giant
stellar stream in the Andromeda galaxy, resolving stars down the red giant
branch in M31 to I ~ 25, a magnitude deeper than our previous INT survey of
this galaxy and extending 1 degree further out. The stream is seen to extend
out to the south-east of M31 as far as we have surveyed (some 4.5 degrees,
corresponding to a projected distance ~60 kpc). It is a linear structure in
projection, and the eastern edge of the stream presents a sharp boundary in
star counts suggesting that it remains a coherent structure. By analysing the
luminosity function of the metal rich component of the stream we find that, at
the furthest extent of our survey, the stream is 100 kpc further away along the
line of sight than M31. It can then be traced to a point on the north-western
side of the galaxy where it is some 30 kpc in front of M31, at which point the
stream turns away from our survey area.


  We examine the measurable chromatic number of distance colorings on the
surface of 2-dimensional spheres of varying radii, showing in particular that
similar arguments to those used to raise lower bounds in the plane work for all
but a countable set of radii. Furthermore, we show that measurable chromatic
number as a function of the radius, or more generally the curvature, is not
monotonic.


  This work concerns with the existence of solutions for the following class of
nonlocal elliptic problems \begin{eqnarray}\label{eq:0.1}
&&\left\{\begin{array}{l} (-\Delta)^{s} u+u=|u|^{p-2} u \text { in } \Omega_{r}
\\ u \geq 0 \quad \text { in }\Omega_{r} \text { and } u \neq 0 \\ u=0 \quad
\mathbb{R}^{N} \backslash \Omega_{r} \end{array}\right., \end{eqnarray}
involving the fractional Laplacian operator $(-\Delta)^{s},$ where $s \in(0,1),
N>2 s$, $\Omega_{r}$ is the half space with a hole in $\mathbb{R}^N$ and $p
\in\left(2,2_{s}^{*}\right) .$ The main technical approach is based on
variational and topological methods.


  Discrete analogs of the Darboux-Egoroff metrics are considered. It is shown
that the corresponding lattices in the Euclidean space are described by
discrete analogs of the Lame equations. It is proved that up to a gauge
transformation these equations are necessary and sufficient for discrete
analogs of rotation coefficients to exist. Explicit examples of the
Darboux-Egoroff lattices are constructed by means of algebro-geometric methods.


  Recently, a number of articles have argued that deep learning models such as
GPT could also capture key aspects of language processing in the human mind and
brain. However, I will argue that these models are not suitable as neural
models of human language. Firstly, because they fail on fundamental boundary
conditions, such as the amount of learning they require. This would in fact
imply that the mechanisms of GPT and brain language processing are
fundamentally different. Secondly, because they do not possess the logistics of
access needed for compositional and productive human language processing.
Neural architectures could possess logistics of access based on small-world
like network structures, in which processing does not consist of symbol
manipulation but of controlling the flow of activation. In this view, two
complementary approaches would be needed to investigate the relation between
brain and cognition. Investigating learning methods could reveal how 'learned
cognition' as found in deep learning could develop in the brain. However,
neural architectures with logistics of access should also be developed to
account for 'productive cognition' as required for natural or artificial human
language processing. Later on, these approaches could perhaps be combined to
see how such architectures could develop by learning and development from a
simpler basis.


  In this paper, we consider the secure transmission design for a
multiple-input single-output Femtocell overlaid with a Macrocell in co-channel
deployment. The Femtocell base station sends confidential messages to
information receiving Femtocell users (FUs) and energy signals to energy
receiving (ER) FUs while limiting the interference to Macrocell users (MUs).
The ER FUs have the potential to wiretap the confidential messages. By taking
fairness into account, we propose a sum logarithmic secrecy rate maximization
beamforming design problem under the interference constraints for MUs and
energy harvesting (EH) constraints for ER FUs. The formulated design problem is
nontrivial to solve due to the nonconvexity which lies in the objective and the
constraints. To tackle the design problem, a semidefinite relaxation and
successive convex approximation based algorithm is proposed. Simulation results
demonstrate the effectiveness of the proposed beamforming design.


  Hydrogen is a crucial source of green energy and has been extensively studied
for its potential usage in fuel cells. The advent of two-dimensional crystals
(2DCs) has taken hydrogen research to new heights, enabling it to tunnel
through layers of 2DCs or be transported within voids between the layers, as
demonstrated in recent experiments by Geim's group. In this study, we
investigate how the composition and stacking of transition-metal dichalcogenide
(TMDC) layers influence the transport and self-diffusion coefficients (D) of
hydrogen atoms using well-tempered metadynamics simulations. Our findings show
that modifying either the transition metal or the chalcogen atoms significantly
affects the free energy barriers (Delta F) and, consequently, the
self-diffusion of hydrogen atoms between the 2DC layers. In the Hh polytype (2H
stacking), MoSe2 exhibits the lowest Delta F, while WS2 has the highest,
resulting in the largest D for the former system. Additionally, hydrogen atoms
inside the RhM (or 3R) polytype encounter more than twice lower energy barriers
and, thus, much higher diffusivity compared to those within the most stable Hh
stacking. These findings are particularly significant when investigating
twisted layers or homo- or heterostructures, as different stacking areas may
dominate over others, potentially leading to directional transport and
interesting materials for ion or atom sieving.


  Limited-valency colloidal particles can self-assemble into polymeric
structures analogous to molecules. While their structural equilibrium
properties have attracted wide attention, insight into their dynamics has
proven challenging. Here, we investigate the polymerization dynamics of
semiflexible polymers in two dimensions (2D) by direct observation of
assembling divalent particles, bonded by critical Casimir forces. The
reversible critical Casimir force creates living polymerization conditions with
tunable chain dissociation, association and bending rigidity. We find that
unlike dilute polymers that show exponential size distributions in excellent
agreement with Flory theory, concentrated samples exhibit arrest of rotational
and translational diffusion due to a continuous isotropic-to-nematic transition
in 2D, slowing down the growth kinetics. These effects are circumvented by
addition of higher-valency particles, cross-linking the polymers into networks.
Our results connecting polymer flexibility, polymer interactions and the
peculiar isotropic-nematic transition in 2D offer insight into polymerization
processes of synthetic two-dimensional polymers, and biopolymers at membranes
and interfaces.


  The paper studies a bounded symmetric operator ${\mathbf{A}}_\varepsilon$ in
$L_2(\mathbf{R}^d)$ with $$ ({\mathbf{A}}_\varepsilon u) (x) =
\varepsilon^{-d-2} \int_{\mathbf{R}^d} a((x-y)/\varepsilon) \mu(x/\varepsilon,
y/\varepsilon) \left( u(x) - u(y) \right)\,dy; $$ here $\varepsilon$ is a small
positive parameter. It is assumed that $a(x)$ is a non-negative
$L_1(\mathbf{R}^d)$ function such that $a(-x)=a(x)$ and the moments $M_k
=\int_{\mathbf{R}^d} |x|^k a(x)\,dx$, $k=1,2,3$, are finite. It is also assumed
that $\mu(x,y)$ is $\mathbf{Z}^d$-periodic both in $x$ and $y$ function such
that $\mu(x,y) = \mu(y,x)$ and $0< \mu_- \leq \mu(x,y) \leq \mu_+< \infty$. Our
goal is to study the limit behaviour of the resolvent
$({\mathbf{A}}_\varepsilon + I)^{-1}$, as $\varepsilon\to0$. We show that, as
$\varepsilon \to 0$, the operator $({\mathbf{A}}_\varepsilon + I)^{-1}$
converges in the operator norm in $L_2(\mathbf{R}^d)$ to the resolvent
$({\mathbf{A}}^0 + I)^{-1}$ of the effective operator ${\mathbf{A}}^0$ being a
second order elliptic differential operator with constant coefficients of the
form ${\mathbf{A}}^0= - \operatorname{div} g^0 \nabla$. We then obtain sharp in
order estimates of the rate of convergence.


  We present an analysis of the dynamics of a nanomechanical resonator coupled
to a superconducting single electron transistor (SSET) in the vicinity of the
Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP)
resonances. For weak coupling and wide separation of dynamical timescales, we
find that for either superconducting resonance the dynamics of the resonator is
given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an
equilibrium heat bath, characterised by an effective temperature, which also
damps the resonator and renormalizes its frequency. Depending on the gate and
drain-source voltage bias points with respect to the superconducting resonance,
the SSET can also give rise to an instability in the mechanical resonator
marked by negative damping and temperature within the appropriate Fokker-Planck
equation. Furthermore, sufficiently close to a resonance, we find that the
Fokker-Planck description breaks down. We also point out that there is a close
analogy between coupling a nanomechanical resonator to a SSET in the vicinity
of the JQP resonance and Doppler cooling of atoms by means of lasers.


  To go beyond standard first-order asymptotics for Cox regression, we develop
parametric bootstrap and second-order methods. In general, computation of
$P$-values beyond first order requires more model specification than is
required for the likelihood function. It is problematic to specify a censoring
mechanism to be taken very seriously in detail, and it appears that
conditioning on censoring is not a viable alternative to that. We circumvent
this matter by employing a reference censoring model, matching the extent and
timing of observed censoring. Our primary proposal is a parametric bootstrap
method utilizing this reference censoring model to simulate inferential
repetitions of the experiment. It is shown that the most important part of
improvement on first-order methods - that pertaining to fitting nuisance
parameters - is insensitive to the assumed censoring model. This is supported
by numerical comparisons of our proposal to parametric bootstrap methods based
on usual random censoring models, which are far more unattractive to implement.
As an alternative to our primary proposal, we provide a second-order method
requiring less computing effort while providing more insight into the nature of
improvement on first-order methods. However, the parametric bootstrap method is
more transparent, and hence is our primary proposal. Indications are that
first-order partial likelihood methods are usually adequate in practice, so we
are not advocating routine use of the proposed methods. It is however useful to
see how best to check on first-order approximations, or improve on them, when
this is expressly desired.


  In this paper, two kinds of coefficient matrixes (channel matrix, measurement
matrix)associated with the pure state for teleportation are presented, the
general relation among channel matrix, measurement matrix and collapsed matrix
is obtained. In addition, a criterion for teleportation that the number of
coefficient of an unknown state is determined by the rank of the collapsed
matrix is given.


  We prove the fractal crumpled structure of collapsed unknotted polymer ring.
In this state the polymer chain forms a system of densely packed folds,
mutually separated in all scales. The proof is based on the numerical and
analytical investigation of topological correlations in randomly generated
dense knots on strips $L_{v} \times L_{h}$ of widths $L_{v}=3,5$. We have
analyzed the conditional probability of the fact that a part of an unknotted
chain is also almost unknotted. The complexity of dense knots and quasi--knots
is characterized by the power $n$ of the Jones--Kauffman polynomial invariant.
It is shown, that for long strips $L_{h} \gg L_{v}$ the knot complexity $n$ is
proportional to the length of the strip $L_{h}$. At the same time, the typical
complexity of the quasi--knot which is a part of trivial knot behaves as $n\sim
\sqrt{L_{h}}$ and hence is significantly smaller. Obtained results show that
topological state of any part of the trivial knot in a collapsed phase is
almost trivial.


  The Fano resonance with a distinctive ultra-sharp, asymmetric line shape and
high quality factor Q, is a widely occurring phenomena that has a large variety
of optical, plasmonic and microwave manifestations. In this paper, we explore
the characteristic robustness of the Fano resonance mode, which is
topologically protected by manufacturing band inversion induced by breaking the
mirror symmetry of a two-dimensional honeycomb photonic crystal (HPC),
associated with C_6 point group symmetry. So the dark and bright topological
edge modes appear in the band gap made by opening of the Dirac cone.
Destructive and constructive interference of the dark and bright modes leads to
the asymmetric line shape of the Fano resonance. The Fano resonance mode which
is very sensitive to the environmental and geometrical perturbations, can be
applied to sensor design. Here we demonstrate that the topological Fano
resonance mode preserves its asymmetric, ultra-sharp line shape in the presence
of the disorder, defects and cavities, and this has useful optical device
applications such as in low threshold lasers, and extremely precise
interferometers


  Background: Agile methods are no longer restricted to small projects and
co-located teams. The last decade has seen the spread of agile into large
scale, distributed and regulated domains. Many case studies show successful
agile adoption in GSD, however, taken as a whole, it remains unclear how
widespread this trend is, and what form the agile adoption takes in a global
software development (GSD) setting.
  Aims: Our objective is to gain a deeper understanding of how organisations
adopt agile development methods in distributed settings. Specifically we aim to
plot the current development process landscape in GSD.
  Method: We analyse industrial survey data from 33 different countries
collected as part of the project that explored the wider use of hybrid
development approaches in software development. We extract and analyse the
results of 263 surveys completed by participants involved in globally
distributed projects.
  Results: In our sample, 72 of globally distributed projects implement a mix
of both agile and traditional approaches (termed `hybrid'). 25 of GSD
organisations are predominantly agile, with only very few (5) opting for
traditional approaches. GSD projects that used only agile methods tended to be
very large.
  Conclusions: Globally Distributed Software Development (and project size) is
not a barrier to adopting agile practices. Yet, to facilitate project
coordination and general project management, many adopt traditional approaches,
resulting in a hybrid approach that follows defined rules.


  We study a highly supercooled two-dimensional fluid mixture via molecular
dynamics simulation. We follow bond breakage events among particle pairs, which
occur on the scale of the $\alpha$ relaxation time $\tau_{\alpha}$. Large scale
heterogeneities analogous to the critical fluctuations in Ising systems are
found in the spatial distribution of bonds which are broken in a time interval
with a width of order $0.05\tau_{\alpha}$. The structure factor of the broken
bond density is well approximated by the Ornstein-Zernike form. The correlation
length is of order $100 \sigma_1$ at the lowest temperature studied, $\sigma_1$
being the particle size. The weakly bonded regions thus identified evolve in
time with strong spatial correlations.


  The design, construction and performance characteristics of a simple
axial-field ionization chamber suitable for identifying ions in a radioactive
beam are presented. Optimized for use with low-energy radioactive beams (< 5
MeV/A) the detector presents only three 0.5 $\mu$m/cm$^2$ foils to the beam in
addition to the detector gas. A fast charge sensitive amplifier (CSA)
integrated into the detector design is also described. Coupling this fast CSA
to the axial field ionization chamber produces an output pulse with a risetime
of 60-70 ns and a fall time of 100 ns, making the detector capable of
sustaining a relatively high rate. Tests with an $\alpha$ source establish the
detector energy resolution as $\sim$8 $\%$ for an energy deposit of $\sim$3.5
MeV. The energy resolution with beams of 2.5 and 4.0 MeV/A $^{39}$K ions and
the dependence of the energy resolution on beam intensity is measured. At an
instantaneous rate of 3 x 10$^5$ ions/s the energy resolution has degraded to
14% with a pileup of 12%. The good energy resolution of this detector at rates
up to 3 x 10$^5$ ions/s makes it an effective tool in the characterization of
low-energy radioactive beams.


  Bias benchmarks are a popular method for studying the negative impacts of
bias in LLMs, yet there has been little empirical investigation of whether
these benchmarks are actually indicative of how real world harm may manifest in
the real world. In this work, we study the correspondence between such
decontextualized "trick tests" and evaluations that are more grounded in
Realistic Use and Tangible {Effects (i.e. RUTEd evaluations). We explore this
correlation in the context of gender-occupation bias--a popular genre of bias
evaluation. We compare three de-contextualized evaluations adapted from the
current literature to three analogous RUTEd evaluations applied to long-form
content generation. We conduct each evaluation for seven instruction-tuned
LLMs. For the RUTEd evaluations, we conduct repeated trials of three text
generation tasks: children's bedtime stories, user personas, and English
language learning exercises. We found no correspondence between trick tests and
RUTEd evaluations. Specifically, selecting the least biased model based on the
de-contextualized results coincides with selecting the model with the best
performance on RUTEd evaluations only as often as random chance. We conclude
that evaluations that are not based in realistic use are likely insufficient to
mitigate and assess bias and real-world harms.


  We present some old and recent regularity results concerning minimal and
almost minimal sets in domains of the Euclidean space. We concentrate on a
sliding variant of Almgren's notion of minimality, which is well suited in the
context of Plateau problems relative to soap films. We are especially
interested in regularity properties near a boundary curve, where we would like
to get a local C1 description of 2-dimensional almost minimal sets in the
spirit of J. Taylor's theorem, but we first study weaker and more general
results (local Ahlfors regularity, rectifiability, limits, monotonicity of
density), which we describe far from the boundary for simplicity. There we
insist on some simpler techniques, in particular the use of Federer-Fleming
projections.


  We study the non-thermal velocities in the quiet-sun using various high
spatial, temporal, and spectral resolution observations from the Interface
Region Imaging Spectrograph (IRIS). We focus our analysis on the transition
region using the optically thin line (Si IV 1393.7 \AA), and select line
profiles that are nearly Gaussian. We find evidence of a centre-to-limb
variation using different observations having different exposure times, ranging
from 5-30 s. The distribution of non-thermal velocities close to the limb are
observed to peak around 20 km s$^{-1}$ while the disc observations show a peak
around 15 km s$^{-1}$. The distributions are also different. The overall
variation in the non-thermal velocities are correlated with the intensity of
the line, as found previously. The on-disc velocities are smaller than most
previous observations. In general, we find that the non-thermal velocities are
independent of the selected exposure times. The Si IV lines didn't seem to
exhibit any significant opacity effects. We conclude that these Doppler motions
are mostly transverse to the radial direction. The possibility of
swaying/torsional motions leading to such variations are validated from these
IRIS observations.


  The most metal-poor stars in dwarf spheroidal galaxies (dSphs) can show the
nucleosynthetic patterns of one or a few supernovae. These supernovae could
have zero metallicity, making metal-poor dSph stars the closest surviving links
to Population III stars. Metal-poor dSph stars also help to reveal the
formation mechanism of the Milky Way halo. We present the detailed abundances
from Keck/HIRES spectroscopy for two very metal-poor stars in two Milky Way
dSphs. One star, in the Sculptor dSph, has [Fe I/H] = -2.40. The other star, in
the Ursa Minor dSph, has [Fe I/H] = -3.16. Both stars fall in the previously
discovered low-metallicity, high-[alpha/Fe] plateau. Most abundance ratios of
very metal-poor stars in these two dSphs are largely consistent with very
metal-poor halo stars. However, the abundances of Na and some r-process
elements lie at the lower end of the envelope defined by inner halo stars of
similar metallicity. We propose that the metallicity dependence of supernova
yields is the cause. The earliest supernovae in low-mass dSphs have less gas to
pollute than the earliest supernovae in massive halo progenitors. As a result,
dSph stars at -3 < [Fe/H] < -2 sample supernovae with [Fe/H] << -3, whereas
halo stars in the same metallicity range sample supernovae with [Fe/H] ~ -3.
Consequently, enhancements in [Na/Fe] and [r/Fe] were deferred to higher
metallicity in dSphs than in the progenitors of the inner halo.


  While single-tree transpiration is challenging to compare with earth
observation, canopy scale data are suitable for this purpose. To test the
potentialities of the second approach, we equipped the trees at two measurement
sites with sap flow sensors in spruce forests. The sites have contrasting
topography. The measurement period covered the months between June 2020 and
January 2021. To link plot scale transpiration with earth observations, we
utilized Sentinel-2 and local meteorological data. Within a machine learning
framework, we have tested the suitability of earth observations for modelling
canopy transpiration. The R2 of the cross-validated trained models at the
measurement sites was between 0.57 and 0.80. These results demonstrate the
relevance of Sentinel-2 data for the data-driven upscaling of ecosystem fluxes
from plot scale sap flow data. If applied to a broader network of sites and
climatic conditions, such an approach could offer unprecedented possibilities
for investigating our forests' resilience and resistance capacity to an
intensified hydrological cycle in the contest of a changing climate.


  We consider a mesoscopic normal metal, where the spin degeneracy is lifted by
a ferromagnetic exchange field or Zeeman splitting, coupled to two
superconducting reservoirs. As a function of the exchange field or the distance
between the reservoirs, the supercurrent through this device oscillates with an
exponentially decreasing envelope. This phenomenon is similar to the tuning of
a supercurrent by a non-equilibrium quasiparticle distribution between two
voltage-biased reservoirs. We propose a device combining the exchange field and
non-equilibrium effects, which allows us to observe a range of novel phenomena.
For instance, part of the field-suppressed supercurrent can be recovered by a
voltage between the additional probes.


  The possibility of making precise predictions for the Casimir force is
essential for the theoretical interpretation of current precision experiments
on the thermal Casimir effect with metallic plates, especially for sub-micron
separations. For this purpose it is necessary to estimate very accurately the
dielectric function of a conductor along the imaginary frequency axis. This
task is complicated in the case of ohmic conductors, because optical data do
not usually extend to sufficiently low frequencies to permit an accurate
evaluation of the standard Kramers-Kronig integral used to compute $\epsilon(i
\xi)$. By making important improvements in the results of a previous paper by
the author, it is shown that this difficulty can be resolved by considering
suitable weighted dispersions relations, which strongly suppress the
contribution of low frequencies. The weighted dispersion formulae presented in
this paper permit to estimate accurately the dielectric function of ohmic
conductors for imaginary frequencies, on the basis of optical data extending
from the IR to the UV, with no need of uncontrolled data extrapolations towards
zero frequency that are instead necessary with standard Kramers-Kronig
relations. Applications to several sets of data for gold films are presented to
demonstrate viability of the new dispersion formulae.


  In this paper, we study an extension of the CPE conjecture to manifolds $M$
which support a structure relating curvature to the geometry of a smooth map
$\varphi : M \to N$. The resulting system, denoted by $(\varphi-\mathrm{CPE})$,
is natural from the variational viewpoint and describes stationary points for
the integrated $\varphi$-scalar curvature functional restricted to metrics with
unit volume and constant $\varphi$-scalar curvature. We prove both a rigidity
statement for solutions to $(\varphi-\mathrm{CPE})$ in a conformal class, and a
gap theorem characterizing the round sphere among manifolds supporting
$(\varphi-\mathrm{CPE})$ with $\varphi$ a harmonic map.


  As a part of an ongoing study of a sample of galaxy groups showing evidence
for AGN/hot gas interaction, we report on the preliminary results of an
analysis of new XMM and GMRT data of the X-ray bright compact group HCG 62.
This is one of the few groups known to possess very clear, small X-ray cavities
in the inner region as shown by the existing Chandra image. At higher
frequencies (>1.4 GHz) the cavities show minimal if any radio emission, but the
radio appears clearly at lower frequencies (<610 MHz). We compare and discuss
the morphology and spectral properties of the gas and of the radio source. We
find that the cavities are close to pressure balance, and that the jets have a
"light" hadronic content. By extracting X-ray surface brightness and
temperature profiles, we also identify a shock front located around 35 kpc to
the south-west of the group center.


  In the backdrop of generalised Randall-Sundrum braneworld scenario, we look
for the possible origin of an effective four dimensional cosmological constant
($\Omega_{vis}$) on the visible 3-brane due to the effects of bulk curvature
and the modulus field that can either be a constant or dependent on extra
dimensional co-ordinate $y$ or a time dependent quantity. In case of constant
or $y$ dependent modulus field, the induced $\Omega_{vis}$ leads to an
exponentially expanding Universe. For such modulus fields the presence of
vacuum energy densities on either of the 3-branes as well as a non-vanishing
bulk curvature $l$ ($l \sim {\Lambda_5}^{-1}$) are essential to generate an
effective $\Omega_{vis}$. In particular for constant modulus field the Hubble
constant turns out to be equal to the visible brane cosmological constant which
agrees with the present result. In an alternative scenario, a time dependent
modulus field is found to be capable of accelerating the Universe. The Hubble
parameter in this case is determined for a slowly time-varying modulus field.


  Here, results are presented on the focusing of $1 \ \mu$m polystyrene
particle suspensions using a synchronous oscillatory pressure-driven flow and
oscillatory electric field in a microfluidic device. The effect of the phase
difference between the oscillatory fields on the focusing position and focusing
efficiency was investigated. The focusing position of negatively charged
polystyrene particles could be tuned anywhere between the channel centerline to
the channel walls. Similarly, the focusing efficiency could range from $20\%$
up to $90\%$, depending on the phase difference, for particle Reynolds numbers
of order $O(10^{-4})$. The migration velocity profile was measured and the peak
velocity was found to scale linearly with both the oscillatory pressure-driven
flow amplitude and oscillatory electric field amplitude. Furthermore, the
average migration velocity was observed to scale with the cosine of the phase
difference between the fields, indicating the coupled non-linear nature of the
phenomenon. Lastly, the peak migration velocity was measured for different
particle radii and found to have an inverse relation, where the velocity
increased with decreasing particle radius for identical conditions.


  We consider light propagation in a silicon dioxide substrate with implanted
${\mathrm{Er}}^{3+}$ ions and silver nanoparticles that are randomly and
homogeneously distributed in the substrate. When their densities are large
enough, the medium can have a negative refractive index over a certain range of
frequencies, within which the following exotic property ensues: increasing the
electric and magnetic plasma frequencies, the medium transparency is augmented.


  Automatic RF modulation recognition is a primary signal intelligence (SIGINT)
technique that serves as a physical layer authentication enabler and automated
signal processing scheme for the beyond 5G and military networks. Most existing
works rely on adopting deep neural network architectures to enable RF
modulation recognition. The application of deep compression for the wireless
domain, especially automatic RF modulation classification, is still in its
infancy. Lightweight neural networks are key to sustain edge computation
capability on resource-constrained platforms. In this letter, we provide an
in-depth view of the state-of-the-art deep compression and acceleration
techniques with an emphasis on edge deployment for beyond 5G networks. Finally,
we present an extensive analysis of the representative acceleration approaches
as a case study on automatic radar modulation classification and evaluate them
in terms of the computational metrics.


  Existing image super-resolution (SR) techniques often fail to generalize
effectively in complex real-world settings due to the significant divergence
between training data and practical scenarios. To address this challenge,
previous efforts have either manually simulated intricate physical-based
degradations or utilized learning-based techniques, yet these approaches remain
inadequate for producing large-scale, realistic, and diverse data
simultaneously. In this paper, we introduce a novel Realistic Decoupled Data
Generator (RealDGen), an unsupervised learning data generation framework
designed for real-world super-resolution. We meticulously develop content and
degradation extraction strategies, which are integrated into a novel
content-degradation decoupled diffusion model to create realistic
low-resolution images from unpaired real LR and HR images. Extensive
experiments demonstrate that RealDGen excels in generating large-scale,
high-quality paired data that mirrors real-world degradations, significantly
advancing the performance of popular SR models on various real-world
benchmarks.


  We study the formation of a giant gas planet by the core--accretion
gas--capture process, with numerical simulations, under the assumption that the
planetary core forms in the center of an anti-cyclonic vortex. The presence of
the vortex concentrates particles of centimeter to meter size from the
surrounding disk, and speeds up the core formation process. Assuming that a
planet of Jupiter mass is forming at 5 AU from the star, the vortex enhancement
results in considerably shorter formation times than are found in standard
core--accretion gas--capture simulations. Also, formation of a gas giant is
possible in a disk with mass comparable to that of the minimum mass solar
nebula.


  In superfluid dark matter the exchange of phonons can create an additional
force that has an effect similar to Modified Newtonian Dynamics (MOND). To test
whether this hypothesis is compatible with observation, we study a set of
strong gravitational lenses from the SLACS survey and check whether the
measurements can be explained by a superfluid in the central region of
galaxies. Concretely, we try to simultaneously fit each lens's Einstein radius
and velocity dispersion with a spherically symmetric density profile of a fluid
that has both a normal and a superfluid component. We demonstrate that we can
successfully fit all galaxies except one, and that the fits have reasonable
stellar mass-to-light-ratios. We conclude that strong gravitational lensing
does not pose a challenge for the idea that superfluid dark matter mimics
modified gravity.


  We study the structure of red-blue edge colorings of complete graphs, with no
copies of the $n$-cycle $C_n$ in red, and no copies of the $n$-wheel $W_n = C_n
\ast K_1$ in blue, for an odd integer $n$. Our first main result is that in any
such coloring, deleting at most two vertices we obtain a vertex-partition of
$G$ into three sets such that the edges inside the partition classes are red,
and edges between partition classes are blue. As a second result, we obtain
bounds for the Ramsey numbers of $r(C_{2k+1},W_{2j})$ for $k < j$ integers,
which asymptotically confirm the values of $4j+1$, as it were conjectured by
Zhang et al.


  Recently, deep learning approaches have been extensively studied for low-dose
CT denoising thanks to its superior performance despite the fast computational
time. In particular, cycleGAN has been demonstrated as a powerful unsupervised
learning scheme to improve the low-dose CT image quality without requiring
matched high-dose reference data. Unfortunately, one of the main limitations of
the cycleGAN approach is that it requires two deep neural network generators at
the training phase, although only one of them is used at the inference phase.
The secondary auxiliary generator is needed to enforce the cycle-consistency,
but the additional memory requirement and increases of the learnable parameters
are the main huddles for cycleGAN training. To address this issue, here we
propose a novel cycleGAN architecture using a single switchable generator. In
particular, a single generator is implemented using adaptive instance
normalization (AdaIN) layers so that the baseline generator converting a
low-dose CT image to a routine-dose CT image can be switched to a generator
converting high-dose to low-dose by simply changing the AdaIN code. Thanks to
the shared baseline network, the additional memory requirement and weight
increases are minimized, and the training can be done more stably even with
small training data. Experimental results show that the proposed method
outperforms the previous cycleGAN approaches while using only about half the
parameters.


  We present a lattice QCD study for the cutoff effects on nuclear forces.
Two-nucleon forces are determined from Nambu-Bethe-Salpeter (NBS) wave
functions using the HAL QCD method. Lattice QCD simulations are performed
employing N_f = 2 clover fermion configurations at three lattice spacings of a
= 0.108, 0.156, 0.215 fm on a fixed physical volume of L^3 x T = (2.5 fm)^3 x 5
fm with a large quark mass corresponding to m_\pi = 1.1 GeV. We observe that
while the discretization artifact appears at the short range part of
potentials, it is suppressed at the long distance region. The cutoff dependence
of the phase shifts and scattering length is also presented.


  Energy spectra of galactic cosmic rays calculated within the framework of the
NoRD (nonlocal relativistic diffusion) model are presented. The model accounts
for the turbulent character of the interstellar medium and the relativistic
speed limit requirement. Calculations account for spiral distribution of
sources, boundedness of halo, spallation of nuclei, energy dependence of the
diffusion coefficient, tempered power law injection spectrum. We show that the
knee in the background spectra from the ensemble of supernovae can arise due to
relativistic speed limit requirement. We compare our calculations with the
results obtained in frames of the local models (LoD and LoRD) and nonlocal
nonrelativistic model (NoD).


  We prove some 3-adic congruences for binomial sums, which were conjectured by
Sun.


  Voice disorders are pathologies significantly affecting patient quality of
life. However, non-invasive automated diagnosis of these pathologies is still
under-explored, due to both a shortage of pathological voice data, and
diversity of the recording types used for the diagnosis. This paper proposes a
novel solution that adopts transformers directly working on raw voice signals
and addresses data shortage through synthetic data generation and data
augmentation. Further, we consider many recording types at the same time, such
as sentence reading and sustained vowel emission, by employing a Mixture of
Expert ensemble to align the predictions on different data types. The
experimental results, obtained on both public and private datasets, show the
effectiveness of our solution in the disorder detection and classification
tasks and largely improve over existing approaches.


  Regarding the rapid growth of the size and complexity of simulation
applications, designing applicable and affordable verification and validation
(V&V) structures is an important problem. On the other hand, nowadays human
behavior models are principles to make decision in many simulations and in
order to have valid decisions based on a reliable human decision model, first
the model must pass the validation and verification criteria. Usually human
behavior models are represented as fuzzy rule bases. In all the recent works,
V&V process is applied on a ready given rule-base. In this work, we are first
supposed to construct a fuzzy rule-base and then apply the V&V process on it.
Considering the professor-student interaction as the case-study, in order to
construct the rule base, a questionnaire is designed in a special way to be
transformed to a hierarchical fuzzy rule-base. The constructed fuzzy rule base
is then mapped to a fuzzy Petri net and then within the verification
(generating and searching the reachability graph) and validation (reasoning the
Petri net) process is searched for probable structural and semantic errors.


  A new asymmetric cryptosystem based on the Integer Factorization Problem is
proposed. It posses an encryption and decryption speed of $O(n^2)$, thus making
it the fastest asymmetric encryption scheme available. It has a simple
mathematical structure. Thus, it would have low computational requirements and
would enable communication devices with low computing power to deploy secure
communication procedures efficiently.


  The organic spacer cation plays a crucial role in determining the exciton
fine structure in two-dimensional (2D) perovskites. Here, we use
low-temperature magneto-optical spectroscopy to gain insight into the influence
of the organic spacer on dark excitons in Ruddlesden-Popper (RP) perovskites.
We show that by using modest magnetic field strengths (<1.5 T), the
spin-forbidden dark exciton state can be identified and its emission properties
significantly modulated through the application of in-plane magnetic fields, up
to temperatures of 15 K. At low temperatures, an increase in collected
photoluminescence efficiency of >30% is demonstrated, signifying the critical
role of the dark exciton state for light-emitting applications of 2D
perovskites. The exciton fine structure and the degree of
magnetic-field-induced mixing are impacted by the choice of organic spacer
cation, with 4-methoxyphenethylammonium (MeO-PEA) showing the largest effect
due to larger bright-dark exciton splitting. Our results suggest that dark
excitons preferentially form biexcitons depending on the choice of spacer. We
distinguish between interior (bulk) and surface dark-exciton emission, showing
that bright-dark exciton splitting differs between the interior and surface.
Our results emphasize the significance of the organic spacer cation in
controlling the exciton fine structure in 2D perovskites and have important
implications for the development of optoelectronic technology based on 2D
perovskites.


  This paper is an exposition of heuristics related to Witten's functional
integral, relating it to Vassiliev invariants and to the Kontsevich integrals
that can be used to produce Vassiliev invariants of knots and links.In
particular, we give a simplified version of the appearance of the Kontsevich
integrals in the perturbation expansion of the functional integral.


  The canonical map from the Kan subdivision of a product of finite simplicial
sets to the product of the Kan subdivisions is a simple map, in the sense that
its geometric realization has contractible point inverses.


  Consider an algorithm computing in a differential field with several
commuting derivations such that the only operations it performs with the
elements of the field are arithmetic operations, differentiation, and zero
testing. We show that, if the algorithm is guaranteed to terminate on every
input, then there is a computable upper bound for the size of the output of the
algorithm in terms of the size of the input. We also generalize this to
algorithms working with models of good enough theories (including for example,
difference fields).
  We then apply this to differential algebraic geometry to show that there
exists a computable uniform upper bound for the number of components of any
variety defined by a system of polynomial PDEs. We then use this bound to show
the existence of a computable uniform upper bound for the elimination problem
in systems of polynomial PDEs with delays.


  We consider the $N$-component generalization of the four-slave-boson approach
to the Hubbard model, where $1/N$ acts as the small parameter that controls the
fluctuations about the saddle point, and address the problem of the appropriate
choice of the bosonic hopping operator $z_{i\g}$. By suitably reorganizing the
Fock space, we show that the square-root form for $z\is$ (originally introduced
by Kotliar and Ruckenstein) reproduces the exact independent-fermion ($U=0$)
results not only at the mean-field ($N=\infty$) level but also to {\evi all
orders in the $1/N$ expansion}, provided one relaxes the usually adopted
normal-ordered prescription for $z\is$. This ensures that $z\is$ needs not be
modified at successive orders in the fluctuation expansion, and implies that
all correlation functions are correctly recovered in the $U=0$ limit, a
nontrivial result for the slave-boson approach. In addition, it provides a
stringent requirement on the form of $z\is$, which might be also generalized to
alternative slave-boson formalisms (like the spin-rotation-invariant
formulation).


  Given two smooth projective varieties X and Y over a field, we say that X
motivates Y if the (suitably defined) motive of Y is contained in the category
generated from X by taking sums, summands and products. This notion has
appeared implicitly in many places, but it seems useful to make it explicit.
  Some techniques are given for checking this condition, but in a nutshell it
involves building a correspondence which "dominates" Y. Among the more
interesting examples dealt with are moduli spaces. We show that in number of
cases moduli spaces of sheaves over curves or surfaces are motivated by underly
curve or surface. This allows us to check (or recheck) the (generalized) Hodge
and Lefschetz standard conjectures for some of these examples. The dominating
correspondence in these examples is built from the universal sheaf, and can, in
some instances, be realized as a kind of Fourier-Mukai transform.


  Consider a system governed by the time-dependent Schr\"odinger equation in
its ground state. When subjected to weak (size $\epsilon$) parametric forcing
by an "ionizing field" (time-varying), the state decays with advancing time due
to coupling of the bound state to radiation modes. The decay-rate of this
metastable state is governed by {\it Fermi's Golden Rule}, $\Gamma[V]$, which
depends on the potential $V$ and the details of the forcing. We pose the
potential design problem: find $V_{opt}$ which minimizes $\Gamma[V]$ (maximizes
the lifetime of the state) over an admissible class of potentials with fixed
spatial support. We formulate this problem as a constrained optimization
problem and prove that an admissible optimal solution exists. Then, using
quasi-Newton methods, we compute locally optimal potentials. These have the
structure of a truncated periodic potential with a localized defect. In
contrast to optimal structures for other spectral optimization problems, our
optimizing potentials appear to be interior points of the constraint set and to
be smooth. The multi-scale structures that emerge incorporate the physical
mechanisms of energy confinement via material contrast and interference
effects.
  An analysis of locally optimal potentials reveals local optimality is
attained via two mechanisms: (i) decreasing the density of states near a
resonant frequency in the continuum and (ii) tuning the oscillations of
extended states to make $\Gamma[V]$, an oscillatory integral, small. Our
approach achieves lifetimes, $\sim (\epsilon^2\Gamma[V])^{-1}$, for locally
optimal potentials with $\Gamma^{-1}\sim\mathcal{O}(10^{9})$ as compared with
$\Gamma^{-1}\sim \mathcal{O}(10^{2})$ for a typical potential. Finally, we
explore the performance of optimal potentials via simulations of the
time-evolution.


  The global dimension of a triangulated category is defined to be the infimum
value of the global dimensions of stability conditions on the triangulated
category. In this paper, we study the global dimension of the derived category
of an orbifold projective line.


  The electric density profile along the normal to the phase interface between
aromatic hydrocarbon toluene and water has been studied by X-ray reflectometry
using synchrotron radiation. According to the experimental data, the width of
the interface under normal conditions is (5.7 +/- 0.2) Angstrom. This value is
much larger than a theoretical value of (3.9 +/- 0.1) Angstrom predicted by the
theory of capillary waves with an interphase tension of (36.0 +/- 0.1) mN/m.
The observed broadening of the interface is attributed to its own diffuse
near-surface structure with a width no less than 4 Angstroms, which is about
the value previously discussed for high-molecular-weight n-alkane - water and
1,2-dichloroethane - water interfaces.


  This paper presents an experimental study on the application of quaternions
in several machine learning algorithms. Quaternion is a mathematical
representation of rotation in three-dimensional space, which can be used to
represent complex data transformations. In this study, we explore the use of
quaternions to represent and classify rotation data, using randomly generated
quaternion data and corresponding labels, converting quaternions to rotation
matrices, and using them as input features. Based on quaternions and multiple
machine learning algorithms, it has shown higher accuracy and significantly
improved performance in prediction tasks. Overall, this study provides an
empirical basis for exploiting quaternions for machine learning tasks.


  Magnon spin Nernst effect was recently proposed as an intrinsic effect in
antiferromagnets, where spin diffusion and boundary spin transmission have been
ignored. However, diffusion processes are essential to convert a bulk spin
current into boundary spin accumulation, which determines the spin injection
rate into detectors through imperfect transmission. We formulate a diffusive
theory to describe the detection of magnon spin Nernst effect with boundary
conditions reflecting real device geometry. Thanks to the spin diffusion
effect, the output signals in both electronic and optical detection grow
rapidly with an increasing system size in the transverse dimension, which
eventually saturate. Counterintuitively, the measurable signals are even
functions of magnetic field, yielding optical detection more favorable than
electronic detection.


  We consider interactions as bidirectional channels. We investigate the
capacities for interaction Hamiltonians and nonlocal unitary gates to generate
entanglement and transmit classical information. We give analytic expressions
for the entanglement generating capacity and entanglement-assisted one-way
classical communication capacity of interactions, and show that these
quantities are additive, so that the asymptotic capacities equal the
corresponding 1-shot capacities. We give general bounds on other capacities,
discuss some examples, and conclude with some open questions.


  Random networks, constrained to reproduce specific features of networks, are
often used to represent and analyze network data as well as their mathematical
descriptions. Chief among them, the configuration model constrains random
networks by their degree distribution and is foundational to many areas of
network science. However, these representations are often selected based on
intuition or mathematical and computational simplicity rather than on
statistical evidence. To evaluate the quality of a network representation we
need to consider both the amount of information required by a random network
model as well as the probability of recovering the original data when using the
model as a generative process. To this end, we calculate the approximate size
of network ensembles generated by the popular configuration model and its
generalizations that include degree-correlations and centrality layers based on
the onion decomposition. We then apply minimum description length as a model
selection criterion and also introduce the Network Onion Divergence: model
selection and network comparison over a nested family of configuration models
with differing level of structural details. Using over 100 empirical sets of
network data, we find that a simple Layered Configuration Model offers the most
compact representation of the majority of real networks. We hope that our
results will continue to motivate the development of intricate random network
models that help capture network structure beyond the simple degree
distribution.


  A new Einstein-Hilbert type (SGM) action describing gravitational interaction
of Nambu-Goldstone(N-G) fermion of nonlinear supersymmetry(NL SUSY) is obtained
by performing the Einstein gravity analogue geometrical arguments in high
symmetric four dimensional (SGM) spacetime. All elementary particles except
graviton are regarded as the composite eigenstates of SO(10) super-Poincar\'e
algebra(SPA) composed of the fundamental N-G fermion ``superons'' of NL SUSY.
Some phenomenological implications of the composite picture of SGM, the
linearlization of SGM and N = 2 Volkov-Akulov model are discussed.


  Differential privacy has become crucial in the real-world deployment of
statistical and machine learning algorithms with rigorous privacy guarantees.
The earliest statistical queries, for which differential privacy mechanisms
have been developed, were for the release of the sample mean. In Geometric
Statistics, the sample Fr\'echet mean represents one of the most fundamental
statistical summaries, as it generalizes the sample mean for data belonging to
nonlinear manifolds. In that spirit, the only geometric statistical query for
which a differential privacy mechanism has been developed, so far, is for the
release of the sample Fr\'echet mean: the \emph{Riemannian Laplace mechanism}
was recently proposed to privatize the Fr\'echet mean on complete Riemannian
manifolds. In many fields, the manifold of Symmetric Positive Definite (SPD)
matrices is used to model data spaces, including in medical imaging where
privacy requirements are key. We propose a novel, simple and fast mechanism -
the \emph{tangent Gaussian mechanism} - to compute a differentially private
Fr\'echet mean on the SPD manifold endowed with the log-Euclidean Riemannian
metric. We show that our new mechanism has significantly better utility and is
computationally efficient -- as confirmed by extensive experiments.


  Online signature verification technologies, such as those available in banks
and post offices, rely on dedicated digital devices such as tablets or smart
pens to capture, analyze and verify signatures. In this paper, we suggest a
novel method for online signature verification that relies on the increasingly
available hand-worn devices, such as smartwatches or fitness trackers, instead
of dedicated ad-hoc devices. Our method uses a set of known genuine and forged
signatures, recorded using the motion sensors of a hand-worn device, to train a
machine learning classifier. Then, given the recording of an unknown signature
and a claimed identity, the classifier can determine whether the signature is
genuine or forged. In order to validate our method, it was applied on 1980
recordings of genuine and forged signatures that we collected from 66 subjects
in our institution. Using our method, we were able to successfully distinguish
between genuine and forged signatures with a high degree of accuracy (0.98 AUC
and 0.05 EER).