  Information over the phonon band structure is crucial to predicting many
thermodynamic properties of materials, such as thermal transport coefficients.
Highly accurate phonon dispersion curves can be, in principle, calculated in
the framework of density-functional perturbation theory (DFPT). However,
well-established techniques can run into trouble (or even catastrophically
fail) in the case of piezoelectric materials, where the acoustic branches
hardly reproduce the physically correct sound velocity. Here we identify the
culprit in the higher-order multipolar interactions between atoms, and
demonstrate an effective procedure that fixes the aforementioned issue. Our
strategy drastically improves the predictive power of perturbative
lattice-dynamical calculations in piezoelectric crystals, and is directly
implementable for high-throughput generation of materials databases.


  Online information systems currently heavily rely on the username and
password traditional method for protecting information and controlling access.
With the advancement in biometric technology and popularity of fields like AI
and Machine Learning, biometric security is becoming increasingly popular
because of the usability advantage. This paper reports how machine learning
based face recognition can be integrated into a web-based system as a method of
authentication to reap the benefits of improved usability. This paper includes
a comparison of combinations of detection and classification algorithms with
FaceNet for face recognition. The results show that a combination of MTCNN for
detection, Facenet for generating embeddings, and LinearSVC for classification
outperforms other combinations with a 95% accuracy. The resulting classifier is
integrated into the web-based system and used for authenticating users.


  We have experimentally determined the energies of the ground and first four
excited excitonic states of the fundamental optical transition in monolayer
WS2, a model system for the growing class of atomically thin two-dimensional
semiconductor crystals. From the spectra, we establish a large exciton binding
energy of 0.32 eV and a pronounced deviation from the usual hydrogenic Rydberg
series of energy levels of the excitonic states. We explain both of these
results using a microscopic theory in which the non-local nature of the
effective dielectric screening modifies the functional form of the Coulomb
interaction. These strong but unconventional electron-hole interactions are
expected to be ubiquitous in atomically thin materials.


  The purpose of this note is to reconcile two different results concerning the
model-free upper bound on the price of an American option, given a set of
European option prices. Neuberger (2007, `Bounds on the American option') and
Hobson and Neuberger (2016, `On the value of being American') argue that the
cost of the cheapest super-replicating strategy is equal to the highest
model-based price, where we search over all models which price correctly the
given European options. Bayraktar, Huang and Zhou (2015, `On hedging American
options under model uncertainty', SIAM J. Financial Math ematics) argue that
the cost of the cheapest super-replicating strategy can strictly exceed the
highest model-based price. We show that the reason for the difference in
conclusion is that Bayraktar et al do not search over a rich enough class of
models.


  Neutral clumps immersed in HII regions are frequently found in star formation
regions. We investigate here the formation of tail of neutral gas, which are
not reached by the direct ionizing flux coming from two massive stars, using
both an analytical approximation, that allows us to estimate the shadow
geometry behind the clumps for different initial geometric configurations, and
three-dimensional numerical simulations. We found a good agreement between both
approaches to this theoretically interesting problem. A particularly important
application could be the proplyds that are found in the Trapezium cluster in
Orion, which are being photoevaporated primordially by the O stars theta-1 Ori
C and theta-2 Ori A.


  We consider the existence and stability of static configurations of a scalar
field in a five dimensional spacetime in which the extra spatial dimension is
compactified on an $S^1/Z_2$ orbifold. For a wide class of potentials with
multiple minima there exist a finite number of such configurations, with total
number depending on the size of the orbifold interval. However, a
Sturm-Liouville stability analysis demonstrates that all such configurations
with nodes in the interval are unstable. Nodeless static solutions, of which
there may be more than one for a given potential, are far more interesting, and
we present and prove a powerful general criterion that allows a simple
determination of which of these nodeless solutions are stable. We demonstrate
our general results by specializing to a number of specific examples, one of
which may be analyzed entirely analytically.


  The Metric Traveling Salesman Problem (TSP) is a classical NP-hard
optimization problem. The double-tree shortcutting method for Metric TSP yields
an exponentially-sized space of TSP tours, each of which approximates the
optimal solution within at most a factor of 2. We consider the problem of
finding among these tours the one that gives the closest approximation, i.e.\
the \emph{minimum-weight double-tree shortcutting}. Burkard et al. gave an
algorithm for this problem, running in time $O(n^3+2^d n^2)$ and memory $O(2^d
n^2)$, where $d$ is the maximum node degree in the rooted minimum spanning
tree. We give an improved algorithm for the case of small $d$ (including planar
Euclidean TSP, where $d \leq 4$), running in time $O(4^d n^2)$ and memory
$O(4^d n)$. This improvement allows one to solve the problem on much larger
instances than previously attempted. Our computational experiments suggest that
in terms of the time-quality tradeoff, the minimum-weight double-tree
shortcutting method provides one of the best known tour-constructing
heuristics.


  Is the universe computable? If yes, is it computationally a polynomial place?
In standard quantum mechanics, which permits infinite parallelism and the
infinitely precise specification of states, a negative answer to both questions
is not ruled out. On the other hand, empirical evidence suggests that
NP-complete problems are intractable in the physical world. Likewise,
computational problems known to be algorithmically uncomputable do not seem to
be computable by any physical means. We suggest that this close correspondence
between the efficiency and power of abstract algorithms on the one hand, and
physical computers on the other, finds a natural explanation if the universe is
assumed to be algorithmic; that is, that physical reality is the product of
discrete sub-physical information processing equivalent to the actions of a
probabilistic Turing machine. This assumption can be reconciled with the
observed exponentiality of quantum systems at microscopic scales, and the
consequent possibility of implementing Shor's quantum polynomial time algorithm
at that scale, provided the degree of superposition is intrinsically, finitely
upper-bounded. If this bound is associated with the quantum-classical divide
(the Heisenberg cut), a natural resolution to the quantum measurement problem
arises. From this viewpoint, macroscopic classicality is an evidence that the
universe is in BPP, and both questions raised above receive affirmative
answers. A recently proposed computational model of quantum measurement, which
relates the Heisenberg cut to the discreteness of Hilbert space, is briefly
discussed. A connection to quantum gravity is noted. Our results are compatible
with the philosophy that mathematical truths are independent of the laws of
physics.


  The phase-field-crystal model is used to access the structure and
thermodynamics of interfaces between two coexisting liquid crystalline phases
in two spatial dimensions. Depending on the model parameters there is a variety
of possible coexistences between two liquid crystalline phases including a
plastic triangular crystal (PTC). Here, we calculate numerically the profiles
for the mean density and the nematic order tensor across the interface for
isotropic-PTC and columnar-PTC respectively smectic A-PTC coexistence. As a
general finding, the width of the interface with respect to the nematic order
parameter characterizing the orientational order is larger than the width of
the mean density interface. In approaching the interface from the PTC side, at
first the mean density goes down and then the nematic order parameter follows.
The relative shift of the two profiles can be larger than a full lattice
constant of the plastic crystal. Finally, we also present numerical results for
the dynamic relaxation of an initial order-parameter profile towards its
equilibrium interfacial profile. Our predictions for the interfacial profiles
can in principle be verified in real-space experiments of colloidal
dispersions.


  We propose a high order numerical decomposition of exponentials of hermitean
operators in terms of a product of exponentials of simple terms, following an
idea which has been pioneered by M. Suzuki, however implementing it for complex
coefficients. We outline a convenient fourth order formula which can be written
compactly for arbitrary number of noncommuting terms in the Hamiltonian and
which is superiour to the optimal formula with real coefficients, both in
complexity and accuracy. We show asymptotic stability of our method for
sufficiently small time step and demonstrate its efficiency and accuracy in
different numerical models.


  A detailed analysis of the optical polarimetric variability of the TeV blazar
1ES 1959+650 from 2007 October 18 to 2011 May 5 is presented. The source showed
a maximum and minimum brightness states in the R-band of 14.08$\pm$0.03 mag and
15.20$\pm$0.03 mag, respectively, with a maximum variation of 1.12 mag, and
also a maximum polarization degree of $P=$(12.2$\pm$0.7)%, with a maximum
variation of 10.7%. From August to November 2009, a correlation between the
optical $R$-band flux and the degree of linear polarization was found, with a
correlation coefficient $r_{pol}$=0.984$\pm$0.025. The source presented a
preferential position angle of optical polarization of $\sim153^{\circ}$, with
variations of $10\degr$-$50\degr$, that is in agreement with the projected
position angle of the parsec scale jet found at 43 GHz. From the Stokes
parameters we infer the existence of two optically-thin synchrotron components
that contribute to the polarized flux. One of them is stable, with a constant
polarization degree of 4%. Assuming a stationary shock for the variable
component, we estimated some parameters associated with the physics of the
relativistic jet: the magnetic field, $B\sim$0.06 G, the Doppler factor,
$\delta_{0}\sim$23, the viewing angle, $\Phi\sim2.4\degr$, and the size of the
emission region $r_b\sim5.6\times10^{17}$ cm. Our study is consistent with the
spine-sheath model to explain the polarimetric variability displayed by this
source during our monitoring.


  We study black-box attacks on machine learning classifiers where each query
to the model incurs some cost or risk of detection to the adversary. We focus
explicitly on minimizing the number of queries as a major objective.
Specifically, we consider the problem of attacking machine learning classifiers
subject to a budget of feature modification cost while minimizing the number of
queries, where each query returns only a class and confidence score. We
describe an approach that uses Bayesian optimization to minimize the number of
queries, and find that the number of queries can be reduced to approximately
one tenth of the number needed through a random strategy for scenarios where
the feature modification cost budget is low.


  The paper investigates the asymptotic behavior of (non-normalized) traces of
certain classes of matrices with non-commutative random variables as entries.
We show that, unlike in the commutative framework, the asymptotic behavior of
matrices with free circular, respectively with Bernoulli distributed Boolean
independent entries is described in terms of free, respectively Boolean
cumulants. We also present an exemple of relation of monotone independence
arising from the study of Boolean independence.


  The ZW-calculus is a graphical language capable of representing 2-dimensional
quantum systems (qubit) through its diagrams, and manipulating them through its
equational theory. We extend the formalism to accommodate finite dimensional
Hilbert spaces beyond qubit systems. First we define a qudit version of the
language, where all systems have the same arbitrary finite dimension d, and
show that the provided equational theory is both complete -- i.e. semantical
equivalence is entirely captured by the equations -- and minimal -- i.e. none
of the equations are consequences of the others. We then extend the graphical
language further to accommodate all finite dimensional Hilbert spaces at the
same time. We again show the completeness of the provided equational theory.


  We compute scattering amplitudes involving both R-R and NS-NS fields in the
presence of a D-brane or orientifold plane. These provide direct evidence for
the anomalous couplings in the D-brane and orientifold actions. The D9-brane
and O9-plane are found to couple to the first Pontrjagin class with the
expected relative strength.


  We study, in theory and experiment, the quantum properties of correlated
light fields measured with click-counting detectors providing incomplete
information on the photon statistics. We establish a correlation parameter for
the conditional statistics, and we derive the corresponding nonclassicality
criteria for detecting conditional quantum correlations. Classical bounds for
Pearson's correlation parameter are formulated that allow us, once they are
violated, to determine nonclassical correlations via the joint statistics. On
the one hand, we demonstrate nonclassical correlations in terms of the joint
click statistics of light produced by a parametric down conversion source. On
the other hand, we verify quantum correlations of a heralded, split
single-photon state via the conditional click statistics together with a
generalization to higher-order moments. We discuss the performance of the
presented nonclassicality criteria to successfully discern joint and
conditional quantum correlations. Remarkably, our results are obtained without
making any assumptions on the response function, quantum efficiency, and
dark-count rate of the photodetectors.


  We discuss gauge theory with a topological N=2 symmetry. This theory captures
the de Rham complex and Riemannian geometry of some underlying moduli space
$\cal M$ and the partition function equals the Euler number of $\cal M$. We
explicitly deal with moduli spaces of instantons and of flat connections in two
and three dimensions.
  To motivate our constructions we explain the relation between the
Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a
new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi
equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point
of view and relate them to supersymmetric quantum mechanics on spaces of
connections. As a consequence of these considerations we propose the Euler
number of the moduli space of flat connections as a generalization to arbitrary
three-manifolds of the Casson invariant. We also comment on the possibility of
constructing a topological version of the Penner matrix model.


  A comparison between the two tracers of magnetic field mirror asymmetry in
solar active regions, twist and current helicity, is presented. It is shown
that for individual active regions these tracers do not possess visible
similarity while averaging by time over the solar cycle, or by latitude,
reveals similarities in their behaviour. The main property of the dataset is
anti-symmetry over the solar equator. Considering the evolution of helical
properties over the solar cycle we find signatures of a possible sign change at
the beginning of the cycle, though more systematic observational data are
required for a definite confirmation. We discuss the role of both tracers in
the context of the solar dynamo theory.


  We consider the problem of multicasting information from a source to a set of
receivers over a network where intermediate network nodes perform randomized
network coding operations on the source packets. We propose a channel model for
the non-coherent network coding introduced by Koetter and Kschischang in [6],
that captures the essence of such a network operation, and calculate the
capacity as a function of network parameters. We prove that use of subspace
coding is optimal, and show that, in some cases, the capacity-achieving
distribution uses subspaces of several dimensions, where the employed
dimensions depend on the packet length. This model and the results also allow
us to give guidelines on when subspace coding is beneficial for the proposed
model and by how much, in comparison to a coding vector approach, from a
capacity viewpoint. We extend our results to the case of multiple source
multicast that creates a virtual multiple access channel.


  We use a combination of deep, high angular resolution imaging data from the
CDFS (HST/ACS GOODS survey) and ground based near-IR $K_s$ images to derive the
evolution of the galaxy major merger rate in the redshift range $0.2 \leq z
\leq 1.2$. We select galaxies on the sole basis of their J-band rest-frame,
absolute magnitude, which is a good tracer of the stellar mass. We find steep
evolution with redshift, with the merger rate $\propto (1+z)^{3.43\pm0.49}$ for
optically selected pairs, and $\propto (1+z)^{2.18\pm0.18}$ for pairs selected
in the near-IR. Our result is unlikely to be affected by luminosity evolution
which is relatively modest when using rest-frame J band selection. The
apparently more rapid evolution that we find in the visible is likely caused by
biases relating to incompleteness and spatial resolution affecting the ground
based near IR photometry, underestimating pair counts at higher redshifts in
the near-IR. The major merger rate was $\sim$5.6 times higher at $z\sim1.2$
than at the current epoch. Overall 41%$\times$($0.5\gyr$/$\tau$) of all
galaxies with $M_J\leq-19.5$ have undergone a major merger in the last $\sim8
\gyr$, where $\tau$ is the merger timescale. Interestingly, we find no effect
on the derived major merger rate due to the presence of the large scale
structure at $z=0.735$ in the CDFS.


  In this paper we consider a class of exoskeletons designed to amplify the
strength of humans through feedback of sensed human-robot interactions and
actuator forces. We define an amplification error signal based on a reference
amplification rate, and design a linear feedback compensator to attenuate this
error. Since the human operator is an integral part of the system, we design
the compensator to be robust to both a realistic variation in human impedance
and a large variation in load impedance. We demonstrate our strategy on a
one-degree of freedom amplification exoskeleton connected to a human arm,
following a three dimensional matrix of experimentation: slow or fast human
motion; light or extreme exoskeleton load; and soft or clenched human arm
impedances. We demonstrate that a slightly aggressive controller results in a
borderline stable system---but only for soft human musculoeskeletal behavior
and a heavy load. This class of exoskeleton systems is interesting because it
can both amplify a human's interaction forces --- so long as the human contacts
the environment through the exoskeleton --- and attenuate the operator's
perception of the exoskeleton's reflected dynamics at frequencies within the
bandwidth of the control.


  We present X-ray flux and spectral analyses of the three pointed Suzaku
observations of the TeV high synchrotron peak blazar Mrk 421 taken throughout
its complete operational duration. The observation taken on 5 May 2008 is, at
364.6 kiloseconds (i.e., 101.3 hours), the longest and most evenly sampled
continuous observation of this source, or any blazar, in the X-ray energy 0.8 -
60 keV until now. We found large amplitude intra-day variability in all soft
and hard bands in all the light curves. The discrete correction function
analysis of the light curves in soft and hard bands peaks on zero lag, showing
that the emission in hard and soft bands are cospatial and emitted from the
same population of leptons. The hardness ratio plots imply that the source is
more variable in the harder bands compared to the softer bands. The source is
harder-when-brighter, following the general behavior of high synchrotron peak
blazars. Power spectral densities of all three light curves are red noise
dominated, with a range of power spectra slopes. If one assumes that the
emission originates very close to the central super massive black hole, a crude
estimate for its mass, of ~ 4 * 10^{8} M_{\odot}, can be made; but if the
variability is due to perturbations arising there that are advected into the
jet and are thus Doppler boosted, substantially higher masses are consistent
with the quickest seen variations. We briefly discuss the possible physical
mechanisms most likely responsible for the observed flux and spectral
variability.


  In this paper we define a novel edit distance for merge trees and compare it
with other metrics appearing in the literature. Then we consider the metric
space obtained and study the properties of such space obtaining completeness
and compactness results, the existence of Frech\'et Means and local
parametrizations by means of euclidean spaces. Whilst doing so, we explore the
geodesic structure of the space of merge trees, stratifying trees by means of
their dimension and decomposing geodesics along different strata. All these
results contribute to understanding how the different strata interact, which is
pivotal for the development of more refined tools and techniques for merge
trees.


  Programmable photonic circuits (PPCs) have garnered substantial interest in
achieving deep learning accelerations and universal quantum computations.
Although photonic computation using PPCs offers critical advantages, including
ultrafast operation, energy-efficient matrix calculation and room-temperature
quantum states, its poor scalability impedes the integration required for
industrial applications. This challenge arises from the temporally one-shot
operation using propagating light in conventional PPCs, which leads to the
light-speed increase of device footprints. Here we propose a concept of
programmable photonic time circuits, which employ time-cycle-based computations
analogous to the gate cycling in the von Neumann architecture and quantum
computation. As a building block, we develop a reconfigurable SU(2) time gate
composed of two resonators, which have tunable resonances and are coupled
through time-coded dual-channel gauge fields. We demonstrate universal U(N)
operations with high fidelity using the systematic assembly of the SU(2) time
gates, achieving improved scalability from O(N^2) to O(N) in both the footprint
and gate number. This result opens a pathway to industrial-level PPC
implementation in very large-scale integration.


  Plasma acceleration is considered a prospective technology for building a
compact multi-TeV electron-positron collider in the future. The challenge of
this endeavor is greater for positrons than for the electrons because usually
the self-generated fields from laser-plasma interaction are not well-suited for
positron focusing and on-axis guiding. In addition, an external positron source
is required, while electrons are naturally available in the plasma. Here, we
study electron-positron pair generation by an orthogonal collision of a
multi-PW laser pulse and a GeV electron beam by the nonlinear Breit-Wheeler
process. We studied conditions favorable for positron deflection in the
direction of the laser pulse propagation, which favors injection into the
plasma for further acceleration. We demonstrate using the OSIRIS
particle-in-cell framework that the radiation reaction triggered by ultra-high
laser intensity plays a crucial role in the positron injection. It provides a
suppression of the initial transverse momentum gained by the positrons from the
Breit-Wheeler process. For the parameters used in this work, the intensity of
at least 2.2x1023 W/cm2 is needed in order to inject more than 1% of positrons
created. Above this threshold, the percentage of injected positrons rapidly
increases with intensity. Moreover, subsequent direct laser acceleration of
positrons in a plasma channel, using the same laser pulse that created them,
can ensure a boost of the final positron energy by a factor of two. The
positron focusing and guiding on the axis is provided by significant electron
beam loading that changes the internal structure of the channel fields.


  The statistical properties of a map of the primary fluctuations in the cosmic
microwave background (CMB) may be specified to high accuracy by a few thousand
power spectra measurements, provided the fluctuations are gaussian, yet the
number of parameters relevant for the CMB is probably no more than about 10-20.
There is consequently a large degree of redundancy in the power spectrum data.
In this paper, we show that the MOPED data compression technique can reduce the
CMB power spectrum measurements to about 10-20 numbers (one for each
parameter), from which the cosmological parameters can be estimated virtually
as accurately as from the complete power spectrum. This offers opportunities
for very fast parameter estimation from real and simulated CMB skies, with
accurate likelihood calculations at Planck resolution being speeded up by a
factor of around five hundred million.


  Knowledge bases, and their representations in the form of knowledge graphs
(KGs), are naturally incomplete. Since scientific and industrial applications
have extensively adopted them, there is a high demand for solutions that
complete their information. Several recent works tackle this challenge by
learning embeddings for entities and relations, then employing them to predict
new relations among the entities. Despite their aggrandizement, most of those
methods focus only on the local neighbors of a relation to learn the
embeddings. As a result, they may fail to capture the KGs' context information
by neglecting long-term dependencies and the propagation of entities'
semantics. In this manuscript, we propose {\AE}MP (Attention-based Embeddings
from Multiple Patterns), a novel model for learning contextualized
representations by: (i) acquiring entities' context information through an
attention-enhanced message-passing scheme, which captures the entities' local
semantics while focusing on different aspects of their neighborhood; and (ii)
capturing the semantic context, by leveraging the paths and their relationships
between entities. Our empirical findings draw insights into how attention
mechanisms can improve entities' context representation and how combining
entities and semantic path contexts improves the general representation of
entities and the relation predictions. Experimental results on several large
and small knowledge graph benchmarks show that {\AE}MP either outperforms or
competes with state-of-the-art relation prediction methods.


  The real-world networks often compose of different types of nodes and edges
with rich semantics, widely known as heterogeneous information network (HIN).
Heterogeneous network embedding aims to embed nodes into low-dimensional
vectors which capture rich intrinsic information of heterogeneous networks.
However, existing models either depend on manually designing meta-paths, ignore
mutual effects between different semantics, or omit some aspects of information
from global networks. To address these limitations, we propose a novel
Graph-Aggregated Heterogeneous Network Embedding (GAHNE), which is designed to
extract the semantics of HINs as comprehensively as possible to improve the
results of downstream tasks based on graph convolutional neural networks. In
GAHNE model, we develop several mechanisms that can aggregate semantic
representations from different single-type sub-networks as well as fuse the
global information into final embeddings. Extensive experiments on three
real-world HIN datasets show that our proposed model consistently outperforms
the existing state-of-the-art methods.


  This paper deals with quon algebras or deformed oscillator algebras, for
which the deformation parameter is a root of unity. We show the interest of
such algebras for fractional supersymmetric quantum mechanics, angular momentum
theory and quantum information. More precisely, quon algebras are used for (i)
a realization of a generalized Weyl-Heisenberg algebra from which it is
possible to associate a fractional supersymmetric dynamical system, (ii) a
polar decomposition of SU_2 and (iii) a construction of mutually unbiased bases
in Hilbert spaces of prime dimension. We also briefly discuss (symmetric
informationally complete) positive operator valued measures in the spirit of
(iii).


  Background: In the continuum-discretized coupled-channel method, a breakup
cross section (BUX) is obtained as an admixture of several components of
different channels in multi-channel scattering. Purpose: Our goal is to propose
an approximate way of decomposing the discretized BUX into components of each
channel. This approximation is referred to as the "probability separation
(P-separation)". Method: As an example, we consider $^{11}$Be scattering by
using the three-body model with core excitation
($^{10}\mathrm{Be}+n+\mathrm{T}$, where T is a target). The structural part is
constructed by the particle-rotor model and the reaction part is described by
the distorted wave Born approximation (DWBA). Results: The validity of the
P-separation is tested by comparing with the exact calculation. The approximate
way reproduces the exact BUXs well regardless of the configurations and/or the
resonance positions of $^{11}$Be. Conclusion: The method proposed here can be
an alternative approach for decomposing discretized BUXs into components in
four- or five-body scattering where the strict decomposition is hard to
perform.


  In this paper, first, we recall the notion of Clairaut Riemannian map (CRM)
${F}$ using a geodesic curve on the base manifold and give the Ricci equation.
We also show that if base manifold of CRM is space form then leaves of
$(ker{F}_\ast)^\perp$ become space forms and symmetric as well. Secondly, we
define Clairaut semi-invariant Riemannian map (CSIRM) from a Riemannian
manifold $(M, g_{M})$ to a K\"ahler manifold $(N, g_{N}, P)$ with a non-trivial
example. We find necessary and sufficient conditions for a curve on the base
manifold of semi-invariant Riemannian map (SIRM) to be geodesic. Further, we
obtain necessary and sufficient conditions for a SIRM to be CSIRM. Moreover, we
find necessary and sufficient condition for CSIRM to be harmonic and totally
geodesic. In addition, we find necessary and sufficient condition for the
distributions $\bar{D_1}$ and $\bar{D_2}$ of $(ker{F}_\ast)^\bot$ (which are
arisen from the definition of CSIRM) to define totally geodesic foliations.
Finally, we obtain necessary and sufficient conditions for $(ker{F}_\ast)^\bot$
and base manifold to be locally product manifold $\bar{D_1} \times \bar{D_2}$
and ${(range{F}_\ast)} \times {(range{F}_\ast)^\bot}$, respectively.


  In this research oriented manuscript, foundational aspects of rigid geometry
are discussed, putting emphasis on birational side of formal schemes and
topological feature of rigid spaces. Besides the rigid geometry itself, topics
include the general theory of formal schemes and formal algebraic spaces, based
on a theory of complete rings which are not necessarily Noetherian (cf.
introduction). The manuscript is encyclopedic and almost self-contained, and
contains plenty of new results. A discussion on relationship with J. Tate's
rigid analytic geometry, V. Berkovich's analytic geometry and R. Huber's adic
spaces is also included. As a model example of applications, a proof of
Nagata's compactification theorem for schemes is given in the appendix. 5th
version (Feb. 28, 2017): minor changes.


  Doped clusters in the gas phase provide nanoconfined model systems for the
study of system-bath interactions. To gain insight into interaction mechanisms
between chromophores and their environment, the ensemble inhomogeneity has to
be lifted and the homogeneous line profile must be accessed. However, such
measurements are very challenging at the low particle densities and low signal
levels in cluster beam experiments. Here, we dope cryogenic rare-gas clusters
with phthalocyanine molecules and apply action-detected two-dimensional
electronic spectroscopy to gain insight into the local molecule-cluster
environment for solid and superfluid cluster species. The high-resolution
homogeneous linewidth analysis provides a benchmark for the theoretical
modelling of binding configurations and shows a promising route for
high-resolution molecular two-dimensional spectroscopy.


  Monocular 3D object detection aims to locate objects in different scenes with
just a single image. Due to the absence of depth information, several monocular
3D detection techniques have emerged that rely on auxiliary depth maps from the
depth estimation task. There are multiple approaches to understanding the
representation of depth maps, including treating them as pseudo-LiDAR point
clouds, leveraging implicit end-to-end learning of depth information, or
considering them as an image input. However, these methods have certain
drawbacks, such as their reliance on the accuracy of estimated depth maps and
suboptimal utilization of depth maps due to their image-based nature. While
LiDAR-based methods and convolutional neural networks (CNNs) can be utilized
for pseudo point clouds and depth maps, respectively, it is always an
alternative. In this paper, we propose a framework named the Adaptive Distance
Interval Separation Network (ADISN) that adopts a novel perspective on
understanding depth maps, as a form that lies between LiDAR and images. We
utilize an adaptive separation approach that partitions the depth map into
various subgraphs based on distance and treats each of these subgraphs as an
individual image for feature extraction. After adaptive separations, each
subgraph solely contains pixels within a learned interval range. If there is a
truncated object within this range, an evident curved edge will appear, which
we can leverage for texture extraction using CNNs to obtain rich depth
information in pixels. Meanwhile, to mitigate the inaccuracy of depth
estimation, we designed an uncertainty module. To take advantage of both images
and depth maps, we use different branches to learn localization detection tasks
and appearance tasks separately.


  Let $\Bbb Z_2:=\Bbb Z/2\Bbb Z$ be the additive group with two elements. In
this article, we focus only on $\Bbb Z_2$-graded commutative ring i.e
commutative ring $R$ such that $R=R_0\oplus R_1$ as Abelian group and
$R_iR_j\subseteq R_{i+j}$ for all $i,j\in \Bbb Z_2$. Our main goals is to
establish a strong relation between $\Bbb Z_2$-graded prime ( maximal ) ideals
of $R$ and prime ( maximal) ideals of $R_0$, for instance, it is showed that,
the $\Bbb Z_2$-graded spectrum of $R$ is homeomorphic to the spectrum of $R_0$
with respect to the Zariski topologies.


  The production of hadrons in Ni-Ni at the GSI is considered in a hadronic gas
model with chemical equilibrium. Special attention is given to the abundance of
strange particles which are treated using the exact conservation of
strangeness. It is found that all the data can be described using a temperature
T = 70 pm 10 MeV and a baryon chemical potential mu_B = 720 pm 20 MeV.


  Science projects are data publishers. The scale and complexity of current and
future science data changes the nature of the publication process. Publication
is becoming a major project component. At a minimum, a project must preserve
the ephemeral data it gathers. Derived data can be reconstructed from metadata,
but metadata is ephemeral. Longer term, a project should expect some archive to
preserve the data. We observe that pub-lished scientific data needs to be
available forever ? this gives rise to the data pyramid of versions and to data
inflation where the derived data volumes explode. As an example, this article
describes the Sloan Digital Sky Survey (SDSS) strategies for data publication,
data access, curation, and preservation.


  Let $a,b$ be elements in a unital C$^*$-algebra with $0\leq a,b\leq 1$. The
element $a$ is absolutely compatible with $b$ if $$\vert a - b \vert + \vert 1
- a - b \vert = 1.$$ In this note we find some technical characterizations of
absolutely compatible pairs in an arbitrary von Neumann algebra. These
characterizations are applied to measure how close is a pair of absolute
compatible positive elements in the closed unit ball from being orthogonal or
commutative. In the case of 2 by 2 matrices the results offer a geometric
interpretation in terms of an ellipsoid determined by one of the points. The
conclusions for 2 by 2 matrices are also applied to describe absolutely
compatible pairs of positive elements in the closed unit ball of
$\mathbb{M}_n$.


  Bayesian neural networks (BNNs) have received an increased interest in the
last years. In BNNs, a complete posterior distribution of the unknown weight
and bias parameters of the network is produced during the training stage. This
probabilistic estimation offers several advantages with respect to point-wise
estimates, in particular, the ability to provide uncertainty quantification
when predicting new data. This feature inherent to the Bayesian paradigm, is
useful in countless machine learning applications. It is particularly appealing
in areas where decision-making has a crucial impact, such as medical healthcare
or autonomous driving. The main challenge of BNNs is the computational cost of
the training procedure since Bayesian techniques often face a severe curse of
dimensionality. Adaptive importance sampling (AIS) is one of the most prominent
Monte Carlo methodologies benefiting from sounded convergence guarantees and
ease for adaptation. This work aims to show that AIS constitutes a successful
approach for designing BNNs. More precisely, we propose a novel algorithm
PMCnet that includes an efficient adaptation mechanism, exploiting geometric
information on the complex (often multimodal) posterior distribution. Numerical
results illustrate the excellent performance and the improved exploration
capabilities of the proposed method for both shallow and deep neural networks.


  Lithium metal cells are key towards achieving high specific energy and energy
density for electrification of transportation and aviation. Anode-free cells
are the limiting case of lithium metal cells involving no excess lithium and
the highest possible specific energy. In addition, anode-free cells are easier,
cheaper and safer as they avoid handling and manufacturing of lithium metal
foils. Issues related to dendrite growth and poor cycling are magnified in
anode-free cells due to lack of excess lithium. Electrolyte and current
collector surface play a crucial role in affecting the cycling performance of
anode-free cells. In this work, we have computationally screened for candidate
current collectors that can nucleate lithium effectively and allow uniform
growth. These are determined by the free energy of lithium adsorption and
lithium surface diffusion barrier on candidate current collectors. Using
density functional theory calculations, we show that Li-alloys possess ideal
characteristics for Li nucleation and growth. These can lead to vastly improved
specific energy compared to current transition metal current collectors.


  Label-noise learning (LNL) aims to increase the model's generalization given
training data with noisy labels. To facilitate practical LNL algorithms,
researchers have proposed different label noise types, ranging from
class-conditional to instance-dependent noises. In this paper, we introduce a
novel label noise type called BadLabel, which can significantly degrade the
performance of existing LNL algorithms by a large margin. BadLabel is crafted
based on the label-flipping attack against standard classification, where
specific samples are selected and their labels are flipped to other labels so
that the loss values of clean and noisy labels become indistinguishable. To
address the challenge posed by BadLabel, we further propose a robust LNL method
that perturbs the labels in an adversarial manner at each epoch to make the
loss values of clean and noisy labels again distinguishable. Once we select a
small set of (mostly) clean labeled data, we can apply the techniques of
semi-supervised learning to train the model accurately. Empirically, our
experimental results demonstrate that existing LNL algorithms are vulnerable to
the newly introduced BadLabel noise type, while our proposed robust LNL method
can effectively improve the generalization performance of the model under
various types of label noise. The new dataset of noisy labels and the source
codes of robust LNL algorithms are available at
https://github.com/zjfheart/BadLabels.


  The spacetime metric around a rotating SuperConductive Ring (SCR) is deduced
from the gravitomagnetic London moment in rotating superconductors. It is shown
that theoretically it is possible to generate Closed Timelike Curves (CTC) with
rotating SCRs. The possibility to use these CTC's to travel in time as
initially idealized by G\"{o}del is investigated. It is shown however, that
from a technology and experimental point of view these ideas are impossible to
implement in the present context.


  Referring to objects in a natural and unambiguous manner is crucial for
effective human-robot interaction. Previous research on learning-based
referring expressions has focused primarily on comprehension tasks, while
generating referring expressions is still mostly limited to rule-based methods.
In this work, we propose a two-stage approach that relies on deep learning for
estimating spatial relations to describe an object naturally and unambiguously
with a referring expression. We compare our method to the state of the art
algorithm in ambiguous environments (e.g., environments that include very
similar objects with similar relationships). We show that our method generates
referring expressions that people find to be more accurate ($\sim$30% better)
and would prefer to use ($\sim$32% more often).


  The two-dimensional (2D) random-bond Ising model has a novel multicritical
point on the ferromagnetic to paramagnetic phase boundary. This random phase
transition is one of the simplest examples of a 2D critical point occurring at
both finite temperatures and disorder strength. We study the associated
critical properties, by mapping the random 2D Ising model onto a network model.
The model closely resembles network models of quantum Hall plateau transitions,
but has different symmetries. Numerical transfer matrix calculations enable us
to obtain estimates for the critical exponents at the random Ising phase
transition. The values are consistent with recent estimates obtained from
high-temperature series.


  We have analysed in detail the discovery measurements of the X-ray burster
SAX J1750.8-2900 by the Wide Field Cameras on board BeppoSAX in spring 1997, at
a position ~1.2 degrees off the Galactic Centre. The source was in outburst on
March 13th when the first observation started and showed X-ray emission for ~ 2
weeks. A total of 9 bursts were detected, with peak intensities varying from ~
0.4 to 1.0 Crab in the 2-10 keV range. Most bursts showed a fast rise time (~
1s), an exponential decay profile with e-folding time of ~ 5s, spectral
softening during decay, and a spectrum which is consistent with few keV
blackbody radiation. These features identify them as type-I X-ray bursts of
thermonuclear origin. The presence of type-I bursts and the source position
close to the Galactic Centre favours the classification of this object as a
neutron star low mass X-ray binary. X-ray emission from SAX J1750.8-2900 was
not detected in the previous and subsequent Galactic bulge monitoring, and the
source was never seen bursting again.


  Let $Ay=f$, $A$ is a linear operator in a Hilbert space $H$, $y\perp
N(A):=\{u:Au=0\}$, $R(A):=\{h:h=Au,u\in D(A)\}$ is not closed,
$\|f_\delta-f\|\leq\delta$. Given $f_\delta$, one wants to construct $u_\delta$
such that $\lim_{\delta\to 0}\|u_\delta-y\|=0$. A version of the DSM (dynamical
systems method) for finding $u_\delta$ consists of solving the problem \bee
  \dotu_\delta(t)=-u_\delta(t)+T^{-1}_{a(t)} A^\ast f_\delta, \quad u(0)=u_0,
\eqno{(\ast)}\eee where $T:=A^\ast A$, $T_a:=T+aI$, and $a=a(t)>0$,
$a(t)\searrow 0$ as $t\to\infty$ is suitably chosen. It is proved that
$u_\delta:=u_\delta(t_\delta)$ has the property $\lim_{\delta\to
0}\|u_\delta-y\|=0$. Here the stopping time $t_\delta$ is defined by the
discrepancy principle: \bee
  \eqno{(\ast\ast)}\eee $c\in(1,2)$ is a constant. Equation $(\ast)$ defines
$t_\delta$ uniquely and $\lim_{\delta\to 0}t_\delta=\infty$. Another version of
the discrepancy principle is also proved in this paper.


  We describe a practical algorithm to compute the (oriented) genus of a graph,
give results of the program implementing this algorithm, and compare the
performance to existing algorithms. The aim of this algorithm is to be fast
enough for many applications instead of focusing on the theoretical asymptotic
complexity. Apart from the specific problem and the results, the article can
also be seen as an example how some design principles used to carefully develop
and implement standard backtracking algorithms can still result in very
competitive programs.


  We present the results of searches for dipolar-type anisotropies in different
energy ranges above $2.5\times 10^{17}$ eV with the surface detector array of
the Pierre Auger Observatory, reporting on both the phase and the amplitude
measurements of the first harmonic modulation in the right-ascension
distribution. Upper limits on the amplitudes are obtained, which provide the
most stringent bounds at present, being below 2% at 99% $C.L.$ for EeV
energies. We also compare our results to those of previous experiments as well
as with some theoretical expectations.


  We consider scenarios in which we wish to perform joint scene understanding,
object tracking, activity recognition, and other tasks in environments in which
multiple people are wearing body-worn cameras while a third-person static
camera also captures the scene. To do this, we need to establish person-level
correspondences across first- and third-person videos, which is challenging
because the camera wearer is not visible from his/her own egocentric video,
preventing the use of direct feature matching. In this paper, we propose a new
semi-Siamese Convolutional Neural Network architecture to address this novel
challenge. We formulate the problem as learning a joint embedding space for
first- and third-person videos that considers both spatial- and motion-domain
cues. A new triplet loss function is designed to minimize the distance between
correct first- and third-person matches while maximizing the distance between
incorrect ones. This end-to-end approach performs significantly better than
several baselines, in part by learning the first- and third-person features
optimized for matching jointly with the distance measure itself.


  Human social interactions are typically recorded as time-specific dyadic
interactions, and represented as evolving (temporal) networks, where links are
activated/deactivated over time. However, individuals can interact in groups of
more than two people. Such group interactions can be represented as
higher-order events of an evolving network. Here, we propose methods to
characterize the temporal-topological properties of higher-order events to
compare networks and identify their (dis)similarities. We analyzed 8 real-world
physical contact networks, finding the following: a) Events of different orders
close in time tend to be also close in topology; b) Nodes participating in many
different groups (events) of a given order tend to involve in many different
groups (events) of another order; Thus, individuals tend to be consistently
active or inactive in events across orders; c) Local events that are close in
topology are correlated in time, supporting observation a). Differently, in 5
collaboration networks, observation a) is almost absent; Consistently, no
evident temporal correlation of local events has been observed in collaboration
networks. Such differences between the two classes of networks may be explained
by the fact that physical contacts are proximity based, in contrast to
collaboration networks. Our methods may facilitate the investigation of how
properties of higher-order events affect dynamic processes unfolding on them
and possibly inspire the development of more refined models of higher-order
time-varying networks.


  In the context of instanton method for stochastic system this paper purposes
a modification of the arclength parametrization of the Hamilton's equations
allowing for an arbitrary instanton speed. The main results of the paper are:
(i) it generalizes the parametrized Hamilton's equations to any speed required.
(ii) corrects the parametric action on the occasion that the Hamiltonian is
small but finite and how it adjusts to the probability density function (pdf).
(iii) Improves instanton approximation to pdf by noise and propagator
renormalization. As an application of the above set up we predict the
statistics of passive scalar gradients in a Lagrangian model for turbulence,
namely the scalar gradient Recent Fluid Deformation Closure (sgRFD).


  We suggest a novel extension to the Kaluza-Klein scheme that allows us to
obtain consistently all SU(n) Einstein-Yang-Mills theories. This construction
is based on allowing the five-dimensional spacetime to carry some non-vanishing
torsion; however, the four-dimensional spacetime remains intrinsically
torsion-free.


  The quantization of the electromagnetic field leads directly to the existence
of quantum mechanical states, called Fock states, with an exact integer number
of photons. Despite these fundamental states being long-understood, and despite
their many potential applications, generating them is largely an open problem.
For example, at optical frequencies, it is challenging to deterministically
generate Fock states of order two and beyond. Here, we predict the existence of
a new effect in nonlinear optics, which enables the deterministic generation of
large Fock states at arbitrary frequencies. The effect, which we call an
n-photon bound state in the continuum, is one in which a photonic resonance
(such as a cavity mode) becomes lossless when a precise number of photons n is
inside the resonance. Based on analytical theory and numerical simulations, we
show that these bound states enable a remarkable phenomenon in which a coherent
state of light, when injected into a system supporting this bound state, can
spontaneously evolve into a Fock state of a controllable photon number. This
effect is also directly applicable for creating (highly) squeezed states of
light, whose photon number fluctuations are (far) below the value expected from
classical physics (i.e., shot noise). We suggest several examples of systems to
experimentally realize the effects predicted here in nonlinear nanophotonic
systems, showing examples of generating both optical Fock states with large n
(n > 10), as well as more macroscopic photonic states with very large
squeezing, with over 90% less noise (10 dB) than the classical value associated
with shot noise.


  The availability of vector magnetogram sequences with sufficient accuracy and
cadence to estimate the time derivative of the magnetic field allows us to use
Faraday's law to find an approximate solution for the electric field in the
photosphere, using a Poloidal-Toroidal Decomposition (PTD) of the magnetic
field and its partial time derivative. Without additional information, however,
the electric field found from this technique is under-determined -- Faraday's
law provides no information about the electric field that can be derived the
gradient of a scalar potential. Here, we show how additional information in the
form of line-of-sight Doppler flow measurements, and motions transverse to the
line-of-sight determined with ad-hoc methods such as local correlation
tracking, can be combined with the PTD solutions to provide much more accurate
solutions for the solar electric field, and therefore the Poynting flux of
electromagnetic energy in the solar photosphere. Reliable, accurate maps of the
Poynting flux are essential for quantitative studies of the buildup of magnetic
energy before flares and coronal mass ejections.


  In the presence of classical phase space singularities the standard methods
are insufficient to attack the problem of quantization.In certain situations
the difficulties can be overcome by means of K\"ahler quantization on
stratified K\"ahler spaces. Such a space is a stratified symplectic space
together with a complex analytic structure which is compatible with the
stratified symplectic structure; in particular each stratum is a K\"ahler
manifold in an obvious fashion. Holomorphic quantization on a stratified
K\"ahler space then yields a costratified Hilbert space, a quantum object
having the classical singularities as its shadow. Given a K\"ahler manifold
with a hamiltonian action of a compact Lie group that also preserves the
complex structure, reduction after quantization coincides with quantization
after reduction in the sense that not only the reduced and unreduced quantum
phase spaces correspond but the invariant unreduced and reduced quantum
observables as well


  Generative models for source code are an interesting structured prediction
problem, requiring to reason about both hard syntactic and semantic constraints
as well as about natural, likely programs. We present a novel model for this
problem that uses a graph to represent the intermediate state of the generated
output. The generative procedure interleaves grammar-driven expansion steps
with graph augmentation and neural message passing steps. An experimental
evaluation shows that our new model can generate semantically meaningful
expressions, outperforming a range of strong baselines.


  Choice overload - by which larger choice sets are detrimental to a chooser's
wellbeing - is potentially of great importance to the design of economic
policy. Yet the current evidence on its prevalence is inconclusive. We argue
that existing tests are likely to be underpowered and hence that choice
overload may occur more often than the literature suggests. We propose more
powerful tests based on richer data and characterization theorems for the
Random Utility Model. These new approaches come with significant econometric
challenges, which we show how to address. We apply our tests to new
experimental data and find strong evidence of choice overload that would likely
be missed using current approaches.


  Grid based fluid simulation methods are not able to monolithically capture
complex non-linear dynamics like the rupture of a dynamic liquid bridge between
freely colliding solids, an exemplary scenario of capillary forces competing
with inertial forces in engineering applications. We introduce a new
Incompressible Smoothed Particle Hydrodynamics method for simulating three
dimensional fluid-solid interaction flows with capillary (wetting and surface
tension) effects at free surfaces. This meshless approach presents significant
advantages over grid based approaches in terms of being monolithic and in
handling interaction with free solids. The method is validated for accuracy and
stability in dynamic scenarios involving surface tension and wetting. We then
present three dimensional simulations of crown forming instability following
the splash of a liquid drop, and the rupture of a liquid bridge between two
colliding solid spheres, to show the method's advantages in the study of
dynamic micromechanical phenomena involving capillary flows.


  A zero-energy mid-band singularity has been found in the energy spectrum of
random matrices with correlations between diagonal and off-diagonal elements
typical of vibrational problems. Two representative classes of matrices,
characterizing the instantaneous configurations in liquids and mechanically
unstable lattices (which mimic the former) have been analysed. At least for
disordered lattice models, the singularity is universal and its origin can be
explained within the mean-field treatment.


  Cloud computing is gaining significant attention, however, security is the
biggest hurdle in its wide acceptance. Users of cloud services are under
constant fear of data loss, security threats and availability issues. Recently,
learning-based methods for security applications are gaining popularity in the
literature with the advents in machine learning techniques. However, the major
challenge in these methods is obtaining real-time and unbiased datasets. Many
datasets are internal and cannot be shared due to privacy issues or may lack
certain statistical characteristics. As a result of this, researchers prefer to
generate datasets for training and testing purpose in the simulated or closed
experimental environments which may lack comprehensiveness. Machine learning
models trained with such a single dataset generally result in a semantic gap
between results and their application. There is a dearth of research work which
demonstrates the effectiveness of these models across multiple datasets
obtained in different environments. We argue that it is necessary to test the
robustness of the machine learning models, especially in diversified operating
conditions, which are prevalent in cloud scenarios. In this work, we use the
UNSW dataset to train the supervised machine learning models. We then test
these models with ISOT dataset. We present our results and argue that more
research in the field of machine learning is still required for its
applicability to the cloud security.


  The game theory techniques are used to find the equilibrium of a market. Game
theory refers to the ways in which strategic interactions among economic agents
produce outcomes with respect to the preferences (or utilities) of those
agents, where the outcomes in question might have been intended by none of the
agents. The oligopolistic market structures are taken and how game theory
applies to them is explained.


  In 1922 the University of Buenos Aires (UBA) Council approved a motion to
send an invitation to Albert Einstein to visit Argentina and give a course of
lectures on his theory of relativity. The motion was proposed by Jorge Duclout
(1856-1927), who had been educated at the Eidgenossische Technische Hochschule,
Zurich (ETH). This proposal was the culmination of a series of initiatives of
various Argentine intellectuals interested in the theory of relativity. In a
very short time Dr. Mauricio Nirenstein (1877-1935), then the university's
administrative secretary, fulfilled all the requirements for the university's
invitation to be endorsed and delivered to the sage in Berlin. The visit took
place three years later, in March-April 1925.
  The Argentine press received Einstein with great interest and respect; his
early exchanges covered a wide range of topics, including international
politics and Jewish matters. Naturally, the journalists were more eager to hear
from the eminent pacifist than from the incomprehensible physicist. However,
after his initial openness with the press, the situation changed and Einstein
restricted his public discourse to topics on theoretical physics, avoiding some
controversial political, religious, or philosophical matters that he had freely
touched upon in earlier interviews.. [abridged].


  In [4] we gave a variational definition of the nonlinear membrane energy
under the constraint "det\nabla u\not=0". In this paper we obtain the nonlinear
membrane energy under the more realistic constraint "det\nabla u>0".


  In the field of Large Eddy Simulation, the Smagorinsky subgrid scale model
(in some form) is the most commonly accepted and used subgrid scale model. The
purpose of this paper is to address the main weakness of the Smagorinsky model,
its poor performance near the wall. The goal is to establish a model that
corrects the Smagorinsky model near the walls while at the same time minimizing
the computational overhead. A version the Dynamic Subgrid Scale model is also
incorporated into the finite element code to facilitate comparisons with the
new model near the walls.
  One of the unique characteristics of Large Eddy Simulations as compared to
other methods of dealing with turbulent flows is the idea of filtering. In this
paper we define what a filter is and also address an issue related to filters;
the error that results when the filtering and differential operations are
interchanged. This error is studied under the context of the Finite Element
Method which allows us to focus on the function being filtered rather than the
filter kernal function, which has been the usual approach in studying this
error.


  Generative adversarial networks (GANs) are known for their strong abilities
on capturing the underlying distribution of training instances. Since the
seminal work of GAN, many variants of GAN have been proposed. However, existing
GANs are almost established on the assumption that the training dataset is
clean. But in many real-world applications, this may not hold, that is, the
training dataset may be contaminated by a proportion of undesired instances.
When training on such datasets, existing GANs will learn a mixture distribution
of desired and contaminated instances, rather than the desired distribution of
desired data only (target distribution). To learn the target distribution from
contaminated datasets, two purified generative adversarial networks (PuriGAN)
are developed, in which the discriminators are augmented with the capability to
distinguish between target and contaminated instances by leveraging an extra
dataset solely composed of contamination instances. We prove that under some
mild conditions, the proposed PuriGANs are guaranteed to converge to the
distribution of desired instances. Experimental results on several datasets
demonstrate that the proposed PuriGANs are able to generate much better images
from the desired distribution than comparable baselines when trained on
contaminated datasets. In addition, we also demonstrate the usefulness of
PuriGAN on downstream applications by applying it to the tasks of
semi-supervised anomaly detection on contaminated datasets and PU-learning.
Experimental results show that PuriGAN is able to deliver the best performance
over comparable baselines on both tasks.


  A supergrid graph is a finite induced subgraph of the infinite graph
associated with the two-dimensional supergrid. The supergrid graphs contain
grid graphs and triangular grid graphs as subgraphs. The Hamiltonian cycle
problem for grid and triangular grid graphs was known to be NP-complete. In the
past, we have shown that the Hamiltonian cycle problem for supergrid graphs is
also NP-complete. The Hamiltonian cycle problem on supergrid graphs can be
applied to control the stitching trace of computerized sewing machines. In this
paper, we will study the Hamiltonian cycle property of linear-convex supergrid
graphs which form a subclass of supergrid graphs. A connected graph is called
$k$-connected if there are $k$ vertex-disjoint paths between every pair of
vertices, and is called locally connected if the neighbors of each vertex in it
form a connected subgraph. In this paper, we first show that any 2-connected,
linear-convex supergrid graph is locally connected. We then prove that any
2-connected, linear-convex supergrid graph contains a Hamiltonian cycle.


  The Random-Facet algorithm of Kalai and of Matousek, Sharir and Welzl is an
elegant randomized algorithm for solving linear programs and more general
LP-type problems. Its expected subexponential time of
$2^{\tilde{O}(\sqrt{m})}$, where $m$ is the number of inequalities, makes it
the fastest known combinatorial algorithm for solving linear programs. We
previously showed that Random-Facet performs an expected number of
$2^{\tilde{\Omega}(\sqrt[3]{m})}$ pivoting steps on some LPs with $m$
inequalities that correspond to $m$-action Markov Decision Processes (MDPs). We
also showed that Random-Facet-1P, a one permutation variant of Random-Facet,
performs an expected number of $2^{\tilde{O}(\sqrt{m})}$ pivoting steps on
these examples. Here we show that the same results can be obtained using LPs
that correspond to instances of the classical shortest paths problem. This
shows that the stochasticity of the MDPs, which is essential for obtaining
lower bounds for Random-Edge, is not needed in order to obtain lower bounds for
Random-Facet. We also show that our new $2^{\tilde{\Omega}(\sqrt{m})}$ lower
bound applies to Random-Bland, a randomized variant of the classical
anti-cycling rule suggested by Bland.


  In this paper, optical and electronic properties of diamond shaped graphene
quantum dots (DQDs) have been studied by employing large-scale
electron-correlated calculations. The computations have been performed using
the \pi-electron Pariser-Parr-Pople model Hamiltonian, which incorporates
long-range Coulomb interactions. The influence of electron-correlation effects
on the ground and excited states has been included by means of the
configuration-interaction approach, used at various levels. Our calculations
have revealed that the absorption spectra are red-shifted with the increasing
sizes of quantum dots. It has been observed that the first peak of the linear
optical absorption, which represents the optical gap, is not the most intense
peak. This result is in excellent agreement with the experimental data, but in
stark contrast to the predictions of the tight-binding model, according to
which the first peak is the most intense peak, pointing to the importance of
electron-correlation effects.


  In the present paper a method of finding the dynamics of the Wigner function
of a particle in an infinite quantum well is developed. Starting with the
problem of a reflection from an impenetrable wall, the obtained solution is
then generalized to the case of a particle confined in an infinite well in
arbitrary dimensions. It is known, that boundary value problems in the phase
space formulation of the quantum mechanics are surprisingly tricky. The
complications arise from nonlocality of the expression involved in calculation
of the Wigner function. Several ways of treating such problems were proposed.
They are rather complicated and even exotic, involving, for example,
corrections to the kinetic energy proportional to the derivatives of the Dirac
delta--function. The presented in the manuscript approach is simpler both from
analytical point of view and regarding numerical calculation. The solution is
brought to a form of convolution of the free particle solution with some
function, defined by the shape of the well. This procedure requires calculation
of an integral, which can be done by developed analytical and numerical
methods.


  Frequency-dependent terahertz conductivities of La$_{2-x}$Sr$_x$CuO$_4$ thin
films with various carrier concentrations were investigated. The imaginary part
of the complex conductivity considerably increased from far above a
zero-resistance superconducting transition temperature,
$T_\text{c}^\text{zero}$, because of the existence of the fluctuating
superfluid density with a short lifetime. The onset temperature of the
superconducting fluctuation is at most $\sim 2T_\text{c}^\text{zero}$ for
underdoped samples, which is consistent with the previously reported analysis
of microwave conductivity. The superconducting fluctuation was not enhanced
under a 0.5 T magnetic field. We also found that the temperature dependence of
the superconducting fluctuation was sensitive to the carrier concentration of
La$_{2-x}$Sr$_x$CuO$_4$, which reflects the difference in the nature of the
critical dynamics near the superconducting transition temperature. Our results
suggest that the onset temperature of the Nernst signal is not related to the
superconducting fluctuation we argued in this paper.


  We analyze certain class of linear maps on matrix algebras that become
entanglement breaking after composing a finite or infinite number of times with
themselves. This means that the Choi matrix of the iterated linear map becomes
separable in the tensor product space. If a linear map is entanglement breaking
after finite iterations, we say the map has a finite index of separability. In
particular we show that every unital PPT-channel becomes entanglement breaking
after a finite number of iterations. It turns out that the class of unital
channels that have finite index of separability is a dense subset of the unital
channels. We construct concrete examples of maps which are not PPT but have
finite index of separability. We prove that there is a large class of unital
channels that are asymptotically entanglement breaking. This analysis is
motivated by the PPT-squared conjecture made by M. Christandl that says every
PPT channel, when composed with itself, becomes entanglement breaking.


  These notes are an introduction to and an overview of the theory of algebraic
surfaces over algebraically closed fields of positive characteristic. After
some background in characteristic-p-geometry, we sketch the Kodaira-Enriques
classification. Next, we turn to more special characteristic-p topics, and end
by lifting results and applications to characteristic zero. We assume that the
reader has a background in complex geometry and has seen the Kodaira-Enriques
classification of complex surfaces before.


  Neutron scattering measurements are used to elucidate interplay of the
field-induced spin gap and the quantum fluctuations in archetypal heavy
electron system CeCu$_{2}$Ge$_{2}$. A spin gap of $\Delta$ = 0.56 meV is found
to develop near the field-induced quantum critical state at $H$$_{c}$$\simeq$ 8
T, driven by fluctuations of the long range antiferromagnetic order parameter.
The superconducting transition temperature in many magnetic superconductors is
found to exhibit one-to-one correspondence with the spin gap. In this regard,
the demonstration of an interplay of the spin gap with the nanoscopic dynamic
correlation provides new arena to explore direct relation between the quantum
critical behavior and the unconventional superconductivity, especially in heavy
electrons systems.


  We determine experimentally the excited-state interatomic forces in
photoexcited bismuth. The forces are obtained by a constrained least-squares
fit of the excited-state dispersion obtained by femtosecond time-resolved x-ray
diffuse scattering to a fifteen-nearest neighbor Born-von Karman model. We find
that the observed softening of the zone-center $A_{1g}$ optical mode and
transverse acoustic modes with photoexcitation are primarily due to a weakening
of three nearest neighbor forces along the bonding direction. This provides a
more complete picture of what drives the partial reversal of the Peierls
distortion previously observed in photoexcited bismuth.


  Many modern machine learning models are trained to achieve zero or near-zero
training error in order to obtain near-optimal (but non-zero) test error. This
phenomenon of strong generalization performance for "overfitted" / interpolated
classifiers appears to be ubiquitous in high-dimensional data, having been
observed in deep networks, kernel machines, boosting and random forests. Their
performance is consistently robust even when the data contain large amounts of
label noise.
  Very little theory is available to explain these observations. The vast
majority of theoretical analyses of generalization allows for interpolation
only when there is little or no label noise. This paper takes a step toward a
theoretical foundation for interpolated classifiers by analyzing local
interpolating schemes, including geometric simplicial interpolation algorithm
and singularly weighted $k$-nearest neighbor schemes. Consistency or
near-consistency is proved for these schemes in classification and regression
problems. Moreover, the nearest neighbor schemes exhibit optimal rates under
some standard statistical assumptions.
  Finally, this paper suggests a way to explain the phenomenon of adversarial
examples, which are seemingly ubiquitous in modern machine learning, and also
discusses some connections to kernel machines and random forests in the
interpolated regime.


  A plethora of attack methods have been proposed to generate adversarial
examples, among which the iterative methods have been demonstrated the ability
to find a strong attack. However, the computation of an adversarial
perturbation for a new data point requires solving a time-consuming
optimization problem from scratch. To generate a stronger attack, it normally
requires updating a data point with more iterations. In this paper, we show the
existence of a meta adversarial perturbation (MAP), a better initialization
that causes natural images to be misclassified with high probability after
being updated through only a one-step gradient ascent update, and propose an
algorithm for computing such perturbations. We conduct extensive experiments,
and the empirical results demonstrate that state-of-the-art deep neural
networks are vulnerable to meta perturbations. We further show that these
perturbations are not only image-agnostic, but also model-agnostic, as a single
perturbation generalizes well across unseen data points and different neural
network architectures.


  A number of new papers have greatly elucidated the derivation of quiver gauge
theories from D-branes at a singularity. A complete story has now been
developed for the total space of the canonical line bundle over a smooth Fano
2-fold. In the context of the AdS/CFT conjecture, this corresponds to eight of
the ten regular Sasaki-Einstein 5-folds. Interestingly, the two remaining
spaces are among the earliest examples, the sphere and T^{11}. I show how to
obtain the (well-known) quivers for these theories by interpreting the
canonical line bundle as the resolution of an orbifold using the McKay
correspondence. I then obtain the correct quivers by undoing the orbifold. I
also conjecture, in general, an autoequivalence that implements the orbifold
group action on the derived cateory. This yields a new order two
autoequivalence for the Z_2 quotient of the conifold.


  Different degrees of freedom of single photons have been entangled and are
used as a resource for various quantum technology applications. We present a
simple scheme to perform Bell's test and show the violation of CHSH inequality
in a path-entangled single photon state using interferometric and its
equivalent non-interferometric approach in beam splitter setting. We
demonstrate this experimentally by generating and controlling path-entangled
state using both, heralded and un-heralded single photons from spontaneous
parametric down-conversion. The experimental results we present show the
transition to violation of CHSH inequality when the purity of single photons
state visibility increase above 70\% , $\mathcal{P} > 0.7$. Our procedure using
single beam splitter and two detector module for un-heralded single photon
source allows a simple way to test for purity of any single photon source and
to study quantum correlations on systems driven by dynamics where single
particle entanglement with position space is prominent.


  When generating in-silico clinical electrophysiological outputs, such as
electrocardiograms (ECGs) and body surface potential maps (BSPMs), mathematical
models have relied on single physics, i.e. of the cardiac electrophysiology
(EP), neglecting the role of the heart motion. Since the heart is the most
powerful source of electrical activity in the human body, its motion
dynamically shifts the position of the principal electrical sources in the
torso, influencing electrical potential distribution and potentially altering
the EP outputs. In this work, we propose a computational model for the
simulation of ECGs and BSPMs by coupling a cardiac electromechanical model with
a model that simulates the propagation of the EP signal in the torso, thanks to
a flexible numerical approach, that simulates the torso domain deformation
induced by the myocardial displacement. Our model accounts for the major
mechano-electrical feedbacks, along with unidirectional displacement and
potential couplings from the heart to the surrounding body. For the numerical
discretization, we employ a versatile intergrid transfer operator that allows
for the use of different Finite Element spaces to be used in the cardiac and
torso domains. Our numerical results are obtained on a realistic 3D
biventricular-torso geometry, and cover both cases of sinus rhythm and
ventricular tachycardia (VT), solving both the electromechanical-torso model in
dynamical domains, and the classical electrophysiology-torso model in static
domains. By comparing standard 12-lead ECG and BSPMs, we highlight the
non-negligible effects of the myocardial contraction on the EP-outputs,
especially in pathological conditions, such as the VT.


  Recent results on short-lived hadronic resonances obtained with the ALICE
detector at LHC energies are presented. These results include system-size and
collision-energy evolution of transverse momentum spectra, yields and the
ratios of resonance yields to those of longer-lived particles, and nuclear
modification factors. Results will be compared with model predictions.


  The growing number of real-time camera feeds in urban areas has made it
possible to provide high-quality traffic data for effective transportation
planning, operations, and management. However, deriving reliable traffic
metrics from these camera feeds has been a challenge due to the limitations of
current vehicle detection techniques, as well as the various camera conditions
such as height and resolution. In this work, a quadtree based algorithm is
developed to continuously partition the image extent until only regions with
high detection accuracy are remained. These regions are referred to as the
high-accuracy identification regions (HAIR) in this paper. We demonstrate how
the use of the HAIR can improve the accuracy of traffic density estimates using
images from traffic cameras at different heights and resolutions in Central
Ohio. Our experiments show that the proposed algorithm can be used to derive
robust HAIR where vehicle detection accuracy is 41 percent higher than that in
the original image extent. The use of the HAIR also significantly improves the
traffic density estimation with an overall decrease of 49 percent in root mean
squared error.


  We prove an analogue of the Lewy extension theorem for a real dimension $2n$
smooth submanifold $M \subset {\mathbb C}^{n}\times {\mathbb R}$, $n \geq 2$. A
theorem of Hill and Taiani implies that if $M$ is CR and the Levi-form has a
positive eigenvalue restricted to the leaves of ${\mathbb C}^n \times {\mathbb
R}$, then every smooth CR function $f$ extends smoothly as a CR function to one
side of $M$. If the Levi-form has eigenvalues of both signs, then $f$ extends
to a neighborhood of $M$. Our main result concerns CR singular manifolds with a
nondegenerate quadratic part $Q$. A smooth CR $f$ extends to one side if the
Hermitian part of $Q$ has at least two positive eigenvalues, and $f$ extends to
the other side if the form has at least two negative eigenvalues. We provide
examples to show that at least two nonzero eigenvalues in the direction of the
extension are needed.


  A generalization of the on-mass-shell scheme of UV renormalization (the
OMS-bar scheme) to the case of presence of unstable fundamental particles (like
W and Z bosons) is proposed. Its basic ingredients are as follows: (i) the
renormalized mass coincides with a real part of the position of the complex
pole of the corresponding propagator, (ii) the imaginary part of the on-shell
self-energy coincides with the imaginary part of the complex pole position. The
latter property implies the gauge-invariance of the imaginary part of the
on-shell self-energy in the OMS-bar scheme and its connection with the lifetime
of an unstable particle. Starting with the three-loops this connection becomes
nontrivial.


  Spiral galaxies can be classified into the {\it Grand-designs} and {\it
Flocculents} based on the nature of their spiral arms. The {\it Grand-designs}
exhibit almost continuous and high contrast spiral arms and are believed to be
driven by density waves, while the {\it Flocculents} have patchy and
low-contrast spiral features and are primarily stochastic in origin. We train a
convolutional neural network (CNN) model to classify spirals into {\it
Grand-designs} and {\it Flocculents}, with a testing accuracy of
$\mathrm{97.2\%}$. We then use the above model for classifying $\mathrm{1,354}$
new spirals from the SDSS. Out of these, $\mathrm{721}$ were identified as {\it
Flocculents}, and the rest as {\it Grand-designs}. We find the median
asymptotic rotational velocities of our newly classified {\it Grand-designs}
and {\it Flocculents} are $218 \pm 86$ and $145 \pm 67$ respectively,
indicating that the {\it Grand-designs} are mostly the high-mass and the {\it
Flocculents} the intermediate-mass spirals. This is further corroborated by the
observation that the median morphological indices of the {\it Grand-designs}
and {\it Flocculents} are $2.6 \pm 1.8$ and $4.7 \pm 1.9$ respectively,
implying that the {\it Flocculents} primarily consist of a late-type galaxy
population in contrast to the {\it Grand-designs}. Finally, an almost equal
fraction of of bars $\sim$ 0.3 in both the classes of spiral galaxies reveals
that the presence of a bar component does not regulate the type of spiral arm
hosted by a galaxy. Our results may have important implications for formation
and evolution of spiral arms in galaxies.


  This paper presents a novel technique for mitigating electrode backgrounds
that limit the sensitivity of searches for low-mass dark matter (DM) using
xenon time projection chambers. In the LUX detector, signatures of low-mass DM
interactions would be very low energy ($\sim$keV) scatters in the active target
that ionize only a few xenon atoms and seldom produce detectable scintillation
signals. In this regime, extra precaution is required to reject a complex set
of low-energy electron backgrounds that have long been observed in this class
of detector. Noticing backgrounds from the wire grid electrodes near the top
and bottom of the active target are particularly pernicious, we develop a
machine learning technique based on ionization pulse shape to identify and
reject these events. We demonstrate the technique can improve Poisson limits on
low-mass DM interactions by a factor of $2$-$7$ with improvement depending
heavily on the size of ionization signals. We use the technique on events in an
effective $5$ tonne$\cdot$day exposure from LUX's 2013 science operation to
place strong limits on low-mass DM particles with masses in the range
$m_{\chi}\in0.15$-$10$ GeV. This machine learning technique is expected to be
useful for near-future experiments, such as LZ and XENONnT, which hope to
perform low-mass DM searches with the stringent background control necessary to
make a discovery.


  Code contains security and functional bugs. The process of identifying and
localizing them is difficult and relies on human labor. In this work, we
present a novel approach (FLAG) to assist human debuggers. FLAG is based on the
lexical capabilities of generative AI, specifically, Large Language Models
(LLMs). Here, we input a code file then extract and regenerate each line within
that file for self-comparison. By comparing the original code with an
LLM-generated alternative, we can flag notable differences as anomalies for
further inspection, with features such as distance from comments and LLM
confidence also aiding this classification. This reduces the inspection search
space for the designer. Unlike other automated approaches in this area, FLAG is
language-agnostic, can work on incomplete (and even non-compiling) code and
requires no creation of security properties, functional tests or definition of
rules. In this work, we explore the features that help LLMs in this
classification and evaluate the performance of FLAG on known bugs. We use 121
benchmarks across C, Python and Verilog; with each benchmark containing a known
security or functional weakness. We conduct the experiments using two state of
the art LLMs in OpenAI's code-davinci-002 and gpt-3.5-turbo, but our approach
may be used by other models. FLAG can identify 101 of the defects and helps
reduce the search space to 12-17% of source code.


  In this article, we consider a generalization of the conjugate Hardy $H^2$
spaces, and give some properties of the minimal norm of the generalization and
some relations between the norm of the generalization and the minimal $L^2$
integrals. As applications, we give some monotonicity results for the conjugate
Hardy $H^2$ kernels and the Bergman kernels on planar regions, and some
relations between the conjugate Hardy $H^2$ kernels and the Bergman kernels on
planar regions.


  The existence and uniqueness of a solution to a generalized Blasius equation
with asymptotic boundary conditions are proved. A new numerical approximation
method is proposed.


  We give 50 digits values of the simple continued fractions whose denominators
are formed from a) prime numbers, b) twin primes, c) generalized $d$-twins, d)
primes of the form $m^2+n^4$, e)primes of the form $m^2+1$, f) Mersenne primes
and g) primorial primes. All these continued fractions belong to the set of
measure zero of exceptions to the theorems of Khinchin and Levy. We claim that
all these continued fractions are transcendental numbers. Next we propose the
conjecture which indicates the way to deduce the transcendence of some
continued fractions from transcendence of another ones.


  It has been shown recently that the charged black hole can be scalarized if
Maxwell field minimally couples with a complex scalar which has nonnegative
nonlinear potential. We firstly prove that such scalarization cannot be a
result of continuous phase transition for general scalar potential.
Furthermore, we numerically find that it is possible that the RN black hole
will be scalarized by a first order phase transition spontaneously and extreme
RN black hole is not stable in micro-canonical ensemble. In addition,
considering a massless scalar perturbation, we compute the quasi-normal modes
of the scalarized charged black hole and the results imply that the
spontaneously scalarized charged black hole is not only favored in
thermodynamics but also is kinetically stable against scalar perturbation at
linear level. Our numerical results also definitely gives negative answer to
Penrose-Gibbons conjecture and two new versions of Penrose inequality in
charged case are suggested.


  We compute the potential energy for the dilaton, complex structure and Kahler
moduli and search of realistic vacua of heterotic M-theory compactified on
Calabi-Yau threefolds. We present a protocol for deriving the potential that
combines the non-perturbative complex structure, gaugino condensate and
worldsheet instanton superpotentials in theories in which the hidden sector
contains an anomalous $U(1)$ structure group. The Green-Schwarz anomaly
cancellation induces inhomogeneous axion transformations for the imaginary
components of the dilaton and Kahler modulus. Using this protocol we obtain
explicit examples in which potential has a global minimum at negative or zero
vacuum density or a metastable minimum with positive vacuum density. In all
three cases, the dilaton, Kahler modulus and associated axion moduli are
completely stabilized. Finally, we show that, for any of these vacua, the
potential energy satisfies the large scalar field Swampland conjecture.


  We discuss two approaches that are used frequently to describe
quantum-classical hybrid system. One is the well-known mean-field theory and
the other adopts a set of hybrid brackets which is a mixture of quantum
commutators and classical Poisson brackets. We prove that these two approaches
are equivalent.


  This paper exploits the potential of physical layer security in massive
multiple-input multiple-output (MIMO) aided two-tier heterogeneous networks
(HetNets). We focus on the downlink secure transmission in the presence of
multiple eavesdroppers. We first address the impact of massive MIMO on the
maximum receive power based user association. We then derive the tractable
upper bound expressions for the secrecy outage probability of a HetNets user.We
show that the implementation of massive MIMO significantly improves the secrecy
performance, which indicates that physical layer security could be a promising
solution for safeguarding massive MIMO HetNets. Furthermore, we show that the
secrecy outage probability of HetNets user first degrades and then improves
with increasing the density of PBSs.


  In this note we prove that the symmetry of the quasi-isometry relation
implies the axiom of choice, even when the relation is restricted to geodesic
hyperbolic spaces. We show that this result is sharp by demonstrating that
symmetry of quasi-isometry in an even more restrictive setting does not imply
the axiom of choice. The "Bottleneck Theorem" of Jason Fox Manning also implies
choice.


  A vortex line is shaped by a zigzag of pinning centers and we study here how
far the stretched vortex line is able to follow this path. The pinning center
is described by an insulating sphere of coherence length size such that in its
surface the de Gennes boundary condition applies. We calculate the free energy
density of this system in the framework of the Ginzburg-Landau theory and study
the critical displacement beyond which the vortex line is detached from the
pinning center.


  A brief review of theoretical and experimental aspects of $b$-quark
production measurements at the LHC.


  The fabrication of ZnSe/ZnTe superlattices grown by the process of rotating
the substrate in the presence of an inhomogeneous flux distribution instead of
successively closing and opening of source shutters is studied via Monte Carlo
simulations. It is found that the concentration of each compound is
sinusoidally modulated along the growth direction, caused by the uneven arrival
of Se and Te atoms at a given point of the sample, and by the variation of the
Te/Se ratio at that point due to the rotation of the substrate. In this way we
obtain a ZnSe$_{1-x}$Te$_x$ alloy in which the composition $x$ varies
sinusoidally along the growth direction. The period of the modulation is
directly controlled by the rate of the substrate rotation. The amplitude of the
compositional modulation is monotonous for small angular velocities of the
substrate rotation, but is itself modulated for large angular velocities. The
average amplitude of the modulation pattern decreases as the angular velocity
of substrate rotation increases and the measurement position approaches the
center of rotation. The simulation results are in good agreement with
previously published experimental measurements on superlattices fabricated in
this manner.


  We develop a systematic information-theoretic framework for quantification
and mitigation of error in probabilistic Lagrangian (i.e., path-based)
predictions which are obtained from dynamical systems generated by uncertain
(Eulerian) vector fields. This work is motivated by the desire to improve
Lagrangian predictions in complex dynamical systems based either on
analytically simplified or data-driven models. We derive a hierarchy of general
information bounds on uncertainty in estimates of statistical observables
$\mathbb{E}^{\nu}[f]$, evaluated on trajectories of the approximating dynamical
system, relative to the "true'' observables $\mathbb{E}^{\mu}[f]$ in terms of
certain $\varphi$-divergences, $\mathcal{D}_\varphi(\mu\|\nu)$, which quantify
discrepancies between probability measures $\mu$ associated with the original
dynamics and their approximations $\nu$. We then derive two distinct bounds on
$\mathcal{D}_\varphi(\mu\|\nu)$ itself in terms of the Eulerian fields. This
new framework provides a rigorous way for quantifying and mitigating
uncertainty in Lagrangian predictions due to Eulerian model error.


  Lead halide perovskite nanocrystals (LHP-NCs) embedded in polymer matrices
are gaining traction for next-generation radiation detectors. While progress
has been made on green-emitting CsPbBr3 NCs, scant attention has been given to
the scintillation properties of CsPbCl3 NCs, which emit size-tunable UV-blue
light matching the peak efficiency of ultrafast photodetectors. In this study,
we explore the scintillation characteristics of CsPbCl3 NCs produced through a
scalable method and treated with CdCl2. Spectroscopic, radiometric and
theoretical analysis on both untreated and treated NCs uncover deep hole trap
states due to surface undercoordinated chloride ions, eliminated by Pb to Cd
substitution. This yields near-perfect efficiency and resistance to
polyacrylate mass-polymerization. Radiation hardness tests demonstrate
stability to high gamma doses while time-resolved experiments reveal ultrafast
radioluminescence with an average lifetime as short as 210 ps. These findings
enhance our comprehension of LHP NCs' scintillation properties, positioning
CsPbCl3 as a promising alternative to conventional fast scintillators.


  Complex organic molecules are readily detected in the inner regions of the
gaseous envelopes of forming protostars. In particular, molecules that contain
nitrogen are interesting due to the role nitrogen plays in the development of
life and the compact scales such molecules have been found to trace around
forming protostars. The goal of this work is to determine the inventory of one
family of nitrogen-bearing organic molecules, complex nitriles (molecules with
a $-$CN functional group) towards two hot corino sources in the low-mass
protostellar binary IRAS 16293$-$2422. This work explores the abundance
differences between the two sources, the isotopic ratios, and the spatial
extent derived from molecules containing the nitrile functional group. Using
data from the Protostellar Interferometric Line Survey (PILS) obtained with
ALMA we determine abundances and excitation temperatures for the detected
nitriles. We also present a new method for determining the spatial structure of
sources with high line density and large velocity gradients $-$
Velocity-corrected INtegrated emission (VINE) maps. We detect methyl cyanide
(CH$_3$CN) as well as 5 of its isotopologues, including the detection of
CHD$_2$CN which is the first detection in the ISM. We also detect ethyl cyanide
(C$_2$H$_5$CN), vinyl cyanide (C$_2$H$_3$CN), and cyanoacetylene (HC$_3$N). We
find that abundances are similar between IRAS 16293A and IRAS 16293B on small
scales except for vinyl cyanide which is only detected towards the latter
source. This suggests an important difference between the sources either in
their evolutionary stage or warm-up timescales. We also detect a spatially
double-peaked emission for the first time in molecular emission in the A
source, suggesting that this source is showing structure related to a rotating
toroid of material.


  Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical
physics in terms of (grand) partition functions, and assume theoretical
significance for the phenomenon of phase transitions. In this paper, motivated
by recent progress in cold Rydberg atom experiments, we explore the LY zeros in
classical Rydberg blockade models. We find that the distribution of zeros of
partition functions for these models in one dimension (1d) can be obtained
analytically. We prove that all the LY zeros are real and negative for such
models with arbitrary blockade radii. Therefore, no phase transitions happen in
1d classical Rydberg chains. We investigate how the zeros redistribute as one
interpolates between different blockade radii. We also discuss possible
experimental measurements of these zeros.


  Some response surface functions in complex engineering systems are usually
highly nonlinear, unformed, and expensive-to-evaluate. To tackle this
challenge, Bayesian optimization, which conducts sequential design via a
posterior distribution over the objective function, is a critical method used
to find the global optimum of black-box functions. Kernel functions play an
important role in shaping the posterior distribution of the estimated function.
The widely used kernel function, e.g., radial basis function (RBF), is very
vulnerable and susceptible to outliers; the existence of outliers is causing
its Gaussian process surrogate model to be sporadic. In this paper, we propose
a robust kernel function, Asymmetric Elastic Net Radial Basis Function
(AEN-RBF). Its validity as a kernel function and computational complexity are
evaluated. When compared to the baseline RBF kernel, we prove theoretically
that AEN-RBF can realize smaller mean squared prediction error under mild
conditions. The proposed AEN-RBF kernel function can also realize faster
convergence to the global optimum. We also show that the AEN-RBF kernel
function is less sensitive to outliers, and hence improves the robustness of
the corresponding Bayesian optimization with Gaussian processes. Through
extensive evaluations carried out on synthetic and real-world optimization
problems, we show that AEN-RBF outperforms existing benchmark kernel functions.


  We introduce a tensor product for symmetric monoidal categories with the
following properties. Let SMC denote the 2-category with objects small
symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells
monoidal natural transformations. Our tensor product together with a suitable
unit is part of a structure on SMC that is a 2-categorical version of the
symmetric monoidal closed categories. This structure is surprisingly simple. In
particular the arrows involved in the associativity and symmetry laws for the
tensor and in the unit cancellation laws are 2-natural and satisfy coherence
axioms which are strictly commuting diagrams. We also show that the category
quotient of SMC by the congruence generated by its 2-cells admits a symmetric
monoidal closed structure.