  We construct a correlation functions evolution corresponding to the Glauber
dynamics in continuum. Existence of the corresponding strongly continuous
contraction semigroup in a proper Banach space is shown. Additionally we prove
the existence of the evolution of states and study their ergodic properties.


  We present observations with the Chandra X-ray Observatory of the pulsar wind
nebula (PWN) within the supernova remnant G0.9+0.1. At Chandra's high
resolution, the PWN has a clear axial symmetry; a faint X-ray point source
lying along the symmetry axis possibly corresponds to the pulsar itself. We
argue that the nebular morphology can be explained in terms of a torus of
emission in the pulsar's equatorial plane and a jet directed along the pulsar
spin axis, as is seen in the X-ray nebulae powered by other young pulsars. A
bright clump of emission within the PWN breaks the axisymmetry and may
correspond to an intermediate-latitude feature in the pulsar wind.


  In the 1980s, Helffer and Sj\"ostrand examined in a series of articles the
concentration of the ground state of a Schr\"odinger operator in the
semiclassical limit. In a similar spirit, and using the asymptotics for the
Szeg\"o kernel, we show a theorem about the localization properties of the
ground state of a Toeplitz operator, when the minimal set of the symbol is a
finite set of non-degenerate critical points. Under the same condition on the
symbol, for any integer K we describe the first K eigenvalues of the operator.


  Understanding how an extinction event affects ecosystem is fundamental to
biodiversity conservation. For this reason, food web response to species loss
has been investigated in several ways in the last years. Several studies
focused on secondary extinction due to biodiversity loss in a bottom-up
perspective using in-silico extinction experiments in which a single species is
removed at each step and the number of secondary extinctions is recorded. In
these binary simulations a species goes secondarily extinct if it loses all its
resource species, that is, when the energy intake is zero. This pure
topological statement represents the best case scenario. In fact a consumer
species could go extinct losing a certain fraction of the energy intake and the
response of quantitative food webs to node loss could be very different with
respect to simple binary predictions. The goal of this paper is to analyze how
patterns of secondary extinctions change when higher species sensitivity are
included in the analyses. In particular, we explored how food web secondary
extinction, triggered by the removal of most connected nodes, varies as a
function of the energy intake threshold assumed as the minimum needed for
species persistence. As we will show, a very low increase of energy intake
threshold stimulates a disproportionate growth of secondary extinction.


  Using medical imaging as case-study, we demonstrate how Intel-optimized
TensorFlow on an x86-based server equipped with 2nd Generation Intel Xeon
Scalable Processors with large system memory allows for the training of
memory-intensive AI/deep-learning models in a scale-up server configuration. We
believe our work represents the first training of a deep neural network having
large memory footprint (~ 1 TB) on a single-node server. We recommend this
configuration to scientists and researchers who wish to develop large,
state-of-the-art AI models but are currently limited by memory.


  HH 50138 is one of the brightest B[e] stars at a distance of $\sim$ 380 pc
with strong infrared excess. The star was observed in [O I] 63 $\mu$m and [C
II] 158 $\mu$m with high velocity resolution with upGREAT on SOFIA. The
velocity resolved [O I] emission provides evidence for a large gas-disk, $\sim$
760 au in size, around HD 50138. Whereas previous interferometric observations
give strong evidence for a hot gas and dust disk in Keplerian rotation, our
bservations are the first to provide unambiguous evidence for a large warm disk
around the star. Herschel/PACS observations showed that the [C II] emission is
extended, therefore the [C II] emission most likely originates in an ionized
gas shell created by a past outflow event. We confirm the isolated nature of HD
50138. It is far from any star forming region and has low proper motion.
Neither is there any sign of a remnant cloud from which it could have formed.
The extended disk around the star appears carbon poor. It shows OH and [O I]
emission, but no CO. The CO abundance appears to be at least an order of
magnitude lower than that of OH. Furthermore $^{13}$CO is enriched by more than
a factor of five, confirming that the star is not a Herbig Be star. Finally we
note that our high spectral resolution [O I] and [C II] observations provide a
very accurate heliocentric velocity of the star, 40.8 $\pm$ 0.2 km~s$^{-1}$.


  We considered a {multi-block} molecular model of biological evolution, in
which fitness is a function of the mean types of alleles located at different
parts (blocks) of the genome. We formulated an infinite population model with
selection and mutation, and calculated the mean fitness. For the case of
recombination, we formulated a model with a multidimensional fitness landscape
(the dimension of the space is equal to the number of blocks) and derived a
theorem about the dynamics of initially narrow distribution. We also considered
the case of lethal mutations. We also formulated the finite population version
of the model in the case of lethal mutations. Our models, derived for the virus
evolution, are interesting also for the statistical mechanics and the
Hamilton-Jacobi equation as well.


  Knowledge graph entity typing (KGET) aims to infer missing entity type
instances in knowledge graphs. Previous research has predominantly centered
around leveraging contextual information associated with entities, which
provides valuable clues for inference. However, they have long ignored the dual
nature of information inherent in entities, encompassing both high-level
coarse-grained cluster knowledge and fine-grained type knowledge. This paper
introduces Cross-view Optimal Transport for knowledge graph Entity Typing
(COTET), a method that effectively incorporates the information on how types
are clustered into the representation of entities and types. COTET comprises
three modules: i) Multi-view Generation and Encoder, which captures structured
knowledge at different levels of granularity through entity-type,
entity-cluster, and type-cluster-type perspectives; ii) Cross-view Optimal
Transport, transporting view-specific embeddings to a unified space by
minimizing the Wasserstein distance from a distributional alignment
perspective; iii) Pooling-based Entity Typing Prediction, employing a mixture
pooling mechanism to aggregate prediction scores from diverse neighbors of an
entity. Additionally, we introduce a distribution-based loss function to
mitigate the occurrence of false negatives during training. Extensive
experiments demonstrate the effectiveness of COTET when compared to existing
baselines.


  We propose and analyze neutral atom traps generated by vortices imprinted by
magnetic field pulse sequences in type-II superconducting disks and rings. We
compute the supercurrent distribution and magnetic field resulting from the
vortices in the superconductor. Different patterns of vortices can be written
by versatile loading field sequences. We discuss in detail procedures to
generate quadrupole traps, self-sufficient traps and ring traps based on
superconducting disks and rings. The ease of creating these traps and the low
current noise in supercurrent carrying structures makes our approach attractive
for designing atom chip interferometers and probes.


  In this paper, the performances of the quasi-Newton BFGS algorithm, the
NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution
Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm
Optimizers (PSO) are compared experimentally on benchmark functions reflecting
important challenges encountered in real-world optimization problems.
Dependence of the performances in the conditioning of the problem and
rotational invariance of the algorithms are in particular investigated.


  Inequivalent N=2 supersymmetrizations of the l-conformal Galilei algebra in
d-spatial dimensions are constructed from the chiral (2,2) and the real (1,2,1)
basic supermultiplets of the N=2 supersymmetry. For non-negative integer and
half-integer l both superalgebras admit a consistent truncation with a
(different) finite number of generators. The real N=2 case coincides with the
superalgebra introduced by Masterov, while the chiral N=2 case is a new
superalgebra. We present D-module representations of both superalgebras. Then
we investigate the new superalgebra derived from the chiral supermultiplet. It
is shown that it admits two types of central extensions, one is found for any d
and half-integer l and the other only for d=2 and integer l. For each central
extension the centrally extended l-superconformal Galilei algebra is realized
in terms of its super-Heisenberg subalgebra generators.


  The representation of the natural-density, heterogeneous connectivity of
neuronal network models at relevant spatial scales remains a challenge for
Computational Neuroscience and Neuromorphic Computing. In particular, the
memory demands imposed by the vast number of synapses in brain-scale network
simulations constitutes a major obstacle. Limiting the number resolution of
synaptic weights appears to be a natural strategy to reduce memory and compute
load. In this study, we investigate the effects of a limited synaptic-weight
resolution on the dynamics of recurrent spiking neuronal networks resembling
local cortical circuits, and develop strategies for minimizing deviations from
the dynamics of networks with high-resolution synaptic weights. We mimic the
effect of a limited synaptic weight resolution by replacing normally
distributed synaptic weights by weights drawn from a discrete distribution, and
compare the resulting statistics characterizing firing rates, spike-train
irregularity, and correlation coefficients with the reference solution. We show
that a naive discretization of synaptic weights generally leads to a distortion
of the spike-train statistics. Only if the weights are discretized such that
the mean and the variance of the total synaptic input currents are preserved,
the firing statistics remains unaffected for the types of networks considered
in this study. For networks with sufficiently heterogeneous in-degrees, the
firing statistics can be preserved even if all synaptic weights are replaced by
the mean of the weight distribution. We conclude that even for simple networks
with non-plastic neurons and synapses, a discretization of synaptic weights can
lead to substantial deviations in the firing statistics, unless the
discretization is performed with care and guided by a rigorous validation
process.


  Rank aggregation systems collect ordinal preferences from individuals to
produce a global ranking that represents the social preference. Rank-breaking
is a common practice to reduce the computational complexity of learning the
global ranking. The individual preferences are broken into pairwise comparisons
and applied to efficient algorithms tailored for independent paired
comparisons. However, due to the ignored dependencies in the data, naive
rank-breaking approaches can result in inconsistent estimates. The key idea to
produce accurate and consistent estimates is to treat the pairwise comparisons
unequally, depending on the topology of the collected data. In this paper, we
provide the optimal rank-breaking estimator, which not only achieves
consistency but also achieves the best error bound. This allows us to
characterize the fundamental tradeoff between accuracy and complexity. Further,
the analysis identifies how the accuracy depends on the spectral gap of a
corresponding comparison graph.


  In this paper we study the energy spectra and related parallel momentum
distributions of the neutrons from the breakup of 11Be. Earlier papers on
transfer to the continuum reactions have shown that the breakup amplitude
reduces to a simple eikonal approximation in the limit of weakly bound
projectiles. The aim is to establish a reliable method to obtain information on
the structure of the halo from the experimental results which depend on the
reaction mechanism.
  Theoretical results for the widths of the parallel momentum distributions and
for the total breakup cross section are compared to recent experimental data.


  The loss of a few neurons in a brain rarely results in any visible loss of
function. However, the insight into what "few" means in this context is
unclear. How many random neuron failures will it take to lead to a visible loss
of function? In this paper, we address the fundamental question of the impact
of the crash of a random subset of neurons on the overall computation of a
neural network and the error in the output it produces. We study fault
tolerance of neural networks subject to small random neuron/weight crash
failures in a probabilistic setting. We give provable guarantees on the
robustness of the network to these crashes. Our main contribution is a bound on
the error in the output of a network under small random Bernoulli crashes
proved by using a Taylor expansion in the continuous limit, where close-by
neurons at a layer are similar. The failure mode we adopt in our model is
characteristic of neuromorphic hardware, a promising technology to speed up
artificial neural networks, as well as of biological networks. We show that our
theoretical bounds can be used to compare the fault tolerance of different
architectures and to design a regularizer improving the fault tolerance of a
given architecture. We design an algorithm achieving fault tolerance using a
reasonable number of neurons. In addition to the theoretical proof, we also
provide experimental validation of our results and suggest a connection to the
generalization capacity problem.


  Bose-Einstein condensates loaded into kicked optical lattices can be treated
as quantum kicked rotor systems. Noninteracting rotors show dynamical
localization in momentum space. The experimentally tunable condensate
interaction is included in a qualitative Gross-Pitaevskii type model based on
two-body interactions. We observe strong and weak chaos regimes of wave packet
spreading in momentum space. In the intermediate strong chaos regime the
condensate energy grows as $t^{1/2}$. In the asymptotic weak chaos case the
growth crosses over into a $t^{1/3}$ law. The results do not depend on the
details of the kicking.


  We develop a microscopic theory for nonlinear optical response of moir\'e
exciton-polaritons in bilayers of transition metal dichalcogenides (TMDs). Our
theory allows to study the tunnel-coupled intralayer and interlayer excitonic
modes for a wide range of twist angles ($\theta$), external electric field, and
light-matter coupling, providing insights into the hybridization regime
inaccessible before. Specifically, we account for the Umklapp scattering
processes of two exciton-polaritons responsible for enhanced nonlinearity, and
show that it is crucial for describing interactions at strong hybridization. We
reveal a regime of attractive nonlinearity for moir\'e polaritons, stemming
from the anisotropic Coulomb interactions, which can explain some of
experimental features of optical response in TMD bilayers. Furthermore, within
our theory we demonstrate that the attractive nonlinearity can be tuned into
repulsive by applying an external electric field. Our findings show that
nonlinear moir\'e polaritons offer a controllable platform nonlinear
polaritonic devices.


  We consider the following "multiway cut packing" problem in undirected
graphs: we are given a graph G=(V,E) and k commodities, each corresponding to a
set of terminals located at different vertices in the graph; our goal is to
produce a collection of cuts {E_1,...,E_k} such that E_i is a multiway cut for
commodity i and the maximum load on any edge is minimized. The load on an edge
is defined to be the number of cuts in the solution crossing the edge. In the
capacitated version of the problem the goal is to minimize the maximum relative
load on any edge--the ratio of the edge's load to its capacity. Multiway cut
packing arises in the context of graph labeling problems where we are given a
partial labeling of a set of items and a neighborhood structure over them, and,
informally, the goal is to complete the labeling in the most consistent way.
This problem was introduced by Rabani, Schulman, and Swamy (SODA'08), who
developed an O(log n/log log n) approximation for it in general graphs, as well
as an improved O(log^2 k) approximation in trees. Here n is the number of nodes
in the graph. We present the first constant factor approximation for this
problem in arbitrary undirected graphs. Our approach is based on the
observation that every instance of the problem admits a near-optimal laminar
solution (that is, one in which no pair of cuts cross each other).


  We study halo assembly bias for cluster-sized halos. Previous work has found
little evidence for correlations between large-scale bias and halo mass
assembly history for simulated cluster-sized halos, in contrast to the
significant correlation found between bias and concentration for halos of this
mass. This difference in behavior is surprising, given that both concentration
and assembly history are closely related to the same properties of the
linear-density peaks that collapse to form halos. Using publicly available
simulations, we show that significant assembly bias is indeed found in the most
massive halos with $M\sim 10^{15}M_\odot$, using essentially any definition of
halo age. For lower halo masses $M\sim 10^{14}M_\odot$, no correlation is found
between bias and the commonly used age indicator $a_{0.5}$, the half-mass time.
We show that this is a mere accident, and that significant assembly bias exists
for other definitions of halo age, including those based on the time when the
halo progenitor acquires some fraction $f$ of the ultimate mass at $z=0$. For
halos with $M_{\rm vir}\sim 10^{14}M_\odot$, the sense of assembly bias changes
sign at $f=0.5$. We explore the origin of this behavior, and argue that it
arises because standard definitions of halo mass in halo finders do not
correspond to the collapsed, virialized mass that appears in the spherical
collapse model used to predict large-scale clustering. Because bias depends
strongly on halo mass, these errors in mass definition can masquerade as or
even obscure the assembly bias that is physically present. More physically
motivated halo definitions using splashback should be free of this particular
defect of standard halo finders.


  Generalized Langevin Equation (GLE) thermostats have been used very
effectively as a tool to manipulate and optimize the sampling of thermodynamic
ensembles and the associated static properties. Here we show that a similar,
exquisite level of control can be achieved for the dynamical properties
computed from thermostatted trajectories. By developing quantitative measures
of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic
oscillator, we show that these analytical results accurately predict the
behavior of strongly anharmonic systems. We also show that it is possible to
correct, to a significant extent, the effects of the GLE term onto the
corresponding microcanonical dynamics, which puts on more solid grounds the use
of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and
could help improve the prediction of dynamical quantities from techniques that
use a Langevin term to stabilize dynamics. Finally we address the use of
thermostats in the context of approximate path-integral-based models of quantum
nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some
of the artifacts associated with these techniques, improving the quality of
results for the modelling of vibrational dynamics of molecules, liquids and
solids.


  Stars observed in the field of an open cluster are ideal for a controlled
test of chemical tagging. Using chemical tagging, one should identify the
cluster members, i.e., those stars of similar chemical composition, if their
composition is indeed different from that of all the non-member stars of the
field. Moreover, the abundance-based membership can be checked against
membership based on radial velocities and proper motions. Here, I report
preliminary results of such an experiment using data from the Gaia-ESO Survey.
Although the three membership criteria usually agree, a few interesting
examples of discrepant membership classification have been found. In addition,
the mean composition of each open cluster was compared to a sample of 1600
Gaia-ESO field stars. Some cases of field stars with abundances matching those
of the open clusters were identified. This experiment suggests that open
clusters do not necessarily have unique abundance patterns that set them apart
from all other clusters.


  In a recent paper, the complete (non-linear) Kaluza-Klein Ansatz for the
consistent embedding of certain scalar plus gravity subsectors of gauged
maximal supergravity in D=4, 5 and 7 was presented, in terms of sphere
reductions from D=11 or type IIB supergravity. The scalar fields included in
the truncations were the diagonal fields in the SL(N,R)/SO(N) scalar
submanifolds of the full scalar sectors of the corresponding maximal
supergravities, with N=8, 6 and 5. The embeddings were used for obtaining an
interpretation of extremal D=4, 5 or 7 AdS domain walls in terms of distributed
M-branes or D-branes in the higher dimensions. Although strong supporting
evidence for the correctness of the embedding Ansatze was presented, a full
proof of the consistency was not given. Here, we complete the proof, by showing
explicitly that the full set of higher-dimensional equations of motion are
satisfied if and only if the lower-dimensional fields satisfy the relevant
scalar plus gravity equations.


  In the framework of collinear factorization and next-to-leading order (NLO)
perturbative QCD, we make predictions for inclusive and diffractive dijet
photoproduction in electron-proton and electron-nucleus scattering in the EIC
kinematics. We establish kinematic ranges in the ${\bar p}_T$, ${\bar \eta}$,
$x_A^{\rm obs}$ and $x_{\gamma}^{\rm obs}$ variables, quantify sensitivity to
small-$x$ nuclear PDFs, and analyze various scenarios of factorization breaking
in the case of diffractive scattering.


  In 2005 Janson, extending earlier work of Mahmoud, Smythe, and Szyma\'nski,
established the joint asymptotic normality of the outdegrees of a random plane
recursive tree. In particular, he gave an explicit description of the limiting
covariance matrix. Our aim here is to provide substantially simplified
expression for the limiting covariance matrix.


  This paper explores the application of automated planning to automated
theorem proving, which is a branch of automated reasoning concerned with the
development of algorithms and computer programs to construct mathematical
proofs. In particular, we investigate the use of planning to construct
elementary proofs in abstract algebra, which provides a rigorous and axiomatic
framework for studying algebraic structures such as groups, rings, fields, and
modules. We implement basic implications, equalities, and rules in both
deterministic and non-deterministic domains to model commutative rings and
deduce elementary results about them. The success of this initial
implementation suggests that the well-established techniques seen in automated
planning are applicable to the relatively newer field of automated theorem
proving. Likewise, automated theorem proving provides a new, challenging domain
for automated planning.


  In this work we show a dualization process of a non-Abelian model with an
antisymmetric tensor gauge field in a three-dimensional space-time. We have
constructed a non-Abelian gauge invariant St\"{u}ckelberg-like master action,
and a duality between a non-Abelian topologically massive $B\wedge\phi$ model
and a non-Abelian massive scalar action, which leads us to a Klein-Gordon-type
action when we consider a particular case.


  For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra
$A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for
products of planar compact sets as well as for graphs of functions.


  The considerable part of the parameter space in the MSSM corresponding to the
infrared quasi fixed point scenario is excluded by LEP II bounds on the
lightest Higgs boson mass. In the NMSSM the mass of the lightest Higgs boson
reaches its maximum value in the strong Yukawa coupling limit when Yukawa
couplings are essentially larger than gauge ones at the Grand Unification
scale. In this case the renormalization group flow of Yukawa couplings and soft
SUSY breaking terms is investigated. The quasi-fixed and invariant lines and
surfaces are briefly discussed. The coordinates of the quasi-fixed points,
where all solutions are concentrated, are given.


  We report on gamma-ray orbital modulation of the transitioning millisecond
pulsar binary XSS J12270-4859 detected in the Fermi Large Area Telescope (LAT)
data. We use long-term optical data taken with the XMM-Newton Optical Monitor
and the Swift UltraViolet Optical Telescope to inspect radio timing solutions
that are limited to relatively short time intervals, and find that
extrapolation of the solutions aligns well the phasing of the optical data over
15 years. The Fermi-LAT data folded on the timing solutions exhibit significant
modulation (p = 5x10^-6) with a gamma-ray minimum at the inferior conjunction
of the pulsar. Intriguingly, the source seems to show similar modulation in
both the low-mass X-ray binary (LMXB) and the millisecond pulsar (MSP) states,
implying that mechanisms for gamma-ray emission in the two states are similar.
We discuss these findings and their implications using an intra-binary shock
scenario.


  We combine confocal imaging, microfluidics and image analysis to record
3D-images of cells in flow. This enables us to recover the full 3D
representation of several hundred living cells per minute. Whereas 3D confocal
imaging has thus far been limited to steady specimen, we overcome this
restriction and present a method to access the 3D shape of moving objects. The
key of our principle is a tilted arrangement of the micro-channel with respect
to the focal plane of the microscope. This forces cells to traverse the focal
plane in an inclined manner. As a consequence, individual layers of passing
cells are recorded which can then be assembled to obtain the volumetric
representation. The full 3D information allows for a detailed comparisons with
theoretical and numerical predictions unfeasible with e.g.\ 2D imaging. Our
technique is exemplified by studying flowing red blood cells in a micro-channel
reflecting the conditions prevailing in the microvasculature. We observe two
very different types of shapes: `croissants' and `slippers'. Additionally, we
perform 3D numerical simulations of our experiment to confirm the observations.
Since 3D confocal imaging of cells in flow has not yet been realized, we see
high potential in the field of flow cytometry where cell classification thus
far mostly relies on 1D scattering and fluorescence signals.


  Barriers of urban mobility may contribute to the segregation of
neighborhoods. However, the empirical knowledge about this issue is limited.
Here, we present a methodological framework to assess the importance of
barriers to urban mobility along their hierarchy, over time and across
neighborhoods. Using GPS mobility data, we construct a network of blocks from
the sequence of individual visits. A community finding algorithm allows us to
evaluate the fit of the neighborhoods detected in this mobility network to
characteristic urban barriers by adjusting the resolution parameter of the
Louvain method to decrease the dominance of mobility hubs. Using the Symmetric
Area Difference index, that quantifies the overlap between the polygons
separated by urban barriers and the network communities, we find that the match
of detected neighborhoods and urban barriers improves as the resolution
parameter increases. However, at high values of the resolution parameter, this
fit gets better for lower rank administrative or road barriers than for their
higher rank pairs. Although the role of urban barriers in hindering mobility
became stronger over the COVID-19 restrictions, their fit with detected
neighborhoods deteriorated for most analyzed barriers. Exceptions are primary
roads, to which the fit of neighborhoods is stable over periods. By increasing
the resolution parameter, we find emergent communities of local mobility flows
that cross primary roads and a consequent optimal value of the resolution
parameter. The Barrier Crossing Ratio, the fraction of barrier crossings that
are network community crossings as well, demonstrates that the barriers' impact
on mobility are significantly different across urban areas. These results
contribute to the ongoing discourse on urban segregation, emphasizing the
importance of barriers to urban mobility in shaping neighborhood interactions
and mixing.


  The paper deals with singular Sturm-Liouville expressions with matrix-valued
distributional coefficients. Due to a suitable regularization, the
corresponding operators are correctly defined as quasi-differentials. Their
resolvent convergence is investigated and all self-adjoint, maximal
dissipative, and maximal accumulative extensions are described in terms of
homogeneous boundary conditions of the canonical form.


  We consider a Laplace eigenfunction $\varphi_\lambda$ on a smooth closed
Riemannian manifold, that is, satisfying $-\Delta \varphi_\lambda = \lambda
\varphi_\lambda$. We introduce several observations about the geometry of its
vanishing (nodal) set and corresponding nodal domains.
  First, we give asymptotic upper and lower bounds on the volume of a tubular
neighbourhood around the nodal set of $\varphi_\lambda$. This extends previous
work of Jakobson and Mangoubi in case $ (M, g) $ is real-analytic. A
significant ingredient in our discussion are some recent techniques due to
Logunov (cf. \cite{L1}).
  Second, we exhibit some remarks related to the asymptotic geometry of nodal
domains. In particular, we observe an analogue of a result of Cheng in higher
dimensions regarding the interior opening angle of a nodal domain at a singular
point. Further, for nodal domains $\Omega_\lambda$ on which $\varphi_\lambda$
satisfies exponentially small $L^\infty$ bounds, we give some quantitative
estimates for radii of inscribed balls.


  Cell segmentation in microscopy is a challenging problem, since cells are
often asymmetric and densely packed. This becomes particularly challenging for
extremely large images, since manual intervention and processing time can make
segmentation intractable. In this paper, we present an efficient and highly
parallel formulation for symmetric three-dimensional (3D) contour evolution
that extends previous work on fast two-dimensional active contours. We provide
a formulation for optimization on 3D images, as well as a strategy for
accelerating computation on consumer graphics hardware. The proposed software
takes advantage of Monte-Carlo sampling schemes in order to speed up
convergence and reduce thread divergence. Experimental results show that this
method provides superior performance for large 2D and 3D cell segmentation
tasks when compared to existing methods on large 3D brain images.


  We investigate whether there is a relationship between the discrete
Bakry-\'{E}mery curvature of a graph and the smooth curvature of an ambient
surface into which the graph is embedded geodesically. As we used weighted
graphs as test objects, we developed a program for the calculation of the
discrete curvature and with the help of this calculator, we observed some
indications of such a relationship.


  It is known that in loop quantum cosmology (LQC) the universe avoids the
singularity by a bounce when the matter density approaches the critical density
$\rho_c$ (the order of Planck density). After incorporating the inverse volume
modifications both in the gravitational and matter part in the improved
framework of LQC, we find that the inverse volume modification can decrease the
bouncing energy scale, and the presence of nonsingular bounce is generic. For
the backward evolution in the expanding branch, in terms of different initial
states the evolution trajectories classify into two classes. One class with
larger initial energy density leads to the occurrence of bounce in the region
$a>a_{ch}$ where $a_{ch}$ marks the different inverse volume modification
region. The other class with smaller initial energy density evolves back into
the region $a<a_{ch}$. In this region, both the energy density for the scalar
field and the bouncing energy scale decrease with the backward evolution.
However, in the deep modification region, because of the inverse volume
modification the scalar field is frozen, such that the bounce is present when
the bouncing energy scale decreases to be equal to the energy density of the
scalar field. Using numerical method, we show the evolution picture for the
second class bounce.


  Recent developements in the calculation of the NNLO QCD corrections to the
charm quark mass dependent matrix elements in B -> X_s gamma are reported.
Special emphasis is put on the new results of the virtual O(alpha_s^2)
fermionic contribution to these matrix elements [1].


  The total energy of acoustic emission (AE) events in externally stressed
materials diverges when approaching macroscopic failure. Numerical and
conceptual models explain this accelerated seismic release (ASR) as the
approach to a critical point that coincides with ultimate failure. Here, we
report ASR during soft uniaxial compression of three silica-based (SiO$_2$)
nanoporous materials. Instead of a singular critical point, the distribution of
AE energies is stationary and variations in the activity rate are sufficient to
explain the presence of multiple periods of ASR leading to distinct brittle
failure events. We propose that critical failure is suppressed in the AE
statistics by dissipation and transient hardening. Some of the critical
exponents estimated from the experiments are compatible with mean field models,
while others are still open to interpretation in terms of the solution of
frictional and fracture avalanche models.


  Bell's theorem reveals contradictions between the predictions of quantum
mechanics and the EPR postulates for a pair of particles only in situations
involving imperfect statistical correlations. However, with three or more
particles, contradictions emerge even for perfect correlations. We describe an
experiment which can be realized in the laboratory, using four-photon entangled
states generated by parametric down-conversion, to demonstrate this
contradiction at the level of perfect correlations.


  We theoretically investigate the microscopic mechanism of conversion between
the electron spin and the microscopic local rotation of atoms in crystals. In
phonon modes with angular momenta, the atoms microscopically rotate around
their equilibrium positions in crystals. In a simple toy model with phonons, we
calculate the spin expectation value by using the adiabatic series expansion.
We show that the time-averaged spin magnetization is generated by the
microscopic local rotation of atoms via the spin-orbit interaction. On the
other hand, in the system with a simple vibration of atoms, time-averaged spin
magnetization becomes zero due to the time-reversal symmetry. Moreover, the
magnitude of the time-averaged spin magnetization depends on the inverse of the
difference of instantaneous eigenenergy, and we show that it becomes smaller in
band insulators with a larger gap.


  An exact solution of the current-free Einstein-Maxwell equations with the
cosmological constant is presented. The solution is of Petrov type D, includes
the negative cosmological constant, and could be a ``background addition'' to
the present-day models of the universe. It has a surprising property such that
its electromagnetic field and cosmological constant are interdependent (this
constant is proportional to the energy density of this field), which may
suggest a new way of measuring the constant in question. The solution describes
a constant electromagnetic background with a preferred direction in the
universe, and defines the entire lifetime of the universe as a simple function
of the negative cosmological constant. According to our solution the absolute
value of this constant should be considerably lower than that recently
estimated, when astrophysical data are taken into account. Our solution is a
special case of that published by Bertotti in 1959. His solution (in terms of
which the cosmological constant and the background electromagnetic field are
independent) and its two other special cases, i.e. the conformally flat
Robinson solution (1959) and the one which is the counterpart of our solution
with the positive cosmological constant, are briefly discussed.


  We discuss surface roughness effects on the conduction of electrons in metals
using both the quantal Kubo-Greenwood formalism and the semi-classical
Fuchs-Sondheimer method. The main purpose here is to compare these methods and
clarify a few subtle conceptual issues. One of such issues is concerned with
the conditions under which the broken translation symmetry along a rough
surface may be restored. This symmetry has often been presumed in existing work
but not always with proper justifications. Another one relates to the physical
meaning of a phenomenological parameter (denoted by $p$) intuitively introduced
in the semi-classical theory. This parameter, called the specularity parameter
or sometimes the \textit{Fuchs} parameter, plays an important role in the
experimental studies of surface roughness but has so far lacked a rigorous
microscopic definition. The third issue arises as to the domain of validity for
the electrical conductivity obtained in those methods. A misplacement of the
domain may have resulted in erroneous analysis of surface effects in a variety
of electrodynamic phenomena including surface plasma waves.


  We show that the Lagrangian of classical mechanics on a Riemannian manifold
of bounded geometry carries a periodic solution of motion with rescribed
energy, provided the potential satisfies an asymptotic growth condition,
changes sign, and the negative set of the potential is non-trivial in the
relative homology.


  During recent years, the study of exotic hadrons including tetraquarks and
pentaquarks has attracted a lot of interests and more studies are in progress
experimentally and theoretically. It is well-known that at sufficiently large
transverse momentum the dominant production mechanism for standard heavy
hadrons (mesons/baryons) is actually the fragmentation so that the same
mechanism is also proposed for the production of heavy exotic hadrons. This
work is the first attempt to study the direct fragmentation of a heavy quark
into ground state heavy tetraquarks in leading order of perturbative QCD. In
this regard, we will present an exact analytical expression for the
fragmentation production of neutral hidden flavor tetraquarks
$(Qq\bar{Q}\bar{q})$ which includes most of the kinematical and dynamical
properties of the process.


  In this article, we study a second-order expansion for the effect induced on
a large quantum particle which undergoes a single scattering with a low-mass
particle via a repulsive point interaction. We give an approximation with
third-order error in $\lambda$ to the map $G\to \Tr_{2}[(I\otimes
\rho)S_{\lambda}^{*}(G\otimes I)S_{\lambda}]$, where $G\in \Bi(L^{2}(\R^{n}))$
is a heavy-particle observable, $\rho\in \Bi_{1}(\R^{n})$ is the density matrix
corresponding to the state of the light particle, $\lambda=\frac{m}{M}$ is the
mass ratio of the light particle to the heavy particle, $S_{\lambda}\in
\Bi(L^{2}(\R^{n})\otimes L^{2}(\R^{n}))$ is the scattering matrix between the
two particles due to a repulsive point interaction, and the trace is over the
light-particle Hilbert space. The third-order error is bounded in operator norm
for dimensions one and three using a weighted operator norm on $G$.


  Whereas contemporary Error Correcting Codes (ECC) designs occupy a
significant fraction of total die area in chip-multiprocessors (CMPs),
approaches to deal with the vulnerability increase of CMP architecture against
Single Event Upsets (SEUs) and Multi-Bit Upsets (MBUs) are sought. In this
paper, we focus on reliability assessment of multithreaded applications running
on CMPs to propose an adaptive application-relevant architecture design to
accommodate the impact of both SEUs and MBUs in the entire CMP architecture.
This work concentrates on leveraging the intrinsic soft-error-immunity feature
of Spin-Transfer Torque RAM (STT-RAM) as an alternative for SRAM-based storage
and operation components. We target a specific portion of working set for
reallocation to improve the reliability level of the CMP architecture design. A
selected portion of instructions in multithreaded program which experience high
rate of referencing with the lowest memory modification are ideal candidate to
be stored and executed in STT-RAM based components. We argue about why we
cannot use STT-RAM for the global storage and operation counterparts and
describe the obtained resiliency compared to the baseline setup. In addition, a
detail study of the impact of SEUs and MBUs on multithreaded programs will be
presented in the Appendix.


  We prove a result on the divisibility of the truncated hypergeometric
function 3F2.


  We consider strongly coupled supersymmetric gauge theories softly broken by
the addition of gaugino masses $m_\lambda$ and (non-holomorphic) scalar masses
$m^2$, taken to be small relative to the dynamical scale $\Lambda$. For
theories with a weakly coupled dual description in the infrared, we compute
exactly the leading soft masses for the "magnetic" degrees of freedom, with
uncalculable corrections suppressed by powers of $(m_{\lambda}/\Lambda),
(m/\Lambda)$. The exact relations hold between the infrared fixed point
"magnetic" soft masses and the ultraviolet fixed point "electric" soft masses,
and correspond to a duality mapping for soft terms. We briefly discuss
implications of these results for the vacuum structure of these theories.


  We introduce affine Stanley symmetric functions for the special orthogonal
groups, a class of symmetric functions that model the cohomology of the affine
Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on
the special linear and symplectic groups, respectively. For the odd orthogonal
groups, a Hopf-algebra isomorphism is given, identifying (co)homology Schubert
classes with symmetric functions. For the even orthogonal groups, we conjecture
an approximate model of (co)homology via symmetric functions. In the process,
we develop type B and type D non-commutative k-Schur functions as elements of
the nilCoxeter algebra that model homology of the affine Grassmannian.
Additionally, Pieri rules for multiplication by special Schubert classes in
homology are given in both cases. Finally, we present a type-free
interpretation of Pieri factors, used in the definition of noncommutative
k-Schur functions or affine Stanley symmetric functions for any classical type.


  In this paper we propose and prove correct a new self-stabilizing velocity
agreement (flocking) algorithm for oblivious and asynchronous robot networks.
Our algorithm allows a flock of uniform robots to follow a flock head emergent
during the computation whatever its direction in plane. Robots are
asynchronous, oblivious and do not share a common coordinate system. Our
solution includes three modules architectured as follows: creation of a common
coordinate system that also allows the emergence of a flock-head, setting up
the flock pattern and moving the flock. The novelty of our approach steams in
identifying the necessary conditions on the flock pattern placement and the
velocity of the flock-head (rotation, translation or speed) that allow the
flock to both follow the exact same head and to preserve the flock pattern.
Additionally, our system is self-healing and self-stabilizing. In the event of
the head leave (the leading robot disappears or is damaged and cannot be
recognized by the other robots) the flock agrees on another head and follows
the trajectory of the new head. Also, robots are oblivious (they do not recall
the result of their previous computations) and we make no assumption on their
initial position. The step complexity of our solution is O(n).


  We show that certain one-dimensional hypergeometric differential systems
underlie objects of the category of irregular mixed Hodge modules, which was
recently introduced by Sabbah, and compute the irregular Hodge filtration for
them. We also provide a comparison theorem between two different types of
Fourier-Laplace transformation for algebraic integrable twistor
$\mathcal{D}$-modules.


  We report on a new design of terahertz quantum cascade laser based on a
single, potential-inserted quantum well active region. The quantum well
properties are engineered through single monolayer InAs inserts. The modeling
is based on atomistic, spds* tight-binding calculations, and performances are
compared to that of the classical three-well design. We obtain a 100% increase
of the oscillator strength per unit length, while maintaining a high, nearly
temperature-independent contrast between phonon-induced relaxation times of the
upper and lower lasing states. The improved performances are expected to allow
THz lasing at room temperature.


  We show here that a direct application of resummation-based quantum Monte
Carlo (QMC) -- implemented recently for sign-problem-free SU(2)-symmetric
Hamiltonians in the stochastic series expansion (SSE) framework -- does not
reduce the sign problem for frustrated SU(2)-symmetric Heisenberg
antiferromagnets on canonical geometrically frustrated lattices composed of
triangular motifs such as the triangular lattice. In the process, we
demonstrate that resummation-based updates do provide an ergodic sampling of
the SSE-based QMC configurations which can be an issue when using the standard
SSE updates, however, severely limited by the sign problem as previously
mentioned. The notions laid out in these notes may be useful in the design of
better algorithms for geometrically frustrated magnets.


  Miquel dynamics were introduced by Ramassamy as a discrete time evolution of
square grid circle patterns on the torus. In each time step every second circle
in the pattern is replaced with a new one by employing Miquel's six circle
theorem. Inspired by these dynamics we define the Miquel move, which changes
the combinatorics and geometry of a circle pattern locally. We prove that the
circle centers under Miquel dynamics are Clifford lattices, considered as an
integrable system by Konopelchenko and Schief. Clifford lattices have the
combinatorics of an octahedral lattice and every octahedron contains six
intersection points of Clifford's four circle configuration. The Clifford move
replaces one of these circle intersection points with the opposite one. We
establish a new connection between circle patterns and the dimer model: If the
distances between circle centers are interpreted as edge weights, the Miquel
move preserves probabilities in the sense of of urban renewal.


  Throughout the study of the geodesics of some popular spherically symmetric
regular black holes, we hereby prove that the analytically extended Hayward
black hole is geodetically incomplete. The simplest extension of the
Culetu-Simpson-Visser's non-analytic smooth black hole is also geodetically
incomplete, with the exception of the antipodal continuation of the radial
geodesics. However, the huge ambiguity in the extension of non analytic
spacetimes is tantamount of geodesic incompleteness and such spacetimes do not
solve the singularity issue unless at least all the extensions turn out to be
complete. Hence, we provide several mere modifications of such spacetimes in
order to make them geodetically complete in all possible extensions beyond r=0.


  A method of indirect measurement of the light quark running mass $\hat{m} =
(m_d + m_u)/2$ is elaborated in detail. It is based on measuring 1\%-level
azimuthal angular asymmetries in the decay $\tau \rightarrow \nu_\tau + 3\pi$.
The latter are then used in QCD sum rules to obtain experimental lower bounds
for $\hat{m}$. For a sample of $2.5 \times 10^5$ $\tau \rightarrow \nu_\tau +
3\pi$ decays free of background, the resulting statistical error in the bound
for $\hat{m}$ is estimated to be 1 MeV, i.e., comparable to the systematic
error due to the use of QCD sum rules. Contribution to the Third Workshop on
the $\tau$ Charm Factory 1-6 June 1993, Marbella, Spain.


  Characters of $E_8\otimes E_8$ and SO(32) heterotic strings involving the
full internal symmetry Cartan subalgebra generators are defined after circle
compactification so that they are T dual. The novel point, as compared with an
earlier study of the type II case (hep-th/9707107), is the appearence of Wilson
lines. Using SO(17,1) transformations between the weight lattices reveals the
existence of an intermediate theory where T duality transformations are
disentangled from the internal symmetry. This intermediate theory corresponds
to a sort of twisted compactification of a novel type. Its modular invariance
follows from an interesting interplay between three representations of the
modular group.


  The field of scientometrics has shown the power of citation-based clusters
for literature analysis, yet this technique has barely been used for
information retrieval tasks. This work evaluates the performance of citation
based-clusters for information retrieval tasks. We simulated a search process
using these clusters with a tree hierarchy of clusters and a cluster selection
algorithm. We evaluated the task of finding the relevant documents for 25
systematic reviews. Our evaluation considered several trade-offs between recall
and precision for the cluster selection, and we also replicated the Boolean
queries self-reported by the systematic review to serve as a reference. We
found that citation-based clusters search performance is highly variable and
unpredictable, that it works best for users that prefer recall over precision
at a ratio between 2 and 8, and that when used along with query-based search
they complement each other, including finding new relevant documents.


  This paper considers fixed effects estimation and inference in linear and
nonlinear panel data models with random coefficients and endogenous regressors.
The quantities of interest -- means, variances, and other moments of the random
coefficients -- are estimated by cross sectional sample moments of GMM
estimators applied separately to the time series of each individual. To deal
with the incidental parameter problem introduced by the noise of the
within-individual estimators in short panels, we develop bias corrections.
These corrections are based on higher-order asymptotic expansions of the GMM
estimators and produce improved point and interval estimates in moderately long
panels. Under asymptotic sequences where the cross sectional and time series
dimensions of the panel pass to infinity at the same rate, the uncorrected
estimator has an asymptotic bias of the same order as the asymptotic variance.
The bias corrections remove the bias without increasing variance. An empirical
example on cigarette demand based on Becker, Grossman and Murphy (1994) shows
significant heterogeneity in the price effect across U.S. states.


  In this article, we address the issue of recovering latent transparent layers
from superimposition images. Here, we assume we have the estimated
transformations and extracted gradients of latent layers. To rapidly recover
high-quality image layers, we propose an Efficient Superimposition Recovering
Algorithm (ESRA) by extending the framework of accelerated gradient method. In
addition, a key building block (in each iteration) in our proposed method is
the proximal operator calculating. Here we propose to employ a dual approach
and present our Parallel Algorithm with Constrained Total Variation (PACTV)
method. Our recovering method not only reconstructs high-quality layers without
color-bias problem, but also theoretically guarantees good convergence
performance.


  It is common and convenient to treat distributed physical parameters as
Gaussian random fields and model them in an "inverse procedure" using
measurements of various properties of the fields. This article presents a
general method for this problem based on a flexible parameterization device
called "anchors", which captures local or global features of the fields. A
classification of all relevant data into two categories closely cooperates with
the anchor concept to enable systematic use of datasets of different sources
and disciplinary natures. In particular, nonlinearity in the "forward models"
is handled automatically. Treatment of measurement and model errors is
systematic and integral in the method; however the method is also suitable in
the usual setting where one does not have reliable information about these
errors. Compared to a state-space approach, the anchor parameterization renders
the task in a parameter space of radically reduced dimension; consequently,
easier and more rigorous statistical inference, interpretation, and sampling
are possible. A procedure for deriving the posterior distribution of model
parameters is presented. Based on Monte Carlo sampling and normal mixture
approximation to high-dimensional densities, the procedure has generality and
efficiency features that provide a basis for practical implementations of this
computationally demanding inverse procedure. We emphasize distinguishing
features of the method compared to state-space approaches and
optimization-based ideas. Connections with existing methods in stochastic
hydrogeology are discussed. The work is illustrated by a one-dimensional
synthetic problem.
  Key words: anchored inversion, Gaussian process, ill-posedness, model error,
state space, pilot point method, stochastic hydrogeology.


  Stars are likely embedded in the gas disks of Active Galactic Nuclei (AGN).
Theoretical models predict that in the inner regions of the disk these stars
accrete rapidly, with fresh gas replenishing hydrogen in their cores faster
than it is burned into helium, effectively stalling their evolution at hydrogen
burning. We produce order-of-magnitude estimates of the number of such stars in
a fiducial AGN disk. We find numbers of order $10^{2-4}$, confined to the inner
$r_{\rm cap} \sim 3000 r_s \sim 0.03\rm pc$. These stars can profoundly alter
the chemistry of AGN disks, enriching them in helium and depleting them in
hydrogen, both by order-unity amounts. We further consider mergers between
these stars and other disk objects, suggesting that star-star mergers result in
rapid mass loss from the remnant to restore an equilibrium mass, while
star-compact object mergers may result in exotic outcomes and even host binary
black hole mergers within themselves. Finally, we examine how these stars react
as the disk dissipates towards the end of its life, and find that they may
return mass to the disk fast enough to extend its lifetime by a factor of
several and/or may drive powerful outflows from the disk. Post-AGN, these stars
rapidly lose mass and form a population of stellar mass black holes around
$10M_{\odot}$. Due to the complex and uncertain interactions between embedded
stars and the disk, their plausible ubiquity, and their order unity impact on
disk structure and evolution, they must be included in realistic disk models.


  In this note we show that McGee's {\omega}-inconsistency result can be
derived from L\"ob's theorem.


  In this paper, we study certain moduli spaces of vector bundles on the blowup
of the projective plane in at least 10 very general points. Moduli spaces of
sheaves on general type surfaces may be nonreduced, reducible and even
disconnected. In contrast, moduli spaces of sheaves on minimal rational
surfaces and certain del Pezzo surfaces are irreducible and smooth along the
locus of stable bundles. We find examples of moduli spaces of vector bundles on
more general blowups of the projective plane that are disconnected and have
components of different dimensions. In fact, assuming the SHGH Conjecture, we
can find moduli spaces with arbitrarily many components of arbitrarily large
dimension.


  We present a new theoretical framework for modelling the cluster growing
process. Starting from the initial tetrahedral cluster configuration, adding
new atoms to the system and absorbing its energy at each step, we find cluster
growing paths up to the cluster sizes of more than 100 atoms. We demonstrate
that in this way all known global minimum structures of the Lennard-Jonnes (LJ)
clusters can be found. Our method provides an efficient tool for the
calculation and analysis of atomic cluster structure. With its use we justify
the magic numbers sequence for the clusters of noble gases atoms and compare it
with experimental observations. We report the striking correspondence of the
peaks in the dependence on cluster size of the second derivative of the binding
energy per atom calculated for the chain of LJ-clusters based on the
icosahedral symmetry with the peaks in the abundance mass spectra
experimentally measured for the clusters of noble gases atoms. Our method
serves an efficient alternative to the global optimization techniques based on
the Monte-Carlo simulations and it can be applied for the solution of a broad
variety of problems in which atomic cluster structure is important.


  This work presents an implementation of the resistive MHD equations for a
generic algebraic Ohm's law which includes the effects of finite resistivity
within full General Relativity. The implementation naturally accounts for
magnetic-field-induced anisotropies and, by adopting a phenomenological
current, is able to accurately describe electromagnetic fields in the star and
in its magnetosphere. We illustrate the application of this approach in
interesting systems with astrophysical implications; the aligned rotator
solution and the collapse of a magnetized rotating neutron star to a black
hole.


  Aiming to train and deploy predictive models, organizations collect large
amounts of detailed client data, risking the exposure of private information in
the event of a breach. To mitigate this, policymakers increasingly demand
compliance with the data minimization (DM) principle, restricting data
collection to only that data which is relevant and necessary for the task.
Despite regulatory pressure, the problem of deploying machine learning models
that obey DM has so far received little attention. In this work, we address
this challenge in a comprehensive manner. We propose a novel vertical DM (vDM)
workflow based on data generalization, which by design ensures that no
full-resolution client data is collected during training and deployment of
models, benefiting client privacy by reducing the attack surface in case of a
breach. We formalize and study the corresponding problem of finding
generalizations that both maximize data utility and minimize empirical privacy
risk, which we quantify by introducing a diverse set of policy-aligned
adversarial scenarios. Finally, we propose a range of baseline vDM algorithms,
as well as Privacy-aware Tree (PAT), an especially effective vDM algorithm that
outperforms all baselines across several settings. We plan to release our code
as a publicly available library, helping advance the standardization of DM for
machine learning. Overall, we believe our work can help lay the foundation for
further exploration and adoption of DM principles in real-world applications.


  This paper proposes an automated method to obtain the extrinsic calibration
parameters between a camera and a 3D lidar with as low as 16 beams. We use a
checkerboard as a reference to obtain features of interest in both sensor
frames. The calibration board centre point and normal vector are automatically
extracted from the lidar point cloud by exploiting the geometry of the board.
The corresponding features in the camera image are obtained from the camera's
extrinsic matrix. We explain the reasons behind selecting these features, and
why they are more robust compared to other possibilities. To obtain the optimal
extrinsic parameters, we choose a genetic algorithm to address the highly
non-linear state space. The process is automated after defining the bounds of
the 3D experimental region relative to the lidar, and the true board
dimensions. In addition, the camera is assumed to be intrinsically calibrated.
Our method requires a minimum of 3 checkerboard poses, and the calibration
accuracy is demonstrated by evaluating our algorithm using real world and
simulated features.


  The purpose of this note is to discuss a few lines appearing in the work of
late Fantappi\`e. They concern the proof of rigidity of a specific real
semisimple Lie algebra: ${\mathfrak O}(4,1)$. Our intention is to discuss to
what extent such proof constitutes a missed opportunity in history of post-war
Italian mathematics.


  We explore amplification and cross-Kerr nonlinearity by a three-level emitter
(3LE) embedded in a waveguide and driven by two light beams. The coherent
amplification and cross-Kerr nonlinearity were demonstrated in recent
experiments, respectively, with a V and a ladder-type 3LE coupled to an open
superconducting transmission line carrying two microwave fields. Here, we
consider $\Lambda$, V, and ladder-type 3LE, and compare the efficiency of
coherent and incoherent amplification as well as the magnitude of the
cross-Kerr phase shift in all three emitters. We apply the Heisenberg-Langevin
equations approach to investigate the scattering of a probe and a drive beams
both initially in a coherent state. We particularly calculate the regime of the
probe and drive powers when the 3LE acts most efficiently as a coherent
amplifier, and derive the second-order coherence of amplified probe photons.
Finally, we apply the Kramers-Kronig relations to correlate the amplitude and
phase response of the probe beam, which are used in finding the coherent
amplification and the cross-Kerr phase shift in these systems.


  We present a new method for learning control law that stabilizes an unknown
nonlinear dynamical system at an equilibrium point. We formulate a system
identification task in a self-supervised learning setting that jointly learns a
controller and corresponding stable closed-loop dynamics hypothesis. The
input-output behavior of the unknown dynamical system under random control
inputs is used as the supervising signal to train the neural network-based
system model and the controller. The proposed method relies on the Lyapunov
stability theory to generate a stable closed-loop dynamics hypothesis and
corresponding control law. We demonstrate our method on various nonlinear
control problems such as n-link pendulum balancing and trajectory tracking,
pendulum on cart balancing, and wheeled vehicle path following.


  Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] showed that linear
optics techniques could be used to implement a nonlinear sign gate. They also
showed that two of their nonlinear sign gates could be combined to implement a
controlled-phase gate, which has a number of practical applications. Here we
describe an alternative implementation of a controlled-phase gate that only
requires the use of a single nonlinear sign gate. This gives a much higher
average probability of success when the required ancilla photons are generated
using heralding techniques. This implementation of a controlled-phase gate
destroys the control qubit, which is acceptable in a number of applications
where the control qubit would have been destroyed in any event, such as in a
postselection process.


  The present study deals with the dynamics of a double emulsion confined in a
microchannel under the presence of a uniform electric field. Towards
investigating the non-trivial electrohydrodynamics of a compound droplet,
confined in between two parallel plate electrodes, a phase field approach has
been adopted. Under the assumption of negligible fluid inertia and small shape
deformation, an asymptotic model is also developed to predict the transient as
well as the steady state droplet dynamics in the limiting case of an unbounded
suspending medium. The phases involved are either assumed to be perfect
dielectric or leaky dielectric. Subsequent investigation shows that shape
deformation of either of the interfaces of the droplet increase with rise in
the channel confinement for a perfect dielectric system. However, for a leaky
dielectric system, the deformation of inner droplet and outer droplet can
increase or decrease with the rise in channel confinement depending on the
electric properties (conductivity and permittivity) of the system. The present
study further takes into account the effect of eccentricity of the inner
droplet. Depending on the relative magnitude of the permittivity and
conductivity of the system, the inner droplet, if eccentrically located, may
exhibit a to and fro or a simple translational motion. It is seen that increase
in the channel confinement results in a translational motion of the inner
droplet thus rendering its motion independent of any electrical properties.
Since the compound droplet model approximately mimics the structure of a cell,
the current investigation is expected to provide a significant impact towards
predicting the effect of an externally imposed electrical field on the dynamics
of a cell in any fluidic confinement and hence has the potential towards
widespread applications in the field of medical diagnostics.


  Motivated by the phenomenon that companies introduce new products to keep
abreast with customers' rapidly changing tastes, we consider a novel online
learning setting where a profit-maximizing seller needs to learn customers'
preferences through offering recommendations, which may contain existing
products and new products that are launched in the middle of a selling period.
We propose a sequential multinomial logit (SMNL) model to characterize
customers' behavior when product recommendations are presented in tiers. For
the offline version with known customers' preferences, we propose a
polynomial-time algorithm and characterize the properties of the optimal tiered
product recommendation. For the online problem, we propose a learning algorithm
and quantify its regret bound. Moreover, we extend the setting to incorporate a
constraint which ensures every new product is learned to a given accuracy. Our
results demonstrate the tier structure can be used to mitigate the risks
associated with learning new products.


  We show that a nondegenerate unitary solution $r(u,v)$ of the associative
Yang-Baxter equation (AYBE) for $\Mat(N,\C)$ (see math.AG/0008156) with the
Laurent series at $u=0$ of the form $r(u,v)=\frac{1\ot 1}{u}+r_0(v)+...$
satisfies the quantum Yang-Baxter equation, provided the projection of $r_0(v)$
to traceless matrices has a period. We classify all such solutions of the AYBE
extending the work of Schedler math.QA/0212258. We also characterize solutions
coming from triple Massey products in the derived category of coherent sheaves
on cycles of projective lines.


  In this paper, we compute the total and differential cross sections for
$e^+e^- \to J/\psi+c+\bar{c}$ at the $B$ factories up to next-to-leading order
(NLO) corrections within the framework of nonrelativistic QCD factorization
theory. We then obtain an improved pQCD prediction for this process by using
the Principle of Maximum Conformality (PMC). We show the first time that the
PMC can be applied for any pQCD calculable observable at the total or
differential levels via a self-consistent way in perturbation theory. By the
recursive use of renormalization group equation, the resultant PMC series
satisfies all the requirements of renormalization group, which is free of
conventional renormalization scheme-and-scale ambiguities at any fixed-order
level. We thus obtain a more precise prompt total cross section at the NLO
level, e.g. $\sigma|_{\rm prompt}^{\rm PMC}=
0.565^{+0.144}_{-0.125}~\text{pb}$. Here the uncertainty is the squared average
of those from the $\alpha_s$ fixed-point uncertainty $\Delta\alpha_s(M_Z)$, the
uncertainty of charm quark mass $\Delta m_c$, and an estimated contribution of
the uncalculated NNLO-terms as predicted by the Pad\'{e} approximation
approach. The differential cross sections $d\sigma/dP_{J/\psi}$,
$d\sigma/d|\cos \theta|$, and $d\sigma/dz$ for $e^+e^- \to J/\psi+c+\bar{c}$
are further examined. Those results show that by further considering the
feed-down contributions, the PMC predictions show better agreement with the
Belle measurements.


  Subgraph representation learning has emerged as an important problem, but it
is by default approached with specialized graph neural networks on a large
global graph. These models demand extensive memory and computational resources
but challenge modeling hierarchical structures of subgraphs. In this paper, we
propose Subgraph-To-Node (S2N) translation, a novel formulation for learning
representations of subgraphs. Specifically, given a set of subgraphs in the
global graph, we construct a new graph by coarsely transforming subgraphs into
nodes. Demonstrating both theoretical and empirical evidence, S2N not only
significantly reduces memory and computational costs compared to
state-of-the-art models but also outperforms them by capturing both local and
global structures of the subgraph. By leveraging graph coarsening methods, our
method outperforms baselines even in a data-scarce setting with insufficient
subgraphs. Our experiments on eight benchmarks demonstrate that fined-tuned
models with S2N translation can process 183 -- 711 times more subgraph samples
than state-of-the-art models at a better or similar performance level.


  The Infrared Array Camera (IRAC) is one of three focal plane instruments on
board the Spitzer Space Telescope. IRAC is a four-channel camera that obtains
simultaneous broad-band images at 3.6, 4.5, 5.8, and 8.0 microns in two nearly
adjacent fields of view. We summarize here the in-flight scientific, technical,
and operational performance of IRAC.


  Recently, Chan, Cooper and Sica conjectured two congruences for coefficients
of classical 2F1 hypergeometric series which also arise from power series
expansions of modular forms in terms of modular functions. We prove these two
congruences using combinatorial properties of the coefficients.


  This is a discussion of the main branching fractions of B Meson decays $(b\to
cW^{-})$. A summary of what has been measured and what remains unmeasured is
presented.


  A normal ordered exponential parametrization is used to obtain equations for
thermal one-and two-particle reduced density matrices, as well as free
energies, partition functions and entropy for both Fermionic (electronic) and
Bosonic (vibrational) Hamiltonians. A first principles derivation of the
equations, relying only on a simple Wick's theorem and starting from the
differential equation $\frac{d \hat{D}}{d \beta}= - (\hat{H}-\mu
\hat{N})\hat{D}$, is presented that yields a differential equation for the
amplitudes representing density cumulants, as well as the grand potential. In
contrast to other approaches reported in the literature the theory does not use
perturbation theory in the interaction picture and an integral formulation as a
starting point, but rather requires a propagation of the resulting differential
equation for the amplitudes. While the theory is applicable to general classes
of many-body problems in principle, here, the theory is illustrated using
simple model systems. For one-body Fermionic Hamiltonians, Fermi-Dirac one-body
reduced density matrices are recovered for the grand-canonical formulation. For
multidimensional harmonic oscillators numerically exact results are obtained
using the thermal normal ordered exponential (TNOE) approach. As an application
of the related time-dependent formulation numerically exact
time-autocorrelation functions and absorption spectra are obtained for harmonic
Franck Condon problems. These examples illustrate the basic soundness of the
scheme and are used for pedagogical purposes. Other approaches in the
literature are only discussed briefly and no detailed comparative discussion is
attempted.


  In recent years a number of new theoretical models have been implemented into
Monte-Carlo neutrino interaction event generators. Being able to compare
multiple model predictions is invaluable to the field, especially as it is
unfortunately still unclear which one provides the best fit to the entire
collection of neutrino cross-section data. Using a recently developed neutrino
generator tuning framework (NUISANCE), we review a selection of models in the
NEUT and NuWro generators through comparisons to existing bubble chamber,
MINERvA, and MiniBooNE cross-section data.


  This paper introduces a new discrete fracture model accounting for
non-isothermal compositional multiphase Darcy flows and complex networks of
fractures with intersecting, immersed and non immersed fractures. The so called
hybrid-dimensional model using a 2D model in the fractures coupled with a 3D
model in the matrix is first derived rigorously starting from the
equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully
implicit time integration combined with the Vertex Approximate Gradient (VAG)
finite volume scheme which is adapted to polyhedral meshes and anisotropic
heterogeneous media. The fully coupled systems are assembled and solved in
parallel using the Single Program Multiple Data (SPMD) paradigm with one layer
of ghost cells. This strategy allows for a local assembly of the discrete
systems. An efficient preconditioner is implemented to solve the linear systems
at each time step and each Newton type iteration of the simulation. The
numerical efficiency of our approach is assessed on different meshes, fracture
networks, and physical settings in terms of parallel scalability, nonlinear
convergence and linear convergence.


  We argue that quantum gravity theories that carry a Lie algebraic
modification of the Poincare' and Heisenberg algebras inevitably provide
inhomogeneities that may serve as seeds for cosmological structure formation.
Furthermore, in this class of theories one must expect a strong polarisation
and spin dependence of various quantum-gravity effects.


  The unexpected emerging stability of a time-modulated magnetic guide,
realized without external offset fields, is demonstrated. We found a steady
periodic solution around which the nonlinear dynamics is linearized. To
investigate the orbital stability of the guiding, a formal criterion based on
the analysis of the eigenvalues of the monodromy matrix of the system dynamics
is used. To circumvent the difficulty in finding an analytical expression for
these eigenvalues, a Lyapunov transformation of the system variables is
proposed. From this transformation, an equation of state for the system
parameters is derived, and it allows one to estimate an upper bound for the
computed stability domains. In particular, we found a general expression for
the threshold modulation frequency below which the guiding is unstable. Using
experimentally accessible parameters, the stable guiding of 87Rb atoms is
investigated.


  We describe measurements of the rotational component of teleseismic surface
waves using an inertial high-precision ground-rotation-sensor installed at the
LIGO Hanford Observatory (LHO). The sensor has a noise floor of 0.4 nrad$/
\sqrt{\rm Hz}$ at 50 mHz and a translational coupling of less than 1 $\mu$rad/m
enabling translation-free measurement of small rotations. We present
observations of the rotational motion from Rayleigh waves of six teleseismic
events from varied locations and with magnitudes ranging from M6.7 to M7.9.
These events were used to estimate phase dispersion curves which shows
agreement with a similar analysis done with an array of three STS-2
seismometers also located at LHO.


  We study two aspects of fermionic T-duality: the duality in purely fermionic
sigma models exploring the possible obstructions and the extension of the
T-duality beyond classical approximation. We consider fermionic sigma models as
coset models of supergroups divided by their maximally bosonic subgroup
OSp(m|n)/SO(m) x Sp(n). Using the non-abelian T-duality and a non-conventional
gauge fixing we derive their fermionic T-duals. In the second part of the
paper, we prove the conformal invariance of these models at one and two loops
using the Background Field Method and we check the Ward Identities.


  The aim of this paper is to use the methods and results of symplectic
homogenization (see [V4]) to prove existence of periodic orbits and invariant
measures with rotation number depending on the differential of the Homogenized
Hamiltonian. We also prove the Conley conjecture on the cotangent bundle of the
torus. Both proofs rely on Symplectic Homogenization and a refinement of it.


  In this article, we are presenting the relationship between environmental
pollution and the income level of the selected twenty-four countries. We
implemented a data-based research analysis where, for each country, we analyzed
the related data for fifty-six years, from 1960 to 2016, to assess the
relationship between the carbon emission and income level. After performing the
related data analysis for each country, we concluded whether the results for
that country were in line with the Environmental Kuznets Curve (EKC)
hypothesis. The EKC hypothesis suggests that the carbon emission per capita
starts a declining trend when the country-specific high level of income is
reached. The results of our data analyses show that the EKC hypothesis is valid
for high-income countries and the declining trends of carbon emission are
clearly observed when the income level reaches a specific high enough level. On
the other hand, for the non-high income countries, our analysis results show
that it is too early to make an assessment at this growth stage of their
economies because they have not reached their related high-enough income per
capita levels yet. Furthermore, we performed two more additional analyses on
high-income countries. First, we analyzed the related starting years of their
carbon emission declining trends. The big variance in the starting years of the
carbon emission declining trends shows that the international policies are
clearly ineffective in initiating the declining trend in carbon emission. In
addition, for the high-income countries, we explained the differences in their
carbon emission per capita levels in 2014 with their SGI indices and their
dependence on high-carbon emission energy production.


  An orthogonality space is a set equipped with a symmetric and irreflexive
binary relation. We consider orthogonality spaces with the additional property
that any collection of mutually orthogonal elements gives rise to the structure
of a Boolean algebra. Together with the maps that preserve the Boolean
structures, we are led to the category ${\mathcal N}{\mathcal O}{\mathcal S}$
of normal orthogonality spaces. Moreover, an orthogonality space of finite rank
is called linear if for any two distinct elements $e$ and $f$ there is a third
one $g$ such that exactly one of $f$ and $g$ is orthogonal to $e$ and the pairs
$e, f$ and $e, g$ have the same orthogonal complement. Linear orthogonality
spaces arise from finite-dimensional Hermitian spaces. We are led to the full
subcategory ${\mathcal L}{\mathcal O}{\mathcal S}$ of ${\mathcal N}{\mathcal
O}{\mathcal S}$ and we show that the morphisms are the orthogonality-preserving
lineations. Finally, we consider the full subcategory ${\mathcal E}{\mathcal
O}{\mathcal S}$ of ${\mathcal L}{\mathcal O}{\mathcal S}$ whose members arise
from positive definite Hermitian spaces over Baer ordered $\star$-fields with a
Euclidean fixed field. We establish that the morphisms of ${\mathcal
E}{\mathcal O}{\mathcal S}$ are induced by generalised semiunitary mappings.


  Existing multi-label frameworks only exploit the information deduced from the
bipartition of the labels into a positive and negative set. Therefore, they do
not benefit from the ranking order between positive labels, which is the
concept we introduce in this paper. We propose a novel multi-label ranking
method: GaussianMLR, which aims to learn implicit class significance values
that determine the positive label ranks instead of treating them as of equal
importance, by following an approach that unifies ranking and classification
tasks associated with multi-label ranking. Due to the scarcity of public
datasets, we introduce eight synthetic datasets generated under varying
importance factors to provide an enriched and controllable experimental
environment for this study. On both real-world and synthetic datasets, we carry
out extensive comparisons with relevant baselines and evaluate the performance
on both of the two sub-tasks. We show that our method is able to accurately
learn a representation of the incorporated positive rank order, which is not
only consistent with the ground truth but also proportional to the underlying
information. We strengthen our claims empirically by conducting comprehensive
experimental studies. Code is available at
https://github.com/MrGranddy/GaussianMLR.


  In this work we construct and analyse non-perturbative stationary and
axially-symmetric black hole solutions in General Relativity coupled to an
electromagnetic and an axion field. The axion field is coupled to the
electromagnetic field, which leads to hairy solutions in the presence of an
electric charge and rotation. We investigate the existence and characteristics
of these solutions for different values of the spin, charge and coupling
constant. Our analysis shows the presence of violations of the Kerr-Newman
bound, solutions with large positive and negative values of the gyromagnetic
ratio, and the existence of multiple branches of solutions with distinct
properties, demonstrating that black hole uniqueness does not hold in this
scenario. The code used in this study is publicly available, providing a
valuable tool for further research on this model.


  Where in the landscape of many-body phases of matter do we place the Higgs
condensate of a gauge theory? On the one hand, the Higgs phase is gapped, has
no local order parameter, and for fundamental Higgs fields is adiabatically
connected to the confined phase. On the other hand, Higgs phases such as
superconductors display rich phenomenology. In this work, we propose a minimal
description of the Higgs phase as a symmetry-protected topological (SPT) phase,
utilizing conventional and higher-form symmetries. In this first part, we focus
on 2+1D $\mathbb Z_2$ gauge theory and find that the Higgs phase is protected
by a higher-form magnetic symmetry and a matter symmetry, whose meaning depends
on the physical context. While this proposal captures known properties of Higgs
phases, it also predicts that the Higgs phase of the Fradkin-Shenker model has
SPT edge modes in the symmetric part of the phase diagram, which we confirm
analytically. In addition, we argue that this SPT property is remarkably robust
upon explicitly breaking the magnetic symmetry. Although the Higgs and confined
phases are then connected without a bulk transition, they are separated by a
boundary phase transition, which we confirm with tensor network simulations.
More generally, the boundary anomaly of the Higgs SPT phase coincides with the
emergent anomaly of symmetry-breaking phases, making precise the relation
between Higgs phases and symmetry breaking. The SPT nature of the Higgs phase
can also manifest in the bulk, e.g., at transitions between distinct Higgs
condensates. Finally, we extract insights which are applicable to general SPT
phases, such as a 'bulk-defect correspondence' generalizing discrete gauge
group analogs of Superconductor-Insulator-Superconductor (SIS) junctions. The
sequel to this work will generalize 'Higgs=SPT' to continuous symmetries,
interpreting superconductivity as an SPT property.


  We consider the reachability problem on transition systems corresponding to
succinct one-counter machines, that is, machines where the counter is
incremented or decremented by a value given in binary.


  We have discovered a population of 29 outlying H$\alpha$ emitters which
appear like unresolved blobs in the DR14 data release of the SDSS IV MaNGA
integral field unit survey. They do not have any underlying optical continuum
emission in deep imaging from the DECam Legacy Survey or Beijing-Arizona Sky
Survey. These blobs either lie away from the disc of the host galaxy in the
MaNGA IFU and/or have velocities which are different from the velocity map of
the host galaxy. Interestingly, all of them show photoionisation due to star
formation. These galaxies have very high specific star formation rates compared
to the known population of dwarf galaxies. However, their metallicities are
consistent with or even lower than those of the local volume dwarfs. Thus, we
can possibly rule out tidal dwarf galaxies. They could represent a new
population of low mass and starbursting dwarf galaxies.


  We show that the generic Hall algebra of nilpotent representations of an
oriented cycle specialised at $q=0$ is isomorphic to the generic extension
monoid in the sense of Reineke. This continues the work of Reineke.


  Multiple controllable spiking patterns are obtained in a 1310 nm Vertical
Cavity Surface Emitting Laser (VCSEL) in response to induced perturbations and
for two different cases of polarized optical injection, namely parallel and
orthogonal. Achievement of reproducible spiking responses in VCSELs operating
at the telecom wavelengths offers great promise for future uses of these
devices in ultrafast neuromorphic photonic systems for non-traditional
computing applications.


  This paper presents the comparison of compression algorithms for voice
transferring method over SMS in satellite communication. Voice transferring
method over SMS is useful in situations when signal strength is low and due to
poor signal strength voice call connection is not possible to initiate or
signal dropped during voice call. This method has one serious flaw that it
produces large number of SMS while converting voice into SMS. Such issue is
catered to some extend by employing any compression algorithm. In this paper
our major aim is to find best compression scheme for said method, for that
purpose we compare 6 different types of compression algorithms which are; LZW
(Lempel-Ziv-Welch), Huffman coding, PPM (Prediction by partial matching),
Arithmetic Coding (AC), BWT (Burrows-Wheeler-Transform), LZMA
(Lempel-Ziv-Markov chain). This comparison shows that PPM compression method
offers better compression ratio and produce small number of SMS. For
experimentation we use Thuraya SG-2520 satellite phone. Moreover, we develop an
application using J2ME platform[Ref:a]. We tested that application more than
100 times and then we compare the result in terms of compression ratio of each
algorithm and number of connected SMS produce after each compression method.
The result of this study will help developers to choose better compression
scheme for their respective applications.
http://www.learnrnd.com/news.php?id=ISSUES_IN_MOLECULAR_COMMUNICATIONS


  Many binary classification problems minimize misclassification above (or
below) a threshold. We show that instances of ranking problems, accuracy at the
top or hypothesis testing may be written in this form. We propose a general
framework to handle these classes of problems and show which known methods
(both known and newly proposed) fall into this framework. We provide a
theoretical analysis of this framework and mention selected possible pitfalls
the methods may encounter. We suggest several numerical improvements including
the implicit derivative and stochastic gradient descent. We provide an
extensive numerical study. Based both on the theoretical properties and
numerical experiments, we conclude the paper by suggesting which method should
be used in which situation.


  The departure of particle distributions from the Maxwellian is commonly
observed in space plasmas. These non-Maxwellian distributions which are typical
for plasmas that are not in thermal equilibrium, can be modeled with
$\kappa$-distribution. Kinetic simulations of quasi-parallel collisionless
shocks show that proton distribution is a composite of thermal, suprathermal,
and non-thermal parts. By using particle-in-cell shock simulations, we show
that $\kappa$-distribution adequately fits thermal and suprathermal parts
together, as a single continuous distribution in early proton spectra. We
derive suprathermal proton distribution directly from the generalized entropy
of non-extensive statistical mechanics, and show that thermal and suprathermal
populations are both naturally embedded in $\kappa$-distribution. We find that
the index $\kappa$ of the distribution increases with the distance from the
shock, following the decrease in suprathermal part. The non-equilibrium plasma
distribution which is continuously being enriched with suprathermal particles
at the reforming shock barrier, reaches the thermal equilibrium in the far
downstream. The suprathermal part completely fades there, and the shape of
proton distribution becomes a Maxwellian from which directly emerges a
power-law.


  For each odd prime $p$, we prove the existence of infinitely many real
quadratic fields which are $p$-rational. Explicit imaginary and real
bi-quadratic $p$-rational fields are also given for each prime $p$. Using a
recent method developed by Greenberg, we deduce the existence of Galois
extensions of $\mathbf{Q}$ with Galois group isomorphic to an open subgroup of
$GL_n(\mathbf{Z_p})$, for $n =4$ and $n =5$ and at least for all the primes $p
<192.699.943$.


  Motivated by experimental studies that have found signatures of a quantum
spin liquid phase in organic crystals whose structure is well described by the
two-dimensional triangular lattice, we study the Hubbard model on this lattice
at half filling using the infinite-system density matrix renormalization group
(iDMRG) method. On infinite cylinders with finite circumference, we identify an
intermediate phase between observed metallic behavior at low interaction
strength and Mott insulating spin-ordered behavior at strong interactions.
Chiral ordering from spontaneous breaking of time-reversal symmetry, a
fractionally quantized spin Hall response, and characteristic level statistics
in the entanglement spectrum in the intermediate phase provide strong evidence
for the existence of a chiral spin liquid in the full two-dimensional limit of
the model.


  In this paper we focus on the uniqueness question for (expanding) solutions
of the Harmonic map flow coming out of smooth 0-homogeneous maps with values
into a closed Riemannian manifold. We introduce a relative entropy for two
purposes. On the one hand, we prove the existence of two expanding solutions
associated to any suitable solution coming out of a $0$-homogeneous map by a
blow-up and a blow-down process. On the other hand, generic uniqueness of
expanding solutions coming out of the same 0-homogeneous map of 0 relative
entropy is proved.


  As a flexible passive 3D sensing means, unsupervised learning of depth from
monocular videos is becoming an important research topic. It utilizes the
photometric errors between the target view and the synthesized views from its
adjacent source views as the loss instead of the difference from the ground
truth. Occlusion and scene dynamics in real-world scenes still adversely affect
the learning, despite significant progress made recently. In this paper, we
show that deliberately manipulating photometric errors can efficiently deal
with these difficulties better. We first propose an outlier masking technique
that considers the occluded or dynamic pixels as statistical outliers in the
photometric error map. With the outlier masking, the network learns the depth
of objects that move in the opposite direction to the camera more accurately.
To the best of our knowledge, such cases have not been seriously considered in
the previous works, even though they pose a high risk in applications like
autonomous driving. We also propose an efficient weighted multi-scale scheme to
reduce the artifacts in the predicted depth maps. Extensive experiments on the
KITTI dataset and additional experiments on the Cityscapes dataset have
verified the proposed approach's effectiveness on depth or ego-motion
estimation. Furthermore, for the first time, we evaluate the predicted depth on
the regions of dynamic objects and static background separately for both
supervised and unsupervised methods. The evaluation further verifies the
effectiveness of our proposed technical approach and provides some interesting
observations that might inspire future research in this direction.


  Within the realm of deep learning, the interpretability of Convolutional
Neural Networks (CNNs), particularly in the context of image classification
tasks, remains a formidable challenge. To this end we present a neurosymbolic
framework, NeSyFOLD-G that generates a symbolic rule-set using the last layer
kernels of the CNN to make its underlying knowledge interpretable. What makes
NeSyFOLD-G different from other similar frameworks is that we first find groups
of similar kernels in the CNN (kernel-grouping) using the cosine-similarity
between the feature maps generated by various kernels. Once such kernel groups
are found, we binarize each kernel group's output in the CNN and use it to
generate a binarization table which serves as input data to FOLD-SE-M which is
a Rule Based Machine Learning (RBML) algorithm. FOLD-SE-M then generates a
rule-set that can be used to make predictions. We present a novel kernel
grouping algorithm and show that grouping similar kernels leads to a
significant reduction in the size of the rule-set generated by FOLD-SE-M,
consequently, improving the interpretability. This rule-set symbolically
encapsulates the connectionist knowledge of the trained CNN. The rule-set can
be viewed as a normal logic program wherein each predicate's truth value
depends on a kernel group in the CNN. Each predicate in the rule-set is mapped
to a concept using a few semantic segmentation masks of the images used for
training, to make it human-understandable. The last layers of the CNN can then
be replaced by this rule-set to obtain the NeSy-G model which can then be used
for the image classification task. The goal directed ASP system s(CASP) can be
used to obtain the justification of any prediction made using the NeSy-G model.
We also propose a novel algorithm for labeling each predicate in the rule-set
with the semantic concept(s) that its corresponding kernel group represents.


  We investigate the role of the boundary in the symmetric simple exclusion
process with competing nonlocal and local hopping events. With open boundaries,
the system undergoes a first order phase transition from a finite density phase
to an empty road phase as the nonlocal hopping rate increases. Using a cluster
stability analysis, we determine the location of such an abrupt nonequilibrium
phase transition, which agrees well with numerical results. Our cluster
analysis provides a physical insight into the mechanism behind this transition.
We also explain why the transition becomes discontinuous in contrast to the
case with periodic boundary conditions, in which the continuous phase
transition has been observed.


  We investigate the time-optimal solution of the selective control of two
uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive
the global time-optimal pulses for two spins with different offsets. We show
that the Pontryagin Hamiltonian can be written as a one-dimensional effective
Hamiltonian. The optimal fields can be expressed analytically in terms of
elliptic integrals. The time-optimal control problem is solved for the
selective inversion and excitation processes. A bifurcation in the structure of
the control fields occurs for a specific offset threshold. In particular, we
show that for small offsets, the optimal solution is the concatenation of
regular and singular extremals.


  Large Language Models (LLMs) have demonstrated impressive and diverse
abilities that can benefit various domains, such as zero and few-shot
information extraction from clinical text without domain-specific training.
However, for the ICD coding task, they often hallucinate key details and
produce high recall but low precision results due to the high-dimensional and
skewed distribution of the ICD codes. Existing LLM-based methods fail to
account for the complex and dynamic interactions among the human agents
involved in coding, such as patients, physicians, and coders, and they lack
interpretability and reliability. In this paper, we present a novel multi-agent
method for ICD coding, which mimics the real-world coding process with five
agents: a patient agent, a physician agent, a coder agent, a reviewer agent,
and an adjuster agent. Each agent has a specific function and uses a LLM-based
model to perform it. We evaluate our method on the MIMIC-III dataset and show
that our proposed multi-agent coding framework substantially improves
performance on both common and rare codes compared to Zero-shot Chain of
Thought (CoT) prompting and self-consistency with CoT. The ablation study
confirms the proposed agent roles' efficacy. Our method also matches the
state-of-the-art ICD coding methods that require pre-training or fine-tuning,
in terms of coding accuracy, rare code accuracy, and explainability.