  We conducted a volume-limited survey at 4.9 GHz of 32 nearby ultracool dwarfs
with spectral types covering the range M7 -- T8. A statistical analysis was
performed on the combined data from the present survey and previous radio
observations of ultracool dwarfs. Whilst no radio emission was detected from
any of the targets, significant upper limits were placed on the radio
luminosities that are below the luminosities of previously detected ultracool
dwarfs. Combining our results with those from the literature gives a detection
rate for dwarfs in the spectral range M7 -- L3.5 of ~ 9%. In comparison, only
one dwarf later than L3.5 is detected in 53 observations. We report the
observed detection rate as a function of spectral type, and the number
distribution of the dwarfs as a function of spectral type and rotation
velocity. The radio observations to date point to a drop in the detection rate
toward the ultracool dwarfs. However, the emission levels of detected ultracool
dwarfs are comparable to those of earlier type active M dwarfs, which may imply
that a mildly relativistic electron beam or a strong magnetic field can exist
in ultracool dwarfs. Fast rotation may be a sufficient condition to produce
magnetic fields strengths of several hundreds Gauss to several kilo Gauss, as
suggested by the data for the active ultracool dwarfs with known rotation
rates. A possible reason for the non-detection of radio emission from some
dwarfs is that maybe the centrifugal acceleration mechanism in these dwarfs is
weak (due to a low rotation rate) and thus cannot provide the necessary density
and/or energy of accelerated electrons. An alternative explanation could be
long-term variability, as is the case for several ultracool dwarfs whose radio
emission varies considerably over long periods with emission levels dropping
below the detection limit in some instances.


  It is shown how a integrable mechanical system provides all the localized
static solutions of a deformation of the linear O(N)-sigma model in two
space-time dimensions. The proof is based on the Hamilton-Jacobi separability
of the mechanical analogue system that follows when time-independent field
configurations are being considered. In particular, we describe the properties
of the different kinds of kinks in such a way that a hierarchical structure of
solitary wave manifolds emerges for distinct N.


  We report observations of 15 high redshift (z = 1-5) galaxies at 350 microns
using the Caltech Submillimeter Observatory and SHARC-II array detector.
Emission was detected from eight galaxies, for which far-infrared luminosities,
star formation rates, total dust masses, and minimum source size estimates are
derived. These galaxies have star formation rates and star formation
efficiencies comparable to other high redshift molecular emission line
galaxies. The results are used to test the idea that star formation in these
galaxies occurs in a large number of basic units, the units being similar to
star-forming clumps in the Milky Way. The luminosity of these extreme galaxies
can be reproduced in a simple model with (0.9-30) *10^6 dense clumps, each with
a luminosity of 5 *10^5 Lsun, the mean value for such clumps in the Milky Way.
Radiative transfer models of such clumps can provide reasonable matches to the
overall SEDs of the galaxies. They indicate that the individual clumps are
quite opaque in the far-infrared. Luminosity to mass ratios vary over two
orders of magnitude, correlating strongly with the dust temperature derived
from simple fits to the SED. The gas masses derived from the dust modeling are
in remarkable agreement with those from CO luminosities, suggesting that the
assumptions going into both calculations are reasonable.


  We present the characteristics and some early scientific results of the first
instrument at the Large Binocular Telescope (LBT), the Large Binocular Camera
(LBC). Each LBT telescope unit will be equipped with similar prime focus
cameras. The blue channel is optimized for imaging in the UV-B bands and the
red channel for imaging in the VRIz bands. The corrected field-of-view of each
camera is approximately 30 arcminutes in diameter, and the chip area is
equivalent to a 23x23 arcmin2 field. In this paper we also present the
commissioning results of the blue channel. The scientific and technical
performance of the blue channel was assessed by measurement of the astrometric
distortion, flat fielding, ghosts, and photometric calibrations. These
measurements were then used as input to a data reduction pipeline applied to
science commissioning data. The measurements completed during commissioning
show that the technical performance of the blue channel is in agreement with
original expectations. Since the red camera is very similar to the blue one we
expect similar performance from the commissioning that will be performed in the
following months in binocular configuration. Using deep UV image, acquired
during the commissioning of the blue camera, we derived faint UV galaxy-counts
in a ~500 sq. arcmin. sky area to U(Vega)=26.5. These galaxy counts imply that
the blue camera is the most powerful UV imager presently available and in the
near future in terms of depth and extent of the field-of-view. We emphasize the
potential of the blue camera to increase the robustness of the UGR multicolour
selection of Lyman break galaxies at redshift z~3.


  A recursion for the joint moments of the external branch lengths for
coalescents with multiple collisions ($\Lambda$-coalescents) is provided. This
recursion is used to derive asymptotic results as the sample size $n$ tends to
infinity for the joint moments of the external branch lengths and for the
moments of the total external branch length of the Bolthausen-Sznitman
coalescent. These asymptotic results are based on a differential equation
approach, which is as well useful to obtain exact solutions for the joint
moments of the external branch lengths for the Bolthausen-Sznitman coalescent.
The results for example show that the lengths of two randomly chosen external
branches are positively correlated for the Bolthausen--Sznitman coalescent,
whereas they are negatively correlated for the Kingman coalescent provided that
$n\ge 4$.


  We observed Raman scattering from magnon in frequency range from 10 to 65
cm-1 in BiFeO3 single crystals at cryogenic temperatures; the temperature
dependence of the magnon frequency at 18.2 cm-1 approximates an S=5/2 Brillouin
function up to the temperature (280 K) at which the magnon becomes overdamped.
The diverging cross-section and the frequency-shift at 140K and 200 K implies a
magnon-reorientation transition as in orthoferrites. Magnons in polar materials
such as BiFeO3 are often termed electromagnons meaning that they possess an
electric dipole moment due to magnetoelectric coupling.


  We give necessary and sufficient conditions for an orthogonal group defined
over a field of characteristic not 2 to contain a maximal torus of a given
type.


  We investigate a static, cylindrically symmetric cosmic string on the brane
without a perturbative approximation. We find there could be a (large)
enhancement of the (effective) string tension when the energy density at the
center of the string is (much) larger than twice the brane tension. We also
point out a new way to evade the cosmic string problem when the energy density
at the center of the string approaches twice the brane tension. These findings
could have experimental and theoretical implications for searching for cosmic
strings on the brane, in particular for cosmic strings generated after
inflation (such as D-term inflation) on the brane.


  We propose three different mechanisms for pumping spin-polarized currents in
a ballistic circuit using a time-dependent magnetic field acting on an
asymmetrically connected quantum ring at half filling. The first mechanism
works thanks to a rotating magnetic field and produces an alternating current
with a partial spin polarization. The second mechanism works by rotating the
ring in a constant field; like the former case, it produces an alternating
charge current but the spin current is d.c.; both methods do not require a
spin-orbit interaction to achieve the polarized current, but the rotating ring
could be used to measure the spin-orbit interaction in the ring using
characteristic oscillations. On the other hand, the last mechanism that we
propose depends on the spin-orbit interaction in an essential way, and requires
a time-dependent magnetic field in the plane of the ring. This arrangement can
be designed to pump a purely spin current. The absence of a charge current is
demonstrated analytically. Moreover, a simple formula for the current is
derived and compared to the numerical results.


  Abdominal Aortic Aneurysm (AAA) is an enlargement in the lower part of the
main artery Aorta by 1.5 times its normal diameter. AAA can cause death if
rupture occurs. Elective surgeries are recommended to prevent rupture based on
geometrical measurements of AAA diameter and diameter growth rate. Reliability
of these geometric parameters to predict the AAA rupture risk has been
questioned, and biomechanical assessment has been proposed to distinguish
between patients with high and low risk of rupture. Stress in aneurysm wall is
the main variable of interest in such assessment. Most studies use finite
element method to compute AAA stress. This requires discretising
patient-specific geometry (aneurysm wall and intraluminal thrombus ILT) into
finite elements/meshes. Tetrahedral elements are most commonly used as they can
be generated in seemingly automated and effortless way. In practice, however,
due to complex aneurysm geometry, the process tends to require time consuming
mesh optimisation to ensure sufficiently high quality of tetrahedral elements.
Furthermore, ensuring solution convergence requires large number of tetrahedral
elements, which leads to long computation times. In this study, we focus on
generation of hexahedral meshes as they are known to provide converged solution
for smaller number of elements than tetrahedral meshes. Generation of
hexahedral meshes for continua with complex/irregular geometry, such as
aneurysms, requires analyst interaction. We propose a procedure for generating
high quality patient-specific hexahedral discretisation of aneurysm wall using
the algorithms available in commercial software package for mesh generation.
For aneurysm cases, we demonstrate that the procedure facilitates
patient-specific mesh generation within timeframe consistent with clinical
workflow constraints while requiring only limited input from the analyst.


  We present an improved light-cone sum rule analysis of the decay form factors
of $D$ and $D_s$ into $\eta$ and $\eta^{\prime}$ and argue that these decays
offer a very promissing possibility to determine the leading Fock-state gluonic
contribution of the $\eta'$ at future experimental facilities as FAIR or
Super-KEKB. We also give the corresponding branching ratios for B decays.


  Using first principle calculations, we examine the sequence of phases in
electron doped dichalcogenides, such as recently realized in field-gated
MoS$_2$. Upon increasing the electron doping level, we observe a succession of
semiconducting, metallic, superconducting and charge density wave regimes, i.e.
in different order compared to the phase diagram of (semi-)metallic
dichalcogenides such as TiSe$_2$. Both instabilities trace back to a softening
of phonons which couple the electron populated conduction band minima. The
superconducting dome, calculated using Eliashberg theory, is found to fit the
experimentally observed phase diagram, obtained from resistivity measurements.
The charge density wave phase at higher electron doping concentrations as
predicted from instabilities in the phonon modes is further corroborated by
detecting the accompanying lattice deformation in density functional based
supercell relaxations. Upon charge density wave formation, doped MoS$_2$
remains metallic but undergoes a Lifschitz transition, where the number of
Fermi pockets is reduced.


  It is proved that the system of string equations of the dispersionless 2-Toda
hierarchy which arises in the planar limit of the hermitian matrix model also
underlies certain processes in Hele-Shaw flows.


  In certain circumstances when two branes pass through each other a third
brane is produced stretching between them. We explain this phenomenon by the
use of chains of dualities and the inflow of charge that is required for the
absence of chiral gauge anomalies when pairs of D-branes intersect.


  The paper is constructed in two parts.In the first part we introduce the
concept of the algebra of Q-meromorphic functions on the quantum plane.The A
(q)-algebra of Q-analytic functions considered in[6]is seen as a proper
subalgebra. In the second part we find a formula for the curvature tensor on
this algebra. It is seen that when the quantization parameter tendsto 1,then
this formula gives the flatness of the usual R^2 .


  The c_2 invariant of a Feynman graph is an arithmetic invariant which detects
many properties of the corresponding Feynman integral. In this paper, we define
the c_2 invariant in momentum space and prove that it equals the c_2 invariant
in parametric space for overall log-divergent graphs. Then we show that the c_2
invariant of a graph vanishes whenever it contains subdivergences. Finally, we
investigate how the c_2 invariant relates to identities such as the four-term
relation in knot theory.


  In this paper we study the role of dynamical friction on the evolution of a
population of large objects ($m>10^{22}$ g) at heliocentric distances $>70$ AU
in the Kuiper Belt. We show that the already flat distribution of these objects
must flatten further due to non-spherically symmetric distribution of matter in
the Kuiper Belt. Moreover the dynamical drag, produced by dynamical friction,
causes objects of masses $\geq 10^{24} g$ to lose angular momentum and to fall
through more central regions in a timescale $\approx 10^9 yr$. This mechanism
is able to transport inwards objects of the size of Pluto, supposing it was
created beyond 50 AU, according to a Stern & Colwell's (1997b) suggestion.


  We discuss some conjectural inequalities that are related to singular
integrals, martingales, quasiconformal mappings, and the calculus of
variations. Specifically, we present evidence for a conjecture of Iwaniec
concerning the best constant for the Beurling-Ahlfors Operator.


  By including the recently introduced thermal shear term that contributes to
the spin polarization vector at local equilibrium, we determine longitudinal
polarization of $\Lambda$ hyperons emitted from a hot and rotating hadronic
medium using the thermal model with single freeze-out. In our analysis, we
consider the RHIC top energies and use the model parameters which were
determined in the earlier analyses of particle spectra and elliptic flow. We
confirm that, unlike the previous calculations done by using only the thermal
vorticity, the thermal shear term alone leads to the correct sign of the
quadrupole structure of the longitudinal component of the polarization
three-vector measured in experiments. However, we find almost complete
cancellation between thermal shear and vorticity terms, which eventually leads
to disagreement with the data. To clarify the role played by velocity and
temperature gradient terms, we present a systematic analysis of different
contributions to the longitudinal polarization.


  We give an explicit method for calculating the equations of state of a
thermodynamical substance from the following information: in the calibrated
case, the system of isotherms and a single adiabat, in the uncalibrated one,
the same but with two adiabats. For simple examples the entropy function can be
computed explicitly from this material but it involves steps (solution of
non-linear equations and an integration) which will usually require numerical
methods for their implementation.


  A Walsh zero space (WZ space) for $f:F_{2^n}\rightarrow F_{2^n}$ is an
$n$-dimensional vector subspace of $F_{2^n}\times F_{2^n}$ whose all nonzero
elements are Walsh zeros of $f$. We provide several theoretical and
computer-free constructions of WZ spaces for Gold APN functions
$f(x)=x^{2^i+1}$ on $F_{2^n}$ where $n$ is odd and $\gcd(i,n)=1$. We also
provide several constructions of trivially intersecting pairs of such spaces.
We illustrate applications of our constructions that include constructing APN
permutations that are CCZ equivalent to $f$ but not extended affine equivalent
to $f$ or its compositional inverse.


  Autonomous agents, such as robots or intelligent devices, need to understand
how to interact with objects and its environment. Affordances are defined as
the relationships between an agent, the objects, and the possible future
actions in the environment. In this paper, we present a Bayesian deep learning
method to predict the affordances available in the environment directly from
RGB images. Based on previous work on socially accepted affordances, our model
is based on a multiscale CNN that combines local and global information from
the object and the full image. However, previous works assume a deterministic
model, but uncertainty quantification is fundamental for robust detection,
affordance-based reason, continual learning, etc. Our Bayesian model is able to
capture both the aleatoric uncertainty from the scene and the epistemic
uncertainty associated with the model and previous learning process. For
comparison, we estimate the uncertainty using two state-of-the-art techniques:
Monte Carlo dropout and deep ensembles. We also compare different types of CNN
encoders for feature extraction. We have performed several experiments on an
affordance database on socially acceptable behaviours and we have shown
improved performance compared with previous works. Furthermore, the uncertainty
estimation is consistent with the the type of objects and scenarios. Our
results show a marginal better performance of deep ensembles, compared to
MC-dropout on the Brier score and the Expected Calibration Error.


  This paper describes a system S' obtained by modifying first-order arithmetic
to 'parameterise' the individual variables so that under any interpretation of
S', the individual variables range over all and only the individuals assigned
to the numerals under this interpretation. Since S' contains Peano arithmetic
and is recursively axiomatised we can modify Goedel's technique to define a
Goedel sentence for S', say (x)R[x]. S' may be shown to be inconsistent since
(x)R[x] must be an S' theorem. Since the syntax of S' and S are identical
however the inconsistency of S itself is implied by this result.


  In this paper, we present a Geometry-aware Neural Interpolation (Geo-NI)
framework for light field rendering. Previous learning-based approaches either
rely on the capability of neural networks to perform direct interpolation,
which we dubbed Neural Interpolation (NI), or explore scene geometry for novel
view synthesis, also known as Depth Image-Based Rendering (DIBR). Instead, we
incorporate the ideas behind these two kinds of approaches by launching the NI
with a novel DIBR pipeline. Specifically, the proposed Geo-NI first performs NI
using input light field sheared by a set of depth hypotheses. Then the DIBR is
implemented by assigning the sheared light fields with a novel reconstruction
cost volume according to the reconstruction quality under different depth
hypotheses. The reconstruction cost is interpreted as a blending weight to
render the final output light field by blending the reconstructed light fields
along the dimension of depth hypothesis. By combining the superiorities of NI
and DIBR, the proposed Geo-NI is able to render views with large disparity with
the help of scene geometry while also reconstruct non-Lambertian effect when
depth is prone to be ambiguous. Extensive experiments on various datasets
demonstrate the superior performance of the proposed geometry-aware light field
rendering framework.


  Given a non-trivial graph $G$, the minimum cardinality of a set of edges $F$
in $G$ such that $\chi'(G \setminus F)<\chi'(G)$ is called the chromatic edge
stability index of $G$, denoted by $es_{\chi'}(G)$, and such a (smallest) set
$F$ is called a (minimum) mitigating set. While $1\le es_{\chi'}(G)\le \lfloor
n/2\rfloor$ holds for any graph $G$, we investigate the graphs with extremal
and near-extremal values of $es_{\chi'}(G)$. The graphs $G$ with
$es_{\chi'}(G)=\lfloor n/2\rfloor$ are classified, and the graphs $G$ with
$es_{\chi'}(G)=\lfloor n/2\rfloor-1$ and $\chi'(G)=\Delta(G)+1$ are
characterized. We establish that the odd cycles and $K_2$ are exactly the
regular connected graphs with the chromatic edge stability index $1$; on the
other hand, we prove that it is NP-hard to verify whether a graph $G$ has
$es_{\chi'}(G)=1$. We also prove that every minimum mitigating set of an
$r$-regular graph $G$, where $r\ne 4$, with $es_{\chi'}(G)=2$ is a matching.
Furthermore, we propose a conjecture that for every graph $G$ there exists a
minimum mitigating set, which is a matching, and prove that the conjecture
holds for graphs $G$ with $es_{\chi'}(G)\in\{1,2,\lfloor n/2\rfloor-1,\lfloor
n/2\rfloor\}$, and for bipartite graphs.


  The Manin constant $c$ of an elliptic curve $E$ over $\mathbb{Q}$ is the
nonzero integer that scales the differential $\omega_f$ determined by the
normalized newform $f$ associated to $E$ into the pullback of a N\'{e}ron
differential under a minimal parametrization $\phi\colon X_0(N)_{\mathbb{Q}}
\twoheadrightarrow E$. Manin conjectured that $c = \pm 1$ for optimal
parametrizations, and we prove that in general $c \mid \mathrm{deg}(\phi)$
under a minor assumption at $2$ and $3$ that is not needed for cube-free $N$ or
for parametrizations by $X_1(N)_{\mathbb{Q}}$. Since $c$ is supported at the
additive reduction primes, which need not divide $\mathrm{deg}(\phi)$, this
improves the status of the Manin conjecture for many $E$. Our core result that
gives this divisibility is the containment $\omega_f \in H^0(X_0(N), \Omega)$,
which we establish by combining automorphic methods with techniques from
arithmetic geometry; here the modular curve $X_0(N)$ is considered over
$\mathbb{Z}$ and $\Omega$ is its relative dualizing sheaf over $\mathbb{Z}$. We
reduce this containment to $p$-adic bounds on denominators of the Fourier
expansions of $f$ at all the cusps of $X_0(N)_{\mathbb{C}}$ and then use the
recent basic identity for the $p$-adic Whittaker newform to establish stronger
bounds in the more general setup of newforms of weight $k$ on $X_0(N)$. To
overcome obstacles at $2$ and $3$, we analyze nondihedral supercuspidal
representations of $\mathrm{GL}_2(\mathbb{Q}_2)$ and exhibit new cases in which
$X_0(N)_{\mathbb{Z}}$ has rational singularities.


  We deduce some elementary pairwise disjointness and semi-disjointness
conditions on triples of subsets in arbitrary groups satisfying the so-called
triple product property (TPP) as originally defined by H. Cohn and C. Umans in
2003. This property TPP for a triple of group subsets, called a TPP triple,
allows the group to "realize" matrix multiplication of dimensions the sizes of
the subsets, with the subsets acting as indexing sets for input matrices which
are embedded into the regular algebra of the group. We derive nine different
disjointness casetypes for an arbitrary TPP triple, and classify these into
four different disjointness classes based on an integer measure of the degree
of pairwise disjointness among the subsets. Finally, we derive lower and upper
bounds for the sum of sizes of the subsets forming a TPP triple, which is the
additive equivalent of the multiplicative bounds originally derived by Cohn and
Umans for the product of sizes of subsets forming a TPP triple.


  We report the dramatic mid-infrared brightening between 2004 and 2006 of HOPS
383, a deeply embedded protostar adjacent to NGC 1977 in Orion. By 2008, the
source became a factor of 35 brighter at 24 microns with a brightness increase
also apparent at 4.5 microns. The outburst is also detected in the
submillimeter by comparing APEX/SABOCA to SCUBA data, and a scattered-light
nebula appeared in NEWFIRM K_s imaging. The post-outburst spectral energy
distribution indicates a Class 0 source with a dense envelope and a luminosity
between 6 and 14 L_sun. Post-outburst time-series mid- and far-infrared
photometry shows no long-term fading and variability at the 18% level between
2009 and 2012. HOPS 383 is the first outbursting Class 0 object discovered,
pointing to the importance of episodic accretion at early stages in the star
formation process. Its dramatic rise and lack of fading over a six-year period
hint that it may be similar to FU Ori outbursts, although the luminosity
appears to be significantly smaller than the canonical luminosities of such
objects.


  Detection of interactions between treatment effects and patient descriptors
in clinical trials is critical for optimizing the drug development process. The
increasing volume of data accumulated in clinical trials provides a unique
opportunity to discover new biomarkers and further the goal of personalized
medicine, but it also requires innovative robust biomarker detection methods
capable of detecting non-linear, and sometimes weak, signals. We propose a set
of novel univariate statistical tests, based on the theory of random walks,
which are able to capture non-linear and non-monotonic covariate-treatment
interactions. We also propose a novel combined test, which leverages the power
of all of our proposed univariate tests into a single general-case tool. We
present results for both synthetic trials as well as real-world clinical
trials, where we compare our method with state-of-the-art techniques and
demonstrate the utility and robustness of our approach.


  To investigate an effect of social interaction on the bystanders'
intervention in emergency situations a rescue model was introduced which
includes the effects of the victim's acquaintance with bystanders and those
among bystanders from a network perspective. This model reproduces the
experimental result that the helping rate (success rate in our model) tends to
decrease although the number of bystanders $k$ increases. And the interaction
among homogeneous bystanders results in the emergence of hubs in a helping
network. For more realistic consideration it is assumed that the agents are
located on a one-dimensional lattice (ring), then the randomness $p \in [0,1]$
is introduced: the $kp$ random bystanders are randomly chosen from a whole
population and the $k-kp$ near bystanders are chosen in the nearest order to
the victim. We find that there appears another peak of the network density in
the vicinity of $k=9$ and $p=0.3$ due to the cooperative and competitive
interaction between the near and random bystanders.


  It is first argued that radiation by a uniformly accelerated charge in flat
space-time indicates the need for a unified geometric theory of gravity and
electromagnetism. Such a theory, based on a metric-affine $U_4$ manifold, is
constructed with the torsion pseudo-vector $\Gamma_\mu$ linking gravity and
electromagnetism. This conceptually simple extension results in (i) Einstein's
equations being modified by a vacuum energy $\Gamma_\mu\Gamma_\nu$ and a scalar
field $\Gamma = \Gamma^\mu\Gamma_\mu$ whose zero-mode is a cosmological
constant $\Lambda$ representing `dark energy', (ii) most of the salient
features of `dark matter'-like phenomena, (iii) a modified electrodynamics
satisfying Heaviside duality, (iv) a finite and small Casimir Effect, and at
the same time, (v) the empirical Schuster-Blackett-Wilson relation for the
amazingly universal gyromagnetic ratio of slowly rotating, neutral
astrophysical bodies.


  Automatic optical inspection (AOI) plays a pivotal role in the manufacturing
process, predominantly leveraging high-resolution imaging instruments for
scanning purposes. It detects anomalies by analyzing image textures or
patterns, making it an essential tool in industrial manufacturing and quality
control. Despite its importance, the deployment of models for AOI often faces
challenges. These include limited sample sizes, which hinder effective feature
learning, variations among source domains, and sensitivities to changes in
lighting and camera positions during imaging. These factors collectively
compromise the accuracy of model predictions. Traditional AOI often fails to
capitalize on the rich mechanism-parameter information from machines or inside
images, including statistical parameters, which typically benefit AOI
classification. To address this, we introduce an external modality-guided data
mining framework, primarily rooted in optical character recognition (OCR), to
extract statistical features from images as a second modality to enhance
performance, termed OANet (Ocr-Aoi-Net). A key aspect of our approach is the
alignment of external modality features, extracted using a single
modality-aware model, with image features encoded by a convolutional neural
network. This synergy enables a more refined fusion of semantic representations
from different modalities. We further introduce feature refinement and a gating
function in our OANet to optimize the combination of these features, enhancing
inference and decision-making capabilities. Experimental outcomes show that our
methodology considerably boosts the recall rate of the defect detection model
and maintains high robustness even in challenging scenarios.


  In this paper we give a complete classification of pointed fusion categories
over $\mathbb{C}$ of global dimension 8. We first classify the equivalence
classes of pointed fusion categories of dimension 8, and then we proceed to
determine which of these equivalence classes have equivalent categories of
modules. This classificaction permits to classify the equivalence classes of
braded tensor equivalences of twisted Drinfeld doubles of finite groups of
order 8.


  It has been widely known that CAM (Class Activation Map) usually only
activates discriminative object regions and falsely includes lots of
object-related backgrounds. As only a fixed set of image-level object labels
are available to the WSSS (weakly supervised semantic segmentation) model, it
could be very difficult to suppress those diverse background regions consisting
of open set objects. In this paper, we propose a novel Cross Language Image
Matching (CLIMS) framework, based on the recently introduced Contrastive
Language-Image Pre-training (CLIP) model, for WSSS. The core idea of our
framework is to introduce natural language supervision to activate more
complete object regions and suppress closely-related open background regions.
In particular, we design object, background region and text label matching
losses to guide the model to excite more reasonable object regions for CAM of
each category. In addition, we design a co-occurring background suppression
loss to prevent the model from activating closely-related background regions,
with a predefined set of class-related background text descriptions. These
designs enable the proposed CLIMS to generate a more complete and compact
activation map for the target objects. Extensive experiments on PASCAL VOC2012
dataset show that our CLIMS significantly outperforms the previous
state-of-the-art methods.


  Recently, we have shown that if the ISM is governed by super-sonic turbulent
flows, the excursion-set formalism can be used to calculate the statistics of
self-gravitating objects over a wide range of scales. On the largest
self-gravitating scales ('first crossing'), these correspond to GMCs, and on
the smallest non-fragmenting self-gravitating scales ('last crossing'), to
protostellar cores. Here, we extend this formalism to rigorously calculate the
auto and cross-correlation functions of cores (and by extension, young stars)
as a function of spatial separation and mass, in analogy to the cosmological
calculation of halo clustering. We show that this generically predicts that
star formation is very strongly clustered on small scales: stars form in
clusters, themselves inside GMCs. Outside the binary-star regime, the projected
correlation function declines as a weak power-law, until a characteristic scale
which corresponds to the characteristic mass scale of GMCs. On much larger
scales the clustering declines such that star formation is not strongly biased
on galactic scales, relative to the actual dense gas distribution. The precise
correlation function shape depends on properties of the turbulent spectrum, but
its qualitative behavior is quite general. The predictions agree well with
observations of young star and core autocorrelation functions over ~4 dex in
radius. Clustered star formation is a generic consequence of supersonic
turbulence if most of the power in the velocity field, hence the contribution
to density fluctuations, comes from large scales. The distribution of
self-gravitating masses near the sonic length is then imprinted by fluctuations
on larger scales. We similarly show that the fraction of stars formed in
'isolated' modes should be small (\lesssim10%).


  We perform a set of general relativistic, radiative, magneto-hydrodynamical
simulations (GR-RMHD) to study the transition from radiatively inefficient to
efficient state of accretion on a non-rotating black hole. We study ion to
electron temperature ratios ranging from $T_{\rm i}/T_{\rm e}=10$ to $100$, and
simulate flows corresponding to accretion rates as low as $10^{-6}\dot M_{\rm
Edd}$, and as high as $10^{-2}\dot M_{\rm Edd}$. We have found that the
radiative output of accretion flows increases with accretion rate, and that the
transition occurs earlier for hotter electrons (lower $T_{\rm i}/T_{\rm e}$
ratio). At the same time, the mechanical efficiency hardly changes and accounts
to ${\approx}\,3\%$ of the accreted rest mass energy flux, even at the highest
simulated accretion rates. This is particularly important for the mechanical
AGN feedback regulating massive galaxies, groups, and clusters. Comparison with
recent observations of radiative and mechanical AGN luminosities suggests that
the ion to electron temperature ratio in the inner, collisionless accretion
flow should fall within $10<T_{\rm i}/T_{\rm e}<30$, i.e., the electron
temperature should be several percent of the ion temperature.


  We present an analysis of the economic, political and social factors that
underlay the Apollo program, one of the most exceptional and costly projects
ever undertaken by the United States in peacetime that culminated in 1969 with
the first human steps on the Moon. This study suggests that the Apollo program
provides a vivid illustration of a societal bubble, defined as a collective
over-enthusiasm as well as unreasonable investments and efforts, derived
through excessive public and/or political expectations of positive outcomes
associated with a general reduction of risk aversion. We show that economic,
political and social factors weaved a network of reinforcing feedbacks that led
to widespread over-enthusiasm and extraordinary commitment by individuals
involved in the project as well as by politicians and by the public at large.
We propose the general concept of ``pro-bubbles,'' according to which bubbles
are an unavoidable development in technological and social enterprise that
benefits society by allowing exceptional niches of innovation to be explored.


  An investigation of the rotational spectrum of the interstellar molecule
thioformaldehyde between 110 and 377 GHz through a pyrolysis reaction revealed
a multitude of absorption lines assignable to H$_2$CS and H$_2$C$^{34}$S in
their lowest four excited vibrational states besides lines of numerous
thioformaldehyde isotopologues in their ground vibrational states reported
earlier as well as lines pertaining to several by-products. Additional
transitions of H$_2$CS in its lowest four excited vibrational states were
recorded in selected regions between 571 and 1386 GHz. Slight to strong
Coriolis interactions occur between all four vibrational states with the
exception of the two highest lying states because both are totally symmetric
vibrations. We present combined analyses of the ground and the four interacting
states for our rotational data of H$_2$CS and H$_2$C$^{34}$S. The H$_2$CS data
were supplemented with two sets of high-resultion IR data in two separate
analyses. The $v_2 = 1$ state has been included in analyses of Coriolis
interactions of low-lying fundamental states of H$_2$CS for the first time and
this improved the quality of the fits substantially. We extended furthermore
assignments in $J$ of transition frequencies of thioketene in its ground
vibrational state.


  We consider $n\times n$ real symmetric and Hermitian Wigner random matrices
$n^{-1/2}W$ with independent (modulo symmetry condition) entries and the (null)
sample covariance matrices $n^{-1}X^*X$ with independent entries of $m\times n$
matrix $X$. Assuming first that the 4th cumulant (excess) $\kappa_4$ of entries
of $W$ and $X$ is zero and that their 4th moments satisfy a Lindeberg type
condition, we prove that linear statistics of eigenvalues of the above matrices
satisfy the central limit theorem (CLT) as $n\to\infty$, $m\to\infty$, $m/n\to
c\in[0,\infty)$ with the same variance as for Gaussian matrices if the test
functions of statistics are smooth enough (essentially of the class
$\mathbf{C}^5$). This is done by using a simple ``interpolation trick'' from
the known results for the Gaussian matrices and the integration by parts,
presented in the form of certain differentiation formulas. Then, by using a
more elaborated version of the techniques, we prove the CLT in the case of
nonzero excess of entries again for essentially $\mathbb{C}^5$ test function.
Here the variance of statistics contains an additional term proportional to
$\kappa_4$. The proofs of all limit theorems follow essentially the same
scheme.


  Conventional fault-tolerant quantum error-correction schemes require a number
of extra qubits that grows linearly with the code's maximum stabilizer
generator weight. For some common distance-three codes, the recent "flag
paradigm" uses just two extra qubits. Chamberland and Beverland (2018) provide
a framework for flag error correction of arbitrary-distance codes. However,
their construction requires conditions that only some code families are known
to satisfy. We give a flag error-correction scheme that works for any
stabilizer code, unconditionally. With fast qubit measurement and reset, it
uses $d+1$ extra qubits for a distance-$d$ code.


  Aims. In this work, we characterize the low mass companion of the A0 field
star HR3549. Methods. We observed HR3549AB in imaging mode with the the NIR
branch (IFS and IRDIS) of SPHERE@VLT, with IFS in YJ mode and IRDIS in the H
band. We also acquired a medium resolution spectrum with the IRDIS long slit
spectroscopy mode. The data were reduced using the dedicated SPHERE GTO
pipeline, purposely designed for this instrument. We employed algorithms such
as PCA and TLOCI to reduce the speckle noise. Results. The companion was
clearly visible both with IRDIS and IFS.We obtained photometry in four
different bands as well as the astrometric position for the companion. Based on
our astrometry, we confirm that it is a bound object and put constraints on its
orbit. Although several uncertainties are still present, we estimate an age of
~100-150 Myr for this system, yielding a most probable mass for the companion
of 40-50MJup and T_eff ~300-2400 K. Comparing with template spectra points to a
spectral type between M9 and L0 for the companion, commensurate with its
position on the color-magnitude diagram.


  A crucial aspect of understanding the complex nature of Deep Neural Networks
(DNNs) is the ability to explain learned concepts within their latent
representations. While various methods exist to connect neurons to textual
descriptions of human-understandable concepts, evaluating the quality of these
explanation methods presents a major challenge in the field due to a lack of
unified, general-purpose quantitative evaluation. In this work, we introduce
CoSy (Concept Synthesis) -- a novel, architecture-agnostic framework to
evaluate the quality of textual explanations for latent neurons. Given textual
explanations, our proposed framework leverages a generative model conditioned
on textual input to create data points representing the textual explanation.
Then, the neuron's response to these explanation data points is compared with
the response to control data points, providing a quality estimate of the given
explanation. We ensure the reliability of our proposed framework in a series of
meta-evaluation experiments and demonstrate practical value through insights
from benchmarking various concept-based textual explanation methods for
Computer Vision tasks, showing that tested explanation methods significantly
differ in quality.


  The Kalmeyer-Laughlin state, which is a lattice version of the bosonic
Laughlin state at filling factor one half, has attracted much attention due to
its topological and chiral spin liquid properties. Here we show that the
Kalmeyer-Laughlin state on the torus can be expressed in terms of a correlator
of conformal fields from the $SU(2)_1$ Wess-Zumino-Witten model. This reveals
an interesting underlying mathematical structure and provides a natural way to
generalize the Kalmeyer-Laughlin state to arbitrary lattices on the torus. We
find that the many-body Chern number of the states is unity for more different
lattices, which suggests that the topological properties of the states are
preserved when the lattice is changed. Finally, we analyze the symmetry
properties of the states on square lattices.


  We investigate the tachyon coupling in a static Robertson--Walker like metric
background. For a tachyon and dilaton field which are only time dependent one
can rewrite this model as a SU(2) Wess--Zumino--Witten model and a scalar
Feigin--Fuchs theory. In this case the restriction to a real exponential
tachyon field fixes the level $k$ of the Wess--Zumino--Witten model. For a
spatially dependent tachyon the world radius and the dilaton are quantized in
terms of $k$ and the tachyon by two integers, i.e. one has a discrete set of
fields. The spatial part of the tachyon is given by Chebyshev polynomials of
the second kind. An investigation of the tachyon mass shows that the tachyon is
massless for $k=1$.


  Today, most automated test generators, such as search-based software testing
(SBST) techniques focus on achieving high code coverage. However, high code
coverage is not sufficient to maximise the number of bugs found, especially
when given a limited testing budget. In this paper, we propose an automated
test generation technique that is also guided by the estimated degree of
defectiveness of the source code. Parts of the code that are likely to be more
defective receive more testing budget than the less defective parts. To measure
the degree of defectiveness, we leverage Schwa, a notable defect prediction
technique.
  We implement our approach into EvoSuite, a state of the art SBST tool for
Java. Our experiments on the Defects4J benchmark demonstrate the improved
efficiency of defect prediction guided test generation and confirm our
hypothesis that spending more time budget on likely defective parts increases
the number of bugs found in the same time budget.


  This paper considers the use of novel technologies for mitigating attacks
that aim at compromising intrusion detection systems (IDSs). Solutions based on
collaborative intrusion detection networks (CIDNs) could increase the
resilience against such attacks as they allow IDS nodes to gain knowledge from
each other by sharing information. However, despite the vast research in this
area, trust management issues still pose significant challenges and recent
works investigate whether these could be addressed by relying on blockchain and
related distributed ledger technologies. Towards that direction, the paper
proposes the use of a trust-based blockchain in CIDNs, referred to as
trust-chain, to protect the integrity of the information shared among the CIDN
peers, enhance their accountability, and secure their collaboration by
thwarting insider attacks. A consensus protocol is proposed for CIDNs, which is
a combination of a proof-of-stake and proof-of-work protocols, to enable
collaborative IDS nodes to maintain a reliable and tampered-resistant
trust-chain.


  Iterative voting is a natural model of repeated strategic decision-making in
social choice when agents have the opportunity to update their votes prior to
finalizing the group decision. Prior work has analyzed the efficacy of
iterative plurality on the welfare of the chosen outcome at equilibrium,
relative to the truthful vote profile, via an adaptation of the price of
anarchy. However, prior analyses have only studied the worst- and average-case
performances when agents' preferences are distributed by the impartial culture.
This work extends average-case analysis to a wider class of distributions and
distinguishes when iterative plurality improves or degrades asymptotic welfare.


  Neural text-to-SQL models have achieved remarkable performance in translating
natural language questions into SQL queries. However, recent studies reveal
that text-to-SQL models are vulnerable to task-specific perturbations. Previous
curated robustness test sets usually focus on individual phenomena. In this
paper, we propose a comprehensive robustness benchmark based on Spider, a
cross-domain text-to-SQL benchmark, to diagnose the model robustness. We design
17 perturbations on databases, natural language questions, and SQL queries to
measure the robustness from different angles. In order to collect more
diversified natural question perturbations, we utilize large pretrained
language models (PLMs) to simulate human behaviors in creating natural
questions. We conduct a diagnostic study of the state-of-the-art models on the
robustness set. Experimental results reveal that even the most robust model
suffers from a 14.0% performance drop overall and a 50.7% performance drop on
the most challenging perturbation. We also present a breakdown analysis
regarding text-to-SQL model designs and provide insights for improving model
robustness.


  A group symmetry analysis of the low lying levels of the spin-1/2 kagom\'e
Heisenberg antiferromagnet is performed for small samples up to N=27. This
approach allows to follow the effect of quantum fluctuations when the sample
size increases. The results contradict the scenario of ``order by disorder''
which has been advanced on the basis of large S calculations. A large enough
second neighbor ferromagnetic exchange coupling is needed to stabilize the
$\sqrt 3 \times \sqrt 3$ pattern: the finite size analysis indicates a quantum
critical transition at a non zero coupling.


  Ice nucleation is a phenomenon that, despite the relevant implications for
life, atmospheric sciences, and technological applications, is far from being
completely understood, especially under extreme thermodynamic conditions. In
this work we present a computational investigation of the homogeneous ice
nucleation at negative pressures. By means of the seeding technique we estimate
the size of the ice critical nucleus Nc for the TIP4P/Ice water model. This is
done along the isotherms 230, 240, and 250 K, from positive to negative
pressures until reaching the liquid-gas kinetic stability limit (where
cavitation cannot be avoided). We find that Nc is nonmonotonic upon
depressurization, reaching a minimum at negative pressures in the doubly
metastable region of water. According to classical nucleation theory we
establish the nucleation rate J and the surface tension gamma, revealing a
retracing behavior of both when the liquid-gas kinetic stability limit is
approached. We also predict a reentrant behavior of the homogeneous nucleation
line. The reentrance of these properties is related to the reentrance of the
coexistence line at negative pressure, revealing new anomalies of water. The
results of this work suggest the possibility of having metastable samples of
liquid water for long times at negative pressure provided that heterogeneous
nucleation is suppressed.


  Based on work of Rasmussen, we construct a concordance invariant associated
to the knot Floer complex, and exhibit examples in which this invariant gives
arbitrarily better bounds on the 4-ball genus than the Ozsvath-Szabo tau
invariant.


  We have made a lot of progress in the study of the MW. In spite of this, much
of our Galaxy remains unknown, and amazing breakthroughs await to be made in
the exploration of the far side of the Galaxy. Focussing on the Galactic
extinction horizon problem with current surveys like the Two Micron All-Sky
Survey (2MASS) and the Vista Variables in the Via Lactea Survey (VVV) and its
extension VVVX, the extinction horizon is a fundamental difficulty, and it is
my intention here to reveal how profound is our ignorance, and also to try to
suggest ways for improvement with future near-IR Galactic surveys.


  In this paper we construct a global, continuous flow of solutions to the
Camassa-Holm equation on the entire space $H^1$. Our solutions are
conservative, in the sense that the total energy $\int (u^2+u_x^2) dx$ remains
a.e. constant in time. Our new approach is based on a distance functional
$J(u,v)$, defined in terms of an optimal transportation problem, which
satisfies ${d\over dt} J(u(t), v(t))\leq \kappa\cdot J(u(t),v(t))$ for every
couple of solutions. Using this new distance functional, we can construct
arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a
general uniqueness result.


  Early-type stars generally tend to be fast rotators. In these stars, mode
identification is very challenging as the effects of rotation are not well
known. We consider here the example of $\alpha$ Ophiuchi, for which dozens of
oscillation frequencies have been measured. We model the star using the
two-dimensional structure code ESTER, and we compute both adiabatic and
non-adiabatic oscillations using the TOP code. Both calculations yield very
complex spectra, and we used various diagnostic tools to try and identify the
observed pulsations. While we have not reached a satisfactory mode-to-mode
identification, this paper presents promising early results.


  We explore the possibility that the dynamics of the universe can be
reproduced choosing appropriately the initial global topology of the Universe.
In this work we start with two concentric spherical three-dimensional branes
S^3, with radius a_1<a_2 immersed in a five-dimensional space-time. The novel
feature of this model is that in the interior brane there exist only spin-zero
fundamental fields (scalar fields), while in the exterior one there exist only
spin-one fundamental interactions. As usual, the bulk of the universe is
dominated by gravitational interactions. In this model, like in the Ekpyrotic
one, the Big Bang is consequence of the collision of the branes and causes the
existence of the particles predicted by the standard model in the exterior
brane (our universe). The scalar fields on the interior brane interact with the
spin-one fields on the exterior one only through gravitation, they induce the
effect of Scalar Field Dark Matter with an ultra-light mass on the exterior
one. We discuss two different regimes where the energy density and the brane
tension are compared, with the aim to obtain the observed dynamics of the
universe after the collision of the branes.


  Using similarity transformations we construct explicit solutions of the
nonlinear Schrodinger equation with linear and nonlinear periodic potentials.
We present explicit forms of spatially localized and periodic solutions, and
study their properties. We put our results in the framework of the exploited
perturbation techniques and discuss their implications on the properties of
associated linear periodic potentials and on the possibilities of stabilization
of gap solitons using polychromatic lattices.


  Flares, energetic eruptions on the surfaces of stars, are an unmistakable
manifestation of magnetically driven emission. Their occurrence rates and
energy distributions trace stellar characteristics such as mass and age. But
before flares can be used to constrain stellar properties, the flaring-age-mass
relation requires proper calibration. This work sets out to quantify flaring
activity of independently age-dated main sequence stars for a broad range of
spectral types using optical light curves obtained by the Kepler satellite.
Drawing from the complete K2 archive, we searched 3435 $\sim 80$ day long light
curves of 2111 open cluster members for flares using the open-source software
packages K2SC to remove instrumental and astrophysical variability from K2
light curves, and AltaiPony to search and characterize the flare candidates. We
confirmed a total of 3844 flares on high probability open cluster members with
ages from zero age main sequence (Pleiades) to 3.6 Gyr (M67). We extended the
mass range probed in the first study of this series to span from Sun-like stars
to mid-M dwarfs. We added the Hyades (690 Myr) to the sample as a comparison
cluster to Praesepe (750 Myr), the 2.6 Gyr old Ruprecht 147, and several
hundred light curves from the late K2 Campaigns in the remaining clusters. The
flare energy distribution was similar in the entire parameter space, following
a power law relation with exponent $\alpha\approx 1.84-2.39$. The flaring rates
declined with age, and declined faster for higher mass stars. We found evidence
that a rapid decline in flaring activity occurred in M1-M2 dwarfs around
Hyades/Praesepe age, when these stars spun down to rotation periods of about 10
days, while higher mass stars had already transitioned to lower flaring rates,
and lower mass stars still resided in the saturated activity regime. (abridged)


  A typical formula of multiple zeta values is the sum formula which expresses
a Riemann zeta value as a sum of all multiple zeta values of fixed weight and
depth. Recently weighted sum formulas, which are weighted analogues of the sum
formula, have been studied by many people. In this paper, we give two formulas
of weighted sums with two parameters of multiple zeta values. As applications
of the formulas, we find some linear combinations of multiple zeta values which
can be expressed as polynomials of usual zeta values with coeffcients in the
rational polynomial ring generated by the two parameters, and obtain some
identities for weighted sums of multiple zeta values of small depths.


  Neural personalized recommendation is the corner-stone of a wide collection
of cloud services and products, constituting significant compute demand of the
cloud infrastructure. Thus, improving the execution efficiency of neural
recommendation directly translates into infrastructure capacity saving. In this
paper, we devise a novel end-to-end modeling infrastructure, DeepRecInfra, that
adopts an algorithm and system co-design methodology to custom-design systems
for recommendation use cases. Leveraging the insights from the recommendation
characterization, a new dynamic scheduler, DeepRecSched, is proposed to
maximize latency-bounded throughput by taking into account characteristics of
inference query size and arrival patterns, recommendation model architectures,
and underlying hardware systems. By doing so, system throughput is doubled
across the eight industry-representative recommendation models. Finally,
design, deployment, and evaluation in at-scale production datacenter shows over
30% latency reduction across a wide variety of recommendation models running on
hundreds of machines.


  Lung cancer is the commonest cause of cancer deaths worldwide, and its
mortality can be reduced significantly by performing early diagnosis and
screening. Since the 1960s, driven by the pressing needs to accurately and
effectively interpret the massive volume of chest images generated daily,
computer-assisted diagnosis of pulmonary nodule has opened up new opportunities
to relax the limitation from physicians' subjectivity, experiences and fatigue.
And the fair access to the reliable and affordable computer-assisted diagnosis
will fight the inequalities in incidence and mortality between populations. It
has been witnessed that significant and remarkable advances have been achieved
since the 1980s, and consistent endeavors have been exerted to deal with the
grand challenges on how to accurately detect the pulmonary nodules with high
sensitivity at low false-positives rate as well as on how to precisely
differentiate between benign and malignant nodules. There is a lack of
comprehensive examination of the techniques' development which is evolving the
pulmonary nodules diagnosis from classical approaches to machine
learning-assisted decision support. The main goal of this investigation is to
provide a comprehensive state-of-the-art review of the computer-assisted
nodules detection and benign-malignant classification techniques developed over
3 decades, which have evolved from the complicated ad hoc analysis pipeline of
conventional approaches to the simplified seamlessly integrated deep learning
techniques. This review also identifies challenges and highlights opportunities
for future work in learning models, learning algorithms and enhancement schemes
for bridging current state to future prospect and satisfying future demand.


  Terms like "Science of Cyber" or "Cyber Science" have been appearing in
literature with growing frequency, and influential organizations initiated
research initiatives toward developing such a science even though it is not
clearly defined. We propose to define the domain of the science of cyber
security by noting the most salient artifact within cyber security -- malicious
software -- and defining the domain as comprised of phenomena that involve
malicious software (as well as legitimate software and protocols used
maliciously) used to compel a computing device or a network of computing
devices to perform actions desired by the perpetrator of malicious software
(the attacker) and generally contrary to the intent (the policy) of the
legitimate owner or operator (the defender) of the computing device(s). We
further define the science of cyber security as the study of relations --
preferably expressed as theoretically-grounded models -- between attributes,
structures and dynamics of: violations of cyber security policy; the network of
computing devices under attack; the defenders' tools and techniques; and the
attackers' tools and techniques where malicious software plays the central
role. We offer a simple formalism of these key objects within cyber science and
systematically derive a classification of primary problem classes within cyber
science.


  Single photon detector (SPD) has a maximum count rate due to its dead time,
which results in that the dynamic range of photon counting optical time-domain
reflectometry (PC-OTDR) de-creases with the length of monitored fiber. To
further improve the dynamic range of PC-OTDR, we propose and demonstrate an
externally time-gated scheme. The externally time-gated scheme is realized by
using a high-speed optical switch, i.e. a Mach-Zehnder interferometer, to
modulate the back-propagation optical signal, and to allow that only a certain
segment of the fiber is monitored by the SPD. The feasibility of proposed
scheme is first examined with theoretical analysis and simulation; then we
experimentally demonstrate it with our experimental PC-OTDR testbed operating
at 800 nm wavelength band. In our studies, a dynamic range of 30.0 dB is
achieved in a 70 meters long PC-OTDR system with 50 ns external gates,
corresponding to an improvement of 11.0 dB in dynamic range comparing with no
gating operation. Furthermore, with the improved dynamic range, a successful
identification of a 0.37 dB loss event is detected with 30-seconds
accumulation, which could not be identified without gating operation. Our
scheme paves an avenue for developing PC-OTDR systems with high dynamic range.


  A fundamental problem in robust learning is asymmetry: a learner needs to
correctly classify every one of exponentially-many perturbations that an
adversary might make to a test-time natural example. In contrast, the attacker
only needs to find one successful perturbation. Xiang et al.[2022] proposed an
algorithm that in the context of patch attacks for image classification,
reduces the effective number of perturbations from an exponential to a
polynomial number of perturbations and learns using an ERM oracle. However, to
achieve its guarantee, their algorithm requires the natural examples to be
robustly realizable. This prompts the natural question; can we extend their
approach to the non-robustly-realizable case where there is no classifier with
zero robust error?
  Our first contribution is to answer this question affirmatively by reducing
this problem to a setting in which an algorithm proposed by Feige et al.[2015]
can be applied, and in the process extend their guarantees. Next, we extend our
results to a multi-group setting and introduce a novel agnostic multi-robust
learning problem where the goal is to learn a predictor that achieves low
robust loss on a (potentially) rich collection of subgroups.


  The top-Higgs coupling plays an important role in particle physics and
cosmology. The precision measurements of this coupling can provide an insight
to new physics beyond the Standard Model. In this paper, we propose to use
Message Passing Neural Network (MPNN) to reveal the CP nature of top-Higgs
interaction through semi-leptonic channel $pp \to t(\to
b\ell^-\nu_\ell)\bar{t}(\to \bar{b}jj)h(\to b\bar{b})$. Using the test
statistics constructed from the event classification probabilities given by the
MPNN, we find that the pure CP-even and CP-odd components can be well
distinguished at the LHC, with at most 300 fb$^{-1}$ experimental data.


  The century of complexity has come. The face of science has changed.
Surprisingly, when we start asking about the essence of these changes and then
critically analyse the answers, the result are mostly discouraging. Most of the
answers are related to the properties that have been in the focus of scientific
research already for more than a century (like non-linearity). This paper is
Preface to the special issue "Grasping Complexity" of the journal "Computers
and Mathematics with Applications". We analyse the change of era in science,
its reasons and main changes in scientific activity and give a brief review of
the papers in the issue.


  The Extended Chandra Deep Field-South (E-CDF-S) survey consists of 4 Chandra
ACIS-I pointings and covers ~1100 square arcminutes (~0.3 deg^2) centered on
the original CDF-S field to a depth of approximately 228 ks (PI: Niel Brandt;
Lehmer et al, 2005). This is the largest Chandra survey ever conducted at such
depth. In our analysis (Virani et al, 2005), we detect 651 unique sources --
587 using a conservative source detection limit and 64 using a lower source
detection limit. Of these 651 sources, 561 are detected in the full 0.5--8.0
keV band, 529 in the soft 0.5--2.0 keV band, and 335 in the hard 2.0--8.0 keV
band. For point sources near the aim point, the limiting fluxes are
approximately $1.7 \times 10^{-16}$ $\rm{erg cm^{-2} s^{-1}}$ and $3.9 \times
10^{-16}$ $\rm{erg cm^{-2} s^{-1}}$ in the 0.5--2.0 keV and 2.0--8.0 keV bands,
respectively. We present the optical properties of these X-ray sources,
specifically the R-band magnitude distribution and a preliminary spectroscopic
redshift distribution. One exciting result is the discovery of 7 new Extreme
X-ray-to-Optical flux ratio objects (EXOs) found in the E-CDF-S field.


  A wave energy converter (WEC) similar to the CETO system developed by
Carnegie Clean Energy is considered for design optimisation. This WEC is able
to absorb power from heave, surge and pitch motion modes, making the
optimisation problem nontrivial. The WEC dynamics is simulated using the
spectral-domain model taking into account hydrodynamic forces, viscous drag,
and power take-off forces. The design parameters for optimisation include the
buoy radius, buoy height, tether inclination angles, and control variables
(damping and stiffness). The WEC design is optimised for the wave climate at
Albany test site in Western Australia considering unidirectional irregular
waves. Two objective functions are considered: (i) maximisation of the annual
average power output, and (ii) minimisation of the levelised cost of energy
(LCoE) for a given sea site. The LCoE calculation is approximated as a ratio of
the produced energy to the significant mass of the system that includes the
mass of the buoy and anchor system. Six different heuristic optimisation
methods are applied in order to evaluate and compare the performance of the
best known evolutionary algorithms, a swarm intelligence technique and a
numerical optimisation approach. The results demonstrate that if we are
interested in maximising energy production without taking into account the cost
of manufacturing such a system, the buoy should be built as large as possible
(20 m radius and 30 m height). However, if we want the system that produces
cheap energy, then the radius of the buoy should be approximately 11-14~m while
the height should be as low as possible. These results coincide with the
overall design that Carnegie Clean Energy has selected for its CETO 6
multi-moored unit. However, it should be noted that this study is not informed
by them, so this can be seen as an independent validation of the design
choices.


  Lepton flavor violating processes $\mu \to e \gamma$ and $\mu \to 3e$ with
polarized muons are studied in the supersymmetric grand unified theory (SUSY
GUT). As a result of a detailed numerical calculation, it is shown that the P-
and T-odd asymmetries defined with the help of the muon polarization and the
ratio of two branching fractions make a good contrast between the SU(5) and
SO(10) SUSY GUT. These observables are useful to extract differences of the two
theories. In particular, the P-odd asymmetry of $\mu \to e \gamma$ varies
100%--100% in SO(10) whereas it is 100% in SU(5) and the T-odd asymmetry of
$\mu \to 3e$ can reach 15% in SU(5) within the EDM constraints whereas it is
small in SO(10).


  We consider the effect of thermal fluctuations on rotating spinor F=1
condensates in axially-symmetric vortex phases, when all the three hyperfine
states are populated. We show that the relative phase among different
components of the order parameter can fluctuate strongly due to the weakness of
the interaction in the spin channel. These fluctuations can be significant even
at low temperatures. Fluctuations of relative phase lead to significant
fluctuations of the local transverse magnetization of the condensate. We
demonstrate that these fluctuations are much more pronounced for the
antiferromagnetic state than for the ferromagnetic one.


  Hybrid transceivers are designed for linear decentralized estimation (LDE) in
a mmWave multiple-input multiple-output (MIMO) IoT network (IoTNe). For a
noiseless fusion center (FC), it is demonstrated that the MSE performance is
determined by the number of RF chains used at each IoT node (IoTNo). Next, the
minimum-MSE RF transmit precoders (TPCs) and receive combiner (RC) matrices are
designed for this setup using the dominant array response vectors, and
subsequently, a closed-form expression is obtained for the baseband (BB) TPC at
each IoTNo using Cauchy's interlacing theorem. For a realistic noisy FC, it is
shown that the resultant mean squared error (MSE) minimization problem is
non-convex. To address this challenge, a block-coordinate descent-based
iterative scheme is proposed to obtain the fully digital TPC and RC matrices
followed by the simultaneous orthogonal matching pursuit (SOMP) technique for
decomposing the fully-digital transceiver into its corresponding RF and BB
components. A theoretical proof of the convergence is also presented for the
proposed iterative design procedure. Furthermore, robust hybrid transceiver
designs are also derived for a practical scenario in the face of channel state
information (CSI) uncertainty. The centralized MMSE lower bound has also been
derived that benchmarks the performance of the proposed LDE schemes. Finally,
our numerical results characterize the performance of the proposed transceivers
as well as corroborate our various analytical propositions.


  We analyze populations of Kuramoto oscillators with a particular distribution
of natural frequencies. Inspired by networks where there are two groups of
nodes with opposite behaviors, as for instance in power-grids where energy is
either generated or consumed at different locations, we assume that the
frequencies can take only two different values. Correlations between the value
of the frequency of a given node and its topological localization are
considered in both regular and random topologies. Synchronization is enhanced
when nodes are surrounded by nodes of the opposite frequency. We find
analytical estimations for the minimum value of the coupling strength between
oscillators that guarantees the achievement of a globally synchronized state,
getting a very good agreement with the numerical simulations.


  The plurigaussian model is particularly suited to describe categorical
regionalized variables. Starting from a simple principle, the thresh-olding of
one or several Gaussian random fields (GRFs) to obtain categories, the
plurigaussian model is well adapted for a wide range ofsituations. By acting on
the form of the thresholding rule and/or the threshold values (which can vary
along space) and the variograms ofthe underlying GRFs, one can generate many
spatial configurations for the categorical variables. One difficulty is to
choose variogrammodel for the underlying GRFs. Indeed, these latter are hidden
by the truncation and we only observe the simple and cross-variogramsof the
category indicators. In this paper, we propose a semiparametric method based on
the pairwise likelihood to estimate the empiricalvariogram of the GRFs. It
provides an exploratory tool in order to choose a suitable model for each GRF
and later to estimate its param-eters. We illustrate the efficiency of the
method with a Monte-Carlo simulation study .The method presented in this paper
is implemented in the R packageRGeostats.


  We derive the Whitham modulation equations for the Zakharov-Kuznetsov
equation via a multiple scales expansion and averaging two conservation laws
over one oscillation period of its periodic traveling wave solutions. We then
use the Whitham modulation equations to study the transverse stability of the
periodic traveling wave solutions. We find that all such solutions are linearly
unstable, and we obtain an explicit expression for the growth rate of the most
unstable wave numbers. We validate these predictions by linearizing the
equation around its periodic solutions and solving the resulting eigenvalue
problem numerically. Finally, we calculate the growth rate of the solitary
waves analytically. The predictions of Whitham modulation theory are in
excellent agreement with both of these approaches.


  All-optical active plasmonic devices are of fundamental importance for
designing efficient nanophotonic circuits. We theoretically propose and
numerically investigate an active plasmonic device made up of a nonlinear
epsilon-near-zero metamaterial slab of thickness smaller than 100 nanometers
lying on a linear epsilon-near-zero metamaterial substrate. We predict that, in
free-space coupling configuration, the device, operating at low-intensity,
would display plasmon mediated hysteresis behavior since the phase difference
between the reflected and the incident optical waves turns out to be
multi-valued and dependent on the history of the excitation process. Such an
hysteresis behavior would allow to regard the proposed device as a compact
memory unit whose state is accessible by measuring either the mentioned phase
difference or the power, which is multi-valued as well, carried by the
nonlinear plasmon wave. Since multiple plasmon powers comprise both positive
and negative values, the device would also operate as a switch of the plasmon
power direction at each jump along an hysteresis loop.


  The quantum S=1 spin model on the spatially anisotropic triangular lattice is
investigated numerically. The nematic and valence-bond-solid (VBS) phases are
realized by adjusting the spatial anisotropy and the biquadratic interaction.
The phase transition between the nematic and VBS phases is expected to be a
continuous one with unconventional critical indices (deconfined criticality).
The geometrical character (spatial anisotropy) is taken into account by
imposing the screw-boundary condition (Novotny's method). Diagonalizing the
finite-size cluster with N \le 20 spins, we observe a clear indication of
continuous phase transition. The correlation-length critical exponent is
estimated as \nu=0.92(10).


  Using propagating surface plasmons (SPs) on silver nanowire (NW), we
demonstrate that focused laser light at the end of silver nanowire can excite
single quantum dot (QD) microns away from the excitation spot. The QD-NW
interaction allows the excited QD convert part of its energy into propagating
SPs which then can be detected at the remote sites. Simultaneous multi-QDs
remote-excitation and detection are also realized. Furthermore, the tight
confinement of propagating SPs around the NW surface enables selective
excitation of QDs very close in space, which cannot be realized under
conventional excitation condition. This remote excitation and detection
approach may find applications in optical imaging and sensing of chemical and
biological systems.


  This note presents a descending method that allows us to classify quotients
of Reed-Muller codes of lenghth 128 under the action of the affine general
linear group.


  We analyze a gradient flow of closed planar curves minimizing the
anisoperimetric ratio. For such a flow the normal velocity is a function of the
anisotropic curvature and it also depends on the total interfacial energy and
enclosed area of the curve. In contrast to the gradient flow for the
isoperimetric ratio, we show there exist initial curves for which the enclosed
area is decreasing with respect to time. We also derive a mixed anisoperimetric
inequality for the product of total interfacial energies corresponding to
different anisotropy functions. Finally, we present several computational
examples illustrating theoretical results.


  Test-time adaptation (TTA) addresses the unforeseen distribution shifts
occurring during test time. In TTA, performance, memory consumption, and time
consumption are crucial considerations. A recent diffusion-based TTA approach
for restoring corrupted images involves image-level updates. However, using
pixel space diffusion significantly increases resource requirements compared to
conventional model updating TTA approaches, revealing limitations as a TTA
method. To address this, we propose a novel TTA method that leverages an image
editing model based on a latent diffusion model (LDM) and fine-tunes it using
our newly introduced corruption modeling scheme. This scheme enhances the
robustness of the diffusion model against distribution shifts by creating
(clean, corrupted) image pairs and fine-tuning the model to edit corrupted
images into clean ones. Moreover, we introduce a distilled variant to
accelerate the model for corruption editing using only 4 network function
evaluations (NFEs). We extensively validated our method across various
architectures and datasets including image and video domains. Our model
achieves the best performance with a 100 times faster runtime than that of a
diffusion-based baseline. Furthermore, it is three times faster than the
previous model updating TTA method that utilizes data augmentation, making an
image-level updating approach more feasible.


  In 2005 Kane & Mele[C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801
(2005)], predicted that at sufficiently low energy, graphene exhibits a
topological state of matter with an energy gap generated by the atomic
spin-orbit interaction. However, this intrinsic gap has not been measured to
this date. In this letter, we exploit the chirality of the low energy states to
resolve this gap. We probe the spin states experimentally, by employing low
temperature microwave excitation in a resistively detected electron spin
resonance on graphene. The structure of the topological bands is reflected in
our transport experiments, where our numerical models allow us to identify the
resonance signatures. We determine the intrinsic spin-orbit bulk gap to be
exactly 42.2 {\mu}eV. Electron-spin resonance experiments can reveal the
competition between the intrinsic spin-orbit coupling and classical Zeeman
energy that arises at low magnetic fields and demonstrate that graphene remains
to be a material with surprising properties.


  A global nucleon-nucleus optical potential for elastic scattering has been
produced which replicates experimental data to high accuracy and compares well
with other recently formulated potentials. The calculation that has been
developed describes proton and neutron scattering from target nuclei ranging
from carbon to nickel and is applicable for projectile energies from 30 to 160
MeV. With these ranges it is suitable for calculations associated with
experiments performed by exotic beam accelerators. The potential is also
isospin dependent and has both real and imaginary isovector asymmetry terms to
better describe the dynamics of chains of isotopes and mirror nuclei. An
analysis of the validity and strength of the asymmetry term is included with
connections established to other optical potentials and charge-exchange
reaction data. An on-line observable calculator is available for this optical
potential.


  In this work we give two new algorithms that use similar techniques for
(non-monotone) submodular function maximization subject to a cardinality
constraint.
  The first is an offline fixed parameter tractable algorithm that guarantees a
$0.539$-approximation for all non-negative submodular functions.
  The second algorithm works in the random-order streaming model. It guarantees
a $(1/2+c)$-approximation for symmetric functions, and we complement it by
showing that no space-efficient algorithm can beat $1/2$ for asymmetric
functions. To the best of our knowledge this is the first provable separation
between symmetric and asymmetric submodular function maximization.


  A general approach to the analysis of optical properties of photonic crystals
based on multiple-quantum-well structures is developed. The effect of the
polarization state and a non-perpendicular incidence of the electromagnetic
wave is taken into account by introduction of an effective excitonic
susceptibility and an effective optical width of the quantum wells. This
approach is applied to consideration of optical properties of structures with a
pre-engineered break of the translational symmetry. It is shown, in particular,
that a layer with different exciton frequency placed at the middle of an MQW
structure leads to appearance of a resonance suppression of the reflection.


  There have been some issues in the past in attempts to simulate magnetic
fields using the Smoothed Particle Hydrodynamics (SPH) method. SPH is well
suited to star formation problems because of its Lagrangian nature. We present
new, stable and conservative methods for magnetohydrodynamics (MHD) in SPH and
present numerical tests on both waves and shocks in one dimension to show that
it gives robust and accurate results.


  The large N limit of D3-branes is expected to correspond to a superconformal
field theory living on the boundary of the anti-de Sitter space appearing in
the near-horizon geometry. Dualizing the D3-brane to a D-instanton, we show
that this limit is equivalent to a type IIB S-duality. In both cases one
effectively reaches the near-horizon geometry. This provides an alternative
approach to an earlier derivation of the same result that makes use of the
properties of a gravitational wave instead of the D-instanton.


  We show that the recent comment by D. Gorokhov, is based on physically
obvious errors and misunderstandings of the content of the criticized papers
and is readily refuted. We show that 1) In our paper [1] there were considered
situations of both strong and weak interband coupling regimes. 2) In the ref
[1] it was given a wide range of physical systems with Josephson coupling
strength ranging from being very strong to being exactly zero on symmetry
grounds. 3) While the ref [1] is not a phenomenological study of $MgB_2$, the
moderately strong Josephson coupling results of [1] apply to $MgB_2$: the
described in [1] double-core vortices have been recently observed in $MgB_2$.


  A covariant gauge independent derivation of the generalized dispersion
relation of electromagnetic waves in a medium with local and linear
constitutive law is presented. A generalized photon propagator is derived. For
Maxwell constitutive tensor, the standard light cone structure and the standard
Feynman propagator are reinstated.


  We study properties of the thermal transition in QCD, using anisotropic,
fixed-scale lattice simulations with $N_f = 2+1$ flavours of Wilson fermion.
Observables are compared for two values of the pion mass, focusing on chiral
properties. Results are presented for the Polyakov loop, various
susceptibilities, the chiral condensate and its susceptibility, and the onset
of parity doubling in the light and strange baryonic sector.


  In this work, we show that the traditional effective field approach can be
applied to the $\mathcal{PT}$-symmetric wrong sign ($-x^{4}$) quartic
potential. The importance of this work lies in the possibility of its extension
to the more important $\mathcal{PT}$-symmetric quantum field theory while the
other approaches which use complex contours are not willing to be applicable.
We calculated the effective potential of the massless $-x^{4}$ theory as well
as the full spectrum of the theory. Although the calculations are carried out
up to first order in the coupling, the predicted spectrum is very close to the
exact one taken from other works. The most important result of this work is
that the effective potential obtained, which is equivalent to the Gaussian
effective potential, is bounded from below while the classical potential is
bounded from above. This explains the stability of the vacuum of the theory.
The obtained quasi-particle Hamiltonian is non-Hermitian but
$\mathcal{PT}$-symmetric and we showed that the calculation of the metric
operator can go perturbatively. In fact, the calculation of the metric operator
can be done even for higher dimensions (quantum field theory) which, up till
now, can not be calculated in the other approaches either perturbatively or in
a closed form due to the possible appearance of field radicals. Moreover, we
argued that the effective theory is perturbative for the whole range of the
coupling constant and the perturbation series is expected to converge rapidly
(the effective coupling $g_{eff}={1/6}$).


  We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo
algorithm, for efficient inference in statistical models involving
high-dimensional discrete state spaces. The sampling scheme uses an auxiliary
variable construction that adaptively truncates the model space allowing
iterative exploration of the full model space in polynomial time. The approach
generalizes conventional Gibbs sampling schemes for discrete spaces and can be
considered as a Big Data-enabled MCMC algorithm that provides an intuitive
means for user-controlled balance between statistical efficiency and
computational tractability. We illustrate the generic utility of our sampling
algorithm through application to a range of statistical models.


  A comprehensive description in all dimensions is provided for the scaling
exponent $y$ of low-energy excitations in the Ising spin glass introduced by
Edwards and Anderson. A combination of extensive numerical as well as
theoretical results suggest that its lower critical dimension is {\it exactly}
$d_l=5/2$. Such a result would be an essential feature of any complete model of
low-temperature spin glass order and imposes a constraint that may help to
distinguish between theories.


  The energy of gravitational waves is a fundamental problem in gravity theory.
The existing descriptions for the energy of gravitational waves, such as the
well-known Isaacson energy-momentum tensor, suffer from several defects. Due to
the equivalence principle, the gravitational energy-momentum can only be
defined quasilocally, being associated with a closed spacelike 2-surface
bounding a region. We propose a new approach to derive the energy of
gravitational waves $directly$ from the quasilocal gravitational energy. Such
an approach is natural and consistent with the quasilocality of gravitational
energy-momentum.


  Runtime-reconfigurable software coupled with reconfigurable hardware is
highly desirable as a means towards maximizing runtime efficiency without
compromising programmability. Compilers for such software systems are extremely
difficult to design as they must leverage different types of hardware at
runtime. To address the need for static and dynamic compiler optimization of
workflows matched to dynamically reconfigurable hardware, we propose a novel
design of the central component of a dynamic software compiler for software
defined hardware. Our comprehensive design focuses not just on static knowledge
but also on semi-supervised extraction of knowledge from program executions and
developing their performance models. Specifically, our novel {\it dynamic and
extensible knowledge base} 1) continuously gathers knowledge during execution
of workflows 2) identifies {\it optimal} implementations of workflows on {\it
optimal} (available) hardware configurations. It plays a hub role in storing
information from, and providing information to other components of the
compiler, as well as the human analyst. Through a rich tripartite graph
representation, the knowledge base captures and learns extensive information on
decomposition and mapping of code steps to kernels and mapping of kernels to
available hardware configurations. The knowledge base is implemented using the
C++ Boost Library and is capable of quickly processing offline and online
queries and updates. We show that our knowledge base can answer queries in
$1ms$ regardless of the number of workflows it stores. To the best of our
knowledge, this is the first design of a dynamic and extensible knowledge base
to support compilation of high-level languages to leverage arbitrary
reconfigurable platforms.


  This paper introduces CINNAMON, a software module that extends and seamlessly
integrates with the AUTOSAR "Secure Onboard Communication" (SecOC) module to
also account for confidentiality of data in transit. It stands for
Confidential, INtegral aNd Authentic on board coMunicatiON (CINNAMON). It takes
a resource-efficient and practical approach to ensure, at the same time,
confidentiality, integrity and authenticity of frames. The main new requirement
that CINNAMON puts forward is the use of encryption and thus, as a result,
CINNAMON exceeds SecOC against information gathering attacks. This paper sets
forth the essential requirements and specification of the new module by
detailing where and how to position it within AUTOSAR and by emphasizing the
relevant upgrades with respect to SecOC. The presentation continues with the
definition of a Security Profile and a summary of a prototype implementation of
ours. While CINNAMON is easily extensible, for example through the definition
of additional profiles, the current performances obtained on inexpensive boards
support the claim that the approach is feasible.


  We establish the finiteness of periodic points, that we called Geometric
Dynamical Northcott Property, for regular polynomials automorphisms of the
affine plane over a function field $\mathbf{K}$ of characteristic zero,
improving results of Ingram.
  For that, we show that when $\mathbf{K}$ is the field of rational functions
of a smooth complex projective curve, the canonical height of a subvariety is
the mass of an appropriate bifurcation current and that a marked point is
stable if and only if its canonical height is zero. We then establish the
Geometric Dynamical Northcott Property using a similarity argument.


  We identify field theories that describe the surfaces of three-dimensional
bosonic point group symmetry protected topological (pgSPT) phases. The
anomalous nature of the surface field theories is revealed via a dimensional
reduction argument. Specifically, we study three different surface field
theories. The first field theory is quantum electrodynamics in three space-time
dimensions (QED3) with four flavors of fermions. We show this theory can
describe the surfaces of a majority of bosonic pgSPT phases protected by a
single mirror reflection, or by $C_{nv}$ point group symmetry for $n=2,3,4,6$.
The second field theory is a variant of QED3 with charge-1 and charge-3 Dirac
fermions. This field theory can describe the surface of a reflection symmetric
pgSPT phase built by placing an $E_{8}$ state on the mirror plane. The third
field theory is an ${\rm O}(4)$ non-linear sigma model with a topological
theta-term at $\theta=\pi$, or, equivalently, a non-compact ${\rm CP}^1$ model.
Using a coupled wire construction, we show this is a surface theory for bosonic
pgSPT phases with ${\rm U}(1) \times \mathbb{Z}_{2}^{P}$ symmetry. For the
latter two field theories, we discuss the connection to gapped surfaces with
topological order. Moreover, we conjecture that the latter two field theories
can describe surfaces of more general bosonic pgSPT phases with $C_{nv}$ point
group symmetry.


  In this note we present a construction of an infinite family of diagonal
quintic threefolds defined over $\Q$ each containing infinitely many rational
points. As an application, we prove that there are infinitely many quadruples
$B=(B_{0}, B_{1}, B_{2}, B_{3})$ of co-prime integers such that for a suitable
chosen integer $b$ (depending on $B$), the equation
$B_{0}X_{0}^5+B_{1}X_{1}^5+B_{2}X_{2}^5+B_{3}X_{3}^{5}=b$ has infinitely many
positive integer solutions.


  Clustering procedures typically estimate which data points are clustered
together, a quantity of primary importance in many analyses. Often used as a
preliminary step for dimensionality reduction or to facilitate interpretation,
finding robust and stable clusters is often crucial for appropriate for
downstream analysis. In the present work, we consider Bayesian nonparametric
(BNP) models, a particularly popular set of Bayesian models for clustering due
to their flexibility. Because of its complexity, the Bayesian posterior often
cannot be computed exactly, and approximations must be employed. Mean-field
variational Bayes forms a posterior approximation by solving an optimization
problem and is widely used due to its speed. An exact BNP posterior might vary
dramatically when presented with different data. As such, stability and
robustness of the clustering should be assessed.
  A popular mean to assess stability is to apply the bootstrap by resampling
the data, and rerun the clustering for each simulated data set. The time cost
is thus often very expensive, especially for the sort of exploratory analysis
where clustering is typically used. We propose to use a fast and automatic
approximation to the full bootstrap called the "linear bootstrap", which can be
seen by local data perturbation. In this work, we demonstrate how to apply this
idea to a data analysis pipeline, consisting of an MFVB approximation to a BNP
clustering posterior of time course gene expression data. We show that using
auto-differentiation tools, the necessary calculations can be done
automatically, and that the linear bootstrap is a fast but approximate
alternative to the bootstrap.


  The present study investigates the insecticidal and herbicidal effects of
leaf extracts from two plants were harvested in the Northern Algerian Sahara.
These are Cleome arabica (Capparaceae) and Pergularia tomentosa
(Asclepiadaceae). The efficacy of the extracts from the plants was evaluated by
the reflux extraction method. The phytochemical screening of the aqueous
extracts of C. arabica shows a remarkable richness in active principles in
comparison with the extract of P. tomentosa; including flavonoids, saponosides,
glycosides, terpenes, sterols, deoxyose, polyphenols and total alkaloids. The
imago of Tribolium confusum treated with aqueous extracts of C. arabica and P.
tomentosa at doses of 80% to 100% respectively have mortality rates of 73.33%
to 96.67%, and 36.67% to 86.67%. The lethal time 50 (TL50%) of the aqueous
extract of C. arabica was estimated about 6.41 days, and 6.94 days for the
extract P. tomentosa for the imago of T. confusum. The extracts of P. tomentosa
is less toxic than the extracts of C. arabica. The allelopathic potentials of
C. arabica and P. tomentosa tested on germination of the seeds of a weed
Dactyloctenium aegyptium (Poaceae) and two cultivated species, including
Hordeumvulgare and Triticumdurum (Poaceae), show that the inhibitory effect of
extracts of C. arabica is very highly significant. It manifests itself in the
growth of the aerial and underground part of the H. vulgar and T. durum. The
inhibition rate is more than 84.44% for D. aegyptium seeds treated with the
different concentrations. The inhibition rates range from 75.56% to 91.11% for
T. durum wheat irrigate at 80% to 100%, but are only 55.56% to 77.78% for
barley seeds treated with the same concentrations (80% to 100%).


  The ever increasing complexity of machine learning techniques used more and
more in practice, gives rise to the need to explain the predictions and
decisions of these models, often used as black-boxes. Explainable AI approaches
are either numerical feature-based aiming to quantify the contribution of each
feature in a prediction or symbolic providing certain forms of symbolic
explanations such as counterfactuals. This paper proposes a generic agnostic
approach named ASTERYX allowing to generate both symbolic explanations and
score-based ones. Our approach is declarative and it is based on the encoding
of the model to be explained in an equivalent symbolic representation, this
latter serves to generate in particular two types of symbolic explanations
which are sufficient reasons and counterfactuals. We then associate scores
reflecting the relevance of the explanations and the features w.r.t to some
properties. Our experimental results show the feasibility of the proposed
approach and its effectiveness in providing symbolic and score-based
explanations.


  In this work, we present limits on natural supersymmetry scenarios based on
searches in data taken during run 1 of the LHC. We consider a set of 22000
model points in a six dimensional parameter space. These scenarios are minimal
in the sense of only keeping those superparticles relatively light that are
required to cancel the leading quadratically divergent quantum corrections
(from the top and QCD sector) to the Higgs mass in the Standard Model. The
resulting mass spectra feature higgsinos as the lightest supersymmetric
particle, as well as relatively light third generation $SU(2)$ doublet squarks
and $SU(2)$ singlet stops and gluinos while assuming a Standard Model like
Higgs boson. All remaining supersymmetric particles and Higgs bosons are
assumed to be decoupled. We check each parameter set against a large number of
LHC searches as implemented in the public code {\tt CheckMATE}. These searches
show a considerable degree of complementarity, i.e. in general many searches
have to be considered in order to check whether a given scenario is allowed. We
delineate allowed and excluded regions in parameter space. For example, we find
that all scenarios where either $m_{\tilde t_1} < 230$ GeV or $m_{\tilde g} <
440$ GeV are clearly excluded, while all model points where $m_{\tilde t_1} >
660$ GeV and $m_{\tilde g} > 1180$ GeV remain allowed.


  Amidst the growing importance of hydrogen in a sustainable future, it is
crucial to develop coatings that can protect hydrogen-sensitive system
components in reactive hydrogen environments. However, the prediction of the
chemical stability of materials in hydrogen is not fully understood. In this
study, we show that the work function is a key parameter determining the
reducibility (i.e., de-nitridation) of transition metal nitrides (TMNs) in
hydrogen radicals (H*) at elevated temperatures. We demonstrate that when the
work function of a TMN system drops below a threshold limit, its reduction
effectively stops. We propose that this is due to the preferential binding of
H* to TM-atoms rather than N-atoms, which makes the formation of volatile
species (NHx) unfavourable. This finding provides a novel perspective for
comprehending the interaction of hydrogen with transition metal compounds and
allows predicting the chemical stability of hydrogen-protective coatings.


  Remote sensing (RS) images are important to monitor and survey earth at
varying spatial scales. Continuous observations from various RS sources
complement single observations to improve applications. Fusion into single or
multiple images provides more informative, accurate, complete, and coherent
data. Studies intensively investigated spatial-temporal fusion for specific
applications like pan-sharpening and spatial-temporal fusion for time-series
analysis. Fusion methods can process different images, modalities, and tasks
and are expected to be robust and adaptive to various types of images (e.g.,
spectral images, classification maps, and elevation maps) and scene
complexities. This work presents solutions to improve existing fusion methods
that process gridded data and consider their type-specific uncertainties. The
contributions include: 1) A spatial-temporal filter that addresses spectral
heterogeneity of multitemporal images. 2) 3D iterative spatiotemporal filter
that enhances spatiotemporal inconsistencies of classification maps. 3)
Adaptive semantic-guided fusion that enhances the accuracy of DSMs and compares
them with traditional fusion approaches to show the significance of adaptive
methods. 4) A comprehensive analysis of DL stereo matching methods against
traditional Census-SGM to obtain detailed knowledge on the accuracy of the DSMs
at the stereo matching level. We analyze the overall performance, robustness,
and generalization capability, which helps identify the limitations of current
DSM generation methods. 5) Based on previous analysis, we develop a novel
finetuning strategy to enhance transferability of DL stereo matching methods,
hence, the accuracy of DSMs. Our work shows the importance of spatial,
temporal, and geometric fusion in enhancing RS applications. It shows that the
fusion problem is case-specific and depends on the image type, scene content,
and application.