  As additivity is a characteristic property of the classical information
measure, Shannon entropy, pseudo-additivity is a characteristic property of
Tsallis entropy. Renyi generalized Shannon entropy by means of
Kolmogorov-Nagumo averages, by imposing additivity as a constraint.In this
paper we show that there exists no generalization for Tsallis entropy, by means
of Kolmogorov-Nagumo averages, which preserves the pseudo-additivity.


  This thesis is concerned with deriving planning algorithms for robot
manipulators. Manipulation has two effects, the robot has a physical effect on
the object, and it also acquires information about the object. This thesis
presents algorithms that treat both problems. First, I present an extension of
the well-known piano mover's problem where a robot pushing an object must plan
its movements as well as those of the object. This requires simultaneous
planning in the joint space of the robot and the configuration space of the
object, in contrast to the original problem which only requires planning in the
latter space. The effects of a robot action on the object configuration are
determined by the non-invertible rigid body mechanics. Second, I consider
planning under uncertainty and in particular planning for information effects.
I consider the case where a robot has to reach and grasp an object under pose
uncertainty caused by shape incompleteness. The approach presented in this
report is to study and possibly extend a new approach to artificial
intelligence (A.I.) which has emerged in the last years in response to the
necessity of building intelligent controllers for agents operating in
unstructured stochastic environments. Such agents require the ability to learn
by interaction with its environment an optimal action-selection behaviour. The
main issue is that real-world problems are usually dynamic and unpredictable.
Thus, the agent needs to update constantly its current image of the world using
its sensors, which provide only a noisy description of the surrounding
environment. Although there are different schools of thinking, with their own
set of techniques, a brand new direction which unifies many A.I. researches is
to formalise such agent/environment interactions as embedded systems with
stochastic dynamics.


  Given 2 points of a smooth hypersurface, their mid-hyperplane is the
hyperplane passing through their mid-point and the intersection of their
tangent spaces. In this paper we study the envelope of these mid-hyperplanes
(EMH) at pairs whose tangent spaces are transversal. We prove that this
envelope consists of centers of conics having contact of order at least 3 with
the hypersurface at both points. Moreover, we describe general conditions for
the EMH to be a smooth hypersurface. These results are extensions of the
corresponding well-known results for curves. In the case of curves, if the EMH
is contained in a straight line, the curve is necessarily affinely symmetric
with respect to the line. We show through a counter-example that this property
does not hold for hypersurfaces.


  We introduce quantum optical dipole radiation fields defined in terms of
photon creation and annihilation operators. These fields are identified through
their spatial dependence, as the components of the total fields that survive
infinitely far from the dipole source. We use these radiation fields to
perturbatively evaluate the electromagnetic radiated energy-flux of the excited
dipole. Our results indicate that the standard interpretation of a bare atom
surrounded by a localised virtual photon cloud, is difficult to sustain,
because the radiated energy-flux surviving infinitely far from the source
contains virtual contributions. It follows that there is a clear distinction to
be made between a radiative photon defined in terms of the radiation fields,
and a real photon, whose identification depends on whether or not a given
process conserves the free energy. This free energy is represented by the
difference between the total dipole-field Hamiltonian and its interaction
component.


  In this paper, we consider signal interpolation of discrete-time signals
which are decimated nonuniformly. A conventional interpolation method is based
on the sampling theorem, and the resulting system consists of an ideal filter
with complex-valued coefficients. While the conventional method assumes band
limitation of signals, we propose a new method by sampled-data H-infinity
optimization. By this method, we can remove the band-limiting assumption and
the optimal filter can be with real-valued coefficients. Moreover, we show that
without band-limited assumption, there can be the optimal decimation patterns
among ones with the same ratio. By examples, we show the effectiveness of our
method.


  This contribution analyzes the COVID-19 outbreak by comparably simple
mathematical and numerical methods. The final goal is to predict the peak of
the epidemic outbreak per country with a reliable technique. This is done by an
algorithm motivated by standard SIR models and aligned with the standard data
provided by the Johns Hopkins University. To reconstruct data for the
unregistered Infected, the algorithm uses current values of the infection
fatality rate and a data-driven estimation of a specific form of the recovery
rate. All other ingredients are data-driven as well. Various examples of
predictions are provided for illustration.


  In the paper we generalize the following characterization of beta
distribution to the symmetric cone setting: let $X$ and $Y$ be independent,
non-degenerate random variables with values in $(0,1)$, then $U=1-XY$ and
$V=\frac{1-X}{U}$ are independent if and only if there exist positive numbers
$p_i$, $i=1,2,3$, such that $X$ and $Y$ follow beta distributions with
parameters $(p_1+p_3,p_2)$ and $(p_3,p_1)$, respectively.


  The quasi-skutterudite superconductor La$_3$Co$_4$Sn$_{13}$ undergoes a phase
transition at $T^*=152$ K. By measuring the temperature dependence of heat
capacity, electrical resistivity, and the superlattice reflection intensity
using X-ray, we explore the character of the phase transition at $T^*$. Our
lattice dynamic calculations found imaginary phonon frequencies around the
${\bf M}$ point, when the high temperature structure is used in the
calculations, indicating that the structure is unstable at the zero temperature
limit. The combined experimental and computational results establish that $T^*$
is associated with a second-order structural transition with $\bf{q}$=(0.5,
0.5, 0) (or the ${\bf M}$ point). Further electronic bandstructure calculations
reveal Fermi surface sheets with low curvature segments, which allow us to draw
qualitative comparison with both Sr$_3$Ir$_4$Sn$_{13}$ and
Sr$_3$Rh$_4$Sn$_{13}$ in which similar physics has been discussed recently.


  We give some new characterizations of exactness for locally compact second
countable groups. In particular, we prove that a locally compact second
countable group is exact if and only if it admits a topologically amenable
action on a compact Hausdorff space. This answers an open question by
Anantharaman-Delaroche.


  The high-cadence survey of Zwicky Transient Facility (ZTF) has completely
dominated the discovery of tidal disruption events (TDEs) in the past few years
and resulted in the largest sample of TDEs with optical/UV light curves
well-sampled around their peaks, providing us an excellent opportunity to
construct a peak luminosity function (LF) of tidal disruption flares (TDFs).
The new construction is necessary particularly considering that the most
updated LF reported in literature has been inferred from only 13 sources from 5
different surveys. Here we present the optical and blackbody LFs calculated by
33 TDFs discovered in the ZTF-I survey. The optical LF can be described by both
a power-law profile $dN/dL_g\propto L_g^{-2.3\pm0.2}$, and a Schechter-like
function. The blackbody LF can be described by a power-law profile $dN/dL_{\rm
bb}\propto L_{\rm bb}^{-2.2\pm0.2}$, shallower than the LF made of previous van
Velzen (2018) sample. A possible low-luminosity turnover in the optical LF
supports an Eddington-limited emission scenario. The drop of volumetric rate at
high luminosity suggests a rate suppression due to direct captures of the black
hole. The total volumetric rate is one order of magnitude lower than the
previous estimation, which is probably not simply caused by the high fraction
post-peak sources (7/13) in the previous sample. Instead, the normalization
step during the previous LF construction to reconcile various surveys might
adversely amplify the influence of serendipitous discoveries. Therefore, TDFs
selected from ongoing and upcoming uniform surveys like ZTF, Vera Rubin
Observatory (VRO) and Wide-Field Survey Telescope (WFST) should yield more
accurate LFs.


  This continuation of the derivation of general beam-referenced stage-two
spin-correlation functions is for the analysis of top-antitop pair-production
at the Tevatron and at the Large Hadron Collider. Both the gluon-production and
the quark-production contributions are included for the
charged-lepton-plus-jets reaction p p or p bar{p} --> t bar{t} --> (W^+ b)(W^-
bar{b}) --> (l^{+} nu b)(W^- bar{b}). There is a simple 4-angle beam-referenced
spin-correlation function for determination of the relative sign of, or for
measurement of a possible non-trivial phase between the two dominant helicity
amplitudes for t --> W^{+} b decay. There is an analogous function and tests
for bar{t} --> W^{-} bar{b} decay. This signature requires use of the (t
bar{t}) c.m.-energy of the hadronically decaying W-boson, or the kinematically
equivalent cosine of the polar-angle of W-boson emission in the anti-top (top)
decay frame. Spinors and their outer-products are constructed so that the
helicity-amplitude phase convention of Jacob & Wick can be used throughout for
the fixing of the signs associated with this large W-boson
longitudinal-transverse interference effect.


  We estimate the rate of near-field microlensing events expected from all-sky
surveys and investigate the properties of these events. Under the assumption
that all lenses are composed of stars, our estimation of the event rate ranges
from \Gamma_{tot}~0.2 yr^{-1}$ for a survey with a magnitude limit of
V_{lim}=12 to \Gamma_{tot}~20 yr^{-1} for a survey with V_{lim}=18. We find
that the average distances to source stars and lenses vary considerably
depending on the magnitude limit, while the dependencies of the average event
time scale and lens-source transverse speed are weak and nearly negligible,
respectively. We also find that the the average lens-source proper motion of
events expected even from a survey with V_{lim}=18 would be <\mu> >~ 40 mas
yr^{-1}, implying that the source and lens of a significant fraction of
near-field events could be resolved from high-resolution follow-up
observations. From the investigation of the variation of the event
characteristics depending on the position of the sky, we find that the average
distances to source stars and lenses become shorter, the lens-source transverse
speed increases, and the time scale becomes shorter as the the galactic
latitude of the field increases. Due to the concentration of events near the
galactic plane, we find that >~ 50 % of events would be detected in the field
with b <= 20^\circ.


  We present a comprehensive study of the mixed valent compound, EuPd3S4, by
electrical transport, X-ray diffraction, time-domain 151Eu synchrotron
M\"ossbauer spectroscopy, and X-ray absorption spectroscopy measurements under
high pressure. The electrical transport measurements show that the
antiferromagnetic ordering temperature, TN, increases rapidly from 2.8 K at
ambient pressure to 23.5 K at ~19 GPa and plateaus between ~19 and ~29 GPa
after which no anomaly associated with TN is detected. A pressure-induced first
order structural transition from cubic to tetragonal is observed, with a rather
broad coexistence region (~20 GPa to ~32 GPa) that corresponds to the TN
plateau. M\"ossbauer spectroscopy measurements show a clear valence transition
from approximately 50:50 Eu2+:Eu3+ to fully Eu3+ at ~28 GPa, consistent with
the vanishing of the magnetic order at the same pressure. X-ray absorption data
show a transition to a fully trivalent state at a similar pressure. Our results
show that pressure first greatly enhances TN, most likely via enhanced
hybridization between the Eu 4f states and the conduction band, and then,
second, causes a structural phase transition that coincides with the conversion
of the europium to a fully trivalent state.


  The present paper analyses the Einstein-Cartan theory of gravitation with
Elko spinors as sources of curvature and torsion. After minimally coupling the
Elko spinors to torsion, the spin angular momentum tensor is derived and its
structure is discussed. It shows a much richer structure than the Dirac
analogue and hence it is demonstrated that spin one half particles do not
necessarily yield only an axial vector torsion component. Moreover, it is
argued that the presence of Elko spinors partially solves the problem of
minimally coupling Maxwell fields to Einstein-Cartan theory.


  For $0<p<\infty$ and $\alpha\in (-\infty,\infty)$ we determine when the $L^p$
integral mean on $\{z\in\mathbb C: |z|\le r\}$ of an entire function with
respect to the Gaussian area measure $e^{-\alpha|z|^2}\,dA(z)$ is logarithmic
convex or logarithmic concave.


  What does a typical road network look like? Existing generative models tend
to focus on one aspect to the exclusion of others. We introduce the
general-purpose \emph{quadtree model} and analyze its shortest paths and
maximum flow.


  Mirai is botnet which targets out-of-date Internet-of-Things (IoT) devices.
The disruptive Distributed Denial of Service (DDoS) attack last year has hit
major Internet companies, causing intermittent service for millions of Internet
users. Since the affected devices typically do not support firmware update, it
becomes challenging to expel these vulnerable devices in the wild.
  Both industry and academia have made great efforts in amending the situation.
However, none of these efforts is simple to deploy, and at the same time
effective in solving the problem. In this work, we design a collaborative
defense strategy to tackle Mirai. Our key idea is to take advantage of human
involvement in the least aggressive way. In particular, at a negotiated time
slot, a customer is required to reboot the compromised device, then a "white"
Mirai operated by the manufacturer breaks into the clean-state IoT devices
immediately. The "white" Mirai expels other malicious Mirai variants, blocks
vulnerable ports, and keeps a heart-beat connection with the server operated by
the manufacturer. Once the heart-beat is lost, the server re-implants the
"white" Mirai instantly. We have implemented a full prototype of the designed
system, and the results show that our system can evade Mirai attacks
effectively.


  Assuming simple properties of the spectator particle in weak decays the form
factors of hadronic current matrix elements are shown to be related to a single
universal function. The Isgur-Wise result for heavy-to-heavy transitions
follows as well as similar relations for heavy-to-light decay processes. The
approximation should hold for total energies of the final particle large
compared to the confinement scale. A comparison with experimentally determined
D-decay form factors and QCD sum rule results for B-decays is very encouraging.


  We compute the operator product expansions of gluons and gravitons in
celestial CFT from the worldsheet OPE of vertex operators of four-dimensional
ambitwistor string theories. Remarkably, the worldsheet OPE localizes on the
short-distance singularity between vertex operator insertions which in turn
coincides with the OPE limit of operator insertions on the celestial sphere.
The worldsheet CFT dynamically produces known celestial OPE coefficients -- as
well as infinite towers of SL$(2,\mathbb{R})$ descendant contributions to the
celestial OPE -- without any truncations or approximations. We obtain these
results for all helicities and incoming/outgoing configurations. Furthermore,
the worldsheet OPE encodes the infinite-dimensional symmetry algebras
associated with the conformally soft sectors of gauge theory and gravity. We
provide explicit operator realizations of the currents generating these
symmetries on ambitwistor space in terms of vertex operators for soft gluons
and gravitons, also computing their actions on hard particles of all
helicities. Lastly, we show that the worldsheet OPE for momentum eigenstates
produces the collinear splitting functions of gluons and gravitons.


  This paper presents error-bounded lossy compression tailored for particle
datasets from diverse scientific applications in cosmology, fluid dynamics, and
fusion energy sciences. As today's high-performance computing capabilities
advance, these datasets often reach trillions of points, posing significant
visualization, analysis, and storage challenges. While error-bounded lossy
compression makes it possible to represent floating-point values with strict
pointwise accuracy guarantees, the lack of correlations in particle data's
storage ordering often limits the compression ratio. Inspired by
quantization-encoding schemes in SZ lossy compressors, we dynamically determine
the number of bits to encode particles of the dataset to increase the
compression ratio. Specifically, we utilize a k-d tree to partition particles
into subregions and generate ``bit boxes'' centered at particles for each
subregion to encode their positions. These bit boxes ensure error control while
reducing the bit count used for compression. We comprehensively evaluate our
method against state-of-the-art compressors on cosmology, fluid dynamics, and
fusion plasma datasets.


  We investigate the critical phenomena of Kerr-AdS black holes in the modified
first law of thermodynamics. It is demonstrated that the modified black hole
thermodynamics exhibits a van derWaals-like phase structure, with different
free energy.


  We propose an iterated version of the Gilbert model, which results in a
sequence of random mosaics of the plane. We prove that under appropriate
scaling, this sequence of mosaics converges to that obtained by a classical
Poisson line process with explicit cylindrical measure. Our model arises from
considerations on tropical plane curves, which are zeros of random tropical
polynomials in two variables. In particular, the iterated Gilbert model
convergence allows one to derive a scaling limit for Poisson tropical plane
curves. Our work raises a number of open questions at the intersection of
stochastic and tropical geometry.


  This paper presents the CMB angular power spectrum obtained using the CAMB
code for three different models of inflation: the Starobinsky inflationary
model, the generalized Starobinsky inflationary model, and the chaotic
inflationary model with a step. The results are compared with the most recent
data reported for the Planck mission. An analysis of the large ($l \lesssim
90$), intermediate ($90 \lesssim l \lesssim 900$), and small ($l \gtrsim 900 $)
angular scales is performed. We report the position of the peaks in the
intermediate region so as the cosmological parameters obtained in each of the
models: age of the universe, $\Omega_m$, $\Omega_b$, $\Omega_{\Lambda}$,
$\Omega_K$ and $n_S$.


  Addition of particles to a viscoelastic suspension dramatically alters the
properties of the mixture, particularly when it is sheared or otherwise
processed. Shear-induced stretching of the polymers results in elastic stress
that causes a substantial increase in measured viscosity with increasing shear,
and an attractive interaction between particles, leading to their chaining. At
even higher shear rates, the flow becomes unstable, even in the absence of
particles. This instability makes it very difficult to determine the properties
of a particle suspension. Here we use a fully immersed parallel plate geometry
to measure the high-shear-rate behavior of a suspension of particles in a
viscoelastic fluid. We find an unexpected separation of the particles within
the suspension resulting in the formation of a layer of particles in the center
of the cell. Remarkably, monodisperse particles form a crystalline layer which
dramatically alters the shear instability. By combining measurements of the
velocity field and torque fluctuations, we show that this solid layer disrupts
the flow instability and introduces a new, single-frequency component to the
torque fluctuations that reflects a dominant velocity pattern in the flow.
These results highlight the interplay between particles and a suspending
viscoelastic fluid at very high shear rates.


  Data is the cornerstone of large language models (LLMs), but not all data is
useful for model learning. Carefully selected data can better elicit the
capabilities of LLMs with much less computational overhead. Most methods
concentrate on evaluating the quality of individual samples in data selection,
while the combinatorial effects among samples are neglected. Even if each
sample is of perfect quality, their combinations may be suboptimal in teaching
LLMs due to their intrinsic homogeneity or contradiction. In this paper, we aim
to uncover the underlying relationships between LLM performance and data
selection. Inspired by the information compression nature of LLMs, we uncover
an ``entropy law'' that connects LLM performance with data compression ratio
and first-epoch training loss, which reflect the information redundancy of a
dataset and the mastery of inherent knowledge encoded in this dataset,
respectively. Through both theoretical deduction and empirical evaluation, we
find that model performance is negatively correlated to the compression ratio
of training data, which usually yields a lower training loss. Based on the
findings of the entropy law, we propose a quite efficient and universal data
selection method named \textbf{ZIP} for training LLMs, which aim to prioritize
data subsets exhibiting a low compression ratio. Based on a multi-stage
algorithm that selects diverse data in a greedy manner, we can obtain a good
data subset with satisfactory diversity. Extensive experiments have been
conducted to validate the entropy law and the superiority of ZIP across
different LLM backbones and alignment stages. We also present an interesting
application of entropy law that can detect potential performance risks at the
beginning of model training.


  This paper introduces FALL-E, a foley synthesis system and its
training/inference strategies. The FALL-E model employs a cascaded approach
comprising low-resolution spectrogram generation, spectrogram super-resolution,
and a vocoder. We trained every sound-related model from scratch using our
extensive datasets, and utilized a pre-trained language model. We conditioned
the model with dataset-specific texts, enabling it to learn sound quality and
recording environment based on text input. Moreover, we leveraged external
language models to improve text descriptions of our datasets and performed
prompt engineering for quality, coherence, and diversity. FALL-E was evaluated
by an objective measure as well as listening tests in the DCASE 2023 challenge
Task 7. The submission achieved the second place on average, while achieving
the best score for diversity, second place for audio quality, and third place
for class fitness.


  The CoRoT space telescope observed nearly 160 000 light curves. Among the
most outstanding is that of the young, active planet host star CoRoT-2A. In
addition to deep planetary transits, the light curve of CoRoT-2A shows strong
rotational variability and a superimposed beating pattern. To study the stars
that produce such an intriguing pattern of photometric variability, we
identified a sample of eight stars with rotation periods between 0.8 and 11
days and photometric variability amplitudes of up to 7.5 %, showing a similar
CoRoT light curve. We also obtained high-resolution follow-up spectroscopy with
TNG/SARG and carried out a spectral analysis with SME and MOOG. We find that
the color dependence of the light curves is consistent with rotational
modulation due to starspots and that latitudinal differential rotation provides
a viable explanation for the light curves, although starspot evolution is also
expected to play an important role. Our MOOG and SME spectral analyses provide
consistent results, showing that the targets are dwarf stars with spectral
types between F and mid-K. Detectable Li i absorption in four of the targets
confirms a low age of 100-400 Myr also deduced from gyrochronology. Our study
indicates that the photometric beating phenomenon is likely attributable to
differential rotation in fast-rotating stars with outer convection zones.


  We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously
resolves three important practical problems in high-dimensional regression
analysis, namely it handles the unknown scale, heteroscedasticity and (drastic)
non-Gaussianity of the noise. In addition, our analysis allows for badly
behaved designs, for example, perfectly collinear regressors, and generates
sharp bounds even in extreme cases, such as the infinite variance case and the
noiseless case, in contrast to Lasso. We establish various nonasymptotic bounds
for $\sqrt{\mathrm {Lasso}}$ including prediction norm rate and sparsity. Our
analysis is based on new impact factors that are tailored for bounding
prediction norm. In order to cover heteroscedastic non-Gaussian noise, we rely
on moderate deviation theory for self-normalized sums to achieve Gaussian-like
results under weak conditions. Moreover, we derive bounds on the performance of
ordinary least square (ols) applied to the model selected by $\sqrt{\mathrm
{Lasso}}$ accounting for possible misspecification of the selected model. Under
mild conditions, the rate of convergence of ols post $\sqrt{\mathrm {Lasso}}$
is as good as $\sqrt{\mathrm {Lasso}}$'s rate. As an application, we consider
the use of $\sqrt{\mathrm {Lasso}}$ and ols post $\sqrt{\mathrm {Lasso}}$ as
estimators of nuisance parameters in a generic semiparametric problem
(nonlinear moment condition or $Z$-problem), resulting in a construction of
$\sqrt{n}$-consistent and asymptotically normal estimators of the main
parameters.


  The presence of the nonbonding XH tension constrains and the presence of the
anti or super hydrogen bond fosters the explosion in aqueous alkali and molten
alkali halides; the combination of the coupled hydrogen bond and the repulsive
anti or super hydrogen bond not only stabilzes the structure but also stores
energy of the energetic molecular assemblies by shortening all covalent bonds.


  A time series model of CDS sequences in complete genome is proposed.
  A map of DNA sequence to integer sequence is given. The correlation
dimensions and Hurst exponents of CDS sequences in complete genome of bacteria
are calculated. Using the average of correlation dimensions, some interesting
results are obtained.


  The goal of document-level relation extraction (RE) is to identify relations
between entities that span multiple sentences. Recently, incomplete labeling in
document-level RE has received increasing attention, and some studies have used
methods such as positive-unlabeled learning to tackle this issue, but there is
still a lot of room for improvement. Motivated by this, we propose a
positive-augmentation and positive-mixup positive-unlabeled metric learning
framework (P3M). Specifically, we formulate document-level RE as a metric
learning problem. We aim to pull the distance closer between entity pair
embedding and their corresponding relation embedding, while pushing it farther
away from the none-class relation embedding. Additionally, we adapt the
positive-unlabeled learning to this loss objective. In order to improve the
generalizability of the model, we use dropout to augment positive samples and
propose a positive-none-class mixup method. Extensive experiments show that P3M
improves the F1 score by approximately 4-10 points in document-level RE with
incomplete labeling, and achieves state-of-the-art results in fully labeled
scenarios. Furthermore, P3M has also demonstrated robustness to prior
estimation bias in incomplete labeled scenarios.


  The determination of the size of the convective core of main-sequence stars
is usually dependent on the construction of models of stars. Here we introduce
a method to estimate the radius of the convective core of main-sequence stars
with masses between about 1.1 and 1.5 $M_{\odot}$ from observed frequencies of
low-degree p-modes. A formula is proposed to achieve the estimation. The values
of the radius of the convective core of four known stars are successfully
estimated by the formula. The radius of the convective core of KIC 9812850
estimated by the formula is $\mathbf{0.140\pm0.028}$ $R_{\odot}$. In order to
confirm this prediction, a grid of evolutionary models were computed. The value
of the convective-core radius of the best-fit model of KIC 9812850 is $0.149$
$R_{\odot}$, which is in good agreement with that estimated by the formula from
observed frequencies. The formula aids in understanding the interior structure
of stars directly from observed frequencies. The understanding is not dependent
on the construction of models.


  Variable impedance control in operation-space is a promising approach to
learning contact-rich manipulation behaviors. One of the main challenges with
this approach is producing a manipulation behavior that ensures the safety of
the arm and the environment. Such behavior is typically implemented via a
reward function that penalizes unsafe actions (e.g. obstacle collision, joint
limit extension), but that approach is not always effective and does not result
in behaviors that can be reused in slightly different environments. We show how
to combine Riemannian Motion Policies, a class of policies that dynamically
generate motion in the presence of safety and collision constraints, with
variable impedance operation-space control to learn safer contact-rich
manipulation behaviors.


  We report a computational 3D microscopy technique, termed Fourier
ptychographic diffraction tomography (FPDT), that iteratively stitches together
numerous variably illuminated, low-resolution images acquired with a
low-numerical aperture (NA) objective in 3D Fourier space to create a wide
field-of-view (FOV), high-resolution, depth-resolved complex refractive index
(RI) image across large volumes. Unlike conventional optical diffraction
tomography (ODT) approaches that rely on controlled bright-field illumination,
holographic phase measurement, and high-NA objective detection, FPDT employs
tomographic RI reconstruction from low-NA intensity-only measurements. In
addition, FPDT incorporates high-angle dark-field illuminations beyond the NA
of the objective, significantly expanding the accessible object frequency. With
FPDT, we present the highest-throughput ODT results with 390nm lateral
resolution and 899nm axial resolution across a 10X FOV of 1.77mm2 and a depth
of focus of ~20{\mu}m. Billion-voxel 3D tomographic imaging results of
biological samples establish FPDT as a powerful non-invasive and label-free
tool for high-throughput 3D microscopy applications.


  We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius
number. For the case of symmetric semigroups with three generators of Frobenius
numbers we found an exact formula, which in a sense is the sum of two
Sylvester's formulaes. We prove that the fraction of the symmetric semigroups
is vanishing in the weak limit.


  The data analysis problem of coherently searching for unmodeled
gravitational-wave bursts in the data generated by a global network of
gravitational-wave observatories has been at the center of research for almost
two decades. As data from these detectors is starting to be analyzed, a renewed
interest in this problem has been sparked. A Bayesian approach to the problem
of coherently searching for gravitational wave bursts with a network of
ground-based interferometers is here presented. We demonstrate how to
systematically incorporate prior information on the burst signal and its source
into the analysis. This information may range from the very minimal, such as
best-guess durations, bandwidths, or polarization content, to complete prior
knowledge of the signal waveforms and the distribution of sources through
spacetime. We show that this comprehensive Bayesian formulation contains
several previously proposed detection statistics as special limiting cases, and
demonstrate that it outperforms them.


  Accurate lake temperature estimation is essential for numerous problems
tackled in both hydrological and ecological domains. Nowadays physical models
are developed to estimate lake dynamics; however, computations needed for
accurate estimation of lake surface temperature can get prohibitively
expensive. We propose to aggregate simulations of lake temperature at a certain
depth together with a range of meteorological features to probabilistically
estimate lake surface temperature. Accordingly, we introduce a spatio-temporal
neural network that combines Bayesian recurrent neural networks and Bayesian
graph convolutional neural networks. This work demonstrates that the proposed
graphical model can deliver homogeneously good performance covering the whole
lake surface despite having sparse training data available. Quantitative
results are compared with a state-of-the-art Bayesian deep learning method.
Code for the developed architectural layers, as well as demo scripts, are
available on https://renkulab.io/projects/das/bstnn.


  We consider a class of partial differential equations with Carlitz
derivatives over a local field of positive characteristic, for which an analog
of the Cauchy problem is well-posed. Equations of such type correspond to
quasi-holonomic modules over the ring of differential operators with Carlitz
derivatives. The above class of equations includes some equations of
hypergeometric type. Building on the work of Thakur, we develop his notion of
the hypergeometric function of the first kind (whose parameters belonged
initially to $\mathbb Z$) in such a way that it becomes fully an object of the
function field arithmetic, with the variable, parameters and values from the
field of positive characteristic.


  Models of electroweak symmetry breaking with extended Higgs sectors are
theoretically well motivated. In this study, we focus on the Two Higgs Doublet
Model with a low energy spectrum containing scalars $H$ and a pseudoscalar $A$.
We study the decays $A\rightarrow HZ$ or $H\rightarrow AZ$, which could reach
sizable branching fractions in certain parameter regions. With detailed
collider analysis, we obtain model independent exclusion bounds as well as
discovery reach at the 14 TeV LHC for the process: $gg\rightarrow
A/H\rightarrow HZ/AZ$, looking at final states bbll, \tau\tau ll and ZZZ(4l2j)
for l =e,\mu. We further interpret these bounds in the context of the Type II
Two Higgs Doublet Model, considering three different classes of processes:
$A\rightarrow h^0Z$, $A\rightarrow H^0Z$, and $H^0 \rightarrow AZ$, in which
$h^0$ and $H^0$ are the light and heavy CP-even Higgses respectively. For 100
fb$^{-1}$ integrated luminosity at the 14 TeV LHC, we find that for parent
particle mass around 300-400 GeV, $A\rightarrow h^0Z$ has the greatest reach
when $H^0$ is interpreted as the 126 GeV Higgs: most regions in the
tan\beta-sin(\beta-\alpha) parameter space can be covered by exclusion and
discovery. For 126 GeV $h^0$, only relatively small tan\beta<10 (5) can be
reached by exclusion (discovery). For $A\rightarrow H^0Z$, the reach is
typically restricted to sin$(\beta-\alpha)\sim\pm 1$ with tan\beta <10 in bbll
and \tau\tau ll channels. The ZZZ (4l2j) channel, on the other hand, covers a
wide range of 0.3<|sin(\beta-\alpha)|<1 for tan\beta<4. $H^0\rightarrow AZ$
typically favors negative values of sin(\beta-\alpha), with exclusion/discovery
reach possibly extending to all values of tan\beta. A study of exotic decays of
extra Higgses would extend the reach at the LHC and provides nice
complementarity to conventional Higgs search channels.


  High-harmonic generation (HHG) provides short-wavelength light that is useful
for precision spectroscopy and probing ultrafast dynamics. We report efficient,
phase-coherent harmonic generation up to 9th-order (333 nm) in chirped
periodically poled lithium niobate waveguides driven by phase-stable
$\leq$12-nJ, 100 fs pulses at 3 $\mu$m with 100 MHz repetition rate. A
mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is
observed, amongst an overall 23% conversion of the fundamental to all
harmonics. We verify the coherence of the harmonic frequency combs despite the
complex highly nonlinear process. Numerical simulations based on a single
broadband envelope equation with quadratic nonlinearity give estimates for the
conversion efficiency within approximately 1 order of magnitude over a wide
range of experimental parameters. From this comparison we identify a
dimensionless parameter capturing the competition between three-wave mixing and
group-velocity walk-off of the harmonics that governs the cascaded HHG physics.
These results can inform cascaded HHG in a range of different platforms.


  We show that every (possibly unbounded) convex polygon $P$ in $R^2$ with $m$
edges can be represented by inequalities $p_1 \ge 0,...,p_n \ge 0,$ where the
$p_i$'s are products of at most $k$ affine functions each vanishing on an edge
of $P$ and $n=n(m,k)$ satisfies $s(m,k) \le n(m,k) \le (1+\epsilon_m) s(m,k)$
with $s(m,k):=\max \{m/k,\log_2 m\}$ and $\epsilon_m \to 0$ as $m \to \infty$.
This choice of $n$ is asymptotically best possible. An analogous result on
representing the interior of $P$ in the form $p_1 > 0,..., p_n > 0$ is also
given. For $k \le m/\log_2 m$ these statements remain valid for representations
with arbitrary polynomials of degree not exceeding $k$.


  Control of legged robots is a challenging problem that has been investigated
by different approaches, such as model-based control and learning algorithms.
This work proposes a novel Imitating and Finetuning Model Predictive Control
(IFM) framework to take the strengths of both approaches. Our framework first
develops a conventional model predictive controller (MPC) using Differential
Dynamic Programming and Raibert heuristic, which serves as an expert policy.
Then we train a clone of the MPC using imitation learning to make the
controller learnable. Finally, we leverage deep reinforcement learning with
limited exploration for further finetuning the policy on more challenging
terrains. By conducting comprehensive simulation and hardware experiments, we
demonstrate that the proposed IFM framework can significantly improve the
performance of the given MPC controller on rough, slippery, and conveyor
terrains that require careful coordination of footsteps. We also showcase that
IFM can efficiently produce more symmetric, periodic, and energy-efficient
gaits compared to Vanilla RL with a minimal burden of reward shaping.


  The urgent need for cleaner, sustainable aviation fuels has driven interest
in the use of hydrogen as a potential replacement for traditional hydrocarbon
fuels in aviation. However, transitioning to hydrogen presents significant
challenges due to its lower volumetric energy density which requires a larger
fuel volume for equivalent energy. This study uses Computational Fluid Dynamics
(CFD) simulations, utilizing the ANSYS Fluent 2022 R1 solver, to conduct a
preliminary investigation on the aerodynamic implications of adopting hydrogen
fuel in small aircraft, specifically the Bonanza G36. Three different types of
hydrogen fuel - gaseous hydrogen at 350 bar, gaseous hydrogen at 700 bar, and
liquid hydrogen - were considered. Despite a promising 64% reduction in fuel
weight in comparison to gasoline, the volume required for hydrogen fuel was
found to increase significantly, with values ranging from 263% to 896% compared
to the base case. The aerodynamic impact was quantified in terms of drag, with
the study revealing increases of 67.32%, 48.42%, and 27.05% for gaseous
hydrogen at 350 bar, gaseous hydrogen at 700 bar, and liquid hydrogen
respectively. While the findings present a challenge, they also set a platform
for exploring innovative fuel tank designs and drag reduction technologies to
mitigate these effects. This study underscores the complexities involved in
transitioning to hydrogen fuel in aviation, contributing valuable insights to
guide further research towards sustainable aviation.


  Comprehensive analysis on the light Higgs scenario of the minimal
supersymmetric standard model is performed in the framework of the
non-universal Higgs mass model (NUHM). The NUHM is known to be the simplest
framework realizing the light Higgs scenario with the unifications of gaugino
and sfermion masses at the scale of grand unified theory being consistent. All
important constraints from collider experiments, flavor-changing processes, and
cosmological observations are considered in order to clarify the allowed region
of the model parameter space, where the Markov Chain Monte Carlo method is used
to obtain the region. We show that the region is excluded by current LHC
results for the SUSY particle searches. We discuss possible extensions to save
the LHS. Even with such extensions, the measurement of B_s to mu^+ mu^- would
enable us to test the LHS in the near future.


  Normalized quantum Stokes operators introduced in [Phys. Rev. A {\bf 95},
042113 (2017)] enable one to better observe non-classical correlations of
entangled states of optical fields with undefined photon numbers. For a given
run of an experiment the new quantum Stokes operators are defined by the
differences of the measured intensities (or photon numbers) at the exits of a
polarizer divided by their sum. It is this ratio that is to be averaged, and
not the numerator and the denominator separately, as it is in the conventional
approach. The new approach allows to construct more robust entanglement
indicators against photon-loss noise, which can detect entangled optical states
in situations in which witnesses using standard Stokes operators fail. Here we
show an extension of this approach beyond phenomena linked with polarization.
We discuss EPR-like experiments involving correlations produced by optical
beams in a multi-mode bright squeezed vacuum state. EPR-inspired entanglement
conditions for all prime numbers of modes are presented. The conditions are
much more resistant to noise due to photon loss than similar ones which employ
standard Glauber-like intensity, correlations.


  This paper presents a new method for automatically detecting words with
lexical gender in large-scale language datasets. Currently, the evaluation of
gender bias in natural language processing relies on manually compiled lexicons
of gendered expressions, such as pronouns ('he', 'she', etc.) and nouns with
lexical gender ('mother', 'boyfriend', 'policewoman', etc.). However, manual
compilation of such lists can lead to static information if they are not
periodically updated and often involve value judgments by individual annotators
and researchers. Moreover, terms not included in the list fall out of the range
of analysis. To address these issues, we devised a scalable, dictionary-based
method to automatically detect lexical gender that can provide a dynamic,
up-to-date analysis with high coverage. Our approach reaches over 80% accuracy
in determining the lexical gender of nouns retrieved randomly from a Wikipedia
sample and when testing on a list of gendered words used in previous research.


  In the description of electron spin obtained through the conventional
Copenhagen interpretation of quantum mechanics, the concrete picture of
rotation was replaced by an abstract mathematical representation; visualization
or visualisability was entirely lost. The work described here takes a step
towards restoring this.


  We investigate the total major (> 1:4 by stellar mass) and minor (> 1:100 by
stellar mass) merger history of a population of 80 massive (M_* > 10^11 M_sol)
galaxies at high redshifts (z = 1.7 - 3). We utilize extremely deep and high
resolution HST H-band imaging from the GOODS NICMOS Survey (GNS), which
corresponds to rest-frame optical wavelengths at the redshifts probed. We find
that massive galaxies at high redshifts are often morphologically disturbed,
with a CAS deduced merger fraction f_m = 0.23 +/- 0.05 at z = 1.7 - 3. We find
close accord between close pair methods (within 30 kpc apertures) and CAS
methods for deducing major merger fractions at all redshifts. We deduce the
total (minor + major) merger history of massive galaxies with M_* > 10^9 M_sol
galaxies, and find that this scales roughly linearly with log-stellar-mass and
magnitude range. We test our close pair methods by utilizing mock galaxy
catalogs from the Millennium Simulation. We compute the total number of mergers
to be (4.5 +/- 2.9) / <\tau_m> from z = 3 to the present, to a stellar mass
sensitivity threshold of ~ 1:100 (where \tau_m is the merger timescale in Gyr
which varies as a function of mass). This corresponds to an average mass
increase of (3.4 +/- 2.2) x 10^11 M_sol over the past 11.5 Gyrs due to merging.
We show that the size evolution observed for these galaxies may be mostly
explained by this merging.


  The first part of this work deals with a formalism of vector coherent states
construction for a system of $M$ Fermi-type modes associated with $N$ bosonic
modes. Then follows a generalization to a Hamiltonian describing the
translational motion of the center of mass of a nanoparticle. The latter gives
rise to a new mechanism for the electronic energy relaxation in nanocrystals,
intensively studied today in condensed matter physics. Finite degeneracies of
the involved Hamiltonian systems are also investigated. The defined vector
coherent states satisfy relevant mathematical properties of continuity,
resolution of identity, temporal stability and action identity.


  Convergence of the block iterative method in image reconstruction for
positron emission tomography (PET) requires careful control of relaxation
parameters, which is a challenging task. The automatic determination of
relaxation parameters for list-mode reconstructions also remains challenging.
Therefore, a different approach would be desirable. In this study, we propose a
list-mode maximum likelihood Dykstra-like splitting PET reconstruction
(LM-MLDS). LM-MLDS converges the list-mode block iterative method by adding the
distance from an initial image as a penalty term into an objective function.
LM-MLDS takes a two-step approach because its performance depends on the
quality of the initial image. The first step uses a uniform image as the
initial image, and then the second step uses a reconstructed image after one
main iteration as the initial image. In a simulation study, LM-MLDS provided a
better tradeoff curve between noise and contrast than the other methods. In a
clinical study, LM-MLDS removed the false hotspots at the edge of the axial
field of view and improved the image quality of slices covering the top of the
head to the cerebellum. List-mode proximal splitting reconstruction is useful
not only for optimizing nondifferential functions but also for converging block
iterative methods without controlling relaxation parameters.


  Classical contact lithography involves patterning of surfaces by embossing or
by transfer of ink. We report direct lithographic transfer of parts of
sacrificial stamps onto counterpart surfaces. Using sacrificial stamps
consisting of the block copolymer polystyrene-block-poly(2-pyridine)
(PS-b-P2VP), we deposited arrays of nanostructured submicron PS-b-P2VP dots
with heights of about 100 nm onto silicon wafers and glass slides. The
sacrificial PS-b-P2VP stamps were topographically patterned with
truncated-pyramidal contact elements and penetrated by spongy-continuous
nanopore systems. The spongy nature of the sacrificial PS-b-P2VP stamps
supported formation of adhesive contact to the counterpart surfaces and the
rupture of the contact elements during stamp retraction. The submicron
PS-b-P2VP dots generated by sacrificial stamping can be further functionalized,
examples include loading submicron PS-b-P2VP dots with dyes and attachment of
gold nanoparticles to their outer surfaces. The arrays of submicron PS-b-P2VP
dots can be integrated into setups for advanced optical microscopy, total
internal reflection fluorescence microscopy or Raman microscopy. Arrays of
nanostructured submicron block copolymer dots may represent a preconcentration
platform for locally resolved sensing and locally resolved monitoring of
cellular interactions or might be used as microreactor arrays in lab-on-chip
configurations.


  The present paper introduces new sentiment data, MaCMS, for
Magahi-Hindi-English (MHE) code-mixed language, where Magahi is a
less-resourced minority language. This dataset is the first
Magahi-Hindi-English code-mixed dataset for sentiment analysis tasks. Further,
we also provide a linguistics analysis of the dataset to understand the
structure of code-mixing and a statistical study to understand the language
preferences of speakers with different polarities. With these analyses, we also
train baseline models to evaluate the dataset's quality.


  In this paper, we show the central limit theorem for the logarithmic
determinant of the sample correlation matrix $\mathbf{R}$ constructed from the
$(p\times n)$-dimensional data matrix $\mathbf{X}$ containing independent and
identically distributed random entries with mean zero, variance one and
infinite fourth moments. Precisely, we show that for $p/n\to \gamma\in (0,1)$
as $n,p\to \infty$ the logarithmic law \begin{equation*} \frac{\log \det
\mathbf{R} -(p-n+\frac{1}{2})\log(1-p/n)+p-p/n}{\sqrt{-2\log(1-p/n)- 2 p/n}}
\overset{d}{\rightarrow} N(0,1)\, \end{equation*} is still valid if the entries
of the data matrix $\mathbf{X}$ follow a symmetric distribution with a
regularly varying tail of index $\alpha\in (3,4)$. The latter assumptions seem
to be crucial, which is justified by the simulations: if the entries of
$\mathbf{X}$ have the infinite absolute third moment and/or their distribution
is not symmetric, the logarithmic law is not valid anymore. The derived results
highlight that the logarithmic determinant of the sample correlation matrix is
a very stable and flexible statistic for heavy-tailed big data and open a novel
way of analysis of high-dimensional random matrices with self-normalized
entries.


  Let $G$ be a group acting freely, properly discontinuously and cellularly on
a finite dimensional $C$W-complex $\Sigma(2n)$ which has the homotopy type of
the $2n$- sphere $\mathbb{S}^{2n}$. Then, this action induces an action of the
group $G$ on the top cohomology of $\Sigma(2n)$. For the family of virtually
cyclic groups, we classify all groups which act on $\Sigma(2n)$, the homotopy
type of all possible orbit spaces and all actions on the top cohomology as
well. \par Under the hypothesis that $\mbox{dim}\,\Sigma(2n)\leq 2n+1$, we
study the groups with the virtual cohomological dimension
$\mbox{vcd}\,G<\infty$ which act as above on $\Sigma(2n)$. It turns out that
they consist of free groups and certain semi-direct products $F\rtimes
\mathbb{Z}_2$ with $F$ a free group. For those groups $G$ and a given action of
$G$ on $\mbox{Aut}(\mathbb{Z})$, we present an algebraic criterion equivalent
to the realizability of an action $G$ on $\Sigma(2n)$ which induces the given
action on its top cohomology. Then, we obtain a classification of those groups
together with actions on the top cohomology of $\Sigma(2n)$.


  We introduce the notion of non-Abelian tensors, and use them to construct a
general non-Abelian time evolving block decimation (NA-TEBD) scheme that uses
an arbitrary number of Abelian and non-Abelian symmetries. Our approach
increases the speed and memory storage efficiency of matrix product state based
computations by several orders of magnitudes, and makes large bond dimensions
accessible even on simple desktop architectures. We use it to study post-quench
dynamics in the repulsive SU(3) Hubbard model, and to determine the time
evolution of various local operators and correlation functions efficiently.
Interactions turn algebraic charge relaxation into exponential, and suppress
coherent quantum oscillations rapidly.


  Derivation of $\kappa$-Poincare bicovariant commutation relations between
coordinates and 1-forms on $\kappa$-Minkowski space is given using Dirac
operator and Allain Connes formula. The deformed U(1) gauge theory and
appearance of an additional spin 0 gauge field is discussed.


  In this paper, we establish Galois theory for partial differential systems
defined over formally real differential fields with a real closed field of
constants and over formally $p$-adic differential fields with a $p$-adically
closed field of constants. For an integrable partial differential system
defined over such a field, we prove that there exists a formally real (resp.
formally $p$-adic) Picard-Vessiot extension. Moreover, we obtain a uniqueness
result for this Picard-Vessiot extension. We give an adequate definition of the
Galois differential group and obtain a Galois fundamental theorem in this
setting. We apply the obtained Galois correspondence to characterise formally
real Liouvillian extensions of real partial differential fields with a real
closed field of constants by means of split solvable linear algebraic groups.
We present some examples of real dynamical systems and indicate some
possibilities of further development of algebraic methods in real dynamical
systems.


  Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how
investigations of complex systems should take into account interactions between
more than two elements, which can be modelled by hypergraphs and studied via
topological data analysis. Following a separate line of enquiry, a broad
literature has developed information-theoretic tools to characterize high-order
interdependencies from observed data. While these could seem to be competing
approaches aiming to address the same question, in this correspondence we
clarify that this is not the case, and that a complete account of higher-order
phenomena needs to embrace both.


  A cascaded iterative Fourier transform (CIFT) algorithm is presented for
optical security applications. Two phase-masks are designed and located in the
input and the Fourier domains of a 4-f correlator respectively, in order to
implement the optical encryption or authenticity verification. Compared with
previous methods, the proposed algorithm employs an improved searching
strategy: modifying the phase-distributions of both masks synchronously as well
as enlarging the searching space. Computer simulations show that the algorithm
results in much faster convergence and better image quality for the recovered
image. Each of these masks is assigned to different person. Therefore, the
decrypted image can be obtained only when all these masks are under
authorization. This key-assignment strategy may reduce the risk of being
intruded.


  In this paper, we present a version of horizontal weighted Hardy-Rellich type
and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and study
some of their consequences. Our results reflect on many results previously
known in special cases. Moreover, a new simple proof of the Badiale-Tarantello
conjecture [2] on the best constant of a Hardy type inequality is provided. We
also show a family of Poincar\'e inequalities as well as inequalities involving
the weighted and unweighted $p$-sub-Laplacians.


  We report the results of the spectroscopic observations carried out at the
SAO RAS 6-m telescope for the optical components of nine new extended radio
sources found in the NVSS catalog. The measured redshifts of the host galaxies
are in the range of z=0.1-0.4. The physical sizes of radio sources were
calculated within the standard cosmological model. The two most extended
objects, 0003+1512 and 0422+0351 reach the sizes of 2.1 Mpc and 4.0 Mpc,
respectively. This is close to the maximum size of known radio sources.


  We suggest several automaton groups as key-agreement platforms for
Anshl-Anshel-Goldfeld metascheme, they include Grigorchuk and universal
Grigorchuk groups, Hanoi 3-Towers group, Basilica group and a subgroup of the
affine group with the unsolvable conjugacy problem


  We introduce a class of Banach algebras of generalized matrices and study the
existence of approximate units, ideal structure, and derivations of them.


  In the CDM cosmological framework structures grow from merging with smaller
structures. Merging should have observable effects on galaxies including
destroying disks and creating spheroids. This proceeding aims to give a brief
overview of how mergers occur in cosmological simulations. In this regard it is
important to understand that dark matter halo mergers are not galaxy mergers; a
theory of galaxy formation is necessary to connect the two. Mergers of galaxies
in hydrodynamical simulations show a stronger dependence on mass than halo
mergers in N-body simulations. If one knows how to connect galaxies to dark
matter halos then the halo merger rate can be converted into a galaxy merger
rate. When this is done it becomes clear that major mergers are many times more
common in more massive galaxies offering a possible explanation of why Hubble
type depends on galaxy mass.


  To gain a better understanding of the interplay between frustrated long-range
interactions and zero-temperature quantum fluctuations, we investigate the
ground-state phase diagram of the transverse-field Ising model with
algebraically-decaying long-range Ising interactions on quasi one-dimensional
infinite-cylinder triangular lattices. Technically, we apply various approaches
including low- and high-field series expansions. For the classical long-range
Ising model, we investigate cylinders with an arbitrary even circumference. We
show the occurrence of gapped stripe-ordered phases emerging out of the
infinitely-degenerate nearest-neighbor Ising ground-state space on the
two-dimensional triangular lattice. Further, while cylinders with
circumferences $6$, $10$, $14$ et cetera are always in the same stripe phase
for any decay exponent of the long-range Ising interaction, the family of
cylinders with circumferences $4$, $8$, $12$ et cetera displays a phase
transition between two different types of stripe structures. For the full
long-range transverse-field Ising model, we concentrate on cylinders with
circumference four and six. The ground-state phase diagram consists of several
quantum phases in both cases including an $x$-polarized phase, stripe-ordered
phases, and clock-ordered phases which emerge from an order-by-disorder
scenario already present in the nearest-neighbor model. In addition, the
generic presence of a potential intermediate gapless phase with algebraic
correlations and associated Kosterlitz-Thouless transitions is discussed for
both cylinders.


  By using the example of photon-photon scattering box diagrams, different
representations for loop integrals are discussed. A connection between
hypergeometric representation and dilogarithms is derived. An explicit analytic
continuation formula to large values of Mandelstam variables is constructed.


  We examine theoretically the superconducting state of
BaFe$_2$(As$_{1-x}$P$_x$)$_2$, an isovalent doping 122 iron pnictide
superconductor. We construct a three dimensional ten orbital model from first
principles band calculation, and investigate the superconducting gap within the
spin fluctuation mediated pairing mechanism. The gap is basically $s\pm$, where
the gap changes its sign between electron and hole Fermi surfaces, but three
dimensional nodal structures appear in the largely warped hole Fermi surface
having strong $Z^2/XZ/YZ$ orbital character. The present result, together with
our previous study on 1111 systems, explains the strong material dependence of
the superconducting gap in the iron pnictides.


  We prove a superdiffusive central limit theorem for the displacement of a
test particle in the periodic Lorentz gas in the limit of large times $t$ and
low scatterer densities (Boltzmann-Grad limit). The normalization factor is
$\sqrt{t\log t}$, where $t$ is measured in units of the mean collision time.
This result holds in any dimension and for a general class of finite-range
scattering potentials. We also establish the corresponding invariance
principle, i.e., the weak convergence of the particle dynamics to Brownian
motion.


  We discuss a Gedanken experiment for the measurement of the area of the
apparent horizon of a black hole in quantum gravity. Using rather general and
model-independent considerations we find a generalized uncertainty principle
which agrees with a similar result obtained in the framework of string
theories. The result indicates that a minimum length of the order of the Planck
length emerges naturally from any quantum theory of gravity, and that the
concept of black hole is not operationally defined if the mass is smaller than
the Planck mass.


  The discovery of atomically thin van der Waals ferroelectric and magnetic
materials encourages the exploration of 2D multiferroics, which holds the
promise to understand fascinating magnetoelectric interactions and fabricate
advanced spintronic devices. In addition to building a heterostructure
consisting of ferroelectric and magnetic ingredients, thinning down layered
multiferroics of spin origin such as NiI2 becomes a natural route to realize 2D
multiferroicity. However, the layer-dependent behavior, widely known in the
community of 2D materials, necessitates a rigorous scrutiny of the multiferroic
order in the few-layer limit. Here, we interrogate the layer thickness
crossover of helimagnetism in NiI2 that drives the ferroelectricity and thereby
type-II multiferroicity. By using wavelength-dependent polarization-resolved
optical second harmonic generation (SHG) to probe the ferroic symmetry, we find
that the SHG arises from the inversion-symmetry-breaking magnetic order, not
previously assumed ferroelectricity. This magnetism-induced SHG is only
observed in bilayer or thicker layers, and vanishes in monolayer, suggesting
the critical role of interlayer exchange interaction in breaking the degeneracy
of geometrically frustrated spin structures in triangular lattice and
stabilizing the type-II multiferroic magnetism in few-layers. While the
helimagnetic transition temperature is layer dependent, the few-layer NiI2
exhibits another thickness evolution and reaches the bulk-like behavior in
trilayer, indicated by the intermediate centrosymmetric antiferromagnetic state
as revealed in Raman spectroscopy. Our work therefore highlights the magnetic
contribution to SHG and Raman spectroscopy in reduced dimension and guides the
optical study of 2D multiferroics.


  The fractional Caffarelli-Kohn-Nirenberg inequality states that $$
\int_{\mathbb{R}^n}\int_{\mathbb{R}^n} \frac{(u(x)-u(y))^2}{|x|^\alpha
|x-y|^{n+2s} |y|^\alpha} \mathrm{d} x \, \mathrm{d} y
  \geq \Lambda_{n, s, p, \alpha,\beta}
  \|u |x|^{-\beta}\|_{L^p}^2, $$ for $0<s<\min\{1, n/2\}$, $2<p<2^*_s$, and
$\alpha,\beta\in\mathbb R$ so that $\beta-\alpha = s - n\big(\frac12 -
\frac1p\big)$ and $-2s < \alpha < \frac{n-2s}{2}$.
  Continuing the program started in Ao et al. (2022), we establish the
non-degeneracy and sharp quantitative stability of minimizers for $\alpha\ge
0$. Furthermore, we show that minimizers remain symmetric when $\alpha<0$ for
$p$ very close to $2$.
  Our results fit into the more ambitious goal of understanding the symmetry
region of the minimizers of the fractional Caffarelli-Kohn-Nirenberg
inequality.
  We develop a general framework to deal with fractional inequalities in
$\mathbb R^n$, striving to provide statements with a minimal set of
assumptions. Along the way, we discover a Hardy-type inequality for a general
class of radial weights that might be of independent interest.


  The significance of social media has increased manifold in the past few
decades as it helps people from even the most remote corners of the world to
stay connected. With the advent of technology, digital media has become more
relevant and widely used than ever before and along with this, there has been a
resurgence in the circulation of fake news and tweets that demand immediate
attention. In this paper, we describe a novel Fake News Detection system that
automatically identifies whether a news item is "real" or "fake", as an
extension of our work in the CONSTRAINT COVID-19 Fake News Detection in English
challenge. We have used an ensemble model consisting of pre-trained models
followed by a statistical feature fusion network , along with a novel heuristic
algorithm by incorporating various attributes present in news items or tweets
like source, username handles, URL domains and authors as statistical feature.
Our proposed framework have also quantified reliable predictive uncertainty
along with proper class output confidence level for the classification task. We
have evaluated our results on the COVID-19 Fake News dataset and FakeNewsNet
dataset to show the effectiveness of the proposed algorithm on detecting fake
news in short news content as well as in news articles. We obtained a best
F1-score of 0.9892 on the COVID-19 dataset, and an F1-score of 0.9073 on the
FakeNewsNet dataset.


  Let A be a positive operator in an infinite sigma-finite von Neumann factor M
and let B_j be a sequence of positive elements in M. We give sufficient
conditions for decomposing A into a sum of elements C_j equivalent to B_j for
all j ( C equivalent to B in M means that C=XX* and B=X*X for some X in M) and
when C_j are unitarily equivalent to B_j for all j. This extends recent work of
Bourin and Lee for the case of B_j= B for all j and M=B(H) and answers
affirmatively their conjecture. For the case when B_j= B for all j we provide
necessary conditions, which in the type III case are also sufficient.


  In this contribution, I review the current observational evidence for the
existence of filaments of Warm-Hot Intergalactic Medium (WHIM). In particular,
I first focus on the controversial issue of the identification of the $z\sim 0$
highly ionized far-ultraviolet (i.e. OVI) and X-ray (i.e. OVII, OVIII and NeIX)
absorbers with either a very tenuous and diffuse WHIM filament, or with much
denser condensations of material at large distances in the Galactic halo. I
then present our recent detection (confidence level $> 3\sigma$) of the OVII
WHIM at $z > 0$ and derive an estimate of the total number of baryons contained
in this hard-to-detect phase of the IGM.


  The nanostructure and magnetic properties of polycrystalline MgCNi_3 were
studied by x-ray diffraction, electron microscopy, and vibrating sample
magnetometry. While the bulk flux-pinning force curve F_p(H) indicates the
expected grain-boundary pinning mechanism just below T_c = 7.2 K, a systematic
change to pinning by a nanometer-scale distribution of core pinning sites is
indicated by a shift of F_p(H) with decreasing temperature. The lack of scaling
of F_p(H) suggests the presence of 10 to 20% of nonsuperconducting regions
inside the grains, which are smaller than the diameter of fluxon cores 2xi at
high temperature and become effective with decreasing temperature when xi(T)
approaches the nanostructural scale. Transmission electron microscopy revealed
cubic and graphite nanoprecipitates with 2 to 5 nm size, consistent with the
above hypothesis since xi(0) = 6 nm. High critical current densities, more than
10^6 A/cm^2 at 1 T and 4.2 K, were obtained for grain colonies separated by
carbon. Dirty-limit behavior seen in previous studies may be tied to electron
scattering by the precipitates, indicating the possibility that strong core
pinning might be combined with a technologically useful upper critical field if
versions of MgCNi_3 with higher T_c can be found.


  This paper presents a simple and effective generalization method for magnetic
resonance imaging (MRI) segmentation when data is collected from multiple MRI
scanning sites and as a consequence is affected by (site-)domain shifts. We
propose to integrate a traditional encoder-decoder network with a
regularization network. This added network includes an auxiliary loss term
which is responsible for the reduction of the domain shift problem and for the
resulting improved generalization. The proposed method was evaluated on
multiple sclerosis lesion segmentation from MRI data. We tested the proposed
model on an in-house clinical dataset including 117 patients from 56 different
scanning sites. In the experiments, our method showed better generalization
performance than other baseline networks.


  Many logic programming based approaches can be used to describe and solve
combinatorial search problems. On the one hand there is constraint logic
programming which computes a solution as an answer substitution to a query
containing the variables of the constraint satisfaction problem. On the other
hand there are systems based on stable model semantics, abductive systems, and
first order logic model generators which compute solutions as models of some
theory. This paper compares these different approaches from the point of view
of knowledge representation (how declarative are the programs) and from the
point of view of performance (how good are they at solving typical problems).


  A short review of scalar curvature invariants in gravity theories is
presented. We introduce how these invariants are constructed and discuss the
minimal number of invariants required for a given spacetime. We then discuss
applications of these invariants and focus on three topics that are of
particular interest in modern gravity theories.


  The paper reports on computation of verified enclosures for the
Titchmarsh-Weyl m-function. It examines some cases in which Lohner's AWA
algorithm must be suplimented by mathematical analysis.


  Digital whole-slide images of pathological tissue samples have recently
become feasible for use within routine diagnostic practice. These gigapixel
sized images enable pathologists to perform reviews using computer workstations
instead of microscopes. Existing workstations visualize scanned images by
providing a zoomable image space that reproduces the capabilities of the
microscope. This paper presents a novel visualization approach that enables
filtering of the scale-space according to color preference. The visualization
method reveals diagnostically important patterns that are otherwise not
visible. The paper demonstrates how this approach has been implemented into a
fully functional prototype that lets the user navigate the visualization
parameter space in real time. The prototype was evaluated for two common
clinical tasks with eight pathologists in a within-subjects study. The data
reveal that task efficiency increased by 15% using the prototype, with
maintained accuracy. By analyzing behavioral strategies, it was possible to
conclude that efficiency gain was caused by a reduction of the panning needed
to perform systematic search of the images. The prototype system was well
received by the pathologists who did not detect any risks that would hinder use
in clinical routine.


  Least squares estimation of phylogenies is an established family of methods
with good statistical properties. State-of-the-art least squares phylogenetic
estimation proceeds by first estimating a distance matrix, which is then used
to determine the phylogeny by minimizing a squared-error loss function. Here,
we develop a method for least squares phylogenetic inference that does not rely
on a pre-estimated distance matrix. Our approach allows us to circumvent the
typical need to first estimate a distance matrix by forming a new loss function
inspired by the phylogenetic likelihood score function; in this manner,
inference is not based on a summary statistic of the sequence data, but
directly on the sequence data itself. We use a Jukes-Cantor substitution model
to show that our method leads to improvements over ordinary least squares
phylogenetic inference, and is even observed to rival maximum likelihood
estimation in terms of topology estimation efficiency. Using a Kimura
2-parameter model, we show that our method also allows for estimation of the
global transition/transversion ratio simultaneously with the phylogeny and its
branch lengths. This is impossible to accomplish with any other distance-based
method as far as we know. Our developments pave the way for more optimal
phylogenetic inference under the least squares framework, particularly in
settings under which likelihood-based inference is infeasible, including when
one desires to build a phylogeny based on information provided by only a subset
of all possible nucleotide substitutions such as synonymous or non-synonymous
substitutions.


  Indian Classical Dance is an over 5000 years' old multi-modal language for
expressing emotions. Preservation of dance through multimedia technology is a
challenging task. In this paper, we develop a system to generate a parseable
representation of a dance performance. The system will help to preserve
intangible heritage, annotate performances for better tutoring, and synthesize
dance performances. We first attempt to capture the concepts of the basic steps
of an Indian Classical Dance form, named Bharatanatyam Adavus, in an
ontological model. Next, we build an event-based low-level model that relates
the ontology of Adavus to the ontology of multi-modal data streams (RGB-D of
Kinect in this case) for a computationally realizable framework. Finally, the
ontology is used for transcription into Labanotation. We also present a
transcription tool for encoding the performances of Bharatanatyam Adavus to
Labanotation and test it on our recorded data set. Our primary aim is to
document the complex movements of dance in terms of Labanotation using the
ontology.


  Our fast-paced digital economy shaped by global competition requires
increased data-driven decision-making based on artificial intelligence (AI) and
machine learning (ML). The benefits of deep learning (DL) are manifold, but it
comes with limitations that have - so far - interfered with widespread industry
adoption. This paper explains why DL - despite its popularity - has
difficulties speeding up its adoption within business analytics. It is shown -
by a mixture of content analysis and empirical study - that the adoption of
deep learning is not only affected by computational complexity, lacking big
data architecture, lack of transparency (black-box), and skill shortage, but
also by the fact that DL does not outperform traditional ML models in the case
of structured datasets with fixed-length feature vectors. Deep learning should
be regarded as a powerful addition to the existing body of ML models instead of
a one size fits all solution.


  ASCA observed the central region of the Small Magellanic Cloud, and found a
hard X-ray source, AX J0051-733, at the position of the ROSAT source RX
J0050.8-7316, which has an optical counterpart of a Be star. Coherent X-ray
pulsations of 323.1 +/- 0.3 s were discovered from AX J0051-733. The pulse
profile shows several sub-peaks in the soft (0.7-2.0 keV) X-ray band, but
becomes nearly sinusoidal in the harder (2.0-7.0 keV) X-ray band. The X-ray
spectrum was found to be hard, and is well fitted by a power-law model with a
photon index of 1.0 +/- 0.4. The long-term flux history was examined with the
archival data of Einstein observatory and ROSAT; a flux variability with a
factor > 10 was found.


  Failures and anomalies in large-scale software systems are unavoidable
incidents. When an issue is detected, operators need to quickly and correctly
identify its location to facilitate a swift repair. In this work, we consider
the problem of identifying the root cause set that best explains an anomaly in
multi-dimensional time series with categorical attributes. The huge search
space is the main challenge, even for a small number of attributes and small
value sets, the number of theoretical combinations is too large to brute force.
Previous approaches have thus focused on reducing the search space, but they
all suffer from various issues, requiring extensive manual parameter tuning,
being too slow and thus impractical, or being incapable of finding more complex
root causes. We propose RiskLoc to solve the problem of multidimensional root
cause localization. RiskLoc applies a 2-way partitioning scheme and assigns
element weights that linearly increase with the distance from the partitioning
point. A risk score is assigned to each element that integrates two factors, 1)
its weighted proportion within the abnormal partition, and 2) the relative
change in the deviation score adjusted for the ripple effect property.
Extensive experiments on multiple datasets verify the effectiveness and
efficiency of RiskLoc, and for a comprehensive evaluation, we introduce three
synthetically generated datasets that complement existing datasets. We
demonstrate that RiskLoc consistently outperforms state-of-the-art baselines,
especially in more challenging root cause scenarios, with gains in F1-score up
to 57% over the second-best approach with comparable running times.


  We present the first experimental measurements of the isotropic and nematic
phases of mixtures of thin, charged semiflexible fd virus, and thick, fd-PEG
created by covalently grafting poly-(ethylene glycol) to the the surface of fd,
rods. The fd-PEG is sterically stabilized and its phase behavior is independent
of ionic strength. The fd is charged. Therefore, by varying the ionic strength
of a mixture of fd and fd-PEG, only the effective diameter of the bare fd rods
changes, subsequently varying the effective diameter ratio (d=D_fd-PEG/D_fd)
from 3.7 to 1. In solution, binary mixtures of fd and fd-PEG are shown to
exhibit isotropic-nematic, isotropic-nematic-nematic and nematic-nematic
coexisting phases with increasing concentration. We measure the binary phase
diagrams as a function of composition, total concentration, and ionic strength.
We find a lower critical point in the nematic-nematic coexistence region which
has not been observed previously. These experimental results resolve a
controversy in the literature concerning the evolution of the nematic-nematic
phase separation with concentration. The experimental results are qualitatively
described by a rescaled Onsager-type theory for the phase behavior of binary
rod mixtures.


  We propose a quantum ghost imaging scheme based on biphotons, that, by using
a collimated pump beam of the right size for biphoton generation, obviates the
need for lenses to achieve imaging. The scheme is found to be analogous to the
classical pinhole camera, where we show that the equivalent to the classical
pinhole size depends mainly on the width of the pump beam, but also on the
thickness of the nonlinear crystal and the wavelengths of the biphoton.


  A direct measurement of the 0.862 MeV 7Be solar neutrino interaction rate
performed with the Borexino detector at the Laboratori Nazionali del Gran Sasso
yields 46.0$\pm1.5_{\rm stat}$$^{+1.6}_{-1.5\,\rm syst}$ counts/day/(100 tons).
Our result is the first direct measurement of a sub-MeV solar neutrino rate
with an accuracy better than 5%. The hypothesis of no oscillation for 7Be solar
neutrinos is rejected at 4.9$\sigma$ C.L. Using the latest Standard Solar Model
(SSM) flux predictions, the result leads directly to a precise determination of
the survival probability for solar $\nu_e$'s in vacuum, and permits us to probe
with unprecedented sensitivity the transition between the matter-enhanced and
vacuum-dominated neutrino oscillation regimes characteristic of the MSW-LMA
solution to the solar neutrino problem.


  The GaAs/AlGaAs materials system is well suited to multi-bandgap applications
such as the multiple quantum well solar cell. GaAs quantum wells are inserted
in the undoped AlGaAs active region of a pin structure to extend the absorption
range while retaining a higher open circuit voltage than would be provided by a
cell made of the well material alone. Unfortunately aluminium gallium arsenide
(AlGaAs) suffers from poor transport characteristics due to DX centres and
oxygen contamination during growth, which degrade the spectral response. We
investigate three mechanisms for improving the spectral response of the MQW
solar cell while an experimental study of the open circuit voltage examines the
voltage enhancement. An optimised structure for a high efficiency GaAs/AlGaAs
solar cell is proposed.


  Comets are considered as the most primitive objects in the Solar System.
Their composition provides information on the composition of the primitive
solar nebula, 4.6 Gyr ago. The radio domain is a privileged tool to study the
composition of cometary ices. Observations of the OH radical at 18 cm
wavelength allow us to measure the water production rate. A wealth of molecules
(and some of their isotopologues) coming from the sublimation of ices in the
nucleus have been identified by observations in the millimetre and
submillimetre domains. We present an historical review on radio observations of
comets, focusing on the results from our group, and including recent
observations with the Nan\c{c}ay radio telescope, the IRAM antennas, the Odin
satellite, the Herschel space observatory, ALMA, and the MIRO instrument aboard
the Rosetta space probe.


  The galactic cosmic rays are generally believed to be originated in supernova
remnants (SNRs), produced in diffusive shock acceleration (DSA) process in
supernova blast waves driven by expanding SNRs. One of the key unsettled issue
in SNR origin of cosmic ray model is the maximum attainable energy by a cosmic
ray particle in the supernova shock. Recently it has been suggested that an
amplification of effective magnetic field strength at the shock may take place
in young SNRs due to growth of magnetic waves induced by accelerated cosmic
rays and as a result the maximum energy achieved by cosmic rays in SNR may
reach the knee energy instead of $\sim 200$ TeV as predicted earlier under
normal magnetic field situation. In the present work we investigate the
implication of such maximum energy scenarios on TeV gamma rays and neutrino
fluxes from the molecular clouds interacting with the SNR W28. The authors
compute the gamma-ray and neutrino flux assuming two different values for the
maximum energy reached by cosmic rays in the SNR, from CR interaction in nearby
molecular clouds. Both protons and nuclei are considered as accelerated
particles and as target material. Our findings suggest that the issue of the
maximum energy of cosmic rays in SNRs can be observationally settled by the
upcoming gamma-ray experiment the Large High Altitude Air Shower Observatory
(LHAASO). The estimated neutrino fluxes from the molecular clouds are ,
however, out of reach of the present/near future generation of neutrino
telescopes.


  In the attempts toward a quantum gravity theory, general relativity faces a
serious difficulty since it is non-renormalizable theory. Ho\v{r}ava-Lifshitz
gravity offers a framework to circumvent this difficulty, by sacrificing the
local Lorentz invariance at ultra-high energy scales in exchange of
power-counting renormalizability. The Lorentz symmetry is expected to be
recovered at low and medium energy scales. If gravitation is to be described by
a Ho\v{r}ava-Lifshitz gravity theory there are a number of issues that ought to
be reexamined in its context, including the question as to whether this gravity
incorporates a chronology protection, or particularly if it allows G\"odel-type
solutions with violation of causality. We show that Ho\v{r}ava-Lifshitz gravity
only allows hyperbolic G\"odel-type space-times whose essential parameters $m$
and $\omega$ are in the chronology respecting intervals, excluding therefore
any noncausal G\"odel-type space-times in the hyperbolic class. There emerges
from our results that the famous noncausal G\"odel model is not allowed in
Ho\v{r}ava-Lifshitz gravity. The question as to whether this quantum gravity
theory permits hyperbolic G\"odel-type solutions in the chronology preserving
interval of the essential parameters is also examined. We show that
Ho\v{r}ava-Lifshitz gravity not only excludes the noncausal G\"odel universe,
but also rules out any hyperbolic G\"odel-type solutions for physically
well-motivated perfect-fluid matter content.


  Discrete time random walks, in which a step of random sign but constant
length $\delta x$ is performed after each time interval $\delta t$, are widely
used models for stochastic processes. In the case of a correlated random walk,
the next step has the same sign as the previous one with a probability $q \neq
1/2$. We extend this model to an inhomogeneous ensemble of random walkers with
a given distribution of persistence probabilites $p(q)$ and show that
remarkable statistical properties can result from this inhomogenity: Depending
on the distribution $p(q)$, we find that the probability density $p(\Delta x,
\Delta t)$ for a displacement $\Delta x$ after lagtime $\Delta t$ can have a
leptocurtic shape and that mean squared displacements can increase
approximately like a fractional powerlaw with $\Delta t$. For the special case
of persistence parameters distributed equally in the full range $q \in [0,1]$,
the mean squared displacement is derived analytically. The model is further
extended by allowing different step lengths $\delta x_j$ for each member $j$ of
the ensemble. We show that two ensembles $[\delta t, {(q_j,\delta x_j)}]$ and
$[\delta t^{\prime}, {(q^{\prime}_j,\delta x^{\prime}_j)}]$ defined at
different time intervals $\delta t\neq\delta t^{\prime}$ can have the same
statistical properties at long lagtimes $\Delta t$, if their parameters are
related by a certain scaling transformation. Finally, we argue that similar
statistical properties are expected for homogeneous ensembles, in which the
parameters $(q_j(t),\delta x_j(t))$ of each individual walker fluctuate
temporarily, provided the parameters can be considered constant for time
periods $T\gg\Delta t$ longer than the considered lagtime $\Delta t$.


  Non-holonomic constraints, both in the Lagragian and Hamiltonian formalism,
are discussed from the geometrical viewpoint of implicit differential
equations. A precise statement of both problems is presented remarking the
similarities and differences with other classical problems with constraints. In
our discussion, apart from a constraint submanifold, a field of permitted
directions and a system of reaction forces are given, the later being in
principle unrelated to the constraint submanifold. An implicit differential
equation is associated to a non-holonomic problem using the Tulczyjew's
geometrical description of the Legendre transformation. The integrable part of
this implicit differential equation is extracted using an adapted version of
the integrability algorithm. Moreover, sufficient conditions are found that
guarantees the compatibility of the non-holonomic problem, i.e., that assures
that the integrability algorithm stops at first step, and moreover it implies
the existence of a vector field whose integral curves are the solutions to the
problem. In addition this vector field turns out to be a second order
differential equation. These compatibility conditions are shown to include as
particular cases many others obtained previously by other authors. Several
examples and further lines of development of the subject are also discussed.


  This work is a continuation of the description of some classes of nilpotent
Zinbiel algebras. We focus on the study of Zinbiel algebras with restrictions
to gradation and characteristic sequence. Namely, the classification of
naturally graded Zinbiel algebras with characteristic sequence equal to $ (n-p,
p)$ is obtained.


  A previous article shows that any linear height bounded normal proof of a
tautology in the Natural Deduction for Minimal implicational logic
$M_{\supset}$ is as huge as it is redundant. More precisely, any proof in a
family of super-polynomially sized and linearly height bounded proofs have a
sub-derivation that occurs super-polynomially many times in it. In this
article, we show that by collapsing all the repeated sub-derivations we obtain
a smaller structure, a rooted Directed Acyclic Graph (r-DAG), that is
polynomially upper-bounded on the size of $\alpha$ and it is a certificate that
$\alpha$ is a tautology that can be verified in polynomial time. In other
words, for every huge proof of a tautology in $M_{\supset}$, we obtain a
succinct certificate for its validity. Moreover, we show an algorithm able to
check this validity in polynomial time on the certificate's size. Comments on
how the results in this article are related to a proof of the conjecture
$NP=CoNP$ appears in conclusion.


  Odyssey 2 will be proposed in December 2010 for the next call of M3 missions
for Cosmic Vision 2015-2025. This mission, under a Phase 0 study performed by
CNES, will aim at Neptune and Triton. Two sets of objectives will be pursued.
The first one is to perform a set of gravitation experiments at the Solar
System scale. Experimental tests of gravitation have always shown good
agreement with General Relativity. There are however drivers to continue
testing General Relativity, and to do so at the largest possible scales. From a
theoretical point of view, Einstein's theory of gravitation shows
inconsistencies with a quantum description of Nature and unified theories
predict deviations from General Relativity. From an observational point of
view, as long as dark matter and dark energy are not observed through other
means than their gravitational effects, they can be considered as a
manifestation of a modification of General Relativity at cosmic scales. The
scientific objectives are to: (i) test the gravitation law at the Solar System
scale; (ii) measure the Eddington parameter; and (iii) investigate the
navigation anomalies during fly-bys. To fulfil these objectives, the following
components are to be on board the spacecraft: (i) the Gravity Advanced Package
(GAP), which is an electrostatic accelerometer to which a rotating stage is
added; (ii) radio-science; (iii) laser ranging, to improve significantly the
measure of the Eddington parameter. The second set of objectives is to enhance
our knowledge of Neptune and Triton. Several instruments dedicated to
planetology are foreseen: camera, spectrometer, dust and particle detectors,
and magnetometer. Depending on the ones kept, the mission could provide
information on the gravity field, the atmosphere and the magnetosphere of the
two bodies as well as on the surface geology of Triton and on the nature of the
planetary rings around Neptune.


  Herein we report experimental evidence of directional SERS from molecules
situated inside a single nanowire-nanoparticle junction cavity. The emission
was confined to a narrow range of wavevectors perpendicular to the axis of the
cavity. In addition to this, the molecules excite multiple guided modes of the
nanowire which were imaged using leakage radiation Fourier microscopy. We
further characterize the emission wavevectors as a function of output
polarization. The excited guided modes of the wire show interesting
polarization signatures. All the results were corroborated using finite element
method based numerical simulations. Essentially, we provide an important
connection between gap-cavity enhanced Raman scattering and its directionality
of emission. The results may be of relevance in understanding the cavity
electrodynamics at the nanoscale and molecular coupling to extremely small gaps
between a one dimensional and a zero-dimensional plasmonic nanostructure.


  The hydrodynamics of a variant of classical Bondi-Hoyle-Lyttleton accretion
is investigated: a totally absorbing sphere moves at various Mach numbers (3
and 10) relative to a medium, which is taken to be an ideal gas having a
density gradient (of 3%, 20% or 100% over one accretion radius) perpendicular
to the relative motion. Similarly to the 3D models published previously, both
with velocity gradients and without, the models with a density gradient
presented here exhibit non-stationary flow patterns, although the Mach cone
remains fairly stable. The accretion rates of mass, linear and angular momenta
do not fluctuate as strongly as published previously for 2D models. No obvious
trend of the dependency of mass accretion rate fluctuations on the density
gradient can be discerned. The average specific angular momentum accreted is
roughly between zero and 70% of the total angular momentum available in the
accretion cylinder in the cases where the average is prograde. Due to the large
fluctuations during accretion, the average angular momentum of some models is
retrograde by up to 25%. Small gradients hardly influence the average accretion
rates as compared to accretion from a homogeneous medium, while very large ones
succeed to dominate and form an accretion flow in which the sense of rotation
is not inverted.


  The problem of Hybrid Linear Modeling (HLM) is to model and segment data
using a mixture of affine subspaces. Different strategies have been proposed to
solve this problem, however, rigorous analysis justifying their performance is
missing. This paper suggests the Theoretical Spectral Curvature Clustering
(TSCC) algorithm for solving the HLM problem, and provides careful analysis to
justify it. The TSCC algorithm is practically a combination of Govindu's
multi-way spectral clustering framework (CVPR 2005) and Ng et al.'s spectral
clustering algorithm (NIPS 2001). The main result of this paper states that if
the given data is sampled from a mixture of distributions concentrated around
affine subspaces, then with high sampling probability the TSCC algorithm
segments well the different underlying clusters. The goodness of clustering
depends on the within-cluster errors, the between-clusters interaction, and a
tuning parameter applied by TSCC. The proof also provides new insights for the
analysis of Ng et al. (NIPS 2001).


  Facing the challenge of statistical diversity in client local data
distribution, personalized federated learning (PFL) has become a growing
research hotspot. Although the state-of-the-art methods with model
similarity-based pairwise collaboration have achieved promising performance,
they neglect the fact that model aggregation is essentially a collaboration
process within the coalition, where the complex multiwise influences take place
among clients. In this paper, we first apply Shapley value (SV) from coalition
game theory into the PFL scenario. To measure the multiwise collaboration among
a group of clients on the personalized learning performance, SV takes their
marginal contribution to the final result as a metric. We propose a novel
personalized algorithm: pFedSV, which can 1. identify each client's optimal
collaborator coalition and 2. perform personalized model aggregation based on
SV. Extensive experiments on various datasets (MNIST, Fashion-MNIST, and
CIFAR-10) are conducted with different Non-IID data settings (Pathological and
Dirichlet). The results show that pFedSV can achieve superior personalized
accuracy for each client, compared to the state-of-the-art benchmarks.


  In the context of two-dimensional (2D) turbulence, we apply the maximum
entropy production principle (MEPP) by enforcing a local conservation of
energy. This leads to an equation for the vorticity distribution that conserves
all the Casimirs, the energy, and that increases monotonically the mixing
entropy ($H$-theorem). Furthermore, the equation for the coarse-grained
vorticity dissipates monotonically all the generalized enstrophies. These
equations may provide a parametrization of 2D turbulence. They do not generally
relax towards the maximum entropy state. The vorticity current vanishes for any
steady state of the 2D Euler equation. Interestingly, the equation for the
coarse-grained vorticity obtained from the MEPP turns out to coincide, after
some algebraic manipulations, with the one obtained with the anticipated
vorticity method. This shows a connection between these two approaches when the
conservation of energy is treated locally. Furthermore, the newly derived
equation, which incorporates a diffusion term and a drift term, has a nice
physical interpretation in terms of a selective decay principle. This gives a
new light to both the MEPP and the anticipated vorticity method.


  Optical afterglows from two-component jets under various configurations are
investigated numerically. Generally, the light curve is characterized by a
rapid rebrightening when the observer is off-axis with respect to the narrow
component, with the amplitude and peak time depending on detailed parameters.
We further show that the optical afterglow of XRF 030723, especially its
notable and rapid rebrightening, can be well explained by a typical
two-component jet. This X-ray flash, together with GRB 030329, strongly hints
the two-component jet model as a unified picture for X-ray flashes and
gamma-ray bursts. With a narrow but ultra-relativistic inner outflow and a wide
but less energetic outer ejecta, a two-component jet will be observed as a
typical gamma-ray burst if our line of sight is within the angular scope of the
narrow outflow. Otherwise, if the line of sight is within or slightly beyond
the cone of the wide component, an X-ray flash will be detected.


  ATLAS-SCT has developed a new ATLAS trigger card, 'Digital Atlas Vme
Electronics' ("DAVE"). The unit is designed to provide a versatile array of
interface and logic resources, including a large FPGA. It interfaces to both
VME bus and USB hosts. DAVE aims to provide exact ATLAS CTP (ATLAS Central
Trigger Processor) functionality, with random trigger, simple and complex
deadtime, ECR (Event Counter Reset), BCR (Bunch Counter Reset) etc. being
generated to give exactly the same conditions in standalone running as
experienced in combined runs. DAVE provides additional hardware and a large
amount of free firmware resource to allow users to add or change functionality.
The combination of the large number of individually programmable inputs and
outputs in various formats, with very large external RAM and other components
all connected to the FPGA, also makes DAVE a powerful and versatile FPGA
utility card