  Resolution lies at the foundation of both logic programming and type class
context reduction in functional languages. Terminating derivations by
resolution have well-defined inductive meaning, whereas some non-terminating
derivations can be understood coinductively. Cycle detection is a popular
method to capture a small subset of such derivations. We show that in fact
cycle detection is a restricted form of coinductive proof, in which the atomic
formula forming the cycle plays the role of coinductive hypothesis.
  This paper introduces a heuristic method for obtaining richer coinductive
hypotheses in the form of Horn formulas. Our approach subsumes cycle detection
and gives coinductive meaning to a larger class of derivations. For this
purpose we extend resolution with Horn formula resolvents and corecursive
evidence generation. We illustrate our method on non-terminating type class
resolution problems.


  We present the environmental properties around high-$z$ radio galaxies
(HzRGs) at $z\sim4$, which have been poorly investigated because of their
rarity. We use the largest samples of HzRGs and $g$-dropout galaxy overdense
regions at $z\sim4$, which were constructed from Hyper Suprime-Cam Subaru
Strategic Program, to characterize the HzRG environments statistically. We
measure the $g$-dropout galaxy overdensities around 21 HzRGs whose rest-frame
1.4 GHz radio luminosities ($L_{1.4\mathrm{GHz}}$) are $10^{26-27}$ W
Hz$^{-1}$. We find that the overdensities around the faint HzRGs with
$L_{1.4\mathrm{GHz}}\sim10^{26.0-26.5}$ W Hz$^{-1}$ tend to be higher than that
of the $g$-dropout galaxies. On the other hand, no significant difference of
density environments is found between the luminous HzRGs with $
L_{1.4\mathrm{GHz}}\sim10^{26.5-27.0} $ W Hz$^{-1}$ and the $g$-dropout
galaxies. The HzRGs are found to occupy more massive halos than $g$-dropout
galaxies through a cross-correlation between the HzRGs and $g$-dropout
galaxies. This trend is more pronounced in the faint HzRGs. These results are
consistent with a scenario where HzRGs get older and more massive as the
radio-luminosity decreases. The HzRGs are expected to trace the progenitors of
local cluster halos from their calculated halo mass. In addition, we find that
surrounding galaxies tend to distribute along the radio-jet major axis of the
HzRGs at angular distances less than $\lesssim500$ physical kpc. Our findings
imply the onset of the filamentary structures around the HzRGs at $z\sim4$.


  We have analytically explored temperature dependence of critical number of
particles for the collapse of a harmonically trapped attractively interacting
Bose gas below the condensation point by introducing a kinetic approach within
the Hartree-Fock approximation. The temperature dependence obtained by this
easy approach is consisted with that obtained from the scaling theory.


  We revisit the effects of the Hubbard repulsion on quantum spin Hall effects
(QSHE) in two-dimensional quantum lattice models. We present both unbiased
exact diagonalization and density-matrix renormalization group simulations with
numerical evidences for a continuous quantum phase transition (CQPT) separating
QSHE from the topologically trivial antiferromagnetic phase. Our numerical
results suggest that, the nature of CQPT exhibits distinct finite-size scaling
behaviors, which may be consistent with either Ising or XY universality classes
for different time-reversal symmetric QSHE systems.


  A dual-purpose ion-accelerator concept, capable of serving as radiation
source in a versatile, nuclear-reaction-based cargo inspection system, is
presented. The system will automatically and reliably detect small,
operationally-relevant quantities of concealed explosives and special nuclear
materials (SNM). It will be cost-effective, employing largely-common hardware,
but different reactions/DAQ-modes. Typical expected throughput is 10-20
aviation containers/hr.
  PACS: 25.20.Dc; 25.40.Ny; 27.20.+n; 29.27.Fh; 79.77.+g; 89.20.Bb; 89.20.Dd
  Keywords: Cargo inspection; Nuclear-reaction-based methods; Explosives
detection; SNM detection


  Let 0<p<1 be fixed. Shamir and Spencer proved in the 1980s that the chromatic
number of a random graph in G(n,p) is concentrated in an interval of length
about n^{1/2}. In this explanatory note, we give a proof of a result due due
Noga Alon, showing that the chromatic number is concentrated in an interval of
length about n^{1/2}/log n.


  This work proposes a technique for constructing a statistical closure model
for reduced-order models (ROMs) applied to stationary systems modeled as
parameterized systems of algebraic equations. The proposed technique extends
the reduced-order-model error surrogates (ROMES) method to closure modeling.
The original ROMES method applied Gaussian-process regression to construct a
statistical model that maps cheaply computable error indicators (e.g., residual
norm, dual-weighted residuals) to a random variable for either (1) the norm of
the state error or (2) the error in a scalar-valued quantity of interest.
Rather than target these two types of errors, this work proposes to construct a
statistical model for the state error itself; it achieves this by constructing
statistical models for the generalized coordinates characterizing both the
in-plane error (i.e., the error in the trial subspace) and a low-dimensional
approximation of the out-of-plane error. The former can be considered a
statistical closure model, as it quantifies the error in the ROM generalized
coordinates. Because any quantity of interest can be computed as a functional
of the state, the proposed approach enables any quantity-of-interest error to
be statistically quantified a posteriori, as the state-error model can be
propagated through the associated quantity-of-interest functional. Numerical
experiments performed on both linear and nonlinear stationary systems
illustrate the ability of the technique (1) to improve (expected) ROM
prediction accuracy by an order of magnitude, (2) to statistically quantify the
error in arbitrary quantities of interest, and (3) to realize a more
cost-effective methodology for reducing the error than a ROM-only approach in
the case of nonlinear systems.


  Markov chain Monte Carlo (MCMC) sampling of posterior distributions arising
in Bayesian inverse problems is challenging when evaluations of the forward
model are computationally expensive. Replacing the forward model with a
low-cost, low-fidelity model often significantly reduces computational cost;
however, employing a low-fidelity model alone means that the stationary
distribution of the MCMC chain is the posterior distribution corresponding to
the low-fidelity model, rather than the original posterior distribution
corresponding to the high-fidelity model. We propose a multifidelity approach
that combines, rather than replaces, the high-fidelity model with a
low-fidelity model. First, the low-fidelity model is used to construct a
transport map that deterministically couples a reference Gaussian distribution
with an approximation of the low-fidelity posterior. Then, the high-fidelity
posterior distribution is explored using a non-Gaussian proposal distribution
derived from the transport map. This multifidelity "preconditioned" MCMC
approach seeks efficient sampling via a proposal that is explicitly tailored to
the posterior at hand and that is constructed efficiently with the low-fidelity
model. By relying on the low-fidelity model only to construct the proposal
distribution, our approach guarantees that the stationary distribution of the
MCMC chain is the high-fidelity posterior. In our numerical examples, our
multifidelity approach achieves significant speedups compared to
single-fidelity MCMC sampling methods.


  We present the CKM-LWG, a collection of working groups whose aim is to
compile world averages of lattice results relevant for high-energy
phenomenology.


  We present the first results from the X-shooter Lens Survey (XLENS): an
analysis of the massive early-type galaxy SDSS J1148+1930 at redshift z=0.444.
We combine its extended kinematic profile -derived from spectra obtained with
X-shooter on the ESO VLT- with strong gravitational lensing and multi-color
information derived from SDSS images. Our main results are (i) The
luminosity-weighted stellar velocity dispersion is \sigma *(<Reff) = 351\pm10
km/s, extracted from a rectangular aperture of 1.8"x1.6", more accurate and
considerably lower than a previously published value of \sim450km/s. (ii) A
single-component (stellar plus dark) mass model of the lens galaxy yields a
logarithmic total-density slope of {\gamma}' = 1.72+0.05-0.06. (iii) The
projected stellar mass fraction, derived solely from lensing, is f*(<Reff) =
0.19+0.04-0.09 inside the Einstein radius for a Hernquist profile and no
anisotropy. The dark-matter fraction inside the effective radius f_DM(<Reff) =
0.60+0.15\pm0.1. (iv) Based on the SDSS colors, we find f*(<Reff)=0.17 \pm 0.06
for a Salpeter IMF and f*(<Reff)=0.07 \pm 0.02 for a Chabrier IMF. The lensing
and dynamics constraints on the stellar mass fraction agree well with those
independently derived from the SDSS colors for a Salpeter IMF, preferred over
Chabrier IMF at variance with standard results for lower mass galaxies.
Dwarf-rich IMFs in the lower mass range of 0.1-0.7 solar mass, with {\alpha} >=
3 (with dN/dM \propto M^(-{\alpha})) -such as that recently suggested for
massive ETGs- are excluded at the > 90 % C.L. and in some cases violate the
total lensing-derived mass limit. We conclude that this very massive ETG is
dark-matter dominated inside one effective radius, consistent with the trend
recently found from massive SLACS galaxies, with a IMF normalization consistent
with Salpeter.


  We have examined the effects of a bound dineutron, n2, upon big bang
nucleosynthesis (BBN) as a function of its binding energy B_n2. We find a
weakly bound dineutron has little impact but as B_n2 increases its presence
begins to alter the flow of free nucleons to helium-4. Due to this disruption,
and in the absence of changes to other binding energies or fundamental
constants, BBN sets a reliable upper limit of B_n2 <~ 2.5 MeV in order to
maintain the agreement with the observations of the primordial helium-4 mass
fraction and D/H abundance.


  Guided image filter is a well-known local filter in image processing.
However, the presence of halo artifacts is a common issue associated with this
type of filter. This paper proposes an algorithm that utilizes gradient
information to accurately identify the edges of an image. Furthermore, the
algorithm uses weighted information to distinguish flat areas from edge areas,
resulting in sharper edges and reduced blur in flat areas. This approach
mitigates the excessive blurring near edges that often leads to halo artifacts.
Experimental results demonstrate that the proposed algorithm significantly
suppresses halo artifacts at the edges, making it highly effective for both
image denoising and detail enhancement.


  In this study, we construct an evolutionary model of a population of DNA
sequences interacting with the surrounding environment on the topological
monoid A* of strings on the alphabet A = { a, c, g, t }. A partial differential
equation governing the evolution of the DNA population is derived as a kind of
diffusion equation on A*. Analyzing the constructed model in a theoretical
manner, we present conditions for sympatric speciation, the possibility of
which continues to be discussed. It is shown that under other same conditions
one condition determines whether sympatric speciation occurs or the DNA
population continues to move around randomly in a subset of A*. We next
demonstrate that the population maintains a kind of equlibrium state under
certain conditions. In this situation, the population remains nearly unchanged
and does not differentiate even if it can differentiate into others.
Furthermore, we calculate the probability of sympatric speciation and the time
expected to elapse before it.


  We demonstrate the sensitivity of magnetic energy and helicity computations
regarding the quality of the underlying coronal magnetic field model. We apply
the method of Wiegelmann & Inhester (2010) to a series of SDO/HMI vector
magnetograms, and discuss nonlinear force-free (NLFF) solutions based on two
different sets of the free model parameters. The two time series differ from
each other concerning their force-free and solenoidal quality. Both force- and
divergence-freeness are required for a consistent NLFF solution. Full
satisfaction of the solenoidal property is inherent in the definition of
relative magnetic helicity in order to insure gauge-independence. We apply two
different magnetic helicity computation methods (Thalmann et al. 2011; Valori
et al. 2012) to both NLFF time series and find that the output is highly
dependent on the level to which the NLFF magnetic fields satisfy the
divergence-free condition, with the computed magnetic energy being less
sensitive than the relative helicity. Proxies for the non-potentiality and
eruptivity derived from both quantities are also shown to depend strongly on
the solenoidal property of the NLFF fields. As a reference for future
applications, we provide quantitative thresholds for the force- and
divergence-freeness, for the assurance of reliable computation of magnetic
energy and helicity, and of their related eruptivity proxies.


  In this proceeding, I discuss results from the BaBar and Belle collaborations
for searches of direct CP violation in the singly Cabibbo-suppressed decay
$\D^\pm\to K^+K^-\pi^\pm$ from $e^+e^-$ annihilation data collected at a
center-of-mass energy at or just below the \Y4S resonance. The Belle
collaboration measures the CP asymmetry as a function of the production angle
of the $D^\pm$ meson in the quasi two-body $\D^\pm\to\phi\pi^\pm$ decay. The
Babar experiment studies the entire phase-space with model-independent and
model-dependent Dalitz plot analysis techniques to search for CP-violating
asymmetries in the various intermediate states, in addition to a phase-space
integrated measurement as a function of the production angle. No evidence for
CP violation is reported from either experiment.


  We consider a model with two parallel (positive tension) 3-branes separated
by a distance $L$ in 5-dimensional spacetime. If the interbrane space is
anti-deSitter, or is not precisely anti-deSitter but contains no event
horizons, the effective 4-dimensional cosmological constant seen by observers
on one of the branes (chosen to be the visible brane) becomes exponentially
small as $L$ grows large.


  Right-handed neutrinos with MeV to GeV mass are very promising candidates for
dark matter (DM). Not only can they solve the missing satellite puzzle, the
cusp-core problem of inner DM density profiles, and the too-big-to fail
problem, {\it i.e.} that the unobserved satellites are too big to not have
visible stars, but they can also account for the Standard Model (SM) neutrino
masses at one loop. We perform a comprehensive study of the right-handed
neutrino parameter space and impose the correct observed relic density and SM
neutrino mass differences and mixings. We find that the DM masses are in
agreement with bounds from big-bang nucleosynthesis, but that these constraints
induce sizeable DM couplings to the charged SM leptons. We then point out that
previously overlooked limits from current and future lepton flavour violation
experiments such as MEG and SINDRUM heavily constrain the allowed parameter
space. Since the DM is leptophilic, we also investigate electron recoil as a
possible direct detection signal, in particular in the XENON1T experiment. We
find that despite the large coupling and low backgrounds, the energy thresholds
are still too high and the predicted cross sections too low due to the heavy
charged mediator, whose mass is constrained by LEP limits.


  Optical coherence tomography (OCT) scanning is useful in detecting various
retinal diseases. However, there are not enough ophthalmologists who can
diagnose retinal OCT images in much of the world. To provide OCT screening
inexpensively and extensively, an automated diagnosis system is indispensable.
Although many machine learning techniques have been presented for assisting
ophthalmologists in diagnosing retinal OCT images, there is no technique that
can diagnose independently without relying on an ophthalmologist, i.e., there
is no technique that does not overlook any anomaly, including unlearned
diseases. As long as there is a risk of overlooking a disease with a technique,
ophthalmologists must double-check even those images that the technique
classifies as normal. Here, we show that our deep-learning-based binary
classifier (normal or abnormal) achieved a perfect classification on 108,308
two-dimensional retinal OCT images, i.e., true positive rate = 1.000000 and
true negative rate = 1.000000; hence, the area under the ROC curve = 1.0000000.
Although the test set included three types of diseases, two of these were not
used for training. However, all test images were correctly classified.
Furthermore, we demonstrated that our scheme was able to cope with differences
in patient race. No conventional approach has achieved the above performances.
Our work has a sufficient possibility of raising automated diagnosis techniques
for retinal OCT images from "assistant for ophthalmologists" to "independent
diagnosis system without ophthalmologists".


  Let F:X->B be a morphism of varieties in characteristic zero. The problem of
semistable reduction of F was stated as a problem in the combinatorics of
polyhedral complexes by Abramovich and Karu (alg-geom/9707012). In this paper
we solve the combinatorial problem when the relative dimension of F is not
bigger than 3.


  The Fast Marching Method is a very popular algorithm to compute
times-of-arrival maps (distances map measured in time units). Since their
proposal in 1995, it has been applied to many different applications such as
robotics, medical computer vision, fluid simulation, etc. Many alternatives
have been proposed with two main objectives: to reduce its computational time
and to improve its accuracy. In this paper, we collect the main approaches
which improve the computational time of the standard Fast Marching Method,
focusing on single-threaded methods and isotropic environments. 9 different
methods are studied under a common mathematical framework and experimentally in
representative environments: Fast Marching Method with binary heap, Fast
Marching Method with Fibonacci Heap, Simplified Fast Marching Method, Untidy
Fast Marching Method, Fast Iterative Method, Group Marching Method, Fast
Sweeping Method, Lock Sweeping Method and Double Dynamic Queue Method.


  We present a non-parametric measure of the ellipticity and the alignment of
the dark matter halos in Abell 901/902 supercluster. This super-cluster is a
system of four separate peaks in a $0.5^{\circ}\times0.5^{\circ}$ field of
view. We map the mass distribution of each individual peak using an improved
version of Particle Based Lensing (PBL) and measure the ellipticity of the dark
matter halos associated with two of the peaks directly from the mass map and by
fitting them to a singular isothermal ellipse. The parametric and
non-parametric measurements are consistent for A901b while the position angle
for the Southwest Group is different for the two techniques. We account for
this discrepancy to substructure present in the Southwest Peak. We estimate an
axis ratio of $0.37\pm 0.1$ for A901b and $0.54^{+0.08}_{-0.09}$ for the
Southwest Group.


  We present abundances of globular clusters in the Milky Way and Fornax from
integrated light spectra. Our goal is to evaluate the consistency of the
integrated light analysis relative to standard abundance analysis for
individual stars in those same clusters. This sample includes an updated
analysis of 7 clusters from our previous publications and results for 5 new
clusters that expand the metallicity range over which our technique has been
tested. We find that the [Fe/H] measured from integrated light spectra agrees
to $\sim$0.1 dex for globular clusters with metallicities as high as
[Fe/H]=$-0.3$, but the abundances measured for more metal rich clusters may be
underestimated. In addition we systematically evaluate the accuracy of
abundance ratios, [X/Fe], for Na I, Mg I, Al I, Si I, Ca I, Ti I, Ti II, Sc II,
V I, Cr I, Mn I, Co I, Ni I, Cu I, Y II, Zr I, Ba II, La II, Nd II, and Eu II.
The elements for which the integrated light analysis gives results that are
most similar to analysis of individual stellar spectra are Fe I, Ca I, Si I, Ni
I, and Ba II. The elements that show the greatest differences include Mg I and
Zr I. Some elements show good agreement only over a limited range in
metallicity. More stellar abundance data in these clusters would enable more
complete evaluation of the integrated light results for other important
elements.


  The contextual word embedding model, BERT, has proved its ability on
downstream tasks with limited quantities of annotated data. BERT and its
variants help to reduce the burden of complex annotation work in many
interdisciplinary research areas, for example, legal argument mining in digital
humanities. Argument mining aims to develop text analysis tools that can
automatically retrieve arguments and identify relationships between
argumentation clauses. Since argumentation is one of the key aspects of case
law, argument mining tools for legal texts are applicable to both academic and
non-academic legal research. Domain-specific BERT variants (pre-trained with
corpora from a particular background) have also achieved strong performance in
many tasks. To our knowledge, previous machine learning studies of argument
mining on judicial case law still heavily rely on statistical models. In this
paper, we provide a broad study of both classic and contextual embedding models
and their performance on practical case law from the European Court of Human
Rights (ECHR). During our study, we also explore a number of neural networks
when being combined with different embeddings. Our experiments provide a
comprehensive overview of a variety of approaches to the legal argument mining
task. We conclude that domain pre-trained transformer models have great
potential in this area, although traditional embeddings can also achieve strong
performance when combined with additional neural network layers.


  We investigate the finite size effect on the vector meson and the baryon
sectors using a subset of the "PACS10" configurations which are generated,
keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the
physical point. Comparing the results on (5.5 fm$)^4$ and (10.9 fm$)^4$
lattices the ground states of octet baryons , which are stable on the lattice,
show no finite size effect within less than 0.5% level of statistical errors.
For those of vector mesons, which are unstable on the lattice, we observe that
the effective masses are well below the experimental resonance levels both on
(5.5 fm$)^4$ and (10.9 fm$)^4$ lattices. For the decuplet baryon sector we have
found that the time dependence of the effective mass looks quite similar to
that for the vector meson sector including the $\Omega$ baryon channel. We
discuss its origin due to a possible mixing with the nearby multihadron states.
Since the $\Xi$ baryon mass can be determined with the smallest ambiguity among
the vector meson and the baryon masses, we use it together with the pion and
kaon masses as the physical inputs to determine the physical point.


  We show that any tangent cone of a singular shrinking K\"ahler-Ricci soliton
is a normal affine algebraic variety. Moreover, the regular set of such a
tangent cone in the metric sense coincides with the regular set in the
algebraic sense. Along the way, we give a parabolic proof of H\"ormander's
$L^{2}$ estimate, which can be used to solve the $\overline{\partial}$-equation
on any singular shrinking K\"ahler-Ricci soliton.


  We study Berry connection polarizability (BCP) induced electric polarization
and third-order Hall (TOH) effect in a two-dimensional electron/hole gas
(2DEG/2DHG) with Rashba-Dresselhaus (RD) spin-orbit couplings in III-V
semiconductor heterostructures. The electric polarization decreases with the
increase of the Fermi energy and is responsive to the electric field
orientation in the presence of RD spin-orbit couplings for both systems. We
determine the BCP-induced TOH conductivity ($\chi_{\perp}^{\text{I}}$) along
with the TOH conductivity associated with the band velocity
($\chi_{\perp}^{\text{II}}$). We find that the presence of an infinitesimal
amount of Dresselhaus coupling in addition to the dominant Rashba coupling
results in finite TOH responses. These conductivities vanish when the field is
aligned with and/or orthogonal to the symmetry lines $k_x\pm k_y=0$ in both
systems. For typical system parameters in a 2DEG with $k$-linear RD
interactions, the magnitude of $\chi_{\perp}^{\text{I}}$ is smaller than that
of $\chi_{\perp}^{\text{II}}$. On the other hand, when both the SO couplings
are comparable, $\chi_{\perp}^{\text{I}}$ shows a notable increase in
magnitude, owing to the distinctive characteristics of BCP. The TOH
conductivity of 2DEG remains unchanged when Rashba and Dresselhaus spin-orbit
couplings are exchanged. For 2DHG with $k$-cubic RD interactions,
$\chi_{\perp}^{\text{I},h}$ exhibits a larger magnitude compared to
$\chi_{\perp}^{\text{II},h}$. Unlike the electron case, the BCP induced
$\chi_{\perp}^{\text{I},h}$ alters under the exchange of spin-orbit coupling
parameters, whereas $\chi_{\perp}^{\text{II},h}$ remains the same.


  Magnetic state of exchanged biased CoO(20nm)/Co($d_F$) bilayer ($d_F$=5-20nm)
was studied by means of polarized neutron reflectometry. By spacing of CoO/Co
bilayer and Al$_2$O$_3$ substrate with Nb(20nm) layer we created waveguide
structure which allowed us to significantly enhance intensity of spin-flip (SF)
scattering in the position of optical resonances. For the trained sample with
thinnest Co(5nm) we detected strong SF scattering at the resonance position (up
to 30\% of incoming intensity) speaking about high non-collinearity of the
system. As $d_F$ increases, the intensity of SF scattering linearly decreases.
At the same time we observed asymmetry of up-down and down-up scattering
channels at the resonance positions. We attribute this asymmetry to the Zeeman
splitting of neutrons energies with different initial polarization taking place
in high external field. Analysis, however, shows that the applied in the PNR
experiment external field is not enough to quantitatively explain the observed
asymmetry for the samples with $d_F > $ 5nm and we have to postulate presence
of additional magnetic field produced by sample. We attribute this additional
field to the stray field produced by chiral Bloch domain walls. The chirality
of the domain walls can be explained by Dzyaloshinskii-Moriya interaction
arising at the CoO/Co interface. Our results can be useful for designing of
spintronic devices using exchange bias effect.


  Maurice Jacob played a key role in bringing together different groups from
the experimental and theoretical nuclear and particle physics communities to
initiate an ultrarelativistic heavy-ion collision program at the CERN SPS, in
order to search for the quark-gluon plasma. I review the history of this
program from its beginnings to the time when the Relativistic Heavy Ion
Collider (RHIC) at Brookhaven National Laboratory (BNL) started operation. I
close by providing a glimpse of the important discoveries made at RHIC and
giving an outlook towards heavy-ion collisions at the Large Hadron Collider
(LHC). During Maurice's life and not least through his perpetually strong
influence, relativistic heavy-ion physics has matured and led to discoveries
that radiate into many other fields of physics. Heavy-ion physicists owe a
great deal to Maurice Jacob.


  We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov
equation $\partial_tu+\Delta\partial_xu+ u\partial_xu=0$ in the Sobolev spaces
$H^s(\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\R^3)$. The proof
is based on a sharp maximal function estimate in time-weighted spaces.


  Variational quantum algorithms (VQAs) that estimate values of widely used
physical quantities such as the rank, quantum entropies, the Bures fidelity and
the quantum Fisher information of mixed quantum states are developed. In
addition, variations of these VQAs are also adapted to perform other useful
functions such as quantum state learning and approximate fractional inverses.
The common theme shared by the proposed algorithms is that their cost functions
are all based on minimizing the quantum purity of a quantum state. Strategies
to mitigate or avoid the problem of exponentially vanishing cost function
gradients are also discussed.


  Classification is the most important process in data analysis. However, due
to the inherent non-convex and non-smooth structure of the zero-one loss
function of the classification model, various convex surrogate loss functions
such as hinge loss, squared hinge loss, logistic loss, and exponential loss are
introduced. These loss functions have been used for decades in diverse
classification models, such as SVM (support vector machine) with hinge loss,
logistic regression with logistic loss, and Adaboost with exponential loss and
so on. In this work, we present a Perceptron-augmented convex classification
framework, {\it Logitron}. The loss function of it is a smoothly stitched
function of the extended logistic loss with the famous Perceptron loss
function. The extended logistic loss function is a parameterized function
established based on the extended logarithmic function and the extended
exponential function. The main advantage of the proposed Logitron
classification model is that it shows the connection between SVM and logistic
regression via polynomial parameterization of the loss function. In more
details, depending on the choice of parameters, we have the Hinge-Logitron
which has the generalized $k$-th order hinge-loss with an additional $k$-th
root stabilization function and the Logistic-Logitron which has a logistic-like
loss function with relatively large $|k|$. Interestingly, even $k=-1$,
Hinge-Logitron satisfies the classification-calibration condition and shows
reasonable classification performance with low computational cost. The
numerical experiment in the linear classifier framework demonstrates that
Hinge-Logitron with $k=4$ (the fourth-order SVM with the fourth root
stabilization function) outperforms logistic regression, SVM, and other
Logitron models in terms of classification accuracy.


  The present study concerns the dynamic radiation force on solid elastic
spheres exerted by a plane wave with two frequencies (bichromatic wave)
considering the nonlinearity of the fluid. Our approach is based on solving the
wave scattering for the sphere in the quasilinear approximation within the
preshock wave range. The dynamic radiation force is then obtained by
integrating the component of the momentum flux tensor at the difference of the
primary frequencies over the boundary of the sphere. Results reveal that
effects of the nonlinearity of the fluid plays a major role in dynamic
radiation force leading it to a parametric amplification regime. The developed
theory is used to calculate the dynamic radiation force on three different
solid spheres (aluminium, silver, and tungsten). Resonances are observed in the
spectrum of the force on the spheres. They have larger amplitude and better
shape than resonances present in static radiation force.


  High computational complexity hinders the widespread usage of Convolutional
Neural Networks (CNNs), especially in mobile devices. Hardware accelerators are
arguably the most promising approach for reducing both execution time and power
consumption. One of the most important steps in accelerator development is
hardware-oriented model approximation. In this paper we present Ristretto, a
model approximation framework that analyzes a given CNN with respect to
numerical resolution used in representing weights and outputs of convolutional
and fully connected layers. Ristretto can condense models by using fixed point
arithmetic and representation instead of floating point. Moreover, Ristretto
fine-tunes the resulting fixed point network. Given a maximum error tolerance
of 1%, Ristretto can successfully condense CaffeNet and SqueezeNet to 8-bit.
The code for Ristretto is available.


  Vision Transformers (ViTs) are increasingly used in computer vision due to
their high performance, but their vulnerability to adversarial attacks is a
concern. Existing methods lack a solid theoretical basis, focusing mainly on
empirical training adjustments. This study introduces SpecFormer, tailored to
fortify ViTs against adversarial attacks, with theoretical underpinnings. We
establish local Lipschitz bounds for the self-attention layer and propose the
Maximum Singular Value Penalization (MSVP) to precisely manage these bounds By
incorporating MSVP into ViTs' attention layers, we enhance the model's
robustness without compromising training efficiency. SpecFormer, the resulting
model, outperforms other state-of-the-art models in defending against
adversarial attacks, as proven by experiments on CIFAR and ImageNet datasets.
Code is released at https://github.com/microsoft/robustlearn.


  Traditional fact checking by experts and analysts cannot keep pace with the
volume of newly created information. It is important and necessary, therefore,
to enhance our ability to computationally determine whether some statement of
fact is true or false. We view this problem as a link-prediction task in a
knowledge graph, and present a discriminative path-based method for fact
checking in knowledge graphs that incorporates connectivity, type information,
and predicate interactions. Given a statement S of the form (subject,
predicate, object), for example, (Chicago, capitalOf, Illinois), our approach
mines discriminative paths that alternatively define the generalized statement
(U.S. city, predicate, U.S. state) and uses the mined rules to evaluate the
veracity of statement S. We evaluate our approach by examining thousands of
claims related to history, geography, biology, and politics using a public,
million node knowledge graph extracted from Wikipedia and PubMedDB. Not only
does our approach significantly outperform related models, we also find that
the discriminative predicate path model is easily interpretable and provides
sensible reasons for the final determination.


  Robust estimation of star formation rates (SFRs) at higher redshifts (z>1)
using UV-optical-NIR photometry is contingent on the ability of spectral energy
distribution (SED) fitting to simultaneously constrain the dust attenuation,
stellar metallicity, and star formation history (SFH). IR-derived dust
luminosities can help break the degeneracy between these parameters, but IR
data is often not available. Here, we explore strategies for SED fitting at z>1
in the absence of IR data using a sample of log M*>10.2 star-forming galaxies
from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey
(CANDELS) for which 24mu data are available. We adopt the total IR luminosity
(L_TIR) obtained from 24mu as the 'ground truth' that allows us to assess how
well it can be recovered (as L_dust) from UV-optical-NIR SED fitting. We test a
variety of dust attenuation models, stellar population synthesis models,
metallicity assumptions, and SFHs separately to identify which assumptions
maximize the agreement (correlation and linearity) between L_TIR and L_dust. We
find that a flexible dust attenuation law performs best. For stellar
populations, we find that BC03 models are favored over those of BPASS. Fixing
the stellar metallicity at solar value is preferred to other fixed values or
leaving it as a free parameter. For SFHs, we find that minimizing the
variability in the recent (<100 Myr) SFH improves the agreement with L_TIR.
Finally, we provide a catalog of galaxy parameters (including M* and SFR) for
CANDELS galaxies with log M*>8 and 0.7<z<1.3 obtained using the models we found
to be the most robust.


  We present a new observable sensitive to a certain combination of CP
violating phases in supersymmetric extensions of the Standard Model, viz. a
triple product of momenta in the cascade decay of a heavy squark via an
on-shell neutralino and off-shell slepton. We investigate the regions of
parameter space in which the signal is strong enough to be detectable at the
LHC with $\sim \bigl(10^2-10^3\bigr)/\sin^2(2\Delta\phi)$ identified events,
where $\Delta\phi$ is a certain combination of phases in the MSSM presented in
the text.


  Given the marginal distribution information of the underlying asset price at
two future times $T_1$ and $T_2$, we consider the problem of determining a
model-free upper bound on the price of a class of American options that must be
exercised at either $T_1$ or $T_2$. The model uncertainty consistent with the
given marginal information is described as the martingale optimal transport
problem. We show that any option exercise scheme associated with any market
model that jointly maximizes the expected option payoff must be nonrandomized
if the American option payoff satisfies a suitable convexity condition and the
model-free price upper bound and its relaxed version coincide. The latter
condition is desired to be removed under appropriate conditions on the cost and
marginals.


  Sensors based on whispering gallery mode resonators can detect single
nanoparticles and even single molecules. Particles attaching to the resonator
induce a doublet in the transmission spectrum which provides a self-referenced
detection signal. However, in practice this spectral feature is often obscured
by the width of the resonance line which hides the doublet structure. This
happens particularly in liquid environments that reduce the effective Q factor
of the resonator. In this paper we demonstrate an interferometric set-up that
allows the direct detection of the hidden doublet and thus provides a pathway
for developing practical sensor applications.


  Optimization-based safety filters, such as control barrier function (CBF)
based quadratic programs (QPs), have demonstrated success in controlling
autonomous systems to achieve complex goals. These CBF-QPs can be shown to be
continuous, but are generally not smooth, let alone continuously
differentiable. In this paper, we present a general characterization of smooth
safety filters -- smooth controllers that guarantee safety in a minimally
invasive fashion -- based on the Implicit Function Theorem. This
characterization leads to families of smooth universal formulas for
safety-critical controllers that quantify the conservatism of the resulting
safety filter, the utility of which is demonstrated through illustrative
examples.


  Preterm births occur at an alarming rate of 10-15%. Preemies have a higher
risk of infant mortality, developmental retardation and long-term disabilities.
Predicting preterm birth is difficult, even for the most experienced
clinicians. The most well-designed clinical study thus far reaches a modest
sensitivity of 18.2-24.2% at specificity of 28.6-33.3%. We take a different
approach by exploiting databases of normal hospital operations. We aims are
twofold: (i) to derive an easy-to-use, interpretable prediction rule with
quantified uncertainties, and (ii) to construct accurate classifiers for
preterm birth prediction. Our approach is to automatically generate and select
from hundreds (if not thousands) of possible predictors using stability-aware
techniques. Derived from a large database of 15,814 women, our simplified
prediction rule with only 10 items has sensitivity of 62.3% at specificity of
81.5%.


  Machine learning, artificial intelligence and especially deep learning based
approaches are often used to simplify or eliminate the burden of programming
industrial robots. Using these approaches robots inherently learn a skill
instead of being programmed using strict and tedious programming instructions.
While deep learning is effective in making robots learn skills, it does not
offer a practical route for teaching a complete task, such as assembly or
machine tending, where a complex logic must be understood and related sub-tasks
need to be performed. We present a model similar to an episodic memory that
allows robots to comprehend sequences of actions using single demonstration and
perform them properly and accurately. The algorithm identifies and recognizes
the changes in the states of the system and memorizes how to execute the
necessary tasks in order to make those changes. This allows the robot to
decompose the tasks into smaller sub-tasks, retain the essential steps, and
remember how they have been performed.


  We show that for two afii varieties over an arbitrary field of characteristic
zero, there is no general form of an algorithm for checking the presence of an
embedding of one algebraic variety in another. Moreover, we establish this for
affine varieties whose coordinate rings are given by generators and defining
relations. Moreover, one of these varieties can be taken as an affine space,
and in the case of a field of real numbers, an affine line.


  Modern programming languages, such as Java and C#, typically provide features
that handle exceptions. These features separate error-handling code from
regular source code and are proven to enhance the practice of software
reliability, comprehension, and maintenance. Having acknowledged the advantages
of exception handling features, the misuse of them can still cause catastrophic
software failures, such as application crash. Prior studies suggested
anti-patterns of exception handling; while little knowledge was shared about
the prevalence of these anti-patterns. In this paper, we investigate the
prevalence of exception-handling anti-patterns. We collected a thorough list of
exception anti-patterns from 16 open-source Java and C# libraries and
applications using an automated exception flow analysis tool. We found that
although exception handling anti- patterns widely exist in all of our subjects,
only a few anti- patterns (e.g. Unhandled Exceptions, Catch Generic,
Unreachable Handler, Over-catch, and Destructive Wrapping) can be commonly
identified. On the other hand, we find that the prevalence of anti- patterns
illustrates differences between C# and Java. Our results call for further
in-depth analyses on the exception handling practices across different
languages.


  Aim of this paper is to study the non-existence of global solutions of the
fractional differential problem involving generalized Katugampola derivative.
We utilize the test function method and fractional integration by parts formula
to obtain the result. An illustrative example is also given.


  The enhancon mechanism is studied in the heterotic string theory. We consider
the N_L=0 winding strings with momentum (NS1-W*) and the Kaluza-Klein dyons
(KK5-NS5*). The NS1-W* and KK5-NS5* systems are dualized to the D4-D0* and
D6-D2* systems, respectively, under the d=6 heterotic/IIA S-duality. The
heterotic form has a number of advantages over the type IIA form. We study
these backgrounds and obtain the enhancon radii by brane probe analysis. The
results are consistent with S-duality.


  The existence of an unparticle sector, weakly coupled to the standard model,
would have a profound impact on supernova (SN) physics. Emission of energy into
the unparticle sector from the core of SN1987A would have significantly
shortened the observed neutrino burst. The unparticle interaction with
nucleons, neutrinos, electrons and muons is constrained to be so weak that it
is unlikely to provide any missing-energy signature at colliders. One important
exception are models where scale invariance in the hidden sector is broken by
the Higgs vacuum expectation value. In this case the SN emission is suppressed
by threshold effects.


  We propose a holographic dual of a conformal field theory defined on a
manifold with boundaries, i.e. boundary conformal field theory (BCFT). Our new
holography, which may be called AdS/BCFT, successfully calculates the boundary
entropy or g-function in two dimensional BCFTs and it agrees with the finite
part of the holographic entanglement entropy. Moreover, we can naturally derive
a holographic g-theorem. We also analyze the holographic dual of an interval at
finite temperature and show that there is a first order phase transition.


  Two relevant points related to the application of the BFKL formalism to
phenomenology are discussed. First, we have presented a set of observables
characterizing multi-jet configurations event by event (average transverse
momentum, average azimuthal angle, average ratio of jet rapidities) which can
be used to find distinct signals of BFKL dynamics at the LHC. A numerical
analysis has been shown using the Monte Carlo event generator BFKLex, modified
to include higher-order collinear corrections in addition to the
transverse-momentum implementation of the NLO kernel. We require to have two
tagged forward/backward jets in the final state. Second, the structure of the
BFKL equation changes if infrared boundary conditions are imposed when
considering the running of the coupling. The cut in the complex angular
momentum plane becomes an infinite series of Regge poles. Integrating along a
contour off the real axis we find a strong dependence of the intercepts and
collinear regions on the choice of the boundary conditions. The mean transverse
scales dominant in the gluon ladder increase. This could have interesting
phenomenological consequences.


  In the domain of unsupervised learning most work on speech has focused on
discovering low-level constructs such as phoneme inventories or word-like
units. In contrast, for written language, where there is a large body of work
on unsupervised induction of semantic representations of words, whole sentences
and longer texts. In this study we examine the challenges of adapting these
approaches from written to spoken language. We conjecture that unsupervised
learning of the semantics of spoken language becomes feasible if we abstract
from the surface variability. We simulate this setting with a dataset of
utterances spoken by a realistic but uniform synthetic voice. We evaluate two
simple unsupervised models which, to varying degrees of success, learn semantic
representations of speech fragments. Finally we present inconclusive results on
human speech, and discuss the challenges inherent in learning distributional
semantic representations on unrestricted natural spoken language.


  Turbophoresis leading to preferential concentration of inertial particles in
regions of low turbulent diffusivity is a unique feature of inhomogeneous
turbulent flows, such as free shear flows or wall-bounded flows. In this work,
the theory for clustering of weakly inertial particles in homogeneous
turbulence is extended to the inhomogeneous case of a turbulent channel flow.
The inhomogeneity contributes to the cluster formation in addition to
clustering in homogeneous turbulence. A space-dependent rate for the creation
of inhomogeneous particle concentration is derived in terms of local statistics
of turbulence. We provide the formula for the pair-correlation function of
concentration that factorizes in product of time and space-dependent average
concentrations and time-independent factor of clustering that obeys a power-law
in the distance between the points. This power-law characterizes inhomogeneous
multifractality of the particle distribution. A unique demonstration and
quantification of the combined effects of turbophoresis and fractal clustering
in a direct numerical simulation of particle motion in a turbulent channel flow
is performed according to the presented theory. The strongest contribution to
clustering coming from the inhomogeneity of the flow occurs in the transitional
region between viscous sublayer and the buffer layer. Further the ratio of
homogeneous and inhomogeneous term depends on the wall distance. The
inhomogeneous terms may significantly increase the preferential concentration
of inertial particles, thus the overall degree of clustering in inhomogeneous
turbulence is potentially stronger compared to particles with the same inertia
in purely homogeneous turbulence.


  We investigate how well CLIP understands texture in natural images described
by natural language. To this end, we analyze CLIP's ability to: (1) perform
zero-shot learning on various texture and material classification datasets; (2)
represent compositional properties of texture such as red dots or yellow
stripes on the Describable Texture in Detail(DTDD) dataset; and (3) aid
fine-grained categorization of birds in photographs described by color and
texture of their body parts.


  We study the optimal investment stopping problem in both continuous and
discrete case, where the investor needs to choose the optimal trading strategy
and optimal stopping time concurrently to maximize the expected utility of
terminal wealth. Based on the work [9] with an additional stochastic payoff
function, we characterize the value function for the continuous problem via the
theory of quadratic reflected backward stochastic differential equation (BSDE
for short) with unbounded terminal condition. In regard to discrete problem, we
get the discretization form composed of piecewise quadratic BSDEs recursively
under Markovian framework and the assumption of bounded obstacle, and provide
some useful prior estimates about the solutions with the help of auxiliary
forward-backward SDE system and Malliavin calculus. Finally, we obtain the
uniform convergence and relevant rate from discretely to continuously quadratic
reflected BSDE, which arise from corresponding optimal investment stopping
problem through above characterization.


  Derivation of the Lorentz transformation without the use of Einstein's Second
Postulate is provided along the lines of Ignatowsky, Terletskii, and others.
This is a write-up of the lecture first delivered in PHYS 4202 E&M class during
the Spring semester of 2014 at the University of Georgia. The main motivation
for pursuing this approach was to develop a better understanding of why the
faster-than-light neutrino controversy (OPERA experiment, 2011) was much ado
about nothing.


  It has been proved that direct bootstrapping of the nonparametric maximum
likelihood estimator (MLE) of the distribution function in the current status
model leads to inconsistent confidence intervals. We show that bootstrapping of
functionals of the MLE can however be used to produce valid intervals. To this
end, we prove that the bootstrapped MLE converges at the right rate in the
$L_p$-distance. We also discuss applications of this result to the current
status regression model.


  We consider the propagation of acoustic time-harmonic waves in a homogeneous
media containing periodic lattices of spherical or cylindrical inclusions. It
is assumed that the wavelength has the order of the periods of the lattice
while the radius $a$ of inclusions is small. A new approach is suggested to
derive the complete asymptotic expansions of the dispersion relations in two
and three-dimensional cases as $a \to 0$ and evaluate explicitly several first
terms. Our method is based on the reduction of the original singularly
perturbed (by inclusions) problem to the regular one. The Neumann, Dirichlet
and transmission boundary conditions are considered. The effective wave speed
is obtained as a function of the wave frequency, the filling fraction of the
inclusions, and the physical properties of the constituents of the mixture.
Dependence of asymptotic formulas obtained in the paper on geometric and
material parameters is illustrated by graphs.


  Results from the state-of-the-art molecular dynamics simulations are
presented for both equilibrium and nonequilibrium dynamics following
vapor-liquid transition in a single component Lennard-Jones system. We have
fixed the overall density close to the vapor-branch of the coexistence curve so
that the liquid phase forms droplet structure in the background of vapor phase.
In the equilibrium case, the motion of a single droplet is studied in both
microcanonical and canonical ensembles, in the latter case a hydrodynamics
preserving Nos\'{e}-Hoover thermostat was used to control the temperature. The
droplet nucleation, motion, collision and coalescence dynamics in the
nonequilibrium case were studied in the canonical ensemble with Nos\'{e}-Hoover
thermostat. There it was observed that the average droplet volume grows
linearly with time. Between two successive collisions, the size of the droplets
remain same even though all the constituent particles do not move with the
droplets \textminus some leave, others join. It is seen that the number of
original particles in a droplet decays exponentially fast. Results from a
liquid-liquid transition are also presented in the equilibrium context.
Dynamics of droplets in equilibrium appears to be at variant with the
nonequilibrium case.


  A self-consistent symmetry arises when the nucleon angular momentum j and the
isospin t are coupled to a grand spin G. Closed G shells become sources of a
classical pion field with a hedgehog shape. Although the amplitude of the pion
field, as measured by the chiral angle, is small, it is found to perturb
significantly the energies of the nucleon orbits.


  We call progressive paths and rushed paths two families of Dyck paths studied
by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry
A287709). We present a bijection proving this fact. Rushed paths turn out to be
in bijection with one-sided trees, introduced by Durhuus and Unel, which have
an asymptotic enumeration involving a stretched exponential. We conclude by
presenting several other classes of related lattice paths and directed animals
that may have similar asymptotic properties.


  Let $\mathbf{k}$ be the field $\mathbb{F}_p$ or the ring $\mathbb{Z}$. We
study combinatorial and topological properties of the universal simplicial
complexes $X(\mathbf{k}^n)$ and $K(\mathbf{k}^n)$ whose simplices are certain
unimodular subsets of $\mathbf{k}^n$. As a main result we show that
$X(\mathbf{k}^n)$, $K(\mathbf{k}^n)$ and the links of their simplicies are
homotopy equivalent to a wedge of spheres specifying the exact number of
spheres in the corresponding wedge decompositions. This is a generalisation of
Davis and Januszkiewicz's result that $K(\mathbb{Z}^n)$ and $K(\mathbb{F}_2^n)$
are $(n-2)$-connected simplicial complexes.
  We discuss applications of these universal simplicial complexes to toric
topology and number theory.


  In this paper we show that for a given set of pairwise comaximal ideals
$\{X_i\}_{i\in I}$ in a ring $R$ with unity and any right $R$-module $M$ with
generating set $Y$ and
$C(X_i)=\sum\limits_{k\in\mathbb{N}}\underline{\ell}_M(X_i^{k})$,
$M=\oplus_{i\in I}C(X_i)$ if and only if for every $y\in Y$ there exists a
nonempty finite subset $J\subseteq I$ and positive integers $k_j$ such that
$\bigcap\limits_{j\in J}X_i^{k_j}\subseteq\underline{r}_R(yR)$. We investigate
this decomposition for a general class of modules. Our main theorem can be
applied to a large class of rings including semilocal rings $R$ with the
Jacobson radical of $R$ equal to the prime radical of $R$, left (or right)
perfect rings, piecewise prime rings, and rings with ACC on ideals and
satisfying the right AR property on ideals. This decomposition generalizes the
decomposition of a torsion abelian group into a direct sum of its p-components.
We also develop a torsion theory associated with sets of pairwise comaximal
ideals.


  In this paper, we get the holographic equipartition form the first order
formulism, that is, the connection and its conjugate momentum are considered to
be the canonical variables. The final results have similar structure as those
from the metric formulism.


  We propose two main applications of Gy\"{o}ngy (1986)'s construction of
inhomogeneous Markovian stochastic differential equations that mimick the
one-dimensional marginals of continuous It\^{o} processes. Firstly, we prove
Dupire (1994) and Derman and Kani (1994)'s result. We then present Bessel-based
stochastic volatility models in which this relation is used to compute
analytical formulas for the local volatility. Secondly, we use these mimicking
techniques to extend the well-known local volatility results to a stochastic
interest rates framework.


  The main aim of this paper is to study existence and stability properties of
rotationally symmetric proper biharmonic maps between two $m$-dimensional
models (in the sense of Greene and Wu). We obtain a complete classification of
rotationally symmetric, proper biharmonic conformal diffeomorphisms in the
special case that $m=4$ and the models have constant sectional curvature. Then,
by introducing the Hamiltonian associated to this problem, we also obtain a
complete description of conformal proper biharmonic solutions in the case that
the domain model is ${\mathbb R}^4$. In the second part of the paper we carry
out a stability study with respect to equivariant variations (equivariant
stability). In particular, we prove that: (i) the inverse of the stereographic
projection from the open $4$-dimensional Euclidean ball to the hyperbolic space
is equivariant stable; (ii) the inverse of the stereographic projection from
the closed $4$-dimensional Euclidean ball to the sphere is equivariant stable
with respect to variations which preserve the boundary data.


  The term "CoRE kernel" stands for correlation-resemblance kernel. In many
applications (e.g., vision), the data are often high-dimensional, sparse, and
non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary
sparse data and demonstrate the effectiveness of the new kernels through a
classification experiment. CoRE kernels are simple with no tuning parameters.
However, training nonlinear kernel SVM can be (very) costly in time and memory
and may not be suitable for truly large-scale industrial applications (e.g.
search). In order to make the proposed CoRE kernels more practical, we develop
basic probabilistic hashing algorithms which transform nonlinear kernels into
linear kernels.


  The substitution of gallium by aluminum, germanium, tin and indium in
PuCoGa5, the actinide-based superconductor with the highest critical
temperature, has been investigated. Only systems with 20% substitution by Al
and Ge (i.e. PuCoGa4Al and PuCoGa4Ge) have been successfully synthesized by
annealing arc-melted samples. X-ray powder diffraction refinements indicate an
enhanced c/a ratio in these two compounds but the magnetic susceptibility
measurements reveal a large reduction of the critical temperature Tc compared
to PuCoGa5. DFT+ED calculations indicate significant changes in the Fermi
surface, probably related to the decrease of Tc, in these compounds. In
addition, the isotopic effect of the atomic mass of gallium, using 69Ga and
71Ga isotopes, was also investigated without observable influence on the
critical temperature of PuCoGa5.


  Most existing video diffusion models (VDMs) are limited to mere text
conditions. Thereby, they are usually lacking in control over visual appearance
and geometry structure of the generated videos. This work presents Moonshot, a
new video generation model that conditions simultaneously on multimodal inputs
of image and text. The model builts upon a core module, called multimodal video
block (MVB), which consists of conventional spatialtemporal layers for
representing video features, and a decoupled cross-attention layer to address
image and text inputs for appearance conditioning. In addition, we carefully
design the model architecture such that it can optionally integrate with
pre-trained image ControlNet modules for geometry visual conditions, without
needing of extra training overhead as opposed to prior methods. Experiments
show that with versatile multimodal conditioning mechanisms, Moonshot
demonstrates significant improvement on visual quality and temporal consistency
compared to existing models. In addition, the model can be easily repurposed
for a variety of generative applications, such as personalized video
generation, image animation and video editing, unveiling its potential to serve
as a fundamental architecture for controllable video generation. Models will be
made public on https://github.com/salesforce/LAVIS.


  The main contribution of the paper is to show that Gaussian sketching of a
kernel-Gram matrix $\boldsymbol K$ yields an operator whose counterpart in an
RKHS $\mathcal H$, is a \emph{random projection} operator---in the spirit of
Johnson-Lindenstrauss (J-L) lemma. To be precise, given a random matrix $Z$
with i.i.d. Gaussian entries, we show that a sketch $Z\boldsymbol{K}$
corresponds to a particular random operator in (infinite-dimensional) Hilbert
space $\mathcal H$ that maps functions $f \in \mathcal H$ to a low-dimensional
space $\mathbb R^d$, while preserving a weighted RKHS inner-product of the form
$\langle f, g \rangle_{\Sigma} \doteq \langle f, \Sigma^3 g \rangle_{\mathcal
H}$, where $\Sigma$ is the \emph{covariance} operator induced by the data
distribution. In particular, under similar assumptions as in kernel PCA (KPCA),
or kernel $k$-means (K-$k$-means), well-separated subsets of feature-space
$\{K(\cdot, x): x \in \cal X\}$ remain well-separated after such operation,
which suggests similar benefits as in KPCA and/or K-$k$-means, albeit at the
much cheaper cost of a random projection. In particular, our convergence rates
suggest that, given a large dataset $\{X_i\}_{i=1}^N$ of size $N$, we can build
the Gram matrix $\boldsymbol K$ on a much smaller subsample of size $n\ll N$,
so that the sketch $Z\boldsymbol K$ is very cheap to obtain and subsequently
apply as a projection operator on the original data $\{X_i\}_{i=1}^N$. We
verify these insights empirically on synthetic data, and on real-world
clustering applications.


  Semantic image synthesis (SIS) aims to generate realistic images that match
given semantic masks. Despite recent advances allowing high-quality results and
precise spatial control, they require a massive semantic segmentation dataset
for training the models. Instead, we propose to employ a pre-trained
unconditional generator and rearrange its feature maps according to proxy
masks. The proxy masks are prepared from the feature maps of random samples in
the generator by simple clustering. The feature rearranger learns to rearrange
original feature maps to match the shape of the proxy masks that are either
from the original sample itself or from random samples. Then we introduce a
semantic mapper that produces the proxy masks from various input conditions
including semantic masks. Our method is versatile across various applications
such as free-form spatial editing of real images, sketch-to-photo, and even
scribble-to-photo. Experiments validate advantages of our method on a range of
datasets: human faces, animal faces, and buildings.


  We construct explicitly noncommutative deformations of categories of
holomorphic line bundles over higher dimensional tori. Our basic tools are
Heisenberg modules over noncommutative tori and complex/holomorphic structures
on them introduced by A. Schwarz. We obtain differential graded (DG) categories
as full subcategories of curved DG categories of Heisenberg modules over the
complex noncommutative tori. Also, we present the explicit composition formula
of morphisms, which in fact depends on the noncommutativity.


  From inspection of 30 Hubble Space Telescope ACS images of M31, we provide a
catalog of 449 galaxies seen through the spiral disk. Measurements of the
positions of the galaxies, their integrated magnitudes in two colors and their
sizes, determined from isophotometry, are included in the catalog. We discuss
the many difficulties of interpreting these data in terms of the effects of
intervening extinction by dust in the disk


  Recent QCD jet production measurements in p-pbar collisions at sqrt(s)=1.96
TeV at the Tevatron Collider at Fermilab are presented. Preliminary: inclusive
jet, dijet, isolated photon + jet and Z + jets measurements are compared to
available perturbative QCD models.


  For stationary, homogeneous Markov processes (viz., L\'{e}vy processes,
including Brownian motion) in dimension $d\geq 3$, we establish an exact
formula for the average number of $(d-1)$-dimensional facets that can be
defined by $d$ points on the process's path. This formula defines a
universality class in that it is independent of the increments' distribution,
and it admits a closed form when $d=3$, a case which is of particular interest
for applications in biophysics, chemistry and polymer science.
  We also show that the asymptotical average number of facets behaves as
$\langle \mathcal{F}_T^{(d)}\rangle \sim 2\left[\ln \left( T/\Delta
t\right)\right]^{d-1}$, where $T$ is the total duration of the motion and
$\Delta t$ is the minimum time lapse separating points that define a facet.


  The Population-based HIV Impact Assessment (PHIA) is an ongoing project that
conducts nationally representative HIV-focused surveys for measuring national
and regional progress toward UNAIDS' 90-90-90 targets, the primary strategy to
end the HIV epidemic. We believe the PHIA survey offers a unique opportunity to
better understand the key factors that drive the HIV epidemics in the most
affected countries in sub-Saharan Africa. In this article, we propose a novel
causal structural learning algorithm to discover important covariates and
potential causal pathways for 90-90-90 targets. Existing constrained-based
causal structural learning algorithms are quite aggressive in edge removal. The
proposed algorithm preserves more information about important features and
potential causal pathways. It is applied to the Malawi PHIA (MPHIA) data set
and leads to interesting results. For example, it discovers age and condom
usage to be important for female HIV awareness; the number of sexual partners
to be important for male HIV awareness; and knowing the travel time to HIV care
facilities leads to a higher chance of being treated for both females and
males. We further compare and validate the proposed algorithm using BIC and
using Monte Carlo simulations, and show that the proposed algorithm achieves
improvement in true positive rates in important feature discovery over existing
algorithms.


  Our view of the universe of genomic regions harboring various types of
candidate human-specific regulatory sequences (HSRS) has been markedly expanded
in recent years. To infer the evolutionary origins of loci harboring HSRS,
analyses of conservations patterns of 59,732 loci in Modern Humans, Chimpanzee,
Bonobo, Gorilla, Orangutan, Gibbon, and Rhesus genomes have been performed. Two
major evolutionary pathways have been identified comprising thousands of
sequences that were either inherited from extinct common ancestors (ECAs) or
created de novo in humans after human/chimpanzee split. Thousands of HSRS
appear inherited from ECAs yet bypassed genomes of our closest evolutionary
relatives, presumably due to the incomplete lineage sorting and/or
species-specific loss or regulatory DNA. The bypassing pattern is prominent for
HSRS associated with development and functions of human brain. Common genomic
loci that may contributed to speciation during evolution of Great Apes comprise
248 insertions sites of African Great Ape-specific retrovirus PtERV1 (45.9%; p
= 1.03E-44) intersecting regions harboring 442 HSRS, which are enriched for
HSRS associated with human-specific (HS) changes of gene expression in cerebral
organoids. Among non-human primates (NHP), most significant fractions of
candidate HSRS associated with HS expression changes in both excitatory neurons
(347 loci; 67%) and radial glia (683 loci; 72%) are highly conserved in Gorilla
genome. Modern Humans acquired unique combinations of regulatory sequences
highly conserved in distinct species of six NHP separated by 30 million years
of evolution. Concurrently, this unique mosaic of regulatory sequences
inherited from ECAs was supplemented with 12,486 created de novo HSRS. These
observations support the model of complex continuous speciation process during
evolution of Great Apes that is not likely to occur as an instantaneous event.


  Language agents have shown impressive problem-solving skills within defined
settings and brief timelines. Yet, with the ever-evolving complexities of
open-world simulations, there's a pressing need for agents that can flexibly
adapt to complex environments and consistently maintain a long-term memory to
ensure coherent actions. To bridge the gap between language agents and
open-world games, we introduce Language Agent for Role-Playing (LARP), which
includes a cognitive architecture that encompasses memory processing and a
decision-making assistant, an environment interaction module with a
feedback-driven learnable action space, and a postprocessing method that
promotes the alignment of various personalities. The LARP framework refines
interactions between users and agents, predefined with unique backgrounds and
personalities, ultimately enhancing the gaming experience in open-world
contexts. Furthermore, it highlights the diverse uses of language models in a
range of areas such as entertainment, education, and various simulation
scenarios. The project page is released at https://miao-ai-lab.github.io/LARP/.


  We present a concise review of the experimental developments on neutrino
mixing and their theoretical implications as presented and discussed at this
Conference. The recent data disfavour many models but the surviving ones still
span a wide range going from Anarchy (no structure, no symmetry in the neutrino
sector) to a maximum of symmetry, as for the models based on discrete
non-abelian flavour groups which can be improved following the indications from
the recent data.


  Blazar jets are extreme environments, in which relativistic proton
interactions with an ultraviolet photon field could give rise to photopion
production. High-confidence associations of individual high-energy neutrinos
with blazar flares could be achieved via spatially and temporally coincident
detections. In 2017, the track-like, extremely high-energy neutrino event IC
170922A was found to coincide with increased $\gamma$-ray emission from the
blazar TXS 0506+056, leading to the identification of the most promising
neutrino point source candidate so far. We calculate the expected number of
neutrino events that can be detected with IceCube, based on a broadband
parametrization of bright short-term blazar flares that were observed in the
first 6.5 years of \textit{Fermi}/LAT observations. We find that the integrated
keV-to-GeV fluence of most individual blazar flares is far too small to yield a
substantial Poisson probability for the detection of one or more neutrinos with
IceCube. We show that the sample of potentially detectable high-energy
neutrinos from individual blazar flares is rather small. We further show that
the blazars 3C 279 and PKS 1510$-$089 dominate the all-sky neutrino prediction
from bright and short-term blazar flares. In the end, we discuss strategies to
search for more significant associations in future data unblindings of IceCube
and KM3NeT.


  This paper presents an approach to deal with safety of dynamical systems in
presence of multiple non-convex unsafe sets. While optimal control and model
predictive control strategies can be employed in these scenarios, they suffer
from high computational complexity in case of general nonlinear systems.
Leveraging control barrier functions, on the other hand, results in
computationally efficient control algorithms. Nevertheless, when safety
guarantees have to be enforced alongside stability objectives, undesired
asymptotically stable equilibrium points have been shown to arise. We propose a
computationally efficient optimization-based approach which allows us to ensure
safety of dynamical systems without introducing undesired equilibria even in
presence of multiple non-convex unsafe sets. The developed control algorithm is
showcased in simulation and in a real robot navigation application.


  In discrete time, customers arrive at random. Each waits until one of three
servers is available; each thereafter departs at random. We seek the
distribution of maximum line length of idle customers. Algebraic expressions
obtained for the two-server scenario do not appear feasible here. We also
review well-known distributional results for maximum wait time associated with
an M/M/1 queue and speculate about their generalization.


  Mental disorders represent critical public health challenges as they are
leading contributors to the global burden of disease and intensely influence
social and financial welfare of individuals. The present comprehensive review
concentrate on the two mental disorders: Major depressive Disorder (MDD) and
Bipolar Disorder (BD) with noteworthy publications during the last ten years.
There is a big need nowadays for phenotypic characterization of psychiatric
disorders with biomarkers. Electroencephalography (EEG) signals could offer a
rich signature for MDD and BD and then they could improve understanding of
pathophysiological mechanisms underling these mental disorders. In this review,
we focus on the literature works adopting neural networks fed by EEG signals.
Among those studies using EEG and neural networks, we have discussed a variety
of EEG based protocols, biomarkers and public datasets for depression and
bipolar disorder detection. We conclude with a discussion and valuable
recommendations that will help to improve the reliability of developed models
and for more accurate and more deterministic computational intelligence based
systems in psychiatry. This review will prove to be a structured and valuable
initial point for the researchers working on depression and bipolar disorders
recognition by using EEG signals.


  We consider the effects of altruistic behavior on random medium access
control (slotted ALOHA) for local area communication networks. For an
idealized, synchronously iterative, two-player game with asymmetric player
demands, we find a Hamiltonian governing the Jacobi dynamics under purely
altruistic behavior. Though the positions of the interior Nash equilibrium
points do not change in the presence of altruistic behavior, the nature of
their local asymptotic stability does. There is a region of partially
altruistic behavior for which neither interior Nash equilibrium point is
locally asymptotically stable. Also, for a power control game with a single
Nash equilibrium, we show how its stability changes as a function of the
altruism parameter. Variations of these altruistic game frameworks are
discussed considering power (instead of throughput) based costs and linear
utility functions.


  In this paper, we considered the spectrum of the Dirichlet Laplacian
$\Delta_\epsilon$ on $\Omega_\epsilon=\{(x,y): -l_1<x<l_2, 0<y<\epsilon
h(x)]\}$ where $ l_1,l_2>0$ and $h(x)$ is a positive analytic function having
$0$ the only point where it achieves its global maximum $M$. In particular we
studied in details about the full asymptotics of the eigenvalues.


  Weak gravitational lensing surveys are rapidly becoming important tools to
probe directly the mass density fluctuations in the universe and its background
dynamics. Earlier studies have shown that it is possible to model the
statistics of the convergence field on small angular scales by suitably
modeling the statistics of the underlying density field in the highly
non-linear regime. We extend such methods to model the complete probability
distribution function, PDF, of the shear as a function of smoothing angle. Our
model relies on a simple hierarchical Ansatz for the behaviour of the
higher-order correlations in the density field. We compare our predictions with
the results of numerical simulations and find excellent agreement for different
cosmological scenarios. Our method provides a new way to study the evolution of
non-Gaussianity in gravitational clustering and should help to break the
degeneracies in parameter estimation based on analysis of the power spectrum
alone.


  From photometric observations of the old nova RW UMi (1956) we have
discovered the presence of five sub-orbital periodicities. The longest period,
P1 = 54.4 min, always observed, could be the beat period between the orbital
period and the white dwarf (WD) spin period that we assume to be P2 = 33.4 min.
The other suborbital periods could be orbital sidebands with respect to P2
and/or correspond to Keplerian resonance radii. We suggest that in its
post-outburst state, characterized by higher mass transfer rate, RW UMi is an
asynchronous intermediate polar with a truncated accretion disc. If the
magnetic momentum of the WD is $\mu_{34} \sim 0.8$, in its quiescent
pre-outburst state, the nova would appear as a discless, synchronous
intermediate polar.


  Nowadays, improving the energy efficiency of high-performance computing (HPC)
systems is one of the main drivers in scientific and technological research. As
large-scale HPC systems require some fault-tolerant method, the opportunities
to reduce energy consumption should be explored. In particular,
rollback-recovery methods using uncoordinated checkpoints prevent all processes
from re-executing when a failure occurs. In this context, it is possible to
take actions to reduce the energy consumption of the nodes whose processes do
not re-execute. This work is an extension of a previous one, in which we
proposed a series of strategies to manage energy consumption at failure-time.
In this work, we have enriched our simulator and the experimentation by
including non-blocking communications (with and without system buffering) and a
largest number of candidate processes to be analyzed. We have called the latter
as \textit{cascade analysis}, because it includes processes that gets blocked
by communication indirectly with the failed process. The simulations show that
the savings were negligible in the worst case, but in some scenarios, it was
possible to achieve significant ones; the maximum saving achieved was 90\% in a
time interval of 16 minutes. As a result, we show the feasibility of improving
energy efficiency in HPC systems in the presence of a failure.


  An asymptotic expansion of the two-loop two-point ``master'' diagram with two
masses $m$ and $M$, on the mass shell $Q^2=M^2$, is presented. The treatment of
the non-analytical terms arising in the expansion around the branching point is
discussed. Some details of the calculation of a new class of two-loop integrals
are given.


  Coalitions are central to politics, including government formation,
international relations, and public policy. Coalitions emerge when actors
engage one another across multiple relational contexts, but existing literature
often approaches coalitions in singular contexts. We introduce complex
coalitions, a theoretical-methodological framework that emphasises the
relevance of multiple contexts and cross-context dependencies in coalition
politics. We also implement tools to statistically infer such coalition
structures using multilayer networks. To demonstrate the usefulness of our
approach, we compare coalitions among Finnish organisations engaging in climate
politics across three con-texts: resource coordination, legacy media discourse,
and social media communication. We show that considering coalitions as complex
and accounting for cross-context dependencies improves the empirical validity
of coalition studies. In our case study, the three contexts represent
complementary, but not congruent, channels for enacting coalitions. In
conclusion, we argue that the complex coalitions approach is useful for
advancing understanding of coalitions in different political realms.


  Scientists from the OPERA experiment have measured neutrinos supposedly
travelling at a velocity faster than light contrary to the theory of
relativity. Even when the measurements are precise, the interpretation of this
problem is being misunderstood. Here it is very easily solved and explained
within the theory of relativity itself proving that neutrinos are not
travelling faster than the speed of light and the early time arrival is due to
the the presence of a gravitational field.


  Cox-Ingersoll-Ross (CIR) processes are widely used in financial modeling such
as in the Heston model for the approximative pricing of financial derivatives.
Moreover, CIR processes are mathematically interesting due to the irregular
square root function in the diffusion coefficient. In the literature, positive
strong convergence rates for numerical approximations of CIR processes have
been established in the case of an inaccessible boundary point. Since
calibrations of the Heston model frequently result in parameters such that the
boundary is accessible, we focus on this interesting case. Our main result
shows for every $p \in (0, \infty)$ that the drift-implicit square-root Euler
approximations proposed in Alfonsi (2005) converge in the strong $L^p$-distance
with a positive rate for half of the parameter regime in which the boundary
point is accessible. A key step in our proof is temporal regularity of Bessel
processes. More precisely, we prove for every $p \in (0, \infty)$ that Bessel
processes are temporally $1/2$-H\"older continuous in $L^p$.


  We prove that every even number $2 \le 2d \le 2g$ is realised as the degree
of a Thurston-Veech pseudo-Anosov stretch factor in every connected component
of every stratum of the moduli space of Abelian differentials.


  The family of titanium oxide superconductors exhibits many intriguing
phenomena comparable to cuprates and iron pnictides/chalcogenides, and thus
provides an ideal platform to contrastively study the unconventional pairing
mechanism of high-temperature superconductors. Here, we successfully deposit
superconducting Mg-Ti-O films on MgAl$_2$O$_4$ substrates with three principal
orientations by ablating a MgTi$_2$O$_4$ target. Particularly, it is striking
to observed that a single-crystalline film of an unintended structure has been
grown on the (011)-oriented substrate, with the highest zero resistance
transition temperature ($T_{\mathrm{c}0}$) of 5.0 K among them. The film has a
highly reduced Mg/Ti ratio and an orthorhombic Ti$_9$O$_{10}$-like structure
(denoted as Mg: Ti$_9$O$_{10}$), demonstrated by further characterizations of
chemical composition and structure. Such a structure is unstable in bulk but
favorable to be epitaxially stabilized on the (011)-surface of MgAl$_2$O$_4$
due to a relatively small strain at the formed interface. An isotropic upper
critical field ($B_{\mathrm{c}2}$) up to 13.7 T that breaks the Pauli limit is
observed in the Mg: Ti$_9$O$_{10}$ film, analogous to other superconducting
titanium oxides. The similarity points to a common origin for the
superconductivity in the family, which will provide valuable opinions for the
mechanism of unconventional superconductivity in transition metal compounds.


  Nickel/Bismuth (Ni/Bi) bilayers have recently attracted attention due to the
occurrence of time-reversal symmetry breaking in the superconducting state.
Here, we report on the structural, magnetic and electric characterization of
thin film Ni/Bi bilayers with several Bi thicknesses. We observed the formation
of a complex layered structure depending on the Bi thickness caused by the
inter-diffusion of Bi and Ni which leads to the stabilization of NiBi$_{3}$ at
the Bi/Ni interface. The superconducting transition temperature and the
transition width are highly dependent on the Bi thickness and the layer
structure. Magnetoelectric transport measurements in perpendicular and parallel
magnetic fields were used to investigate the temperature-dependent upper
critical field within the framework of the anisotropic Ginzburg-Landau theory
and the Werthamer Helfand Hohenberg model. For thicker samples, we observed a
conventional behavior, similar to that shown by NiBi$_{3}$ bulk samples,
including a small Maki parameter ($\alpha_{M}$ = 0), no spin-orbit scattering
($\lambda_{SO}$= 0) and nearly isotropic coherence length ($\gamma$ =
$\xi_{\perp}$(0)/$\xi_{\parallel}$(0) $\approx$ 1). The values obtained for
these properties are close to those characterizing NiBi$_{3}$ single crystals.
On the other hand, in very thin samples the Maki parameter increases to about
$\alpha_{M}$ = 2.8. In addition, the coherence length becomes anisotropic
($\gamma$ = 0.32) and spin-orbit scattering ($\lambda_{SO}$= 1.2) must be taken
into account. Our results unequivocally show that the properties characterizing
the superconducting state in the Ni/Bi are strongly dependent on the sample
thickness.


  We present the first results of a survey to obtain Integral Field
Spectroscopy of merging galaxies along the Toomre Sequence. In the present
work, we concentrate on the star cluster complexes in the Antennae galaxies
(NGC 4038/39) in the overlap region as well as the nuclear region of NGC 4038.
Using optical spectroscopy we derive the extinction age, metallicity, velocity,
velocity dispersion of the gas and star formation rate for each of the eight
complexes detected. We supplement this study with archival HST-WFPC2 U, B, V,
H$\alpha$, and I band imaging. Correcting the observed colours of the star
clusters within the complexes for extinction, measured through our optical
spectra, we compare the clusters with simple stellar population models, with
which we find an excellent agreement. In five of the complexes we detect strong
Wolf-Rayet emission features, indicating young ages (3-5 Myr). The ionized gas
surrounding the complexes is expanding at speeds of 20-40 km/s. This slow
expansion can be understood as a bubble, caused by the stellar winds and
supernovae within the complexes, expanding into the remnant of the progenitor
giant molecular cloud. We also find that the complexes themselves are grouped,
at about the largest scale of which young star clusters are correlated,
representing the largest coherent star forming region. We show that the area
normalized star formation rates of these complexes clearly place them in the
regime of star forming regions in starburst galaxies, thereby justifying the
label of localized starbursts. Finally, we estimate the stability of the
complexes, and find that they will probably loose a large fraction of their
mass to the surrounding environment, although the central regions may merge
into a single large star cluster.


  Kohn introduced in 1979 the algorithm of multipliers to study the subelliptc
estimate of the $\bar\partial$-Neumann problem for a smooth weakly pseudoconvex
domain in a complex Euclidean space which satisfies D'Angelo's finite type
condition of a finite bound for the normalized touching order to the boundary
for any local possibly singular holomorphic curve in the complex Euclidean
space. The problem can be regarded as an example of the formulation of
H\"ormander's 1967 hypoelliptic result for the case of complex-valued
vector-valued unknowns. So far the effective solution of Kohn's problem is
known only for special domains ${\rm Re}(z_{n+1})+\sum_{j=1}^N|f_j|^2<0$ in
${\mathbb C}^{n+1}$ with $f_j$ holomorphic in $z_1,...,z_n$, because for such
domains it suffices to deal with holomorphic multipliers. One main obstacle to
treat the general smooth case is the need to deal with nonholomorphic
multipliers. This note introduces a new technique to handle nonholomorphic
multipliers occurring in more general domains with $f_j$ holomorphic in all the
$n+1$ variables $z_1,...,z_n,z_{n+1}$.


  In the present paper, we characterize Fano Bott manifolds up to
diffeomorphism in terms of three operations on matrix. More precisely, we prove
that given two Fano Bott manifolds $X$ and $X'$, the following conditions are
equivalent: (1) the upper triangular matrix associated to $X$ can be
transformed into that of $X'$ by those three operations; (2) $X$ and $X'$ are
diffeomorphic; (3) the integral cohomology rings of $X$ and $X'$ are isomorphic
as graded rings. As a consequence, we affirmatively answer the cohomological
rigidity problem for Fano Bott manifolds.


  In this paper, we obtain a general expression for the entries of the rth
power of a certain n-square complex anti-tridiagonal matrix where if n is odd,
r is integer or if n is even, r is natural number. In addition, we get the
complex factorizations of Fibonacci polynomials, Fibonacci and Pell numbers.


  As a means to better understanding manifolds with positive curvature, there
has been much recent interest in the study of non-negatively curved manifolds
which contain either a point or an open dense set of points at which all
2-planes have positive curvature. We study infinite families of biquotients
defined by Eschenburg and Bazaikin from this viewpoint, together with torus
quotients of $S^3 \x S^3$.


  We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying
that Hirzebruch-Zagier divisors on a Hilbert modular surface are the
coefficients of an elliptic modular form of weight two. Moreover, we determine
the arithmetic self-intersection number of the line bundle of modular forms
equipped with its Petersson metric on a regular model of a Hilbert modular
surface, and study Faltings heights of arithmetic Hirzebruch-Zagier divisors.


  We discuss the stabilization of the scalar sector, including the radion, in
the gauge model with one universal extra dimension, within Higgs and Higgsless
scenarios. The stabilization occurs at the one-loop level, through the
fermionic contribution to the effective potential; in the Higgs case, for
stabilization to take place the bosonic contribution must be balanced by the
fermionic one, hence the scales of these two cannot differ too much. However,
there is no need for (softly broken) supersymmetry to achieve the stabilization
- it can be arranged for a reasonably wide range of couplings and mass scales.
The primary instability in the model is the run-away of the radion vacuum
expectation value. It turns out that the requirement of the radion stability,
in the Higgs case, favours a Higgs boson mass below 0.26 TeV, which is
consistent with the Standard Model upper bound that follows from the
electroweak precision measurements. The typical radion mass is of the order of
10^{-6} eV. The radion mass can be made larger by rising the scale of fermion
masses, as clearly seen in the Higgsless case. The cosmological constant may be
cancelled by suitable counterterms, in such a way that the stabilization is not
affected.


  We consider CFT's arising from branes probing singularities of internal
manifolds. We focus on holographic models with internal space including
arbtirary Sasaki-Einstein manifolds coming from CY as well as arbitrary sphere
quotients. In all these cases we show that there is a universal upper bound
(depending only on the spacetime dimension) for the conformal dimension of the
first non-trivial spin 2 operator in the dual CFT and a minimal diameter (in
AdS units) for the internal space of the holographic dual and conjecture it
holds for all CFT's.


  Most legged robots are built with leg structures from serially mounted links
and actuators and are controlled through complex controllers and sensor
feedback. In comparison, animals developed multi-segment legs, mechanical
coupling between joints, and multi-segmented feet. They run agile over all
terrains, arguably with simpler locomotion control. Here we focus on developing
foot mechanisms that resist slipping and sinking also in natural terrain. We
present first results of multi-segment feet mounted to a bird-inspired robot
leg with multi-joint mechanical tendon coupling. Our one- and two-segment,
mechanically adaptive feet show increased viable horizontal forces on multiple
soft and hard substrates before starting to slip. We also observe that
segmented feet reduce sinking on soft substrates compared to ball-feet and
cylinder-feet. We report how multi-segmented feet provide a large range of
viable centre of pressure points well suited for bipedal robots, but also for
quadruped robots on slopes and natural terrain. Our results also offer a
functional understanding of segmented feet in animals like ratite birds.


  Experimental data on electromagnetic and weak form factors of the nucleon are
analyzed in a two-component model with a quark-like intrinsic structure
surrounded by a meson cloud. The contribution from strange quarks is discussed
and compared with recent data from the G0 Collaboration.


  The all-orders beta function is used to study disordered Dirac fermions in
2D. The generic strong coupling fixed `points' of anisotropic current-current
interactions at large distances are actually isotropic manifolds corresponding
to subalgebras of the maximal current algebra at short distances. The IR
theories are argued to be current algebra cosets. We illustrate this with the
simple example of anisotropic su(2), which is the physics of
Kosterlitz-Thouless transitions. We work out the phase diagram for the
Chalker-Coddington network model which is in the universality class of the
integer Quantum Hall transition. One massless phase is in the universality
class of dense polymers.


  We present the first principles construction of the low-energy effective
action for bosonic self-organized quantum quasicrystals. Our generalized
elasticity approach retains the appropriate number of phase- and corresponding
conjugate density- degrees-of-freedom required for a proper description of the
Goldstone modes. For the dodecagonal and decagonal quasicrystal structures we
obtain collective longitudinal and transversal excitations with an isotropic
speed of sound. Meanwhile, for the octagonal structure, the coupling between
phononic and phasonic degrees of freedom leads in turn to hybridization of the
latter with the condensate sound mode, producing collective excitations with a
longitudinal and transversal component, and an anisotropic speed of sound.
Finally, we discuss the fate of each excitation mode at the low and high
density phase transitions limiting the quantum quasicrystal phase.


  This paper introduces new methods for analysing the extreme and erratic
behaviour of time series to evaluate the impact of COVID-19 on cryptocurrency
market dynamics. Across 51 cryptocurrencies, we examine extreme behaviour
through a study of distribution extremities, and erratic behaviour through
structural breaks. First, we analyse the structure of the market as a whole and
observe a reduction in self-similarity as a result of COVID-19, particularly
with respect to structural breaks in variance. Second, we compare and contrast
these two behaviours, and identify individual anomalous cryptocurrencies.
Tether (USDT) and TrueUSD (TUSD) are consistent outliers with respect to their
returns, while Holo (HOT), NEXO (NEXO), Maker (MKR) and NEM (XEM) are
frequently observed as anomalous with respect to both behaviours and time. Even
among a market known as consistently volatile, this identifies individual
cryptocurrencies that behave most irregularly in their extreme and erratic
behaviour and shows these were more affected during the COVID-19 market crisis.


No P-immune set having exponential gaps is positive-Turing self-reducible.


  Discovery of an accurate causal Bayesian network structure from observational
data can be useful in many areas of science. Often the discoveries are made
under uncertainty, which can be expressed as probabilities. To guide the use of
such discoveries, including directing further investigation, it is important
that those probabilities be well-calibrated. In this paper, we introduce a
novel framework to derive calibrated probabilities of causal relationships from
observational data. The framework consists of three components: (1) an
approximate method for generating initial probability estimates of the edge
types for each pair of variables, (2) the availability of a relatively small
number of the causal relationships in the network for which the truth status is
known, which we call a calibration training set, and (3) a calibration method
for using the approximate probability estimates and the calibration training
set to generate calibrated probabilities for the many remaining pairs of
variables. We also introduce a new calibration method based on a shallow neural
network. Our experiments on simulated data support that the proposed approach
improves the calibration of causal edge predictions. The results also support
that the approach often improves the precision and recall of predictions.


  In 1990, Hitchin's proved a component of the space of representations of a
surface group in SL(n,R) is homeomorphic to a ball. For n=2,3 this component
has been identified with the holonomies of geometric structures (hyperbolic for
n=2, or real projective for n=3). In the preprint "Anosov flows, Surface groups
and Curves in Projective Space", we extend this interpretation to higher
dimension and show every representation in Hitchin's component is attached to a
(special) curve in projective space, thus giving a geometric interpretation of
these representations. We also prove these representations are faithful,
discrete and purely loxodromic (or hyperbolic)


  Gutman {\it et al.} introduced the concepts of energy $\En(G)$ and Laplacian
energy $\EnL(G)$ for a simple graph $G$, and furthermore, they proposed a
conjecture that for every graph $G$, $\En(G)$ is not more than $\EnL(G)$.
Unfortunately, the conjecture turns out to be incorrect since Liu {\it et al.}
and Stevanovi\'c {\it et al.} constructed counterexamples. However, So {\it et
al.} verified the conjecture for bipartite graphs. In the present paper, we
obtain, for a random graph, the lower and upper bounds of the Laplacian energy,
and show that the conjecture is true for almost all graphs.


  Compensated-current systems created by energetic ion beams are widespread in
space and astrophysical plasmas. The well-known examples are foreshock regions
in the solar wind and around supernova remnants. We found a new oblique
Alfv\'enic instability driven by compensated currents flowing along the
background magnetic field. Because of the vastly different electron and ion
gyroradii, oblique Alfv\'enic perturbations react differently on the currents
carried by the hot ion beams and the return electron currents. Ultimately, this
difference leads to a non-resonant aperiodic instability at perpendicular
wavelengths close to the beam ion gyroradius. The instability growth rate
increases with increasing beam current and temperature. In the solar wind
upstream of Earth's bow shock the instability growth time can drop below 10
proton cyclotron periods. Our results suggest that this instability can
contribute to the turbulence and ion acceleration in space and astrophysical
foreshocks.