  Learning-based approaches to robotic manipulation are limited by the
scalability of data collection and accessibility of labels. In this paper, we
present a multi-task domain adaptation framework for instance grasping in
cluttered scenes by utilizing simulated robot experiments. Our neural network
takes monocular RGB images and the instance segmentation mask of a specified
target object as inputs, and predicts the probability of successfully grasping
the specified object for each candidate motor command. The proposed transfer
learning framework trains a model for instance grasping in simulation and uses
a domain-adversarial loss to transfer the trained model to real robots using
indiscriminate grasping data, which is available both in simulation and the
real world. We evaluate our model in real-world robot experiments, comparing it
with alternative model architectures as well as an indiscriminate grasping
baseline.


  Here, we consider the planning problem for first-order mean-field games
(MFG). When there is no coupling between players, MFG degenerate into optimal
transport problems. Displacement convexity is a fundamental tool in optimal
transport that often reveals hidden convexity of functionals and, thus, has
numerous applications in the calculus of variations. We explore the
similarities between the Benamou-Brenier formulation of optimal transport and
MFG to extend displacement convexity methods from to MFG. In particular, we
identify a class of functions, that depend on solutions of MFG, that are convex
in time and, thus, obtain new a priori bounds for solutions of MFG. A
remarkable consequence is the log-convexity of $L^q$ norms. This convexity
gives bounds for the density of solutions of the planning problem and extends
displacement convexity of $L^q$ norms from optimal transport. Additionally, we
prove the convexity of $L^q$ norms for MFG with congestion.


  In this paper, we embed metric space endowed with a convex combination
operation, named convex combination space, into a Banach space and the
embedding preserves the structures of metric and convex combination. For random
element taking values in this kind of space, applications of embedding are also
established. On the one hand, some nice properties of expectation such as
representation of expected value through continuous affine mappings, the
linearity of expectation will be given. On the other hand, the notion of
conditional expectation will be also introduced and discussed. Thanks to
embedding theorem, we establish some basic properties of conditional
expectation, Jensen's inequality, convergences of martingales and ergodic
theorem.


  We study extremal black hole solutions of D=5 Gauss-Bonnet gravity coupled to
a system of gauge and scalar fields. As in Einstein gravity, we find that the
values of the scalar fields on the horizon must extremize a certain effective
potential that depends on the black hole charges. If the matrix of second
derivatives of the effective potential at this extremum has positive
eigenvalues, we give evidence, based on a near horizon perturbative expansion,
that the attractor mechanism continues to hold in this general class of
theories. We numerically construct solutions to a particular simple single
scalar field model that display the attractor mechanism over a wide range of
asymptotic values for the scalar field. We also numerically construct
non-extremal solutions and show that the attractor mechanism fails to hold away
from extremality.


  Video plethysmographic (vPPG) signals arise from subtle color modulations in
reflected light. vPPG signals can be used to monitor vital signs remotely in a
noninvasive manner. We have used optical coherence tomography (OCT) imaging to
find whether vPPG signals may result from skin optical properties being
modulated by arterial transmural pressure propagation. Our results confirm this
hypothesis and show that the attenuation coefficient of even the most external,
non-vascularized skin, changes at the same frequency as the arterial pulsation.


  Very recently, Alon and Frankl initiated the study of the maximum number of
edges in $n$-vertex $F$-free graphs with matching number at most $s$. For fixed
$F$ and $s$, we determine this number apart from a constant additive term. We
also obtain several exact results.


  As a contribution to reproducible research, this paper presents a framework
and a database to improve the development, evaluation and comparison of methods
for gait recognition from motion capture (MoCap) data. The evaluation framework
provides implementation details and source codes of state-of-the-art
human-interpretable geometric features as well as our own approaches where gait
features are learned by a modification of Fisher's Linear Discriminant Analysis
with the Maximum Margin Criterion, and by a combination of Principal Component
Analysis and Linear Discriminant Analysis. It includes a description and source
codes of a mechanism for evaluating four class separability coefficients of
feature space and four rank-based classifier performance metrics. This
framework also contains a tool for learning a custom classifier and for
classifying a custom query on a custom gallery. We provide an experimental
database along with source codes for its extraction from the general CMU MoCap
database.


  In fruit tree growth, pruning is an important management practice for
preventing overcrowding, improving canopy access to light and promoting
regrowth. Due to the slow nature of agriculture, decisions in pruning are
typically made using tradition or rules of thumb rather than data-driven
analysis. Many existing algorithmic, simulation-based approaches rely on
high-fidelity digital captures or purely computer-generated fruit trees, and
are unable to provide specific results on an orchard scale. We present a
framework for suggesting pruning strategies on LiDAR-scanned commercial fruit
trees using a scoring function with a focus on improving light distribution
throughout the canopy. A scoring function to assess the quality of the tree
shape based on its light availability and size was developed for comparative
analysis between trees, and was validated against yield characteristics,
demonstrating a reasonable correlation against fruit count with an $R^2$ score
of 0.615 for avocado and 0.506 for mango. A tool was implemented for simulating
pruning by algorithmically estimating which parts of a tree point cloud would
be removed given specific cut points using structural analysis of the tree,
validated experimentally with an average F1 score of 0.78 across 144
experiments. Finally, new pruning locations were suggested and we used the
previous two stages to estimate the improvement of the tree given these
suggestions. The light distribution was improved by up to 25.15\%,
demonstrating a 16\% improvement over commercial pruning on a real tree, and
certain cut points were discovered which improved light distribution with a
smaller negative impact on tree volume. The final results suggest value in the
framework as a decision making tool for commercial growers, or as a starting
point for automated pruning since the entire process can be performed with
little human intervention.


  This article introduces strongly near smooth manifolds. The main results are
(i) second countability of the strongly hit and far-miss topology on a family
$\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to
which singletons are added, (ii) manifold strong proximity, (iii) strong
proximity of charts in manifold atlases implies that the charts have nonempty
intersection. The application of these results is given in terms of the
nearness of atlases and charts of proximal manifolds and what are known as
Vorono\" i manifolds.


  Here is a list of chapters:
  1 Introduction
  2 Notation and preliminaries
  Part I: Finite quantum groups
  3 2x2 Matrix quantum groups and the quantum plane
  4 Quantum enveloping algebras at a root of unity
  Part II: q-Oscillators
  5 Representations of q-oscillators at a root of unity
  6 qr-Oscillator at a root of unity
  Part III: Infinite quantum groups
  7 Quantum affine algebras
  8 Quantum affine algebras at a root of unity


  We investigate the effect of the so-called anomalous baryon/meson enhancement
to the nuclear modification factor of non-photonic electrons in Au+Au
collisions at sqrt(s) = 200 GeV. It is demonstrated that an enhancement of the
charm baryon/meson ratio, as it is observed for non-strange and strange
hadrons, can be responsible for part of the amplitude of the nuclear
modification factor of non-photonic electrons. About half of the measured
suppression of non-photonic electrons in the 2-4 pt range can be explained by a
charm baryon/meson enhancement of 5. This contribution to the non-photonic
electron nuclear modification factor has nothing to do with heavy quark energy
loss.


  Recent polarimetric surveys of extragalactic radio sources (ERS) at
frequencies \nu>1GHz are reviewed. By exploiting all the most relevant data on
the polarized emission of ERS we study the frequency dependence of polarization
properties of ERS between 1.4 and 86GHz. For flat-spectrum sources the median
(mean) fractional polarization increases from 1.5% (2-2.5%) at 1.4GHz to 2.5-3%
(3-3.5%) at \nu>10GHz. Steep-spectrum sources are typically more polarized,
especially at high frequencies where Faraday depolarization is less relevant.
As a general result, we do not find that the fractional polarization of ERS
depends on the total flux density at high radio frequencies, i.e >20GHz.
Moreover, in this frequency range, current data suggest a moderate increase of
the fractional polarization of ERS with frequency. A formalism to estimate ERS
number counts in polarization and the contribution of unresolved polarized ERS
to angular power spectra at Cosmic Microwave Background (CMB) frequencies is
also developed and discussed. As a first application, we present original
predictions for the Planck satellite mission. Our current results show that
only a dozen polarized ERS will be detected by the Planck Low Frequency
Instrument (LFI), and a few tens by the High Frequency Instrument (HFI). As for
CMB power spectra, ERS should not be a strong contaminant to the CMB E-mode
polarization at frequencies \nu>70GHz. On the contrary, they can become a
relevant constraint for the detection of the cosmological B--mode polarization
if the tensor-to-scalar ratio is <0.01.


  Verifying the correctness of Bayesian computation is challenging. This is
especially true for complex models that are common in practice, as these
require sophisticated model implementations and algorithms. In this paper we
introduce \emph{simulation-based calibration} (SBC), a general procedure for
validating inferences from Bayesian algorithms capable of generating posterior
samples. This procedure not only identifies inaccurate computation and
inconsistencies in model implementations but also provides graphical summaries
that can indicate the nature of the problems that arise. We argue that SBC is a
critical part of a robust Bayesian workflow, as well as being a useful tool for
those developing computational algorithms and statistical software.


  Let $A\subseteq\mathbb Z_n$ be a weight-set and $S=(x_1,x_2,\ldots, x_k)$ be
a sequence in $\mathbb Z_n$. We say that $S$ is a smooth $A$-weighted zero-sum
sequence if there exists $(a_1,\ldots,a_k)\in A^k$ such that we have
$a_1x_1+\cdots+a_kx_k=0$ and $a_1+\cdots+a_k=0$. It is easy to see that if $S$
is a smooth $A$-weighted zero-sum sequence, then for every $y\in \mathbb Z_n$
the sequence $S+y=(x_1+y,\ldots,x_k+y)$ is also a smooth $A$-weighted zero-sum
sequence. From the well known EGZ-theorem it follows that if $S$ has length at
least $2n-1$, then $S$ has a smooth $A$-weighted zero-sum subsequence of length
$n$. The constant $\bar E_A$ is defined to be the smallest positive integer $k$
such that any sequence of length $k$ in $\mathbb Z_n$ has a smooth $A$-weighted
zero-sum subsequence of length $n$. A sequence in $\mathbb Z_n$ of length $\bar
E_A-1$ which does not have any smooth $A$-weighted zero-sum subsequence of
length $n$ is called an $\bar E$-extremal sequence for $A$. For every $n$ we
consider the weight-sets $\{1\}$ and $\mathbb Z_n\setminus\{0\}$. When $n$ is
an odd prime $p$ we consider the weight-set $Q_p$ of all non-zero quadratic
residues. We also study the related constants $\bar C_A$ and $\bar D_A$.


  The elements of the E\"otv\"os matrix are useful for various geodetic
applications, such as the interpolation of the elements of the deflection of
the vertical, the determination of gravity anomalies and the determination of
geoid heights. A torsion balance instrument is customarily used for the
determination of the E\"otv\"os components. In this work, we show that it is
possible to estimate the E\"otv\"os components, at a point on the physical
surface of the Earth, using gravity measurements at three nearby points,
comprising a very small network. In the first part, we present the method in
detail, while in the second part we demonstrate a numerical example. We
conclude that this method is able to estimate the elements of the E\"otv\"os
matrix with satisfactory accuracy.


  We discuss and propose the minimal generalization of the Witten-Veneziano
relation to finite temperatures, prompted by STAR and PHENIX experimental
results on the multiplicity of eta' mesons. After explaining why these results
show that the zero-temperature Witten-Veneziano relation cannot be
straightforwardly extended to temperatures T too close to the chiral
restoration temperature T_Ch and beyond, we find the quantity which should
replace, at T>0, the Yang-Mills topological susceptibility appearing in the T=0
Witten-Veneziano relation, in order to avoid the conflict with experiment at
T>0. This is illustrated through concrete T-dependences of pseudoscalar meson
masses in a chirally well-behaved, Dyson-Schwinger approach, but our results
and conclusions are of a more general nature and, essentially,
model-independent.


  In this work, we analyze a sequential game played in a graph called the
Multilevel Critical Node problem (MCN). A defender and an attacker are the
players of this game. The defender starts by preventively interdicting vertices
(vaccination) from being attacked. Then, the attacker infects a subset of
non-vaccinated vertices and, finally, the defender reacts with a protection
strategy. We provide the first computational complexity results associated with
MCN and its subgames. Moreover, by considering unitary, weighted, undirected,
and directed graphs, we clarify how the theoretical tractability of those
problems vary. Our findings contribute with new NP-complete,
$\Sigma_2^p$-complete and $\Sigma_3^p$-complete problems. Furthermore, for the
last level of the game, the protection stage, we build polynomial time
algorithms for certain graph classes.


  We study dynamics and relaxation of elementary excitations (magnons) in the
spin nematic (quadrupole ordered) phase of S=1 magnets. We develop a general
phenomenological theory of spin dynamics and relaxation for spin-1 systems.
Results of the phenomenological approach are compared to those obtained by
microscopic calculations for the specific S=1 model with isotropic bilinear and
biquadratic exchange interactions. This model exhibits a rich behavior
depending on the ratio of bilinear and biquadratic exchange constants,
including several points with an enhanced symmetry. It is shown that symmetry
plays an important role in relaxation. Particularly, at the SU(3) ferromagnetic
point the magnon damping $\Gamma$ depends on its wavevector k as $\Gamma\propto
k^{4}$, while a deviation from the high-symmetry point changes the behavior of
the leading term to $\Gamma\propto k^{2}$. We point out a similarity between
the behavior of magnon relaxation in spin nematics to that in an isotropic
ferromagnet.


  We present some formal properties of (symmetrical) commutativity, the major
criterion used in transactional systems, which allow us to fully understand its
advantages and disadvantages. The main result is that commutativity is subject
to the same limitation as compatibility for arbitrary objects. However,
commutativity has also a number of attracting properties, one of which is
related to recovery and, to our knowledge, has not been exploited in the
literature. Advantages and disadvantages are illustrated on abstract data types
of interest. We also show how limits of commutativity have been circumvented,
which gives guidelines for doing so (or not!).


  We propose a magnetic confinement nuclear fusion mechanism for the evolution
of a solar flare in solar atmosphere. The mechanism agree with two observed
characteristics of explosive flares and coronal mass ejections (CMEs) that have
proved to be very difficult to explain with previous mechanisms: the huge
enrichments of $^{3}He$ and the high energy gamma ray radiation. The twisted
magnetic flux rope is a typical structure during the solar flares, which is
closely related to the solar active region that magnetic fields have almost
complete control over the plasma. Consequently, the plasma inside the flux rope
is heated to more than 1.0$\times10^{7}$ K by adiabatic compression process,
and then the thermonuclear fusion can take place in the flux rope accompanied
with high energy gamma rays. We utilize the time-dependent ideal
2.5-dimensional magnetohydrodynamic (MHD) simulation to demonstrate the
physical mechanism for producing flares, which reveals three stages of flare
development with process of magnetic energy conversion and intense release
during the solar flares and CMEs in solar atmosphere. Furthermore, we discuss
the relationship between magnetic reconnection and solar eruptions.


  The maximal $n$ which admits a non-almost regular $m$-gonal form of rank $n$
is $4$. In this article, we consider the $m$-gonal forms of rank $4$ which is
not almost regular.


  We construct the first examples of hypersurfaces in any contact manifold of
dimension 5 and larger that cannot be $C^2$-approximated by convex
hypersurfaces. This contrasts sharply with the foundational result of Giroux in
dimension $3$ and the work of Honda-Huang in the $C^0$ case. The main technical
step is the construction of a Bonatti-Diaz type blender in the contact setting.


  In this paper, we study the Entropic Martingale Optimal Transport (EMOT)
problem on R. We begin by introducing the dual formulation and prove the
exponential convergence of Sinkhorn's algorithm on the dual potential
coefficients. Our analysis does not require prior knowledge of the optimal
potential and confirms that there is no primal-dual gap. Our findings provide a
theoretical guarantee for solving the EMOT problem using Sinkhorn's algorithm.
In applications, our result provides insight into the calibration of stochastic
volatility models, as proposed by Henry-Labordere.


  Smart homes are further development of intelligent buildings and home
automation, where context awareness and autonomous behaviour are added. They
are based on a combination of the Internet and emerging technologies like
wireless sensor nodes. These wireless sensor nodes are challenging because they
consume battery power, they use network bandwidth, and they produce wireless
interferences. Currently, different methods exist for handling these
challenges. These methods are, however, based on adjusting the transmitter
frequency and using duty-cycling in combination with sleep mode approaches.
This paper introduces an approach that considerably lowers the wireless sensor
node power consumption and the amount of transmitted sensor events. It uses
smart objects that include artificial intelligence to efficiently process the
sensor event on location and thereby saves the costly wireless transportation
of these events. In this paper it has been shown that this approach provides
huge savings of power consumption and network load, which in turn reduces the
interference level


  Suicide is the 10th leading cause of death in the US and the 2nd leading
cause of death among teenagers. Clinical and psychosocial factors contribute to
suicide risk (SRFs), although documentation and self-expression of such factors
in EHRs and social networks vary. This study investigates the degree of
variance across EHRs and social networks. We performed subjective analysis of
SRFs, such as self-harm, bullying, impulsivity, family violence/discord, using
>13.8 Million clinical notes on 123,703 patients with mental health conditions.
We clustered clinical notes using semantic embeddings under a set of SRFs.
Likewise, we clustered 2180 suicidal users on r/SuicideWatch (~30,000 posts)
and performed comparative analysis. Top-3 SRFs documented in EHRs were
depressive feelings (24.3%), psychological disorders (21.1%), drug abuse
(18.2%). In r/SuicideWatch, gun-ownership (17.3%), self-harm (14.6%), bullying
(13.2%) were Top-3 SRFs. Mentions of Family violence, racial discrimination,
and other important SRFs contributing to suicide risk were missing from both
platforms.


  Beam cooling enables an increase of peak and average luminosities and
significantly expands the discovery potential of colliders; therefore, it is an
indispensable component of any modern design. Optical Stochastic Cooling (OSC)
is a high-bandwidth, beam-cooling technique that will advance the present
state-of-the-art, stochastic cooling rate by more than three orders of
magnitude. It is an enabling technology for next-generation, discovery-science
machines at the energy and intensity frontiers including hadron and
electron-ion colliders. This paper presents the status of our experimental
effort to demonstrate OSC at the Integrable Optics Test Accelerator (IOTA)
ring, a testbed for advanced beam-physics concepts and technologies that is
currently being commissioned at Fermilab. Our recent efforts are centered on
the development of an integrated design that is prepared for final engineering
and fabrication. The paper also presents a comparison of theoretical
calculations and numerical simulations of the pickup-undulator radiation and
its interaction with electrons in the kicker-undulator.


  We report Eu L3-edge resonant inelastic x-ray scattering (RIXS) investigation
of the electronic structure of EuB6. We observe that the RIXS spectral weight
around 1.1 eV increases dramatically when the system is cooled below the
ferromagnetic ordering temperature and follows the magnetic order parameter.
This spectral feature is attributed to the inter-site excitation from the local
4f orbital to the spin-split 5d orbital on the neighboring site, illustrating
the essential role of exchange splitting of the conducting electrons. Based on
our density functional theory calculations, the RIXS data suggest that EuB6 at
low temperature can be consistently described with a semi-metallic electronic
structure with incomplete spin-polarization. We propose routes to achieve
half-metallicity in EuB6, which utilize the strong tunability of the electronic
structure against gate voltage, strain, and magnetic field.


  Transformers for time series forecasting mainly model time series from
limited or fixed scales, making it challenging to capture different
characteristics spanning various scales. We propose Pathformer, a multi-scale
Transformer with adaptive pathways. It integrates both temporal resolution and
temporal distance for multi-scale modeling. Multi-scale division divides the
time series into different temporal resolutions using patches of various sizes.
Based on the division of each scale, dual attention is performed over these
patches to capture global correlations and local details as temporal
dependencies. We further enrich the multi-scale Transformer with adaptive
pathways, which adaptively adjust the multi-scale modeling process based on the
varying temporal dynamics of the input, improving the accuracy and
generalization of Pathformer. Extensive experiments on eleven real-world
datasets demonstrate that Pathformer not only achieves state-of-the-art
performance by surpassing all current models but also exhibits stronger
generalization abilities under various transfer scenarios. The code is made
available at https://github.com/decisionintelligence/pathformer.


  Coupling of axion-like particles (ALPs) to photons in the presence of
background magnetic field affects propagation of gamma-rays through magnetized
environments. This results in modification in the gamma-ray spectra of sources
in or behind galaxy clusters. We search for the ALP induced effects in the
Fermi/LAT and MAGIC telescope spectra of the radio galaxy NGC 1275 embedded in
Perseus galaxy cluster. We report an order-of-magnitude improved upper limit on
the ALP-photon coupling constant in the 0.1-10 neV mass range from
non-detection of the ALP imprints on the gamma-ray spectra. The improved upper
limit extends into the coupling range in which the ALP particles could form the
dark matter. We estimate the sensitivity improvements for the ALP search
achievable with extension of the measurements to lower and higher energies with
e-ASTROGAM and CTA and show that the gamma-ray probe of ALPs with masses in
$10^{-11}-10^{-7}$ eV range will be have order-of-magnitude better sensitivity
compared to ground-based experiment IAXO.


  We study the vacuum pair production by a time-dependent strong electric field
based on the exact WKB analysis. We identify the generic structure of a Stokes
graph for systems with the vacuum pair production and show that the number of
produced pairs is given by a product of connection matrices for Stokes segments
connecting pairs of turning points. We derive an explicit formula for the
number of produced pairs, assuming the semi-classical limit. The obtained
formula can be understood as a generalization of the divergent asymptotic
series method by Berry, and is consistent with other semi-classical methods
such as the worldline instanton method and the steepest descent evaluation of
the Bogoliubov coefficients done by Brezin and Izykson. We also use the formula
to discuss effects of time-dependence of the applied strong electric field
including the interplay between the perturbative multi-photon pair production
and non-peturbative Schwinger mechanism, and the dynamically assisted Schwinger
mechanism.


  A model to study two-proton emission from nuclei induced by electromagnetic
probes is developed. The process is due to one-body electromagnetic operators,
acting together with short-range correlations, and two-body $\Delta$ currents.
The model includes all the diagrams containing a single correlation function.
The sensitivity of the cross section to the details of the correlation function
is studied by using realistic and schematic correlations. Results for the
$^{16}$O nucleus are presented.


  The system of light quark and heavy antiquark source is studied in 1+1 QCD in
the large N_C limit. The situation is demonstrated to be the two dimensional
analogue of the problem in 3+1 QCD corresponding to the essentially nonlocal
case of zero vacuum correlation length, which does not allow perturbative
treatment. The modified Fock-Schwinger gauge condition is employed to derive
the effective Dirac-type equation for the spectrum, which is proved to be
equivalent to the 't Hooft equation in the limit of one heavy mass. The chiral
condensate is shown to appear naturally in the given approach and to coincide
with the convenient value.


  We consider the concept of fractons in the context of high-$T_{c}$
superconductivity. These objects, which carry rational or irrational quantum
numbers, are classified into universal classes $h$ of particles or
quasiparticles which obey specific fractal distribution function. We show that
the relaxation time associated to Hall conductivity for the superconducting
cuprate systems came to out as $\tau_{H}\propto T^{-2}$. We also consider the
pairing of fractons as a mechanism to produce bosonic systems and therefore
superconducting states. For that an effective mass obtained from the propagator
of a charge-flux system is considered. In this way, some experimental results
of infrared studies of the cuprates for the effective mass,
$m^*=m_{e}(1+\lambda)$, compared with our effective mass expression,
$m_{eff}=m(1+s)$, show us that the dominant factor for interactions came from
the spin. Thus spin flutuactions as a mechanism of high-$T_{c}$
superconductivity and fractons as quasiparticles are related. An expression to
the low temperature specific heat of a quantum liquid of fractons is also
obtained.


  Vision-Language Pre-training (VLP) has shown the merits of analysing medical
images, by leveraging the semantic congruence between medical images and their
corresponding reports. It efficiently learns visual representations, which in
turn facilitates enhanced analysis and interpretation of intricate imaging
data. However, such observation is predominantly justified on single-modality
data (mostly 2D images like X-rays), adapting VLP to learning unified
representations for medical images in real scenario remains an open challenge.
This arises from medical images often encompass a variety of modalities,
especially modalities with different various number of dimensions (e.g., 3D
images like Computed Tomography). To overcome the aforementioned challenges, we
propose an Unified Medical Image Pre-training framework, namely UniMedI, which
utilizes diagnostic reports as common semantic space to create unified
representations for diverse modalities of medical images (especially for 2D and
3D images). Under the text's guidance, we effectively uncover visual modality
information, identifying the affected areas in 2D X-rays and slices containing
lesion in sophisticated 3D CT scans, ultimately enhancing the consistency
across various medical imaging modalities. To demonstrate the effectiveness and
versatility of UniMedI, we evaluate its performance on both 2D and 3D images
across 10 different datasets, covering a wide range of medical image tasks such
as classification, segmentation, and retrieval. UniMedI has demonstrated
superior performance in downstream tasks, showcasing its effectiveness in
establishing a universal medical visual representation.


  Self-Consistent Quasi-Particle RPA (SCQRPA) is for the first time applied to
a more level pairing case. Various filling situations and values for the
coupling constant are considered. Very encouraging results in comparison with
the exact solution of the model are obtained. The nature of the low lying mode
in SCQRPA is identified. The strong reduction of the number fluctuation in
SCQRPA vs BCS is pointed out. The transition from superfluidity to the normal
fluid case is carefully investigated.


  We discuss observational consequences of f(R) dark energy scenarios that
satisfy local gravity constraints (LGC) as well as conditions of the
cosmological viability. The model we study is given by m(r)=C(-r-1)^p (C>0,
p>1) with m=Rf_{,RR}/f_{,R} and r=-Rf_{,R}/f, which cover viable f(R) models
proposed so far in a high-curvature region designed to be compatible with LGC.
The equation of state of dark energy exhibits a divergence at a redshift z_c
that can be as close as a few while satisfying sound horizon constraints of
Cosmic Microwave Background (CMB). We study the evolution of matter density
perturbations in details and place constraints on model parameters from the
difference of spectral indices of power spectra between CMB and galaxy
clustering. The models with p>5 can be consistent with those observational
constraints as well as LGC. We also discuss the evolution of perturbations in
the Ricci scalar R and show that an oscillating mode (scalaron) can easily
dominate over a matter-induced mode as we go back to the past. This violates
the stability of cosmological solutions, thus posing a problem about how the
over-production of scalarons should be avoided in the early universe.


  Over the last 80 years there has been much interest in the problem of finding
an explicit formula for the probability density function of two zero mean
correlated normal random variables. Motivated by this historical interest, we
use a recent technique from the Stein's method literature to obtain a simple
new proof, which also serves as an exposition of a general method that may be
useful in related problems.


  We derive the conditions for unbroken supersymmetry for a Mink_2, (2,0)
vacuum, arising from Type II supergravity on a compact eight-dimensional
manifold M_8. When specialized to internal manifolds enjoying SU(4)xSU(4)
structure the resulting system is elegantly rewritten in terms of generalized
complex geometry. This particular class of vacua violates the correspondence
between supersymmetry conditions and calibrations conditions of D branes
(supersymmetry-calibrations correspondence). Our analysis includes and extends
previous results about the failure of the supersymmetry-calibrations
correspondence, and confirms the existence of a precise relation between such a
failure and a subset of the supersymmetry conditions.


  In the PoS blockchain landscape, the challenge of achieving full
decentralization is often hindered by a disproportionate concentration of
staked tokens among a few validators. This study analyses this challenge by
first formalizing decentralization metrics for weighted consensus mechanisms.
An empirical analysis across ten permissionless blockchains uncovers
significant weight concentration among validators, underscoring the need for an
equitable approach. To counter this, we introduce the Square Root Stake Weight
(SRSW) model, which effectively recalibrates staking weight distribution. Our
examination of the SRSW model demonstrates notable improvements in the
decentralization metrics: the Gini index improves by 37.16% on average, while
Nakamoto coefficients for liveness and safety see mean enhancements of 101.04%
and 80.09%, respectively. This research is a pivotal step toward a more fair
and equitable distribution of staking weight, advancing the decentralization in
blockchain consensus mechanisms.


  For a map $\varphi : \varGamma \rightarrow \varGamma^{\prime}$ between metric
graphs and an isometric action on $\varGamma$ by finite group $K$, $\varphi$ is
a $K$-Galois covering on $\varGamma^{\prime}$ if $\varphi$ is a morphism, the
degree of $\varphi$ coincides with the order of $K$ and $K$ induces a
transitive action on every fibre. We prove that for a metric graph $\varGamma$
with an isometric action by finite group $K$, there exists a rational map, from
$\varGamma$ to a tropical projective space, which induces a $K$-Galois covering
on the image. By using this fact, we also prove that for a hyperelliptic metric
graph without one valent points and with genus at least two, the invariant
linear system of the hyperelliptic involution $\iota$ of the canonical linear
system, the complete linear system associated to the canonical divisor, induces
an $\langle \iota \rangle$-Galois covering on a tree. This is an analogy of the
fact that a compact Riemann surface is hyperelliptic if and only if the
canonical map, the rational map induced by the canonical linear system, is a
double covering on a projective line $\boldsymbol{P}^1$.


  In this note we study the world volume theory of pairs of D-brane and ghost
D-brane, which is shown to have 16 linear supersymmetries and 16 nonlinear
supersymmetries. In particular we study a matrix model based on the pairs of
D(-1)-brane and ghost D(-1)-brane. Since such pairs are supposed to be
equivalent to the closed string vacuum, we expect all 32 supersymmetries should
be unbroken. We show that the world volume theory of the pairs of D-brane and
ghost D-brane has unbroken 32 supersymmetries even though a half of them are
nonlinearly realized.


  Inspired by recent lattice calculations, we model certain aspects of the
$\theta$-vacuum using a matrix model with gaussian weights. The vacuum energy
exhibits a cusp at $\theta <\pi$ that is sensitive to both the accuracy of the
numerical analysis and the maximum density of winding modes present in a finite
volume.


  The supposed information paradox for black holes is based on the fundamental
misunderstanding that black holes are usefully defined by event horizons.
Understood in terms of locally defined trapping horizons, the paradox
disappears: information will escape from an evaporating black hole. According
to classical properties of trapping horizons, a general scenario is outlined
whereby a black hole evaporates completely without singularity, event horizon
or loss of energy or information.


  Digital quadruplets aiming to improve road safety, traffic efficiency, and
driving cooperation for future connected automated vehicles are proposed with
the enlightenment of ACP based parallel driving. The ACP method denotes
Artificial societies, Computational experiments, and Parallel execution modules
for cyber-physical-social systems. Four agents are designed in the framework of
digital quadruplets: descriptive vehicles, predictive vehicles, prescriptive
vehicles, and real vehicles. The three virtual vehicles (descriptive,
predictive, and prescriptive) dynamically interact with the real one in order
to enhance the safety and performance of the real vehicle. The details of the
three virtual vehicles in the digital quadruplets are described. Then, the
interactions between the virtual and real vehicles are presented. The
experimental results of the digital quadruplets demonstrate the effectiveness
of the proposed framework.


  We analyze the absolute magnitude (M_r) and color (u-r) of low redshift
(z<0.06) galaxies in the Sloan Digital Sky Survey Data Release 6. galaxies with
nearly exponential profiles (Sloan parameter fracDeV < 0.1) fall on the blue
sequence of the color - magnitude diagram; if, in addition, these exponential
galaxies have M_r < -19, they show a dependence of u-r color on apparent axis
ratio q expected for a dusty disk galaxy. By fitting luminosity functions for
exponential galaxies with different values of q, we find that the dimming is
well described by the relation Delta M_r = 1.27 (log q)^2, rather than the
Delta M = C log q law that is frequently assumed. When the absolute magnitudes
of bright exponential galaxies are corrected to their "face-on" value, M_r^f =
M_r - Delta M_r, the average u-r color is linearly dependent on M_r^f for a
given value of q. Nearly face-on exponential galaxies (q > 0.9) have a shallow
dependence of mean u-r color on M_r^f (0.096 magnitudes redder for every
magnitude brighter). By comparison, nearly edge-on exponential galaxies (q <
0.3) are 0.265 magnitudes redder for every magnitude brighter. When the dimming
law Delta M = 1.27 (log q)^2 is used to create an inclination-corrected sample
of bright exponential galaxies, their apparent shapes are confirmed to be
consistent with a distribution of mildly non-circular disks, with median
short-to-long axis ratio gamma = 0.22 and median disk ellipticity epsilon =
0.08.


  A path-integral approach to lattice polarons is developed. The method is
based on exact analytical elimination of phonons and subsequent Monte Carlo
simulation of self-interacting fermions. The analytical basis of the method is
presented with emphasis on visualization of polaron effects, which path
integrals provide. Numerical results on the polaron energy, mass, spectrum and
density of states are given for short-range and long-range electron-phonon
interactions. It is shown that certain long-range interactions significantly
reduce the polaron mass, and anisotropic interactions enhance polaron
anisotropy. The isotope effect on the polaron mass and spectrum is discussed. A
path-integral approach to the Jahn-Teller polaron is developed. Extensions of
the method to lattice bipolarons and to more complex polaron models are
outlined.


  In this paper, a cooperative transmission design for a general multi-node
half-duplex wireless relay network is presented. It is assumed that the nodes
operate in half-duplex mode and that channel information is available at the
nodes. The proposed design involves solving a convex flow optimization problem
on a graph that models the relay network. A much simpler generalized-link
selection protocol based on the above design is also presented. Both the
proposed flow-optimized protocol and the generalized-link selection protocol
are shown to achieve the optimal diversity-multiplexing tradeoff (DMT) for the
relay network. Moreover, simulation results are presented to quantify the gap
between the performances of the proposed protocols and that of a
max-flow-min-cut type bound, in terms of outage probability.


  In recent years, deep learning-based methods have been successfully applied
to the image distortion restoration tasks. However, scenarios that assume a
single distortion only may not be suitable for many real-world applications. To
deal with such cases, some studies have proposed sequentially combined
distortions datasets. Viewing in a different point of combining, we introduce a
spatially-heterogeneous distortion dataset in which multiple corruptions are
applied to the different locations of each image. In addition, we also propose
a mixture of experts network to effectively restore a multi-distortion image.
Motivated by the multi-task learning, we design our network to have multiple
paths that learn both common and distortion-specific representations. Our model
is effective for restoring real-world distortions and we experimentally verify
that our method outperforms other models designed to manage both single
distortion and multiple distortions.


  We provide a unified method for obtaining upper bounds for certain functional
integrals appearing in quantum mechanics and non-relativistic quantum field
theory, functionals of the form $E\left[\exp(A_T)\right]$, the (effective)
action $A_T$ being a function of particle trajectories up to time $T$. The
estimates in turn yield rigorous lower bounds for ground state energies, via
the Feynman-Kac formula. The upper bounds are obtained by writing the action
for these functional integrals in terms of stochastic integrals. The method is
first illustrated in familiar quantum mechanical settings: for the hydrogen
atom, for a Schr\"odinger operator with $1/|x|^2$ potential with small
coupling, and, with a modest adaptation of the method, for the harmonic
oscillator. We then present our principal applications of the method, in the
settings of non-relativistic quantum field theories for particles moving in a
quantized Bose field, including the optical polaron and Nelson models.


  We present a combined theoretical and experimental study of two quaternary
Heusler alloys CoFeCrGe (CFCG) and CoMnCrAl (CMCA), promising candidates for
spintronics applications. Magnetization measurement shows the saturation
magnetization and transition temperature to be $3\; \mu_B$, $866$ K and $0.9 \;
\mu_B$, $358$ K for CFCG and CMCA respectively. The magnetization values agree
fairly well with our theoretical results and also obey the Slater-Pauling rule,
a prerequisite for half metallicity. A striking difference between the two
systems is their structure; CFCG crystallizes in fully ordered Y-type structure
while CMCA has L2$_1$ disordered structure. The antisite disorder adds a
somewhat unique property to the second compound, which arises due to the
probabilistic mutual exchange of Al positions with Cr/Mn and such an effect is
possibly expected due to comparable electronegativities of Al and Cr/Mn. {\it
Ab-initio} simulation predicted a unique transition from half metallic
ferromagnet to metallic antiferromagnet beyond a critical excess amount of Al
in the alloy.


  Recent findings by gamma-ray Cherenkov telescopes suggest a higher
transparency of the Universe to very-high-energy (VHE) photons than expected
from current models of the Extragalactic Background Light. It has been shown
that such transparency can be naturally explained by the DARMA scenario, in
which the photon mixes with a new, very light, axion-like particle predicted by
many extensions of the Standard Model of elementary particles. We discuss the
implications of DARMA for the VHE gamma-ray spectra of blazars, and show that
it successfully accounts for the observed correlation between spectral slope
and redshift by adopting for far-away sources the same emission spectrum
characteristic of nearby ones. DARMA also predicts the observed blazar spectral
index to become asymptotically independent of redshift for far-away sources.
Our prediction can be tested with the satellite-borne Fermi/LAT detector as
well as with the ground-based Cherenkov telescopes HESS, MAGIC, CANGAROOIII,
VERITAS and the Extensive Air Shower arrays ARGO-YBJ and MILAGRO.


  Recent realizations of exotic topological states in condensed matter and cold
atoms have advanced the exploration for topological characteristics, such as
invariant topological orders and band inversion. Here we construct a 1D optical
diatomic system made of split ring resonators with electric-magnetic couplings
to implement the topological features. We experimentally measure the dispersion
relationship and sub-lattice pseudo-spin vectors by detecting field strength
distributions, which determines the accompanying winding number of bulk band as
the topological order. The sub-lattice pseudo-spin vector inversion observed at
band-edges evidences the band inversion. We further reconfirm the
band-inversion-induced topological phase transition by measuring the symmetry
exchanges at band-edges. These results have shown the great potential of split
ring resonator platform to experimentally explore the advanced topological
characteristics, such as high winding numbers or even high Chern numbers in
more exotic setups.


  We consider the billiard map in the hypercube of $\mathbb{R}^d$. We obtain a
language by coding the billiard map by the faces of the hypercube. We
investigate the complexity function of this language. We prove that $n^{3d-3}$
is the order of magnitude of the complexity.


  The propagation of cosmic-ray protons in the Galaxy is discussed under the
framework of a three dimensional convection-diffusion model. Starting with the
assumption of a uniform and continuous distribution of cosmic-ray sources
injecting CRs continuously in the Galaxy and by invoking a supernova explosion
at various distances from the Earth, it is found that only those sources
located within a distance of ~ 1.5 kpc can produce appreciable temporal
fluctuations in the CR proton flux observed at the Earth. So, the construction
of the local CR proton spectrum is discussed by seperating the contributions of
the distant sources from that of the nearby sources. The contribution from the
distant sources is treated in the framework of a continuous source distribution
model both in space as well as time, but that of the nearby sources in a
discrete space-time source model. The study predicts the presence of at least
one old nearby source with a characteristic age of ~ 10^5 yrs located at a
distance of ~ 0.1 kpc to explain the observed proton flux below ~ 100 GeV.


  We consider the problem of testing the equality of conditional distributions
of a response variable given a vector of covariates between two populations.
Such a hypothesis testing problem can be motivated from various machine
learning and statistical inference scenarios, including transfer learning and
causal predictive inference. We develop a nonparametric test procedure inspired
from the conformal prediction framework. The construction of our test statistic
combines recent developments in conformal prediction with a novel choice of
conformity score, resulting in a weighted rank-sum test statistic that is valid
and powerful under general settings. To our knowledge, this is the first
successful attempt of using conformal prediction for testing statistical
hypotheses beyond exchangeability. Our method is suitable for modern machine
learning scenarios where the data has high dimensionality and large sample
sizes, and can be effectively combined with existing classification algorithms
to find good conformity score functions. The performance of the proposed method
is demonstrated in various numerical examples.


  We propose an action to describe high spin topologically massive gravity with
a negative cosmological constant. With the frame-like fields and spin
connections being combined into two gauge fields, the action includes two gauge
field Chern-Simons actions with different levels, and also a linear term
proportional to the difference of the gauge field strengths. Such linear term
play the role of imposing the torsion free conditions for high spin fields. We
discuss the gauge symmetry of this action and study the fluctuations around the
AdS$_3$ vacuum. We show how to relate the the fluctuations of the gauge field
to the Frondal fields, using the gauge symmetry. For the gauge group
$SL(n,R)\times SL(n,R)$, we find that the fluctuations of all high spin fields
up to spin $n$ satisfy third order differential equations, and hence there
generically exist massive traceless and trace mode for every spin.


  For $G$ a finite group, let $d_2(G)$ denote the proportion of triples $(x, y,
z) \in G^3$ such that $[x, y, z] = 1$. We determine the structure of finite
groups $G$ such that $d_2(G)$ is bounded away from zero: if $d_2(G) \geq
\epsilon > 0$, $G$ has a class-4 nilpotent normal subgroup $H$ such that $[G :
H] $ and $|\gamma_4(H)|$ are both bounded in terms of $\epsilon$. We also show
that if $G$ is an infinite group whose commutators have boundedly many
conjugates, or indeed if $G$ satisfies a certain more general commutator
covering condition, then $G$ is finite-by-class-3-nilpotent-by-finite.


  In this presentation, we report for the first time the detailed temperature
evolution process of the magnetic flux rope in a failed solar eruption.
Occurred on January 05, 2013, the flux rope was impulsively accelerated to a
speed of ~ 400 km/s in the first minute, then decelerated and came to a
complete stop in two minutes. The failed eruption resulted in a large-size
high-lying (~ 100 Mm above the surface) high-temperature "fire ball" sitting in
the corona for more than two hours. The time evolution of the thermal structure
of the flux rope was revealed through the differential emission measure
analysis technique, which produced temperature maps using observations of the
Atmospheric Imaging Assembly on board Solar Dynamic Observatory. The average
temperature of the flux rope steadily increased from ~ 5 MK to ~ 10 MK during
the first nine minutes of the evolution, which was much longer than the rise
time (about three minutes) of the associated soft X-ray flare. We suggest that
the flux rope be heated by the energy release of the continuing magnetic
reconnection, different from the heating of the low-lying flare loops, which is
mainly produced by the chromospheric plasma evaporation. The loop arcade
overlying the flux rope was pushed up by ~ 10 Mm during the attempted eruption.
The pattern of the velocity variation of the loop arcade strongly suggests that
the failure of the eruption be caused by the strapping effect of the overlying
loop arcade.


  Magnetic fields are everywhere in nature and they play an important role in
every astronomical environment which involves the formation of plasma and
currents. It is natural therefore to suppose that magnetic fields could be
present in the turbulent high temperature environment of the big bang. Such a
primordial magnetic field (PMF) would be expected to manifest itself in the
cosmic microwave background (CMB) temperature and polarization anisotropies,
and also in the formation of large- scale structure. In this review we
summarize the theoretical framework which we have developed to calculate the
PMF power spectrum to high precision. Using this formulation, we summarize
calculations of the effects of a PMF which take accurate quantitative account
of the time evolution of the cut off scale. We review the constructed numerical
program, which is without approximation, and an improvement over the approach
used in a number of previous works for studying the effect of the PMF on the
cosmological perturbations. We demonstrate how the PMF is an important
cosmological physical process on small scales. We also summarize the current
constraints on the PMF amplitude $B_\lambda$ and the power spectral index $n_B$
which have been deduced from the available CMB observational data by using our
computational framework.


  Discourse analysis and discourse parsing have shown great impact on many
important problems in the field of Natural Language Processing (NLP). Given the
direct impact of discourse annotations on model performance and
interpretability, robustly extracting discourse structures from arbitrary
documents is a key task to further improve computational models in NLP. To this
end, we present a new, supervised paradigm directly tackling the domain
adaptation issue in discourse parsing. Specifically, we introduce the first
fully supervised discourse parser designed to alleviate the domain dependency
through a staged model of weak classifiers by introducing the gradient boosting
framework.


  We study algebra endomorphisms and derivations of some localized down-up
algebras $\A$. First, we determine all the algebra endomorphisms of $\A$ under
some conditions on $r$ and $s$. We show that each algebra endomorphism of $\A$
is an algebra automorphism if $r^{m}s^{n}=1$ implies $m=n=0$. When $r=s^{-1}=q$
is not a root of unity, we give a criterion for an algebra endomorphism of $\A$
to be an algebra automorphism. In either case, we are able to determine the
algebra automorphism group for $\A$. We also show that each surjective algebra
endomorphism of the down-up algebra $A(r+s, -rs)$ is an algebra automorphism in
either case. Second, we determine all the derivations of $\A$ and calculate its
first degree Hochschild cohomology group.


  We report five new measurements of central black hole masses based on STIS
and WFPC2 observations with the Hubble Space Telescope and on axisymmetric,
three-integral, Schwarzschild orbit-library kinematic models. We selected a
sample of galaxies within a narrow range in velocity dispersion that cover a
range of galaxy parameters (including Hubble type and core/power-law surface
density profile) where we expected to be able to resolve the galaxy's sphere of
influence based on the predicted value of the black hole mass from the M-sigma
relation. We find masses in units of 10^8 solar masses for the following
galaxies:
  NGC 3585, M_BH = 3.4 (+1.5, -0.6);
  NGC 3607, M_BH = 1.2 (+0.4, -0.4);
  NGC 4026, M_BH = 2.1 (+0.7, -0.4); and
  NGC 5576, M_BH = 1.8 (+0.3, -0.4), all significantly excluding M_BH = 0. For
  NGC 3945, M_BH = 0.09 (+0.17, -0.21), which is significantly below
predictions from M-sigma and M-L relations and consistent with M_BH = 0, though
the presence of a double bar in this galaxy may present problems for our
axisymmetric code.


  This paper studies the limiting behavior of Tyler's M-estimator for the
scatter matrix, in the regime that the number of samples $n$ and their
dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with
$0<y<1$. We prove that when the data samples $x_1, \ldots, x_n$ are identically
and independently generated from the Gaussian distribution $\mathcal{N}(0, I)$,
the operator norm of the difference between a properly scaled Tyler's
M-estimator and $\sum_{i=1}^n x_i x_i^\top/n$ tends to zero. As a result, the
spectral distribution of Tyler's M-estimator converges weakly to the
Mar\v{c}enko-Pastur distribution.


  The transformer is a neural network component that can be used to learn
useful representations of sequences or sets of data-points. The transformer has
driven recent advances in natural language processing, computer vision, and
spatio-temporal modelling. There are many introductions to transformers, but
most do not contain precise mathematical descriptions of the architecture and
the intuitions behind the design choices are often also missing. Moreover, as
research takes a winding path, the explanations for the components of the
transformer can be idiosyncratic. In this note we aim for a mathematically
precise, intuitive, and clean description of the transformer architecture. We
will not discuss training as this is rather standard. We assume that the reader
is familiar with fundamental topics in machine learning including multi-layer
perceptrons, linear transformations, softmax functions and basic probability.


  We propose to extend property-based testing to substructural logics to
overcome the current lack of reasoning tools in the field. We take the first
step by implementing a property-based testing system for specifications written
in the linear logic programming language Lolli. We employ the foundational
proof certificates architecture to model various data generation strategies. We
validate our approach by encoding a model of a simple imperative programming
language and its compilation and by testing its meta-theory via mutation
analysis.


  The geometry of thermodynamic state space is studied for asymptotically
anti-de Sitter black holes in D-dimensional space times. Convexity of
thermodynamic potentials and the analytic structure of the response functions
is analysed. The thermodynamic potentials can be used to define a metric on the
space of thermodynamic variables and two commonly used such metrics are the
Weinhold metric, derived from the internal energy, and the Ruppeiner metric,
derived from the entropy. The intrinsic curvature of these metrics is
calculated for charged and for rotating black holes and it is shown that the
curvature diverges when heat capacities diverge but, contrary to general
expectations, the singularities in the Ricci scalars do not reflect the
critical behaviour.
  When a cosmological constant is included as a state space variable it can be
interpreted as a pressure and the thermodynamically conjugate variable as a
thermodynamic volume. The geometry of the resulting extended thermodynamic
state space is also studied, in the context of rotating black holes, and there
are curvature singularities when the heat capacity at constant angular velocity
diverges and when the black hole is incompressible. Again the critical
behaviour is not visible in the singularities of the thermodynamic Ricci
scalar.


  In this paper, we determine the almost sure values of the $\Phi $-dimensions
of random measures supported on random Moran sets that satisfy a uniform
separation condition. The $\Phi $-dimensions are intermediate Assouad-like
dimensions, the (quasi-)Assouad dimensions and $\theta $-Assouad spectrum being
special cases. Their values depend on the size of $\Phi $, with one size
coinciding with the Assouad dimension and the other coinciding with the
quasi-Assouad dimension. We give many applications, including to
equicontractive self-similar measures and $1$-variable random Moran measures
such as Cantor-like measures with probabilities that are uniformly distributed.
We can also deduce the $\Phi $-dimensions of the underlying random sets.


  Magnetization measurements of Mn12 molecular nanomagnets with spin ground
states of S = 10 and S = 19/2 showresonance tunneling at avoided energy level
crossings. The observed oscillations of the tunnel probability as a function of
the magnetic field applied along the hard anisotropy axis are due to
topological quantum phase interference of two tunnel paths of opposite
windings. Spin-parity dependent tunneling is established by comparing the
quantum phase interference of integer and half-integer spin systems.


  We present the hard matching coefficients for squark and gluino
hadroproduction. The hard matching coefficients follow from the next-to-leading
order cross section near threshold and are an important ingredient for
performing threshold resummation at next-to-next-to-leading logarithmic
accuracy. We discuss the calculation, list the analytical results and study the
numerical impact of these corrections. We find that the impact of the hard
matching coefficients can be considerable, with the largest effect observed for
final states involving gluinos.


  Given a Taylor series with a finite radius of convergence, its Borel
transform defines an entire function. A theorem of P\'olya relates the large d
istance behavior of the Borel transform in different directions to
singularities of the original function. With the help of the new asymptotic
interpolation method of van der Hoeven, we show that from the knowledge of a
large number of Taylor coefficients we can identify precisely the location of
such singularities, as well as their type when they are isolated. There is no
risk of getting artefacts with this method, which also gives us access to some
of the singularities beyond the convergence disk. The method can also be
applied to Fourier series of analytic periodic functions and is here tested on
various instances constructed from solutions to the Burgers equation. Large
precision on scaling exponents (up to twenty accurate digits) can be achieved.


  The quantum properties of quantum measurements are indispensable resources in
quantum information processing and have drawn extensive research interest. The
conventional approach to reveal the quantum properties relies on the
reconstruction of the entire measurement operators by quantum detector
tomography. However, many specific properties can be determined by a part of
matrix entries of the measurement operators, which provides us the possibility
to simplify the process of property characterization. Here, we propose a
general framework to directly obtain individual matrix entries of the
measurement operators by sequentially measuring two non-compatible observables.
This method allows us to circumvent the complete tomography of the quantum
measurement and extract the useful information for our purpose. We
experimentally implement this scheme to monitor the coherent evolution of a
general quantum measurement by determining the off-diagonal matrix entries. The
investigation of the measurement precision indicates the good feasibility of
our protocol to the arbitrary quantum measurements. Our results pave the way
for revealing the quantum properties of quantum measurements by selectively
determining the matrix entries of the measurement operators.


  Gravitational decays in particle physics are expected to violate the B and L
quantum numbers. In the standard theory, where gravity is weak because of the
huge value of Planck mass, the observation of the phenomenon is far from
present and probably future experimental sensitivity. On the other hand, in
theories with low gravity scale, where gravity becomes stronger at shorter
distances, these processes may be dangerous, predicting a too short proton
lifetime. Here I discuss a possible picture of gravitational decays, which is
consistent with present experimental bounds for a true gravity scale of few TeV
and suggests the possibility of observing B and L violating decays with a minor
improvement of the present experimental capability.


  The holographic principle and its realization in the AdS/CFT correspondence
led to unexpected connections between general relativity and quantum
information. This set the stage for studying aspects of quantum gravity models,
which are otherwise difficult to access, in table-top quantum-computational
experiments. Recent works have designed a special teleportation protocol that
realizes a surprising communication phenomenon most naturally explained by the
physics of a traversable wormhole. In this work, we have carried out quantum
experiments based on this protocol on state-of-the-art quantum computers. The
target quantum processing units (QPUs) included the Quantinuum's trapped-ion
System Model H1-1 and five IBM superconducting QPUs of various architectures,
with public and premium user access. We report the observed teleportation
signals from these QPUs with the best one reaching 80% of theoretical
predictions. We outline the experimental challenges we have faced in the course
of implementation, as well as the new theoretical insights into quantum
dynamics the work has led to. We also developed QGLab -- an open-source
end-to-end software solution that facilitates conducting the wormhole-inspired
teleportation experiments on state-of-the-art and emergent generations of QPUs
supported by the Qiskit and tket SDKs. We consider our study and deliverables
as an early practical step towards the realization of more complex experiments
for the indirect probing of quantum gravity in the lab.


  Single-photon cooperative dynamics of an assembly of two-level quantum
emitters coupled by a bosonic bath are investigated. The bosonic bath is
general and it can be anything as long as the exchange of excitations between
quantum emitters and bath is present. In these systems, it is found that the
population on the excited emitter keeps a simple and universal trapping law due
to the existence of system's dark states. Different from the trapping regime
caused by photonemitter dressed states, this type of trapping is only
associated with the number of quantum emitters. According to the trapping law,
the cooperative spontaneous emission at single-photon level in this kind of
systems is universally inhibited when the emitter number is large enough.


  We analyze the dynamics of gauge theories and constrained systems in general
under small perturbations around a classical solution (background) in both
Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory,
described by a quadratic Lagrangian, has the same constraint structure and
number of physical degrees of freedom as the original non-perturbed theory,
assuming the non-degenerate solution has been chosen. We show that the number
of Noether gauge symmetries is the same in both theories, but that the gauge
algebra in the fluctuations theory becomes Abelianized. We also show that the
fluctuations theory inherits all functionally independent rigid symmetries from
the original theory, and that these symmetries are generated by linear or
quadratic generators according to whether the original symmetry is preserved by
the background, or is broken by it. We illustrate these results with the
examples.


  We present a new algorithm for constructive recognition of the Suzuki groups
in their natural representations. The algorithm runs in Las Vegas polynomial
time given a discrete logarithm oracle. An implementation is available in the
Magma computer algebra system.


  Basic scaling laws are used to compare the relative capabilities of gaseous
and solid-state tracking. Conclusions are drawn in the context of physics
processes expected to be at the focus of studies at the International Linear
Collider.


  This paper deals with the long term behavior of the solution to the nonlinear
stochastic heat equation $\partial u /\partial t - \frac{1}{2}\Delta u =
b(u)\dot{W}$, where $b$ is assumed to be a globally Lipschitz continuous
function and the noise $\dot{W}$ is a centered and spatially homogeneous
Gaussian noise that is white in time. Using the moment formulas obtained in [9,
10], we identify a set of conditions on the initial data, the correlation
measure and the weight function $\rho$, which will together guarantee the
existence of an invariant measure in the weighted space
$L^2_\rho(\mathbb{R}^d)$. In particular, our result includes the parabolic
Anderson model (i.e., the case when $b(u) = \lambda u$) starting from the Dirac
delta measure.


  We describe a novel Zeeman slowing method reported in (Petzold et al (2018
New J. Phys. 20 042001)) and compare it to conventional radiative beam slowing
schemes. The scheme is designed to work on a type-II level structure making it
particularly attractive for radiative beam slowing of molecules. Working on the
D$_{1}$-line of atomic $^{39}$K, we demonstrate efficient slowing of an atomic
beam from $\mathrm{400 \, m \, s^{-1}}$ down to $\mathrm{35 \, m \, s^{-1}}$
with a final flux of $3.3 \cdot 10^{9} \, \mathrm{cm}^{-2}\mathrm{s^{-1}}$. We
give experimental details and compare our results to other established
radiative slowing schemes in atomic and molecular physics. We find type-II
Zeeman slowing to outperform white-light slowing commonly used in molecular
beam slowing and to be comparably efficient as traditional type-I Zeeman
slowing being the standard beam slowing technique in atomic physics.


  Head MRI pre-processing involves converting raw images to an
intensity-normalized, skull-stripped brain in a standard coordinate space. In
this paper, we propose an end-to-end weakly supervised learning approach,
called Neural Pre-processing (NPP), for solving all three sub-tasks
simultaneously via a neural network, trained on a large dataset without
individual sub-task supervision. Because the overall objective is highly
under-constrained, we explicitly disentangle geometric-preserving intensity
mapping (skull-stripping and intensity normalization) and spatial
transformation (spatial normalization). Quantitative results show that our
model outperforms state-of-the-art methods which tackle only a single sub-task.
Our ablation experiments demonstrate the importance of the architecture design
we chose for NPP. Furthermore, NPP affords the user the flexibility to control
each of these tasks at inference time. The code and model are freely-available
at \url{https://github.com/Novestars/Neural-Pre-processing}.


  The geometric measure of entanglement, originated by Shimony and by Barnum
and Linden, is determined for a family of tripartite mixed states consisting of
aribitrary mixtures of GHZ, W, and inverted-W states. For this family of
states, other measures of entanglement, such as entanglement of formation and
relative entropy of entanglement, have not been determined. The results for the
geometric measure of entanglement are compared with those for negativity, which
are also determined. The results for the geometric measure of entanglement and
the negativity provide examples of the determination of entanglement for
nontrivial mixed multipartite states.


  One area of research in multi-agent path finding is to determine how
replanning can be efficiently achieved in the case of agents being delayed
during execution. One option is to reschedule the passing order of agents,
i.e., the sequence in which agents visit the same location. In response, we
propose Switchable-Edge Search (SES), an A*-style algorithm designed to find
optimal passing orders. We prove the optimality of SES and evaluate its
efficiency via simulations. The best variant of SES takes less than 1 second
for small- and medium-sized problems and runs up to 4 times faster than
baselines for large-sized problems.


  We present a theoretical study of the two-dimensional spiral antiferromagnet
Ba2CuGe2O7 in the presence of an external magnetic field. We employ a suitable
nonlinear sigma model to calculate the T=0 phase diagram and the associated
low-energy spin dynamics for arbitrary canted fields, in general agreement with
experiment. In particular, when the field is applied parallel to the c axis, a
previously anticipated Dzyaloshinskii-type incommensurate-to-commensurate phase
transition is actually mediated by an intermediate phase, in agreement with our
earlier theoretical prediction confirmed by the recent observation of the
so-called double-k structure. The sudden pi/2 rotations of the magnetic
structures observed in experiment are accounted for by a weakly broken U(1)
symmetry of our model. Finally, our analysis suggests a nonzero
weak-ferromagnetic component in the underlying Dzyaloshinskii-Moriya
anisotropy, which is important for quantitative agreement with experiment.


  Measurements of the radioactive $^{244}$Pu abundances can break the
degeneracy between high-rate/low-yield and low-rate/high-yield scenarios for
the production of heavy $r$-process elements. The first corresponds to
production by core collapse supernovae (cc-SNe) while the latter corresponds to
production by e.g. compact binary mergers. The estimated $^{244}$Pu abundance
in the current interstellar medium inferred from deep-sea measurements (Wallner
et al. 2015) is significantly lower than that corresponding Early Solar System
abundances (Turner et al 2007). We estimate the expected median value of the
$^{244}$Pu abundances and fluctuations around this value in both models. We
show that while the current and Early Solar System abundances are naturally
explained within the low-rate/high-yield (e.g. merger) scenario, they are
incompatible with the high-rate/low-yield (cc-SNe) model. The inferred event
rate remarkably agrees with compact binary merger rates estimated from Galactic
neutron star binaries and from short gamma-ray bursts. Furthermore, the ejected
mass of $r$-process elements per event agrees with both theoretical and
observational macronova/kilonova estimates.


  In the chiral limit the complicated many-body dynamics around the
second-order chiral phase transition of two-flavor QCD can be understood by
appealing to universality. We present a novel formulation of the real-time
functional renormalization group that describes the stochastic hydrodynamic
equations of motion for systems in the same dynamic universality class, which
corresponds to Model G in the Halperin-Hohenberg classification. Our approach
preserves all relevant symmetries of such systems with reversible mode
couplings. We show that the calculations indeed produce the non-trivial value
$z=d/2$ for the dynamic critical exponent, where $d$ is the number of spatial
dimensions. From the momentum and temperature dependence of the diffusion
coefficient of the conserved charge densities, we extract the dimensionless
universal scaling function.


  OSIRIS-REx will return pristine samples of carbonaceous asteroid Bennu. This
article describes how pristine was defined based on expectations of Bennu and
on a realistic understanding of what is achievable with a constrained schedule
and budget, and how that definition flowed to requirements and implementation.
To return a pristine sample, the OSIRIS- REx spacecraft sampling hardware was
maintained at level 100 A/2 and <180 ng/cm2 of amino acids and hydrazine on the
sampler head through precision cleaning, control of materials, and vigilance.
Contamination is further characterized via witness material exposed to the
spacecraft assembly and testing environment as well as in space. This
characterization provided knowledge of the expected background and will be used
in conjunction with archived spacecraft components for comparison with the
samples when they are delivered to Earth for analysis. Most of all, the
cleanliness of the OSIRIS-REx spacecraft was achieved through communication
among scientists, engineers, managers, and technicians.


  In the previous paper (Li, X. Z., Xi, P., Zhai, X. H.: Phys. Lett. B{\bf666},
125-130 (2008)), we show the solutions of Einstein equations with static
spherically-symmetric quintessence-like matter surrounding a global monopole.
Furthermore, this monopole become a black hole with quintessence-like matter
and a deficit solid angle when it is swallowed by an ordinary black hole. We
study its quasinormal modes by WKB method in this paper. The numerical results
show that both the real part of the quasinormal frequencies and the imaginary
part decrease as the state parameter $w$, for scalar and gravitational
perturbations. And we also show variations of quasinormal frequencies of scalar
and gravitational fields via different $\epsilon$ (deficit solid angel
parameter) and different $\rho_0$ (density of static spherically-symmetric
quintessence-like matter at $r=1$), respectively.


  Liquids confined down to the atomic scale can show radically new properties.
However, only indirect and ensemble measurements operate in such extreme
confinement, calling for novel optical approaches enabling direct imaging at
the molecular level. Here, we harness fluorescence originating from
single-photon emitters at the surface of hexagonal boron nitride (hBN) for
molecular imaging and sensing in nanometrically confined liquids. The emission
originates from the chemisorption of organic solvent molecules onto native
surface defects, revealing single-molecule dynamics at the interface through
spatially correlated activation of neighboring defects. Emitter spectra further
offer a direct readout of local dielectric properties, unveiling increasing
dielectric order under nanometer-scale confinement. Liquid-activated native hBN
defects bridge the gap between solid-state nanophotonics and nanofluidics,
opening new avenues for nanoscale sensing and optofluidics.


  The cases of the Hawking radiation field being described by a pure state and
by the usual thermal state are compared within the CGHS dilaton gravity model.
The field-strength fluctuations of the Fourier modes are computed, showing a
discrepancy in the low-energy regime, while coinciding at high energies. Then
by defining a distance for density operators and evaluating it for the cases
concerned, the difference between the pure and thermal descriptions is
quantified and found to be exponentially small with respect to the Hawking
temperature. Possible physical interpretations are discussed.


  In this paper we discuss weak convergence of continuous-time Markov chains to
a non-symmetric pure jump process. We approach this problem using Dirichlet
forms as well as semimartingales. As an application, we discuss how to
approximate a given Markov process by Markov chains.


  Observations of massive galaxies at low redshift have revealed approximately
linear scaling relations between the mass of a supermassive black hole (SMBH)
and properties of its host galaxy. How these scaling relations evolve with
redshift and whether they extend to lower-mass galaxies however remain open
questions. Recent galaxy formation simulations predict a delayed, or
"two-phase", growth of SMBHs: slow, highly intermittent BH growth due to
repeated gas ejection by stellar feedback in low-mass galaxies, followed by
more sustained gas accretion that eventually brings BHs onto the local scaling
relations. The predicted two-phase growth implies a steep increase, or "kink",
in BH-galaxy scaling relations at a stellar mass $M_{*}\sim5\times10^{10}
M_{\odot}$. We develop a parametric, semi-analytic model to compare different
SMBH growth models against observations of the quasar luminosity function (QLF)
at $z\sim0.5-4$. We compare models in which the relation between SMBH mass and
galaxy mass is purely linear versus two-phase models. The models are anchored
to the observed galaxy stellar mass function, and the BH mass functions at
different redshifts are consistently connected by the accretion rates
contributing to the QLF. The best fits suggest that two-phase evolution is
significantly preferred by the QLF data over a purely linear scaling relation.
Moreover, when the model parameters are left free, the two-phase model fits
imply a transition mass consistent with that predicted by simulations. Our
analysis motivates further observational tests, including measurements of BH
masses and AGN activity at the low-mass end, which could more directly test
two-phase SMBH growth.


  In this work we study the applicability of the Equivalence Theorem, either
for unitary models or within an effective lagrangian approach. There are two
types of limitations: the existence of a validity energy window and the use of
the lowest order in the electroweak constants. For the first kind, we consider
some methods, based on dispersion theory or the large $N$ limit, that allow us
to extend the applicability. For the second, we have obtained numerical
estimates of the effect of neglecting higher orders in the perturbative
expansion.


  On infinitesimally short time interval various processes contributing to
population change tend to operate independently so that we can simply add their
contributions (Metz and Diekmann (1986)). This is one of the cornerstones for
differential equations modeling in general. Complicated models for processes
interacting in a complex manner may be built up, and not only in population
dynamics. The principle holds as long as the various contributions are taken
into account exactly. In this paper we discuss commonly used approximations
that may lead to dependency terms affecting the long run qualitative behavior
of the involved equations. We prove that these terms do not produce such
effects in the simplest and most interesting biological case, but the general
case is left open.


  We study disc galaxies in the framework of General Relativity to focus on the
possibility that, even in the low energy limit, there are relevant corrections
with respect to the purely Newtonian approach. Our analysis encompasses the
model both considering a low energy expansion and exact solutions, making it
clear the connection between these different approaches. In particular, we
focus on two different limits: the well known gravitomagnetic analogy and a new
limit, called strong gravitomagnetism, which has corrections in c of the same
order as the Newtonian terms. We show that these two limits of the general
class of solution can account for the observed flat velocity profile, contrary
to what happens using Newtonian models, where a dark matter contribution is
required. Hence, we suggest a geometrical origin for a certain amount of dark
matter effects.


  Since quantum coherence is an undoubted characteristic trait of quantum
physics, the quantification and application of quantum coherence has been one
of the long-standing central topics in quantum information science. Within the
framework of a resource theory of quantum coherence proposed recently, a
\textit{fiducial basis} should be pre-selected for characterizing the quantum
coherence in specific circumstances, namely, the quantum coherence is a
\textit{basis-dependent} quantity. Therefore, a natural question is raised:
what are the maximum and minimum coherences contained in a certain quantum
state with respect to a generic basis? While the minimum case is trivial, it is
not so intuitive to verify in which basis the quantum coherence is maximal.
Based on the coherence measure of relative entropy, we indicate the particular
basis in which the quantum coherence is maximal for a given state, where the
Fourier matrix (or more generally, \textit{complex Hadamard matrices}) plays a
critical role in determining the basis. Intriguingly, though we can prove that
the basis associated with the Fourier matrix is a stationary point for
optimizing the $l_1$ norm of coherence, numerical simulation shows that it is
not a global optimal choice.


  We derive twistorial tensionful bosonic string action by considering on the
world sheet the canonical twistorial 2-form in two-twistor space. We
demonstrate the equivalence of or model to two known momentum formulations of
D=4 bosonic string, with covariant worldsheet vectorial string momenta
$P_\mu^m(\tau,\sigma)$ and the one with tensorial string momenta
$P_{[\mu\nu]}(\tau,\sigma)$. All considered here string actions, in twistorial
and mixed spinor-spacetime formulations, are classically equivalent to the
Nambu-Goto action.


  In networked systems, monitoring devices such as sensors are typically
deployed to monitor various target locations. Targets are the points in the
physical space at which events of some interest, such as random faults or
attacks, can occur. Most often, these devices have limited energy supplies, and
they can operate for a limited duration. As a result, energy-efficient
monitoring of various target locations through a set of monitoring devices with
limited energy supplies is a crucial problem in networked systems. In this
paper, we study optimal scheduling of monitoring devices to maximize network
coverage for detecting and isolating events on targets for a given network
lifetime. The monitoring devices considered could remain active only for a
fraction of the overall network lifetime. We formulate the problem of
scheduling of monitoring devices as a graph labeling problem, which unlike
other existing solutions, allows us to directly utilize the underlying network
structure to explore the trade-off between coverage and network lifetime. In
this direction, first we propose a greedy heuristic to solve the graph labeling
problem, and then provide a game-theoretic solution to achieve near optimal
graph labeling. Moreover, the proposed setup can be used to simultaneously
solve the scheduling and placement of monitoring devices, which yields improved
performance as compared to separately solving the placement and scheduling
problems. Finally, we illustrate our results on various networks, including
real-world water distribution networks.


  We address the problem of making human motion capture in the wild more
practical by using a small set of inertial sensors attached to the body. Since
the problem is heavily under-constrained, previous methods either use a large
number of sensors, which is intrusive, or they require additional video input.
We take a different approach and constrain the problem by: (i) making use of a
realistic statistical body model that includes anthropometric constraints and
(ii) using a joint optimization framework to fit the model to orientation and
acceleration measurements over multiple frames. The resulting tracker Sparse
Inertial Poser (SIP) enables 3D human pose estimation using only 6 sensors
(attached to the wrists, lower legs, back and head) and works for arbitrary
human motions. Experiments on the recently released TNT15 dataset show that,
using the same number of sensors, SIP achieves higher accuracy than the dataset
baseline without using any video data. We further demonstrate the effectiveness
of SIP on newly recorded challenging motions in outdoor scenarios such as
climbing or jumping over a wall.


  Objective: Traumatic brain injuries and damage are major causes of death and
disability. We propose a 3D fully coupled electro-mechanical model of a nerve
bundle to investigate the electrophysiological impairments due to trauma at the
cellular level.
  Methods: The coupling is based on a thermal analogy of the neural electrical
activity by using the finite element software Abaqus CAE 6.13-3. The model
includes a real-time coupling, modulated threshold for spiking activation and
independent alteration of the electrical properties for each 3-layer fibre
within a nerve bundle as a function of strain.
  Results: Results of the coupled electro-mechanical model are validated with
previously published experimental results of damaged axons. Here, the cases of
compression and tension are simulated to induce (mild, moderate and severe)
damage at the nerve membrane of a nerve bundle, made of four fibres. Changes in
strain, stress distribution, and neural activity are investigated for
myelinated and unmyelinated nerve fibres, by considering the cases of an intact
and of a traumatized nerve membrane.
  Conclusion: A fully coupled electro-mechanical modelling approach is
established to provide insights into crucial aspects of neural activity at the
cellular level due to traumatic brain injury.
  Significance: One of the key findings is the 3D distribution of residual
stresses and strains at the membrane of each fibre due to mechanically induced
electrophysiological impairments, and its impact on signal transmission.


  TeV gamma rays emitted by GRBs are converted into electron-positron pairs via
interactions with the extragalactic infrared radiation fields. In turn the
pairs produced, whose trajectories are randomized by magnetic fields, will
inverse Compton scatter off the cosmic microwave background photons. The beamed
TeV gamma ray flux from GRBs is thus transformed into a GeV isotropic gamma ray
flux, which contributes to the total extragalactic gamma-ray background
emission. Assuming a model for the extragalactic radiation fields, for the GRB
redshift distribution and for the GRB luminosity function, we evaluate the
contribution of the GRB prompt and scattered emissions to the measured
extragalactic gamma-ray flux. To estimate this contribution we optimistically
require that the energy flux at TeV energies is about 10 times stronger than
the energy flux at MeV energies. The resulting gamma-ray diffuse background is
only a small fraction of what is observed, allowing blazars and other sources
to give the dominant contribution.


  Halfspaces or linear threshold functions are widely studied in complexity
theory, learning theory and algorithm design. In this work we study the natural
problem of constructing pseudorandom generators (PRGs) for halfspaces over the
sphere, aka spherical caps, which besides being interesting and basic geometric
objects, also arise frequently in the analysis of various randomized algorithms
(e.g., randomized rounding). We give an explicit PRG which fools spherical caps
within error $\epsilon$ and has an almost optimal seed-length of $O(\log n +
\log(1/\epsilon) \cdot \log\log(1/\epsilon))$. For an inverse-polynomially
growing error $\epsilon$, our generator has a seed-length optimal up to a
factor of $O( \log \log {(n)})$. The most efficient PRG previously known (due
to Kane, 2012) requires a seed-length of $\Omega(\log^{3/2}{(n)})$ in this
setting. We also obtain similar constructions to fool halfspaces with respect
to the Gaussian distribution.
  Our construction and analysis are significantly different from previous works
on PRGs for halfspaces and build on the iterative dimension reduction ideas of
Kane et. al. (2011) and Celis et. al. (2013), the \emph{classical moment
problem} from probability theory and explicit constructions of \emph{orthogonal
designs} based on the seminal work of Bourgain and Gamburd (2011) on expansion
in Lie groups.


  We present a theoretical analysis of spin relaxation, for a polarized gas of
spin 1/2 particles undergoing restricted adiabatic diffusive motion within a
container of arbitrary shape, due to magnetic field inhomogeneities of
arbitrary form.


  We have publicly released a blinded mix of simulated SNe, with types (Ia, Ib,
Ic, II) selected in proportion to their expected rate. The simulation is
realized in the griz filters of the Dark Energy Survey (DES) with realistic
observing conditions (sky noise, point spread function and atmospheric
transparency) based on years of recorded conditions at the DES site.
Simulations of non-Ia type SNe are based on spectroscopically confirmed light
curves that include unpublished non-Ia samples donated from the Carnegie
Supernova Project (CSP), the Supernova Legacy Survey (SNLS), and the Sloan
Digital Sky Survey-II (SDSS-II). We challenge scientists to run their
classification algorithms and report a type for each SN. A spectroscopically
confirmed subset is provided for training. The goals of this challenge are to
(1) learn the relative strengths and weaknesses of the different classification
algorithms, (2) use the results to improve classification algorithms, and (3)
understand what spectroscopically confirmed sub-sets are needed to properly
train these algorithms. The challenge is available at
www.hep.anl.gov/SNchallenge, and the due date for classifications is May 1,
2010.


  We present a new teaching and outreach activity based around the construction
of a three-dimensional chart of isotopes using LEGO$^{\circledR}$ bricks. The
activity, \emph{Binding Blocks}, demonstrates nuclear and astrophysical
processes through a seven-meter chart of all nuclear isotopes, built from over
26,000 LEGO$^{\circledR}$ bricks. It integrates A-level and GCSE curricula
across areas of nuclear physics, astrophysics, and chemistry, including:
nuclear decays (through the colours in the chart); nuclear binding energy
(through tower heights); production of chemical elements in the cosmos; fusion
processes in stars and fusion energy on Earth; as well as links to medical
physics, particularly diagnostics and radiotherapy.


  In this note we study `a la Baxter [1] the possible integrable manifolds of
the asymmetric eight-vertex model. As expected they occur when the Boltzmann
weights are either symmetric or satisfy the free-fermion condition but our
analysis clarify the reason both manifolds need to share a universal invariant.
We also show that the free-fermion condition implies three distinct classes of
integrable models.


  Study of the fusion reactions between hydrogen isotopes in muonic molecules
is the first example of the accurate accounting of the nucleus charge screening
by a muon in the fusion process. At LUNA installation the measurements of
astrophysical reaction cross sections were extended down to collision energies
of a few keV. The screening by atomic electrons of the target became
substantial. The possibility to look over screening from unbound electrons is
given by metal-hydrides used as targets in dd reaction measurements. The
classical Debye screening in plasma, applied to quasi-free electrons in metal,
provides an explanation of unexpectedly large screening potentials found for
some metals in the research through the Periodic table of elements.


  We report on a high statistics search for the $\Xi^{--}(1860)$ resonance in
$\Sigma^-$-nucleus collisions at 340GeV/c. No evidence for this resonance is
found in our data sample which contains 676000 $\Xi^-$ candidates above
background. For the decay channel $\Xi^{--}(1860) \to \Xi^-\pi^-$ and the
kinematic range 0.15$<x_F<$0.9 we find a 3$\sigma$ upper limit for the
production cross section of 3.1 and 3.5 $\mu$b per nucleon for reactions with
carbon and copper, respectively.


  Marked mesh patterns are a very general type of permutation pattern. We
examine a particular marked mesh pattern originally defined by Kitaev and
Remmel, and show that its generating function is described by the $r$-Stirling
numbers. We examine some ramifications of various properties of the
$r$-Stirling numbers for this generating function, and find (seemingly new)
formulas for the $r$-Stirling numbers in terms of the classical Stirling
numbers and harmonic numbers. We also answer some questions posed by Kitaev and
Remmel and show a connection to another mesh pattern introduced by Kitaev and
Liese.


  By devising a novel framework, we present a comprehensive theoretical study
of solubilities of alkali (Li, Na, K, Rb, Cs) and alkaline earth (Be, Ca, Sr,
Ba) metals in the he boron-rich Mg-B system. The study is based on
first-principle calculations of solutes formation energies in MgB$_2$, MgB$_4$,
MgB$_7$ alloys and subsequent statistical-thermodynamical evaluation of
solubilities. The advantage of the approach consists in considering all the
known phase boundaries in the ternary phase diagram. Substitutional Na, Ca, and
Li demonstrate the largest solubilities, and Na has the highest (0.5-1 % in
MgB$_7$ at $T=650-1000$ K). All the considered interstitials have negligible
solubilities. The solubility of Be in MgB$_7$ can not be determined because the
corresponding low-solubility formation energy is negative indicating the
existence of an unknown ternary ground state. We have performed a
high-throughput search of ground states in binary Mg-B, Mg-$A$, and B-$A$
systems, and we construct the ternary phase diagrams of Mg-B-$A$ alloys based
on the stable binary phases. Despite its high temperature observations, we find
that Sr$_{9}$Mg$_{38}$ is not a low-temperature equilibrium structure. We also
determine two new possible ground states CaB$_{4}$ and RbB$_{4}$, not yet
observed experimentally.


  We consider the graph $G_n$ with vertex set $V(G_n) = \{ 1, 2, \ldots, n\}$
and $\{i,j\} \in E(G_n)$ if and only if $0<|i-j| \leq 2$. We call $G_n$ the
straight linear 2-tree on $n$ vertices. Using $\Delta$--Y transformations and
identities for the Fibonacci and Lucas numbers we obtain explicit formulae for
the resistance distance $r_{G_n}(i,j)$ between any two vertices $i$ and $j$ of
$G_n$. To our knowledge $\{G_n\}_{n=3}^\infty$ is the first nontrivial family
with diameter going to $\infty$ for which all resistance distances have been
explicitly calculated. Our result also gives formulae for the number of
spanning trees and 2-forests in a straight linear 2-tree. We show that the
maximal resistance distance in $G_n$ occurs between vertices 1 and $n$ and the
minimal resistance distance occurs between vertices $n/2$ and $n/2+1$ for $n$
even (with a similar result for $n$ odd). It follows that $r_n(1,n) \to \infty$
as $n \to \infty$. Moreover, our explicit formula makes it possible to order
the non-edges of $G_n$ exactly according to resistance distance, and this
ordering agrees with the intuitive notion of distance on a graph. Consequently,
$G_n$ is a geometric graph with entirely different properties than the random
geometric graphs investigated in [6]. These results for straight linear 2-trees
along with an example of a bent linear 2-tree and empirical results for
additional graph classes convincingly demonstrate that resistance distance
should not be discounted as a viable method for link prediction in geometric
graphs.


  We show that all perfect odd integer squares not divisible by 3, can be
usefully written as sqrt(N) = a + 18p, where the constant a is determined by
the basic properties of N. The equation can be solved deterministically by an
efficient four step algorithm that is solely based on integer arithmetic. There
is no required multiplication or division by multiple digit integers, nor does
the algorithm need a seed value. It finds the integer p when N is a perfect
square, and certifies N as a non-square when the algorithm terminates without a
solution. The number of iterations scales approximately as log(sqrt(N)/2) for
square roots. The paper also outlines how one of the methods discussed for
squares can be extended to finding an arbitrary root of N. Finally, we present
a rule that distinguishes products of twin primes from squares.