  Drones are a promising technology for autonomous data collection and indoor
sensing. In situations when human-controlled UAVs may not be practical or
dependable, such as in uncharted or dangerous locations, the usage of
autonomous UAVs offers flexibility, cost savings, and reduced risk. The system
creates a simulated quadcopter capable of autonomously travelling in an indoor
environment using the gazebo simulation tool and the ros navigation system
framework known as Navigaation2. While Nav2 has successfully shown the
functioning of autonomous navigation in terrestrial robots and vehicles, the
same hasn't been accomplished with unmanned aerial vehicles and still has to be
done. The goal is to use the slam toolbox for ROS and the Nav2 navigation
system framework to construct a simulated drone that can move autonomously in
an indoor (gps-less) environment.


  We present new capacitance measurements of critical Casimir force-induced
thinning of $^4$He films near the superfluid/normal transition, focused on the
region below $T_{\lambda}$ where the effect is the greatest. $^4$He films of
238, 285, and 340 \AA thickness are adsorbed on N-doped silicon substrates with
roughness $\approx 8 {\AA}$. The Casimir force scaling function $\vartheta $,
deduced from the thinning of these three films, collapses onto a single
universal curve, attaining a minimum $\vartheta = -1.30 \pm 0.03$ at
$x=td^{1/\nu}=-9.7\pm 0.8 {\AA}^{1/\nu}$. The collapse confirms the finite-size
scaling origin of the dip in the film thickness. Separately, we also confirm
the presence down to $2.13 K$ of the Goldstone/surface fluctuation force, which
makes the superfluid film $\sim 2 {\AA}$ thinner than the normal film.


  A new \textsuperscript{3}He-driven IGISOL production station and mass
separator have been designed to produce neutron-deficient low-mass isotopes at
the Cyclotron Institute for the TAMUTRAP facility. The LSTAR design has a mass
resolution $M/\Delta M\geq 3, 000$ to reject contaminants with $\gt95\%$
efficiency.


  Evolutionary optimization algorithms are often derived from loose biological
analogies and struggle to leverage information obtained during the sequential
course of optimization. An alternative promising approach is to leverage data
and directly discover powerful optimization principles via meta-optimization.
In this work, we follow such a paradigm and introduce Evolution Transformer, a
causal Transformer architecture, which can flexibly characterize a family of
Evolution Strategies. Given a trajectory of evaluations and search distribution
statistics, Evolution Transformer outputs a performance-improving update to the
search distribution. The architecture imposes a set of suitable inductive
biases, i.e. the invariance of the distribution update to the order of
population members within a generation and equivariance to the order of the
search dimensions. We train the model weights using Evolutionary Algorithm
Distillation, a technique for supervised optimization of sequence models using
teacher algorithm trajectories. The resulting model exhibits strong in-context
optimization performance and shows strong generalization capabilities to
otherwise challenging neuroevolution tasks. We analyze the resulting properties
of the Evolution Transformer and propose a technique to fully
self-referentially train the Evolution Transformer, starting from a random
initialization and bootstrapping its own learning progress. We provide an open
source implementation under https://github.com/RobertTLange/evosax.


  The narrow component of the iron K$\alpha$ is an almost ubiquitous feature in
the X-ray spectra of active galactic nuclei (AGN) and is believed to originate
in neutral material, possibly located in the molecular torus. This would imply
a tight connection between the Fe K$\alpha$ equivalent width (EW) and the
physical properties of the torus. In a recent work we have shown that the
decrease of the covering factor of the torus with the luminosity, as expected
by luminosity-dependent unification models, would be able to explain the
decrease of Fe K$\alpha$ EW with the luminosity (i.e., the X-ray Baldwin
effect). Recent developments in the study of the mid-IR (MIR) spectrum of AGN
allow important parameters of the torus to be deduced, such as its covering
factor ($f_{\rm\,obs}$) and equatorial column density ($N_{\rm\,H}^{\rm\,T}$),
by applying clumpy torus models. Using XMM-Newton/EPIC observations of a sample
of 24 type-I AGN, we investigate the relation between the physical parameters
of the torus obtained by recent MIR works and the properties of the Fe
K$\alpha$ line. We correct the values of the Fe K$\alpha$ EW by taking the
inclination angle, the photon index, the equatorial column density, and
half-opening angle of the torus into account using a physical torus model of
X-ray reprocessed radiation. We find that the relation between Fe K$\alpha$ EW
and $f_{\rm\,obs}$ shows a slope that is consistent with the expected value,
albeit with a low statistical significance. A trend that is consistent with the
theoretical prediction is also found when comparing the Fe K$\alpha$ EW to
$N_{\rm\,H}^{\rm\,T}$. Our work seems to confirm that the bulk of the narrow Fe
K$\alpha$ line is produced by the same material responsible for the MIR
emission.


  For a K3 surface over a field of characteristic 2 which is finitely generated
over its prime subfield, we prove that the cokernel of the natural map from the
Brauer group of the base field to that of the K3 surface is finite modulo the
2-primary torsion subgroup. In characteristic different from 2, such results
were previously proved by A. N. Skorobogatov and Y. G. Zarhin. We basically
follow their methods with an extra care in the case of superspecial K3 surfaces
using the recent results of W. Kim and K. Madapusi Pera on the Kuga-Satake
construction and the Tate conjecture for K3 surfaces in characteristic 2.


  Deployed machine learning (ML) models often encounter new user data that
differs from their training data. Therefore, estimating how well a given model
might perform on the new data is an important step toward reliable ML
applications. This is very challenging, however, as the data distribution can
change in flexible ways, and we may not have any labels on the new data, which
is often the case in monitoring settings. In this paper, we propose a new
distribution shift model, Sparse Joint Shift (SJS), which considers the joint
shift of both labels and a few features. This unifies and generalizes several
existing shift models including label shift and sparse covariate shift, where
only marginal feature or label distribution shifts are considered. We describe
mathematical conditions under which SJS is identifiable. We further propose
SEES, an algorithmic framework to characterize the distribution shift under SJS
and to estimate a model's performance on new data without any labels. We
conduct extensive experiments on several real-world datasets with various ML
models. Across different datasets and distribution shifts, SEES achieves
significant (up to an order of magnitude) shift estimation error improvements
over existing approaches.


  Silicon stripixel sensors which were developed at BNL will be installed as
part of the RHIC-PHENIX silicon vertex tracker (VTX). RHIC II operations
provide luminosity up to 2x10^32 /cm2/s so the silicon stripixel sensors will
be exposed to a significant amount of radiation. The most problematic radiation
effect for VTX is the increase of leakage current, which degrades the signal to
noise ratio and may saturate the readout electronics.
  We studied the radiation damage using the same diodes as CERN-RD48. First,
the proportionality between the irradiation fluence and the increase of leakage
current of CERN-RD48 was reproduced. Then beam experiments with stripixel
sensor were done in which leakage current was found to increase in the same way
as that of thereference diode.
  A stripixel sensor was also irradiated at the PHENIX interaction region (IR)
during the 2006 run. We found the same relation between the integrated
luminosity and determined fluence from increase of leakage current. The
expected fluence is 3-6x10^12 Neq/cm2 (1 MeV neutron equivalent) in RHIC II
operations for 10 years. Due to this expected exposure, setting the operating
temperature in PHENIX to T< 0 deg. C to suppress leakage current is needed to
avoid saturation of preamplifiers.


  In 1979, Kazhdan and Lusztig developed a combinatorial theory associated with
Coxeter groups. They defined in particular partitions of the group in left and
two-sided cells. In 1983, Lusztig generalized this theory to Hecke algebras of
Coxeter groups with unequal parameters. We propose a definition of left cells
and two-sided cells for complex reflection groups, based on ramification theory
for Calogero-Moser spaces. These spaces have been defined via rational
Cherednik algebras by Etingof and Ginzburg. We conjecture that these coincide
with Kazhdan-Lusztig cells, for real reflection groups. Counterparts of
families of irreducible characters have been studied by Gordon and Martino, and
we provide here a version of left cell representations. The Calogero-Moser
cells will be studied in details in a forthcoming paper, providing thus several
results supporting our conjecture.


  The non-observation of supersymmetric signatures in searches at the Large
Hadron Collider strongly constrains minimal supersymmetric models like the
CMSSM. We explore the consequences on the SUSY particle spectrum in a minimal
SO(10) with large D-terms and non-universal gaugino masses at the GUT scale.
This changes the sparticle spectrum in a testable way and for example can
sufficiently split the coloured and non-coloured sectors. The splitting
provided by use of the SO(10) D-terms can be exploited to obtain light first
generation sleptons or third generation squarks, the latter corresponding to a
compressed spectrum scenario.


  The Empirical Valence Bond (EVB) method offers a suitable framework to obtain
reactive potentials through the coupling of non-reactive force fields. However,
most of the implemented functional forms for the coupling terms depend on
complex spatial coordinates, which precludes the computation of the stress
tensor for condensed phase systems and prevents the possibility to carry out
EVB molecular dynamics in the isothermal-isobaric (NPT) ensemble. In this work,
we make use of coupling terms that depend on the energy gaps, defined as the
energy differences between the participating non-reactive force fields, and
derive an expression for the EVB stress tensor suitable for computations.
Implementation of this new methodology is tested for a model of a single
reactive malonaldehyde solvated in non-reactive water. Computed densities and
classical probability distributions in the NPT ensemble reveals a negligible
role of the reactive potential in the limit of low concentrated solutions, thus
corroborating the validity of standard approximations customarily adopted for
EVB simulations.


  In this paper, we consider a two-hop relay-assisted cognitive downlink OFDMA
system (named as secondary system) dynamically accessing a spectrum licensed to
a primary network, thereby improving the efficiency of spectrum usage. A
cluster-based relay-assisted architecture is proposed for the secondary system,
where relay stations are employed for minimizing the interference to the users
in the primary network and achieving fairness for cell-edge users. Based on
this architecture, an asymptotically optimal solution is derived for jointly
controlling data rates, transmission power, and subchannel allocation to
optimize the average weighted sum goodput where the proportional fair
scheduling (PFS) is included as a special case. This solution supports
decentralized implementation, requires small communication overhead, and is
robust against imperfect channel state information at the transmitter (CSIT)
and sensing measurement. The proposed solution achieves significant throughput
gains and better user-fairness compared with the existing designs. Finally, we
derived a simple and asymptotically optimal scheduling solution as well as the
associated closed-form performance under the proportional fair scheduling for a
large number of users. The system throughput is shown to be
$\mathcal{O}\left(N(1-q_p)(1-q_p^N)\ln\ln K_c\right)$, where $K_c$ is the
number of users in one cluster, $N$ is the number of subchannels and $q_p$ is
the active probability of primary users.


  The tensor contribution can be directly incorporated in the cluster model in
a simplified way. In conventional $\alpha$ cluster models, the contribution of
the non-central interactions exactly cancels because of the antisymmetrization
effect and spatial symmetry of $\alpha$ clusters. The mixing of breaking
components of $\alpha$ clusters to take into account the spin-orbit and tensor
effects is needed. Previously we proposed a simplified method to include the
spin-orbit effect, and also for the tensor part, a simplified model to directly
take into account the contribution of the tensor interaction (called SMT) was
introduced; however the contribution of the tensor interaction was quite
limited. Here we improve SMT, which is called $i$SMT. Using newly proposed
$i$SMT, the contribution of the tensor interaction in $^4$He is more than $-40$
MeV, four times larger than the previous version. The method is applied to
four-$\alpha$ cluster structure of $^{16}$O. In $^{16}$O, the tensor
contribution is also large, and this is coming from the finite size effect for
the distances among $\alpha$ clusters with a tetrahedral configuration.


  In this paper, we propose Posterior Sampling Reinforcement Learning for
Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that
achieves Bayesian regret bound of $O(HS\sqrt{AT})$ in the infinite-horizon
zero-sum stochastic games with average-reward criterion. Here $H$ is an upper
bound on the span of the bias function, $S$ is the number of states, $A$ is the
number of joint actions and $T$ is the horizon. We consider the online setting
where the opponent can not be controlled and can take any arbitrary
time-adaptive history-dependent strategy. Our regret bound improves on the best
existing regret bound of $O(\sqrt[3]{DS^2AT^2})$ by Wei et al. (2017) under the
same assumption and matches the theoretical lower bound in $T$.


  Starting from astrophysical indications that the fine structure constant
might undergo a small cosmological time shift, we discuss the implications of
such an effect from the point of view of particle physics. Grand unification
implies small time shifts for the nucleon mass, the magnetic moment of the
nucleon and the weak coupling constant as well. The relative change of the
nucleon mass is about 40 times larger than the relative change of alpha.
Laboratory measurements using very advanced methods in quantum optics might
soon reveal small time shifts of the nucleon mass, the magnetic moment of the
nucleon and the fine structure constant.


  Galactic outflows produced by stellar feedback are known to be multiphase in
nature. Both observations and simulations indicate that the material within
several kpc of galactic disk mid-planes consists of warm clouds embedded within
a hot wind. A theoretical understanding of the outflow phenomenon, including
both winds and fountain flows, requires study of the interactions among thermal
phases. We develop a method to quantify these interactions via measurements of
mass, momentum, and energy flux exchanges using temporally and spatially
averaged quantities and conservation laws. We apply this method to a
star-forming ISM MHD simulation based on the TIGRESS framework, for Solar
neighbourhood conditions. To evaluate the extent of interactions among the
phases, we first examine the validity of the ``ballistic model,'' which
predicts trajectories of the warm phase ($5050\,\rm{K}<T<2\times10^4\,\rm{K}$)
treated as non-interacting clouds. This model is successful at intermediate
vertical velocities ($ 50$ km s$^{-1}$ $\lesssim |v_z| \lesssim 100 $ km
s$^{-1}$), but at higher velocities we observe an excess in simulated warm
outflow compared to the ballistic model. This discrepancy cannot be fully
accounted for by cooling of high-velocity intermediate-temperature
($2\times10^4\,\rm{K}<T<5\times10^5\,\rm{K}$) gas. By examining the fluxes of
mass, momentum and energy, we conclude that warm phase gains mass via cooling
of the intermediate phase, while momentum transfer occurs from the hot
($T>5\times10^5\,\rm{K}$) to the warm phase. The large energy flux from the hot
outflow that is transferred to the warm and intermediate phases is quickly
radiated away. A simple interaction model implies an effective warm cloud size
in the fountain flow of a few 100~pc, showing that warm-hot flux exchange
mainly involves a few large clouds rather than many small ones.


  We devise new boundary conditions for the near-horizon geometries of extremal
BTZ and Kerr black holes, as well as for the ultra-cold limit of the Kerr-de
Sitter black hole. These boundary conditions are obtained as the
higher-dimensional uplift of recently proposed boundary conditions in
two-dimensional gravity. Their asymptotic symmetries consist in the semi-direct
product of a Virasoro and a current algebra, of which we determine the central
extensions.


  Science communication forms the bridge between computer science researchers
and their target audience. Researchers who can effectively draw attention to
their research findings and communicate them comprehensibly not only help their
target audience to actually learn something, but also benefit themselves from
the increased visibility of their work and person. However, the necessary
skills for good science communication must also be taught, and this has so far
been neglected in the field of software engineering education.
  We therefore designed and implemented a science communication seminar for
bachelor students of computer science curricula. Students take the position of
a researcher who, shortly after publication, is faced with having to draw
attention to the paper and effectively communicate the contents of the paper to
one or more target audiences. Based on this scenario, each student develops a
communication strategy for an already published software engineering research
paper and tests the resulting ideas with the other seminar participants.
  We explain our design decisions for the seminar, and combine our experiences
with responses to a participant survey into lessons learned. With this
experience report, we intend to motivate and enable other lecturers to offer a
similar seminar at their university. Collectively, university lecturers can
prepare the next generation of computer science researchers to not only be
experts in their field, but also to communicate research findings more
effectively.


  Noise can shape the firing behaviors of neurons. Here, we show that noise
acting on the fast variable of the Hedgehog burster can tune the spike counts
of bursts via the self-induced stochastic resonance (SISR) phenomenon. Using
the distance matching condition, the critical transition positions on the slow
manifolds can be predicted and the stochastic periodic orbits for various noise
strengths are obtained. The critical transition positions on the slow manifold
with non-monotonic potential differences exhibit a staircase-like dependence on
the noise strength, which is also revealed by the stepwise change in the period
of the stochastic periodic orbit. The noise-tuned bursting is more coherent
within each step while displaying mixed-mode oscillations near the boundaries
between the steps. When noise is large enough, noise-induced trapping of the
slow variable can be observed, where the number of coexisting traps increases
with the noise strength. It is argued that the robustness of SISR underlies the
generality of the results discovered in this paper.


  Temperature dependent hydrogen bond energetics and dynamical features, such
as the diffusion coefficient and reorientational times, have been determined
for ethanol-water mixtures with 10, 20 and 30 mol % of ethanol. Concerning
pairwise interaction energies between molecules, it is found that water-water
interactions become stronger, while ethanol-ethanol ones become significantly
weaker in the mixtures than the corresponding values characteristic to the pure
substances. Concerning the diffusion processes, for all concentrations the
activation barrier of water and ethanol molecule become very similar to each
other. Reorientation motions of water and ethanol become slower as ethanol
concentration is increasing. Characteristic reorientational times of water in
the mixtures are substantially longer than these values in the pure substance.
On the other hand, this change for ethanol is only moderate. The reorientation
motions of water (especially the ones related to the H-bonded interaction)
become very similar for those of ethanol in the mixtures.


  Circle graphs are intersection graphs of chords in a circle and $k$-polygon
graphs are intersection graphs of chords in a convex $k$-sided polygon where
each chord has its endpoints on distinct sides. The $k$-polygon graphs, for $k
\ge 2$, form an infinite chain of graph classes, each of which contains the
class of permutation graphs. The union of all of those graph classes is the
class of circle graphs. The polygon number $\gp(G)$ of a circle graph $G$ is
the minimum $k$ such that $G$ is a $k$-polygon graph. Given a circle graph $G$
and an integer $k$, determining whether $\gp(G) \le k$ is NP-complete, while
the problem is solvable in polynomial time for fixed $k$.
  In this paper, we show that $\gp(G)$ is always at least as large as the
asteroidal number of $G$, and equal to the asteroidal number of $G$ when $G$ is
a connected distance hereditary graph that is not a clique. This implies that
the classes of distance hereditary permutation graphs and distance hereditary
AT-free graphs are the same, and we give a forbidden subgraph characterization
of that class. We also establish the following upper bounds: $\gp(G)$ is at
most the clique cover number of $G$ if $G$ is not a clique, at most 1 plus the
independence number of $G$, and at most $\lceil n/2 \rceil$ where $n \ge 3$ is
the number of vertices of $G$. Our results lead to linear time algorithms for
finding the minimum number of corners that must be added to a given circle
representation to produce a polygon representation, and for finding the
asteroidal number of a distance hereditary graph, both of which are
improvements over previous algorithms for those problems.


  The ``new fields" or ``superconformal functions" on $N=1$ super Riemann
surfaces introduced recently by Rogers and Langer are shown to coincide with
the Abelian differentials (plus constants), viewed as a subset of the functions
on the associated $N=2$ super Riemann surface. We confirm that, as originally
defined, they do not form a super vector space.


  This work applies the formalism developed in our earlier paper to de Sitter
space. After exactly solving the relevant Heisenberg equations of motion we
give a detailed discussion of the subtleties associated with defining physical
states and the emergence of the classical theory. This computation provides the
striking result that quantum corrections to this long wavelength limit of
gravity eliminate the problem of the big crunch. We also show that the same
corrections lead to possibly measureable effects on the CMB radiation. Finally,
for the sake of completeness we discuss the special case, $\Lambda=0$, and its
relation to Minkowski space.


  Given a structured matrix $A$ we study the problem of finding the closest
normal matrix with the same structure. The structures of our interest are:
Hamiltonian, skew-Hamiltonian, per-Hermitian, and perskew-Hermitian. We develop
a structure-preserving Jacobi-type algorithm for finding the closest normal
structured matrix and show that such algorithm converges to a stationary point
of the objective function.


  Chubukov's proposal concerning the possibility of a nondimerized quantum
nematic phase in the ground-state phase diagram of the bilinear-biquadratic
spin-1 chain is studied numerically. Our results do not support the existence
of this phase, but they rather indicate a direct transition from the
ferromagnetic into the dimerized phase.


  The impact of the outbreak of COVID-19 on health has been widely concerned.
Disease risk assessment, prediction, and early warning have become a
significant research field. Previous research suggests that there is a
relationship between air quality and the disease. This paper investigated the
impact of the atmospheric environment on the basic reproduction number (R$_0$)
in Australia, South Korea, and Italy by using atmospheric environment data,
confirmed case data, and the distributed lag non-linear model (DLNM) model
based on Quasi-Poisson regression. The results show that the air temperature
and humidity have lag and persistence on short-term R$_0$, and seasonal factors
have an apparent decorating effect on R$_0$. PM$_{10}$ is the primary pollutant
that affects the excess morbidity rate. Moreover, O$_3$, PM$_{2.5}$, and SO$_2$
as perturbation factors have an apparent cumulative effect. These results
present beneficial knowledge for correlation between environment and COVID-19,
which guiding prospective analyses of disease data.


  In this paper, we mainly study two notions of pattern avoidance in parking
functions. First, for any collection of length 3 patterns, we compute the
number of parking functions of size $n$ that avoid them under the first notion.
This is motivated by recent work of Adeniran and Pudwell, who obtained
analogous results using a second notion of pattern avoidance. Then, we provide
new purely bijective proofs for two of their results, and improve the formula
of another one. Finally, we apply similar enumeration techniques to the work of
Novelli and Thibon on certain Hopf algebras of generalised parking functions,
and compute their graded dimensions.


  Demands for implementing original OSs that can achieve high I/O performance
on PC/AT compatible hardware have recently been increasing, but conventional OS
debugging environments have not been able to simultaneously assure their
stability, be easily customized to new OSs and new I/O devices, and assure
efficient execution of I/O operations. We therefore developed a novel OS
debugging method using a lightweight virtual machine. We evaluated this
debugging method experimentally and confirmed that it can transfer data about
5.4 times as fast as the conventional virtual machine monitor.


  We study the so-called dynamic coverage problem by agents located in some
topological graph. The agents must visit all regions of interest but they also
should stay connected to the base via multi-hop. We prove that the algorithmic
complexity of this planning problem is PSPACE-complete. Furthermore we prove
that the problem becomes NP-complete for bounded plans. We also prove the same
complexities for the reachability problem of some positions. We also prove that
complexities are maintained for a subclass of topological graphs.


  We propose a novel machine learning algorithm for simulating radiative
transfer. Our algorithm is based on physics informed neural networks (PINNs),
which are trained by minimizing the residual of the underlying radiative
tranfer equations. We present extensive experiments and theoretical error
estimates to demonstrate that PINNs provide a very easy to implement, fast,
robust and accurate method for simulating radiative transfer. We also present a
PINN based algorithm for simulating inverse problems for radiative transfer
efficiently.


  Consider an Galton Watson tree of height $m$: each leaf has one of $k$
opinions or not. In other words, for $i \in \{1, . . . , k\}$, $x$ at
generation $m$ thinks $i$ with probability $p_i$ and nothing with probability
$p_0$. Moreover the opinions are independently distributed for each leaf.
Opinions spread along the tree based on a specific rule: the majority wins! In
this paper, we study the asymptotic behavior of the distribution of the opinion
of the root when $m \to +\infty$.


  Let us have a family of ideals of holomorphic functions vanishing at N
distinct points of a complex manifold, all tending to a single point. As is
known, convergence of the ideals does not guarantee the convergence of the
pluricomplex Green functions to the Green function of the limit ideal;
moreover, the existence of the limit of the Green functions was unclear.
Assuming that all the powers of the ideals converge to some ideals, we prove
that the Green functions converge, locally uniformly away from the limit pole,
to a function which is essentially the upper envelope of the scaled Green
functions of the limits of the powers. As examples, we consider ideals
generated by hyperplane sections of a holomorphic curve near its singular
point. In particular, our result explains recently obtained asymptotics for
3-point models.


  Thanks to the emerging of foundation models, the large language and vision
models are integrated to acquire the multimodal ability of visual captioning,
question answering, etc. Although existing multimodal models present impressive
performance of visual understanding and reasoning, their limits are still
largely under-explored due to the scarcity of high-quality instruction tuning
data. To push the limits of multimodal capability, we Scale up Visual
Instruction Tuning (SVIT) by constructing a dataset of 4.2 million visual
instruction tuning data including 1.6M conversation question-answer (QA) pairs,
1.6M complex reasoning QA pairs, 1.0M referring QA pairs and 106K detailed
image descriptions. Besides the volume, the proposed dataset is also featured
by the high quality and rich diversity, which is generated by prompting GPT-4
with the abundant manual annotations of images. We also propose a new data
recipe to select subset with better diversity and balance, which evokes model's
superior capabilities. Extensive experiments verify that SVIT-v1.5, trained on
the proposed dataset, outperforms state-of-the-art Multimodal Large Language
Models on popular benchmarks. The data and code are publicly available at
https://github.com/BAAI-DCAI/Visual-Instruction-Tuning.


  Partially ordered models of time occur naturally in applications where agents
or processes cannot perfectly communicate with each other, and can be traced
back to the seminal work of Lamport. In this paper we consider the problem of
deciding if a (likely incomplete) description of a system of events is
consistent, the network consistency problem for the point algebra of partially
ordered time (POT). While the classical complexity of this problem has been
fully settled, comparably little is known of the fine-grained complexity of POT
except that it can be solved in $O^*((0.368n)^n)$ time by enumerating ordered
partitions. We construct a much faster algorithm with a run-time bounded by
$O^*((0.26n)^n)$. This is achieved by a sophisticated enumeration of structures
similar to total orders, which are then greedily expanded toward a solution.
While similar ideas have been explored earlier for related problems it turns
out that the analysis for POT is non-trivial and requires significant new
ideas.


  We develop neural network models to predict the black hole mass using 22
reverberating AGN samples in the XMM-Newton archive. The model features include
the fractional excess variance ($F_{\rm var}$) in 2-10 keV band, Fe-K lag
amplitude, 2-10 keV photon counts and redshift. We find that the prediction
accuracy of the neural network model is significantly higher than what is
obtained from the traditional linear regression method. Our predicted mass can
be confined within $\pm (2$-5) per cent of the true value, suggesting that the
neural network technique is a promising and independent way to constrain the
black hole mass. We also apply the model to 21 non-reverberating AGN to rule
out their possibility to exhibit the lags (some have too small mass and $F_{\rm
var}$, while some have too large mass and $F_{\rm var}$ that contradict the
$F_{\rm var}$-lag-mass relation in reverberating AGN). We also simulate 3200
reverberating AGN samples using the multi-feature parameter space from the
neural network model to investigate the global relations if the number of
reverberating AGN increases. We find that the $F_{\rm var}$-mass
anti-correlation is likely stronger with increasing number of newly-discovered
reverberating AGN. Contrarily, to maintain the lag-mass scaling relation, the
tight anti-correlation between the lag and $F_{\rm var}$ must preserve. In an
extreme case, the lag-mass correlation coefficient can significantly decrease
and, if observed, may suggest the extended corona framework where their
observed lags are more driven by the coronal property rather than geometry.


  In neuroimaging, generally, brain CT is more cost-effective and accessible
imaging option compared to MRI. Nevertheless, CT exhibits inferior soft-tissue
contrast and higher noise levels, yielding less precise structural clarity. In
response, leveraging more readily available CT to construct its counterpart
MRI, namely, medical image-to-image translation (I2I), serves as a promising
solution. Particularly, while diffusion models (DMs) have recently risen as a
powerhouse, they also come with a few practical caveats for medical I2I. First,
DMs' inherent stochasticity from random noise sampling cannot guarantee
consistent MRI generation that faithfully reflects its CT. Second, for 3D
volumetric images which are prevalent in medical imaging, naively using 2D DMs
leads to slice inconsistency, e.g., abnormal structural and brightness changes.
While 3D DMs do exist, significant training costs and data dependency bring
hesitation. As a solution, we propose novel style key conditioning (SKC) and
inter-slice trajectory alignment (ISTA) sampling for the 2D Brownian bridge
diffusion model. Specifically, SKC ensures a consistent imaging style (e.g.,
contrast) across slices, and ISTA interconnects the independent sampling of
each slice, deterministically achieving style and shape consistent 3D CT-to-MRI
translation. To the best of our knowledge, this study is the first to achieve
high-quality 3D medical I2I based only on a 2D DM with no extra architectural
models. Our experimental results show superior 3D medical I2I than existing 2D
and 3D baselines, using in-house CT-MRI dataset and BraTS2023 FLAIR-T1 MRI
dataset.


  We use few-body methods to investigate the diffraction of weakly bound
systems by a transmission grating. For helium dimers, He$_2$, we obtain
explicit expressions for the transition amplitude in the elastic channel.


  Video-text retrieval plays an essential role in multi-modal research and has
been widely used in many real-world web applications. The CLIP (Contrastive
Language-Image Pre-training), an image-language pre-training model, has
demonstrated the power of visual concepts learning from web collected
image-text datasets. In this paper, we propose a CLIP4Clip model to transfer
the knowledge of the CLIP model to video-language retrieval in an end-to-end
manner. Several questions are investigated via empirical studies: 1) Whether
image feature is enough for video-text retrieval? 2) How a post-pretraining on
a large-scale video-text dataset based on the CLIP affect the performance? 3)
What is the practical mechanism to model temporal dependency between video
frames? And 4) The Hyper-parameters sensitivity of the model on video-text
retrieval task. Extensive experimental results present that the CLIP4Clip model
transferred from the CLIP can achieve SOTA results on various video-text
retrieval datasets, including MSR-VTT, MSVC, LSMDC, ActivityNet, and DiDeMo. We
release our code at https://github.com/ArrowLuo/CLIP4Clip.


  We study the pole-skipping phenomenon of the scalar retarded Green's function
in the rotating BTZ black hole background. In the static case, the
pole-skipping points are typically located at negative imaginary Matsubara
frequencies $\omega=-(2\pi T)ni$ with appropriate values of complex wave number
$q$. But, in a $(1+1)$-dimensional CFT, one can introduce temperatures for
left-moving and right-moving sectors independently. As a result, the
pole-skipping points $\omega$ depend both on left and right temperatures in the
rotating background. In the extreme limit, the pole-skipping does not occur in
general. But in a special case, the pole-skipping does occur even in the
extreme limit, and the pole-skipping points are given by right Matsubara
frequencies.


  A Fragile CPR Game is an instance of a resource sharing game where a
common-pool resource, which is prone to failure due to overuse, is shared among
several players. Each player has a fixed initial endowment and is faced with
the task of investing in the common-pool resource without forcing it to fail.
The return from the common-pool resource is subject to uncertainty and is
perceived by the players in a prospect-theoretic manner. It is shown in
[A.~R.~Hota, S.~Garg, S.~Sundaram, \textit{Fragility of the commons under
prospect-theoretic risk attitudes}, Games and Economic Behavior \textbf{98}
(2016) 135--164.] that, under some mild assumptions, a Fragile CPR Game admits
a unique Nash equilibrium. In this article we investigate an extended version
of a Fragile CPR Game, in which players are allowed to share multiple
common-pool resources that are also prone to failure due to overuse. We refer
to this game as a Fragile multi-CPR Game. Our main result states that, under
some mild assumptions, a Fragile multi-CPR Game admits a Generalized Nash
equilibrium. Moreover, we show that, when there are more players than
common-pool resources, the set consisting of all Generalized Nash equilibria of
a Fragile multi-CPR Game is of Lebesgue measure zero.


  Chirality is a ubiquitous concept in modern science, from particle physics to
biology. In quantum physics, chirality of fermions is linked to topology of
gauge fields by the chiral anomaly. While the chiral anomaly is usually
associated with the short-distance behavior in field theory, in recent years it
has been realized that it also affects the macroscopic behavior of systems with
chiral fermions. In particular, the local imbalance between left- and
right-handed fermions in the presence of a magnetic field induces
non-dissipative transport of electric charge ("the Chiral Magnetic Effect",
CME). In heavy ion collisions, there is an ongoing search for this effect at
Relativistic Heavy Ion Collider, with results from a dedicated isobar run
presented very recently. An observation of CME in heavy ion collisions could
shed light on the mechanism of baryon asymmetry generation in the Early
Universe. Recently, the CME has been discovered in Dirac and Weyl semimetals
possessing chiral quasi-particles. This observation opens a path towards
quantum sensors, and potentially a new kind of quantum computers.


  Within a self-consistent thermal model using an isospin and momentum
dependent interaction (MDI) constrained by the isospin diffusion data in
heavy-ion collisions, we investigate the temperature dependence of the symmetry
energy $E_{sym}(\rho, T)$ and symmetry free energy $F_{sym}(\rho, T) $ for hot,
isospin asymmetric nuclear matter. It is shown that the symmetry energy
$E_{sym}(\rho, T)$ generally decreases with increasing temperature while the
symmetry free energy $F_{sym}(\rho, T)$ exhibits opposite temperature
dependence. The decrement of the symmetry energy with temperature is
essentially due to the decrement of the potential energy part of the symmetry
energy with temperature. The difference between the symmetry energy and
symmetry free energy is found to be quite small around the saturation density
of nuclear matter. While at very low densities, they differ significantly from
each other. In comparison with the experimental data of temperature dependent
symmetry energy extracted from the isotopic scaling analysis of intermediate
mass fragments (IMF's) in heavy-ion collisions, the resulting density and
temperature dependent symmetry energy $E_{sym}(\rho, T) $ is then used to
estimate the average freeze-out density of the IMF's.used to estimate the
average freeze-out density of the IMF's.


  Cosmic rays have extremely high particle energies (up to $10^{20} \;
\text{eV}$) and can be used to search for violations of Lorentz invariance. We
consider isotropic nonbirefringent Lorentz violation in the photon sector for
the case of a photon velocity larger than the maximum attainable velocity of
the standard fermions. Up to now, Earth-based bounds on this type of Lorentz
violation have been determined from observations of TeV gamma rays. Here, we
elaborate on a novel approach to test Lorentz invariance with greatly improved
sensitivity. This approach is based on investigating extensive air showers
which are induced by cosmic-ray particles in the Earth's atmosphere. We study
the impact of two Lorentz-violating decay processes on the longitudinal
development of air showers, notably the atmospheric depth of the shower maximum
$X_\text{max}$. Specifically, the two Lorentz-violating decay processes
considered are photon decay into an electron-positron pair and modified
neutral-pion decay into two photons. We use Monte Carlo simulations performed
with the CONEX code which was extended to include these two Lorentz-violating
decay processes at a magnitude allowed by the best previous Earth-based bound.
Compared to standard physics, these Lorentz-violating decay processes reduce
the average $X_\text{max}$ for showers with primary energies above
$10^{18}\;\text{eV}$ by an amount that is significantly larger than the average
resolution of current air shower experiments. Comparing the simulations of the
average $X_\text{max}$ to observations, new Earth-based bounds on this type of
Lorentz violation are obtained, which are better than the previous bounds by
more than three orders of magnitude. Prospects of further studies are also
discussed.


  The light-cone superspace version of the d=3, N=8 superconformal theory of
Bagger, Lambert and Gustavsson (BLG) is obtained as a solution to constraints
imposed by OSp(2,2|8) superalgebra. The Hamiltonian of the theory is shown to
be a quadratic form of the dynamical supersymmetry transformation.


  We present subarcsecond resolution mid-infrared (mid-IR) photometry in the
wavelength range from 8 to 20 micron of eighteen Seyfert galaxies, reporting
high spatial resolution nuclear fluxes for the entire sample. We construct
spectral energy distributions (SEDs) that the AGN dominates adding near-IR
measurements from the literature at similar angular resolution. The IR SEDs of
intermediate-type Seyferts are flatter and present higher 10 to 18 micron
ratios than those of Seyfert 2. We fit the individual SEDs with clumpy torus
models using the in-house-developed BayesClumpy tool. The models reproduce the
high spatial resolution measurements. Regardless of the Seyfert type, even with
high spatial resolution data, near- to mid-IR SED fitting poorly constrains the
radial extent of the torus. For the Seyfert 2, we find that edge-on geometries
are more probable than face-on views, with a number of clouds along equatorial
rays of N = 5-15. The 10 micron silicate feature is generally modeled in
shallow absorption. For the intermediate-type Seyferts, N and the inclination
angle of the torus are lower than those of the Seyfert 2 nuclei, with the
silicate feature appearing in weak emission or absent. The columns of material
responsible for the X-ray absorption are larger than those inferred from the
model fits for most of the galaxies, which is consistent with X-ray absorbing
gas being located within the dust sublimation radius whereas the mid-IR flux
arises from an area farther from the accretion disc. The fits yield both the
bolometric luminosity of the intrinsic AGN and the torus integrated luminosity,
from which we derive the reprocessing efficiency of the torus. In the models,
the outer radial extent of the torus scales with the AGN luminosity, and we
find the tori to be confined to scales less than 5 pc.


  This paper proposes an approach to Dense Video Captioning (DVC) without
pairwise event-sentence annotation. First, we adopt the knowledge distilled
from relevant and well solved tasks to generate high-quality event proposals.
Then we incorporate contrastive loss and cycle-consistency loss typically
applied to cross-modal retrieval tasks to build semantic matching between the
proposals and sentences, which are eventually used to train the caption
generation module. In addition, the parameters of matching module are
initialized via pre-training based on annotated images to improve the matching
performance. Extensive experiments on ActivityNet-Caption dataset reveal the
significance of distillation-based event proposal generation and cross-modal
retrieval-based semantic matching to weakly supervised DVC, and demonstrate the
superiority of our method to existing state-of-the-art methods.


  In this work we study the optimality of increasing stability of the inverse
boundary value problem (IBVP) for Schr\"{o}dinger equation. The rigorous
justification of increasing stability for the IBVP for Schr\"{o}dinger equation
were established by Isakov \cite{Isa11} and by Isakov, Nagayasu, Uhlmann, Wang
of the paper \cite{INUW14}. In \cite{Isa11}, \cite{INUW14}, the authors showed
that the stability of this IBVP increases as the frequency increases in the
sense that the stability estimate changes from a logarithmic type to a
H\"{o}lder type. In this work, we prove that the instability changes from an
exponential type to a H\"older type when the frequency increases. This result
verifies that results in \cite{Isa11}, \cite{INUW14} are optimal.


  In this paper we give a method for calculating the rank of a general elliptic
curve over the field of rational functions in two variables. We reduce this
problem to calculating the cohomology of a singular hypersurface in a weighted
projective 4-space. We then give a method for calculating the cohomology of a
certain class of singular hypersurfaces, extending work of Dimca for the
isolated singularity case.


  In the last years, algebraic tools have been proven useful in phylogenetic
reconstruction and model selection through the study of phylogenetic
invariants. However, up to now, the models studied from an algebraic viewpoint
are either too general or too restrictive (as group-based models with a uniform
stationary distribution) to be used in practice.
  In this paper we provide a new framework to study time-reversible models,
which are the most widely used by biologists. In our approach we consider
algebraic time-reversible models on phylogenetic trees (as defined by Allman
and Rhodes) and introduce a new inner product to make all transition matrices
of the process diagonalizable through the same orthogonal eigenbasis. This
framework generalizes the Fourier transform widely used to work with
group-based models and recovers some of the well known results. As
illustration, we combine our technique with algebraic geometry tools to provide
relevant phylogenetic invariants for trees evolving under the Tamura-Nei model
of nucleotide substitution.


  We study the connection between periodic finite-difference Intermediate Long
Wave hydrodynamical systems and integrable many-body models of Calogero and
Ruijsenaars-type. The former describe quantum cohomology and quantum K-theory
of the ADHM moduli space of Abelian instantons, while the latter arise in the
the instanton counting in four and five dimensional supersymmetric gauge
theories with eight supercharges in the presence of defects. Using string
theory dualities we provide correspondences between hydrodynamical and
many-body integrable systems. In particular, we match the energy spectra on
both sides.


  Effective analysis of unusual domain specific video collections represents an
important practical problem, where state-of-the-art general purpose models
still face limitations. Hence, it is desirable to design benchmark datasets
that challenge novel powerful models for specific domains with additional
constraints. It is important to remember that domain specific data may be
noisier (e.g., endoscopic or underwater videos) and often require more
experienced users for effective search. In this paper, we focus on single-shot
videos taken from moving cameras in underwater environments, which constitute a
nontrivial challenge for research purposes. The first shard of a new Marine
Video Kit dataset is presented to serve for video retrieval and other computer
vision challenges. Our dataset is used in a special session during Video
Browser Showdown 2023. In addition to basic meta-data statistics, we present
several insights based on low-level features as well as semantic annotations of
selected keyframes. The analysis also contains experiments showing limitations
of respected general purpose models for retrieval. Our dataset and code are
publicly available at https://hkust-vgd.github.io/marinevideokit.


  We propose a general method for optimization with semi-infinite constraints
that involve a linear combination of functions, focusing on the case of the
exponential function. Each function is lower and upper bounded on sub-intervals
by low-degree polynomials. Thus, the constraints can be approximated with
polynomial inequalities that can be implemented with linear matrix
inequalities. Convexity is preserved, but the problem has now a finite number
of constraints. We show how to take advantage of the properties of the
exponential function in order to build quickly accurate approximations. The
problem used for illustration is the least-squares fitting of a positive sum of
exponentials to an empirical density. When the exponents are given, the problem
is convex, but we also give a procedure for optimizing the exponents. Several
examples show that the method is flexible, accurate and gives better results
than other methods for the investigated problems.


  This paper presents a comparison of various deep learning models such as
Exception, Resnet-50, and Inception V3 for the classification and prediction of
hand hygiene gestures, which were recorded in accordance with the World Health
Organization (WHO) guidelines. The dataset consists of six hand hygiene
movements in a video format, gathered for 30 participants. The network consists
of pre-trained models with image net weights and a modified head of the model.
An accuracy of 37% (Xception model), 33% (Inception V3), and 72% (ResNet-50) is
achieved in the classification report after the training of the models for 25
epochs. ResNet-50 model clearly outperforms with correct class predictions. The
major speed limitation can be overcome with the use of fast processing GPU for
future work. A complete hand hygiene dataset along with other generic gestures
such as one-hand movements (linear hand motion; circular hand rotation) will be
tested with ResNet-50 architecture and the variants for health care workers.


  Given any diagonal cyclic subgroup $\Lambda \subset GL(n+1,k)$ of order $d$,
let $I_d\subset k[x_0,\ldots, x_n]$ be the ideal generated by all monomials
$\{m_{1},\ldots, m_{r}\}$ of degree $d$ which are invariants of $\Lambda$.
$I_d$ is a monomial Togliatti system, provided $r \leq \binom{d+n-1}{n-1}$, and
in this case the projective toric variety $X_d$ parameterized by
$(m_{1},\ldots, m_{r})$ is called a $GT$-variety with group $\Lambda$. We prove
that all these $GT$-varieties are arithmetically Cohen-Macaulay and we give a
combinatorial expression of their Hilbert functions. In the case $n=2$, we
compute explicitly the Hilbert function, polynomial and series of $X_d$. We
determine a minimal free resolution of its homogeneous ideal and we show that
it is a binomial prime ideal generated by quadrics and cubics. We also provide
the exact number of both types of generators. Finally, we pose the problem of
determining whether a surface parameterized by a Togliatti system is aCM. We
construct examples that are aCM and examples that are not.


  The shear viscosity is calculated by means of the perturbative kinetic
partonic cascade BAMPS with CGC initial conditons for various saturation
momentum scale Q_s. eta/s ~ 0.15 stays approximately constant when going from
RHIC to LHC.


  Numerous methods can build predictive models from software data. However,
what methods and conclusions should we endorse as we move from analytics
in-the-small (dealing with a handful of projects) to analytics in-the-large
(dealing with hundreds of projects)?
  To answer this question, we recheck prior small-scale results (about process
versus product metrics for defect prediction and the granularity of metrics)
using 722,471 commits from 700 Github projects. We find that some analytics
in-the-small conclusions still hold when scaling up to analytics in-the-large.
For example, like prior work, we see that process metrics are better predictors
for defects than product metrics (best process/product-based learners
respectively achieve recalls of 98\%/44\% and AUCs of 95\%/54\%, median
values).
  That said, we warn that it is unwise to trust metric importance results from
analytics in-the-small studies since those change dramatically when moving to
analytics in-the-large. Also, when reasoning in-the-large about hundreds of
projects, it is better to use predictions from multiple models (since single
model predictions can become confused and exhibit a high variance).


  Although traffic is one of the massively collected data, it is often only
available for specific regions. One concern is that, although there are studies
that give good results for these data, the data from these regions may not be
sufficiently representative to describe all the traffic patterns in the rest of
the world. In quest of addressing this concern, we propose a speed prediction
method that is independent of large historical speed data. To predict a
vehicle's speed, we use the trajectory road topographical features to fit a
Shared Weight Multilayer Perceptron learning model. Our results show
significant improvement, both qualitative and quantitative, over standard
regression analysis. Moreover, the proposed framework sheds new light on the
way to design new approaches for traffic analysis.


  Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for
calculating various properties of solids as, for instance, the total energy,
the electron density, or the electronic band structure. The KS-DFT method leads
to rather fast calculations, however the accuracy depends crucially on the
chosen approximation for the exchange and correlation (xc) functional
$E_{\text{xc}}$ and/or potential $v_{\text{xc}}$. Here, an overview of xc
methods to calculate the electronic band structure is given, with the focus on
the so-called semilocal methods that are the fastest in KS-DFT and allow to
treat systems containing up to thousands of atoms. Among them, there is the
modified Becke-Johnson potential that is widely used to calculate the
fundamental band gap of semiconductors and insulators. The accuracy for other
properties like the magnetic moment or the electron density, that are also
determined directly by $v_{\text{xc}}$, is also discussed.


  Just a brief comment on the chemical formulae of the rare earth iron arsenide
oxide superconductors


  We show that it is not possible in the absence of dark matter to construct a
four-dimensional metric that explains galactic observations. In particular, by
working with an effective potential it is shown that a metric which is
constructed to fit flat rotation curves in spiral galaxies leads to the wrong
sign for the bending of light i.e. repulsion instead of attraction. Hence,
without dark matter the motion of particles on galactic scales cannot be
explained in terms of geodesic motion on a four- dimensional metric. This
reveals a new bright side to dark matter: it is indispensable if we wish to
retain the cherished equivalence principle.


  If new physics is called upon to explain away fine tunings, like the
hierarchy problem, then, we argue, the principle of Minimal Flavor Violation is
inescapable. We review the principle and recent extensions to the lepton sector
and to Grand-Unified theories.


  We examine the competition among one- and two-photon processes in an
ultra-cold, three-level atom undergoing cascade transitions as a result of its
interaction with a bimodal cavity. We show parameter domains where two-photon
transitions are dominant and also study the effect of two-photon emission on
the mazer action in the cavity. The two-photon emission leads to the loss of
detailed balance and therefore we obtain the photon statistics of the cavity
field by the numerical integration of the master equation. The photon
distribution in each cavity mode exhibits sub- and super- Poissonian behaviors
depending on the strength of atom-field coupling. The photon distribution
becomes identical to a Poisson distribution when the atom-field coupling
strengths of the modes are equal.


  A dipole sequence has been observed and investigated in the 143 Sm nucleus
populated through the heavy-ion induced fusion-evaporation reaction and studied
using the Indian National Gamma Array (INGA) as the detection system. The
sequence has been established as a Magnetic Rotation (MR) band primarily from
lifetime measurements of the band members using the Doppler Shift Attenuation
Method (DSAM). A configuration based on nine quasiparticles, with highly
asymmetric angular momentum blades, has been assigned to the shears band in the
light of the theoretical calculations within the framework of Shears mechanism
with the Principal Axis Cranking (SPAC) model. This is hitherto the maximum
number of quasiparticles along with the highest asymmetricity associated with a
MR band. Further, as it has followed from the SPAC calculations, the
contribution of the core rotation to the angular momentum of this shears band
is substantial and greater than in any other similar sequence, at least in the
neighbouring nuclei. This band can thus be perceived as a unique phenomenon of
shears mechanism in operation at the limits of quasiparticle excitations, as
manifested in MR band-like phenomena, evolving into collectivity.


  In classical statistics, the bias-variance trade-off describes how varying a
model's complexity (e.g., number of fit parameters) affects its ability to make
accurate predictions. According to this trade-off, optimal performance is
achieved when a model is expressive enough to capture trends in the data, yet
not so complex that it overfits idiosyncratic features of the training data.
Recently, it has become clear that this classic understanding of the
bias-variance must be fundamentally revisited in light of the incredible
predictive performance of "overparameterized models" -- models that avoid
overfitting even when the number of fit parameters is large enough to perfectly
fit the training data. Here, we present results for one of the simplest
examples of an overparameterized model: regression with random linear features
(i.e. a two-layer neural network with a linear activation function). Using the
zero-temperature cavity method, we derive analytic expressions for the training
error, test error, bias, and variance. We show that the linear random features
model exhibits three phase transitions: two different transitions to an
interpolation regime where the training error is zero, along with an additional
transition between regimes with large bias and minimal bias. Using random
matrix theory, we show how each transition arises due to small nonzero
eigenvalues in the Hessian matrix. Finally, we compare and contrast the phase
diagram of the random linear features model to the random nonlinear features
model and ordinary regression, highlighting the new phase transitions that
result from the use of linear basis functions.


  Let $\mathbb K$ be a field of characteristic zero, $A$ an integral domain
over $\mathbb K$ with the field of fractions $R = \text{Frac}(A),$ and
$\text{Der}_{\mathbb{K}}A$ the Lie algebra of all $\mathbb K$-derivations on
$A$.
  Let $W(A):=R\text{Der}_{\mathbb{K}} A$ and $L$ a nilpotent subalgebra of rank
$n$ over $R$ of the Lie algebra $W(A).$ We prove that if the center $Z=Z(L)$ is
of rank $\geq n-2$ over $R$ and $F=F(L)$ is the field of constants for $L$ in
$R,$ then the Lie algebra $FL$ is contained in a locally nilpotent subalgebra
of $ W(A)$ of rank $n$ over $R$ with a natural basis over the field $R.$ It is
also also proved that the Lie algebra $FL$ can be isomorphically embedded (as
an abstract Lie algebra) into the triangular Lie algebra $u_n(F)$ which was
studied early by other authors.


  We give examples of anomalous two-fold coverings $p:E\to B$ of connected
spaces: a. one where $B$ is simply connected, b. the other of path-connected
spaces that has an Evil Twin; a non equivalent covering $q:E\to B$ with the
same image of the fundamental group.


  This paper presents a new approach to determine the number of solutions of
three variable Frobenius related problems and to find their solutions by using
order reducing methods. Here, the order of a Frobenius related problem means
the number of variables appearing in the problem. We present two types of order
reduction methods that can be applied to the problem of finding all nonnegative
solutions of three variable Frobenius related problems. The first method is
used to reduce the equation of order three from a three variable Frobenius
related problem to be a system of equations with two fixed variables. The
second method reduces the equation of order three into three equations of order
two, for which an algorithm is designed with an interesting open problem on
solutions left as a conjecture.


  A quantum copying machine producing two (in general non-identical) copies of
an arbitrary input state of a two-dimensional Hilbert space (qubit) is studied
using a quality measure based on distinguishability of states, rather than
fidelity. The problem of producing optimal copies is investigated with the help
of a Bloch sphere representation, and shown to have a well-defined solution,
including cases in which the two copies have unequal quality, or the quality
depends upon the input state (is ``anisotropic'' in Bloch sphere language), or
both. A simple quantum circuit yields the optimal copying machine. With a
suitable choice of parameters it becomes an optimal eavesdropping machine for
some versions of quantum cryptography, or reproduces the Buzek and Hillery
result for isotropic copies.


  For a simple Lie algebra L of type A, D, E we show that any Belavin-Drinfeld
triple on the Dynkin diagram of L produces a collection of Drinfeld twists for
Lusztig's small quantum group u_q(L). These twists give rise to new
finite-dimensional factorizable Hopf algebras, i.e. new small quantum groups.
For any Hopf algebra constructed in this manner, we identify the group of
grouplike elements, identify the Drinfeld element, and describe the irreducible
representations of the dual in terms of the representation theory of the
parabolic subalgebra(s) in L associated to the given Belavin-Drinfeld triple.
We also produce Drinfeld twists of u_q(L) which express a known algebraic group
action on its category of representations, and pose a subsequent question
regarding the classification of all twists.


  The dynamical formation channels of gravitational wave (GW) sources typically
involve a stage when the compact object binary source interacts with the
environment, which may excite its eccentricity, yielding efficient GW emission.
For the wide eccentric compact object binaries, the GW emission happens mostly
near the pericenter passage, creating a unique, burst-like signature in the
waveform. This work examines the possibility of stellar-mass bursting sources
in the millihertz band for future LISA detections. Because of their long
lifetime ($\sim 10^{7}\rm\, yr$) and promising detectability, the number of
millihertz bursting sources can be large in the local universe. For example,
based on our estimates, there will be $\sim 3 - 45$ bursting binary black holes
in the Milky Way, with $\sim 10^{2} - 10^{4}$ bursts detected during the LISA
mission. Moreover, we find that the number of bursting sources strongly depends
on their formation history. If certain regions undergo active formation of
compact object binaries in the recent few million years, there will be a
significantly higher bursting source fraction. Thus, the detection of
millihertz GW bursts not only serves as a clue for distinguishing different
formation channels, but also helps us understand the star formation history in
different regions of the Milky Way.


  We study deep neural networks with polynomial activations, particularly their
expressive power. For a fixed architecture and activation degree, a polynomial
neural network defines an algebraic map from weights to polynomials. The image
of this map is the functional space associated to the network, and it is an
irreducible algebraic variety upon taking closure. This paper proposes the
dimension of this variety as a precise measure of the expressive power of
polynomial neural networks. We obtain several theoretical results regarding
this dimension as a function of architecture, including an exact formula for
high activation degrees, as well as upper and lower bounds on layer widths in
order for deep polynomials networks to fill the ambient functional space. We
also present computational evidence that it is profitable in terms of
expressiveness for layer widths to increase monotonically and then decrease
monotonically. Finally, we link our study to favorable optimization properties
when training weights, and we draw intriguing connections with tensor and
polynomial decompositions.


  In this paper, we introduce a novel framework for the challenging problem of
One-Shot Unsupervised Domain Adaptation (OSUDA), which aims to adapt to a
target domain with only a single unlabeled target sample. Unlike existing
approaches that rely on large labeled source and unlabeled target data, our
Target-driven One-Shot UDA (TOS-UDA) approach employs a learnable augmentation
strategy guided by the target sample's style to align the source distribution
with the target distribution. Our method consists of three modules: an
augmentation module, a style alignment module, and a classifier. Unlike
existing methods, our augmentation module allows for strong transformations of
the source samples, and the style of the single target sample available is
exploited to guide the augmentation by ensuring perceptual similarity.
Furthermore, our approach integrates augmentation with style alignment,
eliminating the need for separate pre-training on additional datasets. Our
method outperforms or performs comparably to existing OS-UDA methods on the
Digits and DomainNet benchmarks.


  The nonlinear response associated with the current dependence of the
superconducting kinetic inductance was studied in capacitively shunted NbTiN
microstrip transmission lines. It was found that the inductance per unit length
of one microstrip line could be changed by up to 20% by applying a DC current,
corresponding to a single pass time delay of 0.7 ns. To investigate nonlinear
dissipation, Bragg reflectors were placed on either end of a section of this
type of transmission line, creating resonances over a range of frequencies.
From the change in the resonance linewidth and amplitude with DC current, the
ratio of the reactive to the dissipative response of the line was found to be
788. The low dissipation makes these transmission lines suitable for a number
of applications that are microwave and millimeter-wave band analogues of
nonlinear optical processes. As an example, by applying a millimeter-wave pump
tone, very wide band parametric amplification was observed between about 3 and
34 GHz. Use as a current variable delay line for an on-chip millimeter-wave
Fourier transform spectrometer is also considered.


  Transform learning is being extensively applied in several applications
because of its ability to adapt to a class of signals of interest. Often, a
transform is learned using a large amount of training data, while only limited
data may be available in many applications. Motivated with this, we propose
wavelet transform learning in the lifting framework for a given signal.
Significant contributions of this work are: 1) the existing theory of lifting
framework of the dyadic wavelet is extended to more generic rational wavelet
design, where dyadic is a special case and 2) the proposed work allows to learn
rational wavelet transform from a given signal and does not require large
training data. Since it is a signal-matched design, the proposed methodology is
called Signal-Matched Rational Wavelet Transform Learning in the Lifting
Framework (M-RWTL). The proposed M-RWTL method inherits all the advantages of
lifting, i.e., the learned rational wavelet transform is always invertible,
method is modular, and the corresponding M-RWTL system can also incorporate
nonlinear filters, if required. This may enhance the use of RWT in applications
which is so far restricted. M-RWTL is observed to perform better compared to
standard wavelet transforms in the applications of compressed sensing based
signal reconstruction.


  This paper studies the subgeometric convergence of the stationary
distribution in taking the infinite-level limit of a finite-level M/G/1-type
Markov chain, that is, in letting the upper boundary level go to infinity. This
study is performed through the fundamental deviation matrix, which is a
block-decomposition-friendly solution for the Poisson equation of the deviation
matrix. The fundamental deviation matrix yields a difference formula for the
respective stationary distributions of the finite-level chain and the
corresponding infinite-level chain. The difference formula plays a crucial role
in deriving the main result of this paper: a subgeometric convergence formula
for the infinite-level limit of the stationary distribution of the finite-level
chain.


  An accurate modelling of baryonic feedback effects is required to exploit the
full potential of future weak-lensing surveys such as Euclid or LSST. In this
second paper in a series of two, we combine Euclid-like mock data of the cosmic
shear power spectrum with an eROSITA X-ray mock of the cluster gas fraction to
run a combined likelihood analysis including both cosmological and baryonic
parameters. Following the first paper of this series, the baryonic effects
(based on the baryonic correction model of Schneider et al. 2019) are included
in both the tomographic power spectrum and the covariance matrix. However, this
time we assume the more realistic case of a $\Lambda$CDM cosmology with massive
neutrinos, and we consider several extensions of the currently favoured
cosmological model. For the standard $\Lambda$CDM case, we show that including
X-ray data reduces the uncertainties on the sum of the neutrino mass by
$\sim30$ percent, while there is only a mild improvement on other parameters
such as $\Omega_m$ and $\sigma_8$. As extensions of $\Lambda$CDM, we consider
the cases of a dynamical dark energy model (wCDM), a $f(R)$ gravity model
(fRCDM), and a mixed dark matter model ($\Lambda$MDM) with both a cold and a
warm/hot dark matter component. We find that combining weak lensing with X-ray
data only leads to a mild improvement of the constraints on the additional
parameters of wCDM, while the improvement is more substantial for both fRCDM
and $\Lambda$MDM. Ignoring baryonic effects in the analysis pipeline leads to
significant false-detections of either phantom dark energy or a light
subdominant dark matter component. Overall we conclude that for all cosmologies
considered, a general parametrisation of baryonic effects is both necessary and
sufficient to obtain tight constraints on cosmological parameters.


  This note aims at understanding the maximum allowable temperature at the hot
spot during a quench in Nb3Sn accelerator magnets, through the analysis of
experimental results previously presented.


  We present new high-resolution observations of Sagittarius A* at wavelengths
of 17.4 to 23.8 cm with the Very Large Array in A configuration with the Pie
Town Very Long Baseline Array antenna. We use the measured sizes to calibrate
the interstellar scattering law and find that the major axis size of the
scattering law is smaller by ~6% than previous estimates. Using the new
scattering law, we are able to determine the intrinsic size of Sgr A* at
wavelengths from 0.35 cm to 6 cm using existing results from the VLBA. The new
law increases the intrinsic size at 0.7 cm by ~20% and <5% at 0.35 cm. The
intrinsic size is 13^{+7}_{-3} Schwarzschild radii at 0.35 cm and is
proportional to lambda^gamma, where gamma is in the range 1.3 to 1.7.


  We propose a procedure to estimate the fatigue loads on wind turbines, based
in a recent framework used for reconstructing data series of stochastic
properties measured at wind turbines. Through a standard fatigue analysis, we
show that it is possible to accurately estimate fatigue loads in any wind
turbine within one wind park, using only the load measurements at one single
turbine and the set of wind speed measurements. Our framework consists of
deriving a stochastic differential equation that describes the evolution of the
torque at one wind turbine driven by the wind speed. The stochastic equation is
derived directly from the measurements and is afterwards used for predicting
the fatigue loads at neighboring turbines. Such a framework could be used to
mitigate the financial efforts usually necessary for placing measurement
devices in all wind turbines within one wind farm. Finally, we also discuss the
limitations and possible improvements of the proposed procedure.


  We study the problem of robust domain adaptation in the context of
unavailable target labels and source data. The considered robustness is against
adversarial perturbations. This paper aims at answering the question of finding
the right strategy to make the target model robust and accurate in the setting
of unsupervised domain adaptation without source data. The major findings of
this paper are: (i) robust source models can be transferred robustly to the
target; (ii) robust domain adaptation can greatly benefit from non-robust
pseudo-labels and the pair-wise contrastive loss. The proposed method of using
non-robust pseudo-labels performs surprisingly well on both clean and
adversarial samples, for the task of image classification. We show a consistent
performance improvement of over $10\%$ in accuracy against the tested baselines
on four benchmark datasets.


  La(Fe,Si)$_{13}$-based compounds are considered to be very promising
magnetocaloric materials for magnetic refrigeration applications. Many studies
have focused on this material family but only in bulk form. In this paper, we
report the fabrication of thick films of La(Fe,Si)$_{13}$, both with and
without post-hydriding. These films exhibit magnetic and structural properties
comparable to those of bulk materials. We also observe that the ferromagnetic
phase transition has a negative thermal hysteresis, a phenomenon not previously
found in this material but which may have its origins in the availability of a
strain energy reservoir, as in the cases of other materials in which negative
thermal hysteresis has been found. Here, it appears that the substrate acts to
store strain energy. Our exploratory study demonstrates the viability of thick
films of the La(Fe,Si)$_{13}$ phase and motivates further work in the area,
while showing that additional perspectives can be gained from reducing the
dimensionality of magnetocaloric materials in which the magneto-volume effect
is large.


  The performance of deep learning-based natural language processing systems is
based on large amounts of labeled training data which, in the clinical domain,
are not easily available or affordable. Weak supervision and in-context
learning offer partial solutions to this issue, particularly using large
language models (LLMs), but their performance still trails traditional
supervised methods with moderate amounts of gold-standard data. In particular,
inferencing with LLMs is computationally heavy. We propose an approach
leveraging fine-tuning LLMs and weak supervision with virtually no domain
knowledge that still achieves consistently dominant performance. Using a
prompt-based approach, the LLM is used to generate weakly-labeled data for
training a downstream BERT model. The weakly supervised model is then further
fine-tuned on small amounts of gold standard data. We evaluate this approach
using Llama2 on three different n2c2 datasets. With no more than 10 gold
standard notes, our final BERT models weakly supervised by fine-tuned
Llama2-13B consistently outperformed out-of-the-box PubMedBERT by 4.7% to 47.9%
in F1 scores. With only 50 gold standard notes, our models achieved close
performance to fully fine-tuned systems.


  We study a functional on the boundary of a compact Riemannian 3-manifold of
nonnegative scalar curvature. The functional arises as the second variation of
the Wang-Yau quasi-local energy in general relativity. We prove that the
functional is positive definite on large coordinate spheres, and more general
on nearly round surfaces including large constant mean curvature spheres in
asymptotically flat 3-manifolds with positive mass; it is also positive
definite on small geodesics spheres, whose centers do not have vanishing
curvature, in Riemannian 3-manifolds of nonnegative scalar curvature. We also
give examples of functions H, which can be made arbitrarily close to the
constant 2, on the standard sphere such that the boundary data consisting of
the standard spherical metric and H has positive Brown-York mass while the
associated functional is negative somewhere.


  Recent work has suggested that in highly correlated systems, such as
sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in
a ferromagnet close to a critical point, the probability distribution of a
global quantity (i.e. total energy dissipation, magnetization and so forth)
that has been normalized to the first two moments follows a specific non
Gaussian curve. This curve follows a form suggested by extremum statistics,
which is specified by a single parameter a (a=1 corresponds to the
Fisher-Tippett Type I ("Gumbel") distribution.) Here, we present a framework
for testing for extremal statistics in a global observable. In any given
system, we wish to obtain a in order to distinguish between the different
Fisher-Tippett asymptotes, and to compare with the above work. The
normalizations of the extremal curves are obtained as a function of a. We find
that for realistic ranges of data, the various extremal distributions when
normalized to the first two moments are difficult to distinguish. In addition,
the convergence to the limiting extremal distributions for finite datasets is
both slow and varies with the asymptote. However, when the third moment is
expressed as a function of a this is found to be a more sensitive method.


  In this work, we formulate two controllability maximization problems for
large-scale networked dynamical systems such as brain networks: The first
problem is a sparsity constraint optimization problem with a box constraint.
The second problem is a modified problem of the first problem, in which the
state transition matrix is Metzler. In other words, the second problem is a
realization problem for a positive system. We develop a projected gradient
method for solving the problems, and prove global convergence to a stationary
point with locally linear convergence rate. The projections onto the
constraints of the first and second problems are given explicitly. Numerical
experiments using the proposed method provide non-trivial results. In
particular, the controllability characteristic is observed to change with
increase in the parameter specifying sparsity, and the change rate appears to
be dependent on the network structure.


  We consider color superconductivity with two flavors of massless quarks which
form Cooper pairs with total spin zero. We solve the gap equation for the
color-superconducting gap parameter to subleading order in the QCD coupling
constant $g$ at zero temperature. At this order in $g$, there is also a
previously neglected contribution from the real part of the quark self-energy
to the gap equation. Including this contribution leads to a reduction of the
color-superconducting gap parameter $\f_0$ by a factor $b_0'=\exp \big[ -(\p
^2+4)/8 \big]\simeq 0.177$. On the other hand, the BCS relation $T_c\simeq
0.57\f_0$ between $\f_0$ and the transition temperature $T_c$ is shown to
remain valid after taking into account corrections from the quark self-energy.
The resulting value for $T_c$ confirms a result obtained previously with a
different method.


  We study the topology of the Megaparsec Cosmic Web in terms of the
scale-dependent Betti numbers, which formalize the topological information
content of the cosmic mass distribution. While the Betti numbers do not fully
quantify topology, they extend the information beyond conventional cosmological
studies of topology in terms of genus and Euler characteristic. The richer
information content of Betti numbers goes along the availability of fast
algorithms to compute them.
  For continuous density fields, we determine the scale-dependence of Betti
numbers by invoking the cosmologically familiar filtration of sublevel or
superlevel sets defined by density thresholds. For the discrete galaxy
distribution, however, the analysis is based on the alpha shapes of the
particles. These simplicial complexes constitute an ordered sequence of nested
subsets of the Delaunay tessellation, a filtration defined by the scale
parameter, $\alpha$. As they are homotopy equivalent to the sublevel sets of
the distance field, they are an excellent tool for assessing the topological
structure of a discrete point distribution. In order to develop an intuitive
understanding for the behavior of Betti numbers as a function of $\alpha$, and
their relation to the morphological patterns in the Cosmic Web, we first study
them within the context of simple heuristic Voronoi clustering models.
  Subsequently, we address the topology of structures emerging in the standard
LCDM scenario and in cosmological scenarios with alternative dark energy
content. The evolution and scale-dependence of the Betti numbers is shown to
reflect the hierarchical evolution of the Cosmic Web and yields a promising
measure of cosmological parameters. We also discuss the expected Betti numbers
as a function of the density threshold for superlevel sets of a Gaussian random
field.


  In the Leggett-Garg approach to testing macrorealism, the two-time
correlation functions, which are normally obtained by sequential measurements
of a dichotomic variable Q, need to be measured in a non-invasive way in order
to exclude certain types of alternative classical explanation. Here, it is
shown, for a class of macrorealistic theories, that the correlation functions
are readily expressed in terms of a time integral of the velocity corresponding
to Q and that this expression can be determined from a single final-time
measurement of an auxiliary system in continual weak interaction with the
primary system. The protocol has the form of a "waiting detector" which clicks
only when Q changes sign. It shares features with both ideal negative
measurements and weak measurements and we argue that it is essentially
non-invasive, under certain reasonable assumptions. We show that the
non-invasiveness persists to a quantum model of the process.


  We present a theoretical study of the emission from a superluminal
polarization current whose distribution pattern rotates (with an angular
frequency $\omega$) and oscillates (with a frequency $\Omega $) at the same
time, and which comprises both poloidal and toroidal components. This type of
polarization current is found in recent practical machines designed to
investigate superluminal emission. We find that the superluminal motion of the
distribution pattern of the emitting current generates localized
electromagnetic waves that do not decay spherically, i.e. that do not have an
intensity diminishing like ${R_P}^{-2}$ with the distance $R_P$ from their
source. The nonspherical decay of the focused wave packets that are emitted by
the polarization currents does not contravene conservation of energy: the
constructive interference of the constituent waves of such propagating caustics
takes place within different solid angles on spheres of different radii ($R_P$)
centred on the source. For a polarization current whose longitudinal
distribution (over an azimuthal interval of length $2\pi$) consists of $m$
cycles of a sinusoidal wave train, the nonspherically decaying part of the
emitted radiation contains the frequencies $\Omega \pm m\omega$; i.e. it
contains {\it only} the frequencies involved in the creation and implementation
of the source. This is in contrast to recent studies of the spherically
decaying emission, which was shown to contain much higher frequencies. The
polarization of the emitted radiation is found to be linear for most
configurations of the source.


  Graphene based THz modulators are promising due to the conical band structure
and high carrier mobility of graphene. Here, we tune the Fermi level of
graphene via electrical gating with the help of ionic liquid to control the THz
transmittance. It is found that, in the THz range, both the absorbance and
reflectance of the device increase proportionately to the available density of
states due to intraband transitions. Compact, stable, and repeatable THz
transmittance modulation up to 93% (or 99%) for a single (or stacked) device
has been demonstrated in a broad frequency range from 0.1 to 2.5 THz, with an
applied voltage of only 3 V at room temperature.


  The abstract link L_d of the complex isolated singularity x^2 + y^2 + z^2 +
v^{2d} = 0 is diffeomorphic to S^3 \times S^2. We classify the embedded links
of these singularities up to regular homotopies precomposed with
diffeomorphisms of S^3 \times S^2. Let us denote by i_d the inclusion of L_d in
S^7. We show that for arbitrary diffeomorphisms \varphi_d of S^3 \times S^2
with L_d the compositions i_d \circ \varphi_d are image regularly homotopic for
two values d_1 and d_2 if and only if d_1-d_2 is even.


  We give a new self-contained proof of Poincar\'e's Polyhedron Theorem on
presentations of discontinuous groups of isometries of a Riemann manifold of
constant curvature. The proof is not based on the theory of covering spaces,
but only makes use of basic geometric concepts. In a sense one hence obtains a
proof that is of a more constructive nature than most known proofs.


  Assuming suitable convergence properties for the Gromov-Witten potential of a
Calabi-Yau manifold $X$ one may construct a polarized variation of Hodge
structure over the complexified K\"ahler cone of $X$. In this paper we show
that, in the case of fourfolds, there is a correspondence between ``quantum
potentials'' and polarized variations of Hodge structures that degenerate to a
maximally unipotent boundary point. Under this correspondence, the WDVV
equations are seen to be equivalent to the Griffiths' trasversality property of
a variation of Hodge structure.


  Masked Modeling (MM) has demonstrated widespread success in various vision
challenges, by reconstructing masked visual patches. Yet, applying MM for
large-scale 3D scenes remains an open problem due to the data sparsity and
scene complexity. The conventional random masking paradigm used in 2D images
often causes a high risk of ambiguity when recovering the masked region of 3D
scenes. To this end, we propose a novel informative-preserved reconstruction,
which explores local statistics to discover and preserve the representative
structured points, effectively enhancing the pretext masking task for 3D scene
understanding. Integrated with a progressive reconstruction manner, our method
can concentrate on modeling regional geometry and enjoy less ambiguity for
masked reconstruction. Besides, such scenes with progressive masking ratios can
also serve to self-distill their intrinsic spatial consistency, requiring to
learn the consistent representations from unmasked areas. By elegantly
combining informative-preserved reconstruction on masked areas and consistency
self-distillation from unmasked areas, a unified framework called MM-3DScene is
yielded. We conduct comprehensive experiments on a host of downstream tasks.
The consistent improvement (e.g., +6.1<EMAIL_ADDRESS>on object detection and +2.2%
mIoU on semantic segmentation) demonstrates the superiority of our approach.


  We present an experimental demonstration of near-field optical trapping and
dynamic manipulation of a single extracellular vesicle using a plasmonic
dielectric nanoantenna that supports an optical anapole state. The optical
anapole is a non-radiating optical state generated by the destructive
interference between electric and toroidal dipoles in the far-field. To enhance
the trapping capabilities, we employ a plasmonic mirror to enhance the anapole
state. By harnessing the enhanced electromagnetic hotspot resulting from the
mirror-enhanced anapole state, we achieve a high trapping potential of
approximately 3.5 KbT. The dynamic manipulation of the vesicle is achieved by
inducing a thermoelectric field in the presence of an ionic surfactant and the
resulting plasmonic heating. Specifically, we introduce cetyltrimethylammonium
chloride (CTAC) as the ionic surfactant and utilize the local heating generated
by the plasmonic reflector to create a thermoelectric field. This enables
active transport, stable trapping, and dynamic manipulation of a single
extracellular vesicle. Moreover, the thermoelectric field contributes to an
increase in the overall trapping potential.


  Complex networks have been characterised by their specific connectivity
patterns (network motifs), but their building blocks can also be identified and
described by node-motifs---a combination of local network features. One
technique to identify single node-motifs has been presented by Costa et al. (L.
D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett.,
87, 1, 2009). Here, we first suggest improvements to the method including how
its parameters can be determined automatically. Such automatic routines make
high-throughput studies of many networks feasible. Second, the new routines are
validated in different network-series. Third, we provide an example of how the
method can be used to analyse network time-series. In conclusion, we provide a
robust method for systematically discovering and classifying characteristic
nodes of a network. In contrast to classical motif analysis, our approach can
identify individual components (here: nodes) that are specific to a network.
Such special nodes, as hubs before, might be found to play critical roles in
real-world networks.


  Let G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G),
is defined as L(G) = D(G) - A(G), where A(G) is the adjacency matrix of G and
D(G) is the diagonal matrix of the vertex degrees of G. A graph G is said to be
L-integral is all eigenvalues of the matrix L(G) are integers. In this paper,
we characterize all L-integral non-bipartite graphs among all connected graphs
with at most two vertices of degree larger than or equal to three.


  Johnson's characterization of amenable groups states that a discrete group
$\Gamma$ is amenable if and only if $H_b^{n \geq 1}(\Gamma; V) = 0$ for all
dual normed $\mathbb{R}[\Gamma]$-modules V. In this paper, we extend the
previous result to homomorphisms by proving the converse of the Mapping
Theorem: a surjective group homomorphism $\phi \colon \Gamma \to K$ has
amenable kernel H if and only if the induced inflation map $H^\bullet_b(K; V^H)
\to H^\bullet_b(\Gamma; V)$ is an isometric isomorphism for every dual normed
$\mathbb{R}[\Gamma]$-module V. In addition, we obtain an analogous
characterization for the (smaller) class of surjective group homomorphisms
$\phi \colon \Gamma \to K$ with the property that the inflation maps in bounded
cohomology are isometric isomorphisms for all Banach $\Gamma$-modules. Finally,
we also prove a characterization of the (larger) class of boundedly acyclic
homomorphisms, that is, the class of group homomorphisms $\phi \colon \Gamma
\to K$ for which the restriction maps in bounded cohomology $H^\bullet_b(K; V)
\to H^\bullet_b(\Gamma; \phi^{-1}V)$ are isomorphisms for a suitable family of
dual normed $\mathbb{R}[K]$-modules V including the trivial
$\mathbb{R}[K]$-module $\mathbb{R}$. We then extend the first and third results
to topological spaces and obtain characterizations of amenable maps and
boundedly acyclic maps in terms of the vanishing of the bounded cohomology of
their homotopy fibers with respect to appropriate choices of coefficients.


  The longitudinal and transverse structure functions are calculated for
inclusive electron scattering from ${}^{12}$C and ${}^{40}$Ca in the
quasielastic and dip region. The microscopic model presented here incorporates
two-body currents derived from one-pion exchange and intermediate $\Delta$
excitation. The reaction mechanism involves both one-nucleon and two-nucleon
knockout processes. It is demonstrated that, even for quasielastic kinematics,
two-body currents give a substantial contribution to the transverse structure
function. Furthermore, the observed excess of transverse strength in the dip
region between the quasielastic and delta peak can be partially ascribed to
direct two-nucleon knockout following photoabsorption on a two-body current.


  This paper deals with a sub-critical Keller-Segel equation. Starting from the
stochastic particle system associated with it, we show well-posedness results
and the propagation of chaos property. More precisely, we show that the
empirical measure of the system tends towards the unique solution of the limit
equation as the number of particles goes to infinity.


  Static solutions of white dwarfs with spherical symmetry and local anisotropy
are studied in the post-Newtonian approximation. It is argued that the
condition for equilibrium must be that the total energy is a minimum for given
baryon number and the question whether there is local isotropy or anisotropy
inside the star should follow from that condition, rather than be postulated "a
priori". It is shown show that, in post-Newtonian gravity, there are stable
configurations with local anisotropy for masses above the Chandrasekhar limit.


  At the 1927 Solvay conference, three different theories of quantum mechanics
were presented; however, the physicists present failed to reach a consensus.
Today, many fundamental questions about quantum physics remain unanswered. One
of the theories presented at the conference was Louis de Broglie's pilot-wave
dynamics. This work was subsequently neglected in historical accounts; however,
recent studies of de Broglie's original idea have rediscovered a powerful and
original theory. In de Broglie's theory, quantum theory emerges as a special
subset of a wider physics, which allows non-local signals and violation of the
uncertainty principle. Experimental evidence for this new physics might be
found in the cosmological-microwave-background anisotropies and with the
detection of relic particles with exotic new properties predicted by the
theory.


  In this paper, we introduce the notion of a grammatical labeling to describe
a recursive process of generating combinatorial objects based on a context-free
grammar. For example, by labeling the ascents and descents of a Stirling
permutation, we obtain a grammar for the second-order Eulerian polynomials. By
using the grammar for $0$-$1$-$2$ increasing trees given by Dumont, we obtain a
grammatical derivation of the generating function of the Andr\'e polynomials
obtained by Foata and Sch\"utzenberger, without solving a differential
equation. We also find a grammar for the number $T(n,k)$ of permutations of
$[n]=\{1,2,\ldots, n\}$ with $k$ exterior peaks, which was independently
discovered by Ma. We demonstrate that Gessel's formula for the generating
function of $T(n,k)$ can be deduced from this grammar. Moreover, by using
grammars we show that the number of the permutations of $[n]$ with $k$ exterior
peaks equals the number of increasing trees on $[n]$ with $2k+1$ vertices of
even degree. A combinatorial proof of this fact is also presented.


  In recent years there has been a tremendous surge in the general capabilities
of AI systems, mainly fuelled by training foundation models on internetscale
data. Nevertheless, the creation of openended, ever self-improving AI remains
elusive. In this position paper, we argue that the ingredients are now in place
to achieve openendedness in AI systems with respect to a human observer.
Furthermore, we claim that such open-endedness is an essential property of any
artificial superhuman intelligence (ASI). We begin by providing a concrete
formal definition of open-endedness through the lens of novelty and
learnability. We then illustrate a path towards ASI via open-ended systems
built on top of foundation models, capable of making novel, humanrelevant
discoveries. We conclude by examining the safety implications of
generally-capable openended AI. We expect that open-ended foundation models
will prove to be an increasingly fertile and safety-critical area of research
in the near future.