  Gravitational instability has been invoked as a possible mechanism of giant
planet formation in protoplanetary disks. Here we critically revise its
viability by noting that for the direct production of giant planets it is not
enough for protoplanetary disks to be gravitationally unstable. They must also
be able to cool efficiently (on a timescale comparable to the local disk
orbital period) to allow the formation of bound clumps by fragmentation.
Combination of dynamical and thermal constraints puts very stringent lower
limits on the surface density and temperature of disks capable of fragmenting
into self-gravitating objects: for the gravitational instability to form giant
planets at 10 AU gas temperature at this location must exceed 10^3 K for a
minimum disk mass of 0.7 M_Sun and minimum disk luminosity of 40 L_Sun.
Although these requirements relax in more distant parts of the disk, masses of
bound objects formed as a result of instability even at 100 AU are too large
(\sim 10 M_Jupiter) to explain characteristics of known extrasolar giant
planets. Such protoplanetary disks (and planets formed in them) have very
unusual observational properties and this severely constrains the possibility
of giant planet formation by direct gravitational instability.


  Evolutionary models of elliptical galaxies are constructed by using a new
population synthesis code. Model parameters are calibrated to reproduce the
observed colour-magnitude (CM) relation of Coma ellipticals in $V-K$ vs.
$M_{V}$ diagram. The SEDs are degenerated in stellar age and metallicity. An
attempt is performed to break this degeneracy, by simulating evolution of the
CM relation of elliptical galaxies, based on the two alternative
interpretations; i.e., the CM relation reflects different mean stellar age or
various stellar metallicity. A confrontation with the CM diagrams of E/S0
galaxies in the two distant clusters Abell 2390 ($z=0.228$) and Abell 851
($z=0.407$) reinsures previous contentions that the CM relation is primarily a
metallicity effect. This conclusion does not depend either on the model
parameters, or on the cosmological parameters adopted.


  Pre-trained large-scale vision-language models (VLMs) have acquired profound
understanding of general visual concepts. Recent advancements in efficient
transfer learning (ETL) have shown remarkable success in fine-tuning VLMs
within the scenario of limited data, introducing only a few parameters to
harness task-specific insights from VLMs. Despite significant progress, current
leading ETL methods tend to overfit the narrow distributions of base classes
seen during training and encounter two primary challenges: (i) only utilizing
uni-modal information to modeling task-specific knowledge; and (ii) using
costly and time-consuming methods to supplement knowledge. To address these
issues, we propose a Conditional Prototype Rectification Prompt Learning (CPR)
method to correct the bias of base examples and augment limited data in an
effective way. Specifically, we alleviate overfitting on base classes from two
aspects. First, each input image acquires knowledge from both textual and
visual prototypes, and then generates sample-conditional text tokens. Second,
we extract utilizable knowledge from unlabeled data to further refine the
prototypes. These two strategies mitigate biases stemming from base classes,
yielding a more effective classifier. Extensive experiments on 11 benchmark
datasets show that our CPR achieves state-of-the-art performance on both
few-shot classification and base-to-new generalization tasks. Our code is
avaliable at \url{https://github.com/chenhaoxing/CPR}.


  The quantum effective action of non-minimal vector fields with Abelian or
non-Abelian gauge degrees of freedom in curved spacetime is studied. The Proca
or Yang-Mills fields are coupled to a local mass-like term acting in both
coordinate and gauge spaces. Pathologies due to gauge invariance in the
ultraviolet are avoided through the introduction of a non-Abelian version of
the Stueckelberg field. It is found that the breaking of gauge invariance
induced by the mass term affects only the tree level part of the effective
action. The ultraviolet divergent part of the effective action to one loop is
obtained using the method of covariant symbols and dimensional regularization.
Formulas are given valid for any spacetime dimension and explicit results are
shown for the two-dimensional case. As already happened for a single vector
field, the ultraviolet divergences are local but not of polynomial type.


  A quantum transition can be seen as a result of interference between various
pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An
attempt to determine the value of f without destroying the coherence between
the pathways produces a weak value of $\bar{f}$. We show $\bar{f}$ to be an
average obtained with amplitude distribution which can, in general, take
negative values which, in accordance with the uncertainty principle, need not
contain information about the actual range of the values $f$ which contribute
to the transition. It is also demonstrated that the moments of such alternating
distributions have a number of unusual properties which may lead to
misinterpretation of the weak measurement results.We provide a detailed
analysis of weak measurements with and without post-selection. Examples include
the double slit diffraction experiment,weak von Neumann and von Neumann-like
measurements, traversal time for an elastic collision, the phase time, the
local angular momentum(LAM) and the 'three-box case' of {\it Aharonov et al}


  In this work, the dynamics of a system of mutually coupled Generalized Lorenz
systems (GLS) is investigated. The state variables of two Lorenz oscillators
are coupled mutually via non-linear controls and synchronization is achieved
between the state variables. We find that by suitably controlling a parameter
having a bearing on the coupling coefficient between the two Lorenz
oscillators, the GLS, while preserving synchronization is rendered to a state
wherein chaotic nature of state variables is suppressed and state variables
exhibit oscillatory character. The suppression of chaos is verified by power
spectra, permutation entropy and Lyapunov exponent calculations. When operated
in chaotic domain, we show the possibility of transition from the state of
synchronization to the state of anti-synchronization.


  Generalizing recent work on isotropic tensor fields in isotropic and achiral
condensed matter systems from two to arbitrary dimensions we address both
mathematical aspects assuming perfectly isotropic systems and applications
focusing on correlation functions of displacement and strain field components
in amorphous solids. Various general points are exemplified using simulated
polydisperse Lennard-Jones particles in two dimensions. It is shown that the
strain components in reciprocal space have essentially a complex
circularly-symmetric Gaussian distribution albeit weak non-Gaussianity effects
become visible for large wavenumbers q where also anisotropy effects become
relevant. The dynamical strain correlation functions are strongly non-monotonic
with respect to q with a minimum roughly at the breakdown of the continuum
limit.


  Since the development of capsule endoscopcy technology, substantial progress
were made in converting passive capsule endoscopes to robotic active capsule
endoscopes which can be controlled by the doctor. However, robotic capsule
endoscopy still has some challenges. In particular, the use of such devices to
generate a precise and globally consistent three-dimensional (3D) map of the
entire inner organ remains an unsolved problem. Such global 3D maps of inner
organs would help doctors to detect the location and size of diseased areas
more accurately, precisely, and intuitively, thus permitting more accurate and
intuitive diagnoses. The proposed 3D reconstruction system is built in a
modular fashion including preprocessing, frame stitching, and shading-based 3D
reconstruction modules. We propose an efficient scheme to automatically select
the key frames out of the huge quantity of raw endoscopic images. Together with
a bundle fusion approach that aligns all the selected key frames jointly in a
globally consistent way, a significant improvement of the mosaic and 3D map
accuracy was reached. To the best of our knowledge, this framework is the first
complete pipeline for an endoscopic capsule robot based 3D map reconstruction
containing all of the necessary steps for a reliable and accurate endoscopic 3D
map. For the qualitative evaluations, a real pig stomach is employed. Moreover,
for the first time in literature, a detailed and comprehensive quantitative
analysis of each proposed pipeline modules is performed using a non-rigid
esophagus gastro duodenoscopy simulator, four different endoscopic cameras, a
magnetically activated soft capsule robot (MASCE), a sub-millimeter precise
optical motion tracker and a fine-scale 3D optical scanner.


  We study internal diffusion-limited aggregation with random starting points
on Z^d. In this model, each new particle starts from a vertex chosen uniformly
at random on the existing aggregate. We prove that the limiting shape of the
aggregate is a Euclidean ball.


  Circulant matrices are an important family of operators, which have a wide
range of applications in science and engineering related fields. They are in
general non-sparse and non-unitary. In this paper, we present efficient quantum
circuits to implement circulant operators using fewer resources and with lower
complexity than existing methods. Moreover, our quantum circuits can be readily
extended to the implementation of Toeplitz, Hankel, and block circulant
matrices. Efficient quantum algorithms to implement the inverses and products
of circulant operators are also provided.


  As modern software systems continue to grow in terms of complexity and
volume, anomaly detection on multivariate monitoring metrics, which profile
systems' health status, becomes more and more critical and challenging. In
particular, the dependency between different metrics and their historical
patterns plays a critical role in pursuing prompt and accurate anomaly
detection. Existing approaches fall short of industrial needs for being unable
to capture such information efficiently. To fill this significant gap, in this
paper, we propose CMAnomaly, an anomaly detection framework on multivariate
monitoring metrics based on collaborative machine. The proposed collaborative
machine is a mechanism to capture the pairwise interactions along with feature
and temporal dimensions with linear time complexity. Cost-effective models can
then be employed to leverage both the dependency between monitoring metrics and
their historical patterns for anomaly detection. The proposed framework is
extensively evaluated with both public data and industrial data collected from
a large-scale online service system of Huawei Cloud. The experimental results
demonstrate that compared with state-of-the-art baseline models, CMAnomaly
achieves an average F1 score of 0.9494, outperforming baselines by 6.77% to
10.68%, and runs 10X to 20X faster. Furthermore, we also share our experience
of deploying CMAnomaly in Huawei Cloud.


  Prostate Cancer (PCa) is a prevalent disease among men, and multi-parametric
MRIs offer a non-invasive method for its detection. While MRI-based deep
learning solutions have shown promise in supporting PCa diagnosis, acquiring
sufficient training data, particularly in local clinics remains challenging.
One potential solution is to take advantage of publicly available datasets to
pre-train deep models and fine-tune them on the local data, but multi-source
MRIs can pose challenges due to cross-domain distribution differences. These
limitations hinder the adoption of explainable and reliable deep-learning
solutions in local clinics for PCa diagnosis. In this work, we present a novel
approach for unpaired image-to-image translation of prostate multi-parametric
MRIs and an uncertainty-aware training approach for classifying clinically
significant PCa, to be applied in data-constrained settings such as local and
small clinics. Our approach involves a novel pipeline for translating unpaired
3.0T multi-parametric prostate MRIs to 1.5T, thereby augmenting the available
training data. Additionally, we introduce an evidential deep learning approach
to estimate model uncertainty and employ dataset filtering techniques during
training. Furthermore, we propose a simple, yet efficient Evidential Focal
Loss, combining focal loss with evidential uncertainty, to train our model
effectively. Our experiments demonstrate that the proposed method significantly
improves the Area Under ROC Curve (AUC) by over 20% compared to the previous
work. Our code is available at https://github.com/med-i-lab/DT_UE_PCa


  We present an exact quantization condition for the time independent solutions
(energy eigenstates) of the one-dimensional Dirac equation with a scalar
potential well that gives only two `effective' turning points (defined by the
roots of $V(x)+mc^2=\pm E$) for a given energy $E$ and satisfies $\min
V(x)+mc^2\geq 0$. This result generalizes the previously known non-relativistic
quantization formula and preserves many physically desirable symmetries,
besides, attaining the correct non-relativistic limit. Numerical calculations
demonstrate the utility of the formula for computing accurate energy
eigenvalues.


  We calculate the exact asymptotic survival probability, Q, of a
one-dimensional Brownian particle, initially located located at the point x in
(-L,L), in the presence of two moving absorbing boundaries located at
\pm(L+ct). The result is Q(y,\lambda) = \sum_{n=-\infty}^\infty (-1)^n
\cosh(ny) \exp(-n^2\lambda), where y=cx/D, \lambda = cL/D and D is the
diffusion constant of the particle. The results may be extended to the case
where the absorbing boundaries have different speeds. As an application, we
compute the asymptotic survival probability for the trapping reaction A + B ->
B, for evanescent traps with a long decay time.


  Cook's distance [Technometrics 19 (1977) 15-18] is one of the most important
diagnostic tools for detecting influential individual or subsets of
observations in linear regression for cross-sectional data. However, for many
complex data structures (e.g., longitudinal data), no rigorous approach has
been developed to address a fundamental issue: deleting subsets with different
numbers of observations introduces different degrees of perturbation to the
current model fitted to the data, and the magnitude of Cook's distance is
associated with the degree of the perturbation. The aim of this paper is to
address this issue in general parametric models with complex data structures.
We propose a new quantity for measuring the degree of the perturbation
introduced by deleting a subset. We use stochastic ordering to quantify the
stochastic relationship between the degree of the perturbation and the
magnitude of Cook's distance. We develop several scaled Cook's distances to
resolve the comparison of Cook's distance for different subset deletions.
Theoretical and numerical examples are examined to highlight the broad spectrum
of applications of these scaled Cook's distances in a formal influence
analysis.


  Deep networks thrive when trained on large scale data collections. This has
given ImageNet a central role in the development of deep architectures for
visual object classification. However, ImageNet was created during a specific
period in time, and as such it is prone to aging, as well as dataset bias
issues. Moving beyond fixed training datasets will lead to more robust visual
systems, especially when deployed on robots in new environments which must
train on the objects they encounter there. To make this possible, it is
important to break free from the need for manual annotators. Recent work has
begun to investigate how to use the massive amount of images available on the
Web in place of manual image annotations. We contribute to this research thread
with two findings: (1) a study correlating a given level of noisily labels to
the expected drop in accuracy, for two deep architectures, on two different
types of noise, that clearly identifies GoogLeNet as a suitable architecture
for learning from Web data; (2) a recipe for the creation of Web datasets with
minimal noise and maximum visual variability, based on a visual and natural
language processing concept expansion strategy. By combining these two results,
we obtain a method for learning powerful deep object models automatically from
the Web. We confirm the effectiveness of our approach through object
categorization experiments using our Web-derived version of ImageNet on a
popular robot vision benchmark database, and on a lifelong object discovery
task on a mobile robot.


  The construction of the semiclassical trace formula for the resonances with
the transverse electric (TE) polarization for two-dimensional dielectric
cavities is discussed. Special attention is given to the derivation of the two
first terms of Weyl's series for the average number of such resonances. The
obtained formulas agree well with numerical calculations for dielectric
cavities of different shapes.


  We give a $q$-congruence whose specializations $q=-1$ and $q=1$ correspond to
supercongruences (B.2) and (H.2) on Van Hamme's 1997 list: $$
\sum_{k=0}^{(p-1)/2}(-1)^k(4k+1)A_k\equiv p(-1)^{(p-1)/2}\pmod{p^3}
\quad\text{and}\quad \sum_{k=0}^{(p-1)/2}A_k\equiv a(p)\pmod{p^2}, $$ where
$p>2$ is prime, $$
A_k=\prod_{j=0}^{k-1}\biggl(\frac{1/2+j}{1+j}\biggr)^3=\frac1{2^{6k}}{\binom{2k}k}^3
\quad\text{for}\ k=0,1,2,\dots, $$ and $a(p)$ is the $p$-th coefficient of (the
weight 3 modular form) $q\prod_{j=1}^\infty(1-q^{4j})^6$. We complement our
result with a general common $q$-congruence for related hypergeometric sums.


  The experimental data on hadron yields and ratios in central lead-lead and
gold-gold collisions at 158 AGeV/$c$ (SPS) and $\sqrt{s} = 130$ AGeV (RHIC),
respectively, are analysed within a two-source statistical model of an ideal
hadron gas. A comparison with the standard thermal model is given. The two
sources, which can reach the chemical and thermal equilibrium separately and
may have different temperatures, particle and strangeness densities, and other
thermodynamic characteristics, represent the expanding system of colliding
heavy ions, where the hot central fireball is embedded in a larger but cooler
fireball. The volume of the central source increases with rising bombarding
energy. Results of the two-source model fit to RHIC experimental data at
midrapidity coincide with the results of the one-source thermal model fit,
indicating the formation of an extended fireball, which is three times larger
than the corresponding core at SPS.


  The two-dimensional Ising model is representable as a lattice free-fermion
field theory in terms of the integral over anticommuting Grassmann variables.
The exact solution in a zero magnetic field then follows by evaluating Gaussian
fermionic integral for partition function. It is argued that by switching on of
a non-zero magnetic field the non-local and non-Gaussian fermionic terms appear
in the action, which rather imply approximating methods of the analysis.


  We study the obtainment of closed-form formulas for the distribution of the
jumps of a doubly-stochastic Poisson process. The problem is approached in two
ways. On the one hand, we translate the problem to the computation of multiple
derivatives of the Hazard process cumulant generating function; this leads to a
closed-form formula written in terms of Bell polynomials. On the other hand,
for Hazard processes driven by L\'evy processes, we use Malliavin calculus in
order to express the aforementioned distributions in an appealing recursive
manner. We outline the potential application of these results in credit risk.


  First-order Fermi acceleration process at a relativistic shock wave is
investigated by means of Monte Carlo simulations involving numerical
integration of particle equations of motion in a turbulent magnetic field near
the shock. In comparison to earlier studies a few 'realistic' features of the
magnetic field structure are included. The upstream field consists of a mean
field component inclined at some angle to the shock normal and finite-amplitude
perturbations imposed upon it. The perturbations are assumed to be static in
the local plasma rest frame. We apply an analytic model for the turbulence with
a flat or a Kolmogorov spectrum within a finite (wide) wave vector range. The
magnetic field is continuous across the shock -- the downstream field structure
is derived from the upstream one from the hydrodynamical shock jump conditions.
We present and discuss the obtained particle spectra and angular distributions
at mildly relativistic sub- and superluminal shocks. We show that particle
spectra diverge from a simple power-law, an exact shape of the spectrum depends
on both an amplitude of the magnetic field perturbations and the considered
wave power spectrum.


  This survey article is a much extended version of a lecture given at a Clay
Institute workshop in October 2006. It describes all known results on the
existence of stable coherent systems on algebraic curves.


  New high-resolution spectropolarimetric observations of solar prominences
require improved radiative modelling capabilities in order to take into account
both multi-dimensional - at least 2D - geometry and complex atomic models. This
makes necessary the use of very fast numerical schemes for the resolution of 2D
non-LTE radiative transfer problems considering freestanding and illuminated
slabs. The implementation of Gauss-Seidel and successive over-relaxation
iterative schemes in 2D, together with a multi-grid algorithm, is thoroughly
described in the frame of the short characteristics method for the computation
of the formal solution of the radiative transfer equation in cartesian
geometry. We propose a new test for multidimensional radiative transfer codes
and we also provide original benchmark results for simple 2D multilevel atom
cases which should be helpful for the further development of such radiative
transfer codes, in general.


  Accurate immunological models offer the possibility of performing
highthroughput experiments in silico that can predict, or at least suggest, in
vivo phenomena. In this chapter, we compare various models of immunological
memory. We first validate an experimental immunological simulator, developed by
the authors, by simulating several theories of immunological memory with known
results. We then use the same system to evaluate the predicted effects of a
theory of immunological memory. The resulting model has not been explored
before in artificial immune systems research, and we compare the simulated in
silico output with in vivo measurements. Although the theory appears valid, we
suggest that there are a common set of reasons why immunological memory models
are a useful support tool; not conclusive in themselves.


  Laboratory courses represent a unique and potentially important component of
the undergraduate physics curriculum, which can be designed to allow students
to authentically engage with the process of experimental physics. Among other
possible benefits, participation in these courses throughout the undergraduate
physics curriculum presents an opportunity to develop students' understanding
of the nature and importance of experimental physics within the discipline as a
whole. Here, we present and compare both a longitudinal and pseudo-longitudinal
analysis of students' responses to a research-based assessment targeting
students' views about experimental physics -- the Colorado Learning Attitudes
about Science Survey for Experimental Physics (E-CLASS) -- across multiple,
required lab courses at a single institution. We find that, while
pseudo-longitudinal averages showed increases in students' E-CLASS scores in
each consecutive course, analysis of longitudinal data indicates that this
increase was not driven by a cumulative impact of laboratory instruction.
Rather, the increase was driven by a selection effect in which students who
persisted into higher-level lab courses already had more expert-like beliefs,
attitudes, and expectations than their peers when they started the lower-level
courses.


  A method of direct solution of the Faddeev equations for the bound-state
problem with zero total angular momentum is used to calculate the binding
energies. The results for binding energies of He$_2$$^6$Li and He$_2$$^7$Li
systems and helium atom - HeLi dimer scattering length are presented. The
results show that modern potential models support two bound states in both
trimers. In both cases the energy of the excited state is very close to the
energy of the lowest two-body threshold.


  We discuss the properties of the nucleon (N) and its excited state with odd
parity (N*) under the aspect of chiral symmetry, identifying them with suitable
representations of the chiral group. It is shown that there are two distinctive
schemes to assign the chiral multiplet to N and N*. We construct linear sigma
models for N and N* with the two assignments to show their physical
implications. We also discuss the in-medium properties of N(1535), comparing
the present model with the other chiral model based on the different picture of
N*.


  We investigate generalized Sherrington--Kirkpatrick glassy systems without
reflection symmetry. In the neighbourhood of the transition temperature we in
general uncover the structure of the glass state building the
full-replica-symmetry breaking solution. Physical example of explicitly
constructed solution is given.


  The emergence of the graphon theory of large networks and their infinite
limits has enabled the formulation of a theory of the centralized control of
dynamical systems distributed on asymptotically infinite networks (Gao and
Caines, IEEE CDC 2017, 2018). Furthermore, the study of the decentralized
control of such systems was initiated in (Caines and Huang, IEEE CDC 2018,
2019), where Graphon Mean Field Games (GMFG) and the GMFG equations were
formulated for the analysis of non-cooperative dynamic games on unbounded
networks. In that work, existence and uniqueness results were introduced for
the GMFG equations, together with an epsilon-Nash theory for GMFG systems which
relates infinite population equilibria on infinite networks to finite
population equilibria on finite networks. Those results are rigorously
established in this paper.


  I point out that standard two dimensional, asymptotically free, non-linear
sigma models, supplemented with terms giving a mass to the would-be Goldstone
bosons, share many properties with four dimensional supersymmetric gauge
theories, and are tractable even in the non-supersymmetric cases. The space of
mass parameters gets quantum corrections analogous to what was found on the
moduli space of the supersymmetric gauge theories. I focus on a simple purely
bosonic example exhibiting many interesting phenomena: massless solitons and
bound states, Argyres-Douglas-like CFTs and duality in the infrared, and
rearrangement of the spectrum of stable states from weak to strong coupling. At
the singularities on the space of parameters, the model can be described by a
continuous theory of randomly branched polymers, which is defined beyond
perturbation theory by taking an appropriate double scaling limit.


  The celebrated exchange fluctuation theorem -- proposed by Jarzynski and
W\'ozcik, (Phys Rev. Lett. 92, 230602 (2004)) for heat exchange between two
systems in thermal equilibrium at different temperatures -- is explored here
for quantum Gaussian states in thermal equilibrium. We employ Wigner
distribution function formalism for quantum states, which exhibits close
resemblance with the classcial phase-space trajectory description, to arrive at
this theorem. For two Gaussian states in thermal equilibrium at two different
temperatures kept in contact with each other for a fixed duration of time we
show that the quantum Jarzyinski-W\'ozcik theorem agrees with the corresponding
classical result in the limit \hbar->0.


  In this paper, we briefly introduce the solution developed by our team,
HFUT-VUT, for the Micro-gesture Online Recognition track in the MiGA challenge
at IJCAI 2024. The Micro-gesture Online Recognition task involves identifying
the category and locating the start and end times of micro-gestures in video
clips. Compared to the typical Temporal Action Detection task, the
Micro-gesture Online Recognition task focuses more on distinguishing between
micro-gestures and pinpointing the start and end times of actions. Our solution
ranks 2nd in the Micro-gesture Online Recognition track.


  We consider instanton contributions to chiral correlators, such as <0| Tr
\lambda^2 (x) Tr \lambda^2(x') |0>, in N=1 supersymmetric Yang-Mills theory
with either light adjoint or fundamental matter. Within the former model,
extraction of the gluino condensate from a connected 1-instanton diagram,
evaluated at strong coupling, can be contrasted with expectations from the
Seiberg-Witten solution perturbed to an N=1 vacuum. We observe a numerical
discrepancy, coinciding with that observed previously in N=1 SQCD. Moreover,
since knowledge of the vacuum structure is complete for softly broken N=2
Yang-Mills, this model serves as a counterexample to the hypothesis of Amati et
al. that 1-instanton calculations at strong coupling can be interpreted as
averaging over vacua. Within N=1 SQCD, we point out that the connected
contribution to the relevant correlators actually vanishes in the weakly
coupled Higgs phase, despite having a nonzero value through infra-red effects
when calculated in the unbroken phase.


  In dynamic wireless ad-hoc networks (DynWANs), autonomous computing devices
set up a network for the communication needs of the moment. These networks
require the implementation of a medium access control (MAC) layer. We consider
MAC protocols for DynWANs that need to be autonomous and robust as well as have
high bandwidth utilization, high predictability degree of bandwidth allocation,
and low communication delay in the presence of frequent topological changes to
the communication network. Recent studies have shown that existing
implementations cannot guarantee the necessary satisfaction of these timing
requirements. We propose a self-stabilizing MAC algorithm for DynWANs that
guarantees a short convergence period, and by that, it can facilitate the
satisfaction of severe timing requirements, such as the above. Besides the
contribution in the algorithmic front of research, we expect that our proposal
can enable quicker adoption by practitioners and faster deployment of DynWANs
that are subject changes in the network topology.


  Recent advances in Artificial Intelligence (AI) have revived the quest for
agents able to acquire an open-ended repertoire of skills. However, although
this ability is fundamentally related to the characteristics of human
intelligence, research in this field rarely considers the processes that may
have guided the emergence of complex cognitive capacities during the evolution
of the species.
  Research in Human Behavioral Ecology (HBE) seeks to understand how the
behaviors characterizing human nature can be conceived as adaptive responses to
major changes in the structure of our ecological niche. In this paper, we
propose a framework highlighting the role of environmental complexity in
open-ended skill acquisition, grounded in major hypotheses from HBE and recent
contributions in Reinforcement learning (RL). We use this framework to
highlight fundamental links between the two disciplines, as well as to identify
feedback loops that bootstrap ecological complexity and create promising
research directions for AI researchers.


  We show that the Modified Newtonian Dynamics (MOND) regime can be fully
recovered as the weak-field limit of a particular theory of gravity formulated
in the metric approach. This is possible when Milgrom's acceleration constant
is taken as a fundamental quantity which couples to the theory in a very
consistent manner. As a consequence, the scale invariance of the gravitational
interaction is naturally broken. In this sense, Newtonian gravity is the
weak-field limit of general relativity and MOND is the weak-field limit of that
particular extended theory of gravity. We also prove that a Noether's symmetry
approach to the problem yields a conserved quantity coherent with this
relativistic MONDian extension.


  We analyze the stochastic response of a finite set of globally coupled noisy
bistable units driven by rather weak time-periodic forces. We focus on the
stochastic resonance and phase frequency synchronization of the collective
variable, defined as the arithmetic mean of the variable characterizing each
element of the array. For single unit systems, stochastic resonance can be
understood with the powerful tools of linear response theory. Proper noise
induced phase frequency synchronization for a single unit system in this linear
response regime does not exist. For coupled arrays, our numerical simulations
indicate an enhancement of the stochastic resonance effects leading to gains
larger than unity as well as genuine phase frequency synchronization. The
non-monotonicity of the response with the strength of the coupling strength is
investigated. Comparison with simplifying schemes proposed in the literature to
describe the random response of the collective variable is carried out.


  We consider the vacuum gravitational collapse for cohomogeneity-two solutions
of the nine dimensional Einstein equations. Using combined numerical and
analytical methods we give evidence that within this model the
Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we
briefly discuss the critical behavior at the threshold of black hole formation.


  A classification of gravitating Yang--Mills systems in all dimensions is
presented. These systems are set up so that they support finite energy
solutions. Both regular and black hole solutions are considered, the former
being the limit of the latter for vanishing event horizon radius. Special
attention is paid to systems necessarily involving higher order Yang--Mills
curvature terms, along with the option of incorporating higher order terms in
the Riemann curvature. The scope here is restricted to Einstein systems, with
or without cosmological constant, and the Yang--Mills(--Higgs) systems.


  We prove the existence and uniqueness of solutions for a family of nonlinear
parabolic systems related to phase field models taking in account variations of
temperature and the possibility of a general class of nonlinearities. The
present results generalizes in certain aspects the already published ones in
the literature.


  String kernels are attractive data analysis tools for analyzing string data.
Among them, alignment kernels are known for their high prediction accuracies in
string classifications when tested in combination with SVM in various
applications. However, alignment kernels have a crucial drawback in that they
scale poorly due to their quadratic computation complexity in the number of
input strings, which limits large-scale applications in practice. We address
this need by presenting the first approximation for string alignment kernels,
which we call space-efficient feature maps for edit distance with moves
(SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP)
and feature maps (FMs) of random Fourier features (RFFs) for large-scale string
analyses. The original FMs for RFFs consume a huge amount of memory
proportional to the dimension d of input vectors and the dimension D of output
vectors, which prohibits its large-scale applications. We present novel
space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of
the original FMs to O(d) of SFMs with a theoretical guarantee with respect to
concentration bounds. We experimentally test SFMEDM on its ability to learn SVM
for large-scale string classifications with various massive string data, and we
demonstrate the superior performance of SFMEDM with respect to prediction
accuracy, scalability and computation efficiency.


  We study Milky Way kinematics using a sample of 18.8 million main-sequence
stars with r<20 and proper-motion measurements derived from SDSS and POSS
astrometry, including ~170,000 stars with radial-velocity measurements from the
SDSS spectroscopic survey. Distances to stars are determined using a
photometric parallax relation, covering a distance range from ~100 pc to 10 kpc
over a quarter of the sky at high Galactic latitudes (|b|>20 degrees). We find
that in the region defined by 1 kpc <Z< 5 kpc and 3 kpc <R< 13 kpc, the
rotational velocity for disk stars smoothly decreases, and all three components
of the velocity dispersion increase, with distance from the Galactic plane. In
contrast, the velocity ellipsoid for halo stars is aligned with a spherical
coordinate system and appears to be spatially invariant within the probed
volume. The velocity distribution of nearby ($Z<1$ kpc) K/M stars is complex,
and cannot be described by a standard Schwarzschild ellipsoid. For stars in a
distance-limited subsample of stars (<100 pc), we detect a multimodal velocity
distribution consistent with that seen by HIPPARCOS. This strong
non-Gaussianity significantly affects the measurements of the velocity
ellipsoid tilt and vertex deviation when using the Schwarzschild approximation.
We develop and test a simple descriptive model for the overall kinematic
behavior that captures these features over most of the probed volume, and can
be used to search for substructure in kinematic and metallicity space. We use
this model to predict further improvements in kinematic mapping of the Galaxy
expected from Gaia and LSST.


  Regulation of intrinsic noise in gene expression is essential for many
cellular functions. Correspondingly, there is considerable interest in
understanding how different molecular mechanisms of gene expression impact
variations in protein levels across a population of cells. In this work, we
analyze a stochastic model of bursty gene expression which considers general
waiting-time distributions governing arrival and decay of proteins. By mapping
the system to models analyzed in queueing theory, we derive analytical
expressions for the noise in steady-state protein distributions. The derived
results extend previous work by including the effects of arbitrary probability
distributions representing the effects of molecular memory and bursting. The
analytical expressions obtained provide insight into the role of
transcriptional, post-transcriptional and post-translational mechanisms in
controlling the noise in gene expression.


  Large-scale pre-trained language models have shown remarkable results in
diverse NLP applications. Unfortunately, these performance gains have been
accompanied by a significant increase in computation time and model size,
stressing the need to develop new or complementary strategies to increase the
efficiency of these models. In this paper we propose DACT-BERT, a
differentiable adaptive computation time strategy for BERT-like models.
DACT-BERT adds an adaptive computational mechanism to BERT's regular processing
pipeline, which controls the number of Transformer blocks that need to be
executed at inference time. By doing this, the model learns to combine the most
appropriate intermediate representations for the task at hand. Our experiments
demonstrate that our approach, when compared to the baselines, excels on a
reduced computational regime and is competitive in other less restrictive ones.


  We will introduce two evolving models that characterize weighted complex
networks. Though the microscopic dynamics are different, these models are found
to bear a similar mathematical framework, and hence exhibit some common
behaviors, for example, the power-law distributions and evolution of degree,
weight and strength. We also study the nontrivial clustering coefficient C and
tunable degree assortativity coefficient r, depending on specific parameters.
Most results are supported by present empirical evidences, and may provide us
with a better description of the hierarchies and organizational architecture of
weighted networks. Our models have been inspired by the weighted network model
proposed by Alain Barrat et al. (BBV for short), and can be considered as a
meaningful development of their original work.


  We investigate the correction of interlayer exciton binding energy in
transition metal dichalcogenides double layers arising from the exciton-optical
phonon coupling using the method of Lee-Low-Pines unitary transformation. We
find that the binding energy varies in several tens of meV, depending on the
polarizability of materials and interlayer distance between double layers.
Moreover, the correction of binding energy results in the remarkable increasing
of the critical temperature for the condensation of dilute excitonic gas basing
on the Berezinskii-Kosterlitz-Thouless model. These results not only enrich the
knowledge for the modulation of interlayer exciton, but also provide potential
insights for the Bose-Einstein condensation and superfluid transport of
interlayer exciton in two-dimensional heterostructures.


  Quantum computers promise to efficiently solve important problems classical
computers never will. However, in order to capitalize on these prospects, a
fully automated quantum software stack needs to be developed. This involves a
multitude of complex tasks from the classical simulation of quantum circuits,
over their compilation to specific devices, to the verification of the circuits
to be executed as well as the obtained results. All of these tasks are highly
non-trivial and necessitate efficient data structures to tackle the inherent
complexity. Starting from rather straight-forward arrays over decision diagrams
(inspired by the design automation community) to tensor networks and the
ZX-calculus, various complementary approaches have been proposed. This work
provides a look "under the hood" of today's tools and showcases how these means
are utilized in them, e.g., for simulation, compilation, and verification of
quantum circuits.


  We prove weighted strong inequalities for the multilinear potential operator
${\cal T}_{\phi}$ and its commutator, where the kernel $\phi$ satisfies certain
growth condition. For these operators we also obtain Fefferman-Stein type
inequalities and Coifman type estimates. On the other hand we prove weighted
weak type inequalities for the multilinear maximal operator
$\mathcal{M}_{\varphi,B}$ associated to a essentially nondecreasing function
$\varphi$ and to a submultiplicative Young function $B$. This result allows us
to obtain a weighted weak type inequality for the operator ${\cal T}_{\phi}$.


  In this note we study some analytic properties of the linearized self-duality
equations on a family of smooth Riemann surfaces $\Sigma_R$ converging for
$R\searrow0$ to a surface $\Sigma_0$ with a finite number of nodes. It is shown
that the linearization along the fibres of the Hitchin fibration gives rise to
a graph-continuous Fredholm family, the index of it being stable when passing
to the limit. We also report on similarities and differences between properties
of the Hitchin fibration in this degeneration and in the limit of large Higgs
fields.


  We present a detailed theoretical analysis of a non-thermal escape of
molecular hydrogen from Mars induced by collisions with hot atomic oxygen from
martian corona. To accurately describe the energy transfer in O + H$_2(v,j)$
collisions, we performed extensive quantum-mechanical calculations of
state-to-state elastic, inelastic, and reactive cross sections. The escape flux
of H$_2$ molecules was evaluated using a simplified 1D column model of the
martian atmosphere with realistic densities of atmospheric gases and hot oxygen
production rates for the low solar activity conditions. An average density of
the non-thermal escape flux of H$_2$ of $1.9\times10^5$ cm$^{-2}$s$^{-1}$ was
obtained considering energetic O atoms produced in dissociative recombinations
of O$_{2}^{+}$ ions. Predicted rovibrational distribution of the escaping H$_2$
was found to contain a significant fraction of higher rotational states. While
the non-thermal escape rate was found to be lower than Jeans flux for H$_2$
molecules, the non-thermal escape rates of HD and D$_2$ are significantly
higher than their respective Jeans rates. The accurate values of non-thermal
escape fluxes of different molecular isotopes of H$_2$ may be important in
analyses of evolution of the martian atmosphere. The described molecular
ejection mechanism is general and expected to contribute to atmospheric escape
of H$_2$ and other light molecules from planets, satellites, and exoplanetary
bodies.


  The new 182 gold supernova Ia data, the baryon acoustic oscillation
measurement and the shift parameter determined from the Sloan Digital Sky
Survey and the three-year Wilkinson Microwave Anisotropy Probe data are
combined to reconstruct the dark energy equation of state parameter $w(z)$ and
the deceleration parameter $q(z)$. We find that the strongest evidence of
acceleration happens around the redshift $z\sim 0.2$ and the stringent
constraints on $w(z)$ lie in the redshift range $z\sim 0.2-0.5$. At the sweet
spot, $-1.2<w(z)<-0.6$ for the dark energy parametrization $w(z)=w_0+w_a
z/(1+z)^2$ at the $3\sigma$ confidence level. The transition redshift $z_t$
when the Universe underwent the transition from deceleration to acceleration is
derived to be $z_t=0.36^{+0.23}_{-0.08}$. The combined data is also applied to
find out the geometry of the Universe, and we find that at the $3\sigma$
confidence level, $|\Omega_k|\alt 0.05$ for the simple one parameter dark
energy model, and $-0.064<\Omega_k<0.028$ for the $\Lambda$CDM model.


  We say that $G \to (F,H)$ if, in every edge colouring $c: E(G) \to \{1,2\}$,
we can find either a $1$-coloured copy of $F$ or a $2$-coloured copy of $H$.
The well-known Kohayakawa--Kreuter conjecture states that the threshold for the
property $G(n,p) \to (F,H)$ is equal to $n^{-1/m_{2}(F,H)}$, where $m_{2}(F,H)$
is given by \[ m_{2}(F,H):= \max \left\{\dfrac{e(J)}{v(J)-2+1/m_2(H)} : J
\subseteq F, e(J)\ge 1 \right\}. \] In this paper, we show the $0$-statement of
the Kohayakawa--Kreuter conjecture for every pair of cycles and cliques.


  Ultra-low end-to-end latency is one of the most important requirements in 5G
networks and beyond to support latency-critical applications. Cloud-RAN and MEC
are considered as the key driving technology that can help reduce end-to-end
latency. However, the use of MEC nodes poses radical changes to the access
network architecture. As it brings the processing and the networking services
closer to the edge, it often requires network functions (for example, the CU/DU
stack and the application processing) to be distributed across different MEC
sites. Therefore, a novel transport mechanism is needed to efficiently
coordinate and connect network functions across MEC nodes.
  In order to address this challenge, we propose a novel two-tier virtualized
PON transport method with schedulers coordination over a virtualised and sliced
MESH-PON architecture. While a MESH-PON architecture enables direct
communication between MEC nodes that are hosting CU/DU and/or the application
processing, our method provides a two tier virtualised PON transport scheme
with coordinated schedulers. This approach greatly reduces latency incurred in
transporting signals across the different PON tiers, while maintaining the
flexibility of the multi-tier methods. We show that our proposed scheme can
achieve end-to-end application-level latency below 1ms or 2ms, depending on the
network configurations.


  Recent developments in statistical regression methodology shift away from
pure mean regression towards distributional regression models. One important
strand thereof is that of conditional transformation models (CTMs). CTMs infer
the entire conditional distribution directly by applying a transformation
function to the response conditionally on a set of covariates towards a simple
log-concave reference distribution. Thereby, CTMs allow not only variance,
kurtosis or skewness but the complete conditional distribution to depend on the
explanatory variables. We propose a Bayesian notion of conditional
transformation models (BCTMs) focusing on exactly observed continuous
responses, but also incorporating extensions to randomly censored and discrete
responses. Rather than relying on Bernstein polynomials that have been
considered in likelihood-based CTMs, we implement a spline-based
parametrization for monotonic effects that are supplemented with smoothness
priors. Furthermore, we are able to benefit from the Bayesian paradigm via
easily obtainable credible intervals and other quantities without relying on
large sample approximations. A simulation study demonstrates the
competitiveness of our approach against its likelihood-based counterpart but
also Bayesian additive models of location, scale and shape and Bayesian
quantile regression. Two applications illustrate the versatility of BCTMs in
problems involving real world data, again including the comparison with various
types of competitors.


  We study the analyticity properties of amplitudes in theories with nonlocal
vertices of the type occurring in string field theory and a wide class of
nonlocal field theory models. Such vertices are given in momentum space by
entire functions of rapid decay in certain (including Euclidean) directions
ensuring UV finiteness but are necessarily of rapid increase in others. A
parametric representation is obtained by integrating out the loop (Euclidean)
momenta after the introduction of generalized Schwinger parameters. Either in
the original or parametric representation, the well-defined resulting
amplitudes are then continued in the complex space of the external momenta
invariants. We obtain the alternative forms of the Landau equations determining
the singularity surfaces showing that the nonlocal vertices serve as UV
regulators but do not affect the local singularity structure. As a result the
full set of singularities known to occur in local field theory also occurs
here: normal and anomalous thresholds as well as acnodes, crunodes, and cusps
that may under certain circumstances appear even on the physical sheet.
Singularities of the second type also appear as shown from the parametric
representation. We obtain the general Cutkosky discontinuity rule for
encircling a singularity by employing contour deformations only in the finite
plane. The unitarity condition (optical theorem) is then discussed as a special
application of the rule across normal thresholds and the hermitian analyticity
property of amplitudes.


  We briefly describe what a two photon capability with KLOE2 can measure and
discuss what this will teach us about the world of light hadrons.


  We revisit classic string problems considered in the area of parameterized
complexity, and study them through the lens of dynamic data structures. That
is, instead of asking for a static algorithm that solves the given instance
efficiently, our goal is to design a data structure that efficiently maintains
a solution, or reports a lack thereof, upon updates in the instance.
  We first consider the Closest String problem, for which we design randomized
dynamic data structures with amortized update times $d^{\mathcal{O}(d)}$ and
$|\Sigma|^{\mathcal{O}(d)}$, respectively, where $\Sigma$ is the alphabet and
$d$ is the assumed bound on the maximum distance. These are obtained by
combining known static approaches to Closest String with color-coding.
  Next, we note that from a result of Frandsen et al.~[J. ACM'97] one can
easily infer a meta-theorem that provides dynamic data structures for
parameterized string problems with worst-case update time of the form
$\mathcal{O}(\log \log n)$, where $k$ is the parameter in question and $n$ is
the length of the string. We showcase the utility of this meta-theorem by
giving such data structures for problems Disjoint Factors and Edit Distance. We
also give explicit data structures for these problems, with worst-case update
times $\mathcal{O}(k2^{k}\log \log n)$ and $\mathcal{O}(k^2\log \log n)$,
respectively. Finally, we discuss how a lower bound methodology introduced by
Amarilli et al.~[ICALP'21] can be used to show that obtaining update time
$\mathcal{O}(f(k))$ for Disjoint Factors and Edit Distance is unlikely already
for a constant value of the parameter $k$.


  We present a mock catalog of gravitationally lensed quasars at
$z_\text{qso}<7.5$ with simulated images for the Rubin Observatory Legacy
Survey of Space and Time (LSST). We adopt recent measurements of quasar
luminosity functions to model the quasar population, and use the CosmoDC2 mock
galaxy catalog to model the deflector galaxies, which successfully reproduces
the observed galaxy velocity dispersion functions up to $z_d\sim1.5$. The mock
catalog is highly complete for lensed quasars with Einstein radius
$\theta_E>0\farcs07$ and quasar absolute magnitude $M_{i}<-20$. We estimate
that there are $\sim10^3$ lensed quasars discoverable in current imaging
surveys, and LSST will increase this number to $\sim2.4\times10^3$. Most of the
lensed quasars have image separation $\Delta \theta>0\farcs5$, which will at
least be marginally resolved in LSST images with seeing of $\sim0\farcs7$.
There will be $\sim200$ quadruply-lensed quasars discoverable in the LSST. The
fraction of quad lenses among all discoverable lensed quasars is about
$\sim10\%-15\%$, and this fraction decreases with survey depth. This mock
catalog shows a large diversity in the observational features of lensed
quasars, in terms of lensing separation and quasar-to-deflector flux ratio. We
discuss possible strategies for a complete search of lensed quasars in the LSST
era.


  An extension of the single-freeze-out model with thermal and geometric
parameters dependent on the spatial rapidity, $\alpha_\parallel$, is used to
describe the rapidity and transverse-momentum spectra of pions, kaons, protons,
and antiprotons measured at RHIC at $\sqrt{s_{NN}}=200 {\rm GeV}$ by the BRAHMS
collaboration. {\tt THERMINATOR} is used to perform the necessary simulation,
which includes all resonance decays. The result of the fit to the rapidity
spectra in the range of the BRAHMS data is the expected growth of the baryon
and strange chemical potentials with the magnitude of $\alpha_\parallel$, while
the freeze-out temperature is kept fixed. The value of the baryon chemical
potential at $\alpha_\parallel \sim 3$, which is the relevant region for
particles detected at the BRAHMS forward rapidity $y \sim 3$, is about $200
{\rm GeV}$, {\em i.e.} lies in the range of the values obtained for the highest
SPS energy. The chosen geometry of the fireball has a decreasing transverse
size as the magnitude of $\alpha_\parallel$ is increased, which also
corresponds to decreasing transverse flow. This feature is verified by
reproducing the transverse momentum spectra of pions and kaons at various
rapidities. The strange chemical potential obtained from the fit to the
$K^+/K^-$ ratio is such that the local strangeness density in the fireball is
compatible with zero. The resulting rapidity spectra of net protons are
described qualitatively in the model. As a result of the study, the knowledge
of the ``topography'' of the fireball is achieved, making other calculations
possible. As an example, we give predictions for the rapidity spectra of
hyperons.


  One of the key points in Galois theory via field extensions is to build up a
correspondence between subfields of a field and subgroups of its automorphism
group, so as to study fields via methods of groups. As an analogue of the
Galois theory, we want to discuss the relations between cluster subalgebras of
a cluster algebra and subgroups of its automorphism group and then set up the
Galois-like method.
  In the first part, we build up a Galois map from a skew-symmetrizable cluster
algebra $\mathcal A$ to its cluster automorphism group, and introduce notions
of Galois-like extensions and Galois extensions. A necessary condition for
Galois extensions of a cluster algebra $\mathcal A$ is given, which is also a
sufficient condition if $\mathcal A$ has a $\mathcal{D}$-stable basis or stable
monomial basis with unique expression. Some properties for Galois-like
extensions are discussed. It is shown that two subgroups $H_1$ and $H_2$ of the
automorphism group $\text{Aut}\mathcal A$ are conjugate to each other if and
only if there exists $ f \in \text{Aut}\mathcal{A} $ and two Galois-like
extension subalgebras $\mathcal A(\Sigma_1)$, $\mathcal A(\Sigma_2)$
corresponding to $H_1$ and $H_2$ such that $f$ is an isomorphism between
$\mathcal A(\Sigma_1)$ and $\mathcal A(\Sigma_2)$.
  In the second part, as the answers of two conjectures proposed in the first
part, for a cluster algebra from a feasible surface, we prove that Galois-like
extension subalgebras corresponding to a subgroup of a cluster automorphism
group have the same rank. Moreover, it is shown that there are order-preserving
reverse Galois maps for these cluster algebras. We also give examples of
$\mathcal{D}$-stable bases and some discussions on the Galois inverse problem
in this part.


  Neodymium nickelate, NdNiO3 attracts attraction due to the simultaneous
occurrence of several phase transitions around the same temperature. The
electronic properties of NdNiO3 are extremely complex as structural distortion,
electron correlation, charge ordering, and orbital overlapping play significant
roles in the transitions. We report the effects of electron and hole injection
via doping a single 3d metal, V, in the NdNiO3 nanostructures to understand the
variations in the electronic properties without any structural distortion. A
reversible resistivity modulation more than five orders of magnitude via hole
doping and complete suppression of metal to insulator transition via electron
doping is observed along with the switching of major charge carriers. The
modulation of electronic properties without any structural distortion and
external strain opens up new directions to consider the NdNi1_xVxO3
nanostructures applicable as emerging electronic devices.


  In this paper, an ontology-based approach is used to organize the knowledge
base of legal documents in road traffic law. This knowledge model is built by
the improvement of ontology Rela-model. In addition, several searching problems
on traffic law are proposed and solved based on the legal knowledge base. The
intelligent search system on Vietnam road traffic law is constructed by
applying the method. The searching system can help users to find concepts and
definitions in road traffic law. Moreover, it can also determine penalties and
fines for violations in the traffic. The experiment results show that the
system is efficient for users' typical searching and is emerging for usage in
the real-world.


  In this paper we discuss the controllability of two-point boundary value
problem (TBVP) for one-dimensional wave equation. Some new concepts are
introduced: TBVP input control problem, minimum-input solution (MS) and
pre-minimum-input solution (PMS). We set the metric in $L^1$ and $L^2$ spaces
on a closed set, and control the input to reach its minimum. And we mainly
discuss the property of input, the existence and uniqueness of MS and PMS for
$L^1$ and $L^2$ metric respectively. The minimum inputs lie on a strip in $L^1$
and PMS for $L^1$ and $L^2$ always exists. Furthermore, to construct PMS, we
also introduce an approximation method which meets certain conditions.


  Algebra objects in $\infty$-categories of spans admit a description in terms
of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects
and extend this correspondence to an equivalence of $\infty$-categories.
Additionally, for every $\infty$-category with finite limits $\mathcal{C}$, we
introduce a notion of a birelative $2$-Segal object in $\mathcal{C}$ and
establish a similar equivalence with the $\infty$-category of bimodule objects
in spans. Examples of these concepts arise from algebraic and hermitian
K-theory through the corresponding Waldhausen $S_{\bullet}$-construction. Apart
from their categorical relevance, these concepts can be used to construct
homotopy coherent representations of Hall algebras.


  We advance spin noise spectroscopy to an ultrafast tool to resolve high
frequency spin dynamics in semiconductors. The optical non-demolition
experiment reveals the genuine origin of the inhomogeneous spin dephasing in
n-doped GaAs wafers at densities at the metal-to-insulator transition. The
measurements prove in conjunction with depth resolved spin noise measurements
that the broadening of the spin dephasing rate does not result from thermal
fluctuations or spin-phonon interaction, as previously suggested, but from
surface electron depletion.


  Making electrical transport measurements on a material is often a time
consuming process that involves testing a large number of samples. It is thus
inconvenient to wire up and rewire samples on to a sample probe. We therefore
present a method of modifying Quantum Design's MPMS SQUID magnetometer
transport probe that simplifies the process of sample mounting. One of the
difficulties to overcome is the small diameter of the sample space. A small
socket is designed and mounted on the probe so that various samples mounted on
individual headers can be readily exchanged in the socket. We also present some
test results on the topological insulator Bi2Te2Se using the modified probe.


  The aim of this paper is to obtain a posteriori error bounds of optimal order
in time and space for the linear second-order wave equation discretized by the
Newmark scheme in time and the finite element method in space. Error estimates
are derived in the $L^{\infty}$-in-time/energy-in-space norm. Numerical
experiments are reported for several test cases and confirm equivalence of the
proposed estimators and the true error.


  In this work, we introduce Speech-Copilot, a modular framework for
instruction-oriented speech-processing tasks that minimizes human effort in
toolset construction. Unlike end-to-end methods using large audio-language
models, Speech-Copilot builds speech processing-specific toolsets by analyzing
pre-collected task instructions and breaking tasks into manageable sub-tasks.
It features a flexible agent based on large language models that performs tasks
through program generation. Our approach achieves state-of-the-art performance
on the Dynamic-SUPERB benchmark, demonstrating its effectiveness across diverse
speech-processing tasks. Key contributions include: 1) developing an innovative
framework for speech processing-specific toolset construction, 2) establishing
a high-performing agent based on large language models, and 3) offering a new
perspective on addressing challenging instruction-oriented speech-processing
tasks. Without additional training processes required by end-to-end approaches,
our method provides a flexible and extendable solution for a wide range of
speech-processing applications.


  In this paper we discuss the threat of malware targeted at extracting
information about the relationships in a real-world social network as well as
characteristic information about the individuals in the network, which we dub
Stealing Reality. We present Stealing Reality, explain why it differs from
traditional types of network attacks, and discuss why its impact is
significantly more dangerous than that of other attacks. We also present our
initial analysis and results regarding the form that an SR attack might take,
with the goal of promoting the discussion of defending against such an attack,
or even just detecting the fact that one has already occurred.


  We consider recent experimental results [W. Pan {\it et al}, Phys. Rev. Lett.
{\bf 90}, 016801 (2003)] for occurrence of the fractional quantum Hall
effect-FQHE under the perspective of our formulation in terms of {\it
fractons}. These objects carry rational or irrational values of spin and
satisfy a {\it fractal distribution function} associated with a {\it fractal
von Neumann entropy}. According to our approach the {\it FQHE occurs in pairs
of dual topological quantum numbers fillings factors} and this geometrical
character comes from the {\it connection betwenn the fractal parameter or
Hausdorff dimension $h$ and the spin $s$ of the particles}. We suggest to the
experimentalists consider our ideas and verify in fact that this phenomenon of
FQHE satisfy a {\it symmetry principle} discovered by us, i.e, {\it the duality
symmetry betwenn universal classes of fractons}.


  We study in detail the Quantum Field Theory of mixing among three generations
of Dirac fermions (neutrinos). We construct the Hilbert space for the flavor
fields and determine the generators of the mixing transformations. By use of
these generators, we recover all the known parameterizations of the
three-flavor mixing matrix and we find a number of new ones. The algebra of the
currents associated with the mixing transformations is shown to be a deformed
$su(3)$ algebra, when CP violating phases are present. We then derive the exact
oscillation formulas, exhibiting new features with respect to the usual ones.
CP and T violation are also discussed.


  An algorithm for detecting unstable periodic orbits in chaotic systems [Phys.
Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising
transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78
(1997), pp. 4733-4736] with a modified semi-implicit Euler iterative scheme and
seeding with periodic orbits of neighbouring periods, has been shown to be
highly efficient when applied to low-dimensional system. The difficulty in
applying the algorithm to higher dimensional systems is mainly due to the fact
that the number of stabilising transformations grows extremely fast with
increasing system dimension. In this thesis, we construct stabilising
transformations based on the knowledge of the stability matrices of already
detected periodic orbits (used as seeds). The advantage of our approach is in a
substantial reduction of the number of transformations, which increases the
efficiency of the detection algorithm, especially in the case of
high-dimensional systems. The performance of the new approach is illustrated by
its application to the four-dimensional kicked double rotor map, a
six-dimensional system of three coupled H\'enon maps and to the
Kuramoto-Sivashinsky system in the weakly turbulent regime.


  We describe those binary quadratic operads generated by a two-dimensional
space that are isomorphic to their Koszul dual operads.


  This paper studies the dynamics of Brazilian interest rates for short-term
maturities. The paper employs developed techniques in the econophysics
literature and tests for long-range dependence in the term structure of these
interest rates for the last decade. Empirical results suggest that the degree
of long-range dependence has changed over time due to changes in monetary
policy, specially in the short-end of the term structure of interest rates.
Therefore, we show that it is possible to identify monetary arrangements using
these techniques from econophysics.


  In many indigenous societies, people are categorised into several cultural
groups, or clans, within which they believe to share ancestors. Clan
attributions provide certain rules for marriage and descent. Such rules between
clans constitute kinship structures. Anthropologists have revealed several
kinship structures. Here, we propose an agent-based model of indigenous
societies to reveal the evolution of kinship structures. In the model, several
societies compete. Societies themselves comprise multiple families with
parameters for cultural traits and mate preferences. These values determine
with whom each family cooperates and competes and are transmitted to a new
generation with mutation. The growth rate of each family is determined by the
number of cooperators and competitors. Through this multi-level evolution,
family traits and preferences diverge to form clusters that can be regarded as
clans. Subsequently, kinship structures emerge, including dual organisation and
generalised or restricted exchange, as well as patrilineal, matrilineal, and
double descent systems. These structures emerge depending on the necessity of
cooperation and the strength of mating competition. Their dependence is also
estimated analytically. Finally, statistical analysis using the Standard
Cross-Cultural Sample, a global ethnographic database, empirically verified
theoretical results. Such collaboration between theoretical and empirical
approaches will unveil universal features in anthropology.


  We classify K\"ahler-Einstein manifolds which admit a K\"ahler immersion
into a finite dimensional complex projective space endowed with the
Fubini-Study metric, whose codimention is not greater than 3 and whose metric
is rotation invariant.


  Following a paper by Athanasios Angelakis and Peter Stevenhagen on the
determination of imaginary quadratic fields having the same absolute Abelian
Galois group A, we study this property for arbitrary number fields. We show
that such a property is probably not easily generalizable, apart from imaginary
quadratic fields, because of some p-adic obstructions coming from the global
units. By restriction to the p-Sylow subgroups of A, we show that the
corresponding study is related to a generalization of the classical notion of
p-rational fields. However, we obtain some non-trivial information about the
structure of the profinite group A, for every number field, by application of
results published in our book on class field theory. This version corrects a
technical error discovered by Peter Stevenhagen in a lemma of their first draft
(arXiv:1209.6005) as well as in the previous versions of our paper reproducing
this lemma; it will also be corrected in their final paper to appear in the
proceedings volume of ANTS-X, San Diego 2012. This does not modify the nature
of the results.


  We propose to exploit the quantum properties of nonlinear media to estimate
the parameters of massless wormholes. The spacetime curvature produces a change
in length with respect to Minkowski spacetime that can be estimated in
principle with an interferometer. We use quantum metrology techniques to show
that the sensitivity is improved with nonlinear media and propose a nonlinear
Mach-Zehnder interferometer to estimate the parameters of massless wormholes
that scales beyond the Heisenberg limit.


  A semigroup $S$ is right noetherian if every right congruence on $S$ is
finitely generated. In this paper we present some fundamental properties of
right noetherian semigroups, discuss how semigroups relate to their
substructures with regard to the property of being right noetherian, and
investigate whether this property is preserved under various semigroup
constructions.


  We prove a Central Limit Theorem for probability measures defined via the
variation of the sum-of-digits function, in base $b\ge 2$. For $r\ge 0$ and $d
\in \mathbb{Z}$, we consider $\mu^{(r)}(d)$ as the density of integers $n\in
\mathbb{N}$ for which the sum of digits increases by $d$ when we add $r$ to
$n$. We give a probabilistic interpretation of $\mu^{(r)}$ on the probability
space given by the group of $b$-adic integers equipped with the normalized Haar
measure. We split the base-$b$ expansion of the integer $r$ into so-called
"blocks", and we consider the asymptotic behaviour of $\mu^{(r)}$ as the number
of blocks goes to infinity. We show that, up to renormalization, $\mu^{(r)}$
converges to the standard normal law as the number of blocks of $r$ grows to
infinity. We provide an estimate of the speed of convergence. The proof relies,
in particular, on a $\phi$-mixing process defined on the $b$-adic integers.


  In this paper, we simplify and extend the results of \cite{GZ} to include the
case in which $\Om =\R^3$. Let ${[L^2({\mathbb{R}}^3)]^3}$ be the Hilbert space
of square integrable functions on ${\mathbb {R}}^3 $ and let ${\mathbb
H}[{\mathbb{R}}^3]^3 =: {\mathbb H}$ be the completion of the set, ${{{\bf{u}}
\in (\mathbb {C}_0^\infty [ \R^3 ])^3. {} | \nabla \cdot {\bf{u}} = 0}}$, with
respect to the inner product of ${[L^2({\mathbb{R}}^3)]^3} $. In this paper, we
consider sufficiency conditions on a class of functions in ${\mathbb H}$ which
allow global-in-time strong solutions to the three-dimensional Navier-Stokes
equations on ${\mathbb {R}}^3$. These equations describe the time evolution of
the fluid velocity and pressure of an incompressible viscous homogeneous
Newtonian fluid in terms of a given initial velocity and given external body
forces. Our approach uses the analytic nature of the Stokes semigroup to
construct an equivalent norm for $\mathbb{H}$ which allows us to prove a
reverse of the Poincar\'e inequality. This result allows us to provide strong
bounds on the nonlinear term. We then prove that, under appropriate conditions,
there exists a positive constant $ {{u}_+}$, depending only on the domain, the
viscosity and the body forces such that, for all functions in a dense set
$\mathbb{D}$ contained in the closed ball ${{\mathbb B} ({\mathbb {R}}^3)}=:
{\mathbb B}$ of radius $ (1/2){{u}_ +} $ in ${\mathbb {H}}$, the Navier-Stokes
equations have unique strong solutions in ${\mathbb C}^{1}
({(0,\infty),{\mathbb {H}}})$.


  We propose a general and model-free approach for Reinforcement Learning (RL)
on real robotics with sparse rewards. We build upon the Deep Deterministic
Policy Gradient (DDPG) algorithm to use demonstrations. Both demonstrations and
actual interactions are used to fill a replay buffer and the sampling ratio
between demonstrations and transitions is automatically tuned via a prioritized
replay mechanism. Typically, carefully engineered shaping rewards are required
to enable the agents to efficiently explore on high dimensional control
problems such as robotics. They are also required for model-based acceleration
methods relying on local solvers such as iLQG (e.g. Guided Policy Search and
Normalized Advantage Function). The demonstrations replace the need for
carefully engineered rewards, and reduce the exploration problem encountered by
classical RL approaches in these domains. Demonstrations are collected by a
robot kinesthetically force-controlled by a human demonstrator. Results on four
simulated insertion tasks show that DDPG from demonstrations out-performs DDPG,
and does not require engineered rewards. Finally, we demonstrate the method on
a real robotics task consisting of inserting a clip (flexible object) into a
rigid object.


  The development of the first X-ray polarimeter, based on the photoelectric
effect 20 years ago and implemented thanks to advances in gas amplification
structures and readout techniques, had a significant impact in opening a new
window for X-ray polarimetry. This system measures the X-ray polarization by
reconstructing the initial direction of the photoelectron, emitted by the
interaction of an incident photon with an atomic electron, in a gas mixture
from an ionization track collected on a two-dimensional plane. However, actual
X-ray polarimeters, are still requiring relatively long exposure time and
cannot coupled with high effective area mirrors or concentrators. In this
context, the high yield polarimetry experiment in X-rays (Hype-X) project is
currently underway, aiming to improve the sensitivity of the next generation
X-ray polarimetry detectors taking advantage of the recent advancements in
imaging techniques for high-resolution time projection chambers. In particular,
we are evaluating the use of TIMEPIX3 to be applied for the read-out of a gas
detector, which will allow us to obtain a three-dimensional image of the
photoelectron track. To evaluate the improvement achievable by using a 3D track
reconstruction, in this paper, we have reproduced a three-dimensional
photoelectron track from a 'Geant4' Monte Carlo simulation and examined the
sensitivity of X-ray polarimetry using a new three-dimensional track
reconstruction algorithm. We report the improvement of the modulation factor
with three-dimensional track reconstruction as $\sim5\%$ (relative) in the 2-8
keV range and $\sim17\%$ (relative) in the 2-4 keV range compared to the
current two-dimensional polarimetry system. This is equivalent to add a further
telescope to the three-telescope systems now employed in space on board the
IXPE mission.


  An old theorem of Weil and Kodaira says that for a compact K\"ahler manifold
$X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only
if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of
this paper, we generalize the above theorem to general compact complex
manifolds by showing that the necessary and sufficient condition in general is
described by a holomorphic invariant called the $\mathcal Q$-flat class. Next,
we prove that the holomorphic criterion is reduced to the topological one when
$X$ has Property $(H)$. Since all K\"ahler manifolds have Property $(H)$, this
gives an alternative proof of Weil and Kodaira's original theorem. Then, we
prove some decomposition theorems for closed meromorphic $1$-forms by applying
the above general theorem. In the second part of the paper, we turn to the
study of pluriharmonic functions on projective manifolds and classify all the
pluriharmonic functions with mild singularity.


  Exploiting the Persistent Homology technique and an associated complementary
representation which enables us to construct a synergistic pipeline for
different topological features quantified by Betti curves in reducing the
degeneracy between cosmological parameters, we investigate the footprint of
summed massive neutrinos ($M_{\nu}$) in different density fields simulated by
the publicly available Quijote suite. Evolution of topological features in the
context of super-level filtration on three-dimensional density fields, reveals
remarkable indicators for constraining the $M_{\nu}$ and $\sigma_8$. The
abundance of 2-holes is more sensitive to the presence of $M_{\nu}$, also the
persistence of topological features plays a crucial role in cosmological
inference and reducing the degeneracy associated with $M_{\nu}$ simulation
rather than their birth thresholds when either the total matter density ($m$)
field or those part including only cold dark matter+baryons ($cb$) is utilized.
Incorporating the Betti-1 and Betti-2 for $cb$ part of $M^+_{\nu}$ simulation
marginalized over the thresholds implies $5\%$ variation compared to the
massless neutrinos simulation. The constraint on $M_{\nu}$ from $\beta_k$ and
its joint analysis with birth threshold and persistency of topological features
for total mass density field smoothed by $R=5$ Mpc h$^{-1}$ at zero redshift
reach to $0.0172$ eV and $0.0152$ eV, at $1\sigma$ confidence interval,
respectively.


  The formation of atomic wires via pseudomorphic step-edge decoration on
vicinal silicon surfaces has been analyzed for Ga on the Si(112) surface using
Scanning Tunneling Microscopy and Density Functional Theory calculations. Based
on a chemical potential analysis involving more than thirty candidate
structures and considering various fabrication procedures, it is concluded that
pseudomorphic growth on stepped Si(112), both under equilibrium and
non-equilibrium conditions, must favor formation of Ga zig-zag chains rather
than linear atom chains. The surface is non-metallic and presents quasi-one
dimensional character in the lowest conduction band.


  We show that a generalized Landau theory for the smectic A and C phases
exhibits a biaxiality induced AC tricritical point. Proximity to this
tricritical point depends on the degree of orientational order in the system;
for sufficiently large orientational order the AC transition is 3D XY-like,
while for sufficiently small orientational order, it is either tricritical or
1st order. We investigate each of the three types of AC transitions near
tricriticality and show that for each type of transition, small orientational
order implies de Vries behavior in the layer spacing, an unusually small layer
contraction. This result is consistent with, and can be understood in terms of,
the "diffuse cone" model of de Vries. Additionally, we show that birefringence
grows upon entry to the C phase. For a continuous transition, this growth is
more rapid the closer the transition is to tricriticality. Our model also
predicts the possibility of a nonmontonic temperature dependence of
birefringence.


  We use a modified Thomas-Fermi approximation to estimate analytically the
critical velocity for the formation of vortices in harmonically trapped BEC. We
compare this analytical estimate to numerical calculations and to recent
experiments on trapped alkali condensates.


  We discuss an extended easy quantum group formalism, with the Schur-Weyl
theoretic Kronecker symbols being as general as possible, and allowed to take
values in $\{-1,0,1\}$, and more generally in $\mathbb T\cup\{0\}$. Our study
includes an axiomatization of the theory, some structure and classification
results, and the study of the basic examples of quantum unitary and reflection
groups, with both positive and negative results.


  The transport coefficients of causal relativistic dissipative fluid dynamics
are calculated both in a field-theoretical and a kinetic approach. We find that
the results from the traditional kinetic calculation by Israel and Stewart are
modified. The new expressions for the viscous transport coefficients agree with
the results obtained in the field-theoretical approach when the contributions
from pair creation and annihilation are neglected.


  In this work we develop a new algorithm for regularized empirical risk
minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015],
which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes.
Moreover, our method is able to better utilize the information in the data
defining the ERM problem. For convex loss functions, our complexity results
match those of QUARTZ, which is a primal-dual method also allowing for
arbitrary mini-batching schemes. The advantage of a dual-free analysis comes
from the fact that it guarantees convergence even for non-convex loss
functions, as long as the average loss is convex. We illustrate through
experiments the utility of being able to design arbitrary mini-batching
schemes.


  From behavioral sciences to biology to quantum mechanics, one encounters
situations where (i) a system outputs several random variables in response to
several inputs, (ii) for each of these responses only some of the inputs may
"directly" influence them, but (iii) other inputs provide a "context" for this
response by influencing its probabilistic relations to other responses. These
contextual influences are very different, say, in classical kinetic theory and
in the entanglement paradigm of quantum mechanics, which are traditionally
interpreted as representing different forms of physical determinism. One can
mathematically construct systems with other types of contextuality, whether or
not empirically realizable: those that form special cases of the classical
type, those that fall between the classical and quantum ones, and those that
violate the quantum type. We show how one can quantify and classify all
logically possible contextual influences by studying various sets of
probabilistic couplings, i.e., sets of joint distributions imposed on random
outputs recorded at different (mutually incompatible) values of inputs.


  We consider the Schr\"odinger system with Newton-type interactions that was
derived by R. Klein, A. Majda and K. Damodaran [18] to modelize the dynamics of
N nearly parallel vortex filaments in a 3-dimensional homogeneous
incompressible uid. The known large time existence results are due to C. Kenig,
G. Ponce and L. Vega [17] and concern the interaction of two filaments and
particular configurations of three filaments. In this article we prove large
time existence results for particular configurations of four nearly parallel
filaments and for a class of configurations of N nearly parallel filaments for
any N\geq 2. We also show the existence of travelling wave type dynamics.
Finally we describe configurations leading to collision.


  In this work, the spin wave calculations were carried out using the
Heisenberg Hamiltonian to study the allowed spin waves of zigzag and armchair
edged stripes for ferromagnetic nanodots arrayed in a 2D honeycomb lattice
\cite{Selim2011}. The Hamiltonian is used to construct the $\mathbf{E}$ matrix
which encodes the exchange flow of magnons in the stripes. It is found that the
allowed spin wave modes are the eigenvalues of the $\mathbf{E}$ matrix and
therefore it is used to study the effects of the stripe width, edge exchange,
the edge uniaxial anisotropy, and impurities on the allowed spin waves of
stripes. The obtained results almost coincide with the results of graphene
nanoribbons described by tight binding Hamiltonian for electronic excitations.
Therefore, we suggest the fabrication of the magnetic counterpart to graphene
as a new technology in the field of spintronic devices and magnetic
applications.


  We investigate one-loop renormalization group evolutions of extended sectors
of Yukawa type couplings. It is shown that Landau Poles which usually provide
necessary low energy upper bounds that saturate quickly with increasing initial
value conditions, lead in some cases to the opposite behaviour: some of the low
energy couplings decrease and become vanishingly small for increasingly large
initial conditions. We write down the general criteria for this to happen in
typical situations, highlighting a concept of {\sl repulsive} quasi-fixed
points, and illustrate the case both within a two-Yukawa toy model as well as
in the minimal supersymmetric standard model with R-parity violation. In the
latter case we consider the theoretical upper bounds on the various couplings,
identifying regimes where $\lambda_{kl3}, \lambda'_{kkk}, \lambda''_{3kl}$ are
dynamically suppressed due to the Landau Pole. We stress the importance of
considering a large number of couplings simultaneously. This leads altogether
to a phenomenologically interesting seesaw effect in the magnitudes of the
various R-parity violating couplings, complementing and in some cases improving
the existing limits.


  We present a dense model grid with tailored input chemical composition
appropriate for the Large Magellanic Cloud. We use a one-dimensional
hydrodynamic stellar evolution code, which accounts for rotation, transport of
angular momentum by magnetic fields, and stellar wind mass loss to compute our
detailed models. We calculate stellar evolution models with initial masses of
70-500 Msun and with initial surface rotational velocities of 0-550 km/s,
covering the core-hydrogen burning phase of evolution. We find our rapid
rotators to be strongly influenced by rotationally induced mixing of helium,
with quasi-chemically homogeneous evolution occurring for the fastest rotating
models. Above 160 Msun, homogeneous evolution is also established through mass
loss, producing pure helium stars at core hydrogen exhaustion independent of
the initial rotation rate. Surface nitrogen enrichment is also found for slower
rotators, even for stars that lose only a small fraction of their initial mass.
For models above 150 MZAMS, and for models in the whole considered mass range
later on, we find a considerable envelope inflation due to the proximity of
these models to their Eddington limit. This leads to a maximum zero-age main
sequence surface temperature of 56000 K, at 180 Msun, and to an evolution of
stars in the mass range 50-100 Msun to the regime of luminous blue variables in
the HR diagram with high internal Eddington factors. Inflation also leads to
decreasing surface temperatures during the chemically homogeneous evolution of
stars above 180 Msun. The cool surface temperatures due to the envelope
inflation in our models lead to an enhanced mass loss, which prevents stars at
LMC metallicity from evolving into pair-instability supernovae. The
corresponding spin-down will also prevent very massive LMC stars to produce
long-duration gamma-ray bursts, which might, however, originate from lower
masses.


  We consider two-hop S-R-D Gaussian networks with a source (S), a relay (R)
and a destination (D), some of which experience additive interference. This
additive interference, which renders the channels state-dependent, is either a)
experienced at the destination D and known non-causally at the source S, or b)
experienced at the relay R and known at the destination D. In both cases, one
would hope to exploit this knowledge of the channel state at some of the nodes
to obtain "clean" or interference-free channels, just as Costa's dirty-paper
coding does for one-hop channels with state non-causally known to the
transmitter. We demonstrate a scheme which achieves to within 0.5 bit of a
"clean" channel. This novel scheme is based on nested-lattice code and a
Decode-and-Forward (DF) relay. Intuitively, this strategy uses the structure
provided by nested lattice codes to cancel the "integer" (or lattice quantized)
part of the interference and treats the "residual" (or quantization noise) as
noise.


  The locality of a graph problem is the smallest distance $T$ such that each
node can choose its own part of the solution based on its radius-$T$
neighborhood. In many settings, a graph problem can be solved efficiently with
a distributed or parallel algorithm if and only if it has a small locality.
  In this work we seek to automate the study of solvability and locality: given
the description of a graph problem $\Pi$, we would like to determine if $\Pi$
is solvable and what is the asymptotic locality of $\Pi$ as a function of the
size of the graph. Put otherwise, we seek to automatically synthesize efficient
distributed and parallel algorithms for solving $\Pi$.
  We focus on locally checkable graph problems; these are problems in which a
solution is globally feasible if it looks feasible in all constant-radius
neighborhoods. Prior work on such problems has brought primarily bad news:
questions related to locality are undecidable in general, and even if we focus
on the case of labeled paths and cycles, determining locality is
$\mathsf{PSPACE}$-hard (Balliu et al., PODC 2019).
  We complement prior negative results with efficient algorithms for the cases
of unlabeled paths and cycles and, as an extension, for rooted trees. We
introduce a new automata-theoretic perspective for studying locally checkable
graph problems. We represent a locally checkable problem $\Pi$ as a
nondeterministic finite automaton $\mathcal{M}$ over a unary alphabet. We
identify polynomial-time-computable properties of the automaton $\mathcal{M}$
that near-completely capture the solvability and locality of $\Pi$ in cycles
and paths, with the exception of one specific case that is
$\mbox{co-$\mathsf{NP}$}$-complete.


  We present optical photometry and spectroscopy of the broad-lined Type Ic
supernova (SNIc-BL) PTF10qts, which was discovered as part of the Palomar
Transient Factory. The supernova was located in a dwarf galaxy of magnitude
$r=21.1$ at a redshift $z=0.0907$. We find that the $R$-band light curve is a
poor proxy for bolometric data and use photometric and spectroscopic data to
construct and constrain the bolometric light curve. The derived bolometric
magnitude at maximum light is $M_{\rm bol} = -18.51\pm0.2$ mag, comparable to
that of SN 1998bw ($M_{\rm bol} = -18.7$ mag) which was associated with a
gamma-ray burst (GRB). PTF10qts is one of the most luminous SNIc-BL observed
without an accompanying GRB. We estimate the physical parameters of the
explosion using data from our programme of follow-up observations, finding that
it produced a larger mass of radioactive nickel compared to other SNeIc-BL with
similar inferred ejecta masses and kinetic energies. The progenitor of the
event was likely a $\sim20$M$_{\odot}$ star.


  Tree amplitudes of 10D supersymmetric Yang-Mills theory (SYM) and 11D
supergravity (SUGRA) are collected in multi-particle counterparts of analytic
on-shell superfields. These have essentially the same form as their chiral 4D
counterparts describing ${\cal N}=4$ SYM and ${\cal N}=8$ SUGRA, but with
components dependent on a different set of bosonic variables. These are the
D=10 and D=11 spinor helicity variables, the set of which includes the spinor
frame variable (Lorentz harmonics) and a scalar density, and generalized
homogeneous coordinates of the coset $\frac{SO(D-2)}{SO(D-4)\otimes U(1)}$
(internal harmonics).
  We present an especially convenient parametrization of the spinor harmonics
(Lorentz covariant gauge fixed with the use of an auxiliary gauge symmetry) and
use this to find (a gauge fixed version of) the 3-point tree superamplitudes of
10D SYM and 11D SUGRA which generalize the 4 dimensional anti-MHV
superamplitudes.


  We analyse the B-R_c colors of galaxies as functions of luminosity and local
galaxy density using a large photometric redshift catalog based on the
Red-Sequence Cluster Survey. We select two samples of galaxies with a magnitude
limit of M_Rc<-18.5 and redshift ranges of 0.2<z< 0.4 and 0.4<z<0.6 containing
\~10^5 galaxies each. We model the color distributions of subsamples of
galaxies and derive the red galaxy fraction and peak colors of red and blue
galaxies as functions of galaxy luminosity and environment. The evolution of
these relationships over the redshift range of z~0.5 to z~0.05 is analysed in
combination with published results from the Sloan Digital Sky Survey. We find
that there is a strong evolution in the restframe peak color of bright blue
galaxies in that they become redder with decreasing redshift, while the colors
of faint blue galaxies remain approximately constant. This effect supports the
``downsizing'' scenario of star formation in galaxies. While the general
dependence of the galaxy color distributions on the environment is small, we
find that the change of red galaxy fraction with epoch is a function of the
local galaxy density, suggesting that the downsizing effect may operate with
different timescales in regions of different galaxy densities.


  In this work, we present an approach to supervisory reinforcement learning
control for unmanned aerial vehicles (UAVs). UAVs are dynamic systems where
control decisions in response to disturbances in the environment have to be
made in the order of milliseconds. We formulate a supervisory control
architecture that interleaves with extant embedded control and demonstrates
robustness to environmental disturbances in the form of adverse wind
conditions. We run case studies with a Tarot T-18 Octorotor to demonstrate the
effectiveness of our approach and compare it against a classic cascade control
architecture used in most vehicles. While the results show the performance
difference is marginal for nominal operations, substantial performance
improvement is obtained with the supervisory RL approach under unseen wind
conditions.


  We present our chemical abundance investigation of the metal-poor
([Fe/H]=-1.60 dex), r-process-enriched ([Eu/Fe]=0.73 dex) halo star HD 20 using
novel and archival high-resolution spectra at outstanding signal-to-noise
ratios. By combining one of the first asteroseismic gravity measurements in the
metal-poor regime from a TESS light curve with non-LTE analyses of iron lines,
we derive a set of highly accurate and precise stellar parameters. These allow
us to delineate a chemical pattern comprised of solid detections of 48
elements, including 28 neutron-capture elements, which establishes HD 20 among
the few benchmark stars that have almost complete patterns with low systematic
dependencies on the stellar parameters. Our light-element (Z<30) abundances are
representative of other, similarly metal-poor stars in the Galactic halo with
contributions from core-collapse supernovae of type II. A comparison to the
scaled solar r-pattern shows that the lighter neutron-capture elements
(37<Z<60) are poorly matched. In particular, we find imprints of the weak
r-process acting at low metallicities. Nonetheless, by comparing our detailed
abundances to the observed metal-poor star BD +17 3248, we find a persistent
residual pattern that is indicative of enrichment contributions from the
s-process. We show that mixing with material from predicted yields of massive,
rotating AGB stars at low metallicity considerably improves the fit. Based on a
solar ratio of heavy- to light-s elements -- at odds with model predictions for
the i-process -- and a missing clear residual pattern with respect to other
stars with claimed contributions from this process, we refute (strong)
contributions from such astrophysical sites providing intermediate neutron
densities. Finally, nuclear cosmochronology is used to tie our detection of the
radioactive element Th to an age estimate for HD 20 of $11.0\pm3.8$ Gyr.
[abridged]


  This work introduces Dareplane, a modular and broad technology agnostic open
source software platform for brain-computer interface research with an
application focus on adaptive deep brain stimulation (aDBS). While the search
for suitable biomarkers to inform aDBS has provided rich results over the last
two decades, development of control strategies is not progressing at the same
pace. One difficulty for investigating control approaches resides with the
complex setups required for aDBS experiments. The Dareplane platform supports
aDBS setups, and more generally brain computer interfaces, by providing a
modular, technology-agnostic, and easy-to-implement software platform to make
experimental setups more resilient and replicable. The key features of the
platform are presented and the composition of modules into a full experimental
setup is discussed in the context of a Python-based orchestration module. The
performance of a typical experimental setup on Dareplane for aDBS is evaluated
in three benchtop experiments, covering (a) an easy-to-replicate setup using an
Arduino microcontroller, (b) a setup with hardware of an implantable pulse
generator, and (c) a setup using an established and CE certified external
neurostimulator. Benchmark results are presented for individual processing
steps and full closed-loop processing. The results show that the
microcontroller setup in (a) provides timing comparable to the realistic setups
in (b) and (c). The Dareplane platform was successfully used in a total of 19
open-loop DBS sessions with externalized DBS and electrocorticography (ECoG)
leads. In addition, the full technical feasibility of the platform in the aDBS
context is demonstrated in a first closed-loop session with externalized leads
on a patient with Parkinson's disease receiving DBS treatment.