  Extending chip performance beyond current limits of miniaturisation requires
new materials and functionalities that integrate well with the silicon
platform. Germanium fits these requirements and has been proposed as a
high-mobility channel material,[1] a light emitting medium in
silicon-integrated lasers,[2,3] and a plasmonic conductor for bio-sensing.[4,5]
Common to these diverse applications is the need for homogeneous, high electron
densities in three-dimensions (3D). Here we use a bottom-up approach to
demonstrate the 3D assembly of atomically sharp doping profiles in germanium by
a repeated stacking of two-dimensional (2D) high-density phosphorus layers.
This produces high-density (10^19 to 10^20 cm-3) low-resistivity (10^-4 Ohmcm)
metallic germanium of precisely defined thickness, beyond the capabilities of
diffusion-based doping technologies.[6] We demonstrate that free electrons from
distinct 2D dopant layers coalesce into a homogeneous 3D conductor using
anisotropic quantum interference measurements, atom probe tomography, and
density functional theory.


  A theoretical study of the magnetization curves of quasiperiodic magnetic
multilayers is presented. We consider structures composed by ferromagnetic
films (Fe) with interfilm exchange coupling provided by intervening
nonferromagnetic layers (Cr). The theory is based on a realistic
phenomenological model, which includes the following contributions to the free
magnetic energy: Zeeman, cubic anisotropy, bilinear and biquadratic exchange
energies. The experimental parameters used here are based on experimental data
recently reported, which contain sufficiently strong biquadratic exchange
coupling.


  We study the exact solutions of quantum integrable model associated with the
$C_n$ Lie algebra, with either a periodic or an open one with off-diagonal
boundary reflections, by generalizing the nested off-diagonal Bethe ansatz
method. Taking the $C_3$ as an example we demonstrate how the generalized
method works. We give the fusion structures of the model and provide a way to
close fusion processes. Based on the resulted operator product identities among
fused transfer matrices and some necessary additional constraints such as
asymptotic behaviors and relations at some special points, we obtain the
eigenvalues of transfer matrices and parameterize them as homogeneous $T-Q$
relations in the periodic case or inhomogeneous ones in the open case. We also
give the exact solutions of the $C_n$ model with an off-diagonal open boundary
condition. The method and results in this paper can be generalized to other
high rank integrable models associated with other Lie algebras.


  We discuss the oscillation features of Beta Cephei, which is a magnetic star
in which the magnetic axis seems to be oblique to the rotation axis. We
interpret the observed equi-distant fine structures of the frequency spectrum
as a manifestation of a magnetic perturbation of an eigenmode, which would be a
radial mode in the absence of the magnetic field. Besides these frequency
components, we interpret another peak in the frequency spectrum as an
independent quadrupole mode. By this mode identification, we deduce the mass,
the evolutionary stage, the rotational frequency, the magnetic field strength,
and the geometrical configuration of Beta Cephei.


  Signal transduction networks can form highly interconnected systems within
cells due to network crosstalk, the sharing of input signals between multiple
downstream responses. To better understand the evolutionary design principles
underlying such networks, we study the evolution of crosstalk and the emergence
of specificity for two parallel signaling pathways that arise via gene
duplication and are subsequently allowed to diverge. We focus on a sequence
based evolutionary algorithm and evolve the network based on two physically
motivated fitness functions related to information transmission. Surprisingly,
we find that the two fitness functions lead to very different evolutionary
outcomes, one with a high degree of crosstalk and the other without.


  In this article, we prove that the complex convergence of the HCIZ free
energy is equivalent to the non-vanishing of the HCIZ integral in a
neighbourhood of $z=0$. Our approach is based on a combinatorial model for the
Maclaurin coefficients of the HCIZ integral together with classical
complex-analytic techniques.


  For nuclei near a maximum of the neutron strength function, the secular
dependence on energy E of s-wave partial neutron widths differs from the
canonical form given by the square root of E. We derive the universal form of
that dependence and show that it is expected to significantly influence the
analysis of neutron resonance data.


  Searchable encryption (SE) is a positive way to protect users sensitive data
in cloud computing setting, while preserving search ability on the server side,
i.e., it allows the server to search encrypted data without leaking information
about the plaintext data. In this paper, a multi-client universal circuit-based
full-blind quantum computation (FBQC) model is proposed. In order to meet the
requirements of multi-client accessing or computing encrypted cloud data, all
clients with limited quantum ability outsource the key generation to a trusted
key center and upload their encrypted data to the data center. Considering the
feasibility of physical implementation, all quantum gates in the circuit are
replaced with the combination of {\pi}/8 rotation operator set {Rz({\pi}/4),
Ry({\pi}/4), CRz({\pi}/4), CRy({\pi}/4), CCRz({\pi}/4), CCRy({\pi}/4)}. In
addition, the data center is only allowed to perform one {\pi}/8 rotation
operator each time, but does not know the structure of the circuit (i.e.,
quantum computation), so it can guarantee the blindness of computation. Then,
through combining this multi-client FBQC model and Grover searching algorithm,
we continue to propose a quantum searchable encryption scheme for cloud data.
It solves the problem of multi-client access mode under searchable encryption
in the cloud environment, and has the ability to resist against some quantum
attacks. To better demonstrate our scheme, an example of our scheme to search
on encrypted 2-qubit state is given in detail. Furthermore, the security of our
scheme is analysed from two aspects: external attacks and internal attacks, and
the result indicates that it can resist against such kinds of attacks and also
guarantee the blindness of data and computation.


  This paper presents an autonomous navigation framework for reaching a goal in
unknown 3D cluttered environments. The framework consists of three main
components. First, a computationally efficient method for mapping the
environment from the disparity measurements obtained from a depth sensor.
Second, a stochastic method to generate a path to a given goal, taking into
account field of view constraints on the space that is assumed to be safe for
navigation. Third, a fast method for the online generation of motion plans,
taking into account the robot's dynamic constraints, model, and environmental
uncertainty and disturbances. To highlight the contribution with respect to the
available literature, we provide a qualitative and quantitative comparison with
the state of the art methods for reaching a goal and for exploration in unknown
environments, showing the superior performance of our approach. To illustrate
the effectiveness of the proposed framework, we present experiments in multiple
indoors and outdoors environments running the algorithm fully on board and in
real-time, using a robotic platform based on the Intel Ready to Fly drone kit,
which represents the implementation in the most frugal platform for navigation
in unknown cluttered environments demonstrated to date. Open source code is
available at:~\url{https://github.com/IntelLabs/autonomousmavs}. The video of
the experimental results can be found at~\url{https://youtu.be/Wq0e7vF6nZM}.


  Quantification of cerebral white matter hyperintensities (WMH) of presumed
vascular origin is of key importance in many neurological research studies.
Currently, measurements are often still obtained from manual segmentations on
brain MR images, which is a laborious procedure. Automatic WMH segmentation
methods exist, but a standardized comparison of the performance of such methods
is lacking. We organized a scientific challenge, in which developers could
evaluate their method on a standardized multi-center/-scanner image dataset,
giving an objective comparison: the WMH Segmentation Challenge
(https://wmh.isi.uu.nl/).
  Sixty T1+FLAIR images from three MR scanners were released with manual WMH
segmentations for training. A test set of 110 images from five MR scanners was
used for evaluation. Segmentation methods had to be containerized and submitted
to the challenge organizers. Five evaluation metrics were used to rank the
methods: (1) Dice similarity coefficient, (2) modified Hausdorff distance (95th
percentile), (3) absolute log-transformed volume difference, (4) sensitivity
for detecting individual lesions, and (5) F1-score for individual lesions.
Additionally, methods were ranked on their inter-scanner robustness.
  Twenty participants submitted their method for evaluation. This paper
provides a detailed analysis of the results. In brief, there is a cluster of
four methods that rank significantly better than the other methods, with one
clear winner. The inter-scanner robustness ranking shows that not all methods
generalize to unseen scanners.
  The challenge remains open for future submissions and provides a public
platform for method evaluation.


  Tensor-Network (TN) states are efficient parametric representations of ground
states of local quantum Hamiltonians extensively used in numerical simulations.
Here we encode a TN ansatz state directly into a quantum simulator, which can
potentially offer an exponential advantage over purely numerical simulation. In
particular, we demonstrate the optimization of a quantum-encoded TN ansatz
state using a variational quantum eigensolver on an ion-trap quantum computer
by preparing the ground states of the extended Su-Schrieffer-Heeger model. The
generated states are characterized by estimating the topological invariants,
verifying their topological order. Our TN encoding as a trapped ion circuit
employs only single-site addressing optical pulses - the native operations
naturally available on the platform. We reduce nearest-neighbor crosstalk by
selecting different magnetic sublevels with well-separated transition
frequencies to encode even and odd qubits.


  Generating images from word descriptions is a challenging task. Generative
adversarial networks(GANs) are shown to be able to generate realistic images of
real-life objects. In this paper, we propose a new neural network architecture
of LSTM Conditional Generative Adversarial Networks to generate images of
real-life objects. Our proposed model is trained on the Oxford-102 Flowers and
Caltech-UCSD Birds-200-2011 datasets. We demonstrate that our proposed model
produces the better results surpassing other state-of-art approaches.


  Recently, Large Language Models (LLMs) have shown impressive language
capabilities. While most of the existing LLMs have very unbalanced performance
across different languages, multilingual alignment based on translation
parallel data is an effective method to enhance the LLMs' multilingual
capabilities. In this work, we discover and comprehensively investigate the
spontaneous multilingual alignment improvement of LLMs. We find that LLMs
instruction-tuned on the question translation data (i.e. without annotated
answers) are able to encourage the alignment between English and a wide range
of languages, even including those unseen during instruction-tuning.
Additionally, we utilize different settings and mechanistic interpretability
methods to analyze the LLM's performance in the multilingual scenario
comprehensively. Our work suggests that LLMs have enormous potential for
improving multilingual alignment efficiently with great language and task
generalization.


  We study inhomogeneous host-pathogen dynamics to model the global amphibian
population extinction in a lake basin system. The lake basin system is modeled
as quenched disorder. In this model we show that once the pathogen arrives at
the lake basin it spreads from one lake to another, eventually spreading to the
entire lake basin system in a wave like pattern. The extinction time has been
found to depend on the steady state host population and pathogen growth rate.
Linear estimate of the extinction time is computed. The steady state host
population shows a threshold behavior in the interaction strength for a given
growth rate.


  The XMM-RM project was designed to provide X-ray coverage of the Sloan
Digital Sky Survey Reverberation Mapping (SDSS-RM) field. 41 XMM-Newton
exposures, placed surrounding the Chandra AEGIS field, were taken, covering an
area of 6.13 deg^2 and reaching a nominal exposure depth of ~15 ks. We present
an X-ray catalog of 3553 sources detected in these data, using a PSF-fitting
algorithm and a sample selection threshold that produces a ~5% fraction of
spurious sources. In addition to the PSF-fitting likelihood, we calculate a
second source reliability measure based on Poisson theory using source and
background counts within an aperture. Using the Poissonian likelihood, we
select a sub-sample with a high purity and find that it has similar number
count profiles to previous X-ray surveys. The Bayesian method "NWAY" was
employed to identify counterparts of the X-ray sources from the optical Legacy
and the IR unWISE catalogs, using a 2-dimensional unWISE magnitude-color prior
created from optical/IR counterparts of Chandra X-ray sources. A significant
number of the optical/IR counterparts correspond to sources with low detection
likelihoods, proving the value of retaining the low-likelihood detections in
the catalog. 932 of the XMM-RM sources are covered by SDSS spectroscopic
observations. 89% of them are classified as AGN, and 71% of these AGN are in
the SDSS-RM quasar catalog. Among the SDSS-RM quasars, 80% are detectable at
the depth of the XMM observations.


  The security of real-world quantum key distribution (QKD) critically depends
on the number of data points the system can collect in a fixed time interval.
To date, state-of-the-art finite-key security analyses require block lengths in
the order of 1E4 bits to obtain positive secret keys. This requirement,
however, can be very difficult to achieve in practice, especially in the case
of entanglement-based satellite QKD systems, where the overall channel loss can
go up to 70 dB or more. Here, we provide an improved finite-key security
analysis which can reduce the block length requirement by 14% to 17% for
standard channel and protocol settings. In practical terms, this reduction
could save entanglement-based satellite QKD weeks of measurement time and
resources, thereby bringing space-based QKD technology closer to reality. As an
application, we use the improved analysis to show that the recently reported
Micius QKD satellite is capable of generating positive secret keys with a
$1E-5$ security level.


  The same concept can mean different things or be instantiated in different
forms depending on context, suggesting a degree of flexibility within the
conceptual system. We propose that a compositional network model can be used to
capture and predict this flexibility. We modeled individual concepts (e.g.,
BANANA, BOTTLE) as graph-theoretical networks, in which properties (e.g.,
YELLOW, SWEET) were represented as nodes and their associations as edges. In
this framework, networks capture the within-concept statistics that reflect how
properties correlate with each other across instances of a concept. We ran a
classification analysis using graph eigendecomposition to validate these
models, and find that these models can successfully discriminate between object
concepts. We then computed formal measures from these concept networks and
explored their relationship to conceptual structure. We find that diversity
coefficients and core-periphery structure can be interpreted as network-based
measures of conceptual flexibility and stability, respectively. These results
support the feasibility of a concept network framework and highlight its
ability to formally capture important characteristics of the conceptual system.


  We introduce the notion of a Galois extension of commutative S-algebras
(E_infty ring spectra), often localized with respect to a fixed homology
theory. There are numerous examples, including some involving Eilenberg-Mac
Lane spectra of commutative rings, real and complex topological K-theory,
Lubin-Tate spectra and cochain S-algebras. We establish the main theorem of
Galois theory in this generality. Its proof involves the notions of separable
and etale extensions of commutative S-algebras, and the Goerss-Hopkins-Miller
theory for E_infty mapping spaces. We show that the global sphere spectrum S is
separably closed, using Minkowski's discriminant theorem, and we estimate the
separable closure of its localization with respect to each of the Morava
K-theories. We also define Hopf-Galois extensions of commutative S-algebras,
and study the complex cobordism spectrum MU as a common integral model for all
of the local Lubin-Tate Galois extensions.


  The paper discusses the challenges of faceted vocabulary organization in
universal classifications which treat the universe of knowledge as a coherent
whole and in which the concepts and subjects in different disciplines are
shared, related and combined. The authors illustrate the challenges of the
facet analytical approach using, as an example, the revision of class 72 in
UDC. The paper reports on the research undertaken in 2013 as preparation for
the revision. This consisted of analysis of concept organization in the UDC
schedules in comparison with the Art & Architecture Thesaurus and class W of
the Bliss Bibliographic Classification. The paper illustrates how such research
can contribute to a better understanding of the field and may lead to
improvements in the facet structure of this segment of the UDC vocabulary.


  The timely transportation of goods to customers is an essential component of
economic activities. However, heavy-duty diesel trucks used for goods delivery
significantly contribute to greenhouse gas emissions within many large
metropolitan areas, including Los Angeles, New York, and San Francisco. To
reduce GHG emissions by facilitating freight electrification, this paper
proposes Joint Routing and Charging scheduling for electric trucks. The
objective of the associated optimization problem is to minimize the cost of
transportation, charging, and tardiness. A large number of possible
combinations of road segments as well as a large number of combinations of
charging decisions and charging durations leads to a combinatorial explosion in
the possible decisions electric trucks can make. The resulting mixed-integer
linear programming problem is thus extremely challenging because of the
combinatorial complexity even in the deterministic case. Therefore, a Surrogate
Level-Based Lagrangian Relaxation (SLBLR) method is employed to decompose the
overall problem into significantly less complex truck subproblems. In the
coordination aspect, each truck subproblem is solved independently of other
subproblems based on the values of Lagrangian multipliers. In addition to
serving as a means of guiding and coordinating trucks, multipliers can also
serve as a basis for transparent and explanatory decision-making by trucks.
Testing results demonstrate that even small instances cannot be solved using
the off-the-shelf solver CPLEX after several days of solving. The SLBLR method,
on the other hand, can obtain near-optimal solutions within a few minutes for
small cases, and within 30 minutes for large ones. Furthermore, it has been
demonstrated that as battery capacity increases, the total cost decreases
significantly; moreover, as the charging power increases, the number of trucks
required decreases as well.


  Dust determines the temperature structure of protoplanetary disks. However,
dust temperature determinations almost invariably rely on a complex modeling of
the Spectral Energy Distribution. We attempt a direct determination of the
temperature of large grains emitting at mm wavelengths.} We observe the edge-on
dust disk of the Flying Saucer, which appears in silhouette against the CO
J=2-1 emission from a background molecular cloud in $\rho$ Oph. The combination
of velocity gradients due to the Keplerian rotation of the disk and intensity
variations in the CO background as a function of velocity allows us to directly
measure the %absorbing dust temperature. The dust opacity can then be derived
from the emitted continuum radiation. The dust disk absorbs the radiation from
the CO clouds at several velocities. We derive very low dust temperatures, 5 to
7 K at radii around 100 au, which is much lower than most model predictions.
The dust optical depth is $> 0.2$ at 230 GHz, and the scale height at 100 au is
at least 8 au (best fit 13 au). However, the dust disk is very flat (flaring
index -0.35), which is indicative of dust settling in the outer parts.


  The effectiveness and validity of applying variation partitioning methods in
community ecology has been questioned. Here, using mathematical deduction and
numerical simulation, we made an attempt to uncover the underlying mechanisms
determining the effectiveness of variation partitioning techniques. The
covariance among independent variables determines the under-fitting and
over-fitting problem with the variation partitioning process. Ideally, it is
assumed that the covariance among independent variables will be zero (no
correlation at all), however, typically there will be some colinearities.
Therefore, we analyzed the role of slight covariance on influencing species
variation partitioning. We concluded that when the covariance between spatial
and environmental predictors is positive, all the three components-pure
environmental, spatial variations and mixed covariation were over-fitted, with
the sign of the true covariation being negative. In contrast, when the
covariance is negative, all the three components were under-fitted with the
sign of true covariation being positive. Other factors, including extra noise
levels, the strengths of variable coefficients and the patterns of landscape
gradients, could reduce the fitting problems caused by the covariance of
variables. The conventional calculation of mixed covariation is incorrect and
misleading, as the true and estimated covariations are always sign-opposite. In
conclusion, I challenge the conventional three-step procedure of variation
partitioning, suggesting that a full regression model with all variables
together is robust enough to correctly partition variations.


  We present the results of a multi-component synthetic spectral analysis of
the archival far ultraviolet spectra of several key nova-like variables
including members of the SW Sex, RW Tri, UX UMa and VY Scl subclasses: KR Aur,
RW Tri, V825 Her, V795 Her, BP Lyn, V425 Cas and HL Aqr. Accretion rates as
well as the possible flux contribution of the accreting white dwarf are
included in our analysis. Except for RW Tri which has a reliable trigonometric
parallax, we computed the distances to the nova-like systems using the method
of Knigge (2006). Our analysis of seven archival IUE spectra of RW Tri at its
parallax distance of 341 pc consistently indicates a low mass (0.4Msun) white
dwarf and an average accretion rate, 6.3 E-9Msun/yr. For KR Aur, we estimate
that the white dwarf has Teff=29,000K, log g = 8.4 and contributes 18% of the
FUV flux while an accretion disk with accretion rate of 3 E-10Msun/yr at an
inclination of 41 degrees, contributes the remainder. We find that an accretion
disk dominates the far UV spectrum of V425 Cas but a white dwarf contributes
non-negligibly with approximately 18% of the FUV flux. For the two high state
nova-likes, HL Aqr and V825 Her, their accretion disks totally dominate with 1
E-9Msun/yr and 3 E-9Msun/yr, respectively. For BP Lyn we find an accretion rate
of 1 E-8Msun/yr while for V795 Her, we find an accretion rate of 1 E-10Msun/yr.
We discuss the implications of our results for the evolutionary status of
nova-like variables.


  This paper presents a method for the automatic extraction of subgrammars to
control and speeding-up natural language generation NLG. The method is based on
explanation-based learning (EBL). The main advantage for the proposed new
method for NLG is that the complexity of the grammatical decision making
process during NLG can be vastly reduced, because the EBL method supports the
adaption of a NLG system to a particular use of a language.


  RSDs (Resistive AC-Coupled Silicon Detectors) are n-in-p silicon sensors
based on the LGAD (Low-Gain Avalanche Diode) technology, featuring a continuous
gain layer over the whole sensor area. The truly innovative feature of these
sensors is that the signal induced by an ionising particle is seen on several
pixels, allowing the use of reconstruction techniques that combine the
information from many read-out channels. In this contribution, the first
application of a machine learning technique to RSD devices is presented. The
spatial resolution of this technique is compared to that obtained with the
standard RSD reconstruction methods that use analytical descriptions of the
signal sharing mechanism. A Multi-Output regressor algorithm, trained with a
combination of simulated and real data, leads to a spatial resolution of less
than 2 $\mu m$ for a sensor with a 100 $\mu m$ pixel. The prospects of future
improvements are also discussed.


  We consider topological groupoids in finite and also in a compact settings.
In the initial sections, we introduce definitions of typical observables and we
studied them in the context of statistical mechanics and quantum mechanics. We
exhibit explicit examples and one of them will be the so-called quantum
ratchet. This is related to Schwinger's algebra of selective measurements. Here
we consider $\mathcal{G}$-kernels, transverse functions, modular functions, and
quasi-invariant measures for Haar systems. Later we present our main result
which is a version of Tannaka's theorem for Hausdorff compact groupoids -
extending the original proof of T. Tannaka.


  The Infra-Red Video Bolometer (IRVB) is a diagnostic equipped with an
infra-red camera that measures the total radiated power in thousands of LOSs
within a large field of view (FOV). Recently validated in MAST-U, it offers a
high spatial resolution map of the radiated power in the divertor region, where
large gradients are expected. The IRVB's sensing element comprises a thin layer
of high Z absorbing material, typically Platinum, usually coated with Carbon to
reduce reflections. It is here explored the possibility of using a relatively
inert material like Titanium, that can be produced in layers up to 1mum
compared to 2.5mum for Pt, and then coat it with Pt of the desired thickness
(0.3mum per side here) and Carbon. This leads to a higher temperature signal (2
to 3 times), and better spatial resolution (about 4 times), resulting in higher
accuracy in the measured power. This assembly is also expected to improve foil
uniformity, as the Pt layer is obtained via deposition rather than mechanical
processes. Given its multi-material composition, measuring the thermal
properties of the foil assembly is vital. Various methods using a calibrated
laser as a heat source have been developed, analysing the temperature profile
shape or fitting the calculated laser power for different intensities and
frequencies. It is here presented a simpler approach, that relies on analysing
the separate components of the foil heat equation for a single laser exposure
in a given area. This can then be iterated over the entire foil to capture
local deviations.


  We present the discovery and the very first analysis of four stellar systems
showing two periods of eclipses, that are the objects classified as doubly
eclipsing systems. Some of them were proved to orbit each other thanks to their
eclipse-timing-variations (ETVs) of both pairs, hence they really constitute
rare quadruples with two eclipsing pairs. Some of them do not, as we are still
waiting for more data to detect their mutual movement. Their light curves and
period changes were analysed. All of them are detached and near-contact, but
none of them contact; moreover, to our knowledge none of these stars can be
considered as blend of two spatially unresolved close components on the sky.
These systems are CzeV2647 (0.5723296 + 0.9637074 days), proved to orbit with
4.5-year periodicity; CzeV1645 (1.0944877 + 1.6594641 days), with a rather
questionable detection of ETV; CzeV3436 (0.6836870 + 0.3833930 days); and,
finally, OGLE SMC-ECL-1758 (0.9291925 + 3.7350826 days), proved to move on its
30-year orbit. Even more surprising is the fact that most of these systems show
the ratio of their two orbital periods close to coupling near some resonant
values of small integers, namely CzeV2647, with only 1% from 3:5 resonance,
CzeV1645 1% from 2:3 resonance, and OGLE SMC-ECL-1758 with only 0.49% from 1:4
resonance. The nature of these near-resonant states still remains a mystery.


  Galaxy-cluster merger shocks efficiently accelerate the ambient electrons
through diffusive shock acceleration and amplify magnetic field by compressing
the Inter Cluster Medium. As a result, such objects produce a significant
amount of synchrotron radio emission. Radio halo and Mpc scale peripheral radio
relics thus help us to trace back the cluster formation history. To study the
dynamical state of the galaxy clusters and their relation to the merging
scenario, as a pilot project, we thus observed four suitable candidates from
the MACS (Massive Cluster Survey) cluster sample. Observations were carried out
simultaneously at 610 and 235 MHz with the GMRT. We observed a rare phenomena
in the cluster MACSJ0014.3-3022, which hosts both a peripheral spectacular
radio relic and an unusually flat spectrum central giant radio halo of more
than 1.5 Mpc dimension. We also report that another cluster MACSJ0152.5-2852 is
possibly showing the sign of one of the earliest and young merging system
where, we saw a faint 0.5 Mpc radio relic at the cluster periphery.


  Since its discovery in the last century, quantum entanglement has challenged
some of our most cherished classical views, such as locality and reality.
Today, the second quantum revolution is in full swing and promises to
revolutionize areas such as computation, communication, metrology, and imaging.
Here, we review conceptual and experimental advances in complex entangled
systems involving many multilevel quantum particles. We provide an overview of
the latest technological developments in the generation and manipulation of
high-dimensionally entangled photonic systems encoded in various discrete
degrees of freedom such as path, transverse spatial modes or time/frequency
bins. This overview should help to transfer various physical principles for the
generation and manipulation from one to another degree of freedom and thus
inspire new technical developments. We also show how purely academic questions
and curiosity led to new technological applications. Here fundamental research
provides the necessary knowledge for coming technologies such as a prospective
quantum internet or the quantum teleportation of all information stored in a
quantum system. Finally, we discuss some important problems in the area of
high-dimensional entanglement and give a brief outlook on possible future
developments.


  We consider variations of coupling strengths and mass ratios in and beyond
the Standard Model, in the light of various mechanisms of mass generation. In
four-dimensional unified models, heavy quark and superparticle thresholds and
the electron mass can completely alter the (testable) relation between Delta ln
alpha and Delta ln mu, where mu \equiv m_p/m_e. In extra-dimensional models
where a compactification scale below the fundamental scale is varying, definite
predictions may result even without unification; we examine some models with
Scherk-Schwarz supersymmetry-breaking.


  The maximum cut problem for a quintic del Pezzo surface ${\rm
Bl}_{4}(\mathbb{P}^2)$ asks: Among all partitions of the 10 exceptional curves
into two disjoint sets, what is the largest possible number of pairwise
intersections? In this article we show that the answer is twelve. More
generally, we obtain bounds for the maximum cut problem for the minuscule
varieties $X_{a,b,c}:={\rm Bl}_{b+c}(\mathbb{P}^{c-1})^{a-1}$ studied by Mukai
and Castravet-Tevelev and show that these bounds are asymptotically sharp for
infinite families. We prove our results by constructing embeddings of the
classes of $(-1)$-divisors on these varieties which are optimal for the
semidefinite relaxation of the maximum cut problem on graphs proposed by
Goemans and Williamson. These results give a new optimality property of the
Weyl orbits of root systems of type $A$,$D$ and $E$.


  Despite its relevance in numerous natural and industrial processes, the
solubility of molecular oxygen has never been directly measured in capillary
condensed liquid water. In this article, we measure oxygen solubility in liquid
water trapped within nanoporous samples, in metastable equilibrium with a
subsaturated vapor. We show that solubility increases two-fold at moderate
subsaturations (RH ~ 0.55). This evolution with relative humidity is in good
agreement with a simple thermodynamic prediction using properties of bulk
water, previously verified experimentally at positive pressure. Our measurement
thus verifies the validity of this macroscopic thermodynamic theory to strong
confinement and large negative pressures, where ignificant non-idealities are
expected. This effect has strong implications for important oxygen-dependent
chemistries in natural and technological contexts.


  We consider an infinite-dimensional system of stochastic differential
equations describing the evolution of type frequencies in a large population.
The type of an individual is the number of deleterious mutations it carries,
where fitness of individuals carrying k mutations is decreased by \alpha k for
some \alpha>0. Along the individual lines of descent, new mutations accumulate
at rate \lambda per generation, and each of these mutations has a probability
\gamma per generation to disappear. While the case \gamma=0 is known as (the
Fleming-Viot version of) Muller's ratchet, the case \gamma>0 is associated with
compensatory mutations in the biological literature. We show that the system
has a unique weak solution. In the absence of random fluctuations in type
frequencies (i.e., for the so-called infinite population limit) we obtain the
solution in a closed form by analyzing a probabilistic particle system and show
that for \gamma>0, the unique equilibrium state is the Poisson distribution
with parameter \lambda/(\gamma+\alpha).


  A new hybrid scheme for numerical relativity will be presented. The scheme
will employ a 3-dimensional spacelike lattice to record the 3-metric while
using the standard 3+1 ADM equations to evolve the lattice. Each time step will
involve three basic steps. First, the coordinate quantities such as the Riemann
and extrinsic curvatures are extracted from the lattice. Second, the 3+1 ADM
equations are used to evolve the coordinate data, and finally, the coordinate
data is used to update the scalar data on the lattice (such as the leg
lengths). The scheme will be presented only for the case of vacuum spacetime
though there is no reason why it could not be extended to non-vacuum
spacetimes. The scheme allows any choice for the lapse function and shift
vectors. An example for the Kasner $T^3$ cosmology will be presented and it
will be shown that the method has, for this simple example, zero discretisation
error.


  We consider many-point correlation functions of discrete fermions in the
two-dimensional FK-Ising model and show that, despite not being commuting
observable, they can be realized with a geometric-probabilistic approach in
terms of loops of the model and their winding.


  A quantum measurement scheme is suggested in two resonant models of quantum
electrodynamics. The first model is the brain, where, for the propagation of
its action potentials, the free electron laser-like coherence mechanism
recently investigated by the author is comprehensively applied. The second
model is an assembly of Preparata et al.'s coherence domains, in which we
incorporate the quantum field theory of memory advocated by Umezawa et al.
These two models are remarkably analogous.


  We study the collapse of pebble clouds with a statistical model to find the
internal structure of comet-sized planetesimals. Pebble-pebble collisions occur
during the collapse and the outcome of these collisions affect the resulting
structure of the planetesimal. We expand our previous models by allowing the
individual pebble sub-clouds to contract at different rates and by including
the effect of gas drag on the contraction speed and in energy dissipation. Our
results yield comets that are porous pebble-piles with particle sizes varying
with depth. In the surface layers there is a mixture of primordial pebbles and
pebble fragments. The interior, on the other hand, consists only of primordial
pebbles with a narrower size distribution, yielding higher porosity there. Our
results imply that the gas in the protoplanetary disc plays an important role
in determining the radial distribution of pebble sizes and porosity inside
planetesimals.


  We study stability properties of $f$-minimal hypersurfaces isometrically
immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature
under volume growth conditions. Moreover, exploiting a weighted version of a
finiteness result and the adaptation to this setting of Li-Tam theory, we
investigate the topology at infinity of $f$-minimal hypersurfaces. On the way,
we prove a new comparison result in weighted geometry and we provide a general
weighted $L^1$-Sobolev inequality for hypersurfaces in Cartan-Hadamard weighted
manifolds, satisfying suitable restrictions on the weight function.


  We present a polymer quantization of the -lambda/r^2 potential on the
positive real line and compute numerically the bound state eigenenergies in
terms of the dimensionless coupling constant lambda. The singularity at the
origin is handled in two ways: first, by regularizing the potential and
adopting either symmetric or antisymmetric boundary conditions; second, by
keeping the potential unregularized but allowing the singularity to be balanced
by an antisymmetric boundary condition. The results are compared to the
semiclassical limit of the polymer theory and to the conventional Schrodinger
quantization on L_2(R_+). The various quantization schemes are in excellent
agreement for the highly excited states but differ for the low-lying states,
and the polymer spectrum is bounded below even when the Schrodinger spectrum is
not. We find as expected that for the antisymmetric boundary condition the
regularization of the potential is redundant: the polymer quantum theory is
well defined even with the unregularized potential and the regularization of
the potential does not significantly affect the spectrum.


  The normal modes of a three-dimensional Yukawa plasma in an isotropic,
harmonic confinement are investigated by solving the linearized cold fluid
equations. The eigenmodes are found analytically and expressed in terms of
hypergeometric functions. It is found that the mode frequencies solely depend
on the dimensionless plasma parameter $\xi=\kappa R$, where $R$ is the plasma
radius and $\kappa$ the inverse screening length. The eigenfrequencies increase
monotonically with $\xi$ and saturate in the limit $\xi\to\infty$. Compared
with the results in the Coulomb limit~[D. H. E. Dubin, Phys. Rev. Lett.
\textbf{66}, 2076 (1991)], we find a new class of modes characterized by the
number $n$ which determines the number of radial nodes in the perturbed
potential. These modes originate from the degenerate bulk modes of the Coulomb
system. Analytical formulas for the eigenfrequencies are derived for limiting
cases.


  A hybrid metal-graphene metamaterial (MM) is reported to achieve the active
control of the broadband plasmon-induced transparency (PIT) in THz region. The
unit cell consists of one cut wire (CW), four U-shape resonators (USRs) and
monolayer graphene sheets under the USRs. Via near-field coupling, broadband
PIT can be produced through the interference between different modes. Based on
different arrangements of graphene positions, not only can we achieve
electrically switching the amplitude of broadband PIT, but also can realize
modulating the bandwidth of the transparent window. Simultaneously, both the
capability and region of slow light can be dynamically tunable. This work
provides schemes to manipulate PIT with more degrees of freedom, which will
find significant applications in multifunctional THz modulation.


  In this work, we introduce the Kaiser-Bessel interpolation basis for the
particle-mesh interpolation in the fast Ewald method. A reliable a priori error
estimate is developed to measure the accuracy of the force computation in
correlated charge systems, and is shown to be effective in optimizing the shape
parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the
optimized Kaiser-Bessel basis with the traditional B-spline basis, we
demonstrate that the former is more accurate than the latter in part of the
working parameter space, saying a relatively small real space cutoff, a
relatively small reciprocal space mesh and a relatively large truncation of
basis. In some cases, the Kaiser-Bessel basis is found to be more than one
order of magnitude more accurate.


  Top quark and Higgs boson decays induced by flavor-changing neutra currents
(FCNC) are very much suppressed in the Standard Model (SM). Their detection in
colliders like the Large Hadron Collider (LHC), Next Linear Collider (NLC) or
Tevatron would be a signal of new physics. We evaluate the FCNC decays t \to
H^0 + c, t \to Z + c, and H^0 \to t + {\bar c} in the context of Alternative
Left-Right symmetric Models (ALRM) with extra isosinglet heavy fermions; in
this case, FCNC decays occurs at tree-level and they are only suppressed by the
mixing between ordinary top and charm quarks, which is poorly constraint by
current experimental values. This provides the possibility for future
colliders, either to detect new physics, or to improve present bounds on the
parameters of the model.


  Deep neural networks produce state-of-the-art results when trained on a large
number of labeled examples but tend to overfit when small amounts of labeled
examples are used for training. Creating a large number of labeled examples
requires considerable resources, time, and effort. If labeling new data is not
feasible, so-called semi-supervised learning can achieve better generalisation
than purely supervised learning by employing unlabeled instances as well as
labeled ones. The work presented in this paper is motivated by the observation
that transfer learning provides the opportunity to potentially further improve
performance by exploiting models pretrained on a similar domain. More
specifically, we explore the use of transfer learning when performing
semi-supervised learning using self-learning. The main contribution is an
empirical evaluation of transfer learning using different combinations of
similarity metric learning methods and label propagation algorithms in
semi-supervised learning. We find that transfer learning always substantially
improves the model's accuracy when few labeled examples are available,
regardless of the type of loss used for training the neural network. This
finding is obtained by performing extensive experiments on the SVHN, CIFAR10,
and Plant Village image classification datasets and applying pretrained weights
from Imagenet for transfer learning.


  Zoonosis refers to the transmission of infectious diseases from animal to
human. The increasing number of zoonosis incidence makes the great losses to
lives, including humans and animals, and also the impact in social economic. It
motivates development of a system that can predict the future number of
zoonosis occurrences in human. This paper analyses and presents the use of
Seasonal Autoregressive Integrated Moving Average (SARIMA) method for
developing a forecasting model that able to support and provide prediction
number of zoonosis human incidence. The dataset for model development was
collected on a time series data of human tuberculosis occurrences in United
States which comprises of fourteen years of monthly data obtained from a study
published by Centers for Disease Control and Prevention (CDC). Several trial
models of SARIMA were compared to obtain the most appropriate model. Then,
diagnostic tests were used to determine model validity. The result showed that
the SARIMA(9,0,14)(12,1,24)12 is the fittest model. While in the measure of
accuracy, the selected model achieved 0.062 of Theils U value. It implied that
the model was highly accurate and a close fit. It was also indicated the
capability of final model to closely represent and made prediction based on the
tuberculosis historical dataset.


  Current diffusion or flow-based generative models for 3D shapes divide to
two: distilling pre-trained 2D image diffusion models, and training directly on
3D shapes. When training a diffusion or flow models on 3D shapes a crucial
design choice is the shape representation. An effective shape representation
needs to adhere three design principles: it should allow an efficient
conversion of large 3D datasets to the representation form; it should provide a
good tradeoff of approximation power versus number of parameters; and it should
have a simple tensorial form that is compatible with existing powerful neural
architectures. While standard 3D shape representations such as volumetric grids
and point clouds do not adhere to all these principles simultaneously, we
advocate in this paper a new representation that does. We introduce Mosaic-SDF
(M-SDF): a simple 3D shape representation that approximates the Signed Distance
Function (SDF) of a given shape by using a set of local grids spread near the
shape's boundary. The M-SDF representation is fast to compute for each shape
individually making it readily parallelizable; it is parameter efficient as it
only covers the space around the shape's boundary; and it has a simple matrix
form, compatible with Transformer-based architectures. We demonstrate the
efficacy of the M-SDF representation by using it to train a 3D generative flow
model including class-conditioned generation with the 3D Warehouse dataset, and
text-to-3D generation using a dataset of about 600k caption-shape pairs.


  Consider two-type linear-fractional branching processes in varying
environments with asymptotically constant mean matrices. Let $\nu$ be the
extinction time. Under certain conditions, we show that both $P(\nu=n)$ and
$P(\nu>n)$ are asymptotically the same as some functions of the products of
spectral radii of the mean matrices. We also give an example for which
$P(\nu=n)$ decays with various speeds such as $\frac{c}{n(\log n)^2},$
$\frac{c}{n^\beta},\beta >1$ et al. which are very different from the ones of
homogeneous multitype Galton-Watson processes.


  This technical report describes a new prototype architecture designed to
integrate top-down and bottom-up analysis of non-standard linguistic input,
where a semantic model of the context of an utterance is used to guide the
analysis of the non-standard surface forms, including their automated
normalization in context. While the architecture is generally applicable, as a
concrete use case of the architecture we target the generation of
semantically-informed target hypotheses for answers written by German learners
in response to reading comprehension questions, where the reading context and
possible target answers are given.
  The architecture integrates existing NLP components to produce candidate
analyses on eight levels of linguistic modeling, all of which are broken down
into atomic statements and connected into a large graphical model using
Probabilistic Soft Logic (PSL) as a framework. Maximum a posteriori inference
on the resulting graphical model then assigns a belief distribution to
candidate target hypotheses. The current version of the architecture builds on
Universal Dependencies (UD) as its representation formalism on the form level
and on Abstract Meaning Representations (AMRs) to represent semantic analyses
of learner answers and the context information provided by the target answers.
These general choices will make it comparatively straightforward to apply the
architecture to other tasks and other languages.


  We give several characterizations of holomorphic mean Besov-Lipschitz space
on the unit ball in $\cn $ and appropriate Besov-Lipschitz space and prove the
equivalences between them. Equivalent norms on the mean Besov-Lipschitz space
involve different types of $L^p$-moduli of continuity, while in
characterizations of Besov-Lipschitz space we use not only the radial
derivative but also the gradient and the tangential derivatives. The
characterization in terms of the best approximation by polynomials is also
given.


  In this paper, the extremal graph with the maximum RRD-value among all the
graphs of order n with given cut vertices or edges is characterized. In
addition, an upper bounds on the reciprocal degree distance in terms of the
number of cut edges is provided.


  Despite the recent advances in unified image segmentation (IS), developing a
unified video segmentation (VS) model remains a challenge. This is mainly
because generic category-specified VS tasks need to detect all objects and
track them across consecutive frames, while prompt-guided VS tasks require
re-identifying the target with visual/text prompts throughout the entire video,
making it hard to handle the different tasks with the same architecture. We
make an attempt to address these issues and present a novel unified VS
architecture, namely UniVS, by using prompts as queries. UniVS averages the
prompt features of the target from previous frames as its initial query to
explicitly decode masks, and introduces a target-wise prompt cross-attention
layer in the mask decoder to integrate prompt features in the memory pool. By
taking the predicted masks of entities from previous frames as their visual
prompts, UniVS converts different VS tasks into prompt-guided target
segmentation, eliminating the heuristic inter-frame matching process. Our
framework not only unifies the different VS tasks but also naturally achieves
universal training and testing, ensuring robust performance across different
scenarios. UniVS shows a commendable balance between performance and
universality on 10 challenging VS benchmarks, covering video instance,
semantic, panoptic, object, and referring segmentation tasks. Code can be found
at \url{https://github.com/MinghanLi/UniVS}.


  Graphical models in probability and statistics are a core concept in the area
of probabilistic reasoning and probabilistic programming-graphical models
include Bayesian networks and factor graphs. In this paper we develop a new
model of mixed (nondeterministic/probabilistic) automata that subsumes both
nondeterministic automata and graphical probabilistic models. Mixed Automata
are equipped with parallel composition, simulation relation, and support
message passing algorithms inherited from graphical probabilistic models.
Segala's Probabilistic Automatacan be mapped to Mixed Automata.


  The excellent capabilities of the ALICE experiment for particle
identification allow to measure the identified hadron production in a wide
range of transverse momentum. In this work we present some results on
identified particle spectra, strange particle production and particle contents
measured in pp collisions at \sqrt{s} = 0.9, 2.76 and 7 TeV. The results are
compared with Monte Carlo event generators predictions.


  The so called one-parameter (often called $\varkappa$) deformed $AdS$ string
sigma models have attracted a lot of attention lately in the study of
integrability in string theory. We construct various circular string solutions
in the $(AdS_3 \times S^3)_{\varkappa}$ background and describe the
characteristics of such solutions qualitatively. We study the Bohr-Sommerfeld
like quantization for these string states to characterise the motion. Further
we find a `long' string limit of such circular strings in the
$\varkappa$-deformed $AdS_3$ and find a novel dependence of the oscillation
number on the energy in the next to leading order expansion.


  We present a detailed numerical study of the orthogonality catastrophe
exponent for a one-dimensional lattice model of spinless fermions with nearest
neighbor interaction using the density matrix remormalization group algorithm.
Keeping up to 1200 states per block we achieve a very great accuracy for the
overlap which is needed to extract the orthogonality exponent reliably. We
discuss the behavior of the exponent for three different kinds of a localized
impurity. For comparison we also discuss the non-interacting case. In the weak
impurity limit our results for the overlap confirm scaling behavior expected
from perturbation theory and renormalization group calculations. In particular
we find that a weak backward scattering component of the orthogonality exponent
scales to zero for attractive interaction. In the strong impurity limit and for
repulsive interaction we demonstrate that the orthogonality exponent cannot be
extracted from the overlap for systems with up to 100 sites, due to finite size
effects. This is in contradiction to an earlier interpretation given by Qin et
al. based on numerical data for much smaller system sizes. Neverthless we find
indirect evidence that the backward scattering contribution to the exponent
scales to 1/16 based on predictions of boundary conformal field theory.


  In this work, we instantiate a regularized form of the gradient clipping
algorithm and prove that it can converge to the global minima of deep neural
network loss functions provided that the net is of sufficient width. We present
empirical evidence that our theoretically founded regularized gradient clipping
algorithm is also competitive with the state-of-the-art deep-learning
heuristics. Hence the algorithm presented here constitutes a new approach to
rigorous deep learning.
  The modification we do to standard gradient clipping is designed to leverage
the PL* condition, a variant of the Polyak-Lojasiewicz inequality which was
recently proven to be true for various neural networks for any depth within a
neighborhood of the initialisation.


  Large language models show a surprising in-context learning ability -- being
able to use a prompt to form a prediction for a query, yet without additional
training, in stark contrast to old-fashioned supervised learning. Providing a
mechanistic interpretation and linking the empirical phenomenon to physics are
thus challenging and remain unsolved. We study a simple yet expressive
transformer with linear attention, and map this structure to a spin glass model
with real-valued spins, where the couplings and fields explain the intrinsic
disorder in data. The spin glass model explains how the weight parameters
interact with each other during pre-training, and most importantly why an
unseen function can be predicted by providing only a prompt yet without
training. Our theory reveals that for single instance learning, increasing the
task diversity leads to the emergence of the in-context learning, by allowing
the Boltzmann distribution to converge to a unique correct solution of weight
parameters. Therefore the pre-trained transformer displays a prediction power
in a novel prompt setting. The proposed spin glass model thus establishes a
foundation to understand the empirical success of large language models.


  Velocity distribution functions (VDFs) that exhibit a power-law dependence on
the high-energy tail have been the subject of intense research by the plasma
physics community. Such functions, known as kappa or superthermal
distributions, have been found to provide a better fitting to the VDFs measured
by spacecraft in the solar wind. One of the problems that is being addressed on
this new light is the temperature anisotropy of solar wind protons and
electrons. In the literature, the general treatment for waves excited by
(bi-)Maxwellian plasmas is well-established. However, for kappa distributions,
the wave characteristics have been studied mostly for the limiting cases of
purely parallel or perpendicular propagation, relative to the ambient magnetic
field. Contributions to the general case of obliquely-propagating
electromagnetic waves have been scarcely reported so far. The absence of a
general treatment prevents a complete analysis of the wave-particle interaction
in kappa plasmas, since some instabilities can operate simultaneously both in
the parallel and oblique directions. In a recent work, Gaelzer and Ziebell [J.
Geophys. Res. 119, 9334 (2014)] obtained expressions for the dielectric tensor
and dispersion relations for the low-frequency, quasi-perpendicular dispersive
Alfv\'en waves resulting from a kappa VDF. In the present work, the formalism
introduced by Ref. 1 is generalized for the general case of electrostatic
and/or electromagnetic waves propagating in a kappa plasma in any frequency
range and for arbitrary angles. An isotropic distribution is considered, but
the methods used here can be easily applied to more general anisotropic
distributions, such as the bi-kappa or product-bi-kappa.


  Despite the success of diffusion models (DMs), we still lack a thorough
understanding of their latent space. To understand the latent space
$\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective.
Our approach involves deriving the local latent basis within $\mathcal{X}$ by
leveraging the pullback metric associated with their encoding feature maps.
Remarkably, our discovered local latent basis enables image editing
capabilities by moving $\mathbf{x}_t$, the latent space of DMs, along the basis
vector at specific timesteps. We further analyze how the geometric structure of
DMs evolves over diffusion timesteps and differs across different text
conditions. This confirms the known phenomenon of coarse-to-fine generation, as
well as reveals novel insights such as the discrepancy between $\mathbf{x}_t$
across timesteps, the effect of dataset complexity, and the time-varying
influence of text prompts. To the best of our knowledge, this paper is the
first to present image editing through $\mathbf{x}$-space traversal, editing
only once at specific timestep $t$ without any additional training, and
providing thorough analyses of the latent structure of DMs. The code to
reproduce our experiments can be found at
https://github.com/enkeejunior1/Diffusion-Pullback.


  Understanding the influence that copper substrate surface symmetry and oxygen
impurities have on the growth of graphene by chemical vapor deposition is
important for developing techniques for producing high quality graphene.
Therefore, we have studied the growth of graphene by catalytic decomposition of
ethylene in an ultra-high vacuum chamber on both a clean Cu(100) surface and a
Cu(100) surface pre-dosed with a layer of chemisorbed oxygen. The crystal
structure of the graphene films was characterized with \emph{in-situ} low
energy electron diffraction. By heating the clean Cu(100) substrate from room
temperature to the growth temperature in ethylene, epitaxial graphene films
were formed. The crystal quality was found to depend strongly on the growth
temperature. At 900 $^\circ$C, well-ordered two-domain graphene films were
formed. Pre-dosing the Cu(100) surface with a chemisorbed layer of oxygen
before graphene growth was found to adversely affect the crystal quality of the
graphene overlayer by inducing a much higher degree of rotational disorder of
the graphene grains with respect to the Cu(100) substrate. The growth
morphology of the graphene islands during the initial stages of nucleation was
monitored with \emph{ex-situ} scanning electron microscopy. The nucleation rate
of the graphene islands was observed to drop by an order of magnitude by
pre-dosing the Cu(100) surface with a chemisorbed oxygen layer before growth.
This reduction in nucleation rate results in the formation of much larger
graphene islands. Therefore, the presence of oxygen during graphene growth
affects both the relative orientation and average size of grains within the
films grown on Cu(100) substrates.


  The presence of polarization splitting of exciton-polariton branches in
planar semiconductor microcavities has a pronounced effect on vortices in
polariton condensates. We show that the TE-TM splitting leads to the coupling
between the left and right half-vortices (vortices in the right and left
circular components of the condensate), that otherwise do not interact. We
analyze also the effect of linear polarization pinning resulted from a fixed
splitting between two perpendicular linear polarizations. In this case,
half-vortices acquire strings (solitons) attached to them. The half-vortices
with strings can be detected by observing the interference fringes of light
emitted from the cavity in two circular polarizations. The string affects the
fringes in both polarizations. Namely, the half-vortex is characterized by an
asymmetric fork-like dislocation in one circular polarization; the fringes in
the other circular polarization are continuous, but they are shifted by
crossing the string.


  This note states a simple property of optimality of the Bayes-Kelly algorithm
for conformal testing and poses a related open problem.


  The stability of planets in the alpha-Centauri AB stellar system has been
studied extensively. However, most studies either focus on the orbital plane of
the binary or consider inclined circular orbits.
  Here, we numerically investigate the stability of a possible planet in the
alpha-Centauri AB binary system for S-type orbits in an arbitrary spatial
configuration. In particular, we focus on inclined orbits and explore the
stability for different eccentricities and orientation angles.
  We show that large stable and regular regions are present for very eccentric
and inclined orbits, corresponding to libration in the Lidov-Kozai resonance.
We additionally show that these extreme orbits can survive over the age of the
system, despite the effect of tides. Our results remain qualitatively the same
for any compact binary system.


  This paper presents results concerning bifurcations of 2D piecewise-smooth
vector fields. In particular, the generic unfoldings of codimension three
fold-addle singularities of Filippov systems, where a boundary-saddle and a
fold coincide, are considered and the bifurcation diagrams exhibited.


  Driven by significant improvements in architectural design and training
pipelines, computer vision has recently experienced dramatic progress in terms
of accuracy on classic benchmarks such as ImageNet. These highly-accurate
models are challenging to deploy, as they appear harder to compress using
standard techniques such as pruning. We address this issue by introducing the
Correlation Aware Pruner (CAP), a new unstructured pruning framework which
significantly pushes the compressibility limits for state-of-the-art
architectures. Our method is based on two technical advancements: a new
theoretically-justified pruner, which can handle complex weight correlations
accurately and efficiently during the pruning process itself, and an efficient
finetuning procedure for post-compression recovery. We validate our approach
via extensive experiments on several modern vision models such as Vision
Transformers (ViT), modern CNNs, and ViT-CNN hybrids, showing for the first
time that these can be pruned to high sparsity levels (e.g. $\geq 75$%) with
low impact on accuracy ($\leq 1$% relative drop). Our approach is also
compatible with structured pruning and quantization, and can lead to practical
speedups of 1.5 to 2.4x without accuracy loss. To further showcase CAP's
accuracy and scalability, we use it to show for the first time that
extremely-accurate large vision models, trained via self-supervised techniques,
can also be pruned to moderate sparsities, with negligible accuracy loss.


  Rare information on photodisintegration reactions of nuclei with mass numbers
$A \approx 160$ at astrophysical conditions impedes our understanding of the
origin of $p$-nuclei. Experimental determination of the key ($p,\gamma$) cross
sections has been playing an important role to verify nuclear reaction models
and to provide rates of relevant ($\gamma,p$) reactions in $\gamma$-process. In
this paper we report the first cross section measurements of
$^{160}$Dy($p,\gamma$)$^{161}$Ho and $^{161}$Dy($p,n$)$^{161}$Ho in the beam
energy range of 3.4 - 7.0 MeV, partially covering the Gamow window. Such
determinations are possible by using two targets with various isotopic
fractions. The cross section data can put a strong constraint on the nuclear
level densities and gamma strength functions for $A \approx$ 160 in the
Hauser-Feshbach statistical model. Furthermore, we find the best parameters for
TALYS that reproduce the A $\thicksim$ 160 data available,
$^{160}$Dy($p,\gamma$)$^{161}$Ho and $^{162}$Er($p,\gamma$)$^{163}$Tm, and
recommend the constrained $^{161}$Ho($\gamma,p$)$^{160}$Dy reaction rates over
a wide temperature range for $\gamma$-process network calculations. Although
the determined $^{161}$Ho($\gamma$, p) stellar reaction rates at the
temperature of 1 to 2 GK can differ by up to one order of magnitude from the
NON-SMOKER predictions, it has a minor effect on the yields of $^{160}$Dy and
accordingly the $p$-nuclei, $^{156,158}$Dy. A sensitivity study confirms that
the cross section of $^{160}$Dy($p$, $\gamma$)$^{161}$Ho is measured precisely
enough to predict yields of $p$-nuclei in the $\gamma$-process.


  This paper is devoted to studying the weak convergence for a slow-fast system
with jumps modulated by Markovian switching regimes with the martingale method.
However, due to the coexistence of fast component and Markovian switching
regimes, the martingale method and perturbed test functions can not be applied
directly. In this situation, a combination of perturbed test functions and the
time discretization is applied efficiently. And the choice of appropriate
perturbed test functions, which are related to the averaged coefficients, plays
a decisive role. Our results also cover the case of slow-fast system without
Markovian switching regimes. Finally, some examples are presented,and numerical
simulations are carried out to observe a good agreement.


  In this new era of "big data", traditional DBMSs are under attack from two
sides. At one end of the spectrum, the use of document store NoSQL systems
(e.g. MongoDB) threatens to move modern Web 2.0 applications away from
traditional RDBMSs. At the other end of the spectrum, big data DSS analytics
that used to be the domain of parallel RDBMSs is now under attack by another
class of NoSQL data analytics systems, such as Hive on Hadoop. So, are the
traditional RDBMSs, aka "big elephants", doomed as they are challenged from
both ends of this "big data" spectrum? In this paper, we compare one
representative NoSQL system from each end of this spectrum with SQL Server, and
analyze the performance and scalability aspects of each of these approaches
(NoSQL vs. SQL) on two workloads (decision support analysis and interactive
data-serving) that represent the two ends of the application spectrum. We
present insights from this evaluation and speculate on potential trends for the
future.


  It has been the dominant view for over two decades that all waves are
localized in two dimensions for any given amount of disorder. Here, I would
like to raise questions about this assertion. The discussion leads to the
conclusion that there is a lack of the conclusive and definite support of the
claim. Rather, the recent evidence tends to indicate that waves are not
necessarily always localized in two dimensional random systems. Reasons are
elaborated.


  Conjecture F from [VW12] states that the complements of closures of certain
strata of the symmetric power of a smooth irreducible complex variety exhibit
rational homological stability. We prove a generalization of this conjecture to
the case of connected manifolds of dimension at least 2 and give an explicit
homological stability range.


  As a fundamental NLP task, semantic role labeling (SRL) aims to discover the
semantic roles for each predicate within one sentence. This paper investigates
how to incorporate syntactic knowledge into the SRL task effectively. We
present different approaches of encoding the syntactic information derived from
dependency trees of different quality and representations; we propose a
syntax-enhanced self-attention model and compare it with other two strong
baseline methods; and we conduct experiments with newly published deep
contextualized word representations as well. The experiment results demonstrate
that with proper incorporation of the high quality syntactic information, our
model achieves a new state-of-the-art performance for the Chinese SRL task on
the CoNLL-2009 dataset.


  Despite decades of studies on charge density wave (CDW) of 2H-NbSe2, the
origin of its incommensurate CDW ground state has not been understood. We
discover that CDW of 2H-NbSe2 is composed of two different, energetically
competing, structures. The lateral heterostructures of two CDWs are entangled
as topological excitations, which give rise to a CDW phase shift and the
incommensuration without a conventional domain wall. A partially melt network
of the topological excitations and their vertices explain an unusual landscape
of domains. The unconventional topological role of competing phases disclosed
here can be widely applied to various incommensuration or phase coexistence
phenomena in materials.


  Their highly adaptive nature and the combinatorial explosion of possible
configurations makes testing context-oriented programs hard. We propose a
methodology to automate the generation of test scenarios for developers of
feature-based context-oriented programs. By using combinatorial interaction
testing we generate a covering array from which a small but representative set
of test scenarios can be inferred. By taking advantage of the explicit
separation of contexts and features in such context-oriented programs, we can
further rearrange the generated test scenarios to minimise the reconfiguration
cost between subsequent scenarios. Finally, we explore how a previously
generated test suite can be adapted incrementally when the system evolves to a
new version. By validating these algorithms on a small use case, our initial
results show that the proposed test generation approach is efficient and
beneficial to developers to test and improve the design of context-oriented
programs.


  The influence of the incompressible strips on the integer quantized Hall
effect (IQHE) is investigated, considering a cleaved-edge overgrown (CEO)
sample as an experimentally realizable sharp edge system. We propose a set of
experiments to clarify the distinction between the large-sample limit when bulk
disorder defines the IQHE plateau width and the small-sample limit smaller than
the disorder correlation length, when self-consistent edge electrostatics
define the IQHE plateau width. The large-sample or bulk QH regime is described
by the usual localization picture, whereas the small-sample or edge regime is
discussed within the compressible/incompressible strips picture, known as the
screening theory of QH edges. Utilizing the unusually sharp edge profiles of
the CEO samples, a Hall bar design is proposed to manipulate the edge potential
profile from smooth to extremely sharp. By making use of a side-gate
perpendicular to the two dimensional electron system, it is shown that the
plateau widths can be changed or even eliminated altogether. Hence, the
visibility of IQHE is strongly influenced when adjusting the edge potential
profile and/or changing the dc current direction under high currents in the
non-linear transport regime. As a second investigation, we consider two
different types of ohmic contacts, namely highly transmitting (ideal) and
highly reflecting (non-ideal) contacts. We show that if the injection contacts
are non-ideal, however still ohmic, it is possible to measure directly the
non-quantized transport taking place at the bulk of the CEO samples. The
results of the experiments we propose will clarify the influence of the edge
potential profile and the quality of the contacts, under quantized Hall
conditions.


  Half integer Josephson vortices in 0-$\pi$-junctions, discussed theoretically
and observed experimentally, spontaneously appear at the point where the
Josephson phase is $\pi$-discontinuous. The creation of \emph{arbitrary}
discontinuities of the Josephson phase has been demonstrated recently. Here we
study fractional vortices formed at an arbitrary $\kappa$-discontinuity,
discuss their stability and possible ground states. The two stable states are
not mirror symmetric. Furthermore, the possible ground states formed at two
$\kappa$-discontinuities separated by a distance $a$ are investigated, and the
energy and the regions of stability of each ground state are calculated. We
also show that the ground states may strongly depend on the distance $a$
between the discontinuities. There is a crossover distance $a_c$ such that for
$a<a_c$ and for $a>a_c$ the ground states may be qualitatively different.


  In this work we propose a multi-task spatio-temporal network, called SUSiNet,
that can jointly tackle the spatio-temporal problems of saliency estimation,
action recognition and video summarization. Our approach employs a single
network that is jointly end-to-end trained for all tasks with multiple and
diverse datasets related to the exploring tasks. The proposed network uses a
unified architecture that includes global and task specific layer and produces
multiple output types, i.e., saliency maps or classification labels, by
employing the same video input. Moreover, one additional contribution is that
the proposed network can be deeply supervised through an attention module that
is related to human attention as it is expressed by eye-tracking data. From the
extensive evaluation, on seven different datasets, we have observed that the
multi-task network performs as well as the state-of-the-art single-task methods
(or in some cases better), while it requires less computational budget than
having one independent network per each task.


  In this work, we introduce a lightweight discourse connective detection
system. Employing gradient boosting trained on straightforward, low-complexity
features, this proposed approach sidesteps the computational demands of the
current approaches that rely on deep neural networks. Considering its
simplicity, our approach achieves competitive results while offering
significant gains in terms of time even on CPU. Furthermore, the stable
performance across two unrelated languages suggests the robustness of our
system in the multilingual scenario. The model is designed to support the
annotation of discourse relations, particularly in scenarios with limited
resources, while minimizing performance loss.


  We prove a conjecture on uniqueness and existence of the irregular vertex
operators of rank $r$ introduced in our previous paper. We also introduce
ramified irregular vertex operators of the Virasoro algebra. As applications,
we give conjectural formulas for series expansions of Painlev\'e III and II tau
functions in terms of our ramified irregular conformal blocks.


  We present the first on-sky results of the micro-lens ring tip-tilt (MLR-TT)
sensor. This sensor utilizes a 3D printed micro-lens ring feeding six
multi-mode fibers to sense misaligned light, allowing centroid reconstruction.
A tip-tilt mirror allows the beam to be corrected, increasing the amount of
light coupled into a centrally positioned single-mode (science) fiber. The
sensor was tested with the iLocater acquisition camera at the Large Binocular
Telescope in November 2019. The limit on the maximum achieved root mean square
reconstruction accuracy was found to be 0.19 $\lambda$/D in both tip and tilt,
of which approximately 50% of the power originates at frequencies below 10 Hz.
We show the reconstruction accuracy is highly dependent on the estimated Strehl
ratio and simulations support the assumption that residual adaptive optics
aberrations are the main limit to the reconstruction accuracy. We conclude that
this sensor is ideally suited to remove post-adaptive optics non-common path
tip tilt residuals. We discuss the next steps for the concept development,
including optimizations of the lens and fiber, tuning of the correction
algorithm and selection of optimal science cases.


  Mechanistic learning, the synergistic combination of knowledge-driven and
data-driven modeling, is an emerging field. In particular, in mathematical
oncology, the application of mathematical modeling to cancer biology and
oncology, the use of mechanistic learning is growing. This review aims to
capture the current state of the field and provide a perspective on how
mechanistic learning may further progress in mathematical oncology. We
highlight the synergistic potential of knowledge-driven mechanistic
mathematical modeling and data-driven modeling, such as machine and deep
learning. We point out similarities and differences regarding model complexity,
data requirements, outputs generated, and interpretability of the algorithms
and their results. Then, organizing combinations of knowledge- and data-driven
modeling into four categories (sequential, parallel, intrinsic, and extrinsic
mechanistic learning), we summarize a variety of approaches at the interface
between purely data- and knowledge-driven models. Using examples predominantly
from oncology, we discuss a range of techniques including physics-informed
neural networks, surrogate model learning, and digital twins. We see that
mechanistic learning, with its intentional leveraging of the strengths of both
knowledge and data-driven modeling, can greatly impact the complex problems of
oncology. Given the increasing ubiquity and impact of machine learning, it is
critical to incorporate it into the study of mathematical oncology with
mechanistic learning providing a path to that end. As the field of mechanistic
learning advances, we aim for this review and proposed categorization framework
to foster additional collaboration between the data- and knowledge-driven
modeling fields. Further collaboration will help address difficult issues in
oncology such as limited data availability, requirements of model transparency,
and complex input data


  In this paper, it is elaborated the theory the Ricci flows for manifolds
enabled with nonintegrable (nonholonomic) distributions defining nonlinear
connection structures. Such manifolds provide a unified geometric arena for
nonholonomic Riemannian spaces, Lagrange mechanics, Finsler geometry, and
various models of gravity (the Einstein theory and string, or gauge,
generalizations). We follow the method of nonholonomic frames with associated
nonlinear connection structure and define certain classes of nonholonomic
constraints on Riemann manifolds for which various types of generalized Finsler
geometries can be modelled by Ricci flows. We speculate on possible
applications of the nonholnomic flows in modern geometry, geometric mechanics
and physics.


  Let $D=(V,A)$ be a digraph and consider an arc subset $A'\subseteq A$ and an
exhaustive mapping $\phi: A\to A'$ such that
  $(i)$ the set of heads of $A'$ is $H(A')=V$; $(ii)$ the map fixes the
elements of $A'$, that is, $\phi|A'=Id$, and for every vertex $j\in V$,
$\phi(\omega^-(j))\subset \omega^-(j)\cap A'$.
  Then, {\it the partial line digraph} of $D$, denoted by
$\mathcal{L}_{(A',\phi)}D $ (for short $\mathcal{L}D$ if the pair $(A', \phi)$
is clear from the context), is the digraph with vertex set $V
(\mathcal{L}D)=A'$ and set of arcs $A(\mathcal{L}D) = \{(ij, \phi(j,k)) :
(j,k)\in A\}.$ In this paper we prove the following results:
  Let $k,l$ be two natural numbers such that $1\le l \le k$, and $D$ a digraph
with minimum in-degree at least 1. Then the number of $(k,l)$-kernels of $D$ is
less than or equal to the number of $(k,l)$-kernels of $\mathcal{L} D$.
Moreover, if $l<k$ and the girth of $D$ is at least $l+1$, then these two
numbers are equal.
  The number of semikernels of $D$ is equal to the number of semikernels of
$\mathcal{L} D$.
  Also we introduce the concept of $(k,l)$-Grundy function as a generalization
of the concept of Grundy function and we prove that the number of
$(k,l)$-Grundy functions of $D$ is equal to the number of $(k,l)$-Grundy
functions of any partial line digraph $\mathcal{L} D$.


  We propose a link between logical independence and quantum physics. We
demonstrate that quantum systems in the eigenstates of Pauli group operators
are capable of encoding mathematical axioms and show that Pauli group quantum
measurements are capable of revealing whether or not a given proposition is
logically dependent on the axiomatic system. Whenever a mathematical
proposition is logically independent of the axioms encoded in the measured
state, the measurement associated with the proposition gives random outcomes.
This allows for an experimental test of logical independence. Conversely, it
also allows for an explanation of the probabilities of random outcomes observed
in Pauli group measurements from logical independence without invoking quantum
theory. The axiomatic systems we study can be completed and are therefore not
subject to Goedel's incompleteness theorem.


  Since the science white paper of the Large High Altitude Air Shower
Observatory (LHAASO) published on arXiv in 2019 [e-Print: 1905.02773
(astro-ph.HE)], LHAASO has completed the transition from a project to an
operational gamma-ray astronomical observatory LHAASO is a new generation
multi-component facility located in Daocheng, Sichuan province of China, at an
altitude of 4410 meters. It aims at measuring with unprecedented sensitivity
the spectrum, composition, and anisotropy of cosmic rays in the energy range
between 10$^{12}$ and 10$^{18}$~eV, and acting simultaneously as a wide
aperture (one stereoradiant) continuously operating gamma-ray telescope in the
energy range between 10$^{11}$ and $10^{15}$~eV with the designed sensitivity
of 1.3\% of the Crab Unit (CU) above 100 TeV. LHAASO's capability of measuring
simultaneously different shower components (electrons, muons, and
Cherenkov/fluorescence light), will allow it to investigate the origin,
acceleration, and propagation of CR through measurement of the energy spectrum,
elemental composition, and anisotropy with unprecedented resolution. The
remarkable sensitivity of LHAASO will play a key role in CR physics and
gamma-ray astronomy for a general and comprehensive exploration of the high
energy universe and will allow important studies of fundamental physics (such
as indirect dark matter search, Lorentz invariance violation, quantum gravity)
and solar and heliospheric physics. The LHAASO Collaboration organized an
editorial working group and finished all editorial work of this science book,
to summarize the instrumental features and outline the prospects of scientific
researches with the LHAASO experiment.


  Using the radiative return method, experiments at high luminosity
electron-positron colliders allow to explore the kaon and the pion form factors
in the time-like region up to fairly high energies. This opens the possibility
to study kaon and pion pair production at and around the narrow resonances
J/psi and psi(2S) and explore the interference between electromagnetic and
hadronic amplitudes. Parameterizations of charged and neutral kaon as well as
pion form factors are derived, which lead to an improved description of the
data in the region of large invariant masses of the meson pair. These form
factors are combined with the hadronic couplings of charged and neutral kaons
to J/psi and psi(2S) and implemented into the Monte Carlo generator PHOKHARA,
which is now, for the first time, able to simulate the production of narrow
resonances and their decay into kaon, pion and muon pairs.


  A new framework for adaptive regulation to invariant sets is proposed.
Reaching the target dynamics (invariant set) is to be ensured by state feedback
while adaptation to parametric uncertainties is provided by additional
adaptation algorithm. We show that for a sufficiently large class of nonlinear
systems it is possible to adaptively steer the system trajectories to the
desired non-equilibrium state without requiring knowledge or existence of a
specific strict Lyapunov function.


  It is extremely uncommon to be able to predict the velocity profile of a
turbulent flow. In two-dimensional flows, atmosphere dynamics, and plasma
physics, large scale coherent jets are created through inverse energy transfers
from small scales to the largest scales of the flow. We prove that in the
limits of vanishing energy injection, vanishing friction, and small scale
forcing, the velocity profile of a jet obeys an equation independent of the
details of the forcing. We find another general relation for the maximal
curvature of a jet and we give strong arguments to support the existence of an
hydrodynamic instability at the point with minimal jet velocity. Those results
are the first computations of Reynolds stresses and self consistent velocity
profiles from the turbulent dynamics, and the first consistent analytic theory
of zonal jets in barotropic turbulence.


  Decades of observations show that CMEs can deflect from a purely radial
trajectory yet no consensus exists as to the cause of these deflections. Many
of theories attribute the CME deflection to magnetic forces. We developed
ForeCAT (Kay et al. 2013, Kay et al. 2015), a model for CME deflections based
solely on magnetic forces, neglecting any reconnection effects. Here we compare
ForeCAT predictions to the observed deflection of the 2008 December 12 CME and
find that ForeCAT can accurately reproduce the observations. Multiple
observations show that this CME deflected nearly 30{\deg} in latitude (Byrne et
al. 2010, Gui et al. 2011) and 4.4{\deg} in longitude (Gui et al. 2011). From
the observations, we are able to constrain all of the ForeCAT input parameters
(initial position, radial propagation speed, and expansion) except the CME mass
and the drag coefficient that affects the CME motion. By minimizing the reduced
chi-squared, $\chi^2_{\nu}$, between the ForeCAT results and the observations
we determine an acceptable mass range between 4.5x10$^{14}$ and 1x10$^{15}$ g
and the drag coefficient less than 1.4 with a best fit at 7.5x10$^{14}$ g and 0
for the mass and drag coefficient. ForeCAT is sensitive to the magnetic
background and we are also able to constrain the rate at which the quiet sun
magnetic field falls to be similar or to or fall slightly slower than the
Potential Field Source Surface model.


  With the investigation of the production cross section of $\ ^{51}\rm Mn$ off
of $\ ^{\rm nat}\rm Fe$ in mind, two stacked target experiments were conducted
at the Berkeley Lab 88-Inch Cyclotron. Proton beams with energies of $25$ and
$55\,\rm MeV$ result in a total of 14 data points for various reactions. Gamma
spectra of the activated foils were taken and analyzed, then cross sections
calculated.


  The ultimate goal of any sparse coding method is to accurately recover from a
few noisy linear measurements, an unknown sparse vector. Unfortunately, this
estimation problem is NP-hard in general, and it is therefore always approached
with an approximation method, such as lasso or orthogonal matching pursuit,
thus trading off accuracy for less computational complexity. In this paper, we
develop a quantum-inspired algorithm for sparse coding, with the premise that
the emergence of quantum computers and Ising machines can potentially lead to
more accurate estimations compared to classical approximation methods. To this
end, we formulate the most general sparse coding problem as a quadratic
unconstrained binary optimization (QUBO) task, which can be efficiently
minimized using quantum technology. To derive at a QUBO model that is also
efficient in terms of the number of spins (space complexity), we separate our
analysis into three different scenarios. These are defined by the number of
bits required to express the underlying sparse vector: binary, 2-bit, and a
general fixed-point representation. We conduct numerical experiments with
simulated data on LightSolver's quantum-inspired digital platform to verify the
correctness of our QUBO formulation and to demonstrate its advantage over
baseline methods.


  We propose a convex optimization formulation with the nuclear norm and
$\ell_1$-norm to find a large approximately rank-one submatrix of a given
nonnegative matrix. We develop optimality conditions for the formulation and
characterize the properties of the optimal solutions. We establish conditions
under which the optimal solution of the convex formulation has a specific
sparse structure. Finally, we show that, under certain hypotheses, with high
probability, the approach can recover the rank-one submatrix even when it is
corrupted with random noise and inserted as a submatrix into a much larger
random noise matrix.


  We study stability of solitary vortices in the two-dimensional trapped
Bose-Einstein condensate (BEC) with a spatially localized region of
self-attraction. Solving the respective Bogoliubov-de Gennes equations and
running direct simulations of the underlying Gross-Pitaevskii equation reveals
that vortices with topological charge up to S = 6 (at least) are stable above a
critical value of the chemical potential (i.e., below a critical number of
atoms, which sharply increases with S). The largest nonlinearity-localization
radius admitting the stabilization of the higher-order vortices is estimated
analytically and accurately identified in a numerical form. To the best of our
knowledge, this is the first example of a setting which gives rise to stable
higher-order vortices, S > 1, in a trapped self-attractive BEC. The same
setting may be realized in nonlinear optics too.


  The interactions between the excited states of a single chromophore with
static and dynamic electric fields confined to a plasmonic cavity of picometer
dimensions are investigated in a joint experimental and theoretical effort. In
this configuration, the spatial extensions of the confined fields are smaller
than the one of the molecular exciton, a property that is used to generate
fluorescence maps of the chromophores with intra-molecular resolution.
Theoretical simulations of the electrostatic and electrodynamic interactions
occurring at the chromophore-picocavity junction are able to reproduce and
interpret these hyper-resolved fluorescence maps, and reveal the key role
played by subtle variations of Purcell, Lamb and Stark effects at the
chromophore-picocavity junction.


  Coded caching was introduced as a technique of systematically exploiting
locally available storage at the clients to increase the channel throughput via
coded transmissions. Most known coded caching schemes in literature enable
large gains in terms of the rate, however at the cost of subpacketization that
is exponential in $K^{\frac{1}{r}}$ ($K$ being the number of clients, $r$ some
positive integer). Building upon recent prior work for coded caching design via
line graphs and finite-field projective geometries, we present a new scheme in
this work which achieves a subexponential (in $K$) subpacketization of
$q^{O((log_qK)^2)}$ and rate $\Theta\left(\frac{K}{(log_qK)^2}\right)$, for
large $K$, and the cached fraction $\frac{M}{N}$ being upper bounded by a
constant $\frac{2}{q^{\alpha-1}}$ (for some prime power $q$ and constant
$\alpha \geq 2$) . Apart from this asymptotic improvement, we show that through
some numerical comparisons that our present scheme has much lower
subpacketization than previous comparable schemes, with some increase in the
rate of the delivery scheme, for the same memory requirements. For instance, we
obtain practically relevant subpacketization levels such as $10^2 - 10^7$ for
$10^2 - 10^4$ number of clients. Leveraging prior results on adapting coded
caching schemes for the error-free broadcast channel to device to device
networks, we obtain a low-subpacketization scheme for D2D networks also, and
give numerical comparison for the same with prior work.


  We relate small 1-form Laplacian eigenvalues to relative cycle complexity on
closed hyperbolic manifolds: small eigenvalues correspond to closed geodesics
no multiple of which bounds a surface of small genus.
  We describe potential applications of this equivalence principle toward
proving optimal torsion homology growth in families of hyperbolic 3-manifolds
Benjamini-Schramm converging to $\mathbb{H}^3.$


  In this report we describe a mesh editing system that we implemented that
uses a natural stretching and bending energy defined over smooth surfaces. As
such, this energy behaves uniformly under various mesh resolutions. All of the
elements of our approach already exist in the literature. We hope that our
discussions of these energies helps to shed light on the behaviors of these
methods and provides a unified discussion of these methods.


  Recent results of arXiv:1907.08788 on universal black holes in $d$ dimensions
are summarized. These are static metrics with an isotropy-irreducible
homogeneous base space which can be consistently employed to construct
solutions to virtually any metric theory of gravity in vacuum.


  We solve Virasoro constraints on the KP hierarchy in terms of minimal
conformal models. The constraints we start with are implemented by the Virasoro
generators depending on a background charge $Q$. Then the solutions to the
constraints are given by the theory which has the same field content as the
David-Distler-Kawai theory: it consists of a minimal matter scalar with
background charge $Q$, dressed with an extra `Liouville' scalar. The
construction is based on a generalization of the Kontsevich parametrization of
the KP times achieved by introducing into it Miwa parameters which depend on
the value of $Q$. Under the thus defined Kontsevich-Miwa transformation, the
Virasoro constraints are proven to be equivalent to a master equation depending
on the parameter $Q$. The master equation is further identified with a
null-vector decoupling equation. We conjecture that $W^{(n)}$ constraints on
the KP hierarchy are similarly related to a level-$n$ decoupling equation. We
also consider the master equation for the $N$-reduced KP hierarchies. Several
comments are made on a possible relation of the generalized master equation to
{\it scaled} Kontsevich-type matrix integrals and on the form the equation
takes in higher genera.


  Incorporating conservation laws explicitly into matrix product states (MPS)
has proven to make numerical simulations of quantum many-body systems much less
resources consuming. We will discuss here, to what extent this concept can be
used in simulation where the dynamically evolving entities are matrix product
operators (MPO). Quite counter-intuitively the expectation of gaining in speed
by sacrificing information about all but a single symmetry sector is not in all
cases fulfilled. It turns out that in this case often the entanglement imposed
by the global constraint of fixed particle number is the limiting factor.


  Large language models (LLMs) face a daunting challenge due to the excessive
computational and memory requirements of the commonly used Transformer
architecture. While state space model (SSM) is a new type of foundational
network architecture offering lower computational complexity, their performance
has yet to fully rival that of Transformers. This paper introduces DenseSSM, a
novel approach to enhance the flow of hidden information between layers in
SSMs. By selectively integrating shallowlayer hidden states into deeper layers,
DenseSSM retains fine-grained information crucial for the final output. Dense
connections enhanced DenseSSM still maintains the training parallelizability
and inference efficiency. The proposed method can be widely applicable to
various SSM types like RetNet and Mamba. With similar model size, DenseSSM
achieves significant improvements, exemplified by DenseRetNet outperforming the
original RetNet with up to 5% accuracy improvement on public benchmarks. code
is avalaible at https://github.com/WailordHe/DenseSSM


  Champarnaud and Ziadi, and Khorsi et al. show how to compute the equation
automaton of word regular expression $E$ via the $k$-C-Continuations.
  Kuske and Meinecke extend the computation of the equation automaton to a
regular tree expression $E$ over a ranked alphabet $\Sigma$ and produce a
$O(R\cdot|E|^2)$ time and space complexity algorithm, where $R$ is the maximal
rank of a symbol occurring in $\Sigma$ and $|E|$ is the size of $E$. In this
paper, we give a full description of the algorithm based on the acyclic
minimization of Revuz. Our algorithm, which is performed in an $O(|Q|\cdot|E|)$
time and space complexity, where $|Q|$ is the number of states of the produced
automaton, is more efficient than the one obtained by Kuske and Meinecke.


  In networking applications, one often wishes to obtain estimates about the
number of objects at different parts of the network (e.g., the number of cars
at an intersection of a road network or the number of packets expected to reach
a node in a computer network) by monitoring the traffic in a small number of
network nodes or edges. We formalize this task by defining the 'Markov Chain
Monitoring' problem.
  Given an initial distribution of items over the nodes of a Markov chain, we
wish to estimate the distribution of items at subsequent times. We do this by
asking a limited number of queries that retrieve, for example, how many items
transitioned to a specific node or over a specific edge at a particular time.
We consider different types of queries, each defining a different variant of
the Markov chain monitoring. For each variant, we design efficient algorithms
for choosing the queries that make our estimates as accurate as possible. In
our experiments with synthetic and real datasets we demonstrate the efficiency
and the efficacy of our algorithms in a variety of settings.