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We present GR-NLP-TOOLKIT, an open-source natural language processing (NLP) toolkit developed specifically for modern Greek. The toolkit provides state-of-the-art performance in five core NLP tasks, namely part-of-speech tagging, morphological tagging, dependency parsing, named entity recognition, and Greeklishto-Greek transliteration. The toolkit is based on pre-trained Transformers, it is freely available, and can be easily installed in Python (pip install gr-nlp-toolkit). It is also accessible through a demonstration platform on HuggingFace, along with a publicly available API for non-commercial use. We discuss the functionality provided for each task, the underlying methods, experiments against comparable open-source toolkits, and future possible enhancements. The toolkit is available at: https://github.com/nlpaueb/gr-nlp-toolkit, Comment: Accepted Demo Paper @ COLING 2025 (Github: https://github.com/nlpaueb/gr-nlp-toolkit/, Demo: https://huggingface.co/spaces/AUEB-NLP/greek-nlp-toolkit-demo, API: https://huggingface.co/spaces/AUEB-NLP/The-Greek-NLP-API)

Minimal surfaces in the Riemannian product of surfaces of constant curvature have been considered recently, particularly as these products arise as spaces of oriented geodesics of 3-dimensional space-forms. This papers considers more general Riemannian products of surfaces and explores geometric and topological restrictions that arise for minimal surfaces. We show that generically, a totally geodesic surface in a Riemannian product is locally either a slice or a product of geodesics. If the Gauss curvatures of the factors are negative, it is proven that there are no minimal 2-spheres, while minimal 2-tori are Lagrangian with respect to both product symplectic structures. If the surfaces have non-zero bounded curvatures, we establish a sharp lower bound on the area of minimal 2-spheres and explore the properties of the Gauss and normal curvatures of general compact minimal surfaces., Comment: 22 pages LaTeX

Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of random trees to represent narratives as hierarchies of key points, where each node is a compressed representation of its descendant leaves, which are the original narrative segments. Recall is modeled as constrained by working memory capacity from this hierarchical structure. Our analytical solution aligns with observations from large-scale narrative recall experiments. Specifically, our model explains that (1) average recall length increases sublinearly with narrative length, and (2) individuals summarize increasingly longer narrative segments in each recall sentence. Additionally, the theory predicts that for sufficiently long narratives, a universal, scale-invariant limit emerges, where the fraction of a narrative summarized by a single recall sentence follows a distribution independent of narrative length., Comment: 16 pages, 4 figures

We consider the problem of steering a collection of n particles that obey identical n-dimensional linear dynamics via a common state feedback law towards a rearrangement of their positions, cast as a controllability problem for a dynamical system evolving on the space of matrices with positive determinant. We show that such a task is always feasible and, moreover, that it can be achieved arbitrarily fast. We also show that an optimal feedback control policy to achieve a similar feat, may not exist. Furthermore, we show that there is no universal formula for a linear feedback control law to achieve a rearrangement, optimal or not, that is everywhere continuous with respect to the specifications. We conclude with partial results on the broader question of controllability of dynamics on orientation-preserving diffeomorphisms., Comment: 15 pages, 2 figures

We consider $n$ unit-speed mobile agents initially positioned at the center of a unit disk, tasked with inspecting all points on the disk's perimeter. A perimeter point is considered covered if an agent positioned outside the disk's interior has unobstructed visibility of it, treating the disk itself as an obstacle. For $n=1$, this problem is referred to as the shoreline problem with a known distance. Isbell in 1957 derived an optimal trajectory that minimizes the worst-case inspection time for that problem. The one-agent version of the problem was originally proposed as a more tractable variant of Bellman's famous lost-in-the-forest problem. Our contributions are threefold. First, and as a warm-up, we extend Isbell's findings by deriving worst-case optimal trajectories addressing the partial inspection of a section of the disk, hence deriving an alternative proof of optimality for inspecting the disk with $n \geq 2$ agents. Second, we analyze the average-case inspection time, assuming a uniform distribution of perimeter points (equivalent to randomized inspection algorithms). Using spatial discretization and Nonlinear Programming (NLP), we propose feasible solutions to the continuous problem and evaluate their effectiveness compared to NLP solutions. Third, we establish Pareto-optimal bounds for the multi-objective problem of jointly minimizing the worst-case and average-case inspection times.

Reaction-diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to experimental data. In the present work, we introduce a novel formalism to construct reaction-diffusion models that is grounded in the principle of maximum entropy. This new formalism aims to incorporate various types of experimental data, including ensemble currents, distributions at different points in time, or moments of such. To this end, we expand the framework of Schr\"odinger bridges and Maximum Caliber problems to nonlinear interacting systems. We illustrate the usefulness of the proposed approach by modeling the evolution of (i) a morphogen across the fin of a zebrafish and (ii) the population of two varieties of toads in Poland, so as to match the experimental data., Comment: 15 pages, 3 figures

Photometric galaxy surveys, despite their limited resolution along the line of sight, encode rich information about the large-scale structure (LSS) of the Universe thanks to the large number density and extensive depth of the data. However, the complicated selection effects in wide and deep surveys will potentially cause significant bias in the angular two-point correlation function (2PCF) measured from those surveys. In this paper, we measure the 2PCF from the newly published KiDS-Legacy sample. Given an $r$-band $5\sigma$ magnitude limit of $24.8$ and survey footprint of $1347$ deg$^2$, it achieves an excellent combination of sky coverage and depth for such a measurement. We find that complex selection effects, primarily induced by varying seeing, introduce over-estimation of the 2PCF by approximately an order of magnitude. To correct for such effects, we apply a machine learning-based method to recover an ``organised random'' (OR) that presents the same selection pattern as the galaxy sample. The basic idea is to find the selection-induced clustering of galaxies using a combination of self-organising maps (SOM) and hierarchical clustering (HC). This unsupervised machine learning method is able to recover complicated selection effects without specifying their functional forms. We validate this ``SOM+HC'' method on mock deep galaxy samples with realistic systematics and selections derived from the KiDS-Legacy catalogue. Using mock data, we demonstrate that the OR delivers unbiased 2PCF cosmological parameter constraints, removing the $27\sigma$ offset in the galaxy bias parameter that is recovered when adopting uniform randoms. Blinded measurements on the real KiDS-Legacy data show that the corrected 2PCF is robust to the SOM+HC configuration near the optimal setup suggested by the mock tests. Our software is open-source for future usage., Comment: 29 pages, 27 figures, 4 tables

The Workflows Community Summit gathered 111 participants from 18 countries to discuss emerging trends and challenges in scientific workflows, focusing on six key areas: time-sensitive workflows, AI-HPC convergence, multi-facility workflows, heterogeneous HPC environments, user experience, and FAIR computational workflows. The integration of AI and exascale computing has revolutionized scientific workflows, enabling higher-fidelity models and complex, time-sensitive processes, while introducing challenges in managing heterogeneous environments and multi-facility data dependencies. The rise of large language models is driving computational demands to zettaflop scales, necessitating modular, adaptable systems and cloud-service models to optimize resource utilization and ensure reproducibility. Multi-facility workflows present challenges in data movement, curation, and overcoming institutional silos, while diverse hardware architectures require integrating workflow considerations into early system design and developing standardized resource management tools. The summit emphasized improving user experience in workflow systems and ensuring FAIR workflows to enhance collaboration and accelerate scientific discovery. Key recommendations include developing standardized metrics for time-sensitive workflows, creating frameworks for cloud-HPC integration, implementing distributed-by-design workflow modeling, establishing multi-facility authentication protocols, and accelerating AI integration in HPC workflow management. The summit also called for comprehensive workflow benchmarks, workflow-specific UX principles, and a FAIR workflow maturity model, highlighting the need for continued collaboration in addressing the complex challenges posed by the convergence of AI, HPC, and multi-facility research environments.

We introduce OneCovariance, an open-source software designed to accurately compute covariance matrices for an arbitrary set of two-point summary statistics across a variety of large-scale structure tracers. Utilising the halo model, we estimate the statistical properties of matter and biased tracer fields, incorporating all Gaussian, non-Gaussian, and super-sample covariance terms. The flexible configuration permits user-specific parameters, such as the complexity of survey geometry, the halo occupation distribution employed to define each galaxy sample, or the form of the real-space and/or Fourier space statistics to be analysed. We illustrate the capabilities of OneCovariance within the context of a cosmic shear analysis of the final data release of the Kilo-Degree Survey (KiDS-Legacy). Upon comparing our estimated covariance with measurements from mock data and calculations from independent software, we ascertain that OneCovariance achieves accuracy at the per cent level. When assessing the impact of ignoring complex survey geometry in the cosmic shear covariance computation, we discover misestimations at approximately the $10\%$ level for cosmic variance terms. Nonetheless, these discrepancies do not significantly affect the KiDS-Legacy recovery of cosmological parameters. We derive the cross-covariance between real-space correlation functions, bandpowers, and COSEBIs, facilitating future consistency tests among these three cosmic shear statistics. Additionally, we calculate the covariance matrix of photometric-spectroscopic galaxy clustering measurements, validating Jackknife covariance estimates for calibrating KiDS-Legacy redshift distributions. The OneCovariance can be found on github Hub together with a comprehensive documentation and examples., Comment: 37 pages, 11 figures, to be submitted to A&A, code available at https://github.com/rreischke/OneCovariance

The paper highlights a relatively unknown link between algorithm design in optimization and control synthesis in robust control. Specifically, quadratic optimization can be recast as a regulation problem within the framework of $\mathcal{H}_\infty$ control. From this vantage point, the optimality of Polyak's fastest heavy-ball algorithm can be ascertained as a solution to a gain margin optimization problem. The approach is independent of Polyak's original and brilliant argument, yet simpler, and relies on the foundational work by Tannenbaum that introduced and solved the gain margin optimization via Nevanlinna--Pick interpolation theory. The link between first-order optimization methods and robust control theory sheds new light into limits of algorithmic performance for such methods, and suggests a new framework where similar computational problems can be systematically studied and algorithms optimized. In particular, it raises the question as to whether periodically scheduled algorithms can achieve faster rates for quadratic optimization, in a manner analogous to periodic control that extends gain margin beyond that of time-invariant control. This turns out not to be the case, due to the analytic obstruction of a transmission zero that is inherent in causal optimization algorithms. Interestingly, this obstruction can be removed with implicit algorithms, cast in a similar manner as feedback regulation problems with causal, but not strictly causal dynamics, thereby devoid of the transmission zero at infinity and able to achieve superior convergence rates. The confluence of the fields of optimization algorithms and control provides a frame to tackle questions pertaining to speed, accuracy, distributed computation, and so forth, and to delineate respective limits to performance and tradeoffs in a systematic manner, utilizing the formalism of robust control., Comment: 25 pages, 8 figures

A class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasi-characteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner distribution associated with these observables can be rigorously approximated by such measures. These measures are given by affine combinations of Dirac delta distributions supported over the finite spectral range of the quantum observables and give the correct probability marginals when coarse-grained along any principal axis. We specialize to bivariate quasi-probability distributions for the spin measurements of spin-1/2 particles and derive their closed-form expressions. As a side result, we point out a connection between the convergence of these particle approximations and the Mehler-Heine theorem. Finally, we interpret the supports of these quasi-probability distributions in terms of repeated thought experiments., Comment: 19 pages, 9 figures

We explore the enhanced self-calibration of photometric galaxy redshift distributions, $n(z)$, through the combination of up to six two-point functions. Our $\rm 3\times2pt$ configuration is comprised of photometric shear, spectroscopic galaxy clustering, and spectroscopic-photometric galaxy-galaxy lensing (GGL). We further include spectroscopic-photometric cross-clustering; photometric GGL; and photometric auto-clustering, using the photometric shear sample as density tracer. We perform simulated likelihood forecasts of the cosmological and nuisance parameter constraints for Stage-III- and Stage-IV-like surveys. For the Stage-III-like case, we employ realistic but perturbed redshift distributions, and distinguish between "coherent" shifting in one direction, versus more internal scattering and full-shape errors. For perfectly known $n(z)$, a $\rm 6\times2pt$ analysis gains $\sim40\%$ in Figure of Merit (FoM) in the $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}$ and $\Omega_{\rm m}$ plane relative to the $\rm 3\times2pt$ analysis. If untreated, coherent and incoherent redshift errors lead to inaccurate inferences of $S_8$ and $\Omega_{\rm m}$, respectively. Employing bin-wise scalar shifts $\delta{z}_i$ in the tomographic mean redshifts reduces cosmological parameter biases, with a $\rm 6x2pt$ analysis constraining the shift parameters with $2-4$ times the precision of a photometric $\rm 3^{ph}\times2pt$ analysis. For the Stage-IV-like survey, a $\rm 6\times2pt$ analysis doubles the FoM($\sigma_8{-}\Omega_{\rm m}$) compared to any $\rm 3\times2pt$ or $\rm 3^{ph}\times2pt$ analysis, and is only $8\%$ less constraining than if the $n(z)$ were perfectly known. A Gaussian mixture model for the $n(z)$ reduces mean-redshift errors and preserves the $n(z)$ shape. It also yields the most accurate and precise cosmological constraints for any $N\rm\times2pt$ configuration given $n(z)$ biases., Comment: 38 pages, 20 figures, to be submitted to A&A

A generative diffusion model is used to produce probabilistic ensembles of precipitation intensity maps at the 1-hour 5-km resolution. The generation is conditioned on infrared and microwave radiometric measurements from the GOES and DMSP satellites and is trained with merged ground radar and gauge data over southeastern United States. The generated precipitation maps reproduce the spatial autocovariance and other multiscale statistical properties of the gauge-radar reference fields on average. Conditioning the generation on the satellite measurements allows us to constrain the magnitude and location of each generated precipitation feature. The mean of the 128- member ensemble shows high spatial coherence with the reference fields with 0.82 linear correlation between the two. On average, the coherence between any two ensemble members is approximately the same as the coherence between any ensemble member and the ground reference, attesting that the ensemble dispersion is a proper measure of the estimation uncertainty. From the generated ensembles we can easily derive the probability of the precipitation intensity exceeding any given intensity threshold, at the 5-km resolution of the generation or at any desired aggregated resolution.

In this work, we introduce Y-Drop, a regularization method that biases the dropout algorithm towards dropping more important neurons with higher probability. The backbone of our approach is neuron conductance, an interpretable measure of neuron importance that calculates the contribution of each neuron towards the end-to-end mapping of the network. We investigate the impact of the uniform dropout selection criterion on performance by assigning higher dropout probability to the more important units. We show that forcing the network to solve the task at hand in the absence of its important units yields a strong regularization effect. Further analysis indicates that Y-Drop yields solutions where more neurons are important, i.e have high conductance, and yields robust networks. In our experiments we show that the regularization effect of Y-Drop scales better than vanilla dropout w.r.t. the architecture size and consistently yields superior performance over multiple datasets and architecture combinations, with little tuning., Comment: Draft paper version

We investigate the effect of pressure-dependent wall slip on the steady Newtonian annular Poiseuille flow employing Navier's slip law with a slip parameter that varies exponentially with pressure. The dimensionless governing equations and accompanying auxiliary conditions are solved analytically up to second order by implementing a regular perturbation scheme in terms of the small dimensionless pressure-dependence slip parameter. An explicit formula for the average pressure drop, required to maintain a constant volumetric flowrate, is also derived. This is suitably post-processed by applying a convergence acceleration technique to increase the accuracy of the original perturbation series. The effects of pressure-dependent wall slip are more pronounced when wall slip is weak. However, as the slip coefficient increases, these effects are moderated and eventually eliminated as the perfect slip case is approached. The results show that the average pressure drop remains practically constant until the Reynolds number becomes sufficiently large. It is worth noting that all phenomena associated with pressure-dependent wall slip are amplified as the annular gap is reduced., Comment: 19 pages, 9 figures

This study revisits the development of viscoplastic flow in pipes and channels, focusing on the flow of a Bingham plastic. Using finite element simulations and the Papanastasiou regularisation, results are obtained across a range of Reynolds and Bingham numbers. The novel contributions of this work include: (a) investigating a definition of the development length based on wall shear stress, a critical parameter in numerous applications; (b) considering alternative definitions of the Reynolds number in an effort to collapse the development length curves into a single master curve, independent of the Bingham number; (c) examining the patterns of yielded and unyielded regions within the flow domain; and (d) assessing the impact of the regularisation parameter on the accuracy of the results. The findings enhance the existing literature, providing a more comprehensive understanding of this classic flow problem.

The theory of Monge-Kantorovich Optimal Mass Transport (OMT) has in recent years spurred a fast developing phase of research in stochastic control, control of ensemble systems, thermodynamics, data science, and several other fields in engineering and science. Specifically, OMT endowed the space of probability distributions with a rich Riemannian-like geometry, the Wasserstein geometry and the Wasserstein $\mathcal W_2$-metric. This geometry proved fruitful in quantifying and regulating the uncertainty of deterministic and stochastic systems, and in dealing with problems related to the transport of ensembles in continuous and discrete spaces. We herein introduce a new type of transportation problems. The salient feature of these problems is that particles/agents in the ensemble, that are to be transported, are labeled and their relative position along their journey is of interest. Of particular importance in our program are closed orbits where particles return to their original place after being transported along closed paths. Thereby, control laws are sought so that the distribution of the ensemble traverses a closed orbit in the Wasserstein manifold without mixing. This feature is in contrast with the classical theory of optimal transport where the primary object of study is the path of probability densities, without any concern about mixing of the flow, which is expected and allowed when traversing curves in the Wasserstein space. In the theory that we present, we explore a hitherto unstudied sub-Riemannian structure of Monge-Kantorovich transport where the relative position of particles along their journey is modeled by the holonomy of the transportation schedule. From this vantage point, we discuss several other problems of independent interest., Comment: 16 pages, 8 figures

Electronic flying qubits offer an interesting alternative to photonic qubits: electrons propagate slower, hence easier to control in real time, and Coulomb interaction enables direct entanglement between different qubits. While their coherence time is limited, picosecond-scale control would make them competitive in terms of number of possible coherent operations. The key challenge lies in achieving the dynamical regime, where the injected plasmonic pulse width is shorter than the quantum device dimensions. Here we reach this new regime in a quantum nanoelectronic system by injecting ultrashort single electron plasmonic pulses into a 14-micrometer-long Mach-Zehnder interferometer. Our findings reveal that quantum coherence is preserved for ultrashort plasmonic pulses, exhibiting enhanced contrast of coherent oscillations compared to the DC regime. Moreover, this coherence remains robust even under large bias voltages. This milestone demonstrates the feasibility of flying qubits as a promising alternative to localized qubit architectures, offering reduced hardware footprint, increased connectivity, and potential for scalable quantum information processing.

Within the family of explainable machine-learning, we present Fredholm neural networks (Fredholm NNs), deep neural networks (DNNs) which replicate fixed point iterations for the solution of linear and nonlinear Fredholm Integral Equations (FIE) of the second kind. Applications of FIEs include the solution of ordinary, as well as partial differential equations (ODEs, PDEs) and many more. We first prove that Fredholm NNs provide accurate solutions. We then provide insight into the values of the hyperparameters and trainable/explainable weights and biases of the DNN, by directly connecting their values to the underlying mathematical theory. For our illustrations, we use Fredholm NNs to solve both linear and nonlinear problems, including elliptic PDEs and boundary value problems. We show that the proposed scheme achieves significant numerical approximation accuracy across both the domain and boundary. The proposed methodology provides insight into the connection between neural networks and classical numerical methods, and we posit that it can have applications in fields such as Uncertainty Quantification (UQ) and explainable artificial intelligence (XAI). Thus, we believe that it will trigger further advances in the intersection between scientific machine learning and numerical analysis., Comment: 22 pages, 11 figures Replacement reason: corrected licence to arXiv.org perpetual, non-exclusive license

In contradistinction to the case of massive excitations, the connection between integrability and the tree-level massless scattering matrix of integrable $\sigma$-models is lost. Namely, in well-known 2-d integrable models the tree-level massless S-matrix exhibits particle production and fails to factorise. This is conjectured to happen due to IR ambiguities in the massless tree-level amplitudes. We present a definition of the massless S-matrix which has all the nice properties of integrable theories, there is no particle production and the S-matrix factorises. As an example, we present in detail the case of the $SU(2)$ principal chiral model (PCM)., Comment: 32 pages

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

While extensive research has focused on ChatGPT in recent years, very few studies have systematically quantified and compared linguistic features between human-written and Artificial Intelligence (AI)-generated language. This study aims to investigate how various linguistic components are represented in both types of texts, assessing the ability of AI to emulate human writing. Using human-authored essays as a benchmark, we prompted ChatGPT to generate essays of equivalent length. These texts were analyzed using Open Brain AI, an online computational tool, to extract measures of phonological, morphological, syntactic, and lexical constituents. Despite AI-generated texts appearing to mimic human speech, the results revealed significant differences across multiple linguistic features such as consonants, word stress, nouns, verbs, pronouns, direct objects, prepositional modifiers, and use of difficult words among others. These findings underscore the importance of integrating automated tools for efficient language assessment, reducing time and effort in data analysis. Moreover, they emphasize the necessity for enhanced training methodologies to improve the capacity of AI for producing more human-like text.

Spin polarization in chiral molecules is a magnetic molecular response associated with electron transport and enantioselective bond polarization that occurs even in the absence of an external magnetic field. An unexpected finding by Santos and co-workers reported enantiospecific NMR responses in solid-state cross-polarization (CP) experiments, suggesting a possible additional contribution to the indirect nuclear spin-spin coupling in chiral molecules induced by bond polarization in the presence of spin-orbit coupling. Herein we provide a theoretical treatment for this phenomenon, presenting an effective spin-Hamiltonian for helical molecules like DNA and density functional theory (DFT) results on amino acids that confirm the dependence of J-couplings on the choice of enantiomer. The connection between nuclear spin dynamics and chirality could offer insights for molecular sensing and quantum information sciences. These results establish NMR as a potential tool for chiral discrimination without external agents., Comment: 102 pages, 16 figures, 40 tables

We consider \emph{weighted group search on a disk}, which is a search-type problem involving 2 mobile agents with unit-speed. The two agents start collocated and their goal is to reach a (hidden) target at an unknown location and a known distance of exactly 1 (i.e., the search domain is the unit disk). The agents operate in the so-called \emph{wireless} model that allows them instantaneous knowledge of each others findings. The termination cost of agents' trajectories is the worst-case \emph{arithmetic weighted average}, which we quantify by parameter $w$, of the times it takes each agent to reach the target, hence the name of the problem. Our work follows a long line of research in search and evacuation, but quite importantly it is a variation and extension of two well-studied problems, respectively. The known variant is the one in which the search domain is the line, and for which an optimal solution is known. Our problem is also the extension of the so-called \emph{priority evacuation}, which we obtain by setting the weight parameter $w$ to $0$. For the latter problem the best upper/lower bound gap known is significant. Our contributions for weighted group search on a disk are threefold. \textit{First}, we derive upper bounds for the entire spectrum of weighted averages $w$. Our algorithms are obtained as a adaptations of known techniques, however the analysis is much more technical. \textit{Second}, our main contribution is the derivation of lower bounds for all weighted averages. This follows from a \emph{novel framework} for proving lower bounds for combinatorial search problems based on linear programming and inspired by metric embedding relaxations. \textit{Third}, we apply our framework to the priority evacuation problem, improving the previously best lower bound known from $4.38962$ to $4.56798$, thus reducing the upper/lower bound gap from $0.42892$ to $0.25056$.

We present several advancements in search-type problems for fleets of mobile agents operating in two dimensions under the wireless model. Potential hidden target locations are equidistant from a central point, forming either a disk (infinite possible locations) or regular polygons (finite possible locations). Building on the foundational disk evacuation problem, the disk priority evacuation problem with $k$ Servants, and the disk $w$-weighted search problem, we make improvements on several fronts. First we establish new upper and lower bounds for the $n$-gon priority evacuation problem with $1$ Servant for $n \leq 13$, and for $n_k$-gons with $k=2, 3, 4$ Servants, where $n_2 \leq 11$, $n_3 \leq 9$, and $n_4 \leq 10$, offering tight or nearly tight bounds. The only previous results known were a tight upper bound for $k=1$ and $n=6$ and lower bounds for $k=1$ and $n \leq 9$. Second, our work improves the best lower bound known for the disk priority evacuation problem with $k=1$ Servant from $4.46798$ to $4.64666$ and for $k=2$ Servants from $3.6307$ to $3.65332$. Third, we improve the best lower bounds known for the disk $w$-weighted group search problem, significantly reducing the gap between the best upper and lower bounds for $w$ values where the gap was largest. These improvements are based on nearly tight upper and lower bounds for the $11$-gon and $12$-gon $w$-weighted evacuation problems, while previous analyses were limited only to lower bounds and only to $7$-gons.

Newly diagnosed Type 1 Diabetes (T1D) patients often struggle to obtain effective Blood Glucose (BG) prediction models due to the lack of sufficient BG data from Continuous Glucose Monitoring (CGM), presenting a significant "cold start" problem in patient care. Utilizing population models to address this challenge is a potential solution, but collecting patient data for training population models in a privacy-conscious manner is challenging, especially given that such data is often stored on personal devices. Considering the privacy protection and addressing the "cold start" problem in diabetes care, we propose "GluADFL", blood Glucose prediction by Asynchronous Decentralized Federated Learning. We compared GluADFL with eight baseline methods using four distinct T1D datasets, comprising 298 participants, which demonstrated its superior performance in accurately predicting BG levels for cross-patient analysis. Furthermore, patients' data might be stored and shared across various communication networks in GluADFL, ranging from highly interconnected (e.g., random, performs the best among others) to more structured topologies (e.g., cluster and ring), suitable for various social networks. The asynchronous training framework supports flexible participation. By adjusting the ratios of inactive participants, we found it remains stable if less than 70% are inactive. Our results confirm that GluADFL offers a practical, privacy-preserving solution for BG prediction in T1D, significantly enhancing the quality of diabetes management.

Cosmic shear is a powerful probe of cosmology, but it is affected by the intrinsic alignment (IA) of galaxy shapes with the large-scale structure. Upcoming surveys like Euclid and Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) require an accurate understanding of IA, particularly for higher-order cosmic shear statistics that are vital for extracting the most cosmological information. In this paper, we report the first detection of third-order IA correlations using the LOWZ galaxy sample from the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey (BOSS). We compare our measurements with predictions from the MICE cosmological simulation and an analytical NLA-inspired model informed by second-order correlations. We also explore the dependence of the third-order correlation on the galaxies' luminosity. We find that the amplitude $A_\mathrm{IA}$ of the IA signal is non-zero at the $4.7\sigma$ ($7.6\sigma$) level for scales between $6 h^{-1} \mathrm{Mpc}$ ($1 h^{-1} \mathrm{Mpc}$) and $20 h^{-1} \mathrm{Mpc}$. For scales above $6 h^{-1}\mathrm{Mpc}$ the inferred AIA agrees both with the prediction from the simulation and estimates from second-order statistics within $1\sigma$ but deviations arise at smaller scales. Our results demonstrate the feasibility of measuring third-order IA correlations and using them for constraining IA models. The agreement between second- and third-order IA constraints also opens the opportunity for a consistent joint analysis and IA self-calibration, promising tighter parameter constraints for upcoming cosmological surveys., Comment: 10 pages + appendix, 4 figures, replaced by version accepted by Astronomy and Astrophysics after minor changes

Commercially impactful quantum algorithms such as quantum chemistry and Shor's algorithm require a number of qubits and gates far beyond the capacity of any existing quantum processor. Distributed architectures, which scale horizontally by networking modules, provide a route to commercial utility and will eventually surpass the capability of any single quantum computing module. Such processors consume remote entanglement distributed between modules to realize distributed quantum logic. Networked quantum computers will therefore require the capability to rapidly distribute high fidelity entanglement between modules. Here we present preliminary demonstrations of some key distributed quantum computing protocols on silicon T centres in isotopically-enriched silicon. We demonstrate the distribution of entanglement between modules and consume it to apply a teleported gate sequence, establishing a proof-of-concept for T centres as a distributed quantum computing and networking platform., Comment: 14 pages, 13 figures

Advances in Large Language Models (LLMs) have led to significant interest in their potential to support human experts across a range of domains, including public health. In this work we present automated evaluations of LLMs for public health tasks involving the classification and extraction of free text. We combine six externally annotated datasets with seven new internally annotated datasets to evaluate LLMs for processing text related to: health burden, epidemiological risk factors, and public health interventions. We initially evaluate five open-weight LLMs (7-70 billion parameters) across all tasks using zero-shot in-context learning. We find that Llama-3-70B-Instruct is the highest performing model, achieving the best results on 15/17 tasks (using micro-F1 scores). We see significant variation across tasks with all open-weight LLMs scoring below 60% micro-F1 on some challenging tasks, such as Contact Classification, while all LLMs achieve greater than 80% micro-F1 on others, such as GI Illness Classification. For a subset of 12 tasks, we also evaluate GPT-4 and find comparable results to Llama-3-70B-Instruct, which scores equally or outperforms GPT-4 on 6 of the 12 tasks. Overall, based on these initial results we find promising signs that LLMs may be useful tools for public health experts to extract information from a wide variety of free text sources, and support public health surveillance, research, and interventions., Comment: 33 pages. Feedback and comments are highly appreciated

We study the spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice for $S\!=\!1/2$, $1$ and $3/2$, by using the coupled cluster method (CCM) of microscopic quantum many-body theory. This system is one of the earliest extensions of the Kitaev model and is believed to contain two extended spin liquid phases for any value of the spin quantum number $S$. We show that the CCM delivers accurate estimates for the phase boundaries of these spin liquid phases, as well as other transition points in the phase diagram. Moreover, we find evidence of two unexpected narrow phases for $S\!=\!1/2$, one sandwiched between the zigzag and ferromagnetic phases and the other between the N\'eel and the stripy phases. The results establish the CCM as a versatile numerical technique that can capture the strong quantum-mechanical fluctuations that are inherently present in generalized Kitaev models with competing bond-dependent anisotropies., Comment: 16 pages, 10 figures. This version: figures 5,8 and 10 updated, Table I updated, references added

In this work, we introduce a modular framework for specifying distributed systems that we call AMECOS. Specifically, our framework departs from the traditional use of sequential specification, which presents limitations both on the specification expressiveness and implementation efficiency of inherently concurrent objects, as documented by Casta\~neda, Rajsbaum and Raynal in CACM 2023. Our framework focuses on the interactions between the various system components, specified as concurrent objects. Interactions are described with sequences of object events. This provides a modular way of specifying distributed systems and separates legality (object semantics) from other issues, such as consistency. We demonstrate the usability of our framework by (i) specifying various well-known concurrent objects, such as registers, shared memory, message-passing, reliable broadcast, and consensus, (ii) providing hierarchies of ordering semantics (namely, consistency hierarchy, memory hierarchy, and reliable broadcast hierarchy), and (iii) presenting a novel axiomatic proof of the impossibility of the well-known Consensus problem.

The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows. Specifically, in the context of estimation, we seek the most likely evolution realizing measured spatio-temporal marginals of killed particles. In the context of control, we seek a suitable control action directing the killed process toward spatio-temporal probabilistic constraints. To this end, we derive a new Schr\"odinger system of coupled, in space and time, partial differential equations to construct the solution of the proposed problem. Further, we show that a Fortet-Sinkhorn type of algorithm is available to attain the associated bridge. A key feature of our framework is that the obtained bridge retains the Markovian structure in the prior process, and thereby, the corresponding controller takes the form of state feedback., Comment: 6 pages, 2 figures

Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or encoding political of friendship differences in social networks. However, it is often the case that only an aggregate consequence of such edge weights that characterize relations may be directly observable, as in protein expression of in gene regulatory networks. Thus, learning edge weights poses a significant challenge that is further exacerbated for intricate and large-scale networks. In this article, we address a model problem to determine the strength of sign-indefinite relations that explain marginal distributions that constitute our data. To this end, we develop a paradigm akin to that of the Schr\"odinger bridge problem and an efficient Sinkhorn type algorithm (more properly, Schr\"odinger-Fortet-Sinkhorn algorithm) that allows fast convergence to parameters that minimize a relative entropy/likelihood criterion between the sought signed adjacency matrix and a prior. The formalism that we present represents a novel generalization of the earlier Schr\"odinger formalism in that marginal computations may incorporate weights that model directionality in underlying relations, and further, that it can be extended to high-order networks -- the Schr\"odinger-Fortet-Sinkhorn algorithm that we derive is applicable all the same and allows geometric convergence to a sought sign-indefinite adjacency matrix or tensor, for high-order networks. We demonstrate our framework with synthetic and real-world examples.