Arboreal categories were introduced as an axiomatic framework for game comonads, which provide a comonadic view on many model-comparison games in logic. We demonstrate the inadequacy of the axiom stating that paths are connected. We then propose the notion of ``tree-connectedness'' to address this deficiency, and show that all the essential properties of arboreal categories that we are aware of remain valid under this new definition. Furthermore, we show that the path functor is a Street fibration.

We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the tensor coupling a constant term is also included, since this gives rise to an effective Coulomb potential, which is necessary for the formation of bound states in a pure tensor coupling configuration. The exact bound-state solutions for this generalized Coulomb problem are computed by exploiting the freedom in choosing the coefficients of the \textit{Ansätze} for the radial functions, which leads to wave functions in terms of generalized Laguerre polynomials. From the quantization condition, the exact energy spectrum is also determined and its dependence on the parameters of the potentials is discussed. We show that similar features of the equations for the problem in the plane and the spherically symmetric problem allow a simple and direct mapping between them, thereby providing the solution to the spherical Coulomb problem. Our results are validated by showing that the solutions correctly encompass several previous solutions available in the literature for particular cases of this problem, for which we further develop the analysis of the parameters. We also derive two new particular cases not yet reported in the literature: the case of breaking of spin and pseudospin symmetries by the addition of a Coulomb plus constant tensor potential and the problem of a scalar plus tensor Coulomb potentials.

Despite significant progress in cosmological simulations of galaxy formation, the role of subgrid physics in shaping the detailed properties of galaxies remains incompletely understood. In this work, we analyze two sets of zoom-in simulations that share identical initial conditions but adopt distinct implementations of baryonic physics, enabling a controlled comparison of their predictions. We examine the stellar properties, morphological structures, and satellite populations of the simulated galaxies at $z=0$. We find that AURIGA galaxies systematically exhibit higher stellar masses and surface densities than their APOSTLE counterparts. These differences are primarily driven by variations in the efficiency of gas cooling from the circumgalactic medium (CGM) into the star-forming gas. Both simulations form well-defined disk galaxies; however, AURIGA systems generally display higher disk-to-total mass ratios, earlier disk formation, and more prominent dynamical structures such as bars and spiral arms. Nevertheless, strongly disk-dominated systems are present in both simulations, although they do not arise in the same host haloes. The vertical disk structure in both simulations is well described by a sech density profile, with scale heights below ~ 1 kpc in the inner regions. The satellite populations also differ, with AURIGA producing systematically more massive satellites, including a ~ 0.3 dex increase in the most massive system, while the number of satellites above $10^6 M_{\odot}$ remains comparable in most halo pairs. Both simulations reproduce similar satellite stellar mass--metallicity relations, albeit ~ 0.25 dex higher than observation. This comparative study therefore provides useful benchmarks for future efforts to better constrain galaxy formation models.

In this paper, we present a Hybrid Wavelet-based Physics-Informed Neural Networks (HW-PINNs) framework for portfolio management that provides a promising alternative to Physics-Informed Neural Networks (PINNs). Here, we first discuss the generalized framework of the Merton jump diffusion model and the associated HW-PINNs, followed by the one-dimensional case of a European option. Our work adapts the HW-PINN framework to the Merton jump-diffusion model for a European option, using a simplified direct coefficient optimization strategy, a mathematically corrected log-space formulation, and an efficient FFT -based computation of the integro-differential operator. Through numerical experiments across realistic market scenarios, we show that our proposed model achieves high accuracy and robustness, with a mean relative error of 0.27\% in low jump intensity scenarios compared to high-fidelity benchmarks. Our results validate that the implementation of this specific HW-PINN framework is a computationally efficient and reliable tool for pricing derivatives in markets with high jump risk. In addition, we further discuss risk analysis using Value at Risk (VaR) and Conditional Value at Risk (CVaR), which provide insights into downside risk across different market scenarios.

Modern democracies face an existential crisis of waning public trust in election results. While End-to-End Verifiable (E2E-V) voting systems promise mathematically secure elections, their reliance on complex cryptography creates a ``black box'' that forces blind trust in opaque software or external experts, ultimately failing to build genuine public confidence. To solve this, we introduce the concept of Software-Free Verification (SFV) -- a standard requiring that voters can independently verify election integrity without relying on any software. We propose a practical, non-cryptographic in-booth voting scheme that achieves SFV for national-scale elections. Our approach leverages a public bulletin board of randomized (Pseudonym, Candidate) pairs, where a mechanically generated pseudonym is hidden among real decoy votes on a physical receipt. Our scheme empowers citizens to audit the election using only basic arithmetic via a hierarchical Public Ledger, while anchoring the overall digital tally to physical evidence and Risk-Limiting Audits (RLAs) to guarantee systemic integrity. The result is a system that bridges the gap between mathematical security and public transparency, offering a viable blueprint for restoring trust in democratic infrastructure.

There is an increasing interest in telling serious stories with data. Designers organize information, construct narratives, and present findings to inform audiences. However, many of these practices emerge from modern information visualization rhetoric and ethical frameworks which may marginalize communities with low digital and media literacy. In a ten-month-long ethnographic study in three Bangladeshi villages, we investigated how these communities use entertainment and cultural practices, namely Puthi, Bhandari Gaan, and Pot music, to instruct, communicate traditional moral lessons and recall history. We found that these communities embrace polyvocality and multiple ethical frameworks in their performances, construct narratives combining factuality, emotionality, and aesthetics, and adapt their performances to changing technology and audience needs. Our findings provide HCI, visualization, and ethical data practitioners with implications for the design of accessible and culturally appropriate ways of presenting data narratives in data-driven systems.

Hedonic games are an archetypal problem in coalition formation, where a set of selfish agents want to partition themselves into stable coalitions. In this work, we focus on two natural constraints on the possible outcomes. First, we require that exactly k coalitions are created. Then, loosely following the model of Bilò et al. (AAAI 2022), we assume that each of the k coalitions is additionally associated with a lower and upper bound on its size. The notion of stability that we study is that of individual rationality (IR), which requires that no agent strictly prefers to be alone compared to being in his or her coalition. Although IR is trivially satisfiable even in the most general models of hedonic games, the complexity picture of deciding whether an IR allocation exists, considering the above constraints, is unexpectedly rich. We reveal that tractable fragments of this computational problem require surprisingly nontrivial arguments, even if we restrict ourselves to additively separable and fractional hedonic games. Our tractability results, achieved by exploiting the structure of the underlying preference graph, are also complemented by their intractability counterparts, painting a fairly complete picture of the tractability landscape of this problem.

In this paper, we consider $C^1$ cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the construction and basic properties of polynomial and rational $C^1$ cubic Powell-Sabin spline representations on unstructured triangulations. Then, we discuss how these flexible representations can be exploited to create geometry mappings suited for a precise description of (classes of) surface domains. This is illustrated with several examples. Finally, the obtained domain descriptions are utilized in the isogeometric analysis framework for solving various Poisson and biharmonic problems. It is demonstrated that $C^1$ cubic Powell-Sabin splines form a powerful alternative to $C^0$ cubic Lagrange elements and bicubic NURBS.

A finite, normal cover $f: X\longrightarrow \bbP^2$ of degree $m\geq 3$ (the case $m=2$ is well known and we do not consider it in this paper) is called \emph{simple}, if there is a pencil $\mathcal P$ of rational curves of $\bbP^2$ such that the pull back via $f$ of $\mathcal P$ is a pencil of rational curves on $X$. Up to Cremona equivalence $\mathcal P$ can be assumed to be the pencil of lines through a fixed point $p\in \bbP^2$. If $\frakB$ is the branch curve of such a multiple plane, the general line through $p$ has to intersect $\frakB$ in $2m-2$ branch points (counted with multiplicities). If $p$ is not one of these branch points, then the multiple plane is said to be \ \emph{simpler}. \ In that case the branch curve will have a point of multiplicity $°(\frakB)-2m+2$ at $p$. In this paper we classify, under suitable generality conditions for the branch curve, { simpler } triple planes up to Cremona equivalence (they belong to infinitely many non--Cremona equivalent families) and we give examples of infinitely many non--Cremona equivalent families of {simpler } multiple planes of degree $m\geq 4$.

We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many interacting particles. Moreover, we also provide non-asymptotic quantitative bounds on the spatial decay of correlations at times $t>0$ and then apply these results to show that interacting particle systems on $\mathbb{Z}$ whose interaction strengths decays exponentially fast cannot spontaneously break the time-translation symmetry, neither in the strong, nor in the weak sense.

Bipartite graphs serve as a natural model for representing relationships between two different types of entities. When analyzing bipartite graphs, butterfly counting is a fundamental research problem that aims to count the number of butterflies (i.e., 2x2 bicliques) in a given bipartite graph. While this problem has been extensively studied in the literature, existing algorithms usually necessitate access to a large portion of the entire graph, presenting challenges in real scenarios where graphs are extremely large and I/O costs are expensive. In this paper, we study the butterfly counting problem under the query model, where the following query operations are permitted: degree query, neighbor query, and vertex-pair query. We propose TLS, a practical two-level sampling algorithm that can estimate the butterfly count accurately while accessing only a limited graph structure, achieving significantly lower query costs under the standard query model. TLS also incorporates several key techniques to control the variance, including "small-degree-first sampling" and "wedge sampling via small subsets". To ensure theoretical guarantees, we further introduce two novel techniques: "heavy-light partition" and "guess-and-prove", integrated into TLS. With these techniques, we prove that the algorithm can achieve a (1+eps) accuracy for any given approximation parameter 0 < eps < 1 on general bipartite graphs with a promised time and query complexity. In particular, the promised time is sublinear when the input graph is dense enough. Extensive experiments on 15 datasets demonstrate that TLS delivers robust estimates with up to three orders of magnitude lower query costs and runtime compared to existing solutions.

The ultrawide-bandgap semiconductor $β$-Ga2O3 holds exceptional promise for next-generation power electronics and deep-ultraviolet optoelectronics, yet its widespread application is hindered by the lack of cost-effective, high-quality heteroepitaxial thin films. Here, we demonstrate an interpretable machine learning framework that efficiently navigates the complex, multiparameter process space of pulsed laser deposition (PLD) to achieve high-crystallinity $β$-Ga2O3 epitaxy on c-plane sapphire. By systematically benchmarking nine regression algorithms under limited experimental data conditions, we identify quadratic polynomial ridge regression as the optimal surrogate model, which combines predictive accuracy (R$^2$ $\approx$ 0.86) with full physical transparency through explicit analytical coefficients. Coupling this model with SHAP (SHapley Additive exPlanations) analysis and iterative experimental design, we construct a closed-loop optimization workflow that progressively refines the process-performance landscape over only three experimental rounds. This data-efficient strategy reduces the X-ray rocking curve (RC) full-width at half-maximum (FWHM) by 70$\%$ from > 3$^{\circ}$ to 0.92$^{\circ}$, which is the best reported value for PLD-grown $β$-Ga2O3 on sapphire. Intriguingly, concurrent modeling of surface roughness reveals that crystalline quality and surface morphology are governed by distinct dominant factors: temperature primarily controls bulk crystallinity, whereas oxygen pressure dictates surface kinetics. This decoupled mechanism, quantitatively captured for the first time via feature importance analysis, provides actionable physical insight for independent optimization of structural and morphological properties. Our work establishes a generalizable, resource-efficient paradigm for intelligent process development in oxide epitaxy and beyond.

Theories of ion-scale microinstabilities in tokamaks and stellarators typically assume that the passing electrons respond adiabatically due to their fast propagation speed. However, when the magnetic shear becomes sufficiently small, ion-scale modes can extend far along the magnetic field and the non-adiabatic response of passing electrons becomes important. We derive a theory of extended modes at low magnetic shear through a multiscale expansion of the gyrokinetic equation. The theory elucidates the physics of the geodesic extended mode, a new type of microinstability. The new mode couples the non-adiabatic physics of both electrons and ions, unlike extended modes at magnetic shear of order unity. The theory is validated against gyrokinetic simulations and the parameter dependences of the new mode are studied.

Integrating the scalability of individually addressable arrays of optical-tweezer-trapped single atoms with the efficient light-matter interface provided by nanophotonic waveguides has been a long-standing challenge in quantum technologies based on atoms and photons. Here we realize a quantum interface between photons guided in an optical nanofiber with a diameter of 310 nm and an array of on average 155 individually addressable atoms. Using a spatial light modulator and an objective lens with NA = 0.45, single cesium atoms are trapped in a one-dimensional array of 200 optical tweezer spots with micrometer-scale trap sizes on the nanofiber. Individual atoms are addressed by spatially scanning an excitation laser beam, focused to a spot size comparable to that of the traps through the same objective lens, along the nanofiber. We confirm the single-atom nature of the individual trapping sites through photon-correlation measurements of the guided fluorescence, observing strong photon antibunching with $g^{(2)}(0) \approx 0.26$. We measure trap lifetimes of a few hundred milliseconds, with a maximum value of 460 ms, at an atom-surface separation of 670 nm without active cooling, representing an order-of-magnitude improvement over previous nanofiber traps. This platform opens a new regime for atom-photon interfaces, paving the way for scalable distributed quantum computing and quantum networks, as well as for the exploration of collective radiative effects in waveguide QED with individually addressable atoms.

We study the many-body localization (MBL) transition in interacting fermionic systems on disordered one-dimensional lattices using a physics-informed machine-learning framework. Instead of feeding full many-body wave functions into the model, we construct a compact feature representation based on four physically motivated observables: the inverse participation ratio, the Shannon entropy, the many-body hybridization parameter, and the mean level-spacing ratio. These quantities capture complementary aspects of localization, entanglement, and spectral correlations, and are used to train a Kolmogorov--Arnold Network (KAN) classifier on eigenstates deep in the weak and strong disorder regimes. The resulting KAN achieves a validation accuracy exceeding $99.9\%$, comparable to that of convolutional neural networks trained directly on high-dimensional wave-function data, while requiring substantially reduced input dimensionality and significantly shorter training time. Applying the trained classifier across the full energy spectrum yields energy-resolved phase diagrams that reveal a clear many-body mobility edge and provide a consistent estimate of the critical disorder strength. The approach is inherently extensible: additional physically relevant observables can be incorporated into the feature space in a systematic manner without altering the overall architecture. Our results demonstrate that feature-based learning with KAN provides an efficient, scalable, and interpretable methodology for identifying many-body localization transitions, offering a practical alternative to raw-data-based neural network approaches.

We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the energy. However, for initial conditions in a suitable subspace, a detailed analysis of the resolvent norm for low frequencies leads to sharp polynomial time-decay rates for the solution and its energy.

This paper studies coordinated trajectory planning and tracking control for multiple unmanned surface vessels (USVs) under strict privacy requirements. To avoid the privacy risks associated with direct position sharing in conventional cooperative methods, the proposed approach adopts an estimated fleet centroid as the only shared variable, preventing individual trajectory disclosure while enabling coordination. Based on this interaction mechanism, a formation-oriented trajectory is generated for the fleet. The collective dynamics are modeled using Port-Hamiltonian systems, and a passivity-based tracking controller is designed for each USV to accurately follow the planned trajectories. The stability of the closed-loop system is rigorously proven, and experiments on a real USV platform confirm effective formation tracking and privacy preservation. The proposed result extends and validates through experimental results the approach in [26] that was limited to idealized pointmass models and lacked a feedback control.

We propose a method for reasoning about trust in multi-agent systems, specifying a language for describing communication protocols and making trust assumptions and derivations. This is given an interpretation in a modal logic for describing the beliefs and communications of agents in a network. We define how information in the network can be shared via forwarding, and how trust between agents can be generalized to trust across networks. We give specifications for the modal logic which can be readily adapted into a lambda calculus of proofs. We show that by nesting modalities, we can describe chains of communication between agents, and establish suitable notions of trust for such chains. We see how this can be applied to trust models in public key infrastructures, as well as other interaction protocols in distributed systems.

Solitons are localized nonlinear wave packets that propagate without spreading because nonlinearity balances dispersion. Their robustness is well understood in effectively one-dimensional systems, but introducing additional spatial dimensions is generally expected to destabilize them or destroy their coherent character. Here we experimentally investigate how deep-water gravity-wave solitons behave when a controlled transverse degree of freedom is introduced through diffraction. Using a large-scale water-wave facility, we generate solitonic wave packets whose transverse structure is imposed across a segmented wavemaker through either a sharp slit or a smooth Gaussian apodization. The resulting two-dimensional wave fields are measured with high spatial resolution. Diffraction reshapes the transverse profile of the wave packet while its longitudinal dynamics retain the characteristic features of a soliton. Nonlinear spectral analysis confirms that the solitonic content is preserved along the direction of propagation, whereas the transverse evolution follows the linear Fresnel laws of diffraction. These observations reveal an unexpected coexistence of nonlinear soliton dynamics and classical wave diffraction.

Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in $BMO^{-1}$. Inspired by their breakthrough work, we develop their schemes for the incompressible magnetohydrodynamic equations and obtain a similar result in 5 dimensional case. More precisely, we construct two distinct global solutions with a initial data, which has nonvanishing velocity and magnetic fields in $BMO^{-1}(\mathbb{T}^5)$.

The sequence of eclipses of binary stars is subject to inequalities for various reasons. The presence of a third component in the system causes periodic motion of the binary's center of mass along the line of sight of an observer. The finite value of the light velocity implies that the epochs of eclipses periodically advance and delay with respect to the exact orbital period of the binary, a phenomenon termed the light-time effect (LITE). We aim to refine two aspects of the mathematical treatment of LITE. First, we provide both generalized and more accurate analytic formulation describing the light-travel time in the binary system itself presented in previous works. Second, we analytically estimate the so far neglected coupling of LITE with the dynamical interaction of the binary orbit with the motion of the third star. Our principal results are given in a simple analytical form, which is suitable for the analysis of photometric observations that require minimization over a multidimensional parameter space of the triple system. The leading correction to the traditional formulation of LITE due to the light-travel time in the binary system may be detectable for triple systems with a period ratio of $P_2/P_1\lesssim 20$, for which accurate photometric observations are available. On the other hand, the correction due to the dynamical coupling of the two orbits with $P_2$ periodicity is small, but may become relevant in the future.

In the present study, wakefield amplification via coherent resonant excitation using two co propagating laser pulses in a homogeneous plasma is investigated. The proposed scheme is based on linearly polarized leading seed pulse followed by a trailing pulse with identical or controlled parameters, enabling phase synchronized energy transfer to the plasma wave. By systematically varying the temporal pulse widths and inter pulse separation, conditions for resonant enhancement of the wakefield are established. Analytical modelling, supported by particle in cell simulations, reveals that maximum amplification occurs when the pulse separation approaches a quarter of the plasma wavelength, ensuring constructive interference of the plasma oscillations driven by successive pulses. Under optimal conditions, the coherent resonant excitation leads to a significant enhancement of the wakefield amplitude, reaching up to three times of that produced by a single laser pulse. The results demonstrate that precise control of pulse spacing and duration enables efficient energy coupling into plasma waves, providing a robust pathway for enhanced wakefield generation in laser plasma interaction regimes.

As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier--Stokes equations in the half-plane $R^2_+$ with no-slip boundary condition and point vortices as initial data. We focus on the paradigmatic example of a single vortex in an otherwise stagnant fluid, which is already quite challenging from a mathematical point of view. We prove that this system has a unique global solution for all values of the Reynolds number $|Γ|/ν$, where $Γ$ is the circulation of the vortex and $ν$ the kinematic viscosity of the fluid. The solution we construct has finite energy for positive times and converges to zero in energy norm as $t \to +\infty$. Uniqueness holds under the assumption that the solution is close to a Lamb--Oseen vortex for small times. To our knowledge, all previous results in domains with boundaries assume that the initial vorticity has small or zero atomic part. In our particular situation, we remove the smallness condition by decomposing the solution into a vortex and a boundary layer term, so that we can apply the techniques developed in the whole plane $R^2$ to avoid the difficulties related to the large circulation of the vortex.

Africa's participation in modern AI development is constrained by severe infrastructural and policy gaps. Important barriers include limited access to high-performance computing (HPC), restricted cloud access due to payment system mismatches, volatile exchange rates, and strict data sovereignty laws that fragment regional collaboration between African Union (AU) member states. Although initiatives such as Cassava AI's network of AI factories to be deployed across the continent signal the growing interest in adopting AI in Africa, these projects remain very targeted, while continental adoption still requires better coordination between African stakeholders. Drawing on official declarations on AI adoption across the continent, this paper offers both qualitative and quantitative evidence that sustainable AI adoption requires robust digital foundations through balanced access to compute, data, and the energy that makes it possible. We refer to these foundations as the "right enablers", considering them as crucial components for success within the current context of the global AI race. We also introduce the \textit{Africa AI Compute Tracker (ACT)}, an interactive map to monitor the availability of AI-ready HPC systems throughout the continent. This tool represents the first open-source effort to consolidate data on Africa's evolving HPC landscape, and aims to encourage more transparency from local AI stakeholders while facilitating broader access for AI developers. The work presented in this paper underscores the urgency of tangible actions aimed at closing the AI divide and allowing Africa to actively shape its AI future.

We investigate putative quantum Hall effect states, labeled by their K-matrix equal to (1 1 3), by defining them on the torus and computing their Hall viscosity. Such states have been introduced on the sphere as a phase distinct from Pfaffian and anti-Pfaffian ones. This was done in order to explain certain results on thermal Hall conductivity in favor of particle-hole symmetric Pfaffian topological order in presence of Landau level mixing. The requirements of boundary conditions, modular invariance and ground state degeneracy are enough to uniquely fix the form of the proposed wave functions. We generalize a method to enforce them which we call monodromy matching and check our results on wave functions and Hall viscosity against realizations on the torus of Laughlin and hierarchical states. We highlight the issues in the realization of these states, which turn out to exhibit the formation of clusters. We show that the effect of anti-symmetrization on the system is not enough to prevent clustering; we compute the Hall viscosity for the Halperin version of these states and the fully anti-symmetrized one and we find them being dependent on the geometry and the particle number.

We show that, given an evolving quantum system and the quasiprobability distribution generated by the spatiotemporal generalization of the Born rule in pseudo density-matrices (PDMs), this distribution deviates from the sequential measurements probability distribution, given by the Lüders von-Neumann distribution, if and only if the non-signaling in time (NSIT) is violated; equivalently, if and only if the macroscopic realism (MR) is violated. Furthermore, we propose a definition of temporal entanglement according to the structure of the PDMs that is analogous to the definition of spatial entanglement in density matrices, showing that temporal entanglement is necessary for the violation of temporal Bell inequalities and the violation of MR. We employ our results to study the relationship between the negativity of the PDM, temporal entanglement, violation of temporal Bell inequalities, and MR.

Convolutional neural networks (CNNs) require a large number of multiply-accumulate (MAC) operations. To meet real-time constraints, they often need to be executed on specialized accelerators composed of an on-chip memory and a processing unit. However, the on-chip memory is often insufficient to store all the data required to compute a CNN layer. Thus, the computation must be performed in several offloading steps. We formalise such sequences of steps and apply our formalism to a state of the art decomposition of convolutions. In order to find optimal strategies in terms of duration, we encode the problem with a set of constraints. A Python-based simulator allows to analyse in-depth computed strategies.

X-ray transients on sub-observation timescales represent a diverse and underexplored class of astrophysical phenomena, from stellar flares and magnetar bursts to extragalactic fast transients and supernova shock breakouts. We present a systematic search for such events across 20,212 Chandra ACIS observations using a new detection pipeline that combines source identification, light-curve analysis, catalogue cross-matching, and a novel statistical classifier, the cumulative distribution discriminator (CuDiDi). From 1420 initial candidates, we identified a high-confidence golden sample of 765 transients spanning a broad range of timescales, fluxes, and spectral shapes. The candidates are distributed across the whole sky and show a wide range of durations with a median of 10 ks. A subset of fast events lasting < 30 s displays very soft spectra and is likely due to flaring dwarf stars, although extragalactic phenomena cannot be ruled out for all of them. The comparison with previously published samples showed that CuDiDi identifies most known transients while imposing somewhat stricter variability criteria, and it also extends the total sample of Chandra transients to include shorter events. We deliver a comprehensive catalogue of sub-observation Chandra X-ray transients and establish a general method for exploiting archival datasets to uncover rare short-lived high-energy phenomena.

Recent research on computing the diameter of geometric intersection graphs has made significant strides, primarily focusing on the 2D case where truly subquadratic-time algorithms were given for simple objects such as unit-disks and (axis-aligned) squares. However, in three or higher dimensions, there is no known truly subquadratic-time algorithm for any intersection graph of non-trivial objects, even basic ones such as unit balls or (axis-aligned) unit cubes. This was partially explained by the pioneering work of Bringmann et al. [SoCG '22] which gave several truly subquadratic lower bounds, notably for unit balls or unit cubes in 3D when the graph diameter $Δ$ is at least $Ω(\log n)$, hinting at a pessimistic outlook for the complexity of the diameter problem in higher dimensions. In this paper, we substantially extend the landscape of diameter computation for objects in three and higher dimensions, giving a few positive results. Our highlighted findings include: - A truly subquadratic-time algorithm for deciding if the diameter of unit cubes in 3D is at most 3 (Diameter-3 hereafter), the first algorithm of its kind for objects in 3D or higher dimensions. Our algorithm is based on a novel connection to pseudolines, which is of independent interest. - A truly subquadratic time lower bound for \Diameter-3 of unit balls in 3D under the Orthogonal Vector (OV) hypothesis, giving the first separation between unit balls and unit cubes in the small diameter regime. Previously, computing the diameter for both objects was known to be truly subquadratic hard when the diameter is $Ω(\log n)$. - A near-linear-time algorithm for Diameter-2 of unit cubes in 3D, generalizing the previous result for unit squares in 2D. - A truly subquadratic-time algorithm and lower bound for Diameter-2 and Diameter-3 of rectangular boxes (of arbitrary dimension and sizes), respectively.

Path planning for multiple unmanned aerial vehicles is a difficult task, and even more for a fleet of fixed-wing aircraft. One specific case is the transition to, or between, formation flight patterns, which requires synchronous arrivals while ensuring minimal separation, and ideally maintaining cruise speed. We present a centralized method to solve this problem based on enumerating different Dubins paths. Given a travel time for the fleet, it builds a set of possible paths for each aircraft. Then, it checks in parallel separation between each path pair. This yields coefficients for an Integer Linear Programming problem determining if a fleet-wide conflict-free solution exists. This process is repeated for different travel times sampled with increasing resolution until the user-defined accuracy is met. The method is benchmarked with Monte-Carlo simulations considering up to 20 aircraft simultaneously, achieving an 95% success rate for an average 8 seconds computation time.