Data management can be a complex challenge in fields such as bioinformatics and health sciences, which continuously generate extensive heterogeneous datasets. In the context of collaborative global health initiatives, secure storage and sharing of data are crucial to support impactful research. However, the absence of a unified data management platform complicates efficient data exchange and governance within these initiatives. In this paper, we introduce the design process of OpenHealth Lake, a data management prototype platform based on a data lakehouse architecture, data federation, and the FAIR principles. The platform is designed using open-source tools, guided by system requirements identified in previously published studies and complemented by insights from the existing literature. The current prototype platform comprises a user-friendly website, an open API, Python and R packages, allowing users to interact with the platform in multiple ways. Through a user study that included participants with varying technical backgrounds, we showed that our proposed data management prototype is both usable and useful. Our prototype design showcases the adaptability, scalability, and reproducibility of a lakehouse system that can be used by any organisation. It is designed as a flexible and complementary approach that allows organisations to customise data management systems to their specific requirements and resources, including cloud-based or self-hosted storage choices.

We investigate two-point velocity-gradient correlation functions in homogeneous isotropic turbulence using exact relations and direct numerical simulations. The second-order gradient correlation is shown to be exactly related to the Laplacian of the velocity correlation, implying inertial-range scaling $C_2^{1,1}(r)\sim r^{-4/3}$. At higher orders, we uncover a parity-dependent organization of gradient correlations: odd-odd correlations exhibit scaling close to $r^{-4/3}$ with weak dependence on order, whereas even-even correlations display systematically different exponents. We show that this distinction originates from the sign structure of the gradient field: sign decorrelation suppresses intermittent contributions in odd-odd sectors, while even-even correlations retain them and remain sensitive to the spatial organization of intense structures. The measured even-even exponents are quantitatively consistent, across two Reynolds numbers, with independently measured box-counting dimensions of intermittent gradient structures. These results identify parity under sign reversal as a fundamental organizing principle for higher-order turbulent correlations and establish a direct connection between sparse intermittent geometry and scaling exponents in turbulence.

In this paper, a novel dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations is introduced. The discretization satisfies pointwise conservation of mass, magnetic Gauss's law, and conservation of current density. It also obeys a discrete energy law that exactly captures the energy dissipation in the dissipative case and reduces to conservation of energy in the ideal case. Numerical experiments demonstrate the temporal and spatial accuracy, as well as the properties of structure-preservation, are provided.

Can a closed quantum system generate persistent time-crystal-like dynamics without external driving? Within the Bateman dual oscillator framework, we show that the answer is affirmative. We consider a nonrelativistic (2+1)-dimensional system in which spin-induced spatial deformation generates an effective Bateman oscillator structure. After quantization, the system is governed by a time-independent Hermitian Hamiltonian describing coherent coupling between damped and amplified oscillator sectors while preserving the total energy of the global doubled system. Tracing over the amplified sector, we derive an effective non-Markovian reduced dynamics for the observable subsystem. The resulting memory effects sustain persistent oscillations of subsystem observables and generate emergent time-crystal-like temporal ordering without external periodic driving or equilibrium spontaneous symmetry breaking. Since the oscillatory behavior originates from nonequilibrium reduced subsystem dynamics rather than equilibrium expectation values of the full Hamiltonian, the mechanism lies outside the assumptions of conventional no-go theorems for equilibrium time crystals. The same dynamics further exhibits logarithmic-spiral trajectories and self-similar fractal scaling, revealing a direct connection between coherent dissipative dynamics, non-Markovian memory effects, and emergent temporal ordering in a globally unitary quantum system. In this specific sense, "watching the growth" of these self-similar structures corresponds to observing the gradual formation of time-crystal-like ordering.

Classical models of opinion dynamics assume human participants with bounded rationality and limited coordination. The rise of LLM-based agents introduces a qualitative shift: agents can now participate in online discussions at scale, maintain consistent persuasion strategies, and coordinate systematically. This paper argues that LLM agents make collective belief dynamics programmable, enabling deliberate steering of population-level beliefs. We term this emerging problem programmable collective belief control. Through controlled multi-agent simulations, we provide proof-of-concept evidence that coordinated AI agents can induce measurable belief shifts that stabilize within a few interaction rounds. We identify four structural properties (indistinguishability, persistence, contextuality, and configurability) that make detection and defense fundamentally difficult. Based on these findings, we outline a research agenda spanning theoretical foundations for adversarial belief dynamics, operational methods for system-level detection and intervention, and simulation infrastructure for scalable experimentation. Our goal is not to present a complete solution, but to articulate why this problem demands urgent attention and to provide a conceptual foundation for future work.

We study the scattering of charged massive particles impinging on a Reissner-Nordström (RN) black hole immersed in perfect fluid dark matter (PFDM). We obtain an approximation of absorption cross section in the low-frequency regime via the matching method. In the high-frequency regime, we derive the weak-field deflection angle up to second order. The numerical results are in excellent agreement with classical approximation and glory scattering. The effects of dark matter, particle charge, and mass upon scattering and absorption are examined in detail. The results show that as the dark matter parameter $λ$ increases, the absorption cross section of the black hole is strongly suppressed, and its high-frequency limit depends only on the black hole charge $Q$ and $λ$. The scattering cross section also decreases overall. In the superradiant regime, the amplification factor of the PFDM black hole is much larger than that of the RN black hole. Finally, we discuss the behavior of the absorption cross section as $ω/m\rightarrow1$, as well as the scattering cross section at small scattering angles.

Photonic neuromorphic computing offers a promising route to overcoming the limitations of conventional von Neumann architectures by exploiting the high bandwidth, low latency, and massive parallelism of optical systems. However, most existing implementations rely on fixed dynamical substrates such as classic reservoir computing, where learning is restricted to external readout layers and memory is limited to transient fading effects. In this work, I propose a Reconfigurable Nonlinear Photonic Decision Network (RNPDN), a physically grounded neuromorphic framework in which computation, memory, and learning emerge directly from driven-dissipative dynamics. Through numerical simulations, I demonstrate the simultaneous realization of key properties: local physical learning rules enabling adaptive state evolution, a tunable stability-plasticity tradeoff governed by decay and hysteresis mechanisms, controlled memory formation and erasure via bistable photonic states, fading memory, in-situ learning, and hardware-faithful nonlinear dynamics incorporating saturation and dissipation. In contrast to conventional approaches, the proposed system enables intrinsic adaptation within the physical layer while supporting both transient and persistent memory. These results establish a unified framework for adaptive photonic information processing and provide a pathway toward scalable and energy-efficient neuromorphic photonic hardware.

The simulation of quantum transport in nanodevices requires the solution of the Dyson and Keldysh equations, a task dominated by the inversion of massive, block-tridiagonal matrices. While the Recursive Green's Function (RGF) method has long been the standard $O(N)$ solver for quasi-1D systems, its formulation has typically been restricted to sequential execution and nearest-neighbor interactions. In this work, we carefully reformulate RGF through the lens of Domain Decomposition and Schur Complement theory. This allows us to extend the recursive formalism to block $n$-diagonal systems (handling higher-order stencils) and to derive a parallel algorithm, Domain-Decomposition based RGF (DDRGF), which stitches macroscopic domains via reduced interface systems. We explore data dependencies in DDRGF in detail, by means of block-sparse structures and tracing back to the desired output as a block tridiagonal approximation, giving a clear, reproducible and extensible formulation. We validate these algorithms using \texttt{LibNEGF.jl}, a Julia-based implementation, demonstrating that the structural insights of domain decomposition provide a robust pathway for high-performance quantum transport simulations on modern multi-core clusters. The theory presented here lays down the base for tackling the Keldysh problem, to be similarly handled in future stages of our work. Although the target here is the acceleration of kernels in the non-equilibrium Green's function method, the algorithms and the implementations presented can be immediately used in any application involving block $n$-diagonal systems.

Reinforcement learning (RL) has emerged as a promising paradigm for Internet congestion control, achieving higher link utilization than classical heuristics. However, RL-based controllers trained in single-flow environments are not guaranteed to share bandwidth equitably when deployed in multi-flow networks. This paper investigates the fairness properties of Aurora~\cite{jay2019aurora}, a state-of-the-art deep RL congestion controller, and evaluates three post-hoc fairness strategies that preserve Aurora's RL architecture: \emph{reward shaping} (Strategy~A), \emph{observation augmentation} (Strategy~B), and \emph{loss-sensitivity tuning} (Strategy~C). Using a custom shared-bottleneck simulator and Jain's fairness index as the primary metric, we find that modest reward shaping achieves the best fairness while preserving aggregate throughput. All strategies maintain the total bandwidth budget with fairness being achieved through redistribution, not reduction. Beyond the 2-flow homogeneous setting, an extended evaluation across mixed Aurora--CUBIC competition and dynamic flow entry/exit scenarios shows that Strategy~C's loss-sensitivity emerges as the most TCP-friendly mechanism, while Strategy~B is the most stable through dynamic flow-set changes.

We investigate thermoelectric transport in monolayer graphene across a finite complex barrier within a Landauer scattering framework. Solving the Dirac-Weyl problem exactly, we show that the imaginary part of the barrier renders the scattering matrix nonunitary and replaces the usual Hermitian flux conservation by a generalized flux-balance relation determined by the net gain or loss inside the barrier. In the Hermitian limit, the standard graphene $n$-$p$-$n$ barrier behavior is recovered, including perfect transmission at normal incidence and Fabry-Perot-type resonances. For a finite imaginary part, however, the same resonant channels are selectively attenuated or amplified, which significantly modifies both the angular response and the conductance profile. We further show that the lead-resolved conductances become dependent on the bias partition, providing a direct signature of the breakdown of gauge invariance in the effective two-terminal response. At finite temperature, the exact linear-response coefficients reveal a clear trade-off controlled by the imaginary part of the barrier: gain enhances both the electrical and thermal conductances, whereas loss suppresses the thermal conductance more efficiently and yields the largest thermoelectric figure of merit within the parameter range considered. These results demonstrate that complex barriers extend the range of transport behaviors accessible in graphene beyond the usual Hermitian $n$-$p$-$n$ junction. They also suggest a practical interpretation of the imaginary potential as an effective reduced description of unresolved source-sink channels or additional probes coupled to the device, particularly when a fully microscopic model of the environment is not available.

The Fornberg-Whitham (FW) equation was introduced by Fornberg and Whitham [Fornberg and Whitham, Phil. Trans. R. Soc. Lond. A (1978)] as a nonlocal model for unidirectional shallow water waves capable of capturing wave steepening and breaking. Despite its similarities with integrable shallow-water equations, the FW equation is not completely integrable. Nevertheless, the FW equation is part of the family of peakon-type models as it supports peaked traveling wave solutions. In this paper, we consider smooth solitary wave solutions to the FW equation. We use a variational approach to show that some are orbitally stable.

The set of tritangent planes to smooth tropical space sextic curves has 15 connected components, recording continuous displacements of planes preserving the tritangency condition. These 15 tritangent classes are polyhedral complexes in $\mathbf{R}^3$, and each of them contains the tropicalization of precisely eight tritangent planes to any smooth space sextic curve with the given tropicalization. Prior joint work of the authors with Len confirms that each tropical tritangent plane has 0, 1, 2, 4 or 8 lifts to classical tritangent planes defined over the algebraic closure of the field over which the original algebraic curve is defined. Our main theorem states that when the input classical curve is generic, then only six out of the ten possible partitions of 8 into powers of 2 arise from lifting multiplicities of tritangent classes. Furthermore, we show that these partitions are completely determined by the dimension of a suitable connected subcomplex of the class and the existence of a member with a tropical tangency of a predetermined combinatorial type.

We derive a recursive formula for the moments of the number of flips using a possibly biased coin to produce a prescribed finite binary string $S$ when $S$ is either a run of heads or a run of heads followed by a tails. Our recursive formula involve certain sums, which we simplify by using a one-parameter extension of the well-studied Eulerian number, which belongs to the two-parameter family of numbers introduced by Graham, Knuth, and Patashnik. We also use the Goulden--Jackson cluster method and Faà di Bruno's formula to establish a closed formula for the moments in a more general situation where a die having an arbitrary number of faces with possibly different probabilities is rolled repeatedly until a prescribed finite word occurs.

We present new multielement NanoSIMS isotopic measurements (C, N, Si, Mg-Al, Ti, and Ni) for four putative nova SiC grains and 79 AB SiC grains from the Murchison meteorite to reassess their stellar origins. High-resolution imaging and a revised Mg/Al relative sensitivity factor for SiC yield substantially improved 26Al/27Al ratios and the most reliable multielement characterization to date for 13C-rich presolar SiC grains. To interpret these data, we computed an expanded suite of hydrodynamic CO, ONe, and recurrent nova models spanning a range of white-dwarf masses and pre-enrichment parameters. When all isotopic systems are considered together (C, N, Mg-Al, Si, Ti, and Ni), the CO nova models provide the closest and most self-consistent match to both the putative nova grains and the subset of AB grains lacking s-process signatures. CO novae of low- to intermediate-mass naturally reproduce the observed 14N/15N-26Al/27Al trend, the Si isotope compositions of AB grains which dominantly reflect Galactic chemical evolution (GCE), and the mild Si isotope shifts in putative nova grains relative to the GCE trend defined by AB grains. In contrast, ONe and recurrent nova models fail multiple isotopic constraints simultaneously. These results demonstrate that low- to intermediate-mass CO novae (0.6-1.0 Msun) are the most plausible stellar sources of 13C-rich SiC dust lacking s-process signatures (1-2\% of all presolar SiC), and they establish a multielement, model-anchored framework for quantifying nova contributions to the dust reservoir in the interstellar medium.

Background: Large Language Models (LLMs) are increasingly used for code generation. However, their ability to generate multi-class projects that require object-oriented design (OOD) remains unclear, especially relative to projects developed with human involvement. Aims: The primary objective of this study is to compare OOD quality in projects from three authorship conditions: PreAI (human-involved projects produced before widespread LLM use), PostAI (human-involved projects produced after widespread LLM use), and PureAI (projects generated end-to-end by contemporary LLMs). Method: We conducted a comparative case study on a postgraduate Java assignment. Two offerings of the same assignment were selected as the PreAI and PostAI datasets. PureAI projects were generated using three contemporary LLMs. We analyzed OOD quality using project-level OOD metrics, code smell density, and domain modeling. Results: Relative to human-involved projects, PureAI projects show lower code smell density and generally appear simpler in terms of total size, complexity, and coupling. However, this is consistent with oversimplification, as it is associated with missing abstractions and weaker responsibility separation. PostAI is closer to PureAI than PreAI on many OOD measures and also shows tendencies toward oversimplification. Conclusions: Our findings indicate that appropriate human guidance on object-oriented decomposition and responsibility assignment remains important when LLMs are used for object-oriented design.

This paper studies a uniform projection criterion for space-filling designs under the stratified $L_2$-discrepancy. The criterion, denoted by $Φ_{SD}$, is the average squared stratified $L_2$-discrepancy over all two-dimensional projections. For U-type $(n,m,s^p)$ designs, we derive an explicit formula for $Φ_{SD}$ in terms of row-pairwise weighted hierarchical distances, and we establish sharp lower and upper bounds with equality conditions. We further show that many known optimal constructions attain the lower bound of $Φ_{SD}$, and that designs attaining the lower bound of the full stratified $L_2$-discrepancy also attain the lower bound of $Φ_{SD}$. The criterion can be evaluated in $O(n^2m)$ time, with a modest reduction in arithmetic operations compared with direct projection-wise evaluation. Numerical studies illustrate the theoretical results and show that $Φ_{SD}$ is effective for assessing low-dimensional projection uniformity.

The rapid advancement of information technology has introduced a noticeable shift from traditional offline practices to more efficient and interconnected online environments. This transition, while offering convenience, has also increased exposure to various cyber threats such as identity theft, impersonation, and phishing scams. Reconnaissance, or briefly known as information gathering, is a key stage for threat actors, often relying on open-source intelligence (OSINT) to collect sensitive and extensive data on targets. In response to this challenge, this study introduces reconCTI, a command-line tool built using Python for Linux systems. The tool is designed to search for sensitive data leaks across both surface web and dark web platforms. It allows users to input specific keywords, scan multiple sites at once, and then assess the findings by referencing the MITRE ATT&CK framework. The results are compiled into a threat report that also includes possible mitigation strategies. reconCTI is intended to support both cybersecurity professionals and individuals in identifying risks early and taking appropriate action.

We show that a generic analytic strongly convex billiard is "maximally chaotic" in the sense that, for every rational number $\frac{p}{q} \in \mathbb{Q} \cap (0,1)$, all intersections between the stable and unstable manifolds of maximizing periodic orbits with rotation number $\frac{p}{q}$ are transverse.

Motivated by multimodal estimation, we study a multi-view spiked Wigner model in which several noisy matrix observations contain correlated latent spikes. We derive a spectral estimator for the latent spikes by linearizing approximate message passing (AMP). Our main result is an explicit sharp transition formula for its spectrum: for $L \geq 2$ views, letting $λ$ be the $L$-dimensional vector of spike strengths and $B$ the $L\times L$ limiting Gram matrix of the spikes, the critical parameter is $\mathsf{SNR}(λ,B)=λ_{\max}[\mathrm{Diag}(\sqrtλ) (B \odot B) \mathrm{Diag}(\sqrtλ)]$. When $\mathsf{SNR}(λ,B)<1$, the linearized AMP matrix has no outlier beyond the right edge of its bulk spectrum. When $\mathsf{SNR}(λ,B)>1$, an informative outlier is pinned at the distinguished point $1$, and the associated eigenvector has explicit, nontrivial overlaps with the latent signals. Thus $\mathsf{SNR}(λ,B)=1$ gives the exact spectral weak-recovery threshold for the linearized AMP method. To establish our results, we analyze the correlated Gaussian noise matrix through a matrix Dyson equation and combine this deterministic description with finite-rank perturbation arguments adapted to the multi-view spike structure. We also show that, for a broad class of spike priors, the spectral threshold $\mathsf{SNR}(λ,B)=1$ coincides with the information-theoretic threshold for weak recovery, ruling out a statistical-computational gap for this class of priors.

Spontaneous symmetry breaking underlies functional electronic phenomena in quantum materials. Breaking space-inversion ($\mathcal{P}$) or time-reversal ($\mathcal{T}$) symmetry can generate spin-split electronic bands central to modern spintronics. By contrast, parity-violating antiferromagnetic (AFM) order breaks both $\mathcal{P}$ and $\mathcal{T}$ while preserving the combined $\mathcal{PT}$ symmetry, enabling spin-degenerate yet momentum-asymmetric electronic bands. This momentum asymmetry has been proposed as a microscopic origin of unconventional nonreciprocal and nonlinear responses but its experimental verification has remained challenging because it requires establishing both the symmetry-breaking magnetic order and the associated electronic structure. Here we combine soft x-ray angle-resolved photoemission spectroscopy (ARPES) and polarization-resolved optical second-harmonic generation (SHG) microscopy to study LaMnSi, a candidate parity-violating AFM metal. Soft x-ray ARPES resolves the three-dimensional bulk band structures in agreement with density functional theory calculations for the AFM phase, whereas SHG microscopy detects sign-reversing nonlinear optical responses from opposite AFM domains that carry $\mathcal{T}$-odd parity-violating order. Together, these results provide direct evidence for parity-violating AFM state in LaMnSi, establish LaMnSi as a parity-violating AFM metal, and identify this class of AFMs as a promising platform for symmetry-controlled nonreciprocal and nonlinear electronic responses.

Gel-elastomer composites, comprising an active swellable hydrogel and a passive elastomer, are a compelling class of programmable material systems (PMS) capable of shape morphing under multiphysics actuation. The precise design of the topology and material distribution unlocks complex programmability instrumental in wearable electronics, soft robots, and drug delivery; however, the structure-function relationship is highly non-intuitive, rendering both trial-and-error and conventional design approaches largely intractable. To address this, we present a topology optimization (TO) framework for the automated design of such structures, enabling systematic exploration of the design space for target functionalities realized via programmable shape morphing. In particular, we propose a multi-material TO framework that concurrently optimizes the structural topology and the spatial distribution of the gel-elastomer phases. The design is represented via a coordinate-based neural network, and the mechanical response of both phases is described within a unified constitutive framework based on the Flory-Rehner theory. Furthermore, we present an end-to-end differentiable design framework with implicit differentiation that accommodates various objective functions, constraints, and discretizations. We demonstrate the framework on shape-programming structures and soft actuators. The framework is further validated through the design of organogel-hydrogel composites for multi-stimuli responsiveness across chemically distinct solvent environments, and of anisotropic hydrogels wherein the local fiber orientation is optimized concurrently with the topology. The codebase implemented in JAX is publicly shared to support benchmarking and reproducibility.

Reaction-diffusion epidemic models with vital dynamics are an important framework for describing the spatial and temporal spread of infectious diseases. In this work, we present a constraint-aware, physics-informed neural network (PINN) approach to an SEIR reaction-diffusion system with homogeneous Neumann boundary conditions. Due to the scarcity of spatial epidemiological datasets, we generate synthetic benchmark data using structure-preserving implicit-explicit nonstandard finite difference (NSFD) schemes that ensure positivity, boundedness, and numerical stability. The PINN framework integrates PDE residuals, observational data, boundary conditions, and epidemiological constraints within a unified optimization procedure. Specifically, the loss function incorporates the non-negativity of compartment populations and the admissibility of epidemiological parameters. We apply the method to forward simulation and inverse parameter estimation in one- and two-dimensional settings. Numerical experiments demonstrate the framework's ability to accurately reconstruct spatiotemporal epidemic dynamics and reliably identify parameters, even when data is sparse or noisy. These results underscore the potential of constraint-aware PINNs as a robust, data-driven methodology for spatial epidemic modeling.

This paper studies the use of Set Shaping Theory (SST) as a reversible payload-shaping layer for least significant bit (LSB) image steganography. The proposal is not intended to replace existing steganographic methods or to compete with them as a new embedding scheme. Instead, SST is positioned as a complementary preprocessing stage that makes an existing embedding method easier to apply with lower statistical disturbance. The SST transformation increases the message length by K symbols and is implemented with the approximate and fast transformation algorithm developed by Glen Tankersley. Although the embedded payload is lengthened from N to N+K bits, the selected representation can reduce D_KL(P||Q) and therefore make the subsequent steganographic insertion less detectable under histogram-based criteria. Across 1,800 controlled simulations on four synthetic cover-image models, SST reduced D_KL(P||Q) by an average of 25.16 percent relative to a fair N+K LSB baseline, with a 95 percent confidence interval of +/- 1.22 percent. For K=8, the average reduction reached 42.81 percent. Additional robustness simulations with keyed random embedding paths confirmed the effect across several distances: at K=8, SST reduced KL divergence by 42.44 percent, Jensen-Shannon divergence by 29.62 percent, total variation by 12.41 percent, and symmetric chi-square distance by 28.30 percent. An additional image-based matrix-embedding/STC-like simulation showed that SST also reduces the minimum weighted insertion cost: relative to the unshaped K=0 reference, K=8 reduced the cost by 6.93 percent.

Assume that $X$ is a connected, open, oriented smooth surface, $B$ is a compact Euclidean neighbourhood retract, and $\mathscr{J}=\{J_b\}_{b\in B}$ is a continuous family of complex structures on $X$ of local Hölder class $\mathscr{C}^α$ for some $0<α<1$. We construct a continuous family of $J_b$-conformal minimal immersions $u_b:X\to \mathbb{R}^3$, $b\in B$, properly projecting to $\mathbb{R}^2$ and having an arbitrary given family of flux homomorphisms ${\rm Flux}_{u_b}:H_1(X,\mathbb{Z})\to\mathbb{R}^3$. In particular, there are continuous families of proper $J_b$-holomorphic null immersions $X\to \mathbb{C}^3$ and of proper $J_b$-holomorphic immersions $X\to\mathbb{C}^2$, $b\in B$.

Many barred galaxies, including the Large Magellanic Cloud (LMC), display strong lopsidedness and off-centre bars. The dynamical connection between bar-disc misalignments, internal mass asymmetries, and arm morphology is not yet fully characterised. We investigate how internal mass imbalances within the bar and global offsets between the bar and the centre of mass of the system modify the equilibrium-point structure and the invariant manifolds that organise arms. We construct a barred galaxy model which includes an off-centred and asymmetric in shape bar. Using numerical continuation, we track the position, stability, and bifurcations of the Lagrangian equilibrium points as functions of the displacement of the asymmetric mass component along the bar and of the offset between the bar and the system's centre of mass. For representative configurations we compute the invariant manifolds of planar Lyapunov orbits around unstable points and analyse the resulting arm structures. Internal bar lopsidedness and modest bar-disc offsets that keep the centre of mass inside the bar preserve the classical configuration with five equilibrium points, but strongly distort the associated invariant manifolds, producing two arms with different densities and shapes. The bar-disc offset reaches a threshold at the point at which the galactic centre of mass exits the bar ellipsoid, in which a pitchfork bifurcation removes the collinear unstable points and the system transitions to a three-equilibrium-point configuration in which a single unstable point and its associated manifold supports one arm. This framework is compatible with the observed correlation between off-centre bars and photometric lopsidedness, and it provides a dynamical explanation for the strongly asymmetric arm morphology of galaxies such as the LMC.

In 1994, Orlik and Terao introduced a commutative Artinian analog S/I(A) of the Orlik-Solomon algebra of a hyperplane arrangement A to answer a question of Aomoto. A central topic of investigation in the study of Artinian algebras is the Weak Lefschetz Property (WLP). We analyze WLP for the Artinian Orlik-Terao algebra of graphc arrangements. Even for chordal graphs (which give rise to Koszul algebras) WLP sometimes fails; conversely an analysis of the state polytope shows WLP can hold even when WLP fails for all possible initial ideals. More generally, for any algebra with a tensor product decomposition, we construct canonical elements in the kernel of the multiplication map, refining previous results in the literature.

Tolerance limits have received considerable attention in the statistical literature, with applications reaching far beyond their initial role in quality control. The well-known formula of Scheffé and Tukey (1944) establishes a simple, distribution-free relation between sample size and population coverage by two given order statistics and a given confidence level. A key requirement in applying this formula is the availability of an unbiased, representative sample from the population of interest. However, as it often happens in biological and medical applications, various logistical constraints may preclude the possibility of obtaining an unbiased sample. We derive extensions of this formula which accommodate a large class of biased sampling schemes including weight bias and censoring. The modified formulae are validated through a simulation study and compared to its unmodified counterpart. We illustrate the use of the modified formulae using the partially observed failure times for individuals with dementia using data collected from the Canadian Study of Health and Aging.

Accretion-disc corona sources are high-inclination low-mass X-ray binaries in which the innermost regions are hidden and the observed X-ray emission is dominated by radiation scattered above the disc. 4U 1822-37 is a key binary system of this class, but its geometry is still debated. X-ray polarimetry offers a direct probe of the scattering structure. We present the first X-ray spectro-polarimetric study of 4U 1822-37 and test whether its spectrum and polarisation can be explained within the accretion-disc-corona scenario. We analysed a coordinated campaign with IXPE, XMM-Newton, NuSTAR, and Swift. We performed broadband spectral modelling and model-independent, energy-resolved, and orbital-phase-resolved polarimetric analyses. The broadband spectrum requires a soft thermal component, a Comptonised continuum, a hard power-law tail, and relativistically blurred reflection. The observed 0.1-100 keV luminosity, $L_{\rm obs}\simeq6.1\times10^{36}\ {\rm erg\,s^{-1}}$, is far below the intrinsic luminosity expected from the orbital evolution, supporting a geometry in which only a small fraction of the intrinsic emission is scattered into the line of sight by an extended, optically thin corona. In the 2-8 keV band, IXPE measures ${\rm PD}=7.9\pm0.6\%$ and ${\rm PA}=-24^\circ\pm2^\circ$. The PD increases with energy, while the PA remains approximately constant. During eclipse, the PD decreases to ${\rm PD}=5.5\pm1.7\%$, with no significant PA variation. This behaviour is consistent with the companion occulting the most polarimetrically efficient part of the extended corona. The high PD, stable PA, energy-dependent polarisation, and eclipse behaviour support a picture in which 4U 1822-37 is observed in an extreme high-inclination, scattering-dominated regime. The extended corona is the main structure shaping both the observed X-ray emission and its polarisation.

Despite the low solar irradiation it receives, Neptune shows a very active atmosphere with some of the most intense dynamics observed in Solar System atmospheres. Characterizing the atmospheric temperature profiles of the planet is a key to understand these observed processes. In this work, we derived the Neptune pressure-latitude thermal field, using 2016 ALMA measurements of the CO(3-2) spectral line at 345.796 GHz, with a spatial resolution of about 0.37" on Neptune's 2.24" disk. To analyse the data, we developed MCMC retrieval methods to derive both the temperature profiles and the CO abundance profile. We find that our data probes the upper troposphere and the lower stratosphere of the planet, between 2 bar and 0.1 mbar. Although temperature and CO profile are strongly correlated, simultaneous retrievals of both parameters for disk-integrated observations reveal a factor of 2-3 larger CO abundance in the stratosphere than in the troposphere, reinforcing the hypothesis of CO delivery by a recent cometary impact. CO retrievals with fixed temperature profile do not fit the spatially-resolved observations, implying underlying temperature variations. By performing temperature retrievals with spatially constant CO, we find distinct trends of the thermal profile between the southern polar region, mid-latitudes and the equator. At 10--100 mbar, this structure is consistent with that observed by Voyager 2 in 1989, i.e. colder mid-latitudes, with a warmer equator and south polar regions. At 300-600 mbar, however, we find a cold layer of about 45 K at Southern polar regions (-80°) which disappears towards mid-latitudes and the equator. By probing pressure levels not easily accessible to other observing methods e.g. infrared sounding, submillimeter observations offer a new view of the complex thermal structure in the upper troposphere and lower stratosphere of the Icy Giants.

Twisted light carries orbital angular momentum (OAM) and can drive excitations of confined, interacting electrons that are dark to uniform dipolar probes. Here we show how this ``beyond-Kohn's-Theorem'' optical channel can become a concrete control primitive for quantum computing. Correlation sectors in few-electron quantum dots -- characterized by the relative angular momentum quantum number -- form a tunable ladder of many-body states that are robust in the limited sense of symmetry-protected selection rules and persistent chiral spectroscopic fingerprints; full topological gap protection requires three or more electrons. A twisted-light pulse with prescribed OAM index and polarization provides fast optical write, read, and scalable addressing of these sectors via the selection rule $Δ|m|=\pm(l+σ)$. In the analytically solvable Calogero ($1/r^2$) interaction limit, both the energy spectrum and the twisted-light matrix elements are closed-form functions of the interaction strength, allowing gate parameters (Rabi frequency, qubit frequency, anharmonicity, and leakage rates) to be written down explicitly. We map these results onto a universal single-qubit gate set, propose a concrete two-qubit entangling mechanism via state-dependent Coulomb coupling between adjacent dots, and identify the dominant decoherence channel (quadrupolar charge noise). A semi-analytic $N=3$ extension using the $1/N$ expansion provides a design-level scaffold for the topological roadmap, including quasihole sector addressing. The central operational message is that twisted light enables WRITE (pulse-create a correlation sector), READ (spectroscopically diagnose correlations), and SCALE (optical addressing via spatial light modulator) in a unified photonic control layer. Throughout, screened and Coulomb interactions preserve the same qualitative chiral fingerprints established in the solvable limit.