We consider the Hamiltonian $H$ of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called {\em abstract ladder operators}, in the attempt to find its eigenvalues and eigenvectors. We don't assume that $H$ is self-adjoint, while we focus on the case of a factorizable operator. We show then that pseudo-bosonic operators play a relevant role in this analysis, and we construct bi-coherent states attached to these operators. Explicit examples are discussed.

Spectral functions measured with angle-resolved photoemission spectroscopy (ARPES) provide key insight to elucidate the band structure of materials. Comparison with theory requires computing dynamical one-point functions in some equilibrium state, which can be classically challenging. Their measurement on quantum computers poses multiple problems and comes with a large sampling overhead when standard techniques are used. We introduce an efficient way of measuring spectral functions on a quantum computer by directly modeling the interaction of the system with the environment involved in ARPES experiments. We develop quantum circuits whose local expectation values are proportional to the spectral function $A(k,ω)$ for all momentum $k$ and a specific chosen frequency $ω$. Although coming with a qubit and two-qubit gate overhead, our approach requires $O(N)$ times less sampling than previous approaches, translating into a factor $O(N)$ faster in runtime, and is particularly adapted to ion-trap quantum computers. The algorithm requires to implement a fermionic Fourier transform (FFT). We write out an efficient gate decomposition for generic radix-$n$ FFT and benchmark it on hardware for radix-$3$ on $27$ qubits. We finally demonstrate our algorithm on a Quantinuum System Model H2 ion-trap system, computing the spectral function on a one-dimensional system of $27$ sites, using $54$ qubits.

Reservoir computing is a powerful framework for modeling dynamical systems due to its universality and computational efficiency. However, a major challenge is achieving a forecast with accurate long-time statistics, or climate, which is essential for inferring ergodic properties such as Lyapunov exponents. A common approach is to optimize the reservoir's macroscopic parameters, such as the spectral radius, by maximizing prediction time. But here we show that even predictions accurate over multiple Lyapunov times do not guarantee the correct long-time statistics. Instead, we choose reservoir properties by minimizing the error in the reconstructed invariant distribution (or its projections), which is easily available from data. We demonstrate that this approach reproduces the Lyapunov exponents of model dynamical systems, including the logistic and standard maps, as well as the double pendulum, even with partial observations. We further show that recurrent connections, and resulting reservoir memory, are only required in the partially-observed case. We introduce a temporal scaling which reliably separates system and reservoir dynamics. In the posture time series of the nematode C. elegans we show that our approach quantitatively reproduces a chaotic behavioral attractor, but this requires a further constraint on the maximal conditional Lyapunov exponent to ensure the reservoir remains consistently synchronized to the complex biological input.

Direct fidelity estimation benefits from tailoring measurements to a fixed target, but the operator-aware shadow importance sampling (OASIS) method optimizes an outcome-wise linear-program surrogate rather than the exact worst-case variance over physical states. We propose an exact spectral replacement for arbitrary target states under the same non-adaptive single-copy measurement model. Specifically, we characterize unbiased linear estimators by a single operator identity, determine the state-wise optimal sampling law for fixed reconstruction coefficients, and convert the exact minimax problem into a semidefinite program. The resulting offline design and online estimator are presented as an algorithm and implemented with local Pauli measurements. Numerical simulations under depolarizing noise demonstrate that our exact spectral optimization outperforms the OASIS surrogate in terms of estimation variance.

The propagation of solar energetic particles (SEPs) in interplanetary space is modulated by solar wind turbulence, which significantly influences particle diffusion and energy evolution through scattering processes. Traditional analyses based on absolute flux measurements face inherent difficulties in disentangling source acceleration from subsequent transport, while temporal features such as onset and peak times are less affected and better suited for studying SEP transport. This study establishes a statistical relationship between the rise time of SEP events at different energies using multi-satellite observations at Earth and Mars. We use data from SOHO/ERNE and Tianwen-1/MEPA between November 2020 and March 2025, selecting 75 SEP events at 1 AU and 58 near Mars. For each energy range, onset times are determined by linear fitting, and peak times are extracted via a sliding median filter combined with Savitzky-Golay smoothing; the difference gives the SEP rise time. Comparing with the pure diffusion equation prediction, we examine the statistical behavior of rise time at Earth and Mars. Despite event selection uncertainties, SEP rise time follows a clear power-law relation with energy. The flatter power-law at Mars indicates weaker energy dependence with increasing solar distance. Using these empirical relations, we constrain the rigidity dependence of the parallel mean free path within the parallel diffusion model. Our results show that turbulence scattering at Mars approaches a rigidity-independent regime, reflecting turbulence evolution toward a dissipation-dominated state from Earth to Mars.

We constrain Einstein-aether gravity -- a Lorentz-violating extension of General Relativity in which a dynamical, unit timelike vector field selects a preferred frame -- using updated high-precision pulsar timing observations of PSR J1738+0333 from EPTA second Data Release and the NANOGrav 9-year release, in combination with ToAs from Arecibo, Green Bank, Nancay, Parkes, and Westerbork. Our method accounts for both conservative and dissipative first post-Newtonian corrections arising from Lorentz violation; here we apply it to PSR J1738+0333 using the Bayesian timing pipeline Vela to process the full ToA dataset. We sample the joint posterior over binary component masses, post-Keplerian parameters and center-of-mass velocity components, and then apply a resampling scheme to propagate posteriors into robust constraints on the fundamental theory parameters, obtaining the most stringent strong-field bounds on the Einstein-aether coupling constants from a single binary pulsar system to date.

We study a variant of the classical Wythoff's game. The classical form is played with two piles of stones, from which two players take turns to remove stones from one or both piles. When removing stones from both piles, an equal number must be removed from each. The player who removes the last stone or stones is the winner. Equivalently, we consider a single chess queen placed somewhere on a large grid of squares. Each player can move the queen toward the upper-left corner of the grid, either vertically, horizontally, or diagonally in any number of steps. The winner is the player who moves the queen to the terminal position in the upper-left corner, the position (0,0) in our coordinate system. Let k be a positive integer, and we consider the variant of Wythoff's game with the terminal set {(x,y):x,y are non-negative integers and x+y <=k}. The set of P-positions of this variant is described by the Fibonacci sequence without using recursion.

Partial-transpose (PT) moments are among the most practically relevant nonlinear quantities accessible from local Pauli classical shadows, because they directly underpin mixed-state entanglement certification and recent PT-moment-based phase diagnostics. The online framework of Marso \emph{et al.} rewrote the exact PT-moment statistic into a fixed-memory recurrence that updates a small collection of accumulated matrices after each new shadow snapshot. Its update cost is independent of the shot number, but each step treats the incoming partially transposed snapshot as a generic dense matrix. Therefore, the arithmetic cost scales cubically with the dimension of the Hilbert space. We show that the same estimator can be updated exactly in subcubic time per shot while retaining the same memory. The key point is that the accumulated matrices become dense, but the fresh partially transposed snapshot still factorizes into local factors. Right-multiplication by that factorized snapshot can therefore be executed by exact column-pair sweeps. For the second PT moment, we further optimize the process by utilizing a Pauli basis update.

This paper proposes a finite-horizon optimal control strategy for set-point tracking using a nonlinear model predictive control framework with integrated avoidance capabilities. The formulation employs a smooth point-to-cloud distance metric that ensures continuously differentiable and numerically well-conditioned gradients, even in the presence of regions with complex and nonconvex geometries. This smoothness allows safety constraints to be formulated consistently and differentiably through control barrier functions, resulting in a reliable avoidance behavior for the closed-loop system. Additionally, stationary artificial variables are introduced in the optimal control problem to preserve feasibility under changing set-points. The proposed approach is validated through numerical experiments of an aerial robot, demonstrating accurate tracking and smooth obstacle avoidance in complex environments.

This study systematically compares Bardeen's, de Vries's, and Grenzebach et al.'s celestial coordinate definitions of the critical curve ("shadow") of Kerr-like black holes. We find that all three definitions agree for black holes in vacuum or surrounded by inhomogeneous plasma observed from large distances. However, they diverge for observers located at a finite distance: Bardeen's definition yields the smallest critical curve, while de Vries's yields the largest. When homogeneous plasma is considered, critical curve computed using Bardeen's definition deviates from the other two even at large distances and contracts compared to the vacuum case with increasing plasma density. This is in clear contradiction with the behaviour predicted by de Vries's, Grenzebach et al.'s definitions, and previous gravitational lensing studies. We derive de Vries's definition assuming a critical curve on the observer's sky plane and explain its discrepancy with Grenzebach et al.'s definition. We further explore the effect of the change of tetrad on the critical curve. Using Bardeen and Carter tetrads, we plot the critical curve for Schwarzschild and Kerr black holes in the presence of plasma, highlighting that tetrad changes introduce only a horizontal shift in the critical curve.

Soft, repulsive run-and-tumble particles display emergent effective interactions as they appear to stick to each other in spite of the absence of attractive forces. This effective attraction emerges at strong enough repulsion and large self-propulsion. Complementing a companion paper that characterises effective attraction between two soft run-and-tumble particles [Garcia-Millan et al., Effective attraction by repulsion (2026)], here we provide a thorough derivation of our microscopic theory, which is an exact representation of the particle dynamics. We report the systematic calculation of the effective interaction vertices iteratively, in a perturbation expansion about the interaction couplings, by adding, order by order, loop corrections. We use the effective interaction vertices to calculate the two-point correlation function, fully characterising the stationary state. Other observables, such as the structure factor, overlap probability and entropy production rate are calculated as well.

Repulsive self-propelled particles tend to cluster, leading to Motility-Induced Phase Separation (MIPS). By analogy with equilibrium phase separation, the onset of MIPS has been associated with a transition to effective attraction between particles. Using an exact microscopic theory, we quantify the emergence of effective attraction in a minimal model: two soft run-and-tumble particles in a periodic domain. We show that, as repulsion increases, the leading-order behaviour is that of effective repulsion, while effective attraction emerges as a higher-order contribution to the renormalisation of the pair potential.

Understanding the behavior of simulated architectures in gem5 is critical for studying complex, deeply integrated computing systems. However, conventional analysis methods provide only an indirect view of the simulated system internals. In this work, we show that call-stack profiling of gem5 itself offers a powerful yet underutilized perspective: the simulator's own call-stack directly reflects the activity of the simulated system, exposing insights that conventional statistics may overlook. Profiling gem5's call-stacks is challenging due to its highly layered and complex software design patterns. To address this, we introduce a specialized, lightweight profiling framework built on Linux's perf_event interface which samples gem5's runtime call-stacks throughout the simulation, resolves symbols on the fly, and merges samples into a hierarchical call-tree representation supporting both high-level structural views and focused, user-defined, component-specific analysis. Moreover, all profiling is performed in a separate process running alongside the main gem5 process, avoiding intrusive changes and overheads to the simulation itself. We apply our framework to gem5's three major CPU models -- AtomicSimpleCPU, TimingSimpleCPU, and O3CPU -- together with the Ruby memory system, and uncover behaviors that are not easily observable in conventional gem5 statistics. Our case studies reveal, for example, that TimingSimpleCPU is inefficient due to its use of a lockup-cache model and, despite its conceptual simplicity, does not simulate faster than a full out-of-order core. In addition, our tool makes it straightforward to detect cache coherence protocol deadlock and livelock -- issues that are otherwise difficult to identify, since the simulation either appears to run normally or terminates abruptly, making it hard to pinpoint when these conditions occur.

In the context of 6G ubiquitous connectivity, the space-air-ground-sea integrated network (SAGSIN) emerges as a new paradigm to provide critical services for resource-limited ocean environments. To realize this paradigm efficiently, we propose an innovative dynamic task and resource scheduling approach for green SAGSIN that delivers computing support for vessels while minimizing overall task execution delay. To address the challenge of multi-layer task scheduling, a layer-wise task offloading algorithm is developed specifically for SAGSIN. It adapts to real-time, multi-dimensional system dynamics and integrates an anticipatory handover strategy that adaptively controls the amount of data offloaded to the satellite, thereby preventing post-handover congestion while improving satellite resource utilization. Furthermore, the bandwidth allocation of uncrewed aerial vehicles and base station, UAV trajectories, and computing resource allocation are jointly optimized to enhance connectivity among low-altitude devices and facilitate demand-driven resource allocation for green network development. Simulation results verify that the proposed method better adapts to dynamic system resources and achieves at least a 23% reduction in average task delay compared with benchmarks.

Nonlocal gravity is a promising super-renormalizable or finite quantum gravity theory consistent with unitarity. In this paper, we focus on the classical equations of motion and explicitly show that a particular subclass of Gödel-type Universes, where closed time-like curves are allowed, is an exact solution of nonlocal gravity in vacuum. The result is consistent with a well defined theory at quantum level, but it is realized only with a special, although large, class of nonlocal form factors. Therefore, by itself the renormalizability requirement is not a sufficient guiding principle in vacuum whether we want to avoid the causality violation. From the physical point of view, the causality violation takes place from the non locality fundamental scale to macroscopic scales. Therefore, it is the presence of matter to break the classical degeneracy between the Minkowski and the Gödel Universe. Finally, we have shown that at the non-perturbative quantum level the transition from a flat to a Gödel Universe is ridiculously small.

Let $D\in\mathbb{N}$, let $A>D+1$, and let $Q\geqslant3$. Consider the class of multiplicative functions $f:\mathbb{N}\to\mathbb{C}$ such that $|\sum_{n\leqslant x}f(n)|\le x(\log Q)^{A-D-1}/(\log x)^A$ for all $x\geqslant Q$, and such that $|Λ_f|\leqslant DΛ$, where $Λ_f$ is defined via the Dirichlet convolution identity $f\log=Λ_f*f$ and $Λ$ denotes von Mangoldt's function. We prove there exist parameters $m\in\{0,1,\dots,D\}$ and $Q=Q_D\leqslant Q_{D-1}\le \cdots\leqslant Q_m<Q_{m+1}=\infty$ such that $\sum_{p\in I} \mathrm{Re}(f(p)+j)/p=O_{A,D}(1)$ for all $j=m,m+1,\dots,D$ and all compact intervals $I\subset[Q_{j+1},Q_j)$. Moreover, when $|\sum_{n\leqslant x}f(n)|\le x^{1-1/\log Q}/(\log x)^{D+1}$ for all $x\geqslant Q$, we relate the parameters $m$ and $Q_j$ to the location of zeroes of the Dirichlet series $\sum_{n\geqslant1} f(n)/n^s$ in the ball $B(1,1/\log Q)$. These results generalize work of the author when $D=1$. Their proof builds on earlier work of the author with Soundararajan, and of Sachpazis.

Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show how to recursively construct the solution of the non-linear stochastic master equation (the conditional state). Moreover, by the notion of ``exclusive probability densities" we can describe all the probabilities related to the jumps, in particular, the waiting times of the jumps and their probability distributions. This general formulation and the idea of hybrid system allow to unify and generalize different fields: evolutions under non-Hermitian Hamiltonians, unitary dynamics interspersed by quantum channels at random times, quantum renewal processes, continuous time open quantum walks, Lindblad rate equation, ...

We approach the cycle double cover conjecture by looking for a circular 2-cell embedding of cubic graphs on an arbitrary surface. It is easy to see that if such an embedding exists, we can get to it from an arbitrary starting 2-cell embedding by repeating ``twists of an edge''. We study this twisting operation in detail and deduce bounds on the number of singular edges (edges where a face meets itself).

Black hole supernovae (BHSNe), the term we use for core-collapse events in which black hole (BH) formation occurs after shock revival but before the explosion is complete, have emerged as a natural outcome of multidimensional simulations as these calculations have been extended to seconds after bounce. Yet they remain one of the least studied outcomes of core collapse. Here, we assess whether they are confined to the most compact and massive progenitors, whose birth rates are low, or whether they arise systematically across a wider range of progenitor structures. We perform 23 long-term axisymmetric core-collapse simulations of progenitors spanning 19.51-60$\,M_\odot$ and compactnesses $0.31 \lesssim ξ_{2.5} \lesssim 0.63$. We find 18 BHSN outcomes across nearly the full ZAMS mass range considered, corresponding to progenitors with $0.40 \lesssim ξ_{2.5} \lesssim 0.63$. BH formation occurs between $\sim0.7$ s and $\sim4.4$ s after bounce. After BH formation, we continue the evolution with an excision treatment to at least 5000 s. The final explosion energies span $\sim2\times10^{49}$-$3\times10^{51}$ erg, while the final BH gravitational masses span $\sim3$-$26\,M_\odot$. We find a clear remnant-mass trend with CO-core mass, but show that the CO core alone is not an adequate proxy for the final BH mass, especially for progenitors at the low- and high-mass ends of the CO-core distribution. Except for the highest CO-core mass models, no single spherical mass coordinate cleanly separates ejecta from remnant material. Finally, a 2D axisymmetric and a 3D model are compared as we discuss differences between the two geometries.

Let $p$ be an odd rational prime and consider the cyclotomic number field $K = \mathbb{Q}(ζ_{p})$ of conductor $p$. We construct a directed graph $Y$ on $p-1$ vertices for which the torsion part of the corresponding Bowen--Franks group is closely related to the minus part of the class group of $K$. In particular, both groups have the same cardinality up to an explicit power of $p$. Furthermore, they are both $\mathrm{Gal}(K/\mathbb{Q})$-modules, and we prove the equality of the cardinalities of their isotypic components after tensoring them with the valuation ring of an appropriate $\ell$-adic field for $\ell \nmid p-1$.

For an operator $T:X\to Y$, denote $m(T)=\inf\{\|Tx\|:x\in S_X\}$. A sequence $(x_n)$ in $S_X$ is said to be minimizing for $T$ if $\|Tx_n\|\to m(T)$. The weak minimizing property (WmP), introduced by Chakraborty, requires that every operator admitting a non-weakly null minimizing sequence attains its minimum modulus. More recently, Han~\cite{Han2026} introduced the Compact Perturbation Property for the minimum modulus (CPPm), which requires that for every operator $T:X\to Y$ that does not attain its minimum modulus, \[ \sup_{K\in\mathcal{K}(X,Y)} m(T+K)=m(T). \] In~\cite{Han2026}, it is shown that $(\ell_1,\ell_1)$ fails both properties, while $(c_0,c_0)$ fails the WmP. However, whether $(c_0,c_0)$ has the CPPm was left open (Problem~3.6). In this paper, we give a negative answer to this question by proving that $(c_0,c_0)$ does not have the CPPm. The proof is constructive, exhibiting a non-min-attaining operator whose minimum modulus is strictly increased by a rank-one compact perturbation. Moreover, we show that this phenomenon is not specific to $c_0$: if $X=\mathbb{K}\oplus_\infty Y$ with $Y$ non-reflexive, then the pair $(X,X)$ fails the CPPm.

We show that a moment-angle manifold associated to a neighbourly triangulation of an odd dimensional sphere is homotopy equivalent to a connected sum of products of two spheres, resolving a problem of Buchstaber and Panov. The methods are entirely homotopy theoretic, allowing for an extension to a corresponding result in the case of generalized moment-angle manifolds.

Aims. We aim to identify the presence of atomic and molecular species in the upper atmosphere of the warm Neptune-sized transiting planet GJ 436 b, which has a radiative equilibrium temperature of 690 K and a mass of 25.4 Earth masses. Methods. Using transmission spectroscopy, we observed two full transits of GJ 436 b with the ESPRESSO spectrograph, covering the wavelength range from 3800 to 7880 Angstrom. We searched for traces of atomic (H I, Li I, Na I, Mg I, V I, Cr I, Fe I, and Fe II) and molecular (TiO, VO) species by directly detecting planetary absorption features and by cross-correlating the planetary spectrum with theoretical spectra computed for each investigated species. Results. Our analysis reveals no strong planetary detection for any of the species, consistent with a featureless optical spectrum. We derived upper limits by combining all ESPRESSO observations. Post-transit stellar flares were detected on both nights, primarily affecting chromospheric lines. A tentative Fe I signal appears in the first transit (S/N = 3.4 +/- 0.2) at a wind velocity of about -18.6 km/s, which is unexpectedly large for a cool planet. This weak signal is not present in the second transit and, combined with its low significance, suggests an origin in noise. In the less probable scenario where the feature is suppressed during the second transit by the higher stellar activity state, the T1 tentative signal peaks at 1300 K, which is above the equilibrium temperature of GJ 436 b. Ultimately, this result would imply a neutral iron abundance comparable to or exceeding that of the host star.

This paper studies multi-operator wireless communication systems aided by general reconfigurable intelligent surface (RIS), including both conventional single-connected RIS and beyond-diagonal RIS (BD-RIS). Specifically, we consider a system where multiple operators coexist in the same area over different frequency bands, each with a single-antenna base station, while one operator serves its single-antenna user with the aid of an RIS. In such a system, the RIS may unintentionally reflect signals from the non-serving operators, leading to inter-operator interference and rapid fluctuations of their effective channels. To address this issue, we propose a practical RIS design framework that maximizes the received signal power of the serving operator while enforcing fixed RIS-reflected channels of the non-serving operators. We derive closed-form solutions to the resulting optimization problem, based on a novel technique to deal with the coupled unitary and linear equality constraints. We further give scaling law analysis of the received signal power. For a two-operator system, the received signal power scales quadratically with the number of RIS elements for group-connected BD-RIS with group size Gs>=2, whereas for conventional single-connected RIS it scales only linearly. More generally, for an L-operator system with L-1 non-serving operators, the scaling-law transition occurs at Gs=L, where quadratic scaling is achieved when Gs>=L, and linear scaling otherwise. These results demonstrate that, in a multi-operator system, quadratic scaling is achievable only with BD-RIS architectures having enough interconnections. Simulation results validate the analysis and show the significant gain of BD-RIS over conventional RIS in multi-operator systems. In particular, group-connected BD-RIS with Gs=2 achieves a 13dB gain over conventional RIS in a two-operator system with a 128-element RIS.

High-harmonic generation (HHG) in strongly correlated Mott insulators is investigated using exact diagonalization and time-dependent density-matrix propagation of a laser-driven one-dimensional Hubbard chain. By projecting onto equilibrium Hubbard bands, we use the doublon population and its dynamics as a diagnostic to analyze intraband (spin-wave-like) and interband (doublon-holon creation) excitation channels. A filling-dependent crossover emerges: Bloch-like intraband response at dilute filling, mixed dynamics at intermediate filling, and interband-dominated HHG with plateau and cutoff near half filling. In the considered parameter range, increasing interaction strength $U$ strongly suppresses interband contributions through the enlarged Mott gap and correlation-induced localization. Intra- and interband current decomposition reveals opposing flows below the Mott gap (Δ_{\mathrm{Mott}}) and selective dephasing suppression of interband coherence, enhancing net doublon accumulation. Time-frequency analysis uncovers the filling-dependent features of quantum trajectories, manifesting in distinct below-Δ_{\mathrm{Mott}} emission. This doublon-based analysis provides a transparent link between equilibrium spin-charge separation and nonequilibrium strong-field response, and clarifies how dephasing modifies interband coherence and doublon accumulation.

We study the explicit construction of the Haar measure on the compact $p$-adic rotation group $\textrm{SO}(3)_p$ by nautical (Cardano) parametrization. Exploiting its topological group isomorphism with $\mathbb{H}_p^\times/\mathbb{Q}_p^\times$ of $p$-adic quaternions modulo scalars, we derive the corresponding change of variables formulas and compute the associated Jacobian in the $p$-adic setting, which we combine with the known Haar measure on the multiplicative group of $p$-adic quaternions $\mathbb{H}_p^\times$. This yields an explicit formula for the normalized Haar measure on $\textrm{SO}(3)_p$ in nautical coordinates, with a factorized density in the three angles. Our construction provides a concrete tool suited for applications of non-Archimedean models where an explicit angular description of invariant integration is required.

Portfolio optimization is constrained by linear assumptions and insufficient integration of multi-modal information in traditional models. This paper proposes a cross-modal BERT-driven Actor-Critic framework SBCA for multi-asset portfolio optimization to address the deficiencies of existing deep reinforcement learning DRL methods in fusing price data and financial text sentiment, as well as lacking practical trading constraints. The framework adopts a cross-modal gated fusion mechanism to adaptively integrate price time-series features and text semantic features, embeds downside risk and turnover penalty constraints into the reward function, and constructs a complete empirical system for validation. Experiments on 11-year U.S. stock multi-asset datasets show that SBCA outperforms equal weight, buy-and-hold and market benchmark strategies in portfolio value, annual return, Sharpe ratio and maximum drawdown. Ablation studies verify the complementary enhancement of Actor-Critic mechanism and cross-modal fusion module. Cost sensitivity analysis confirms the model's robustness under varying transaction costs. SBCA provides an effective and interpretable end-to-end solution for dynamic quantitative portfolio decision-making.

Over the past decade, reionization studies have yielded persistent factor-of-two-to-five disagreements in the inferred ionizing escape fraction $f_{\mathrm{esc}}$ and peak star formation efficiency $f_{*,0}$, compounded by JWST's discovery of unexpectedly bright $z>10$ galaxies. We show that this discrepancy arises from an algebraically exact structural degeneracy: the ionizing photon rate $\dot{n}_{\mathrm{ion}} \propto f_{\mathrm{esc}} \times f_{*,0}$ renders all reionization-history probes, including Thomson optical depth, neutral hydrogen fraction, UV luminosity function, and quasar proximity zones, sensitive only to their product, leading to an intrinsically non-invertible mapping between model parameters and observations. We demonstrate the robustness of this degeneracy using a large suite of N-body simulations of self-interacting dark matter haloes spanning $10^9$-$10^{11} M_\odot$. Despite substantial changes to galaxy-scale structure, observables remain indistinguishable once the effective ionizing emissivity is matched, severely limiting reionization-based dark matter probes. We identify that only observables sensitive to the spatial topology of ionized regions can break this degeneracy. Our results provide a unified explanation for the scatter among published constraints and establish a framework for interpreting reionization observations and their implications for early galaxy formation and dark matter.

Data privacy has increasingly become a daunting challenge because it limits data availability, which is essential in estimating statistical models such as generalized linear mixed models. Access to personal data often involves considerable time, effort, and paperwork, which can impede research progress and collaboration. Existing approaches that do not use individual-level data for model estimation are either prone to ecological bias, cannot handle heterogeneity, or require iterative communication. In this paper, we propose an approach to estimate generalized linear mixed models based on summary statistics shared only once. We used linear, logistic, and Poisson mixed models as examples to demonstrate the methodology. Our strategy involves generating pseudo-data whose summary statistics match those of the actual but unavailable data. These pseudo-data are then used for model estimation instead of the actual data. The estimates we achieve are identical (up to the third decimal place) to those derived from actual data and have similar bias, coverage, and prediction performance. Communication and resource efficiency distinguish our approach from existing methods.

Identifying phenotype-associated genes is a common first step in polygenic risk score construction, enrichment testing, target prioritisation and variant interpretation, but relevant evidence is distributed across heterogeneous databases with different interfaces, formats and evidence models. Here, we present PhenotypeToGeneDownloaderR, a phenotype-guided R/Python pipeline for automated gene retrieval, harmonisation, symbol validation and cross-source summary analysis. Given a phenotype term, the pipeline queries integrated biological databases, standardises per-source outputs, combines gene lists, validates retrieved symbols against the NCBI human gene reference and generates summary tables and visualisations. Across 13 clinically relevant phenotypes and 13 databases, PhenotypeToGeneDownloaderR generated 136,487 raw gene retrievals, with at least one source returning genes for every phenotype. Across all 13 phenotypes, 100,175 of 114,345 combined input symbols were retained after direct or synonym-based validation, corresponding to an 87.6\% validation rate. Cross-source overlap was low, supporting the complementarity of integrated evidence sources. Against an HPO/ClinVar/OMIM-derived gold standard, the pipeline recovered 1,039 of 1,056 known phenotype-associated genes, corresponding to 98.4\% recall. PhenotypeToGeneDownloaderR provides a lightweight, reproducible upstream framework for generating candidate gene sets for downstream prioritisation and interpretation. The pipeline is implemented in R and Python, released under the MIT licence, and available at https://github.com/MuhammadMuneeb007/PhenotypeToGeneDownloaderR.