Large Language Models (LLMs) increasingly act as gateways to web content, shaping how millions of users encounter online information. Unlike traditional search engines, whose retrieval and ranking mechanisms are well studied, the selection processes of web-connected LLMs add layers of opacity to how answers are generated. By determining which news outlets users see, these systems can influence public opinion, reinforce echo chambers, and pose risks to civic discourse and public trust. This work extends two decades of research in algorithmic auditing to examine how LLMs function as news engines. We present the first audit comparing three leading agents, GPT-4o-Mini, Claude-3.7-Sonnet, and Gemini-2.0-Flash, against Google News, asking: \textit{How do LLMs differ from traditional aggregators in the diversity, ideology, and reliability of the media they expose to users?} Across 24 global topics, we find that, compared to Google News, LLMs surface significantly fewer unique outlets and allocate attention more unevenly. In the same way, GPT-4o-Mini emphasizes more factual and right-leaning sources; Claude-3.7-Sonnet favors institutional and civil-society domains and slightly amplifies right-leaning exposure; and Gemini-2.0-Flash exhibits a modest left-leaning tilt without significant changes in factuality. These patterns remain robust under prompt variations and alternative reliability benchmarks. Together, our findings show that LLMs already enact \textit{agentic editorial policies}, curating information in ways that diverge from conventional aggregators. Understanding and governing their emerging editorial power will be critical for ensuring transparency, pluralism, and trust in digital information ecosystems.

We develop a theory of noncommutative Poisson extensions. For an augmented dg algebra \(A\), we show that any shifted double Poisson bracket on \(A\) induces a graded Lie algebra structure on the reduced cyclic homology. Under the Kontsevich--Rosenberg principle, we further prove that the noncommutative Poisson extension is compatible with noncommutative Hamiltonian reduction. Moreover, we show that shifted double Poisson structures are independent of the choice of cofibrant resolutions and that they induce shifted Poisson structures on the derived moduli stack of representations.

We introduce and study Zoll manifolds with boundary: compact Riemannian manifolds with smooth boundary such that every geodesic issuing orthogonally from the boundary returns orthogonally and is nowhere tangent to it. We first show that all such free boundary geodesics are embedded and have a common length, and that the boundary has at most two connected components. If there are two components, we prove that the manifold is a product of an interval with a closed manifold. When the boundary is connected, we show that the manifold is a tubular neighborhood of a closed embedded submanifold, the "soul", and that the complement of the soul is diffeomorphic to a half-open cylinder over the boundary. We further prove that all free boundary geodesics are maximally degenerate critical points of the energy functional and have the same Morse index, which equals the multiplicity of the unique focal point occurring at the midpoint of each geodesic. The projection from the boundary to the soul is then either a nontrivial two-fold covering or a smooth sphere bundle, according to the value of this index. As applications, we obtain a complete classification of Zoll surfaces with boundary and of three-dimensional Zoll manifolds with boundary.

Let $D$ be a digraph of order $p\geq5$ with minimum degree at least $p-1$ and with minimum semi-degree at least $p/2-1$. In his excellent and renowned paper, ``Long Cycles in Digraphs" (Proc. London Mathematical Society (3), 42 (1981), Thomassen fully characterized the following for $p=2n+1$: (i) $D$ has a cycle of length at least $2n$; and (ii) $D$ is Hamiltonian. Motivated by this result, and building on some of the ideas in Thomassen's paper, we investigated the Hamiltonicity (when $p$ is even) and pancyclcity (when $p$ is arbitrary) such digraphs. We have given a complete description of whether such digraphs are Hamiltonian ($p$ is even), are pancyclic ($p$ is arbitrary). Since the proof is very long, we have divided it into three parts. In this paper, we provide a full description of the following: (iii) for $k=3$ and $k=4$, the digraph $D$ contains a cycle of length $k$; and (iv) the digraph $D$ contains a pre-Hamiltonian cycle, i.e. a cycle of length $p-1$.

A self-consistent model is presented for the formation and propagation of kinetic Alfvén (KA) solitons in mass-loaded filaments within the pulsar wind, where a magnetized electron--positron--ion plasma flows along open magnetic field lines beyond the light cylinder. Using a reductive perturbation approach, we derive a Korteweg--de Vries (KdV) equation governing the nonlinear evolution of KA solitons in this environment. The soliton amplitude and width depend sensitively on key pulsar observables, including spin period, spin-down rate, and pair multiplicity, as well as on plasma composition and suprathermal particle distributions. Heavy ion species such as Fe$^{26+}$ produce significantly broader solitons through enhanced inertia and dispersion, while increasing pair multiplicity leads to smaller solitons through stronger screening. More oblique propagation (larger $θ$) yields wider but lower-amplitude solitons, whereas more thermalized pair plasmas (higher $κ$) support taller and broader structures. A population-level analysis of 1174 pulsars quantifies the physical scales of these nonlinear structures, showing that millisecond pulsars host the most compact solitons, whereas slower pulsars support broader structures. Within the adopted admissible finite-$β$ regime, this work links soliton properties to measurable pulsar parameters and provides a self-consistent framework for characterizing localized nonlinear plasma structures in finite-magnetization regions of pulsar winds and for assessing their role in modulating the local plasma environment.

We solve constrained optimal transport problems in which the marginal laws are given by the laws of solutions of stochastic differential equations (SDEs). We consider SDEs with irregular coefficients, making only minimal regularity assumptions. We show that the so-called synchronous coupling is optimal among bicausal couplings, that is couplings that respect the flow of information encoded in the stochastic processes. Our results provide a method to numerically compute the adapted Wasserstein distance between laws of SDEs with irregular coefficients. We show that this can be applied to quantifying model uncertainty in stochastic optimisation problems. Moreover, we introduce a transformation-based semi-implicit numerical scheme and establish the first strong convergence result for SDEs with exponentially growing and discontinuous drift.

We define a commutative monoid structure on the poset of left-exact localizations of a higher topos, that we call the acyclic product. Our approach is anchored in a structural analogy between the poset of left-exact localizations of a topos and the poset of ideals of a commutative ring. The acyclic product is analogous to the product of ideals. The sequence of powers of a given left-exact localization defines a tower of localizations. We show how this recovers the towers of Goodwillie calculus in the unstable homotopical setting. We use this to describe the topoi of $n$-excisive functors as classifying $n$-nilpotent objects.

This paper generalizes Watatani's finiteness theorem for intermediate subfactors to a wide class of monoidal categories. We characterize the sublattices of Frobenius subalgebra posets in abelian monoidal categories by introducing a notion of ambient selfduality. By extending several key results -- such as the planar algebraic exchange relation and Landau's theorems -- to linear monoidal categories, we establish a structural rigidity property for a formal angle associated to every coherent pair of Frobenius subalgebras (that is, whose intersection and sum are ambiently selfdual). Furthermore, within a weak positivity framework, we deduce that such coherent sublattices are finite for any connected Frobenius algebra. This significantly generalizes Watatani's theorem, since the unitary Frobenius subalgebra lattices are inherently coherent through a property termed rigidity invariance. Applications of this work include a unified framework that encompasses several previously unrelated finiteness results. Specifically, we recover the finiteness of the left coideal subalgebra lattice of a finite-dimensional semisimple Hopf algebra (Etingof-Walton theorem) modulo a well-supported coherence hypothesis, as well as the finiteness of the intermediate C*-algebra lattice for a finite-index unital irreducible inclusion of C*-algebras (relaxing simplicity in Ino-Watatani theorem) under an E-compatibility condition shown to be unavoidable. Furthermore, we present a variety of new applications involving abstract spin chains and vertex operator algebras, alongside speculations on quantum arithmetic that include extensions of Ore's theorem, Euler's totient and sigma functions, and RH.

Implementation of a two-level non-Hermitian qubit via post-selection of a three-level system has been demonstrated. The post-selection procedure, which discards quantum jump to the ground-state manifold while retaining excitations in the first and second excited-state manifolds, effectively generates a non-Hermitian qubit exhibiting PT symmetry. In this work, we perform continuous homodyne measurement of this non-Hermitian qubit and analyze the interplay between decay introduced by post-selection and measurement backaction. We compare the ensemble-averaged dynamics obtained from measurement trajectories with the the Liouvillian average. We formulate the no-jump stochastic differential equation describing the post-selected non-Hermitian qubit and show that its ensemble-averaged dynamics agree with those of the jump-updated post-selected evolution at drive strengths far from the Liouvillian exceptional point (EP). The degree of deviation near the EP depends sensitively on the nature of the drive. This discrepancy is attributed to the interplay between measurement backaction and the non-Hermitian decay introduced by post-selection. Furthermore, we determine the optimal path of the non-Hermitian qubit by extremizing the action within the path-integral formulation of the quantum trajectory framework Our results provide insights into how measurement backaction and non-Hermitian dynamics together shape the transient behavior of open quantum systems and enable controlled manipulation of qubits near exceptional points.

Large-scale simulations of light-matter interaction in natural photosynthetic antenna complexes of the Chlorobium Tepidum green sulfur bacteria (GSB) containing more than one hundred thousand chlorophyll molecules, comparable with natural size, have been performed. Here we have modeled the entire process of the exciton energy transfer, from sunlight absorption to exciton trapping in the reaction centers (RCs) in presence of a thermal bath. The energy transfer has been analyzed using the radiative non-Hermitian Hamiltonian and solving the rate equations for the populations. Sunlight pumping has been modeled as black-body radiation with an attenuation factor that takes the Sun-Earth distance into account. Cylindrical structures typical of GSB antenna complexes, and the dimeric baseplate comparable to natural size have been considered. Our analysis shows that under natural sunlight, in photosynthetic antennae of GSB the number of excitations reaching the RC per unit time matches the RC closure rate and the internal efficiency shows values close to 80%. We also considered cylindrical structures where the orientation of the dipoles does not reflect the natural one. Specifically, we vary continuously the angle of the transition dipole with respect to the cylinder main axis, focusing on the case where all dipoles are parallel to the cylinder axis. We also consider the important case where the dipoles are randomly oriented. In all cases the light-harvesting efficiency is lower than in the natural structure, showing the high sensitivity of light harvesting to the specific orientation of the dipole moments. Our results allow for a better understanding of the relationship between structure and functionality in photosynthetic antennae of GSB and could drive the design of efficient light-harvesting devices.

We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of `localized and transportable endomorphisms', which produce anyonic excitations from the ground state. Following the Doplicher--Haag--Roberts (DHR) sector theory from AQFT, we organize these endomorphisms into a braided monoidal category capturing the fusion and braiding properties of the anyons. We show that this category is equivalent to $\mathrm{Rep}_f \mathcal{D}(G)$, the representation category of the quantum double of $G$. This establishes for the first time the full DHR structure for a class of 2d quantum lattice models with non-abelian anyons.

We create the first large-scale mock spectroscopic survey of gas absorption sightlines traversing the interstellar medium (ISM), circumgalactic medium (CGM), and intergalactic medium (IGM) surrounding galaxies of virtual Universes. That is, we create mock, or synthetic, absorption spectra by drawing lines-of-sight through cosmological hydrodynamical simulations, using a new mesh-free Voronoi ray-tracing algorithm. The result is the Synthetic Absorption Line Spectral Almanac (SALSA), which is publicly released on a feature-rich online science platform (www.tng-project.org/spectra). It spans a range of ions, transitions, instruments, observational characteristics, assumptions, redshifts, and simulations. These include, but are not limited to: (ions) HI, OI, CI, MgI, MgII, FeII, SiII, CaII, ZnII, SiIII, SiIV, NV, CII, CIV, OVI; (instruments) SDSS-BOSS, KECK-HIRES, UVES, COS, DESI, 4MOST, WEAVE, XSHOOTER; (model choices) with/without dust depletion, noise, quasar continua, foregrounds; (redshift) from z=0 to z~6; (ancillary data) integrated equivalent widths, column densities, distances and properties of nearby galaxies; (simulations) IllustrisTNG including TNG50, TNG-Cluster, EAGLE, and SIMBA. This scope is not fixed, and will grow and evolve with community interest and requests over time -- suggestions are welcome. The resulting dataset is generic and broadly applicable, enabling diverse science goals such as: (i) studies of the underlying physical gas structures giving rise to particular absorption signatures, (ii) galaxy-absorber and halo-absorber correlations, (iii) virtual surveys and survey strategy optimization, (iv) stacking experiments and the identification of faint absorption features, (v) assessment of data reduction methods and completeness calculations, (vi) inference of physical properties from observables, and (vii) apples-to-apples comparisons between simulations and data.

We introduce a general integral framework for computing fractional, complex, absolute, and logarithmic moments from the moment-generating function (MGF) under explicit regularity conditions. By evaluating a complex extension of the MGF along a vertical contour, we obtain exact integral expressions that bypass the need for explicit probability densities and high-order derivatives. We establish conditions for negative fractional moments using the symmetric Cauchy principal value, including the requirement that the distribution have no point mass at the centering point. We demonstrate the theoretical scope and computational practicality of the framework through applications to the normal-inverse Gaussian distribution and a semicontinuous compound Poisson-Gamma distribution. In the latter case, the framework handles point masses at the boundary by evaluating conditional fractional moments.

Hot-wire anemometry is used to investigate the recovery of smooth-wall turbulent boundary layers from spatially localised (i.e. impulsive) pressure gradient history (PGH) effects. Measurements are performed at multiple stations downstream of spatial distributions of favourable-adverse pressure gradient sequences, followed by relaxation to zero-pressure-gradient (ZPG) conditions. The analysis focuses on matched friction Reynolds numbers at $Re_τ\approx 2300$, $3000$, and $5500$, where the local Clauser pressure gradient (PG) parameter $β$ is nominally matched at $1.7$, $0.6$, and $-0.1$, respectively. PGH strength is quantified using the integral history parameter $Δβ$, proposed by Preskett et al. (J. Fluid Mech., vol. 1010, 2025, A30), which allows isolation of PGH as the primary source of variation. The imposed PGH amplifies the wake component of the mean velocity profile and enhances the streamwise Reynolds stress throughout the boundary layer, including the emergence of an outer peak. Spectral analysis reveals an additional outer-layer energetic feature with streamwise length scales of $2$-$3δ$ ($δ$ is the local boundary layer thickness), identified as the PG peak, distinguishable from the very-large-scale motion (VLSM). Even after $β$ has relaxed (to zero) for sufficiently long distances, mean flow has not recovered to ZPG state. Once $Δβ\lesssim 0.1$, mean flow and inner/log-layer turbulence statistics recover; however, the outer-layer turbulence retains a persistent imprint of PGH. Finally, we observe that recovery involves reorganisation of large-scale structures - where VLSMs appear to be shorter even after the PG peak has vanished - which indicates prolonged history effects.

Altermagnets are a recently discovered class of compensated magnets with momentum-dependent spin splittings and unusual transport properties, even without a net magnetization. In the presence of combined four-fold rotation and time-reversal ($C_4\mathcal{T}$) symmetry, linear and also second-order, driven by a Berry curvature dipole, anomalous Hall responses are forbidden in any pure $d$-wave altermagnet. Nevertheless, here we find that the nontrivial quantum metric of the occupied Bloch states allows for an electric field induced Berry curvature dipole, which generates a strong and tunable second-order Hall current, enabling it to be switched on or off by simply adjusting the relative orientation between the symmetry-reducing dc field and the ac probe field. Specifically, we investigate the electric field induced second-order anomalous Hall response in a two-dimensional Rashba-coupled hybrid altermagnet that interpolates between $d_{x^2-y^2}$ ($B_{1g}$) and $d_{xy}$ ($B_{2g}$) altermagnet symmetry, motivated by recent proposals for mixed-symmetry states. Crucially, the nonlinear signal is highly sensitive to the underlying symmetry of the altermagnetic order at specific doping levels, offering a purely electrical method to distinguish distinct altermagnetic orders. Our results position hybrid altermagnets as a promising platform for controllable nonlinear transport and spintronic applications.

In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is decomposed into a set of weighted paths from a fixed source node to a fixed sink node that precisely represents the flow distribution across all edges. MFD problems permeate multiple important applications, including reconstructing genomic sequences to representing the flow of goods or passengers in distribution networks. Inspired by these applications, we generalize the MFD to an inexact case with bounded flow values, provide a detailed analysis, and explore different variants that are solvable in polynomial time. Moreover, we introduce the concept of robust flow decomposition by incorporating uncertain bounds and applying different robustness concepts to handle the uncertainty. Finally, we present two different adjustably robust problem formulations and perform computational experiments illustrating the benefit of adjustability.

This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how Hamming distance serves as a metric for analyzing deviations in function classification. Our extensive experimental results confirm that the Hamming distance is a pivotal metric for validating nearest neighbors in the process of classifying random functions. One of the significant conclusions we arrived is that the successful classification probability decreases monotonically with the Hamming distance. However, key exceptions were found in specific classes, revealing intra-class heterogeneity. We have established that these deviations are not random but are systemic and predictable. Furthermore, we were able to quantify these irregularities, turning potential errors into manageable phenomena. The most important novelty of this work is the demarcation, for the first time to the best of our knowledge, of precise Hamming distance intervals for the classification probability. These intervals bound the possible values the probability can assume, and provide a new foundational tool for probabilistic assessment in quantum classification. Practitioners can now endorse classification results with high certainty or dismiss them with confidence. This framework can significantly enhance any quantum classification algorithm's reliability and decision-making capability.

The intrinsic complexity of nonlinear optical phenomena offers a fundamentally new resource to analog brain-inspired computing, with the potential to address the pressing energy requirements of artificial intelligence. We introduce and investigate the concept of nonlinear inference capacity in optical neuromorphic computing in highly nonlinear fiber-based optical Extreme Learning Machines. We demonstrate that this capacity scales with nonlinearity to the point where it surpasses the performance of a deep neural network model with five hidden layers on a scalable nonlinear classification benchmark. By comparing normal and anomalous dispersion fibers under various operating conditions and against digital classifiers, we observe a direct correlation between the system's nonlinear dynamics and its classification performance. Our findings suggest that image recognition tasks, such as MNIST, are incomplete in showcasing deep computing capabilities in analog hardware. Our approach provides a framework for evaluating and comparing computational capabilities, particularly their ability to emulate deep networks, across different physical and digital platforms, paving the way for a more generalized set of benchmarks for unconventional, physics-inspired computing architectures.

This paper investigates the rank aggregation problem through the lens of multi-way comparison data derived from rater scores. Departing from traditional parametric frameworks, such as the Bradley-Terry and Plackett-Luce models, we propose a model-free method that accommodates highly heterogeneous preference distributions across raters and encompasses weak stochastic transitivity in pairwise comparisons as a special case. We establish the theoretical foundations of the proposed estimator by proving its consistency, demonstrating that the proportion of discordant pairs (Kendall tau) converges to zero in probability as the number of raters diverges. Furthermore, we derive upper and lower bounds for a performance metric based on Kendall's tau. In certain asymptotic regimes, these bounds coincide up to logarithmic factors, so the estimator is nearly minimax optimal. These results are obtained by analyzing the convergence behavior of a U-empirical process; the novel technical results developed for this analysis may be of independent theoretical interest. The practical utility of our method is validated through extensive simulations and applications to sports player rankings and survey preference aggregation.

Traditional Reynolds-averaged Navier-Stokes (RANS) closures, based on the Boussinesq eddy viscosity hypothesis and calibrated on canonical flows, often yield inaccurate predictions of both mean flow and turbulence statistics. Here, we consider flow past a circular cylinder over a range of Reynolds numbers (3,900-100,000) and Mach numbers (0-0.3), encompassing incompressible and weakly compressible regimes, with the goal of improving predictions of mean velocity and Reynolds stresses. To this end, we assemble a cross-validated dataset comprising hydrodynamic particle image velocimetry (PIV) in a towing tank, aerodynamic PIV in a wind tunnel, and high-fidelity spectral element DNS and LES. Analysis of these data reveals a universal distribution of Reynolds stresses across the parameter space, which provides the foundation for a data-driven closure. We employ physics-informed neural networks (PINNs), trained with the unclosed RANS equations, to infer the velocity field and Reynolds-stress forcing from boundary information alone. The resulting closure, embedded in a forward PINN solver, significantly improves RANS predictions of both mean flow and turbulence statistics relative to conventional models.

In Ref.~\cite{Grozdanov:2024wgo}, we derived a spectral duality relation applicable to the spectra of 3$d$ conformal field theories (CFTs) and their holographically dual 4$d$ black holes. In this work, we further elaborate on the properties of this duality relation and argue that the same relation can be applied to certain pairs of thermal correlator spectra in large-$N$ quantum field theories in any number of spacetime dimensions, provided the correlators are meromorphic functions with only simple poles and satisfy the thermal product formula. We discuss a rich set of properties that such retarded two-point functions must exhibit. We then show that the spectral duality relation and its implications apply to pairs of correlators in double-trace deformed CFTs and, more generally, to correlators in theories related by the Legendre transform. We illustrate, through several examples, how the spectrum of one correlator can be reconstructed from that of its dual correlation function. Notably, this includes cases relating the thermal spectra of scalar primary operators at ultraviolet and infrared fixed points, as well as current operators in a CFT$_3$ and its particle-vortex dual.

The integration of external data using Bayesian mixture priors has become a powerful approach in clinical trials, offering significant potential to improve trial efficiency. Despite their strengths in analytical tractability and practical flexibility, existing methods such as the robust meta-analytic-predictive (rMAP) and self-adapting mixture (SAM) often presume borrowing without rigorously assessing whether external information is appropriate to incorporate. When external and concurrent data are discordant, excessive borrowing can bias estimation and lead to misleading conclusions. To address this, we introduce WOW, a Kullback-Leibler-based gating strategy guided by the widely applicable information criterion (WAIC). Within the mixture-prior framework, WAIC-Optimized Weighting (WOW) conducts a preliminary compatibility assessment between external and concurrent trial data to determine eligibility for borrowing. Only if this gating criterion is satisfied does borrowing proceed; a downstream mixture prior procedure, using user-specified fixed or adaptive weights, can then be applied to determine the amount of borrowing. Simulation studies demonstrate that incorporating the WOW strategy before Bayesian mixture prior borrowing methods effectively mitigates excessive borrowing and improves estimation accuracy. A real-data illustration further highlights the feasibility and interpretability of the proposed gate-then-borrow strategy. By providing a practical safeguard against inappropriate borrowing, WOW strengthens the reliability of mixture-prior methods and supports better decision-making in clinical trials.

We propose a contrast-based estimation method for Gaussian processes with time-inhomogeneous drifts, observed under high-frequency sampling. The process is modeled as the sum of a deterministic drift function and a stationary Gaussian component with a parametric kernel. Our method constructs a local contrast function from adjacent increments, which avoids inversion of large covariance matrices and allows for efficient computation. We prove consistency and asymptotic normality of the resulting estimators under general ergodicity conditions. A distinctive feature of our approach is that the drift estimator attains a nonstandard convergence rate, stemming from the direct Riemann integrability of the drift density. This highlights a fundamental difference from standard estimation regimes. Furthermore, when the local contrast fails to identify all parameters in the covariance kernel, moment-based corrections can be incorporated to recover identifiability. The proposed framework is simple, flexible, and particularly well suited for high-frequency inference with time-inhomogeneous structure.

Context: Open Source Software (OSS) is a vital public good, included across most of modern software stacks, significantly impacting GDP and national tech growth, while supporting interoperability, sovereignty, and transparency. However, systematic measurement of governmental OSS adoption remain limited. Research Aim: This study contributes to digital government maturity indexes by analyzing policies and support actions leveraging OSS for software reuse and collaborative development across 16 digitally mature countries, and proposing potential indicators for said indexes. It examines OSS policy formation, stated goals, key actors, and support mechanisms. Methodology: A qualitative approach is used combining desk research of policy documents with semi-structured interviews of government representatives, producing detailed country reports. These are cross-analyzed, focusing on OSS policy promotion, rationale, and implementation support. Results: Policies facilitating OSS reuse are widespread, targeting both inbound acquisition and outbound sharing, and are predominantly governed by central public sector organizations. Policy goals include interoperability, digital sovereignty, transparency, and cost efficiency, with security framed both as a risk and strength. Implementation is supported by diverse Open Source Program Offices (OSPOs) at multiple government levels, which foster capacity building, resource pooling, and sustainable project governance. Indicators are synthesized and proposed across 14 areas covering policy incentives and design, and implementation and support. Conclusions: OSS is a strategic enabler for public sector digital transformation. Clear policy frameworks, coupled with institutional support such as OSPOs, are essential. International digital maturity frameworks should expand OSS indicators to better guide and assess government adoption and impact.

We study a class of mixed local and nonlocal $p$-Laplace equations with prototype \[ -Δ_p u + (-Δ_p)^s u = f \quad \text{in } Ω, \] where $Ω\subset \mathbb{R}^n$ is bounded and open. We provide sufficient condition on $f$ to ensure weak Harnack inequality with a tail term for sign-changing supersolutions. Two different proofs are presented, avoiding the Krylov--Safonov covering lemma and expansion of positivity: one via the John--Nirenberg lemma, the other via the Bombieri--Giusti lemma. To our knowledge, these approaches are new, even for $p = 2$ with $f \equiv 0$, and include a new proof of the reverse Hölder inequality for supersolutions. Further, we establish Harnack inequality for solutions by first deriving a local boundedness result, together with a tail estimate and an initial weak Harnack inequality.

We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test statistic is a discrete analogue of a new optimal-transport formulation of the structural model. Both test statistic and critical values rely on simulation draws from the distribution of latent variables and are computed using solutions to discrete optimal transport, hence linear programming problems. We also propose a fast preliminary search in the parameter space with an alternative, more conservative yet consistent test, based on a parameter-free critical value. We compare size and power of our procedure with competing proposals in simulations based on a regression with interval valued regressors. Finally, we apply our methodology to the model of airline entry and price competition in Ciliberto et al. [2021].

We present comprehensive \textsl{ab initio} fully quantum calculations of CO$_{\rm 2}$--H$_{\rm 2}$ and CO$_{\rm 2}$--He collisional properties. Our framework combines CCSD(T) potential-energy-surface calculations with close-coupling dynamical scattering in the \YUMI~framework to derive elastic and inelastic cross sections, rate coefficients, and pressure broadening parameters. We characterize the rotational dependence of the broadening coefficients up to $j=25$ for CO$_{\rm 2}$--H$_{\rm 2}$ and $j=40$ for CO$_{\rm 2}$--He, and their temperature dependence over 40--800 K. We also provide Padé fits as a function of rotational quantum number, enabling extrapolation and integration into spectroscopic databases including HITRAN and HITEMP. The resulting pressure broadening coefficients reproduce available experimental measurements on an absolute scale, without empirical correction factors, and meet the $\sim$10\% precision requirement identified for \textit{JWST}-era exoplanet atmospheric studies. This represents a substantial improvement over previously available parameters, which at higher temperatures ($T>400$ K) can fall outside the desired precision by up to a factor of five. All derivations, computed collisional properties, and database-ready products are provided with this manuscript. Together, these results establish a comprehensive \textsl{ab initio}, parameter-free, fully quantum foundation for CO$_2$ collisional broadening by H$_2$ and He, while demonstrating the transformative potential of the ab-initio approach for next-generation spectroscopic needs across planetary atmospheres, combustion, health sciences, and fusion-plasma diagnostics.

Stellar streams are sensitive tracers of low-mass dark matter subhalos and provide a means to test the Cold Dark Matter (CDM) paradigm on small scales. In this work, we connect the intrinsic velocity dispersion of the GD-1 stream to the number density and internal structure of dark matter subhalos in the mass range $10^5$-$10^9 M_\odot$. We measure the radial velocity dispersion of GD-1 based on 160 identified member stars across four different spectroscopic catalogs. We use repeat observations of the same stars to constrain binarity. We find that the stream's intrinsic radial velocity dispersion ranges from approximately $2$-$5 \textrm{km} \textrm{s}^{-1}$ across its length. The region of GD-1 with the highest velocity dispersion represents a $4σ$ deviation from unperturbed stream models formed in a smooth Milky Way potential, which are substantially colder. We use perturbation theory to model the stream's velocity dispersion as a function of dark matter subhalo population parameters, including the number of low-mass subhalos in the Milky Way, the dark matter half-mode mass, and the mass-concentration relation of subhalos. We find that the observed velocity dispersion can be explained by numerous impacts with low-mass dark matter subhalos, or by a single impact with a very compact subhalo with $M \gtrsim 10^8 M_\odot$. Our constraint on the fraction of mass in subhalos is $f_{\mathrm{sub}} = 0.05^{+0.08}_{-0.03}$ (68\% confidence). In both scenarios, our model prefers subhalos that are more compact compared to CDM mass-size expectations. These results suggest a possible deviation from CDM at low subhalo masses.

It is generally assumed that scalar field dark matter halos would contain solitonic cores -- spherically symmetric ground state configurations -- at their centers. This is especially interesting in the case of ultralight dark matter (ULDM), where the solitons sizes are on the order of galaxies. In this work, we show that the paradigm of a spherically symmetric soliton embedded in the center of each halo is not universally valid in a scenario with multiple interacting scalar fields. In particular, sufficiently strong repulsive interspecies interactions make the fields immiscible. In such models, the ground state configuration can fall into a number of different phases that depend on the fields' relative densities, masses, and interaction strengths. This raises the possibility that the inner regions of ULDM halos are more complex and diverse than previously assumed.

Dynamic topology optimization problems often suffer from convergence to low-performing local optima. This typically results in stiff designs that do not exploit dynamical phenomena such as antiresonance and decoupling. To obtain better designs, researchers often repeat their optimizations with different initial guesses. However, such reruns are computationally expensive and the required number is unknown. To quantify this problem, random initial guesses are sampled and tested for different frequencies on two case studies: (1) dynamic compliance minimization of a reinforced cantilever, which exhibits poor optima for driving frequencies below the first natural frequency, and (2) sound transmission loss maximization of a sandwich panel, which additionally sees a strong tendency toward low-performing optima at high frequencies. To address this issue, the study first divides techniques to reduce the needed number of reruns into four categories: global optimization, exclusion, relaxation, and frequency shift methods. For the latter three, continuation strategies are proposed, illustrated, evaluated and compared on the sound transmission loss case, using Monte Carlo sampling to estimate success rates. All strategies show measurable benefits and trade-offs. To support broader applicability, the study concludes with practical guidelines for dealing with convergence to poor local optima in dynamic topology optimization.