In this short note, we present a flux-correction form of the third-order edge-based scheme for the Euler equations that enables the direct use of a general flux function. The core idea is to replace, without loss of accuracy, the arithmetic average of the flux extrapolations by a general numerical flux evaluated at the edge midpoint, together with a correction term. We show that the proposed flux-correction form preserves third-order accuracy, provided that the general numerical flux is evaluated with the left and right states that are computed exactly for a quadratic function, which can be achieved effectively by the U-MUSCL scheme with κ = 1/2. Numerical results are presented to verify third-order accuracy with the HLLC and LDFSS flux functions on irregular tetrahedral grids.

We extend opinion dynamics on discourse sheaves to incorporate "directional stubbornness": agents may hold fixed positions in specified directions of their opinion stalk while remaining flexible in others. This converts the equilibrium problem from harmonic extension to a forced sheaf equation: the free-opinion component satisfies a sheaf Poisson equation with forcing induced by the clamped directions. We develop a parallel theory for "selective learning" of expression policies. When only a designated subset of incidence maps may adapt, the resulting gradient flow is sheaf diffusion on an auxiliary structure sheaf whose global sections correspond to sheaf structures making a fixed opinion profile publicly consistent. For joint evolution of beliefs and expressions, we give conditions (and regularized variants) guaranteeing convergence to nondegenerate equilibria, excluding spurious agreement via vanishing opinions or trivialized communication maps. Finally, we derive stagnation bounds in terms of the rate ratio between opinion updating and structural adaptation, quantifying when rapid rhetorical accommodation masks nearly unchanged beliefs, and conversely when flexible beliefs conform to rigid communication norms.

The next-to-leading order (NLO) Standard Model Effective Field Theory (SMEFT) renormalization group equations are needed to account for phenomenologically relevant operator mixing and ensure renormalization scale independence in NLO calculations of observables. For the first time, we present the renormalization group equations of the baryon-number-conserving sector of the dimension-six SMEFT up to two-loop order. Our calculations have been performed using functional methods with an anticommuting $ γ_5 $-scheme. A variety of strategies are employed to mitigate the reading-point ambiguities inherent to this scheme choice. We also describe how a local version of the $ \boldsymbol{R}^\ast $-method is adapted to handle the evanescent operators arising in dimensional regularization. The results are provided in various supplementary files to make them accessible for both human inspection and numerical implementation.

Studying Nambu solutions of the rainbow-ladder gap equation in QCD at zero temperature and chemical potential, we prove that the mass function emerges continuously from zero as the interaction strength is increased past the critical point for all positive, asymptotically perturbative kernels almost everywhere continuous in $L^1$ using the Krasnosel'skii-Guo Cone Compression Theorem. We prove that the coupled system of equations must have a positive, continuous Nambu solution with decreasing mass function for all current quark masses for a class of models which includes the physical point of a popular model of QCD by using a hybrid Krasnosel'skii-Schauder Fixed Point Theorem.

This article presents a novel fabrication route for miniaturized piezoelectric actuators that relies exclusively on processes based on femtosecond (fs) laser ablation. Previous work has already demonstrated that fs-lasers are uniquely suited for the fabrication of piezoelectric actuators based on PMN-PT, which are required for multiaxial strain-tuning of quantum dots (QDs) to enable, e.g. the generation of highly entangled photon pairs. Building on these foundations, the present work advances actuator performance and capabilities by introducing a local thinning strategy. This approach allows the realization of smaller devices, which in turn enables lower operating voltages, while simultaneously offering the possibility of integrating multiple quantum light sources on a single chip. The article provides a detailed description of the full fabrication chain, entirely based on fs-laser processing steps, from substrate thinning to metal layer structuring and final device definition. A particular focus is placed on the final cutting process, where the implementation of a third-harmonic ultraviolet (UV) fs-laser wavelength significantly improves edge quality and shape definition compared to the second harmonic (SH) wavelength used in previous work. The device fabricated through the combination of local thinning and UV-based cutting promises not only to enhance the efficiency of strain transfer but also to ensure the mechanical stability required for practical applications. These results establish fs-laser-based fabrication as a versatile and scalable method for next-generation piezoelectric actuators, paving the way for advanced strain-engineering approaches in semiconductor quantum optics and integrated quantum photonics.

The Access Traffic Steering, Switching, and Splitting (ATSSS) defined in the latest 3GPP Release 19 enables traffic flow over the multiple access paths to achieve the lower-latency End-to-end (E2E) delivery for 6G time-sensitive services. However, the existing E2E multi-path operation often falls short of more stringent QoS requirements for 6G time-sensitive services. This work proposes a Reconfigurable Intelligent Surfaces (RIS)-aided E2E multi-path uplink (UL) transmission architecture that explicitly accounts for both radio link latency and N3 backhaul latency, via the coupled designs of the UL traffic-splitting ratio, transmit power, receive combining, and RIS phase shift under practical constraints to achieve the minimum average E2E latency. We develop an alternating optimization framework that updates the above target parameters to be optimized. The simulations were conducted to compare the effectiveness of the proposed E2E optimization framework that lowers the average E2E latency up to 43% for a single user and 32% for the whole system compared with baselines in our prior work [1].

The preparation of the next-generation of large-scale radio experiments requires running a large number of simulations to explore multiple detector configurations over vast areas and develop novel methods for the reconstruction of air shower parameters. While Monte Carlo simulations are accurate and reliable tools, they are too computationally expensive to explore the full parameter space of these new detectors within a reasonable timescale, and faster and more efficient methods are needed. We introduce a new version of Radio Morphing, a semi-analytical tool designed to simulate the radio emission of any cosmic-ray induced air shower with zenith angle $θ>60^{\circ}$, at any desired antenna position, from the simulation data of a few reference showers at given positions. This version incorporate refined scaling laws of the radio emission with the shower zenith angle, a novel interpolation method, the implementation of the charge-excess mechanism and the possibility to enable shower-to-shower fluctuations. We present the latest performances of Radio Morphing, tuned for a GRAND-like detector, which now provides an estimation of air shower radio signals four orders of magnitude faster than standard Monte Carlo simulations, while keeping an accuracy on the peak amplitude better than $17\%$ on unfiltered traces, better than $13\%$ in the [50 - 200] MHz band, and below $\sim 10\%$ in the [30 - 80] MHz band.

Primordial black holes (PBHs) are theorized to form from the collapse of overdensities in the very early Universe. PBHs in the asteroid-mass range $10^{17} \, {\rm g}\lesssim M \lesssim 10^{23} \, {\rm g}$ could serve as all or most of the dark matter today, but are particularly difficult to detect due to their modest rates of Hawking emission and sub-micron Schwarzschild radii. We consider whether the steep gradients of a PBH's gravitational field could generate tidal forces strong enough to disrupt atoms and nuclei. Such phenomena may yield new observables that could uniquely distinguish a PBH from a macroscopic object of the same mass. We first consider the gravitational ionization of ambient neutral hydrogen and evaluate prospects for detecting photon radiation from the recombination of ionized atoms. During the present epoch, this effect would be swamped by Hawking radiation -- which would itself be difficult to detect for PBHs at the upper end of the asteroid-mass window. We then consider the gravitational ionization and heating of neutral hydrogen immediately following recombination at $z\simeq1090$, and identify a broad class of PBH distributions with typical mass $5\times10^{21}\,{\rm g}\lesssim M \lesssim 10^{23}\, {\rm g}$ within which gravitational interactions would have been the dominant form of energy deposition to the medium. We also identify conditions under which tidal forces from a transiting PBH could overcome the strong nuclear force, either by dissociating deuterons, which would be relevant during big bang nucleosynthesis (BBN), or by inducing fission of heavy nuclei. We find that gravitational dissociation of deuterons dominates photodissociation rates due to Hawking radiation for PBHs with masses $10^{14}\,{\rm g}\lesssim M \lesssim 10^{16}\,{\rm g}$. We additionally identify the phenomenon of gravitationally induced fission of heavy nuclei via tidal deformation.

Given a set $S$ of $n$ points in the plane, we study the two-line-center problem: finding two lines that minimize the maximum distance from each point in $S$ to its closest line. We present a $(1+\varepsilon)$-approximation algorithm for the two-line-center problem that runs in $O((n/\varepsilon) \log (1/\varepsilon))$ time, which improves the previously best $O(n\log n + ({n}/{\varepsilon^2}) \log ({1}/{\varepsilon}) + (1/\varepsilon^3)\log ({1}/{\varepsilon}))$-time algorithm. We also consider three variants of this problem, in which the orientations of the two lines are restricted: (1) the orientation of one of the two lines is fixed, (2) the orientations of both lines are fixed, and (3) the two lines are required to be parallel. For each of these three variants, we give the first $(1+\varepsilon)$-approximation algorithm that runs in linear time. In particular, for the variant where the orientation of one of the two lines is fixed, we also give an improved exact algorithm that runs in $O(n \log n)$ time and show that it is optimal.

This paper explores how a recent European Union proposal, the so-called Chat Control, which creates regulatory incentives for providers to implement content detection and communication scanning, could transform the foundations of human-robot interaction (HRI). As robots increasingly act as interpersonal communication channels in care, education, and telepresence, they convey not only speech but also gesture, emotion, and contextual cues. We argue that extending digital surveillance laws to such embodied systems would entail continuous monitoring, embedding observation into the very design of everyday robots. This regulation blurs the line between protection and control, turning companions into potential informants. At the same time, monitoring mechanisms that undermine end-to-end encryption function as de facto backdoors, expanding the attack surface and allowing adversaries to exploit legally induced monitoring infrastructures. This creates a paradox of safety through insecurity: systems introduced to protect users may instead compromise their privacy, autonomy, and trust. This work does not aim to predict the future, but to raise awareness and help prevent certain futures from materialising.

NashOpt is an open-source Python library for computing and designing generalized Nash equilibria (GNEs) in noncooperative games with shared constraints and real-valued decision variables. The library exploits the joint Karush-Kuhn-Tucker (KKT) conditions of all players to handle both general nonlinear GNEs and linear-quadratic games, including their variational versions. Nonlinear games are solved via nonlinear least-squares formulations, relying on JAX for automatic differentiation. Linear-quadratic GNEs are reformulated as mixed-integer linear programs, enabling efficient computation of multiple equilibria. The framework also supports inverse-game and Stackelberg game-design problems. The capabilities of NashOpt are demonstrated through several examples, including noncooperative game-theoretic control problems of linear quadratic regulation and model predictive control. The library is available at https://github.com/bemporad/nashopt

Directional memory in amorphous solids is commonly quantified through the Bauschinger effect, yet the observation of the inverse Bauschinger effect suggests that the sign of memory can invert, pointing to distinct underlying plastic organization. Here, we connect directional memory to the nature of yielding in steadily sheared amorphous solids. Using simulations of two-dimensional polydisperse glasses, we show that the type of directional memory (Bauschinger versus inverse Bauschinger) is jointly controlled by deformation history, strain rate, and parent temperature. We identify a critical history amplitude $γ_{N,\mathrm{crit}}(T_p,\dotγ)$ and construct a phase diagram that delineates regimes with memory inversion from those showing only conventional Bauschinger response. Microscopically, memory inversion correlates with network-like shear-band morphology and plastic healing, whereas conventional memory is associated with persistent localization and cumulative damage. These results establish directional memory as an order parameter for a shear-rate and annealing-controlled brittle-ductile crossover and suggest that plastic healing provides a generic route to memory inversion in disordered solids.

In the immediate aftermath of the Big Bang, the universe existed in an extremely hot, dense state in which particle interactions occurred not in a vacuum but within a thermal medium. Under such conditions, the standard framework of quantum field theory (QFT) requires a finite temperature extension, wherein propagators -- and hence the fundamental structure of the theory -- are modified to reflect thermal background effects. These thermal modifications are central to understanding the nature of electroweak symmetry breaking (EWSB) as a high temperature phase transition, potentially leading to qualitatively different vacuum structures for the Higgs field as the universe cooled. Finite temperature corrections naturally regulate ultraviolet divergences in propagators, hinting at a possible route toward ultraviolet completion. However, these same thermal effects exacerbate infrared pathologies and can lead to imaginary contributions to the effective potential, particularly when analysing metastable or multi-vacuum configurations. Additional theoretical challenges, such as gauge dependence and renormalization scale ambiguity, further obscure the precise characterization of the electroweak phase transition even in minimal extensions of the Standard Model (SM). This review presents the theoretical foundations of finite temperature QFT with an emphasis on how different field species respond to thermal effects, identifying the bosonic sector as the primary source of key theoretical subtleties. We focus particularly on the scalar extension of the SM, which offers a compelling framework for realizing first order electroweak phase transitions, electroweak baryogenesis, and accommodating dark matter candidates depending on the underlying $Z_2$ symmetry structure.

We extend the capabilities of correlation energy functionals based on the adiabatic-connection fluctuation-dissipation theorem by implementing the analytical atomic forces within the random phase approximation (RPA), in the context of plane waves and pseudopotentials. Forces are calculated at self-consistency through the optimized effective potential method and the Hellmann-Feynman theorem. In addition, non-self-consistent RPA forces, starting from the PBE generalized gradient approximation, are evaluated using density functional perturbation theory. In both cases, we find forces of excellent numerical quality. Furthermore, for most molecules and solids studied, self-consistency is found to have a negligible impact on the computed geometries and vibrational frequencies. The RPA is shown to systematically improve over PBE and, by including the exact-exchange kernel within RPA + exchange (RPAx), through finite-difference total energy calculations, we obtain an accuracy comparable to advanced wavefunction methods. Finally, we estimate the anharmonic shift and provide accurate theoretical references based on RPA and RPAx for the zone-center optical phonon of diamond, silicon, and germanium.

Kapitza-Dirac scattering, the diffraction of matter waves from a standing light field, is widely utilized in ultracold gases, but its behavior in the strongly interacting regime is an open question. Here we develop a numerically-exact two-body description of Kapitza-Dirac scattering for two contact-interacting atoms in a one-dimensional harmonic trap subjected to a pulsed optical lattice, enabling us to obtain the numerically exact dynamics. We map how interaction strength, lattice depth, lattice wavenumber, and pulse duration reshape the diffraction pattern, leading to an interaction-dependent population redistribution in real and momentum-space. By comparing the exact dynamics to an impulsive sudden-approximation description, we delineate the parameter regimes where it remains accurate and those, notably at strong attraction and small lattice wavenumber, where it fails. Our results provide a controlled few-body benchmark for interacting Kapitza-Dirac scattering and quantitative guidance for Kapitza-Dirac-based probes of ultracold atomic systems.

The order picking problem seeks the shortest warehouse route that visits all required item locations. Strict conditions are known for single-block rectangular layouts under which optimal routes never require double traversals, while broader results show that double traversals serving cross-aisle connectivity can always be avoided. We strengthen these findings by proving that no double traversals are needed in the boundary subaisles, the uppermost and lowermost subaisle segments, of warehouses with at least two non-empty aisles. This yields a unified strict condition for all single-block layouts and for two-block layouts with more than one aisle. For these widely used layouts, exact methods such as dynamic programming and mathematical programming can therefore exclude the double-traversal configuration from every boundary subaisle, reducing the number of admissible edge configurations without loss of optimality.

Dark pions are promising dark matter candidates, yet most analyses rely on leading-order (LO) chiral perturbation theory (ChPT). Motivated by the fact that, even for QCD pi-pi scattering, LO ChPT near threshold underestimates the isoscalar s-wave amplitude by an O(1) factor relative to high-precision dispersive results, we quantify how unitarization modifies the standard LO ChPT picture using the chiral unitary method, a nonperturbative resummation that implements the correct analytic structure with minimal input, and assess its impact on the phenomenology of dark-pion dark matter, taking SIMP and WIMP scenarios as canonical examples. We fix the subtraction constant to its natural estimate, interpreted as an effective cutoff at the chiral scale, so that the unitarized amplitudes depend only on the dark-pion mass and decay constant. We show that, depending on the coupling, the unitarized amplitudes develop resonance poles absent at LO, leading to sizable departures in 2-to-2 self-scattering, relevant for SIMP scenarios, and in annihilation including initial-state interaction effects, relevant for WIMP scenarios. These modifications, in turn, affect the viable parameter space. Although the subtraction constant is, from a model-building perspective, merely a parameter, a substantial deviation from its natural value would point to additional elementary resonances with the same quantum numbers.

Understanding infectious disease transmission in institutional settings requires models that capture how contacts arise from structured routines, roles, and spatial constraints. In aged care facilities, interactions are driven by care delivery, staff scheduling, and resident mobility, producing patterns that differ from those assumed in population-level models. This study develops an agent-based framework to generate high-resolution contact matrices by simulating task-driven behaviour, staff workflows, and movement through shared spaces. Rather than prescribing contacts, interactions emerge from scheduled activities and proximity during task execution. The model is parameterised using activity-diary data from aged care workers and separates behavioural logic from physical layout, enabling adaptation to different facility designs without altering core mechanisms. Results show strong heterogeneity in contact patterns across care levels and staff shifts. Low and medium care residents had higher contact frequencies than high care residents, while day and afternoon staff shifts accounted for most resident-staff interactions. Contacts clustered around daily routines such as meals and communal activities. Incorporating a proximity-based airborne transmission component showed that risk was concentrated during high-contact shifts and among more mobile residents. Vaccination scenarios substantially reduced predicted transmission, with the greatest impact when both staff and residents were vaccinated. By linking organisational processes to emergent contact structure, this framework provides a reproducible approach to contact matrix generation for institutional settings, supporting more realistic transmission modelling and evaluation of targeted infection control strategies.

We study bulk two-point correlation functions of a massless scalar field in Jackiw-Teitelboim gravity around the eternal black hole saddle. While same-side correlators exhibit exponential decay, two sided correlators, at the next to leading order in steepest descent approximation, exhibit a ramp followed by a plateau after the initial semiclassical exponential decay. Our results indicate that the late-time saturation of two-sided correlators is already visible within the perturbative saddle expansion of the bulk path integral, without invoking nonperturbative e^{-S} effects. Finally, we show that the dip-time, defined as the minimum of the correlator, grows inversely with the black hole temperature, consistent with expectations from the holographic dual.

The precise role of e-ph coupling in graphene and related materials on a honeycomb lattice is not yet fully understood, despite extensive research on these systems. Here, we perform sign-problem-free determinant quantum Monte Carlo (DQMC) simulations of the optical Su-Schrieffer-Heeger (oSSH)-Hubbard model on the honeycomb lattice, focusing on the parameters relevant to graphene. Performing finite-size scaling analyzes, we obtain the model's ground state phase diagram, which includes the semi-metal (SM), Kekulé Valence Bond Solid (KVBS), and anti-ferromagnetic (AFM) phases, as well as indications of a small KVBS/AFM coexistence region. We find that a weak to moderate Hubbard repulsion, tuned toward the SM-AFM critical value in the pure honeycomb Hubbard model, enhances KVBS correlations and can even stabilize the KVBS phase. Estimating the effective parameters for graphene places it in the SM region of the phase diagram, but near the SM-KVBS phase boundary. Notably, we predict that increasing either the on-site Hubbard repulsion or the e-ph coupling strength drives graphene toward the KVBS phase rather than the AFM phase, highlighting a synergistic effect that can be exploited to further control the remarkable properties of graphene and related materials.

We update the analysis of the viability of the lepton mixing patterns originating from $A_4$, $S_4$ and $A_5$ discrete flavour symmetries and leading to predictions for the solar neutrino mixing angle, $θ_{12}$. We perform a statistical analysis using as an input (i) the results of the latest global fit to neutrino oscillation data, and (ii) the first JUNO measurement of $\sin^2θ_{12}$. Out of the five (four) cases compatible with the global data at $3σ$ for normal (inverted) neutrino mass ordering, only three (two) cases remain compatible with the global data at the same confidence level after taking into account the JUNO result.

A well-known testing method for the safety evaluation and real-time validation of automotive software systems (ASSs) is Fault Injection (FI). In accordance with the ISO 26262 standard, the faults are introduced artificially for the purpose of analyzing the safety properties and verifying the safety mechanisms during the development phase. However, the current FI method and tools have a significant limitation in that they require manual identification of FI attributes, including fault type, location and time. The more complex the system, the more expensive, time-consuming and labour-intensive the process. To address the aforementioned challenge, a novel Large Language Models (LLMs)-assisted fault test cases (TCs) generation approach for utilization during real-time FI tests is proposed in this paper. To this end, considering the representativeness and coverage criteria, the applicability of various LLMs to create fault TCs from the functional safety requirements (FSRs) has been investigated. Through the validation results of LLMs, the superiority of the proposed approach utilizing gpt-4o in comparison to other state-of-the-art models has been demonstrated. Specifically, the proposed approach exhibits high performance in terms of FSRs classification and fault TCs generation with F1-score of 88% and 97.5%, respectively. To illustrate the proposed approach, the generated fault TCs were executed in real time on a hardware-in-the-loop system, where a high-fidelity automotive system model served as a case study. This novel approach offers a means of optimizing the real-time testing process, thereby reducing costs while simultaneously enhancing the safety properties of complex safety-critical ASSs.

We explore interactions between equally charged surfaces, in the presence of simple salt and either neutral or monovalently charged polyampholytes. We consider the possibility of using these charged polymers as crude models of ion clusters. The latter have been hypothesised to form in concentrated aqueous salt solutions, and are possibly related to anomalous underscreening. This phenomenon usually manifests itself by unexpectedly strong and long-ranged effective forces at very high ionic strengths. If ion clusters are formed, they are expected to carry at most a weak net charge. Keeping this in mind, we investigate how polyampholyte chains mediate interactions between charged surfaces. A significant amount of simple salt is also present, in most cases. We highlight that if the charges of the polyampholytes are unevenly distributed, there is a polarisation response that in turn can generate very strong and long-ranged surface forces, even at rather high concentrations of simple salt. Aside from their possible relevance to ion clusters and underscreening phenomena, these results also suggest the possibility of tailoring synthetic polyampholytes, in order to regulate colloidal stability.

In mixed quantum-classical simulations of molecule-metal surface interactions, the discretization of the metallic electronic continuum typically results in a closed-system representation that fails to capture the open-system nature of the true physical process. This approximation can introduce significant artifacts, including deviations in the dynamical evolution and a violation of the principle of detailed balance. To address this fundamental challenge, we introduce an electronic thermostat into our previously developed orbital surface hopping (OSH) framework, generalizing the method to efficiently handle many discrete electronic states. We first outline the derivation of electronic thermostat orbital surface hopping, where the amplitude of the electronic thermostat is well justified. We then demonstrate that this method can reproduce accurate dynamics and detailed balance in long time, whereas without electronic thermostat the detailed balance is violated. Thus, this method offers a reliable tool for studying nonadiabatic dynamics near metal surfaces.

Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this Perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented including construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this Perspective serves as a gentle introduction of state-of-the-art quantum algorithms to the computational science community, and inspires future development on scalable quantum computational science methodologies that bridge theory and practice.

We exploit quasi-random variation around the multi-threshold criteria used to classify Census Towns (CTs) and focus on settlements near the thresholds that are likely to obtain statutory recognition. Using a local fuzzy regression discontinuity design and a multi-threshold criteria, we show that meeting the CT eligibility in 2001 raises the probability of statutory recognition by 2011. Instrumenting statutory recognition with CT eligibility, we estimate the effects of ULB status on local public goods provision: government schools increase by 13.86 (primary), 7.72 (middle), and 4.89 (secondary) units, healthcare infrastructure expands by 2.53 hospitals and 3.00 family welfare centers, and financial access deepens with 4.09 cooperative banks and 2.84 agricultural credit societies. Community amenities also improve, while sports infrastructure declines by 5.71 facilities, consistent with reallocation of urban land. The corresponding reduced-form estimates are directionally consistent and indicate that crossing the CT eligibility frontier improves public goods provision. Our findings indicate that timely municipalization of emerging urban areas can expand provision of public goods.

Graph rigidity theory is an important tool for examining the solvability of sensor network localization (SNL) problems, and ensuring global convergence of localization algorithms. Along this direction, diverse measurements such as signed angle (SA) and ratio of distance (RoD) have been considered. However, little is known about how the bipartition of nodes based on perceptual abilities affects the rigidity property of the network. In this paper, we study the rigidity and localization of networks with heterogeneous nodes, namely, two types of sensors measuring SA and RoD, respectively. Interestingly, the rigidity property is shown to be strongly dependent on the bipartition of nodes, and exhibits a duality. Moreover, an SA-RoD constrained network can be uniquely determined up to uniform rotations, translations, and scalings (global SA-RoD rigidity) even if it is neither SA rigid nor RoD rigid. A scalable approach to construction of globally SA-RoD rigid frameworks is proposed. Localizability analysis and localization algorithm synthesis are both conducted based on weaker network topology conditions, compared with SA- or RoD-based SNL approaches. Numerical simulations are worked out to validate the theoretical results.

We study natural evaluation and interpolation problems for elliptic functions and prove that they allow a recursive treatment using a variant of classical butterflies first introduced by Gauss. We deduce the existence of straight-line programs with complexity scaling with $d\log(d)$ for these problems and present applications to finite field arithmetic, coding theory and cryptography.

We present the Hyper Millennium (HM) simulation, an extremely large cosmological simulation designed to support next-generation galaxy surveys. The simulation follows 4.2 trillion dark matter particles in a comoving box of $2.5\ h^{-1}{\rm Gpc}$, with a mass resolution of $3.2 \times 10^8\, {h^{-1}\rm M_{\odot}}$ and a force resolution of $3.0\ h^{-1}{\rm kpc}$. Its combination of scale and resolution is ideal for studying large-scale structures and rare cosmic objects. In this first paper of the HM project, we explore whether the massive galaxy cluster Abell~2744 (A2744) can be reproduced in detail in the simulation. Pixel-based statistics of galaxy number density $N_{\rm gal}$, luminosity density $L_{\rm gal}$, and projected mass density $κ$ show excellent agreement between A2744 and its analogues down to $\sim 50$ kpc, once field-selection biases toward high galaxy surface density are accounted for. This concordance, achieved in one of the most extreme known galaxy environments, is a validation of the underlying $Λ{\rm CDM}$ model in the extreme regime of A2744. It also showcases the robustness and accuracy of the HM simulation, which, when coupled with a sophisticated semi-analytic galaxy formation model, is capable of producing galaxy and mass catalogues of comparable quality out to high redshift across its full comoving volume of 50.4 ${\rm Gpc^3}$.

Data products are reusable, self-contained assets designed for specific business use cases. Automating their discovery is of great industry interest, as it enables efficient data access in large data lakes and supports analytical workflows. However, no benchmark currently exists for data product discovery over hybrid table-text corpora. Existing datasets focus on answering single factoid questions over individual tables rather than assembling multiple related data assets into coherent products. To address this gap, we present DPDisc, the first large-scale benchmark for data product discovery, where systems must retrieve coherent collections of tables and passages to satisfy high-level Data Product Requests (DPRs). We introduce DPForge, an automated pipeline that systematically repurposes table-text QA datasets by clustering related tables and passages into coherent data products, generating professional-level analytical requests using an LLM ensemble, and validating quality through multi-phase LLM evaluation. DPDisc comprises 13,076 validated instances with full provenance, derived from three representative datasets spanning open-domain and financial domains. Baseline experiments with sparse, dense, and hybrid retrieval methods imply evaluation feasibility while revealing substantial performance gaps across domains, indicating opportunities for future research in structure-aware data product discovery. Code and datasets are available at: Dataset: https://huggingface.co/datasets/ibm-research/data-product-benchmark Code: https://github.com/ibm/data-product-benchmark