Low Earth Orbit (LEO) satellite constellations in the 6G era are evolving into intelligent in-orbit computational platforms, forming Space Computing Power Networks (SCPNs) to deliver global-scale computing services. However, the intensive computation within SCPN incurs a significant ``unseen cost'': the frequent charge-discharge cycles accelerate the physical degradation of satellites' life-limiting and high-cost batteries, thereby threatening the long-term operational viability of such a system. Existing approaches, often relying on indirect metrics like Depth of Discharge (DoD) and neglecting the complex, nonlinear degradation process of battery aging, fail to accurately quantify this cost. To address this, we introduce a high-fidelity, physics-driven model that quantitatively links computational workload parameters to the nonlinear battery degradation. Building on this model, we formulate a degradation-aware scheduling problem and analyze heuristic policies across different energy regimes. Simulations reveal that the optimal strategy should be adaptive: in solar-rich conditions, a myopic policy maximizing instantaneous solar utilization is superior, whereas under energy scarcity, a reactive policy leveraging real-time battery state significantly extends lifetime.

This work investigates the influence of Lorentz symmetry breaking, introduced by an aether-like field $α_ϕ$, on the Casimir effect within a five-dimensional flat spacetime. By considering a quasiperiodic condition regulated by the parameter $β$ and an extra dimension compactified at scale $b$, we derive closed-form expressions for the Casimir energy and the resulting force between two parallel plates under Neumann boundary conditions. Our results demonstrate that $β$ acts as a crucial control parameter, enabling a continuous transition between attractive and repulsive regimes, with a characteristic symmetry around $β= 0.5$. We show that the Lorentz-violating parameter $α_ϕ$ functions as an enhancement factor, significantly amplifying the vacuum interaction, while the geometric ratio $a/b$ proves decisive for system stabilization. Specifically, we find that the high-compactification regime leads to a plateau in the Casimir force, effectively stabilizing the interaction. Furthermore, we analyze the mass spectrum of the field, recovering standard geometric forms in the massless limit and demonstrating that while light fields ($M \ll 1$) exhibit subtle quadratic corrections, heavy fields ($M \gg 1$) lead to an exponential suppression of the Casimir effect. The interplay between Lorentz violation and extra-dimensional compactification provides a rich mechanism with potential applications in the modulation of vacuum-induced interactions at micro and nano scales.

Skewed distributions are fundamental in modelling asymmetric data on the d-dimensional torus. In this context, asymmetry is introduced through the sine-skewing mechanism, which is the only skewing mechanism that has been proposed on the hyper-torus in the literature. Some sine-skewed models are known to suffer from a singular Fisher information matrix in the vicinity of symmetry, which poses a significant issue for inferential purposes. It is an open question to determine for which sine-skewed models Fisher information singularity occurs. In this paper, a general characterization of the class of models that exhibit this singularity is given in the general d-dimensional setting.

Accurate channel estimation is essential for massive multiple-input multiple-output (MIMO) technologies in next-generation wireless communications. Recently, the radio radiance field (RRF) has emerged as a promising approach for wireless channel modeling, offering a comprehensive spatial representation of channels based on environmental geometry. State-of-the-art RRF reconstruction methods, such as RF-3DGS, can render channel parameters, including gain, angle of arrival, angle of departure, and delay, within milliseconds. However, creating the required 3D environment typically demands precise measurements and advanced computer vision techniques, limiting accessibility. This paper introduces a locally deployable tool that simplifies 3D environment creation for RRF reconstruction. The system combines finetuned language models, generative 3D modeling frameworks, and Blender integration to enable intuitive, chat-based scene design. Specifically, T5-mini is finetuned for parsing user commands, while all-MiniLM-L6-v2 supports semantic retrieval from a local object library. For model generation, LLaMA-Mesh provides fast mesh creation, and Shap-E delivers high-quality outputs. A custom Blender export plugin ensures compatibility with the RF-3DGS pipeline. We demonstrate the tool by constructing 3D models of the NIST lobby and the UW-Madison wireless lab, followed by corresponding RRF reconstructions. This approach significantly reduces modeling complexity, enhancing the usability of RRF for wireless research and spectrum planning.

Privacy policies are long, complex, and rarely read, which limits their effectiveness in informed consent. We investigate scrollytelling, a scroll-driven narrative approach, as a privacy policy presentation format. We built a prototype that interleaves the full policy text with animated visuals to create a dynamic reading experience. In an online study (N=454), we compared our tool against text, two nutrition-label variants, and a standalone interactive visualization. Scrollytelling improved user experience over text, yielding higher engagement, lower cognitive load, greater willingness to adopt the format, and increased perceived clarity. It also matched other formats on comprehension accuracy and confidence, with only one nutrition-label variant performing slightly better. Changes in perceived understanding, transparency, and trust were small and statistically inconclusive. These findings suggest that scrollytelling can preserve comprehension while enhancing the experience of policy reading. We discuss design implications for accessible policy communication and identify directions for increasing transparency and user trust.

We point out that, in the usual way of specifying a sinusoidal waviness of the wall of a tube of circular cross section, in which the mean radius is kept constant, the interior volume of the tube increases with increasing wave amplitude. We compare this case with the case where the interior volume is kept constant by reducing the mean radius as the wave amplitude increases. We present and compare numerical results of these two cases for steady, pressure driven, laminar viscous flow in a tube with a stationary wavy wall, for both circular and annular tubes. The volume flow rate and the hydraulic resistance can differ in the two cases by as much as 10% for wave amplitudes as small as 20% of the mean radius and as much as 50% for larger wave amplitudes. For a circular tube, we derive a scaling law that relates the two cases based on dimensional analysis, allowing the behavior in the constant-volume case to be determined from that in the constant-mean-radius case. Additionally, we consider peristaltic pumping due to a moving sinusoidal wall wave and show that the volume-change effect is significant even at small wave amplitudes, and that the volume flow rates in the two cases can differ significantly, by as much as 50% as the wave amplitude approaches its maximum value.

Low Earth orbit (LEO) satellite constellations have become a critical enabler for global coverage, utilizing numerous satellites orbiting Earth at high speeds. By decomposing complex network services into lightweight service functions, network function virtualization (NFV) transforms global network services into diverse service function chains (SFCs), coordinated by resource-constrained LEOs. However, the dynamic topology of satellite networks, marked by highly variable inter-satellite link delays, poses significant challenges for designing efficient routing strategies that ensure reliable and low-latency communication. Many existing routing methods suffer from poor scalability and degraded performance, limiting their practical implementation. To address these challenges, this paper proposes a novel SFC routing approach that leverages the statistical properties of network link states to mitigate instability caused by instantaneous modeling in dynamic satellite networks. Through comprehensive simulations on end-to-end shortest-path propagation delays in LEO networks, we identify and validate the statistical stability of multi-hop routes. Building on this insight, we introduce the Stability-Aware Multi-Stage Graph Routing (SA-MSGR) algorithm, which incorporates pre-computed average delays into a multi-stage graph optimization framework. Extensive simulations demonstrate the superior performance of SA-MSGR, achieving significantly lower and more predictable end-to-end SFC delays compared to representative baseline strategies.

The large population of broad-line Active Galactic Nuclei (AGN) observed with the James Webb Space Telescope (JWST) at $z \gtrsim 4$ opens a new window onto the black hole-galaxy connection in the first Gyr of cosmic history. We use the JADES survey-level dataset and develop a forward-modeling Bayesian framework that explicitly accounts for broad H$α$ detectability, ensuring that selection effects are incorporated into the likelihood function. With this approach, we constrain the black hole-stellar mass ($M_{\mathrm{BH}}$-$M_\star$) relation to be $\log M_{\rm BH} = -4.06^{+0.50}_{-0.51} + 1.17^{+0.06}_{-0.06}\,\log M_\star$, with an intrinsic orthogonal scatter of $σ_{\rm int} = 0.63^{+0.14}_{-0.11}$ dex. The slope and normalization are consistent with local determinations, indicating that the average scaling was already established by $z \sim 4$-6. This suggests that the primary evolution of the relation occurs in its dispersion rather than in its mean normalization. In contrast, the substantially larger intrinsic scatter relative to the nearby Universe reveals a wider diversity of black hole-galaxy growth histories, likely driven by bursty accretion, delayed feedback, and differences in merger or seeding histories. Future JWST samples will be crucial to test whether this increased scatter is a persistent feature of the high-redshift Universe.

This paper focuses on error thresholds for Pauli channels. We numerically compute lower bounds for the thresholds using the analytic framework of coset weight enumerators pioneered by DiVincenzo, Shor and Smolin in 1998. In particular, we study potential non-additivity of a variety of small stabilizer codes and their concatenations, and report several new concatenated stabilizer codes of small length that show significant non-additivity. We also give a closed form expression of coset weight enumerators of concatenated phase and bit flip repetition codes. Using insights from this formalism, we estimate the threshold for concatenated repetition codes of large lengths. Finally, for several concatenations of small stabilizer codes we optimize for channels which lead to maximal non-additivity at the hashing point of the corresponding channel. We supplement these results with a discussion on the performance of various stabilizer codes from the perspective of the non-additivity and threshold problem. We report both positive and negative results, and highlight some counterintuitive observations, to support subsequent work on lower bounds for error thresholds.

This paper introduces Exp-ParaDiag, a novel time-parallel method that combines the strength of exponential integrators into the ParaDiag framework. We develop and analyze Exp-ParaDiag based on first and second order accurate exponential integrators. We establish the convergence of the proposed methods both as preconditioned fixed-point iterations and as precon- ditioners within the GMRES framework. Furthermore, we extend the Exp-ParaDiag formulation to achieve sixth-order temporal accuracy using exponential integrators. The proposed approach is also generalized to nonlinear problems, for which convergence is rigorously demonstrated. A series of numerical experiments is presented to validate the theoretical results and to illustrate the robustness and efficiency of the developed methods.

Geometric (also known as spatial) quantiles, introduced by Chaudhury and representing one of the three principal approaches to defining multivariate quantiles, have been well studied in the literature. In this work, we focus on the extremal behaviour of these quantiles. We establish new extremal properties, namely general lower and upper bounds for the norm of extreme geometric quantiles, free of any moment conditions. We discuss the impact of such results on the characterization of distribution behaviour. Importantly, the lower bound can be directly linked to univariate quantiles and to halfspace (Tukey) depth central regions, highlighting a novel connection between these two fundamental notions of multivariate quantiles.

We study the design of fair allocation rules for the abatement of riparian pollution. To do so, we consider the so-called river pollution claims model, recently introduced by Yang et al. (2025) to distribute a budget of emissions permits among agents (cities, provinces, or countries) located along a river. In such a model, each agent has a claim reflecting population, emission history, and business-as-usual emissions, and the issue is to allocate among them a budget that is lower (or equal) than the aggregate claim. For environmental reasons, the specific location along the river where pollutants are emitted is an important concern (the more upstream the location is the higher the damage of polluting the river). We characterize a class of geometric rules that adjust proportional allocations to compromise between fairness and environmental concerns. Our class is an alternative to the one proposed by Yang et al. (2025). We compare both alternatives through an axiomatic study, as well as an illustration for the case study of the Tuojiang Basin in China.

We study packet routing in the Kautz digraph K(d,D), where every ordered pair of distinct vertices is connected by a unique shortest directed path. The regular routing introduced in earlier work schedules all ordered pairs in tau(d,D) = (D-1)d^(D-2) + D d^(D-1) steps. We show that, for every fixed outdegree d at least 2 and all sufficiently large diameters D, no shortest-path routing scheme can match this makespan. More precisely, we prove that K(d,D) contains an edge whose shortest-path congestion strictly exceeds tau(d,D) when D is sufficiently large. Our construction uses edge-words drawn from a subset of ternary unbordered square-free words, together with a trimming inequality that propagates large congestion at distance D down to shorter distances. Computations for d=2 and small D show that for all D at least 4 there is an edge in K(2,D) with congestion greater than tau(2,D).

Quantum simulations on current NISQ hardware are limited by its noisy nature, making efficient quantum error mitigation methods highly demanded. In this paper we introduce a novel mitigation scheme, applicable to arbitrary quantum simulations of time-dependent Hamiltonian dynamics on NISQ devices. The scheme uses a polynomial subset of extended qubit Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equations as a sampling criterion of possible mitigated candidates for the quantum observables. We show that for favorable Hamiltonians the polynomial subset of BBGKY hierarchy equations leads to a polynomial overhead in both classical and quantum resources. We employ the method to mitigate simulations of the chiral magnetic effect (CME), a chiral feature of the Schwinger model. We empirically show the effectiveness of our scheme at recovering the real-time dynamics of the CME from noisy quantum simulations of the Schwinger model, for a range of different parameter values of the model. We numerically demonstrate a systematic reduction of quantum noise, together with an increasing noise reduction capability as the amount of BBGKY constraints grows.

The modified Langevin noise formalism (MLNF) models the interaction of the quantized electromagnetic field with an arbitrary lossy magneto-dielectric object placed in vacuum using three types of non-interacting bosonic polaritons: scattering, electric, and magnetic. These respectively represent free-space photons scattered by the object, and photons radiated by quantized electric and magnetic dipolar sources embedded within its volume. Recently [A. Ciattoni, Phys. Rev. A 110, 013707 (2024)], this formalism was justified from the canonical quantization of macroscopic electromagnetism (CQME) [Philbin, New J. Phys. 12, 123008 (2010)] in the Heisenberg picture. This was achieved by identifying the polariton operators within the formal solution of the macroscopic Maxwell equations, assuming they obey bosonic commutation relations to retrieve the canonical ones, and showing they diagonalize the CQME Hamiltonian. However, the explicit functional dependence of these polaritons on the underlying canonical field operators remained undetermined. In this paper, we derive the exact analytical expressions for the polariton operators in terms of the canonical CQME field operators. Using these mappings, we provide a direct and rigorous derivation of the MLNF from the canonical theory in the Schrödinger picture. Our derivation is structured in three foundational steps: 1) adopting the derived analytical expressions as the constitutive definitions of the polariton operators; 2) mathematically proving that these operators are strictly bosonic as a direct consequence of the canonical commutation relations; and 3) demonstrating that they exactly diagonalize the macroscopic CQME Hamiltonian.

This paper studies enhanced droop-free control strategies with sparse neighboring communication for achieving effective active power sharing of distributed energy resources (DERs) while maintaining the frequency stability of islanded microgrids. The normalized active power consensus (NAPC) based droop-free control can share the load among controllable DERs in proportion to their available capacities. However, existing literature exclusively takes the asymptotic stability of the NAPC based droop-free control for granted, lacking a comprehensive theoretical proof that is critical for ensuring its effective design and practical implementation. This paper, for the first time, provides a thorough theoretical proof of the asymptotic stability of two NAPC-based droop-free control schemes: ordinary NAPC (ONAPC) and amplifier-equipped NAPC (A-NAPC), by testifying that all effective eigenvalues have negative real parts. The effect of various system settings on the stability margins is further analyzed with respect to the average admittance of the electrical network, the sparseness of the communication network, and the average available capacity of controllable DERs. Based on the sensitivity of eigenvalues with respect to perturbations, a vulnerability analysis is conducted to identify the weaknesses in the microgrids. Case studies demonstrate that the available capacity of controllable DERs has the most decisive influence on the stability margin of NAPC-based droop-free control, while O-NAPC/ANAPC control scheme is more suitable for microgrids with DERs of larger/ smaller available capacities.

We investigate the intrinsic ambiguity in the definition of correlation functions arising from the inevitable invasiveness of quantum measurements. While algebraic correlations defined as expectation values of products of observables are widely used, their relationship to operational ones defined through actual measurement procedures remain unclear. We demonstrate that the differences among various definitions of correlation functions and those among their underlying (quasi-)joint probability distributions are bounded above by a quantitative measure of measurement invasiveness. We further obtain a lower bound on the discrepancy among operational and algebraic (quasi-)joint probability distributions, providing a new form of the uncertainty relation. In addition, we identify an equivalence condition under which operational and algebraic correlations coincide. As an application, we analyze the quantum violation of the Leggett-Garg inequality and clarify the structural origin of the equivalence among different approaches to observing the violation, including sequential projective measurements and weak-measurement. Our results provide an operational foundation for the commonly used algebraic concepts of quantum theory.

In this paper, we consider an age-structured mechanical model for tumor growth. This model takes into account the life-cycle of tumor cells by including an age variable. The underlying process for tumor growth is the same as classical tumor models, where growth is driven by pressure-limited cell proliferation, and cell movement away from regions of high pressure. The main contribution of this paper is establishing the convergence of solutions of the age-structured model to a limit satisfying a Hele-Shaw free boundary problem. This limiting problem describes the geometric motion of the tumor as it grows according to a nonlinear Darcy's law.

Gallium oxide is an ultra-wide bandgap semiconductor with excellent opto-electronic properties, making it a highly promising material for a wide range of applications and devices. In this article, we report how the optical, morphological, structural, and compositional properties of $β$-Ga$_2$O$_3$ thin films deposited by RF sputtering on silicon substrates are affected by thermal treatments. Ellipsometric spectra recorded at multiple angles of incidence from several samples subjected to thermal annealing in the range of 550-1000 $^\circ$C were analyzed to extract the optical functions using appropriate multilayer models. This analysis is complemented by compositional, structural, and morphological characterization techniques. A significant increase of the refractive index was found after annealing at 1000 $^\circ$C, accompanied by a stark improvement in the samples' crystalline structure, as confirmed by complementary structural and compositional characterization techniques.

We derive a hydrodynamics formulation for a modified Dirac equation with a nonlinear mass term that preserves the homogeneity of the original Dirac equation. The nonlinear Dirac equation admits a symmetric split into the left and right-handed spinor components. It is formulated using Clifford algebra tools. We prove global existence for a regularized equation.

Simulated phishing campaigns are widely deployed, yet the behavioral data they produce is endogenous: because training is triggered by clicking, the employees receiving intervention have already demonstrated susceptibility. This endogeneity, combined with the difficulty of separating genuine habit formation from stable individual differences, means standard analyses can mischaracterize program effectiveness. In this Research Note, we develop a generalizable analytic framework addressing both biases simultaneously. We utilize marginal structural models (MSMs) to correct for the endogenous, click-triggered assignment of training, while integrating correlated random effects (CRE) to disentangle true state dependence from stable employee heterogeneity. Applying the MSM+CRE estimator to logs from 17 campaigns delivered to university staff (192,840 observations) reveals that analyses ignoring stable differences overstate the causal persistence of clicking; most repeat clicking reflects who employees are, not the effect of recent failures. This persistence is context-dependent, amplifying when successive campaigns share persuasion cues. Teachable-moment features also matter: emotion framing and explicit reporting pitches can largely eliminate persistence, while annotated-email cues modestly exacerbate it. Finally, employees engaging with the education page exhibit greater persistence than those dismissing it, consistent with an emboldening mechanism. We contribute methodologically by integrating MSMs and CRE into a portable framework for analyzing standard simulation logs, and practically by identifying specific design levers so organizations can better sequence and evaluate their phishing programs.

The explosion of multimedia data in information-rich environments has intensified the challenges of personalized content discovery, positioning recommendation systems as an essential form of passive data management. Multimodal sequential recommendation, which leverages diverse item information such as text and images, has shown great promise in enriching item representations and deepening the understanding of user interests. However, most existing models rely on heuristic fusion strategies that fail to capture the dynamic and context-sensitive nature of user-modal interactions. In real-world scenarios, user preferences for modalities vary not only across individuals but also within the same user across different items or categories. Moreover, the synergistic effects between modalities-where combined signals trigger user interest in ways isolated modalities cannot-remain largely underexplored. To this end, we propose CAMMSR, a Category-guided Attentive Mixture of Experts model for Multimodal Sequential Recommendation. At its core, CAMMSR introduces a category-guided attentive mixture of experts (CAMoE) module, which learns specialized item representations from multiple perspectives and explicitly models inter-modal synergies. This component dynamically allocates modality weights guided by an auxiliary category prediction task, enabling adaptive fusion of multimodal signals. Additionally, we design a modality swap contrastive learning task to enhance cross-modal representation alignment through sequence-level augmentation. Extensive experiments on four public datasets demonstrate that CAMMSR consistently outperforms state-of-the-art baselines, validating its effectiveness in achieving adaptive, synergistic, and user-centric multimodal sequential recommendation.

Precise and high efficiency concentration of mid-infrared (mid-IR) light into sub wavelength volumes is essential for probing low-energy excitations and achieving strong field enhancements, which can be hindered by absorption losses and coupling inefficiencies at long wavelengths. Here, we introduce an innovative diamond-based metal-insulator-metal campanile probe that adiabatically compresses free-space mid infrared light (10 \mum) into \approx 1 \mum domains. Integrated into a scanning photovoltage microscope, the probe enables sub-wavelength mapping of locally driven photocurrents in graphene, resolving polarization dependent and contact-sensitive responses at energies down to \approx 0.1 eV. Experiments reveal a photocurrent signal density enhancement of 10^3 and coupling efficiencies approaching 80%, in agreement with numerical simulations. Operation of the probe with quantum cascade and free electron lasers demonstrates a robust, spectrally tunable platform for high-resolution exploration of low-energy carrier dynamics in atomically thin materials, opening opportunities for mid-IR optoelectronics and quantum photonics.

Integral-equation-based fast direct solvers for electromagnetic scattering can substantially reduce computational costs, especially in the presence of multiple excitations. We recently proposed a new high-frequency fast direct solver strategy that combines preconditioning techniques with acceleration algorithms. However, the validity of this approach applied to non-canonical geometries requires further justification. In this contribution, we collect relevant semiclassical microlocal results and use them to assess the legitimacy and effectiveness of the proposed fast direct solver in the high-frequency regime.

To characterize the community structure in network data, researchers have developed various block-type models, including the stochastic block model, the degree-corrected stochastic block model, the mixed membership block model, the degree-corrected mixed membership block model, and others. A critical step in applying these models effectively is determining the number of communities in the network. However, to the best of our knowledge, existing methods for estimating the number of network communities either rely on explicit model fitting or fail to simultaneously accommodate network sparsity and a diverging number of communities. In this paper, we propose a model-free spectral inference method based on eigengap ratios that addresses these challenges. The inference procedure is straightforward to compute, requires no parameter tuning, and can be applied to a wide range of block models without the need to estimate network distribution parameters. Furthermore, it is effective for both dense and sparse networks with a divergent number of communities. Technically, we show that the proposed spectral test statistic converges to a {function of the type-I Tracy-Widom distribution via the Airy kernel} under the null hypothesis, and that the test is asymptotically powerful under weak alternatives. Simulation studies on both dense and sparse networks demonstrate the efficacy of the proposed method. Three real-world examples are presented to illustrate the usefulness of the proposed test.

Coupled cell systems model interacting dynamical units and provide a natural framework for studying synchrony phenomena arising from collective behavior. Graph symmetries often induce such patterns, but certain networks exhibit additional synchronies not associated with automorphisms, commonly referred to as exotic synchronies. In undirected asymmetric graphs, any synchrony, if present, must be non-symmetry-induced, and determining when such exotic patterns occur remains a challenging structural problem. In this work, we address this question for networks whose underlying coupling graph is a tree, a class of graphs that naturally models hierarchical interactions among elements. We prove that exotic synchronizations do not arise in tree-type networks, showing that every balanced coloring is a fixed-point coloration determined by graph automorphisms. Furthermore, we identify the importance of the role played by the leaves of a graph in this context. Beyond existence results, we investigate the dynamical consequences of these structures by analyzing the linear stability of equilibria and the Lyapunov stability of synchrony subspaces for admissible vector fields defined on tree networks. Particular attention is devoted to cherry- type configurations, where local symmetries generated by leaves attached to a common vertex influence the stability properties of the associated synchronous states, thereby clarifying how the combinatorial architecture of trees constrains both the emergence and the stability of synchrony.

The core is a central concept in multi-winner social choice, ensuring that no coalition of voters can support an alternative outcome whose size or cost exceeds the group's share of the electorate. This idea originates from the Lindahl equilibrium in classical public goods theory. Yet Lindahl equilibria may fail to exist when voters have ordinal preferences over a finite set of outcomes and monetary transfers are not allowed. We introduce Lindahl Equilibrium with Ordinal Preferences (LEO), extending the equilibrium framework to discrete collective choice. Using LEO, we construct randomized outcomes that satisfy (approximate) core constraints for a probabilistic set of voters, while ensuring that each voter is represented with high probability. We also provide a deterministic approximate core guarantee with a factor of 6.24, improving on the previous bound of 32. In structured environments, these outcomes can be computed efficiently. Overall, our results extend classical equilibrium concepts, providing a normative foundation for proportional representation and practical algorithms for applications in voting and fair machine learning.

Renormalization group methods generate low-resolution Hamiltonians that are more diagonal and easier to solve. This chapter reviews the similarity renormalization group for nuclear Hamiltonians, which is a popular method for generating low-resolution nuclear forces. It presents the similarity renormalization group flow equations, analyzes how the similarity renormalization group drives the Hamiltonian towards the diagonal, and studies the effect of induced many-body interactions. It concludes by highlighting the progress in first-principles calculations of nuclei driven by low-resolution nuclear Hamiltonians.

Magic states, by allowing non-Clifford gates through gate teleportation, are important building blocks of fault-tolerant quantum computation. Magic state distillation protocols aim to create clean copies of magic states from many noisier copies. However, the prevailing protocols require substantial qubit overhead. We present a distillation protocol based on permutation-invariant gnu codes, as small as two qubits. The two-qubit protocol achieves a 0.5 error threshold and 1/2 distillation rate, surpassing prior schemes for comparable codes. Our protocol furthermore distils magic states with arbitrary magic by varying the position of the ideal input states on the Bloch sphere. We achieve this by departing from the usual magic state distillation formalism, allowing the use of non-Clifford gates in the distillation protocol, and allowing the form of the output state to differ from the input state. Our protocol is compatible for use in tandem with existing magic state distillation protocols to enhance their performance.

Understanding how social networks form, whether through reciprocity, shared attributes, or triadic closure, is central to computational social science. Exponential Random Graph Models (ERGMs) offer a principled framework for testing such formation theories, but translating qualitative social hypotheses into stable statistical specifications remains a significant barrier, requiring expertise in both network theory and model estimation. We present Forge (Formation-Oriented Reasoning with Guarded ERGMs), a framework that uses large language models to automate this translation. Given a network and an informal description of the social context, Forge proposes candidate formation mechanisms, validates them against feasibility and stability constraints, and iteratively refines specifications using goodness-of-fit diagnostics. Evaluation across twelve benchmark networks spanning schools, organizations, and online communication shows that Forge converges in 10 of 12 cases, and conditional on convergence it achieves the best likelihood-based fit in 9 of 10 while meeting adequacy thresholds. By combining LLM-based proposals with statistical guardrails, Forge reduces the manual effort required for ERGM specification.