Incoherent radio emission at meter--decimeter wavelengths provides a key diagnostic of the coronal thermal plasma, but at frequencies below $\sim$\,1\,GHz coronal refraction can substantially bend ray paths and modify the apparent source size and brightness distribution. We develop a forward-modeling framework that combines refractive ray tracing through a global 3D coronal model with radiative transfer along each ray. The method tracks the ray-tube cross-sectional area $S(s)$ using a step-wise perturbation retracing approach and incorporates a geometric magnification term proportional to $d\ln S/ds$ to enforce flux conservation under focusing/defocusing. Thermal free--free emission and absorption are then computed with the \texttt{GRFF} radiative transfer code to produce synthetic radio maps over 40--800\,MHz. Applying the framework to Carrington rotation 2298, we find that including propagation effects allows the quiet-Sun background spectrum to be well reproduced. However, active region brightness is less accurately modeled, suggesting that additional physical factors should be considered in future work. These results establish a physics-based method for generating low-frequency quiet-Sun synthetic images suitable for quantitative comparison with interferometric observations and for assessing how propagation effects shape the observed morphology.

Classically deformed nuclear geometries are commonly employed in standard descriptions of relativistic collisions between two even-even nuclei, despite the fact that their exact ground states are rotationally invariant $0^+$ states. In this paper, we formulate the collision geometry directly from the eikonal scattering matrix based on a nonorthogonal Generator Coordinate Method construction of rotationally invariant ground states. In the optical limit, using a localized transported-density approximation for the collision-channel one-body response, rotational overlap localization generates an effective one-body density associated with the scattering process. Within this approximation, using the Gaussian Overlap Approximation and its heat-kernel representation, we show that rotational symmetry restoration acts as a geometric low-pass filter which exponentially suppresses effective deformation modes. The classical rigid-rotor limit is recovered for large intrinsic angular momentum fluctuations. We establish a microscopic framework connecting rotational symmetry restoration, collective overlap localization, and the effective deformation geometries of nuclei in high energy collisions.

Collective intelligence emerges from local interactions among agents with limited information, yet how internal controller organization relates to emergent collective order remains unclear. Here, we study evolved swarms with shallow neural controllers under explicit sensory and actuation constraints and compare collective order with hidden-layer complexity and output nonlinearity across 3024 conditions. Under these constraints, the most ordered regimes exhibit two simultaneous and seemingly contrasting effects: hidden-layer complexity increases, while the effective output mapping becomes more linear. The diversity of recurrent collective behaviors varies nonmonotonically across the control parameters, with pattern richness shaped by parameter-specific tradeoffs rather than a single generic constraint optimum. Unevolved controls show that output linearization persists without adaptation, whereas the hidden-complexity relation depends on optimization. These two effects are respectively consistent with the law of requisite complexity and ecological rationality, suggesting that adaptive collective intelligence can arise through a partitioned controller organization in which representational complexity and action-level linearization coexist within the same system.

Two-arm phase II clinical trials often benefit from an interim analysis that allows early stopping for futility, but Bayesian calibration of such designs is usually based on computationally intensive Monte Carlo simulation. In this work, a simulation-free methodology is developed to obtain Bayesian optimal two-stage designs in two-arm phase II trials with binary endpoints using Bayes factors as the primary measure of evidence. Building on recent matrix-search methods for fixed-sample two-arm Bayes factor designs and earlier correction formulas for one-arm two-stage designs, the proposed approach derives exact expressions for the operating characteristics of a two-stage two-arm design with a single futility interim. Bayesian power and type-I error are obtained by correcting the corresponding fixed-sample quantities for trajectories that would have been removed by early stopping, yielding a fully numerical calibration procedure that avoids Monte Carlo error entirely. The resulting method searches over admissible interim and final sample sizes to identify the optimal design that satisfies target constraints on Bayesian power, type-I error, and the probability of compelling evidence in favour of the null hypothesis, while minimizing the expected sample size under the null hypothesis. The methodology is illustrated in realistic phase II settings, including a detailed re-analysis of the riociguat trial in systemic sclerosis. Overall, the approach extends simulation-free Bayes factor design methodology to the practically important setting of two-arm two-stage phase II trials and provides a transparent basis for Bayesian design calibration and sensitivity analysis.

This note combines a result of Bökstedt and Waldhausen concerning the so-called derivative map on tubes with the existence theorem for generating functions of tube type for nearby Lagrangian homotopy spheres due to Abouzaid, Courte, Guillermou and Kragh to obtain a restriction on the smooth structure of nearby Lagrangian homotopy spheres. Concretely, if a homotopy $n$-sphere $L$ admits a Lagrangian embedding in the cotangent bundle of some other homotopy $n$-sphere $M$, then the difference $[L]-[M]$ in $θ_n/bP_{n+1}$ is a multiple of the Hopf element $η\in π^1_s$. In particular it follows that $[L]-[M]$ is 2-torsion in $θ_n/bP_{n+1}$, hence if $n$ is even then $L\# L$ is diffeomorphic to $M \# M$. As another application, if a homotopy $8$-sphere $L$ admits a Lagrangian embedding in $T^*S^8$, then $L$ is diffeomorphic to $S^8$. The results presented in this note are subsumed by a joint work with Abouzaid, Courte and Kragh which treats the general case in which $M$ is an arbitrary smooth manifold. When $M$ is a homotopy sphere the situation is significantly simpler and the purpose of this note is to give a concise exposition of the main result in this special case.

We formulate a structure-informed multiple sequence alignment problem, denoted MSA-S. The model abstracts biological sequences as strings and structural information as designated position-pairs. It augments a fixed pairwise string score, defined by a fixed non-gap symbol-pair scoring rule and fixed affine gap penalties, with a binary overlap score on designated position-pairs, which can be interpreted as a contact-map overlap score in structural applications. This yields a fixed-score, integer-valued optimization model suitable for complexity-theoretic analysis. Under this formulation, we show that the decision problem MSA-S-DEC is NP-complete for a broad class of fixed pairwise string scoring schemes. We also show that NP-hardness persists even under the restriction that every designated position-pair set is nonempty and the pair-overlap threshold is strictly positive. For the associated scalarized optimization problem MSA-S-OPT(lambda) with any fixed rational constant lambda >= 1, we further show that, under the canonical unit scheme for the non-gap symbol-pair scoring rule, MSA-S-OPT(lambda) admits no polynomial-time approximation scheme (PTAS) even for two input strings (k = 2), unless P = NP. These results establish a formal complexity-theoretic baseline for structure-informed multiple sequence alignment.

For the Lindelöf Hypothesis concerning the Riemann zeta function $ζ(s)$, upper bounds as $\Im(s)\to\infty$ have been extensively studied for many years. In particular, the Lindelöf Hypothesis is one of the most important open problems in analytic number theory. It is also known to be equivalent to certain mean value estimates, which provide a fundamental connection between pointwise upper bounds and integral mean values of zeta-functions. In this paper, we consider an analogue of the Lindelöf Hypothesis for the Barnes multiple zeta function $ζ_r (s,a,(w_1,\dots,w_r)) = \sum_{m_1=0}^\infty \cdots \sum_{m_r=0}^\infty (a+m_1 w_1+\cdots+m_r w_r)^{-s} $, and establish equivalent conditions in terms of integral mean values. In particular, the situation depends essentially on the $\Q$-rank of $\langle w_1,\dots,w_r\rangle$, and it is especially interesting that phenomena peculiar to the Barnes multiple zeta function appear according to this rank.

We prove that the bilinear generating function for Wronskians of Hermite polynomials can be expressed as the classical Mehler kernel multiplied by a polynomial, thereby extending the result of Pupasov-Maksimov for exceptional Hermite polynomials. We establish several properties of the polynomials appearing in this extended version of the Mehler formula and present four conjectures about them.

We prove that stable degeneration, the canonical degeneration associated to the normalized volume minimizer of a Kawamata log terminal (klt) singularity, preserves non-degenerate reflexive differential forms. In particular, the stable degeneration of a symplectic singularity is again symplectic. Combining this with a deformation-theoretic rigidity result for symplectic degenerations, we confirm Kaledin's conjecture that the formal completion of any symplectic singularity is conical. As applications, we show that the natural base of any normalized nilpotent orbit closure is a K-semistable Fano variety, and that the normalized volume minimizer of a hypertoric singularity is induced by the standard dilation.

The nitrogen vacancy (NV) center has emerged as a powerful quantum sensor in high-pressure research, with the observation of optically detected magnetic resonance at megabar pressures. However, some aspects of NV physics require further investigation to optimize the development of NV-based sensing under pressure. Here, we study both experimentally and theoretically the optical properties of the NV center under hydrostatic pressure. We investigate the evolution of the zero-phonon line (ZPL) position, radiative lifetimes, optical lineshapes, and photoionization thresholds of the NV center under pressures up to ~120 GPa. We also provide spectroscopic guidelines for performing high-pressure optical experiments. Our results confirm that the NV center remains a robust quantum sensor under extreme hydrostatic pressures, especially for magnetic characterization.

We investigate the stability of discrete structures comprising of woven elastic beams in a plane, exposing a connection between admissible over / under patterns and the first-order and static rigidity of an associated tensegrity that is related through a natural polarity transformation. The relationship between the Airy and Whiteley stress functions for the tensegrity and weaving structures is explored. Our results lead to an efficient method for finding such an over / under pattern. The method is illustrated through a worked example modelled on the complete bipartite graph $K_{4,4}$.

We show that any three-ball with mean convex boundary contains an embedded free boundary minimal disk. Moreover, when the three-ball is a strictly convex domain with nonnegative Ricci curvature (for instance, a compact convex domain in Euclidean three-space), we prove the existence of at least three embedded free boundary minimal disks. Our approach is based on a multiplicity-one theorem for the free boundary Simon-Smith min-max theory.

Permuted-basement Macdonald polynomials $E_α^σ(\mathbf{x};q,t)$ are nonsymmetric generalizations of symmetric Macdonald polynomials that form a basis for the polynomial ring $\mathbb{Q}(q,t)[\mathbf{x}]$ for each fixed $σ$. There are combinatorial formulas for them as generating functions over composition-shaped non-attacking fillings. In this extended abstract, we bijectively prove identities for the relationship between $E_α^σ$, $E_α^{σs_i}$, $E_{s_iα}^σ$, and $E_{s_iα}^{σs_i}$. These identities correspond to two combinatorial operations on non-attacking fillings: (1) swapping adjacent entries in the basement, generalizing a result of Alexandersson (2019), and (2) swapping adjacent parts in the shape, which yields a straightening rule for expanding $E_α^σ$ in the polynomials $\{E_{s_iα}^τ\}_τ$.

We consider a fragment of Higher-Order Datalog with negation and argue that it generalizes the familiar and important fragment of Linear Datalog. We investigate the expressive power of this fragment, establishing a tight connection with the hierarchy of space complexity classes. In particular, we demonstrate that for all $k \ge 1$, the $(k+1)$-order fragment of Stratified Linear Higher-Order Datalog$^\neg$ captures $(k-1)$-EXPSPACE. This result suggests that restricting programs to linear recursion shifts the expressive power of the corresponding fragments from time to space, generalizing the classical result that (Stratified) Linear Datalog captures NL. Unlike the first-order setting where an ordering assumption is required to capture NL, our results hold without any such assumption on the input database. The proof relies on simulating space-bounded Turing machines using Stratified Linear Higher-Order Datalog$^\neg$ programs and providing a space-efficient evaluation of the query program. We argue that identifying such computationally well-behaved fragments is a crucial step towards paving the way for practical implementations of Higher-Order Datalog.

We provide a novel geometric regularization mechanism for black bounce spacetimes based on an effective gravitational tension screening inspired by Schwinger like saturation effects. The construction assumes that the gravitational tension associated with the vacuum geometry does not grow indefinitely in high curvature and short scales regimes, but dynamically approaches a finite critical value. As a result, the scale function acquires tension dependent corrections, giving rise to a regular bounce structure without introducing ad hoc regular cores. The mechanism generates regular geometries with spherical, planar, and hyperbolic transverse sections, describing regular black holes (RBHs), extremal RBHs, and traversable wormholes. A key result is that the bounce location emerges dynamically from the interplay between gravitational tension and geometric screening. Depending on the regime, the bounce may remain associated with short distance scales or be displaced toward larger finite scale regions, indicating that saturation effects can modify not only the inner structure of compact objects at short scales but also their global geometry. Hiperbolic and planar RBHs may satisfy the standard energy conditions near the bounce. Moreover, the hyperbolic geometry exhibits distinctive features, including regular negative mass configurations and a strong dependence of the energy conditions on the system parameters. In contrast, the matter sources supporting wormhole geometries, as expected, violate the energy conditions near the throat.

We ask whether dependency topology correlates with functional load-bearing organization as recoverable geometry -- not as a metaphor, but as a measurable structural property detectable by multilayer network analysis. Across seven independent substrates, we show that hub persistence and rank divergence under the Functional Proximity Law recover operational organization that domain experts describe as logic: axiomatic load-bearing structure in formal mathematics, control and contract structure in legacy software, conserved hub grammar across approx. 600 million years of neural evolution, catalytic role organization in a published prebiotic autocatalytic network, carry-path dominance in a 4-bit digital circuit, betweenness persistence in the ISCAS85 c432 standard benchmark (n=196), and a directional formal-systems replication in the Coq Corelib (n=17). A key methodological finding: degree-based hub persistence is weak between physical wiring and simulation state-correlation layers (r=0.21 in c432), while betweenness-based persistence is stronger (r=0.77 in the 4-bit ALU post-hoc; r=0.34 in c432). The ISCAS85 pre-registered primary hypothesis was CONFIRMED (degree r=0.426, p=0.002, Spearman r=0.551). The formal-systems claim is supported by two proof-assistant corpora: Lean 4 mathlib4 (CONFIRMED, r=0.777, p=0.004) and Coq Corelib (PARTIAL, direction confirmed, r=0.288, p=0.287, n=17, underpowered). All seven experiments were pre-registered before analysis.

Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature. Effective field theory (EFT) approaches enable the quantitative study of this emergence, providing a controlled framework to capture late-time observables. These lectures introduce the organizing principles behind equilibrium and out-of-equilibrium dynamics in these thermalizing systems. A central focus is the modern construction of these EFTs, which frames fluctuating hydrodynamics through the lens of "strong-to-weak" spontaneous symmetry breaking. Drawing examples from both high-energy and condensed matter physics, we show how this paradigm adapts to systems ranging from spin chains to relativistic quantum field theories, including models with generalized symmetries or symmetries with 't Hooft anomalies. Finally, we discuss UV/IR constraints on transport parameters -- viewed as the Wilson coefficients of hydrodynamic EFTs -- both in continuum and on the lattice.

Every knot $K \subset S^3$ that admits a symmetric union presentation bounds an immersed ribbon disk in $S^3$, while the converse is an open problem due to Christoph Lamm. The symmetric ribbon number $r_s(K)$ of $K$ is the minimum number of ribbon singularities in any symmetric ribbon disk bounded by $K$. In this paper, we undertake a systematic investigation of symmetric ribbon numbers of knots with at most 12 crossings. Along the way, we exhibit novel lower bounds for $r_s(K)$ arising from knot determinants, Alexander polynomials, Jones polynomials, and Kauffman polynomials.

An old conjecture of Burr and Erd\H os states that the Ramsey number of any $n$-vertex tree $T$ is at most $2n-2$. In 2012, Schelp asked whether a degree version of the Burr--Erdős conjecture holds. More precisely, Schelp asked if is it true that for any $\varepsilon>0$ and $Δ\ge 2$, if $G$ is a graph on $N\ge (2+\varepsilon)n$ vertices and minimum degree $δ(G)\ge \lfloor 3N/4\rfloor$, then every blue/red colouring of the edges of $G$ yields a monochromatic copy of each $n$-vertex tree with maximum degree at most $Δ$. We prove this conjecture in a strong form, showing that it is true even if one removes the extra $\varepsilon n$ term in the size of the host graph.

One of the most significant achievements of equilibrium logic was the characterization of strong equivalence, a property crucial for program transformation and optimization in Answer Set Programming (ASP). While ASP has recently been extended to a higher-order setting to enhance its expressive power, the lack of a comparable purely logical foundation has made verifying strong equivalence for higher-order programs or even proving the correctness of simple program transformations, a difficult challenge. This paper addresses this gap by developing a logical semantics for higher-order ASP by extending the equilibrium logic framework. Within this extended framework we demonstrate that every stratified higher-order logic program possesses a unique equilibrium model. Moreover, we establish definability results demonstrating that the syntax of our higher-order language is sufficiently expressive to capture its semantic domains. Finally, and most importantly, we generalize the classical theorem of strong equivalence to the higher-order setting: we prove that two programs are strongly equivalent if and only if they share the same higher-order models.

Modern command, control, communications, computers, cyber, intelligence, surveillance, and reconnaissance (C5ISR) environments place substantial attentional demands on mission commanders. Failures in attention allocation in these high-risk settings can have severe operational consequences. This study investigates the efficacy of gaze-driven, attention-guided adaptive decision support tools, including visual-only and multimodal designs, in a high-fidelity simulated military command center. To characterize gaze and attentional dynamics during interaction with these tools, recurrence quantification analysis was applied to eye-tracking data. Stepwise regression using the Bayesian information criterion was then used to identify recurrence-based gaze metrics associated with performance. Results showed that the multimodal adaptive decision support tool was associated with significantly higher performance than the visual-only attention-guided tool. Average diagonal line length showed a negative linear association with performance, whereas entropy showed a positive linear association. Recurrence rate, determinism, and entropy also showed nonlinear quadratic relationships with performance. In particular, recurrence rate and determinism followed an inverted-U pattern consistent with the Yerkes-Dodson law. These findings suggest that effective performance in dynamic C5ISR contexts depends on a balance between structured and flexible visual scanning, and that recurrence-based gaze metrics can help characterize attentional dynamics during interaction with adaptive decision support systems.

We establish a descent principle for $\otimes$-localizing subcategories along smooth presentations using a notion of descendability due to Balmer and Mathew. This allows us to classify $\otimes$-localizing subcategories of the derived category of complexes with quasi-coherent cohomology on suitable algebraic stacks in terms of subsets of its underlying topology.

Email archives offer a rare view of social relationships through repeated communication, but it remains unclear how well classical ego network layering applies to digital interaction data. This paper compares two public email archives with sharply contrasting structures: Enron, a workplace corpus involving around 150 users, and Jmail, a single-ego archive centered on an exceptionally active focal actor whose communication volume is more than twenty times higher than the average Enron user. We ask, in each case, whether Dunbar-like layered organization is recoverable from email communication frequency and how it should be interpreted. For Jmail, we show that extreme communication intensity causes standard layering methods (whether clustering-based or threshold-based) to break down. Jmail is not a broad communication environment with many occasional contacts, but a selective pool of high-interest alters operating on a much higher frequency scale than ordinary email. Once the Dunbar frequency ladder is anchored to the empirical support-clique boundary, a clearer layered structure emerges. Reciprocity analysis confirms that the recovered layers reflect genuine bidirectional relationships rather than artifacts of the focal actor's outgoing activity. Enron serves as a workplace benchmark that grounds the comparison: its ego networks partially reproduce Dunbar-like organization, with stable inner circles and an outermost recovered layer corresponding to Dunbar's affinity group ($\sim50$), confirming that layered structure is recoverable from ordinary organizational email. Overall, the findings show that Dunbar-like organization can be meaningfully studied in email archives, but that selective high-frequency archives require frequency normalization before the layered structure becomes interpretable.

According to recent observations, the topological surface states of Weyl semimetals may develop a superconducting gap, while bulk superconductivity remains absent. What drives the formation of this novel superconducting state is an open question. Here, we show that this phenomenon can arise from the interaction of Fermi arc electrons with both surface and bulk phonons in time-reversal-invariant Weyl semimetals. We identify two competing pairing channels, intra-arc and inter-arc, whose relative strength is governed by the efficiency of Coulomb screening at the surface. The combined effect of the Fermi arcs being disconnected and the weak screening of the Coulomb repulsion at the system's surface causes nodes to appear in the superconducting gap, as observed recently by photoelectron spectroscopy experiments on PtBi2. This suggests manipulation of the Coulomb screening, e.g. by a surface layer coating, as a pathway to engineer the critical temperature, as well as size and symmetry of the surface superconducting gap.

Microwave linear analog computers (MiLACs) offer a transformative paradigm for future multiple-input multiple-output (MIMO) systems by shifting complex signal processing into the analog domain, thereby significantly reducing computational complexity, radio-frequency chains, and analog-digital converters, while speeding up computation. However, the practical deployment of MiLACs is severely constrained by the inherent hardware losses of the tunable admittance components (TACs) interconnecting MiLAC ports, which introduce severe inter-stream interference and fundamentally limit the spectral efficiency (SE) of the system. In addition, while denser architectures offer greater spatial degrees of freedom to mitigate inter-stream interference, the cumulative hardware losses and power consumption of massive TACs severely degrade the system's energy efficiency (EE). Consequently, designing architectures for lossy MiLACs emerges as a critical yet unresolved challenge, as it necessitates striking a delicate tradeoff between interference suppression and cumulative hardware losses/power consumption. To address this challenge, this paper investigates the joint MiLAC architecture design and performance (SE/EE) maximization in lossy MiLAC-aided MIMO systems. We propose a novel learning-based joint architecture and performance optimization framework (LJAPOF) that unifies the design of MiLAC architectures and analog beamforming configurations for lossy MiLACs under both SE- and EE-oriented objectives. Numerical results demonstrate that by intelligently navigating the fundamental tradeoff between interference suppression and hardware/power consumption, the proposed LJAPOF can design optimal MiLAC architectures that consistently outperform stem-connected and fully-connected MiLACs in maximizing the system's SE and EE.

Packet networks are controlled dynamical systems with discontinuities, delayed observations, and partial state information. Adaptive or learning-driven proposers can improve performance, but an unsafe proposal may still cause starvation, tail-delay spikes, or unstable queue behaviour. This paper treats packet-network control as an executed-action certification problem. A certified operator sits between any proposer and the dataplane. At each control tick, the proposer emits an arbitrary candidate action $\tilde u(t)$. The operator either projects it to an executable action $u(t)$ that satisfies a configuration-compiled certificate, or reports INFEASIBLE and executes an always-defined fallback with quantified slack. The certificate also exports an auditable envelope $\bar z(t)$ for downstream composition. The guarantees are conditional and explicit. They apply on ticks where the operator reports CERTIFIED, the declared arrival envelope and backlog bound are valid, and the platform realises the assumed service lower bound. Under these conditions, one mechanism covers backlog caps, service floors, mitigation caps, Foster--Lyapunov drift constraints, and compositional envelope contracts. We prove operator-level safety, feed-forward compositional safety and stability using exported envelopes, and a cyclic closure result under a small-gain condition. We also define breach and infeasibility semantics, discuss calibration of the service-tracking factor that links certified targets to realised scheduler behaviour, and evaluate the design under delayed telemetry, delayed actuation, weak proposers, envelope mismatch, overload, and millisecond-scale certification. The present evaluation validates the certified execution boundary in a byte-level closed-loop backend; deployment-level scheduler tracking is left to future Linux or hardware experiments.

Large required courses in theoretical computer science face two related challenges: helping students engage with abstract material and supporting reliable student assessment at scale. This paper describes LogicLab, a lightweight computational toolkit developed for CS 245, Logic and Computation, at the University of Waterloo. The course is required for undergraduate computer science students and serves a large annual cohort. The main pedagogical objective is to help students concretize the ideas they encounter in lectures and assignments. Handwritten formulas and proof steps do not give students immediate correctness feedback. This can slow their development of confidence in formal reasoning and makes assessment harder to apply consistently at scale. LogicLab addresses this by allowing students to manipulate formulas, transformations, clauses, valuations, and proof steps as computational objects in Racket, building directly on their Scheme/Racket experience from the first-year curriculum. LogicLab provides tools for parsing and displaying formulas, applying equivalence transformations, converting to normal forms, simplifying formulas, working with valuations, applying resolution rules, running a Davis-Putnam style procedure, and verifying formal deduction steps. The system is lighter than a general proof assistant such as Coq or Lean and uses notation aligned with the course. It exposes composable functions students can invoke individually or use to program their own automations. The paper presents the design rationale, system organization, and planned course integration of LogicLab as a practical model for using computational tools to support engagement, conceptual concreteness, and more consistent assessment in large formalreasoning courses.

Let $m,l\in\N$ be relatively prime and let \[ Ω_{m/l}^{n+1}=\bigl\{(z,w)\in\C^n\times\C:\ \norm{z}^{m}<\abs{w}^{l}<1\bigr\} \] be the rational generalized Hartogs triangle of exponent $m/l$ in $\C^{n+1}$. In this paper, we study the Berezin transform $\BB_{m/l,n}$ associated with the Bergman kernel of $Ω_{m/l}^{n+1}$, and prove that $\BB_{m/l,n}$ is bounded on $L^p(Ω_{m/l}^{n+1})$ if and only if $p>m+nl$.

This paper investigates the conditions under which the Easterlin hypothesis holds within a neoclassical overlapping generations model with endogenous capital accumulation, wages, interest rates, and fertility. We develop a tractable analytical framework that maps economic transitions into utility space via a continuously differentiable first-order difference equation for cohort lifetime utilities. This reformulation allows for a transparent normative evaluation of non-steady-state paths without requiring explicit solutions to the underlying nonlinear system. Within this framework, we show that when fertility cycles emerge and children are normal goods, the utility of small cohorts strictly exceeds that of large cohorts. Crucially, this cohort-welfare asymmetry is driven by fertility preferences and is independent of the economy's position relative to the golden rule.

We propose a universal expression for the domain-wall width in generic multi-sublattice Heisenberg magnets, applicable to ferro-, antiferro-, and ferrimagnetic orders. The result follows from an exact connection between the domain-wall profile and the long-wavelength spin-wave dispersion, yielding a unified framework for describing magnetic textures across distinct ordering types. The predictions show excellent quantitative agreement with large-scale atomistic spin dynamics simulations over a broad range of exchange and anisotropy values and spin multi-sublattice structures, including three-dimensional rock-salt-type magnets and two-dimensional honeycomb and kagome ferromagnets. Moreover, we establish a general microscopic foundation for the temperature dependence of the domain-wall width. Our approach offers a powerful tool for understanding domain-wall profiles in complex spin systems.