We study the nontrivial topological dynamics inherent in the Minkowskian Higgs model with vacuum BPS monopoles quantized by Dirac. It comes to persistent collective solid rotations inside the physical BPS monopole vacuum, accompanied by never vanishing vacuum "electric" fields (vacuum monopoles) $\bf E$. The enumerated rotary effects inside the physical BPS monopole vacuum suffered the Dirac fundamental quantization are the specific display of the Josephson effect, whose nature will be reveal in the present study.

Localized topological defects inherently possess a multiscale character. While their microstructure configuration depends on the specific physical system, their topological features and mutual interactions can be described on the macroscale in terms of a particle representation. However, determining the physical properties associated with a given defect pattern often requires knowledge of the underlying microscopic structure. In this work, we extend a Wasserstein generative adversarial neural network by incorporating physical constraints and Fourier-space information to generate microscopic spin configurations consistent with prescribed macroscopic patterns and thermodynamic parameters. Using the two-dimensional XY model as a test case, where vortex-antivortex pairs act as long-range interacting defects, we show that the model generates spin configurations that accurately reproduce magnetization, susceptibility, helicity modulus, and spin-spin correlations over a wide range of temperatures below the Kosterlitz-Thouless transition. At the same time, deviations in the specific heat reveal limitations in reproducing higher order energy fluctuations. A complementary analysis based on topological data analysis uncovers subtle differences in global spin-correlation structures at near critical temperatures that are not apparent from conventional correlation functions alone. These results demonstrate both the promise and current limitations of generative approaches for multiscale studies of defect-dominated spin systems and at the same time highlight topological methods as valuable tools for characterizing critical behavior.

The reconstruction of physically valid transport fields from subject-specific imaging data is a fundamental challenge in image-based computational modeling due to measurement noise, modeling uncertainties and discretization errors. Without a methodology to construct models that faithfully reflect the underlying physics, mechanistic understanding of complex biological systems is inherently limited. In this work, we address this challenge in the glymphatic system, the brain's waste-clearance network, where cerebrospinal fluid (CSF) is transported through perivascular spaces into the brain parenchyma to facilitate metabolic waste removal. We introduce a computational framework for the high-fidelity reconstruction of subject-specific glymphatic transport fields from spatiotemporal imaging data. The formulation utilizes an advection-diffusion model with a velocity decomposition that imposes mass conservation, enabling the recovery of solenoidal (divergence-free) velocity fields through the solution of a constrained inverse problem. The system is discretized using immersed isogeometric analysis with quadratic B-spline basis functions, providing smooth, high-continuity solutions and inherent regularization of imaging noise. We demonstrate the framework's utility by using contrast-enhanced magnetic resonance imaging of tracer transport in a mouse brain, obtaining spatially varying estimates of CSF velocity, diffusivity, and clearance parameters. Forward simulations using the recovered fields show close agreement with experimental observations, validating the framework's ability to characterize complex transport dynamics while preserving physical integrity. This approach provides a generalizable methodology for the robust inference of physically consistent transport fields from imperfect imaging data, with broad applicability to the image-guided modeling of biological and engineering systems.

We study a fundamental instability mechanism in nonlinear, nonlocal dynamical systems arising from the interaction of long-range memory and stochastic regime switching. The dynamics are governed by network-coupled, operator-valued Volterra evolutions with completely monotone memory kernels whose excitation operators and kernel parameters are modulated by an ergodic finite-state continuous-time Markov chain. We formalize a sharp separation between annealed stability (in expectation) and quenched behaviour (along typical sample paths). On the annealed side, we identify an averaged memory gain that yields uniform moment bounds and a memory-adapted Lyapunov functional implying mean-square control under an averaged subcriticality condition. On the quenched side, we show that rare but persistent excursions into supercritical regimes are amplified by memory, producing intermittent macroscopic bursts with heavy-tailed statistics and a deterministic almost sure growth exponent obtained via a subadditive ergodic argument. This establishes an annealed--quenched dichotomy specific to non-Markovian switching systems, where stability in expectation can coexist with pathwise growth and metastable burst phases. We further derive a micro--macro correspondence by proving that a population of regime-modulated self-exciting point processes converges, both annealed and quenched, to the random-coefficient Volterra limit, transferring the burst mechanism from microscopic branching dynamics to macroscopic long-memory flows. Numerical experiments illustrate how burst localization depends on graph geometry and on noncommuting excitation operators.

We obtain Sion's minimax theorem in Hadamard spaces and discuss its applications. Among other things, we study several fundamental properties of resolvents of saddle functions in Hadamard spaces. An application to the proximal point algorithm for minimax problems in Hadamard spaces are also included.

The hyperon-nucleon interaction is investigated through the final-state interaction in the $K^-d\toπ^-Λp$ reaction. We focus on the $ΛN$-$ΣN$ coupled-channel interaction, which produces characteristic structures around the $ΣN$ thresholds in the $Λp$ invariant mass spectrum. The spin-triplet $ΣN\toΛp$ conversion amplitude is constructed within the $K$-matrix formalism using scattering lengths in the isospin basis. We first examine the dependence of the conversion amplitude on the $ΣN$ scattering lengths and find that the threshold structure is particularly sensitive to the sign of the real part of the $I=1/2$ scattering length. We then calculate the $Λp$ invariant mass spectrum of the $K^-d\toπ^-Λp$ reaction, including the contributions from the background diagrams. The resulting spectra show characteristic structures around the $ΣN$ thresholds, whose shapes depend on the choice of the interaction parameters. These results suggest that the $Λp$ invariant mass spectrum can serve as a useful observable for constraining the $ΛN$-$ΣN$ coupled-channel interaction.

Urban traffic management is essential for reducing congestion and supporting sustainable mobility. However, the task is becoming more challenging due to the growing penetration of electric vehicles and their charging demands. This paper presents a regional traffic coordination framework that combines route guidance and charging management to improve traffic network efficiency. Regional traffic dynamics are modeled by the macroscopic fundamental diagram, which allows for the analysis of congestion at the system level. The framework jointly optimizes routes and charging decisions, and it also uses demand management to regulate external inflows into the network. A case study on a 16-region urban network demonstrates the effectiveness of the proposed approach.

We investigate the quantum dynamics of a levitated nanoparticle in a structured light rotating saddle-like optical potential consisting of a superposition of Gaussian and Laguerre-Gauss modes with detuned frequencies. This rotating saddle trap offers unique opportunities for quantum experiments, such as reduced decoherence due to photon recoil and absorption, the possibility of large delocalization of the particle's center-of-mass motion, particle recovery protocols, the generation of motional entanglement and momentum squeezing. As an application, we show that this saddle-trap architecture enables force detection with sensitivity in the zepto-Newton regime.

We present the discovery of a second coherent radio burst from the thermally emitting neutron star 2XMM J104608.7$-$594306 in our follow-up observations with the Murriyang Ultra-Wideband Low receiver. This burst shows complex morphology with multiple components and wideband emission spanning from 704 to 4032MHz. We measured a steep spectral index of $α=-2.18\pm0.16$. Our polarimetric analysis demonstrates that the burst is highly polarised with a linear and circular polarisation fraction of 54% and 22%, respectively. We identified an orthogonal jump in the polarisation position angles of the burst, resembling those seen in radio pulsars. We compared this burst with the first radio burst detected from the source with MeerKAT. These two bursts detected in a total of 40 hours on source with MeerKAT and Murriyang, combined, show that 2XMM J104608.7$-$594306 can emit sporadic radio emission with luminosity jumps comparable to those seen in the bright bursts from SGR 1935+2154. This suggests that previously thought radio-quiet neutron stars such as X-ray dim isolated neutron stars and central compact objects could exhibit rare radio bursting activity.

We explore the crucial interplay between climate change and power system planning, highlighting the urgent need to systematically integrate climate information into energy system studies. Climate change impacts the energy sector on multiple fronts. Short-term weather variability drives daily and seasonal fluctuations in supply and demand. Long-term trends and increased frequency of extremes pose risks to infrastructure performance, asset lifetimes, and system adequacy. Representing compound events and spatial correlations across borders is a complex challenge, and uncertainties persist due to uncertainties from different models, scenarios, and downscaling methodologies. The Pan-European Climate Database (PECD4.2), developed in partnership between ENTSO-E and C3S, marks a change in how energy system planning is conducted. The PECD4.2 integrates historical reanalysis and six climate models across four SSP's, providing harmonised, openly available datasets tailored for power system studies. The physical conversion models for wind and solar energy better reflect technological progression than machine learning methods trained on historical data, improving robustness under changing future conditions. Despite these advances, challenges remain. Particularly in hydropower modelling and the lack of public harmonised energy datasets that are required to train these models. Complex processing chains from raw climate data to actionable insights and the lack of standardized integration of climate information lengthen lead times for energy-sector adoption. This leads to diverging approaches and variable consideration of climate risks. Closer, more generalised collaboration and communication between climate service providers and energy stakeholders are therefore necessary, as are the development of user-friendly tools for data manipulation and analysis and robust feedback loops.

Coating thermal noise in high-reflectivity test-mass mirrors is a major limitation for future gravitational-wave detectors, especially in the 10--300 Hz band. ET-Pathfinder therefore requires mirror coatings that combine very high reflectance at 1.55 micrometer with low thermal noise under cryogenic conditions. Conventional dielectric Bragg mirrors provide high reflectance but require thick coatings, whereas metasurface mirrors can reduce coating-related noise but are limited by fabrication tolerances and line-edge roughness. We present a hybrid metasurface--Bragg mirror concept tailored to ET-Pathfinder. The design combines a fabrication-tolerant one-layer metasurface, an anti-resonant Fabry--Perot spacer, and a reduced dielectric Bragg stack. Optical performance is evaluated using full-wave electromagnetic simulations, while fabrication robustness is assessed with a truncated-Gaussian Monte Carlo analysis. Line-edge roughness is included as a systematic edge-smoothing effect. The resulting reflectance distributions are used to determine the minimum Bragg-stack support required to meet system-level specifications. The ideal metasurface exceeds 99.999% reflectance. When fabrication uncertainties and line-edge roughness are included, the metasurface reflectance is limited to about 99.9% at the 95% yield level. The remaining transmission can be compensated by a supporting Bragg stack with as few as seven layer pairs. For this configuration, the hybrid mirror achieves a total thermal displacement noise about one order of magnitude below the projected ET-Pathfinder coating-noise budget. These results show that fabrication-limited metasurface reflectance can be compensated within a hybrid architecture, enabling reduced coating thickness and thermal noise for next-generation gravitational-wave detectors.

We provide an explicit description of the smallest filtered sub-isocrystal generated by the Hodge filtered piece of the crystalline cohomology for an abelian scheme over a $p$-adic ring. Our method is based on the theory of arithmetic jet spaces and delta characters associated to the abelian scheme, introduced by Buium and later studied by Borger and Saha using a functor of points approach. In particular, we prove that the delta isocrystal constructed by Borger and Saha is indeed isomorphic to the fundamental smallest sub-isocrystal of the crystalline cohomology in the category of filtered $F$-isocrystals. As an application, we establish a comparison isomorphism between the delta isocrystal and the crystalline cohomology of abelian schemes, which is governed by the group of order $1$ delta characters of the abelian scheme.

The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the remarkable role to change the topological structure from one system to another system.

We study decentralized optimization over networks where agents cooperatively minimize a smooth (strongly) convex sum of local losses while communicating only with immediate neighbors. Prevailing decentralized methods require either centralized knowledge of global problem and network parameters for stepsize tuning--hence impractical, or costly per-iteration line-searches that demand access to local function values. We propose line-search-free, fully decentralized algorithms in which each agent adapts its stepsize using only past local iterates and gradients--with no extra function evaluations and no global tuning. The key technical ingredient is a new Lyapunov function, from which a natural adaptive stepsize rule emerges: at each iteration, each agent selects the largest stepsize that guarantees descent, based solely on a local curvature estimate built from successive gradients. The proposed algorithms enjoy strong theoretical guarantees: sublinear convergence rates for merely convex objectives and linear rates under strong convexity. Numerical experiments on standard benchmarks show consistent improvements over the state of the art, both adaptive and non-adaptive.

We present a near-linear-time algorithm that, given a bridgeless cubic graph, finds a perfect matching intersecting every 3-edge-cut in exactly one edge. This improves over a cubic algorithm of Boyd et al. for the same problem, and over our previous algorithm, which worked only for 3-edge-connected graphs. The main ingredient is a cactus representation of the 2-edge-cuts, together with an efficient update procedure under 2-cut reductions.

This paper develops bootstrap procedures for inference in linear regression models with two-way clustered data. We characterize the estimator's asymptotic behavior in five mutually exclusive and exhaustive regimes: three Gaussian and two non-Gaussian. We establish four impossibility results: heterogeneous score components preclude uniform consistency; uniform consistency also fails in one non-Gaussian (infeasible) regime; the infeasible regime is not uniformly distinguishable from a feasible one; and uniform validity over all feasible regimes rules out uniform conservativeness over the infeasible regime. To address the feasible regimes, we propose a data-driven regime classifier and a projection-based wild bootstrap procedure. The procedure delivers uniformly valid inference across the four feasible regimes while allowing serial dependence along the second clustering dimension and spatial dependence along the first. This combination of regime adaptivity and flexible dependence is new to the two-way clustering literature. Monte Carlo simulations confirm the accuracy and flexibility of the proposed methods in settings with complex clustering structures.

We develop a toric topological framework for studying the cohomology of Vietoris--Rips complexes $VR(Q_n;r)$ of hypercube graphs. Using total domination invariants and spectral methods, we establish general lower bounds on connectivity, which leads to infinite families of counterexamples to Shukla's conjecture, and derive first global upper bounds on coconnectivity. Our approach interprets Vietoris--Rips complexes via Stanley--Reisner rings, moment-angle complexes, and Tor algebras, allowing global topological information to be extracted from combinatorial data. In a second direction, we construct explicit cohomology classes using the Koszul resolution and show that they decomposable products of $1$-dimensional classes, and that their representatives can be combimbinatorially realised as the boundary of cross polytopes positively answering the question posed by Adams and Virk. We introduce ghost vertices as a new tool for detecting, extending, and proving linear independence of cohomology classes.

TrueEBSD is an open-source MATLAB program for image alignment and spatial distortion correction of images and electron backscatter diffraction (EBSD) maps. We have re-implemented TrueEBSD as an add-on to MTEX, an established toolbox for EBSD data analysis. Spatial alignment enables correlative analysis methods, such as augmenting EBSD orientation maps with data from other imaging modes. The augmented EBSD maps can then be analysed further using MTEX. We demonstrate TrueEBSD on two example case studies: one for measuring Co phase fraction and WC contiguity in a WC-Co composite, and another for determining the relative susceptibility of grain boundaries to void formation in a copper polycrystal. In both examples, the EBSD map was augmented with scanning electron microscopy (SEM) image data. This enabled quantitative crystallographic measurements which would not be possible from analysing the EBSD maps and images separately.

An improvement of a {\em Global (strong) Gagliardo-Nienberg inequality with a BMO term} is established by replacing local derivatives by {\em and fractional Laplacians.} Local versions are also given.

The surface characterization of rocky exoplanets via emission spectroscopy represents a frontier of current (JWST) and future (HWO) observational efforts. Here, we implement new features in the open-source retrieval code $\texttt{POSEIDON (v1.4)}$ to fully account for an emitting and reflecting planetary surface and an overlying absorbing and scattering atmosphere. We show that realistic rocky surfaces (with wavelength-dependent albedos derived from laboratory measurements) affect emission spectra by imparting mid-infrared diagnostic absorption features, imprinting pseudo-features due to atmospheric transparency windows, and flipping absorption features to emission via surface-atmosphere interface pseudo-temperature inversions. We demonstrate that current JWST spectral data can distinguish between tenuous (low surface pressure, $\leq$ 1 bar) and thick (high surface pressures, $\geq$ 0.1 bar) atmospheres by performing atmosphere + surface retrievals on published JWST emission data of the rocky worlds TOI-1685b and 55 Cancri e. We then explore JWST MIRI LRS's capability to constrain surface geology of rocky worlds, finding that with sufficient SNR retrievals can distinguish between granite-like and basaltic surfaces for synthetic datasets. Finally, we provide an open-source database of lab-derived surface albedos (in the form of directional-hemispherical reflectances), organized by geologic classification and include supplemental tables developed to foster future collaboration between geology and exoplanet science. Our atmosphere + surface retrieval technique provides a pathway to probe geologic processes on rocky exoplanets, showing that upcoming JWST data for terrestrial worlds will enable a deeper exploration of rocky surfaces beyond our Solar System.

We prove an analogue of Morley's categoricity theorem where cardinality is replaced by the recursion-theoretic notion of arithmetic degree. We say that a complete arithmetically definable theory $T$ is $D$-categorical if any two arithmetically extendible models of $T$ of arithmetic degree $D$, considered over a common elementary submodel with arithmetical elementary diagram, are isomorphic over that submodel by an isomorphism which preserves the complexity of sets of degree $D$. Here an arithmetically extendible model means an elementary substructure of a model whose elementary diagram is arithmetical. Our main result is: If $T$ is $D_1$-categorical for some nonzero arithmetic degree $D_1$, then $T$ is $D_2$-categorical for every nonzero arithmetic degree $D_2$. We also show that, assuming ZFC, $D$-categoricity for some nonzero arithmetic degree is equivalent to uncountable categoricity.

Let $d(n)$ denote the number of divisors of a positive integer $n$. A classical problem in analytic number theory is given by the asymptotic behavior of the divisor sum $\sum_{n \leq x} \frac{1}{d(n)}$, with Ramanujan having introduced an asymptotic formula for this sum with an explicit evaluation for the constant $A_1$ for the leading term $A_1 \frac{x}{\sqrt{\log x}}$. Gabdullin et al. recently considered a hybrid of this problem and the Titchmarsh divisor problem concerning $\sum_{p\leq x} d(p-1)$, proving that $$\sum_{p\leq x} \frac{1}{d(p-1)} \asymp \frac{x}{(\log x)^{3/2}}.$$ This result, together with Erdős's asymptotic formula $\sum_{n \leq x} d(d(n)) \sim c \, x \log \log x $ for a constant $c \in (0, \infty)$, lead us to consider the hybrid $\sum_{n \leq x} \frac{1}{d(d(n))}$ of the Erdős and Ramanujan divisor sums. The presence of the reciprocal significantly complicates the analysis, as it amplifies the contribution of integers for which $d(d(n))$ is exceptionally small. In this paper, we prove that $$\sum_{n \leq x} \frac{1}{d(d(n))} \asymp \frac{x}{ \log \log x}, $$ through a combined application of Golomb's estimate for powerful numbers and Turán's quantitative form of the Hardy-Ramanujan theorem.

We establish the first general regularity result for constrained optimal control problems arising naturally in mathematical physics and mathematical biology. Namely, we prove that for a large class of problems of the form ``maximise $\int ψ(Θ_m)-c\int m$ where $-ΔΘ_m=mΘ_m+B(x,Θ_m)$, under the constraint $0\leq m\leq 1$ a.e.", the solution $m^*$ is bang-bang, in the sense that $m^*=χ_{E^*}$, and that $\partial E^*$ is smooth up to a $(d-2)$-dimensional subset. Moreover, we prove that the solutions to the volume constrained problem ``maximise $\int ψ(Θ_m)$ where $-ΔΘ_m=mΘ_m+B(x,Θ_m)$, under the constraint $0\leq m\leq 1$ a.e and $\int m=m_0$" are bang-bang in the sense that $m^*=χ_{E^*}$ and that, in the two-dimensional case, $\partial E^*$ is a finite union of smooth curves. This is done via reduction to an unstable free boundary problem, the regularity analysis of which was pioneered by Monneau \& Weiss and Chanillo, Kenig \& To. In our case, the free boundary is not minimising, and the laplacian of the state function is sign-changing, which creates significant difficulties, in particular regarding the non-degeneracy of blow-ups. This requires a new approach blending tools from optimal control theory, free boundary and measure theory to establish the regularity of the free boundary.

The foundation for modeling the coupling of the internal structure of compact objects in binary systems to their dynamics and emitted gravitational waves is a systematic effective field theory (EFT) framework, where each compact object is replaced by a worldline endowed with a set of internal degrees of freedom. These degrees of freedom encode finite-size effects and thereby distinguish between different classes of compact objects. Among finite-size effects, tidal interactions play a central role, as they are associated to various kinds of deformations of a body under the influence of external tidal fields. In this work, we analyze the dynamical tidal response of Kerr black holes to generic-spin perturbations, focusing primarily on the scalar and gravitational cases, and working to linear order in frequency. We establish an EFT description of the perturbed black hole that accounts for the couplings between the spin, gravitoelectric and -magnetic tidal fields. We match this to wave-like solutions to the full black hole perturbation equations in order to determine the tidal response coefficients. In particular, we obtain the dynamical Love number, which appears at linear order in frequency for spinning black holes, and derive an approximate expression for the dynamical tidal response, including both dissipative and conservative pieces. We also examine several technical subtleties that arise in the matching procedure, with special emphasis on the mixing of multipolar modes induced by the spin of the compact object, which proves to be essential for a consistent treatment.

This study investigates the properties and stability of the Multiplicative Kantian Equilibrium (MKE) in symmetric games. We first demonstrate that MKE lacks strategic equivalence: the Kantian best-response function is not invariant under monotonic strategy rescaling. This strategic non-equivalence implies that the choice of measurement scale - a subjective interpretation of the game - materially impacts equilibrium outcomes. Exploiting this non-equivalence, in a game where players may be Kantian or Nasher, we propose an efficient strategy rescaling that allows Kantians to neutralize the free-rider advantage of Nashers, while preserving Pareto-efficient outcomes among themselves. In a dynamic framework, we show that the subgame-perfect Nash equilibrium with endogenous choice of optimization type leads all players to prefer Kantian optimization over Nash optimization. In an evolutionary setup, we show that Kantian optimization is an evolutionarily stable strategy (ESS). Our results suggest that the inherent strategic non-equivalence of Kantian optimization provides a robust pathway to stable cooperation.

Distributed blackbox consensus optimization is a fundamental problem in multi-agent systems, where agents must improve a global objective using only local objective queries and limited neighbor communication. Existing methods largely rely on handcrafted update rules and static cooperation patterns, which often struggle to balance local adaptation, global coordination, and communication efficiency in heterogeneous nonconvex environments. In this paper, we take an initial step toward trajectory-driven self-design for distributed black-box consensus optimization. We first redesign the agent-level swarm dynamics with an adaptive internal mechanism tailored to decentralized consensus settings, improving the balance between exploration, convergence, and local escape. Built on top of this adaptive execution layer, we propose Learning to Act and Cooperate (LACMAS), a trajectorydriven framework in which large language models provide sparse highlevel guidance for shaping both agentinternal action behaviors and agentexternal cooperation patterns from historical optimization trajectories. We further introduce a phased cognitive scheduling strategy to activate different forms of adaptation in a resource-aware manner. Experiments on standard distributed black-box benchmarks and real-world distributed tasks show that LAC-MAS consistently improves solution quality, convergence efficiency, and communication efficiency over strong baselines, suggesting a practical route from handcrafted distributed coordination toward self-designing multi-agent optimization systems.

This paper is concerned with portfolio selection for an investor with exponential, power, and logarithmic utility in multi-asset financial markets allowing jumps. We investigate the classical Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate Volterra--Heston model with jumps driven by an independent Poisson random measure. Owing to the non-Markovian and non-semimartingale nature of the model, classical stochastic control techniques are not directly applicable. Instead, the problem is tackled using the martingale optimality principle by constructing a family of supermartingale processes characterized via solutions to an original Riccati backward stochastic differential equation with jumps (Riccati BSDEJ).The resulting optimal strategies for Merton's problems are derived in semi-closed form depending on the solutions to time-dependent multivariate Riccati-Volterra equations, while the optimal value is expressed using the solution to this original Riccati BSDEJ. Numerical experiments on a two-dimensional rough Heston model illustrate the impact of both path roughness and jumps components on the value function and optimal strategies in the Merton problem.

A kinematic analysis of the young stellar association TWHya has been performed. The components of the displacement matrix in the Ogorodnikov-Milne linear model have been estimated both graphically and by solving the basic kinematic equations. The association's volume expansion with a coefficient of $K_{xyz}=103\pm9$ km s$^{-1}$ kpc$^{-1}$ was confirmed, which yields a dynamical age estimate of $t=9.7 \pm0.8$ Myr. Using the graphical method, estimates of the association's proper rigid-body rotation parameters $ω$ around the galactic axes x and y have been obtained for the first time, with velocity values in the range of 50-70 km s$^{-1}$ kpc$^{-1}$ and errors in their determination of 14-19 km s$^{-1}$ kpc$^{-1}$. However, these values are not confirmed by another method. For example, when solving kinematic equations only using proper motions, all three components of rigid body rotation do not differ significantly from zero, $(ω_x,ω_y,ω_z)=(4,7,11)\pm(5,5,5)$ km s$^{-1}$ kpc$^{-1}$.

Recent megakernel designs for Mixture-of-Experts (MoE) inference fuse expert computation with fine-grained, GPU-initiated communication into a single persistent GPU kernel, and outperform collective-based MoE on a single node by overlapping data transfer with compute at tile granularity. This benefit does not carry over cleanly to multi-node inference, where experts span many nodes connected by an RDMA fabric. Communication-bound MoE models regress by up to $10\times$ on 8 nodes, and the regression worsens with node count. We trace this regression to hidden serialization in proxy-based RDMA transports. The ordering requirement between each tile transfer and its completion signal forces a fence that drains the NIC pipeline, and its cost grows with the number of concurrent transfers. As a result, models whose per-expert compute is too small to absorb this inflated network latency expose communication on the critical path. We present \emph{Perseus}, which eliminates this serialization through two techniques. \emph{Decoupled signaling} batches fences at per-destination granularity, reducing fence count by $8\times$. \emph{NIC-side ordering} replaces proxy stalls with hardware fence flags, so the proxy never blocks. On proxy-based transports, Perseus achieves up to 10.3$\times$ end-to-end speedup. Perseus on IBRC matches or exceeds IBGDA GPU-direct by up to 1.2$\times$, which shows that serialization, rather than the choice between proxy-based and GPU-direct transport, is what bounds multi-node megakernel performance.

The color structure of two-loop gluon amplitudes is examined both from a color trace basis expansion and an alternative based upon structure constants. We use use this as a vehicle for systemising relations between the partial amplitudes of the color trace formalism.