The widespread bra-ket formalism offers valuable tools for conducting representation-free considerations in quantum theory. However, it is not without its drawbacks. In this work, we discuss these drawbacks in detail and subsequently construct a new representation-free scheme. Similar to the bra-ket formalism, the present scheme provides essential means to facilitate representation-free considerations. At the same time, it is entirely free from the drawbacks of the bra-ket formalism. Unlike the dual-space bra-ket formalism, the present scheme allows both one-space and dual-space interpretations, which is a beneficial feature. The constructed universal scheme is very well-suited for performing representation-free practical calculations.

In simulations of colloidal matter, frictional contacts between particles are often neglected. For spherical colloids, such an approximation can be problematic, since frictional contacts couple translational and rotational degrees of freedom, which may affect the collective behavior of, e.g., colloids under shear and chiral active matter. Deterministic models for frictional contacts have been proposed in the granular matter community. On the colloidal scale, however, thermal fluctuations are important and should be included in a thermodynamically consistent manner. Here, we derive the correct fluctuation-dissipation relation for linear and nonlinear instantaneous frictional contact interactions. Among other, this generates a new generalized class of dissipative particle dynamics (DPD) thermostats with rotation-translation coupling. We demonstrate effects of frictional contact interactions using the examples of Poiseuille flow and motility induced phase separation in active Langevin particles.

This paper introduces specular differentiation, which generalizes Gâteaux and Fréchet differentiation in normed vector spaces. We investigate its fundamental theoretical properties and establish weak forms of the Mean Value Theorem and Fermat's Theorem in the specular sense. Finally, we identify a distinguished element of the Fréchet subdifferential of a convex function through specular differentiation.

Large regions of giant planets are thought to possess unstable thermal gradients stabilised by gradients in heavy-element composition. The fluid can then develop semi-convection, a double-diffusive instability driven by the unequal molecular diffusivities of heat and composition. While previous studies have focus mainly on local Cartesian models, we investigate semi-convection in rotating spherical shells, the geometry relevant to planetary interiors, using direct numerical simulations In a first nonlinear phase, the flow spontaneously forms concentric density staircases composed of well-mixed layers separated by thin, strongly stratified interfaces. We propose scalings for both the thickness of these layers and their survival time in terms of the rotation rate and stratification. Over longer timescales, layers merge to produce statistically steady states consisting either of a fully convective shell or of a convective layer ovelain by a persistent stably stratified layer (SSL), depending on the balance between stratification and rotational constraint. This shows that a layer subject to a semi-convection instability can self-organise into a convective layer and a SSL. These layers can generate a self-sustained magnetic field. Our dynamo simulations show that magnetic fields generated within the turbulent convective region are filtered by zonal flows in the overlying SSL, resulting in strongly a dipolar and axisymmetric external field, in encouraging agreement with Saturn's magnetic field. Across the explored parameter range, both the Rossby number and the thickness of the stably stratified layer are governed by a single combination of control parameters. This enable identification of a regime favourable to planetary-like dynamos.

We study equivariant perfect matchings on the Boolean hypercube $\B^6$ under the Klein four-group $K_4 = \langle \comp, \rev \rangle$ generated by bitwise complement and reversal. Among matchings using only $\comp$ or $\rev$ pairings, there is a unique Hamming-cost minimizer, given by a simple ``reverse-priority rule'': pair each element with its reversal unless it is a palindrome, in which case pair it with its complement. This matching has total Hamming cost 120, compared to 192 for the complement-only matching. The historically significant King Wen sequence of the I Ching realizes precisely this matching. Pure Hamming minimization over the full $K_4$ action is different: allowing $\comp \circ \rev$ lowers the cost to 96. The King Wen rule is recovered, however, as the unique Hamming-weight-preserving optimum: it minimizes failures of Hamming-weight preservation before Hamming distance, and it is stable for the weighted energy $α|Δw|+βd_H$ throughout the open region $α>β$. The finite orbit counts and case distinctions are checked in Lean~4.

There is a method for constructing from first principles, a holographic bulk dual action in Euclidean $AdS_{d+1}$ space for a $d$-dimensional Euclidean CFT on the boundary, starting from the Polchinski's Exact Renormalization Group (ERG) equation that describes the RG evolution of the interaction part of the boundary Wilson action. The bulk action in $AdS_{d+1}$ has an $SO(1,d+1)$ symmetry and is obtained from the evolution operator of the Polchinski's ERG equation by a map that involves a field redefinition and requires a $\textit{special}$ form of the UV cutoff function in the ERG equation. In this paper, we show that for $\textit{any form}$ of the cutoff function, the ERG evolution operator has an $SO(1,d+1)$ symmetry. The generators of the special conformal transformation depend on the cutoff function. For the special cutoff function that maps to $AdS$ space, the transformations have the standard form of $AdS$ isometry. We also show that the ERG evolution operator for the $\textit{full}$ Wilson action can be put in the same form as the Polchinski's ERG equation by a field redefinition and consequently also has an $SO(1,d+1)$ symmetry for any cutoff function.

We consider again a classical theorem relating capacities and algebraic integers and the question of the simultaneous approximation of $ n-1$ different complex numbers by conjugate algebraic integers of degree $n$.

Type Ia supernovae, type II supernovae, and asymptotic giant branch (AGB) stars are important sites of stellar nucleosynthesis, but they differ greatly in their rates, their location within a galaxy, and the mean thermal energy and abundance distribution of their ejecta. In earlier papers in this series we have shown that a significant fraction of metals newly synthesized by type II supernovae are promptly lost to galactic winds -- i.e., galactic winds are metal loaded. Here we investigate whether the elements returned by type Ia supernovae and AGB stars are similarly metal loaded, or whether metal loading varies significantly with nucleosynthetic site. We use a series of high-resolution ``tall box'' simulations of the interstellar medium with the \quokka~GPU-accelerated code, within which we systematically vary the galaxy gas surface density, metallicity, and the scale heights and relative rates of the different nucleosynthetic sources. We show that the metal loadings of galactic winds differ substantially between metals produced by different sources, with typical variations at the level of $\approx 0.3$ dex, a phenomenon we term differential metal loading. Which set of metals suffers preferential loss from this phenomenon varies depending on the galactic environment, and is not easily predictable \textit{a priori}. Our findings call into question the the interpretation of diagnostics of galaxy formation, for example star formation timescales and initial mass functions, based on abundance diagnostics, since the abundance variations upon which these techniques rely are often at levels comparable to those we show can be induced by differential metal loading.

Wisdom-Holman (WH) integrators are symplectic operator-splitting methods widely used for long-term N-body simulations of planetary systems. Most implementations use either Jacobi coordinates or democratic heliocentric coordinates (DHC) for the Hamiltonian splitting, resulting in slightly different algorithms. In this paper we report results from numerical experiments, which show that integrations of the Solar System using DHC coordinates with typical timesteps of a few days suppress instabilities of the planet Mercury. We further show that this is due to an eccentricity dependent artificial numerical precession introduced by the DHC splitting. While the DHC splitting converges to the correct results at shorter timesteps of ~0.6 days, we argue that Jacobi coordinates remain reliable to significantly longer timesteps when orbits become moderately eccentric, and are thus a better choice when the innermost planet can reach high eccentricities.

A search is performed for lepton-number-violating $B^-\to D^{(*)+}μ^-μ^-$ decays, using data collected by the LHCb experiment in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb$^{-1}$. No significant signal is observed, and upper limits are set on the branching fractions, ${\cal B}(B^-\to D^{+}μ^-μ^-) < 4.6 \times 10^{-8}$ and ${\cal B}(B^-\to D^{*+}μ^-μ^-) < 5.9 \times 10^{-8}$, at the 95% confidence level.

Entropy production quantifies the amount of irreversibility of a physical process, leading to fundamental bounds for thermodynamic quantities. It captures the inability to run a physical system forward and then backward, bringing it to the same initial state. Considerable research has been carried out in the last decades to extend entropy production to non-equilibrium quantum processes. We experimentally investigate the entropy production of such forward-backward cycles affected by genuinely quantum irreversibility. Namely, we consider processes realized to erase different types of correlations between two interacting systems, from obliterating solely quantum coherence to completely decorrelating local states. This makes the measurement of entropy production experimentally challenging. Addressing this challenge is the purpose of this paper.

Open-source software (OSS) is a critical component of modern software systems, yet supply chain security remains challenging in practice due to unavailable or obfuscated source code. Consequently, security teams often rely on runtime observations collected from sandboxed executions to investigate suspicious third-party components. We present HeteroGAT-Rank, an industry-oriented runtime behavior mining system that supports analyst-in-the-loop supply chain threat investigation. The system models execution-time behaviors of OSS packages as lightweight heterogeneous graphs and applies attention-based graph learning to rank behavioral patterns that are most relevant for security analysis. Rather than aiming for fully automated detection, HeteroGAT-Rank surfaces actionable runtime signals - such as file, network, and command activities - to guide manual investigation and threat hunting. To operate at ecosystem scale, the system decouples offline behavior mining from online analysis and integrates parallel graph construction for efficient processing across multiple ecosystems. An evaluation on a large-scale OSS execution dataset shows that HeteroGAT-Rank effectively highlights meaningful and interpretable behavioral indicators aligned with real-world vulnerability and attack trends, supporting practical security workflows under realistic operational constraints.

A polytope is called indecomposable if it cannot be expressed nontrivially as a Minkowski sum of other polytopes. Since Gale introduced the concept in 1954, several increasingly strong criteria have been developed to characterize indecomposability. In this paper, we introduce a new approach to indecomposability for frameworks and polytopes based on the graph of implicit edge dependencies, which records proportionalities between edge lengths across all deformations. This yields a new indecomposability criterion that unifies and generalizes most previous approaches, and has additional consequences in the study of deformation cones. As a main application, we construct new indecomposable deformed permutahedra that are not matroid polytopes. In 1970, Edmonds already noted the difficulty of characterizing the extreme rays of the submodular cone, equivalently, indecomposable deformed permutahedra. Matroid polytopes of connected matroids form a well-known family of such examples. We exhibit a new infinite family of indecomposable deformations of the permutahedron, not arising from matroid polytopes, obtained by suitable truncations of certain graphical zonotopes. We further demonstrate the scope of our methods through several additional applications. In particular, we refute a conjecture of Smilansky (1987) on the relation between the numbers of vertices and facets of indecomposable polytopes. Moreover, we obtain new bounds on the dimensions of deformation cones and we construct and analyze uniquely decomposable polytopes.

Existing theoretical analyses on Faraday instability in Hele-Shaw cells typically adopt gap-averaged governing equations and rely on Hamraoui's model coming from molecular kinetics theory, thereby oversimplifying essential transverse information, such as contact line velocity and capillary hysteresis, and conflicting with the unsteady meniscus dynamics. In this paper, a gap-resolved approach is developed by directly modeling the transverse gap flow and the contact angle dynamics, which overcomes the aforementioned limitations, ultimately yielding a modified damping with respect to the static contact angle and hysteresis range. A novel amplitude equation for linear Faraday instability is derived that combines this damping and the gap-averaged counterpart based on the oscillatory Stokes boundary layer, with the viscous dissipation preserved. By means of Lyapunov's first method, an explicit analytical expression for the critical stability boundary is established. Two series of laboratory experiments are performed that focus, respectively, on evolutions of the lateral meniscus and the longitudinal free surface near the Faraday onset, from which key parameters relevant to the theory are precisely measured. Based on the experimental data, the validity of the proposed mathematical model for addressing the Faraday instability problem in Hele-Shaw cells is confirmed, and the generation and development mechanisms of the onset are clarified. In the asymptotic analysis, the inclusion of contact angle dynamics increases the overall damping and thus partially compensates for the frequency detuning introduced by oscillatory Stokes flow approximation.

Photon detection is a cornerstone of quantum technology, traditionally regarded as a static device-level operation constrained by the intrinsic physical properties of single-photon detectors (SPDs). Consequently, high-performance detection has been heavily reliant on superconducting technologies, whose requirement for cryogenic temperatures imposes significant infrastructure burdens and limits scalable deployment. To circumvent these constraints, we propose the Enhanced Single-Photon Detection (ESPD) framework, which shifts the photon-detection paradigm from device-centric optimization to an integrated quantum-information-processing (QIP) task. By incorporating state preparation, controlled operations, projective measurements, and multi-copy decision analysis, we establish a nonlinear dynamical model that reformulates detection as an iteratively enhanced process. This architecture enables systematic performance upgrades through structural design rather than material modification, allowing high-performance detection with exclusively room-temperature hardware. Through analytical approximations, Monte Carlo analysis, and numerical simulations, we show that the ESPD dynamics converge to a high-performance basin of attraction even when initialized by low-performance SPDs. While physical realization requires further component integration efforts, this work establishes a rigorous theoretical foundation for enhancing detection via architectural QIP principles. It provides not only a blueprint for next-generation room-temperature photon detection but also a general methodology for transcending device-level constraints in broader quantum technologies.

We develop energy-conserving numerical methods for a two-dimensional hyperbolic approximation of the Serre-Green-Naghdi equations with variable bathymetry and either periodic or reflecting boundary conditions. The hyperbolic formulation avoids the costly inversion of an elliptic operator present in the classical model. Our schemes combine split forms with summation-by-parts (SBP) operators to construct semi-discretizations that conserve the total water mass and the total energy. We provide analytical proofs of these conservation properties and also verify them numerically. While the framework is general, our implementation focuses on second-order finite-difference SBP operators. The methods are implemented in Julia for CPU and GPU architectures (AMD and NVIDIA) and achieve substantial speedups on modern accelerators. We validate the approach through convergence studies based on solitary-wave and manufactured-solution tests, and by comparisons to analytical, experimental, and existing numerical results. All source code to reproduce our results is available online.

SplitFed Learning (SFL) combines federated learning and split learning to enable collaborative training across distributed edge devices; however, it faces significant challenges in heterogeneous environments with diverse computational and communication capabilities. This paper proposes \textit{SuperSFL}, a federated split learning framework that leverages a weight-sharing super-network to dynamically generate resource-aware client-specific subnetworks, effectively mitigating device heterogeneity. SuperSFL introduces Three-Phase Gradient Fusion (TPGF), an optimization mechanism that coordinates local updates, server-side computation, and gradient fusion to accelerate convergence. In addition, a fault-tolerant client-side classifier and collaborative client--server aggregation enable uninterrupted training under intermittent communication failures. Experimental results on CIFAR-10 and CIFAR-100 with up to 100 heterogeneous clients show that SuperSFL converges $2$--$5\times$ faster in terms of communication rounds than baseline SFL while achieving higher accuracy, resulting in up to $20\times$ lower total communication cost and $13\times$ shorter training time. SuperSFL also demonstrates improved energy efficiency compared to baseline methods, making it a practical solution for federated learning in heterogeneous edge environments.

Spatially extended Ly$α$ nebulae, known as Ly$α$ blobs (LABs), are a rare population at $z > 2$ that are thought to trace proto-groups or the progenitors of massive galaxies in the present-day universe. However, their dark matter halo properties (e.g., halo mass) are still uncertain due to their rarity and strong field-to-field variation. The One-hundred-deg$^2$ DECam Imaging in Narrowbands (ODIN) survey has discovered 103 and 112 LABs in the extended ($\sim$9~\sqdeg) COSMOS field at $z\sim2.4$ and 3.1, respectively, enabling estimation of their bias and host halo masses through clustering analysis. We measure the angular auto-correlation functions (ACFs) of LABs and derive galaxy bias factors of $b$ = $4.0\pm0.8$ and $3.8\pm0.7$, corresponding to minimum halo masses of $2.8^{+3.0}_{-1.8}$ and $0.7^{+0.8}_{-0.5}\times10^{12}~M_\odot$ and median halo masses of $4.2^{+3.8}_{-2.5}$ and $1.1^{+1.1}_{-0.7}\times10^{12}~M_\odot$ at $z\sim2.4$ and 3.1, respectively. LABs occupy $\sim$11$^{+39}_{-8}$\% and $\sim$3$^{+9}_{-2}$\% of all dark matter halos above these minimum halo masses. These findings suggest that LABs inhabit massive dark matter halos, likely tracing proto-group environments that evolve into present-day massive halos ($\sim$10$^{13}~M_\odot$), where massive elliptical galaxies or galaxy groups reside, by $z=0$.

We demonstrated crystalline silicon-on-sapphire (c-SOS) metasurfaces that convert a Gaussian beam into arrays of complex optical traps, including arrays of optical bottle beams that trap atoms in dark regions interleaved with bright tweezer arrays. The high refractive index and indirect band gap of crystalline silicon makes it possible to design high-resolution near-infrared ($λ>700$ nm) metasurfaces that can be manufactured at scale using CMOS-compatible processes. Compared with active components like spatial light modulators (SLMs) that have become widely used to generate trap arrays, metasurfaces provide an indefinitely scalable number of pixels, enabling large arrays of complex traps in a very small form factor, as well as reduced dynamic noise. To design metasurfaces that can generate three-dimensional bottle beams to serve as dark traps, we modified the Gerchberg-Saxton algorithm to enforce complex-amplitude profiles at the focal plane of the metasurface and to optimize the uniformity of the traps across the array. We fabricated and measured c-SOS metasurfaces that convert a Gaussian laser beam into arrays of bright traps, dark traps, and interleaved bright/dark traps.

Let $x,y$ be freely independent selfadjoint elements in a $W^{*}$-probability space, where $y$ has free Poisson distribution of parameter $p$. We pursue a methodology for computing the absolutely continuous part of the Brown measure of $x + i y$, which relies on the matrix-valued subordination function $Ω$ of the Hermitization of $x + i y$, and on the fact that $Ω$ has an explicitly described left inverse $H$. Our main point is that the Brown measure of $x + i y$ becomes more approachable when it is reparametrized via a certain change of variable $h : \mathcal{D} \to \mathcal{M}$, with $\mathcal{D}, \mathcal{M}$ open subsets of $\mathbb{C}$, where $\mathcal{D}$ and $h$ are defined in terms of the aforementioned left inverse $H$, and $\mathrm{cl} \,(\mathcal{M})$ contains the support of the Brown measure. More precisely, we find (with some conditions on the distribution of $x$, which have to be imposed for certain values of the parameter $p$) the following formula: \[ f(s + i \, t) =\frac{1}{4π}\left[\frac{2}{t}\left(\frac{\partial α}{\partial s} +\frac{\partial β}{\partial t}\right)-\frac{2}{t}-\frac{2β}{t^2}\right], \ \ s + i \, t \in \mathcal{M}, \] where $f$ is the density of the absolutely continuous part of the Brown measure and the functions $α, β: \mathcal{M} \to \mathbb{R}$ are the real and respectively the imaginary part of $h^{-1}$.

We provide some up-to-date discussions related to cosmological event horizon and entropy of our universe, then introduce an intriguing idea that there may be a universal finite upper bound for entropy accessible to an observer in consistent theories of quantum gravity. We argue that the Berenstein-Maldacena-Nastase (BMN) strings provide a test of the idea. More speculatively, in an optimistic scenario, this also provides a possible estimate of the cosmological constant.

This paper presents a matrix formulation of the scalar laws of radiative transfer. The method applies to coupled mixed boundary condition problems on general domains. Participating media can range from transparent to absorbing, emitting, and scattering, with boundaries ranging from absorbing to reflecting. Given a non-dimensional first-interaction exchange factor matrix $\mathbf{F}$, the formulation partitions $\mathbf{F}$ into a single-step absorption matrix and a single-step reflection-scattering matrix via Hadamard products with a column-constant matrix of reflection-scattering coefficients. The resulting linear system encodes the radiative energy balance for arbitrary combinations of prescribed temperatures and prescribed source terms, with a proven non-singularity result for the mixed-boundary system. The method is shown to admit a unique non-negative solution for non-negative source terms whenever the maximum reflection-scattering coefficient is strictly less than unity, with unconditional energy conservation to machine precision. Validation is provided symbolically against the textbook closed-form solutions for infinite parallel plates and concentric cylinders, and numerically against the diffusion approximation in the high-extinction limit and against the results of Crosbie and Schrenker for pure and partial scattering cases. A comparison with Noble's matrix formulation of Hottel's zonal method reveals a discrepancy in that classical approach, not previously identified to the author's knowledge; the proposed formulation avoids this discrepancy. The method requires a single linear solve whose sparsity inherits from that of $\mathbf{F}$, making it applicable to medium-scale dense problems and to large-scale sparse problems with high extinction.

In this paper, we introduce a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically constructed from building blocks of two types: iterated snakes and irreducible meanders. We find out that iterated snakes allow efficient enumeration, and thus the problem of enumerating meanders reduces to the problem of enumerating irreducible meanders. Additionally, we present some results concerning the asymptotic of meanders of both classes.

In this paper, we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the Beris-Edwards model of nematic liquid crystals in $\R^3$ with an arbitrary parameter $ξ\in\R$, which measures the ratio of tumbling and alignment effects caused by the flow. This result is obtained by proposing a new uniqueness criterion in terms of $(ΔQ,\nabla u)$ with regularity $L_t^qL_x^p$ for $\frac{2}{q}+\frac{3}{p}=\frac{3}{2}$ and $2\leq p\leq 6$, which enables us to deal with the additional nonlinear difficulties arising from the parameter $ξ$. Compared with the known results, our finding reveals that the criterion of weak-strong uniqueness for $ξ\ne 0$ is a sub-regime of the one for the corotational case. The associated regularity assumption rises with the nonlinearity of the model. Moreover, we establish the global well-posedness of this model for small initial data in $H^s$-framework.

Reliability-based design optimization (RBDO) is a methodology for designing systems and components under the consideration of probabilistic uncertainty. In practical engineering, the number of input data is often limited, which can damage the validity of the optimal results obtained by RBDO. Confidence-based design optimization (CBDO) has been proposed to account for the uncertainty of the input distribution. However, this approach faces challenges, computational cost and accuracy when dealing with highly nonlinear performance constraints. In this paper, we consider the compliance minimization problem of truss structures with uncertain external forces. Armed with the advanced risk measure, conditional Value-at-Risk (CVaR), we formulate a bi-objective optimization problem for the worst-case expected value and the worst-case CVaR of compliance, which allows us to account for the tail risk of performance functions not addressed in CBDO. Employing kernel density estimation for estimation of the input distribution allows us to eliminate the need for modeling the input distribution. We show that this problem reduces to a second-order cone programming when assigning either uniform kernel or triangular kernel. Finally, through numerical experiments, we obtain the Pareto front for the bi-objective optimization problem of the worst-case expected value and CVaR of compliance of truss structures, and confirm the changes in the Pareto solutions.

Catastrophic disruptions of planetesimals occur in high-velocity collisions. Radioisotope dating of planetesimal disruption events recorded in meteorites confirms frequent catastrophic collisions in the first 10 Myr of the Solar System, reflecting a violent environment of the time. However, the nebula gas can damp the eccentricity of planetesimals and suppress the frequency of planetesimal collisions. Strong dynamical mechanisms that excited the protoplanetary disk are required. Here we show that the sweeping secular resonances of Jupiter and Saturn induced by the nebular gas dissipation, together with the mean motion resonances of Jupiter, can trigger a large number of catastrophic collisions, which occur episodically when the secular resonances are at 2-3 astronomical units and continue thereafter. After the gas dissipation completes, catastrophic collisions decrease in frequency, with scattering by planetary embryos becoming the major driving force of the collisions. Our results suggest that the violent environment excited by secular and mean motion resonances can be ubiquitous in protoplanetary disks during nebula dissipation.

We present a functional calculus treatment of Entropic Optimal Transport (EOT) between Gaussian measures on separable Hilbert spaces, providing a unified framework that handles infinite-dimensional degeneracy. By leveraging the notion of proper alignment and the Schur complement, we reveal that the Gaussian EOT solution operates as a precise \textit{spectral shrinkage}: the optimal coupling is uniquely determined by contracting the spectrum of the correlation operator via a universal scalar function. This geometric insight facilitates an algorithmic shift from iterative fixed-point schemes (e.g., Sinkhorn) to direct algebraic computation, enabling efficient multi-scale analysis, where a single spectral decomposition allows for the exact evaluation of entropic costs across arbitrary regularization parameters $\varepsilon > 0$ at negligible additional cost. Furthermore, we investigate the asymptotic behavior as $\varepsilon \downarrow 0$ in settings where the unregularized Optimal Transport problem admits non-unique solutions. We establish a selection principle that the regularized limit converges to the most diffusive optimal coupling --characterized as the centroid of the convex set of optimal Kantorovich plans. This demonstrates that in degenerate regimes, the entropic limit systematically rejects deterministic Monge solutions (extremal points) in favor of the optimal solution with minimal Hilbert-Schmidt correlation, effectively filtering out spurious correlations in the null space. Finally, we derive stability bounds and convergence rates, recovering established parametric rates ($\varepsilon \log(1/\varepsilon)$) in finite dimensions while identifying distinct non-parametric rates dependent on spectral decay in infinite-dimensional settings.

In earlier work, we introduced a discrete Fibonacci-based ontogenetic model in which the metabolic scaling exponent $b(n)$ is treated as a dynamic function of an organism's developmental stage, and we estimated $b(n)$ for selected mammalian species. In the present article, we revisit this framework with a complementary aim. Rather than proposing new parameter estimates or statistical fits, we provide a didactic, step-by-step reconstruction of the derivation that leads from the recursive growth hypothesis to analytical expressions for the stage-dependent exponent $b(n)$. Building directly on these previously obtained exponents, we then incorporate Kleiber's classical result into the model by interpreting the constant $70$ in the law $B \approx 70\,M^{3/4}$ (with $B$ denoting basal metabolic rate and $M$ body mass) as a metabolic "anchoring point". This yields a stage-dependent basal metabolic rate of the form $B(n) = 70\,M^{b(n)}$, which defines an ontogenetic metabolic trajectory linking recursive growth to changes in scaling. We show, at a conceptual level, how this anchored formulation can describe a shift from strongly sublinear behavior at early stages towards an almost linear regime as development proceeds, while still producing basal rates that are compatible, in order of magnitude, with those reported for mammals of different sizes. In this way, the paper offers a self-contained and pedagogical presentation of the model, emphasizing how ontogenetic changes in metabolic rate can be understood through the combined ideas of Fibonacci-like recursion and metabolic anchoring.

Hadronic tensors encode the nonperturbative structure of hadrons probed in deep inelastic scattering (DIS), yet their direct evaluation requires real-time evolution that presents a challenge for traditional Euclidean lattice approaches. In this work, we present the first quantum simulation of real-time hadronic current-current correlators in a confining gauge theory, from which DIS-inspired structure functions are extracted as a proof-of-principle demonstration in the Schwinger model, i.e (1+1)-dimensional QED. Using two complementary quantum-simulation strategies -- quantum-circuit and tensor-network methods -- we compute the real-time current-current correlator directly on the lattice and validate our results against exact diagonalization where applicable. From this correlator, we compute the hadronic tensor and determine the longitudinal structure function, the sole nonvanishing DIS observable in two space-time dimensions. Our study demonstrates that quantum simulation offers a viable complementary pathway towards the evaluation of real-time observables relevant for hadronic structure. It also provides a foundation for extending the calculations from Schwinger model to other gauge theories.

The recently discovered gravitational wave event GW231123 was interpreted as the merger of two black holes with a total mass of 190-265 $M_\odot$, making it the heaviest such merger detected to date. Whilst much of the post-discovery literature has focused on its astrophysical origins, primary analyses have exhibited considerable discrepancies in the measurement of source properties between waveform models, which cannot reliably be reproduced by simulations. Such discrepancies may arise when an unaccounted overlapping signal is present in the data, or from phenomena that produce similar effects, such as gravitational lensing or overlapping noise artifacts. In this work, we analyse GW231123 using a flexible model that allows for two overlapping signals, and find that it is favoured over the isolated signal model with Bayes factors of $\sim 10^2 - 10^{4}$, depending on the waveform model. These values lie within the top few per cent of the background distribution. Similar effects are not observed in GW190521, another high-mass event. Under the overlapping signals model, discrepancies in the measurement of source properties between waveform models are largely mitigated. We also find that neglecting an additional signal in overlapping-signal data can lead to discrepancies in the estimated source properties resembling those reported in GW231123. Although the overlapping signal model provides a higher Bayesian evidence, the astrophysical prior probability of two short signals overlapping is low. However, we find that the two recovered sources show similar properties. This, taken with the higher evidence of the two signal model, suggests that gravitational lensing may provide an alternative explanation.