We report the emergence of Log-normal Superstatistics in the collective motion of ants confined in a quasi-2D arena and exposed to a panic-inducing stimulus. A data-driven superstatistical Langevin model accurately reproduces the transition from stationary behavior to an organized escape response, characterized by non-Gaussian velocity distributions and a stochastic diffusion coefficient. Our findings show that danger information propagates via a memory-limited, cascade-like mechanism, resulting in a stable cluster formation despite individual memory constraints. These results indicate that a slowly varying diffusivity arises from the multiplicative combination of interaction-mediated processes under confinement, leading naturally to Log-normal fluctuations. The persistence of this statistical structure under panic reveals a form of collective resilience, establishing a mechanistic bridge between Superstatistics and living active matter in confined environments.

In 1963 Grünbaum introduced the following variation of the Banach-Mazur distance for arbitrary convex bodies $K, L \subset \mathbb{R}^n$: $d_G(K, L) = \inf \{ |r| \ : \ K' \subset L' \subset rK' \}$ with the infimum taken over all non-degenerate affine images $K'$ and $L'$ of $K$ and $L$ respectively. In 2004 Gordon, Litvak, Meyer and Pajor proved that the maximal possible distance is equal to $n$, confirming the conjecture of Grünbaum. In 2011 Jiménez and Naszódi asked if the equality $d_G(K, L)=n$ implies that $K$ or $L$ is a simplex and they proved it under the additional assumption that one of the bodies is smooth or strictly convex. The aim of the paper is to give a stability result for a smooth case of the theorem of Jiménez and Naszódi. We prove that for each smooth convex body $L$ there exists $\varepsilon_0(L)>0$ such that if $d_G(K, L) \geq (1-\varepsilon)n$ for some $0 \leq \varepsilon \leq \varepsilon_0(L)$, then $d(K, S_n) \leq 1 + 40n^3r(\varepsilon)$, where $S_n$ is the simplex in $\mathbb{R}^n$, $r(\varepsilon)$ is a specific function of $\varepsilon$ depending on the modulus of the convexity of the polar body of $L$ and $d$ is the usual Banach-Mazur distance. As a consequence, we obtain that for arbitrary convex bodies $K, L \subset \mathbb{R}^n$ their Banach-Mazur distance is less than $n^2 - 2^{-22}n^{-7}$.

An exposition on Spivakovsky's dual graphs of valuations on function fields of dimension two is first given, leading to a proof of minimal generating sequences for the non-divisorial valuations. It should be noted that the definition of generating sequence used in this paper is different from Spivakovsky's original usage. This change leads to an explicit formulation of generating sequence values for the non-divisorial cases in terms of data from their dual graphs. The proofs are elementary in the sense that only continued fractions and the linear Diophantine Frobenius problem from classical number theory are used.

After melting, at ambient pressure, the density of water continues to increase with temperature until it reaches a maximum around 4 °C. For nearly a century, this phenomenon has been qualitatively attributed to a mixture of ordered and disordered structures. Herein, we employ a deep neural network to train a machine learned (ML) interatomic potential for water using electronic structure data from advanced density functional theory. Notably, molecular dynamics simulations with the ML potential reproduce both the experimental water density anomaly and the thermal expansion coefficient. Detailed structural analysis of the computed hydrogen-bond network reveals that the density anomaly arises from an emergent liquid structure that retains nearly ideal tetrahedral coordination at short range but collapses at intermediate range. Our findings point to a more delicate mechanism causing the density maximum than the conventional picture, emphasizing the collective roles of structural orderings at different length scales.

We present an exact phase-space analytical treatment of the power-law damped contact oscillator governed by $m\ddotδ + α\sqrt{mk_H}\,δ^{(p-1)/2}\dotδ + k_Hδ^p = 0$, valid for all force-law exponents $p \geq 1$ and all initial impact velocities $v_0$. The central result is the transformation $δ= Ax^{2/(p+1)}$, where $A = [(p+1)/2]^{1/(p+1)}$, which maps the nonlinear phase-space equation $v\,dv/dδ+ \dots = 0$ exactly onto a linear spring-dashpot (LSD) system with effective damping ratio $α_\text{eff} = \fracα{\sqrt{2(p+1)}}$. The phase portrait $v(δ)$, coefficient of restitution $e$, and maximum penetration $δ_\text{max}$ follow in closed form. The physical time-domain solution $(δ(t), v(t))$ is obtained parametrically via a single quadrature, which evaluates analytically for $p=1$ and at negligible numerical cost for all other $p$. We prove that $e$ is exactly independent of $v_0$ for all $p \geq 1$ and derive the universal calibration formula: $α= \sqrt{2(p+1)}\cdot\frac{-\ln e}{\sqrt{π^2 + \ln^2 e}}$. This generalises the known results for $p=1$ (linear spring-dashpot) and $p=3/2$ (Hertz contact, Antypov and Elliott, 2011) to the entire power-law family. A closed-form estimate for the critical timestep of explicit time integration is also derived, exhibiting universal scaling with impact velocity and force-law exponent.

We revisit the recently proposed ``self-Wiener" (SW) filtering method for robust deconvolution, and generalize it to the classical denoising problem. The resulting estimator, termed generalized SW (GSW) filtering, retains the nonlinear shrinkage structure of SW but introduces a tunable threshold parameter. This tunability enables GSW to flexibly adapt to varying signal-to-noise ratio (SNR) regimes by balancing noise suppression and signal preservation. We derive closed-form expressions for its mean-square error (MSE) performance in both low- and high-SNR regimes, and demonstrate that GSW closely approximates the oracle MMSE at high SNR while maintaining strong robustness at low SNR. Simulation results validate the analytical findings, showing that GSW consistently achieves favorable denoising performance across a wide range of SNRs. Its analytical tractability, parameter flexibility, and close connection to the optimal Wiener filter structure make it a promising tool for practical applications including compressive sensing, sparse signal recovery, and domain-specific shrinkage in wavelet, Fourier, and potentially learned orthonormal representations.

High-fidelity quantum gates require precise classical control signals, yet the analog hardware delivering these signals introduces nonlinear distortions that degrade gate performance. We demonstrate digital predistortion of an acousto-optic modulator used to generate multi-tone entangling-gate waveforms in a trapped-ion processor based on $^{88}$Sr$^+$. By measuring and inverting the static nonlinear amplitude response of the modulator, we apply a feed-forward correction that extends its linear operating range and suppresses spurious intermodulation products. Spectral analysis of the gate beam shows 3--5 dB suppression of the dominant intermodulation tones, approximately doubling the usable diffraction efficiency at a $10^{-3}$ estimated gate-error threshold. Direct two-qubit Bell-state fidelity measurements confirm that predistortion consistently improves entangling-gate performance. The calibrate-and-invert methodology is device and platform agnostic, applicable to any nonlinear element in the classical control chain of a quantum processor.

We report the thermal conductances of molecular junctions made of self-assembled monolayers of benzo-bis(imidazole) molecules, without side groups or functionalized with two phenylamine side groups. In the two cases, when the molecules are connected to the electrodes by thiol anchoring groups in the meta-position, the thermal conductance is decreased compared to the same molecules connected in the para-position (ca. 16-29 nW/K and ca. 37-40 nW/K, respectively) in agreement with the theoretically predicted phonon interference effect in molecular junctions. Upon protonation, the thermal conductances of the meta-connected molecular junction increase by about 50% (reversible behavior upon deprotonation). The fact that only the thermal conductance of the meta-connected molecular junction is sensitive to the protonation/deprotonation is tentatively related to modifications of the structural organization of the molecules in the monolayer, which modifies the thermal conductance at the molecule/electrode interfaces. The electrical conductance is lower for the meta-connected molecule than for the para-connected one, due to destructive quantum interferences, as expected and reported for other molecular junctions. The conductance further decreases (reversibly) upon protonation. The energy position of the molecular orbital involved in the electron transport is not modified by the protonation and the decrease in current is related to changes in the molecule organization in the monolayer, which modulate the electronic coupling energy at the molecule/electrode interfaces.

Hydrogen fuel cells are a key technology in the transition toward carbon-neutral energy systems, offering clean power with water as the only byproduct. Microfluidic fuel cells, which operate at the microliter scale, are an emerging variant that offer fine control over fluid and thermal dynamics, along with compact, efficient designs. However, scaling these systems to meet practical power demands remains a major challenge -- particularly due to the limitations of conventional simulation methods like Computational Fluid Dynamics (CFD), which are computationally expensive and scale poorly. In this work, we propose a reduced-order simulation method that models the behavior of individual microfluidic fuel cells and efficiently extends it to large scale stacks. This approach significantly reduces simulation time while maintaining close agreement with detailed CFD results. The method is validated, evaluated for scalability, and discussed in the context of ongoing advancements in microfluidic fuel cell fabrication. The obtained results demonstrate that this abstraction can support the design and development of scalable microfluidic fuel cell systems and, for the first time, the consideration of first macroscale instances of practical value.

We introduce the notions of tauberian, cotauberian and weakly compact pair of closed subspaces of a Banach space. The theory produced by these notions is richer than that of the corresponding operators since an operator can be regarded as a suitable pair of closed subspaces. We investigate into these classes of pairs of subspaces and describe several applications in order to define some notions of indecomposability for Banach spaces and in order to extend definitions from the case of bounded operators to the case of closed operators.

Recent results from LHCb have confirmed the long-standing $P_5^\prime$ anomaly, an intriguing discrepancy in the angular distribution of the $B \to K^* μ^+μ^-$ decay that might be a sign of new physics. In addition, the new results hint at a non-zero value for $S_7$, another observable that characterizes the $B \to K^* μ^+μ^-$ angular distribution. We stress that a non-zero $S_7$ cannot be explained by heavy new physics but instead necessarily requires a sizable hadronic effect that introduces a strong phase. We argue that, under plausible assumptions, the hadronic effect is of the correct size to also explain $P_5^\prime$. The direct CP asymmetry in $B \to K^* μ^+μ^-$ emerges in principle as a clean probe of new physics in such a scenario. We show that a combined fit of hadronic parameters and Wilson coefficients retains sensitivity to new physics and we find strong bounds on imaginary parts of new physics Wilson coefficients.

We investigate the roles of spin and packing fraction on the dynamics of cratering when a solid projectile impacts a granular bed at different incident angles. For that, we carried out DEM (discrete element method) computations in which we varied the magnitude and direction of the projectile spin, the impact velocity, the bed packing fraction, and the incident angle. For a given incident velocity, we found that the projectile can rebound for small angles, or be completely or partially buried for larger angles, and that when buried it can sometimes migrate large horizontal distances depending on the incident angle. We also found that increasing the packing fraction strengthens rebounds, and that the initial spin, depending on its direction and orientation, induces rebound, burying, or transverse deviations. The crater morphology also changes with the varying parameters, acquiring circular, elliptical, goutte-like, tadpole-like, and transitional shapes, correlating well with the projectile behavior. Finally, we propose diagrams organizing and classifying the dynamics observed. Our results shed new light on the different shapes of craters found in nature and the fate of the impacting material.

High-performance infrared photodetection underpins various applications spanning surveillance, environmental monitoring, optical communications and biomedical imaging. However, conventional bulk detectors remain limited by poor spectral tunability, mechanical rigidity, and high dark currents, motivating the pursuit of low-dimensional material platforms such as graphene and transition metal dichalgenides. Black phosphorus (BP) is particularly compelling in this context, owing to its thickness-tunable direct bandgap, high carrier mobility, and pronounced in-plane anisotropy. Nevertheless, its atomically thin nature inherently restricts light absorption, posing a fundamental bottleneck for device performance. Here, we demonstrate quasi-bound states in the continuum (quasi-BICs) within a dielectric metasurface integrated with BP, enabling strongly enhanced and spectrally selective light-matter interactions. By introducing controlled symmetry breaking at the unit-cell level, high-quality-factor resonances are realized, resulting in pronounced electromagnetic field confinement within the BP layer. This resonant enhancement substantially increases photocarrier generation while preserving the intrinsic polarization anisotropy of BP, which elucidates a robust pathway for overcoming the optical absorption bottleneck in anisotropic 2D optoelectronics via quasi-BIC platforms.

Centralized stablecoins such as USDT and USDC enforce financial sanctions through contract-layer blacklist functions, yet on public blockchains a freeze is merely an ordinary transaction that must compete for execution priority. We identify a fundamental gap between contract-layer authority and consensus-layer enforcement: when a sanctioned entity's transfer and the issuer's freeze race for inclusion in the same block, the outcome is determined not by regulatory mandate but by the economically motivated ordering decisions of block producers. We term the resulting value extraction Sanction-Evasion MEV (SE-MEV). To quantify this vulnerability, we construct the first comprehensive dataset of on-chain sanctions enforcement and evasion for Ethereum-based USDC and USDT (Nov 2017-Aug 2025), covering over $1.5 billion in frozen assets. We find that 7.3% of sanctioned USDT addresses and 18.7% of sanctioned USDC addresses were drained to zero balances before enforcement took effect, and document a clear escalation trajectory-from issuer-side out-of-gas failures, to public gas auctions, to private order flow, to direct proposer bribery. We further develop a game-theoretic model that yields three results: (i) compliant issuers cannot rationally stay outside the MEV market; (ii) fixed participation costs concentrate evasion among specialized, MEV-aware actors; and (iii) the implicit MEV tax extracted by block proposers grows without bound as regulatory penalties intensify, creating structural incentives for issuers to vertically integrate into block-building infrastructure. Our findings demonstrate that on any blockchain where ordering power is allocated by economic incentives, ordering power is sanctioning power-and contract-level authority alone cannot guarantee enforcement.

The APSP Hypothesis states that the All-Pairs Shortest Paths (APSP) problem requires time $n^{3-o(1)}$ on graphs with polynomially bounded integer edge weights. Two increasingly stronger assumptions are the Strong APSP Hypothesis and the Directed Unweighted APSP Hypothesis, which state that the fastest-known APSP algorithms on graphs with small weights and unweighted graphs, respectively, are best-possible. In this paper, we design an efficient universe reduction for APSP, which proves that these three hypotheses are, in fact, equivalent, conditioned on $ω= 2$ and a plausible additive combinatorics assumption. Along the way, we resolve the fine-grained complexity of many long-standing graph and matrix problems with "intermediate" complexity such as Node-Weighted APSP, All-Pairs Bottleneck Paths, Monotone Min-Plus Product in certain settings, and many others, by designing matching APSP-based lower bounds.

Social sustainability in software development means creating and maintaining systems that promote pro-social values (e.g., human well-being, equity), both now and in the future. However, social sustainability lacks clear conceptual and methodological foundations, and often takes a back seat to speed and profit. This paper therefore reports a narrative review of existing definitions of social sustainability in software development and identifies key aspects of social sustainability including social equity, well-being, and community cohesion. Challenges around measuring and integrating social sustainability into practice are conceptually analyzed. The paper then proposes a comprehensive definition of social sustainability and outlines a roadmap for measuring and integrating social sustainability into software engineering processes.

We study joint compression and detection in distributed sensing systems motivated by emerging applications such as IoT-based localization. Two spatially separated sensors observe noisy signals and can exchange only a $k$-bit message over a reliable one-way low-rate link. One sensor compresses its observation into a $k$-bit description to help the other decide whether their observations share a common underlying signal or are statistically independent. We propose a simple extremum-based strategy, in which the encoder sends the index of its largest sample and the decoder performs a scalar threshold test. We derive exact nonasymptotic false-alarm and misdetection probabilities and validate the analysis with representative simulations.

Controlling collective electronic phases in low-dimensional materials is a central challenge for developing technologies based on charge-density waves. Here, we report that perpendicular electric and magnetic fields can be used to tune charge-density-wave transport in the quasi-two-dimensional material 1T-TaS2. Using h-BN-encapsulated thin-film heterostructures with both top-gate and bottom-gate configurations, we find that electrical gating produces a non-monotonic shift in the depinning threshold, a behavior distinct from that of quasi-one-dimensional charge-density-wave systems. We further show that a perpendicular magnetic field increases the threshold voltage for domain depinning and can drive the nearly commensurate-to-incommensurate charge-density-wave phase transition, demonstrating magnetic control over a two-dimensional electron-lattice condensate. The obtained results shed light on mechanisms governing charge-density-wave domain dynamics and reveal combined electrical and magnetic-field control as a strategy for engineering low-power-dissipation devices and electronics for extreme environments.

In this paper, we study arbitrary models of the first-order theory of a ring $A$ where the additive group $A$ is a finitely generated abelian group. Following an earlier paper by this author, Alexei G. Myasnikov and Francis Oger, we call these rings the FDZ-rings or FDZ-algebras. The rings considered are not necessarily unitary, commutative, or associative. We provide criteria for such rings to be quasi finitely axiomatizable (QFA) or bi-interpretable with the ring of integers $\mathbb Z$. We shall also describe all rings elementarily equivalent to such a ring $A$ given certain constraints on $A$.

The first globally convergent numerical method is developed for a coefficient inverse problem (CIP) for the $n-$d, $n\geq 2$ wave equation with the unknown potential in the most challenging case when the $δ-$ function is present in the initial condition with a single location of the point source. In fact, an approximate mathematical model for that CIP is derived. That globally convergent numerical method is developed for this model. This is a new version of the so-called convexification numerical method. Uniqueness theorem is proven as well within the framework of that approximate mathematical model. The question about uniqueness of this CIP was first posed by a famous mathematician I. M. Gelfand in 1954 as an $n-$d ($n=2,3$) extension of the fundamental theorem of V.A. Marchenko in the 1-d case (1950). Based on a Carleman estimate, convergence analysis is carried out. This analysis ensures the global convergence of the proposed numerical method, i.e. it is not necessary to have a good first guess for the solution. Exhaustive computational experiments with noisy data demonstrate a high reconstruction accuracy of complicated structures. In particular, this accuracy points towards a high adequacy of that approximate mathematical model.

We solve the problem of Davenport--Lewis--Schinzel (DLS), originating in the 1950s, regarding the reducibility of $f(X)-g(Y)\in\mathbb C[X,Y]$. This yields an almost-complete solution to the Hilbert--Siegel problem: For a polynomial map $f$ whose composition factors avoid only very specific low-degree polynomials, we explicitly describe over which integers the fibers of $f$ are reducible. We further apply the solution to stability of iterates of $f$ in arithmetic dynamics, and to solving the functional equation $f(X)=g(Y)$ in $X,Y\in\mathbb{C}(z)$.

To advance integrated sensing and communications (ISAC) in sixth-generation (6G) extremely large-scale multiple-input multiple-output (XL-MIMO) networks, a low-complexity compressed sensing (CS)-based dictionary design is proposed for wideband near-field (WB-NF) target localization. Currently, the massive signal dimensions in the WB-NF regime impose severe computational burdens and high spatial-frequency coherence on conventional grid-based algorithms. Furthermore, a unified framework exploiting both wideband (WB) and near-field (NF) effects is lacking, and the analytical conditions for simplifying this model into decoupled approximations remain uncharacterized. To address these challenges, the proposed algorithm mathematically decouples the mutual coherence function and introduces a novel angle-distance sampling grid with customized distance adjustments, drastically reducing dictionary dimensions while ensuring low coherence. To isolate the individual WB and NF impacts, two coherence-based metrics are formulated to establish the effective boundaries of the narrowband near-field (NB-NF) and wideband far-field (WB-FF) regions, where respective multiple signal classification (MUSIC) algorithms are utilized. Simulations demonstrate that the CS-based method achieves robust performance across the entire regime, and the established boundaries provide crucial theoretical guidelines for WB and NF effect decoupling.

The European Union Emissions Trading System is set to substantially increase the effective carbon price faced by airlines. To quantify the impact of this carbon regulation on the European airline industry, we estimate a two-stage model of airline competition with endogenous route entry, flight frequencies, and pricing using European data on market shares and prices. Counterfactual simulations reveal that the impacts of carbon pricing are highly asymmetric across carrier types and market segments. Consumer surplus declines by up to 25% overall, with medium-haul markets bearing the brunt at up to 90%, while short-haul markets experience positive net welfare gains (including carbon revenue and the social value of avoided emissions) as airlines reallocate capacity toward shorter routes. We find that airline profits decline by 8-45% across scenarios, while carbon tax revenue of $0.9-3.1 billion and a social value of avoided CO2 emissions of $0.5-1.4 billion partially offset the welfare losses. We also show that a hypothetical Wizz Air-Ryanair merger primarily benefits firm profits through network expansion synergies.

This paper investigates the physical layer security of a non-orthogonal multiple access (NOMA) system assisted by a tertiary-mode simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS), which can perform transmission, reflection, and jamming simultaneously. The system comprises a base station (BS) serving two users located on opposite sides of the STAR-RIS, assuming perfect channel state information (CSI) at the transmitter. To enhance secrecy performance, a subset of STAR-RIS elements is adaptively configured for jamming. A penalty-based alternating optimization algorithm is developed to jointly optimize the BS's active beamforming and the STAR-RIS's passive beamforming and mode selection. Simulation results demonstrate that the proposed design substantially improves the achievable sum rate and secrecy performance compared to conventional RIS-assisted and no-RIS benchmarks, highlighting the potential of tertiary-mode STAR-RIS for secure and efficient next-generation wireless communications.

This paper develops an interpretive framework for divergence P-values and S-values within a descriptive frequentist perspective. Statistical analysis is framed as operating within idealized worlds defined by a set of assumptions and a target hypothesis, where probabilities describe the behavior of data under the model but do not assign truth values to hypotheses. Within this view, P-values are interpreted as graded indices of compatibility between the observed result and the predictions generated by the assumed model; accordingly, small P-values should not be read as indicating logical impossibility or strict inconsistency of the model itself. Building on this distinction, the paper argues that practical inference requires moving beyond the internal logic of the model toward judgments of overall acceptability, which depend not only on data-model compatibility but also on multiple contextual considerations such as subject-matter knowledge, plausibility of assumptions, data quality, usefulness, and loss - all interpreted through the competence, intentions, perceptions, and moral values of the specific analyst. S-values are therefore interpreted not as evidence against the epistemic status of the model, but as a specific form of refutational information that contributes to the broader body of information used by the analyst to judge whether a model remains acceptable for an intended practical purpose. The paper also examines the linguistic and conceptual risks associated with the language of incompatibility, distinguishes probability from rarity, and clarifies different notions of surprise - including a possible definition of Shannon-type surprise, to be distinguished from Bayesian belief revision. Overall, the article proposes a more cautious and explicit interpretation of frequentist measures, centered on model-based description, analyst responsibility, and decision acceptability.

Exact similarity search over large collections of data series is a fundamental operation in modern applications, yet existing solutions are often fragmented, specialized, or tailored to specific execution environments. In this paper, we present DaiSy, a unified library for exact data series similarity search that integrates multiple state-of-the-art algorithms within a single, coherent framework. DaiSy is the first library to support exact similarity search across diverse execution environments, including implementations for disk-based, in-memory, GPU-accelerated, and distributed scalable similarity search. Although designed for data series, DaiSy is also directly applicable to exact similarity search over vector data, enabling its use in a broader range of applications. The library supports interfaces in both C++ and Python, enabling users to easily integrate its functionality into a variety of tasks. DaiSy is open-sourced and available at: https://github.com/MChatzakis/DaiSy.

We study the assessment of semiparametric and other highly-parametrised models from the perspective of foundational principles of parametric statistical inference. In doing so, we highlight the possibility of avoiding the usual semiparametric considerations, which typically require estimation of nuisance components through kernel smoothing or basis expansion, with the associated difficulties of tuning-parameter choice that blur the distinction between estimation and model assessment. A key aspect is the availability of preliminary manoeuvres that induce an internal replication of known form under the postulated model. This can be cast as a generalised version of the Fisherian sufficiency/co-sufficiency separation, replacing out-of-sample prediction error as a criterion for semiparametric model assessment by a type of within-sample prediction error. Framed in this light are new methodological contributions in multiple example settings, including model assessment for the proportional hazards model, for a time-dependent Poisson process with semiparametric intensity function, and for matched-pair and two-group examples. Also subsumed within the framework is a post-reduction inference approach to the construction of confidence sets of sparse regression models. Numerical work confirms recovery of nominal error rates under the postulated model and high sensitivity to departures in the direction of semiparametric alternatives. We conclude by emphasising open challenges and unifying perspectives.

This study investigates the relationship between coin demand, payment innovation, COVID-19, and a coin's purchasing power, particularly in emerging countries like Indonesia. The rapid advancement of payment platforms, combined with high adoption during the pandemic, has positioned non-cash payments as a complement or substitute for coin money for transactions. However, there is notably limited coin-money-related research in the economic literature. Employing the autoregressive distributed lag (ARDL) bounds test methodology's cointegration approach using monthly data from 2011 to 2022, our findings reveal a long-term relationship between coin demand and its determinants: payment innovations, the pandemic, coin depreciation, and income. Despite the swift advancement of payment innovations and their usage, coins remain vital to the economy and are unlikely to become obsolete soon. Our study offers essential policy recommendations and enriches the field of knowledge on coin money demand. Policymakers must understand the driving factors of coin demand in both economic and non-economic contexts to improve coin production-related issues and coin circulation policies. Reviewing the Rupiah denomination structure is crucial in addressing the problem of ineffective coin circulation in the economy.

This work reformulates Chiba's affine-order prescription as a polynomial-moment problem for a transformed positive measure, and develops an alternative finite-precision construction route based on this reformulation. The proposed construction proceeds through discrete-measure realization, symmetric Lanczos reduction, and Golub--Welsch extraction, replacing the conventional moment--Pade pipeline. The subgroup total levels and probabilities are obtained by a Gauss-type compression step that preserves nonnegative-realness, while the reaction-channel levels are recovered on the compressed nodes by orthogonal-basis matching. In five tested resonance-channel cases, the proposed construction yields lower effective-cross-section errors and avoids the order-induced emergence of complex responses observed in the conventional construction.

We introduce the notion of Cayley--Hamilton tuples: these are commuting operator tuples that are annihilated by a non-zero polynomial and such that its Taylor joint spectrum coincides with the algebraic variety determined by its annihilating ideal. Commuting matrix tuples are Cayley--Hamilton tuples. We provide two families of Cayley--Hamilton tuples in the infinite dimensional setting with additional details. What arises as a by-product is a concrete characterization of distinguished varieties in the polydisk in terms of Taylor joint spectrum of commuting isometries. These varieties have been of interest in various fields of mathematics over the last two decades. The Taylor and Waelbroeck joint spectrum of a Cayley--Hamilton tuple are shown to be the same. It is also shown that the support of the annihilating ideal of a Cayley--Hamilton tuple is the same as its joint spectrum. As an application, we deduce an algebraic characterization of bi-variate polynomials whose zero set intersected with the closed bidisk is the joint spectrum of a commuting isometric pair.