arXiv subjects

Sabin Roman

Publications and source records attributed to Sabin Roman.

12 recordsLinked to original sources

arXiv2026

A Generalized Gompertz Law for the Rise and Fall of Empires

Human societies tend to evolve toward increasing scale and complexity, often followed by stagnation and decline. Historical empires provide a prominent example of this trajectory; however, existing quantitative models capture expansion and rarely account for decline within a unified framework. Here, we introduce a minimal dynamical model that describes both growth and collapse in a single formalism. The model yields a closed-form trajectory that generalizes the Gompertz law and admits equivalent maximum-entropy and optimal-control formulations. We show that this functional form captures the rise and fall of fourteen diverse empires across widely varying time scales. Despite substantial historical heterogeneity, all cases follow a common asymmetric rise-peak-decline pattern governed by a small number of interpretable parameters. We identify the mechanism driving this behavior as the chronophage: an exponentially accumulating burden of administrative and coordination costs that offsets the gains of expansion. These findings uncover a general quantitative principle, yielding new insights into how increasing complexity constrains large-scale social systems.

physics.soc-ph↗

arXiv2026

Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration

We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT estimates expansion coefficients directly from observations using L1-regularized regression, avoiding explicit quadrature or analytic inner-product evaluation. The central application is data-driven discovery of ordinary differential equations: vector fields are represented in chosen orthogonal bases and learned as sparse coefficient expansions. This provides a complementary route to symbolic regression, grammar-based discovery, and SINDy-style sparse identification by first recovering a compact spectral representation, which can later guide searches for simpler analytic forms. Across the dynamical-system experiments, SORT matches or improves upon library-based sparse-regression baselines when the basis is well adapted to the problem, and shows more stable degradation under sparse sampling, noisy derivative estimates, and representation mismatch. Specific examples illustrate why this representation is useful: if a finite library misses the problem-specific nonlinearity, the resulting model can fail. SORT is not immune to mismatch, but it shifts the problem away from brittle selection among generic terms to basis design adapted to the problem domain. The experiments also show that dominant low-order coefficients persist as model order increases, supporting order-consistent model growth. Beyond equation discovery, the same learned expansion supports nonlinear approximation and estimation of complex, high-dimensional integrals by coefficient readout. Overall, SORT provides a reusable intermediate representation for system identification, approximation, and integration, while making basis design an explicit part of the scientific modeling problem.

cs.LG↗

arXiv2026

Exploratory Modelling of Multi-System Transformation Pathways from Real-World Data: A SINDy-Inspired Sparse Orthogonal Regression Technique

Sustainability transitions unfold through interacting dynamics across social, technological, economic, environmental, and governance dimensions. However, many modelling approaches either isolate subsystems or rely on optimisation-based pathways that do not explicitly represent feedbacks, path dependence, and institutional constraints. This study develops a Sparse Orthogonal Regression Technique (SORT), a data-driven dynamical-systems framework for reconstructing multi-system transformation dynamics from harmonised European indicators. Inspired by Sparse Identification of Nonlinear Dynamical Systems (SINDy), SORT infers parsimonious cross-domain dependencies from observed data rather than specifying a full structural model ex ante. The prototype covers energy, emissions, innovation, digitalisation, resource productivity, environmental stress, policy, finance, wellbeing, and resilience. The compact dynamical system is interpreted as a structural representation of medium-term interactions, not as a forecasting tool. It reproduces differentiated empirical patterns, including steady renewable expansion, nonlinear scaling in transition finance, diffusion-like digitalisation, oscillatory environmental stress, and sustained reduction in ETS-regulated emissions. Forward simulations diverge from simple linear extrapolation where reinforcing feedbacks are present, illustrating the conditional nature of accelerated decarbonisation. By translating inferred dependencies into a feedback structure, the analysis identifies reinforcing decarbonisation sequences alongside balancing ecological constraints. The model contributes to sustainability transitions research by providing an empirically grounded representation of multi-system feedback dynamics that bridges quantitative modelling and transition theory. SORT offers a compact technique for exploratory reconstruction from real-world transition data.

physics.soc-ph↗

arXiv2026

Limits of spectral learning under noise

Learning functional relationships from noisy data is a central problem in scientific inference. Spectral methods approximate unknown functions by expanding them in a basis and estimating the corresponding coefficients from data, but the stability of these coefficients under noise remains poorly understood. Here we study supervised regression with additive label noise using sparse spectral representations across multiple bases and dimensions. We show that noise induces a predictable drift in the learned coefficient vector whose magnitude depends on the effective number of active spectral modes. After whitening the empirical feature geometry, we derive a closed-form expression for the overlap between noisy and noiseless coefficient vectors, revealing a universal degradation curve governed by a single intrinsic noise scale. Numerical experiments across Fourier, Legendre, Bessel, and Haar bases confirm the theoretical prediction. The results demonstrate that spectral learning exhibits a fundamental noise threshold beyond which coefficient estimates become unstable, placing intrinsic limits on recovering functional structure from noisy data.

cs.LG↗

arXiv2026

Toward a new AI winter? How diffusion of technological innovation on networks leads to chaotic boom-bust cycles

Technological developments and the impact of artificial intelligence (AI) are omnipresent themes and concerns of the present day. Much has been written on these topics but applications of quantitative models to understand the techno-social landscape have been much more limited. We propose a mathematical model that can help understand in a unified manner the patterns underlying technological development and also identify the different regimes in which the technological landscape evolves. First, we develop a model of innovation diffusion between different technologies, the growth of each reinforcing the development of the others. The model has a variable that quantifies the level of development (or innovation, discovery) potential for a given technology. The potential, or market capacity, increases via diffusion from related technologies, reflecting the fact that a technology does not develop in isolation. Hence, the growth of each technology is influenced by how developed its neighboring (related) technologies are. This allows us to reproduce long-term trends seen in computing technology and large language models (LLMs). We then present a three-dimensional system of supply, demand, and investment which shows oscillations (business cycles) emerging if investment is too high into a given technology, product, or market. We finally combine the two models through a common variable and show that if investment or diffusion is too high in the network context, chaotic boom-bust cycles can emerge. These quantitative considerations allow us to reproduce the boom-bust patterns seen in non-fungible token (NFT) transaction data and also have deep implications for the development of AI which we highlight, such as the arrival of a new AI winter.

physics.soc-ph↗

arXiv2025

Approximating the universal thermal climate index using sparse regression with orthogonal polynomials

The Universal Thermal Climate Index (UTCI) is a measure of thermal comfort that quantifies how humans experience environmental conditions. Due to its robustness and versatility as a bioclimatic indicator, it has been extensively employed across a wide range of studies in bioclimatology and is increasingly used as an operational measure of outdoor thermal comfort. Calculating the UTCI value from the relevant environmental parameters is nominally not straightforward, which is why using a 6th-degree polynomial approximation has become the standard way to calculate UTCI values. Although it is computationally efficient, the error of this polynomial approximation can be substantial. The goal of this study was to develop an improved version of the polynomial approximation - one that retains comparable computational efficiency but is more robust in terms of numerical stability and substantially more accurate, particularly in reducing the frequency of larger errors. This goal was achieved using sparse orthogonal regression, namely sparse regression with an orthogonal polynomial basis, which not only substantially reduces the average errors (i.e., the mean error, the mean absolute error, and the root mean square error) but also drastically reduces the frequency of large errors. By leveraging Legendre polynomial bases, approximation models could be constructed that efficiently populate a Pareto front of accuracy versus complexity and exhibit stable, hierarchical coefficient structures across varying model capacities. Training the new approximation models over only 20% of the data, with the testing performed over the remaining 80%, highlights successful generalization, with the results being robust under bootstrapping. The decomposition effectively approximates the UTCI as a Fourier-like expansion in an orthogonal basis, yielding results near the theoretical optimum in the L2 (least squares) sense.

physics.ao-ph↗

arXiv2025

Maximum Entropy Models for Unimodal Time Series: Case Studies of Universe 25 and St. Matthew Island

We present a maximum entropy modeling framework for unimodal time series: signals that begin at a reference level, rise to a single peak, and return. Such patterns are commonly observed in ecological collapse, population dynamics, and resource depletion. Traditional dynamical models are often inapplicable in these settings due to limited or sparse data, frequently consisting of only a single historical trajectory. In addition, standard fitting approaches can introduce structural bias, particularly near the mode, where most interpretive focus lies. Using the maximum entropy principle, we derive a least-biased functional form constrained only by minimal prior knowledge, such as the starting point and estimated end. This leads to analytically tractable and interpretable models. We apply this method to the collapse of the Universe 25 mouse population and the reindeer crash on St. Matthew Island. These case studies demonstrate the robustness and flexibility of the approach in fitting diverse unimodal time series with minimal assumptions. We also conduct a cross-comparison against established models, including the Richards, Skewnormal, and Generalized Gamma functions. While models typically fit their own generated data best, the maximum entropy models consistently achieve the lowest off-diagonal root-mean-square losses, indicating superior generalization. These results suggest that maximum entropy methods provide a unifying and efficient alternative to mechanistic models when data is limited and generalization is essential.

stat.AP↗

arXiv2025

Black Holes as Non-Abelian Anyon Condensates: Implications for the Information Paradox

We propose a black-hole model in which the would-be horizon is replaced by a thin, topologically ordered timelike shell of condensed non-Abelian anyons surrounding a regular, topologically trivial vacuum interior. The transition is modeled as an effective bosonization of the underlying matter, producing a $(2+1)$-dimensional many-body phase in which area is the natural extensive variable. The shell microstates form a finite constrained fusion Hilbert space that reproduces the Bekenstein--Hawking entropy. The associated discrete area and mass spectra yield logarithmic and inverse-area thermodynamic corrections. Classical equipartition of coarse-grained shell modes recovers the Hawking temperature and motivates a quadratic collective Hamiltonian whose canonical entropy reproduces the leading and logarithmic terms. Matching these descriptions relates the collective mode number to the quantum dimension and points to candidate anyon theories. We use conformal gravity as an effective high-curvature description of the transition region. The condensate can persist as a Planck-thick ultraviolet remnant within a spacetime well described by Einstein gravity at larger scales. The conformal field equations admit local nonsingular matching between the vacuum interior and a Schwarzschild-like exterior, while the leading radial dynamics admit a conditionally stable near-horizon branch with a finite constitutive threshold, unlike the divergent near-horizon response of the corresponding Israel shell in general relativity. Information remains encoded nonlocally in fusion channels, allowing radiation through shell-state transitions without bulk trans-horizon entanglement or an independent holographic microscopic description. Strong absorption suppresses an equilibrium interior radiation bath and conventional surface-emission signatures, while residual reflectivity can generate gravitational-wave echoes.

gr-qc↗

arXiv2023

Planetary Surface Temperatures from First Principles: Geometric Insights into Energy Balance and Implications for Habitable Exoplanets

A previously overlooked relation governing planetary surface temperatures in terms of solar irradiance and top-of-atmosphere Bond albedo is identified. It reproduces the observed climates of Venus, Earth, and Titan, predicts condensation-level temperatures in the gas giants Jupiter, Saturn, Uranus, and Neptune, and extends naturally to rocky planets and large moons with substantial atmospheres. The relation encodes global energy conservation and highlights Bond albedo as a key bulk radiative constraint. Its central result is an empirical proportionality between Bond albedo and the fraction of outgoing longwave radiation returned downward by the atmosphere, termed the inner albedo. A geometric argument based on local beam-aligned parabolic wavefronts provides a rationale for a coefficient linked to the parabolic constant. Compared with classical one- or multi-layer models, the formulation achieves strong agreement using directly measurable quantities and no planet-by-planet tuning. Applied to exoplanets, it yields first-order estimates of equilibrium surface conditions across the habitable zone, suggesting that a substantial part of planetary temperature structure may be constrained by a simple relation among bulk radiative observables.

physics.ao-ph↗

arXiv2022

A Master Equation for Power Laws

We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson's law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value. In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log-log plots in the frequency and rank distributions.

cond-mat.stat-mech↗

arXiv2017

Topology-dependent rationality and quantal response equilibria in structured populations

Given that the assumption of perfect rationality is rarely met in the real world, we explore a graded notion of rationality in socioecological systems of networked actors. We parametrize an actors' rationality via their place in a social network and quantify system rationality via the average Jensen-Shannon divergence between the games Nash and logit quantal response equilibria. Previous work has argued that scale-free topologies maximize a system's overall rationality in this setup. Here we show that while, for certain games, it is true that increasing degree heterogeneity of complex networks enhances rationality, rationality-optimal configurations are not scale-free. For the Prisoner's Dilemma and Stag Hunt games, we provide analytic arguments complemented by numerical optimization experiments to demonstrate that core-periphery networks composed of a few dominant hub nodes surrounded by a periphery of very low degree nodes give strikingly smaller overall deviations from rationality than scale-free networks. Similarly, for the Battle of the Sexes and the Matching Pennies games, we find that the optimal network structure is also a core-periphery graph but with a smaller difference in the average degrees of the core and the periphery. These results provide insight on the interplay between the topological structure of socioecological systems and their collective cognitive behavior, with potential applications to understanding wealth inequality and the structural features of the network of global corporate control.

physics.soc-ph↗

arXiv2013

Large-volume results in SU(2) with adjoint fermions

Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, and extrapolate to thermodynamic limit when possible.

hep-lat↗