arXiv subjects

Dima Watkins

Publications and source records attributed to Dima Watkins.

4 recordsLinked to original sources

arXiv2026

A Canonical Lagrangian Formulation of the Two-Dimensional Lotka-Volterra System

Hamiltonian and Lagrangian mechanics are powerful frameworks for analyzing physical systems. Previous work has extended these formalisms to ecological systems, such as the predator-prey Lotka-Volterra (LV) system. In this Article, we derive a canonical Lagrangian for the two-dimensional LV model directly from its Hamiltonian representation. We find that the two-dimensional LV system admits a standard canonical Lagrangian formulation with one degree of freedom and a non-quadratic kinetic structure. This formulation admits a mechanical interpretation in terms of a particle moving in a potential well, where the non-standard kinetic structure produces a position-dependent damping term that can instead act as "revving." The derivation provides a direct connection between predator-prey dynamics and a canonical formulation of mechanical dynamics. As a verification of the construction, we apply Noether's procedure to the explicitly time-independent derived Lagrangian and reveal that the well-known Hamiltonian of the LV system is the corresponding conserved quantity. We also uncover a subtle redundancy associated with the choice of canonical momentum and its identification with the original population variables.

nlin.CD↗

arXiv2026

Differentiable Principal-Value Inversion for Neural-Network Extraction of Generalized Parton Distributions

We present a machine-learning method for the nonparametric extraction of generalized parton distributions (GPDs) from Compton form factors (CFFs) constrained by experimental data. The method addresses the longstanding inverse problem posed by the principal-value (PV) linear integral transform with a singular kernel that relates the charge-conjugation-even (C-even) quark GPD $H^{(+)}$ to the real part of the deeply virtual Compton scattering (DVCS) amplitude. Our approach constructs a differentiable representation of the Quantum Chromodynamics (QCD) PV kernel and embeds it as a fixed, physics-preserving layer inside a neural network that parameterizes the GPD $H^{(+)}(x,ξ,t,Q^{2})$ itself. The model enforces exact oddness in $x$, implements endpoint suppression, and includes curvature-based regularization that stabilizes the inversion in kinematically ill-conditioned regions. A Monte Carlo ensemble of CFFs, obtained from a global neural-network fit to unpolarized DVCS measurements with propagated experimental uncertainties, serves as input to a replica ensemble of GPD networks, yielding a fully probabilistic extraction of $H^{(+)}$ over the phase space. We demonstrate the method using a global determination of $\mathrm{Re}\,\mathcal{H}$ for Jefferson Lab measurements, and present a direct neural-network reconstruction of three-dimensional GPD surfaces $H^{(+)}(x_{0},ξ,t,Q_{0}^{2})$ obtained from experimental CFF inputs. This work establishes a flexible, scalable, and model-independent strategy for extracting multidimensional hadronic structure from current and future DVCS data and other GPD-related processes.

hep-ph↗

arXiv2025

Hyperchaos and complex dynamical regimes in $N$-dimensional neuron lattices

We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and small and large lattices over a wide range of electrical coupling strengths. As the coupling strength is varied, the neurons exhibit a number of complex dynamical regimes, including unsynchronized chaotic spiking, local quasi-bursting, synchronized chaotic bursting, and synchronized hyperchaos. For lattices in higher spatial dimensions, we discover dynamical effects arising from the "destructive interference" of many connected neurons and miniature "phase transitions" from coordinated spiking threshold crossings. In large two- and three-dimensional neuron lattices, we observe emergent dynamics such as local synchronization, quasi-synchronization, and lag synchronization. These results illustrate the rich dynamics that emerge from coupled neurons in multiple spatial dimensions, highlighting how dimensionality, connectivity, and heterogeneity critically shape the collective behavior of neuronal systems.

nlin.CD↗

arXiv2024

Baryon number violation involving tau leptons

Baryon number violation is our most sensitive probe of physics beyond the Standard Model, especially through the study of nucleon decays. Angular momentum conservation requires a lepton in the final state of such decays, kinematically restricted to electrons, muons, or neutrinos. We show that operators involving taus, which are at first sight too heavy to play a role in nucleon decays, still lead to clean nucleon decay channels with tau neutrinos. While many of them are already constrained from existing two-body searches such as $p\to π^+ν$, other operators induce many-body decays such as $p \to ηπ^{+} \barν_τ$ and $n\to K^+ π^-ν_τ$ that have never been searched for.

hep-ph↗