We employ a variational neural annealing approach for solving large-scale constrained portfolio optimization problems, mapped onto classical Ising-like Hamiltonians, and study its performance under finite annealing times. The method enables efficient exploration of high-dimensional feasible spaces and achieves competitive solutions on standard financial indices. To characterize the underlying optimization dynamics, we analyze the decay of the residual energy as a function of annealing steps and observe a power-law behavior for fixed problem size. Extending this analysis across different portfolio sizes, we examine whether the optimization dynamics are consistent with a dynamical finite-size scaling form and find that the residual energy data collapse onto a single scaling curve within the studied range. This scaling analysis yields an effective annealing-time exponent that quantifies how computational effort grows with problem size. Our results demonstrate that finite-size scaling concepts provide a useful framework for understanding and forecasting the performance of neural annealing-based optimization methods in realistic, constrained settings.
We investigate linear perturbations of an incompressible, weakly collisional, anisotropic plasma in the low frequency limit using an extended 16-moment fluid description that retains parallel and perpendicular heat fluxes. We identify a class of linear perturbations associated with a conserved thermomechanic invariant, a time independent, aperiodic structure involving coupled perturbations of heat fluxes, velocity, and magnetic field. In the standard CGL limit, where heat fluxes are neglected, no direct analog of this invariant exists. Retaining heat flux dynamics alters the linear structure of the system promoting third order velocity moments to autonomous variables and gives rise to a thermomechanic mode with coupled thermal, kinetic, and magnetic components. The associated perturbations are inherently localized, favoring compact, filamentary aperiodic structures. The thermomechanic invariant reveals a stationary sector of collisionless anisotropic plasma dynamics, characterized by a fixed algebraic polarization that enforces time independent relations among the relevant perturbation fields.
The stationary equilibria of N point vortices in a rectangular domain with doubly periodic boundary conditions offer a foundational framework for understanding the stationary lattices of coherent vortex structures. In this paper, we obtain new continuous families of these lattices. These solutions are constructed using methods from complex analysis including conformal mapping and special function theory. First, the doubly periodic rectangular domain is mapped to an annulus by a conformal mapping. Next, a loxodromic function is used to construct a solution consisting of stationary point vortices embedded in a smooth background vorticity field which is exponentially related to the stream function (Liouville-type background vorticity). This solution contains three continuous parameters, and by considering the limits of one of these parameters, a stationary point vortex solution without a background vorticity field is constructed. Until now, stationary point vortex solutions under doubly periodic boundary conditions have been mainly symmetric. Varying the other two parameters noted above, we generate families of asymmetric stationary point vortex lattices.
Extracellular ion concentrations directly influence neuronal excitability, synaptic transmission, and the generation of electrical signals. Capturing the ionic dynamics is essential for modeling both healthy and pathophysiological brain function. Here we explore how variations in ion concentration in the extracellular space affect the generation and propagation of traveling fronts of activity in cortical tissue. To this end, we develop a neural field model in which neuronal excitability is modulated by the local extracellular ionic concentration. Using an interface dynamics approach, we derive an analytic expression for the speed of propagating activity fronts. We demonstrate that increasing the ionic diffusion coefficient leads to a reduction in front speed. In addition, analysis of stationary bump solutions reveals that increases in the diffusion rate reduces the size of a region of high activity required to initiate a propagating front.
The critical behavior of the equilibrium Ising model, famously governed by the Wilson-Fisher universality class (UC), is a cornerstone of statistical physics. A natural question is whether its properties are modified when the interacting spins are allowed to move. This can be explored within the framework of active motility by, e.g., prescribing that the spins self-propel along the direction of their orientation. In such a system, the spin number density necessarily constitutes a soft hydrodynamic mode and can therefore modify the scaling behavior. In this letter, we show that this is indeed the case in a critical active Ising model where density impedes the system's collective motion. Using a perturbative dynamic renormalization group analysis at a one-loop level, We identify six UCs, including three previously unidentified ones, one of which supersedes the Wilson-Fisher UC as the generic UC governing the critical behavior.
