Related papers: Time-dependent gradient curves on CAT(0) spaces
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
We provide the set of equations for non-relativistic fluid dynamics on arbitrary, possibly time-dependent spaces, in general coordinates. These equations are fully covariant under either local Galilean or local Carrollian transformations,…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
Time-dependent calculation has been a suitable method to investigate the quantum dynamical processes. In Ref. [1] = [T. Oishi et al., J. of Phys. G 45, 105101 (2018)], we applied this method to the one-dimensional two-fermion tunneling in…
We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a…
Because reinforcement learning suffers from a lack of scalability, online value (and Q-) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman…
We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
Traditional derivation of the material time derivative of volume, surface, and line integrals relies upon the notion of a referential configuration of continuum. Such a notion, however, is artificial and, probably, somewhat misleading in…
In arXiv:2205.02920 a variant of the classical elastic flow for closed curves in $\mathbb{R}^{n}$ was introduced, that is more suitable for numerical purposes. Here we investigate the long-time properties of such evolution demonstrating…
We study stochastic Amari-type neural field equations, which are mean-field models for neural activity in the cortex. We prove that under certain assumptions on the coupling kernel, the neural field model can be viewed as a gradient flow in…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
We prove optimal error bounds for a second order in time finite element approximation of curve shortening flow in possibly higher codimension. In addition, we introduce a second order in time method for curve diffusion. Both schemes are…
We consider the case of a deformable material interface between two immiscible moving media, both of them being magnetiable. The time dependence of the metric at the interface introduces a non linear term, proportional to the mean…
We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function satisfies a suitable convexity condition. These…
A recently proposed schematic model for the non--linear rheology of dense colloidal dispersions is compared to flow curves measured in suspensions that consist of thermosensitive particles. The volume fraction of this purely repulsive model…
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us…
We prove the existence of semiorthogonal decompositions of derived categories of Quot schemes of zero-dimensional quotients on curves in terms of derived categories of symmetric products of curves. The above result is a categorical analogue…
This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…
We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We introduce and discuss three different generators of the flow that transform a linear non-Hermitian operator into a diagonal one. We…