14 citations · 47 across the 12 of their papers we have counts for
12 papers
Integrable Elasticity via Neural Demand Potentials
Carlos Heredia, Daniel Roncel
We propose the Integrable Context-Dependent Demand Network (ICDN), a demand-first neural model for multiproduct retail demand. ICDN learns log-demand as a smooth, context-condition…
From Adam to Adam-Like Lagrangians: Second-Order Nonlocal Dynamics
Carlos Heredia
In this paper, we derive an accelerated continuous-time formulation of Adam by modeling it as a second-order integro-differential dynamical system. We relate this inertial nonlocal…
Nonlocal Mechanics
Carlos Heredia, Josep Llosa
We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a (trajectory-based) variational principle and…
Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations
Carlos Heredia
In this paper, we propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms by modeling them as first-order integro-differential equations. W…
Are nonlocal Lagrangian systems fatally unstable?
Carlos Heredia, Josep Llosa
We prove that higher-derivative and genuinely nonlocal Lagrangian systems can be Lyapunov-stable even when their Hamiltonians lack a lower bound. Explicit free and coupled Pais-Uhl…
Nonlocal Lagrangian fields and the second Noether theorem. Non-commutative gauge theory
Carlos Heredia, Josep Llosa
This article focuses on three main contributions. Firstly, we provide an in-depth overview of the nonlocal Lagrangian formalism. Secondly, we introduce an extended version of the s…
Nonlocal Lagrangian formalism
Carlos Heredia
This thesis aims to study nonlocal Lagrangians with a finite and an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for…
Infinite Derivatives vs Integral Operators. The Moeller-Zwiebach Puzzle
Carlos Heredia, Josep Llosa
We study the relationship between integral and infinite-derivative operators. In particular, we examine the operator that appears in the theory of …
Non-local Lagrangian fields: Noether's theorem and Hamiltonian formalism
Carlos Heredia, Josep Llosa
This article aims to study non-local Lagrangians with an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagran…
Infinite-derivative linearized gravity in convolutional form
Carlos Heredia, Ivan Kolář, Josep Llosa +2
This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local. To achieve it, we use the theory of gener…
Non-local Lagrangian Mechanics: Noether theorem and Hamiltonian formalism
Carlos Heredia, Josep Llosa
We study Lagrangian systems with a finite number of degrees of freedom that are non-local in time. We obtain an extension of Noether theorem and Noether identities to this kind of…
Energy-momentum tensor for the electromagnetic field in a dispersive medium as an application of Noether theorem
Carlos Heredia, Josep Llosa
On the basis of a non-local Lagrangian for Maxwell equations in a dispersive medium, the energy-momentum tensor of the field is derived. We obtain the Field equations through varia…