Related papers: Calculus of variations on hypergraphs
MaxCal is a variational principle that can be used to infer distributions of paths in the phase space of dynamical systems. It has been successfully applied to different areas of classical physics, in particular statistical mechanics in and…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when…
We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations,…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…
We consider the numerical construction of minimal Lagrangian graphs, which is related to recent applications in materials science, molecular engineering, and theoretical physics. It is known that this problem can be formulated as an…
A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the Lagrangian is replaced by a section of a…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions between totally disconnected spaces). We study generalized…
We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Previous attempts to analyse when these are minima ex- ist, but mainly…
We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also…
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the…
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…