Related papers: Local, Smooth, and Consistent Jacobi Set Simplific…
Jacobi sets are an important tool to study the relationship between functions. Defined as the set of all points where the function's gradients are linearly dependent, Jacobi sets extend the notion of critical point to multifields. In…
The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a…
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…
A trivializing map is a field transformation whose Jacobian determinant exactly cancels the interaction terms in the action, providing a representation of the theory in terms of a deterministic transformation of a distribution from which…
In recent research, the parallel performances of sweeping-type algorithms for high-frequency time-harmonic wave problems have been improved by departing from standard layer-type domain decomposition and introducing a new sweeping strategy…
We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse…
We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets…
Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set…
We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a…
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…
We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common…
By using the Hadamard matrix product concept, this paper introduces two generalized matrix formulation forms of numerical analogue of nonlinear differential operators. The SJT matrix-vector product approach is found to be a simple,…
Spectral differentiations are basic ingredients of spectral methods. In this work, we analyze the pointwise rate of convergence of spectral differentiations for functions containing singularities and show that the deteriorations of the…
The Jacobi set is a useful descriptor of mutual behavior of functions defined on a common domain. We introduce the piecewise linear Jacobi set for general vector fields on simplicial complexes. This definition generalizes the definition of…
Based on the ideas of Optimal Control, we introduce the new basic characteristic of a bracket generating distribution, the Jacobi symbol. In contrast to the classical Tanaka symbol, the set of Jacobi symbols is discrete and classifiable. We…
Easy lowering local minima, after introducing valley functions on smooth manifolds gives, without gluing technicities, "M. Morse's lemma's" canonical form, moving critical values and eliminating pair of critical points theorems, reducing…
We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological…
Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multi-field data, topological analysis requires simultaneous advances both mathematically…
The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the…
Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…