17 citations · 50 across the 17 of their papers we have counts for
19 papers
On the Optimal Laplacian Jordan Structure for Synchronizability
Luca Dieci, Cinzia Elia, Alessandro Pugliese
In this work, for a network of differential equations with a prescribed graph structure, our goal is to show how to select the Laplacian of the network in order to obtain the most…
Generic Cuspidal Points and Their Localization
Luca Dieci, Alessandro Pugliese
In this work we consider generic coalescing of eigenvalues of smooth complex valued matrix functions depending on 2 parameters. We call generic cuspidal points the parameter values…
On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion
Luca Dieci, Cinzia Elia, Alessandro Pugliese
In this work, motivated by the study of stability of the synchronous orbit of a network with tridiagonal Laplacian matrix, we first solve an inverse eigenvalue problem which builds…
SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters
Luca Dieci, Alessandro Pugliese
In this work we consider generic losses of rank for complex valued matrix functions depending on two parameters. We give theoretical results that characterize parameter regions whe…
Forming a symmetric, unreduced, tridiagonal matrix with a given spectrum
Luca Dieci, Alessandro Pugliese
Given a set of distinct real numbers, our goal is to form a symmetric, unreduced, tridiagonal, matrix with those numbers as eigenvalues. We give an algorithm which is a stable…
Solving Semi-Discrete Optimal Transport Problems: star shapedeness and Newton's method
Luca Dieci, Daniyar Omarov
In this work, we propose a novel implementation of Newton's method for solving semi-discrete optimal transport (OT) problems for cost functions which are a positive combination of…
On the Injectivity of Mean Value Mapping between Convex Quadrilaterals
Luca Dieci, Fabio V. Difonzo
We prove that Mean Value mapping between convex quadrilaterals is injective, affirmatively proving a conjecture stated in M. S. Floater and J. Kosinka, On the injectivity of Wachsp…
Master stability function for piecewise smooth networks
L. Dieci, C. Elia
We consider a network of identical piecewise smooth systems that synchronizes on the manifold given by a periodic orbit of a single agent. We explicitly characterize the fundamenta…
Takagi factorization of matrices depending on parameters and locating degeneracies of singular values
Luca Dieci, Alessandra Papini, Alessandro Pugliese
In this work we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the…
A continuation multiple shooting method for Wasserstein geodesic equation
Jianbo Cui, Luca Dieci, Haomin Zhou
In this paper, we propose a numerical method to solve the classic -optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continu…
Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters
Luca Dieci, Alessandra Papini, Alessandro Pugliese
In this work, we consider symmetric positive definite pencils depending on two parameters. That is, we are concerned with the generalized eigenvalue problem , where …
Time Discretizations of Wasserstein-Hamiltonian Flows
Jianbo Cui, Luca Dieci, Haomin Zhou
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the -Wasserstein metric. Based on discrete optimal transport theory, several…
A study of deformation localization in nonlinear elastic lattices
Raj Kumar Pal, Federico Bonetto, Luca Dieci +1
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete h…
Double Descent and Intermittent Color Diffusion for Global Optimization and landscape exploration
Luca Dieci, Manuela Manetta, Haomin Zhou
In this work, we present a method to explore the landscape of a smooth potential in the search of global minimizers,combining a double-descent technique and a basin-escaping techni…
General auction method for real-valued optimal transport
J. D. Walsh, Luca Dieci
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algor…
The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation
Luca Dieci, J. D. Walsh
We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduc…
Entropy dissipation semi-discretization schemes for Fokker-Planck equations
Shui-Nee Chow, Luca Dieci, Wuchen Li +1
We propose a new semi-discretization scheme to approximate nonlinear Fokker-Planck equations, by exploiting the gradient flow structures with respect to the 2-Wasserstein metric. W…
Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?
Luca Dieci, Cinzia Elia
We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold . Within the class of Filippov solutions, if is attractive, one should e…
Orthonormal integrators based on Householder and Givens transformations
Luca Dieci, Erik S. Van Vleck
We carry further our work [DV2] on orthonormal integrators based on Householder and Givens transformations. We propose new algorithms and pay particular attention to appropriate im…