Related papers: Open-Loop Linearization of Non-Linear Discrete Inp…
A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided. In the particular case of second order linear and nonlinear PDEs and systems of PDEs, necessary and sufficient conditions…
Nonlinear computation is essential for various information processing tasks. Optical implementations are attractive because passive light propagation can manipulate high-dimensional signals with extreme throughput and parallelism; yet…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
A widely established set of unsupervised node embedding methods can be interpreted as consisting of two distinctive steps: i) the definition of a similarity matrix based on the graph of interest followed by ii) an explicit or implicit…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
This paper deals with the problem of designing a distributed fault detection and isolation algorithm for nonlinear large-scale systems that are subjected to multiple fault modes. To solve this problem, a network of communicating detection…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
Finding a provably correct subquadratic synchronization algorithm for many filesystem replicas is one of the main theoretical problems in Operational Transformation (OT) and Conflict-free Replicated Data Types (CRDT) frameworks. Based on…
Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
In this work, the synchronization problem of a master-slave system of autonomous ordinary differential equations (ODEs) is considered. Here, the systems are, chaotic with a nonlinearity represented by a piecewise linear function,…