A categorical and Łukasiewicz-Topos framework for Łukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Łukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generaliz...

The singularity of Jacobian happens when we are looking for a root, with multiplicity greater than one, of a system of nonlinear equations. The purpose of this article is two-fold. Firstly, we will present a modification of an existing method that computes roots with known multiplicities. Secondly, will propose the generalization of a family of methods for solving nonlinear equations with unkno...

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear χ(2) and χ(3) frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and two-dimensional slab microcavities exhibiting long lifetimes Q≳104, small modal volumes V≳(λ/2n)3<...

A categorical and Łukasiewicz-Topos framework for Łukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Łukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generaliz...

The variational iteration method (VIM) proposed by Ji-Haun He is a new analytical method tosolve linear and nonlinear equation. In this paper, the Variational Iteration Method (VIM) has been applied for solving Davey-Stewartson equations which arise as higher dimensional generalizations of the Nonlinear Shrodinger (NLS) equation, as well as from physical considerations [1]. Comparison the absol...

The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally nonlinear equality-constrained problems, called neADMM. difficulty neADMM nonconvex subproblems. We provide globally optimal solutions them in two important applications. Experiments on synthetic and real-world datasets ...

Abstract We present a new generalization of the nonlinear variational wave equation. prove existence local, smooth solutions for this system. As limiting case, we recover

Theoretical and computational justiication is given for improved generalization when the training set is learned with less accuracy. The model used for this investigation is a simple linear one. It is shown that learning a training set with a tolerance improves generalization, over zero-tolerance training, for any testing set satisfying a certain closeness condition to the training set. These r...

Within a simple model context, the sensitivity and stability of the thermohaline circulation to finite amplitude perturbations is studied. A new approach is used to tackle this nonlinear problem. The method is based on the computation of the so-called Conditional Nonlinear Optimal Perturbation (CNOP) which is a nonlinear generalization of the linear singular vector approach (LSV). It is shown t...