Related papers: On the chaotic behavior of the Primal--Dual Affine…
In this paper we study the problem of learning a shallow artificial neural network that best fits a training data set. We study this problem in the over-parameterized regime where the number of observations are fewer than the number of…
In this paper, we study the chaotic behavior of a discrete-time linear inclusion.
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
Saddle-point or primal-dual methods have recently attracted renewed interest as a systematic technique to design distributed algorithms which solve convex optimization problems. When implemented online for streaming data or as dynamic…
In this note we will discuss the notion of robust chaos, and show that (i) there are natural one-parameter families with robust chaos and (ii) hyperbolicity is dense within generic one-parameter families (and so these families are not…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Designing chaotic maps with complex dynamics is a challenging topic. This paper introduces the nonlinear chaotic processing (NCP) model, which contains six basic nonlinear operations. Each operation is a general framework that can use…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…
For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit…
Software for the resolution of certain kind of problems, those that rate high in the Stringent Performance Objectives adjustment factor (IFPUG scheme), can be described using a combination of game theory and autonomous systems. From this…
Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though…
Chaotic logic gates or `chaogates' are a promising mixed-signal approach to designing universal computers. However, chaotic systems are exponentially sensitive to small perturbations, and the effects of noise can cause chaotic computers to…
In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
We investigate primal gradient method with l1-norm and conditional gradient method (both methods are non accelerated). We show that these methods can outperform well known accelerated approaches for some classes of sparse quadratic…
In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for…
We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points.…