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Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
A Boolean network is a mapping $f :\{0,1\}^n \to \{0,1\}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
Techniques for coordination of multi-agent systems are vast and varied, often utilizing purpose-built solvers or controllers with tight coupling to the types of systems involved or the coordination goal. In this paper, we introduce a…
Computers are nonlinear dynamical systems that exhibit complex and sometimes even chaotic behavior. The models used in the computer systems community, however, are linear. This paper is an exploration of that disconnect: when linear models…
Building upon the concepts and mechanisms used for the development in Moving Points Algorithm, we will now explore how non linear decision boundaries can be developed for classification tasks. First we will look at the classification…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…
This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The…
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…
Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. We investigate what sort of self-stabilising…
It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the…
We consider linear dynamical systems with quadratic output. We first define the two transfer functions, a single-variable and a multivariate one, that fully describe the dynamics of these special nonlinear systems. Then, using the samples…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…
We propose a characteristic representation ofone-dimensional and 2-state, 3-neighbor cellular automaton rules, which describes an effective form of each rule after many time steps. Simulated results of the representation show that complex…
Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but…
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
This paper studies the number conservation property of 1-dimensional non-uniform cellular automata (CAs). In a non-uniform cellular automaton (CA), different cells may follow different rules. The present work considers that the cells follow…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…