The Surprising Ease of Finding Optimal Solutions for Controlling Nonlinear Phenomena in Quantum and Classical Complex Systems

This Perspective addresses the often observed surprising ease of achieving optimal control of nonlinear phenomena in quantum and classical complex systems. The circumstances involved are wide-ranging, with scenarios including manipulation of atomic scale processes, maximization of chemical and material properties or synthesis yields, Nature's optimization of species' populations by natural selection, and directed evolution. Natural evolution will mainly be discussed in terms of laboratory experiments with microorganisms, and the field is also distinct from the other domains where a scientist specifies the goal(s) and oversees the control process. We use the word "control" in reference to all of the available variables, regardless of the circumstance. The empirical observations on the ease of achieving at least good, if not excellent, control in diverse domains of science raise the question of why this occurs despite the generally inherent complexity of the systems in each scenario. The key to addressing the question lies in examining the associated control landscape, which is defined as the optimization objective as a function of the control variables that can be as diverse as the phenomena under consideration. Controls may range from laser pulses, chemical reagents, chemical processing conditions, out to nucleic acids in the genome and more. This Perspective presents a conjecture, based on present findings, that the systematics of readily finding good outcomes from controlled phenomena may be unified through consideration of control landscapes with the same common set of three underlying assumptions─the existence of an optimal solution, the ability for local movement on the landscape, and the availability of sufficient control resources─whose validity needs assessment in each scenario. In practice, many cases permit using myopic gradient-like algorithms while other circumstances utilize algorithms having some elements of stochasticity or introduced noise, depending on whether the landscape is locally smooth or rough. The overarching observation is that only relatively short searches are required despite the common high dimensionality of the available controls in typical scenarios.

Hitting Times of Some Critical Events in RNA Origins of Life

Can a replicase be found in the vast sequence space by random drift? We partially answer this question through a proof-of-concept study of the times of occurrence (hitting times) of some critical events in the origins of life for low-dimensional RNA sequences using a mathematical model and stochastic simulation studies from Python software. We parameterize fitness and similarity landscapes for polymerases and study a replicating population of sequences (randomly) participating in template-directed polymerization. Under the ansatz of localization where sequence proximity correlates with spatial proximity of sequences, we find that, for a replicating population of sequences, the hitting and establishment of a high-fidelity replicator depends critically on the polymerase fitness and sequence (spatial) similarity landscapes and on sequence dimension. Probability of hitting is dominated by landscape curvature, whereas hitting time is dominated by sequence dimension. Surface chemistries, compartmentalization, and decay increase hitting times. Compartmentalization by vesicles reveals a trade-off between vesicle formation rate and replicative mass, suggesting that compartmentalization is necessary to ensure sufficient concentration of precursors. Metabolism is thought to be necessary to replication by supplying precursors of nucleobase synthesis. We suggest that the dynamics of the search for a high-fidelity replicase evolved mostly during the final period and, upon hitting, would have been followed by genomic adaptation of genes and to compartmentalization and metabolism, effecting degree-of-freedom gains of replication channel control over domain and state to ensure the fidelity and safe operations of the primordial genetic communication system of life.

Common foundations of optimal control across the sciences: evidence of a free lunch

A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favourable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide-ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond the laboratory set-up overhead). The full scope and implications of this observed common control behaviour pose an open question for assessment in further work.This article is part of the themed issue 'Horizons of cybernetical physics'.

Exploring experimental fitness landscapes for chemical synthesis and property optimization

The topology of experimental fitness landscapes for chemical optimization objectives is assessed through svr-based HDMR modeling.