Coarse-graining of cellular automata, emergence, and the predictability of complex systems

Quasiequilibrium multistate cellular automata

In our effort to tackle the problem of letting nontrivial interactions, thermodynamic equilibrium, and full synchronicity coexist, and in the hope of reviving interest in cellular automata as promising tools for the quantitative, large-scale investigation of multiparticle systems, we built a fully synchronous cellular automaton rule for the simulation of occupancy-based lattice systems with multistate cells and neighboring interactions. The core of this rule, which constitutes an actual synchronous sampling scheme, is a negotiation stage; it produces cell occupancy distributions in very good agreement with their sequential Monte Carlo counterparts, and it satisfies a cellwise detailed balance principle thanks to the use of "mixed" intermediate states that allow for the computation of locally averaged acceptance probabilities. We took a square lattice (but the rule itself is not bound by dimensionality) as a basis for comparison with sequential Monte Carlo for showing that this synchronous rule leads to quasiequilibrium; the fulfillment of cellwise detailed balance is shown through results obtained for a small one-dimensional system, where the transition matrix could be computed exactly.

Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.

Fate of Duplicated Neural Structures

Statistical physics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under specific conditions, self-replicating and computationally complex patterns become favored, yielding life, cognition, and Darwinian evolution. Neurons and neural circuits sit at a crossroads between statistical physics, computation, and (through their role in cognition) natural selection. Can we establish a statistical physics of neural circuits? Such theory would tell what kinds of brains to expect under set energetic, evolutionary, and computational conditions. With this big picture in mind, we focus on the fate of duplicated neural circuits. We look at examples from central nervous systems, with stress on computational thresholds that might prompt this redundancy. We also study a naive cost-benefit balance for duplicated circuits implementing complex phenotypes. From this, we derive phase diagrams and (phase-like) transitions between single and duplicated circuits, which constrain evolutionary paths to complex cognition. Back to the big picture, similar phase diagrams and transitions might constrain I/O and internal connectivity patterns of neural circuits at large. The formalism of statistical physics seems to be a natural framework for this worthy line of research.

Criticality in Pareto Optimal Grammars?

What are relevant levels of description when investigating human language? How are these levels connected to each other? Does one description yield smoothly into the next one such that different models lie naturally along a hierarchy containing each other? Or, instead, are there sharp transitions between one description and the next, such that to gain a little bit accuracy it is necessary to change our framework radically? Do different levels describe the same linguistic aspects with increasing (or decreasing) accuracy? Historically, answers to these questions were guided by intuition and resulted in subfields of study, from phonetics to syntax and semantics. Need for research at each level is acknowledged, but seldom are these different aspects brought together (with notable exceptions). Here, we propose a methodology to inspect empirical corpora systematically, and to extract from them, blindly, relevant phenomenological scales and interactions between them. Our methodology is rigorously grounded in information theory, multi-objective optimization, and statistical physics. Salient levels of linguistic description are readily interpretable in terms of energies, entropies, phase transitions, or criticality. Our results suggest a critical point in the description of human language, indicating that several complementary models are simultaneously necessary (and unavoidable) to describe it.

Self-referential basis of undecidable dynamics: From the Liar paradox and the halting problem to the edge of chaos

In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of Gödel's proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of Gödel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.

Local free energies for the coarse-graining of adsorption phenomena: The interacting pair approximation

We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly and for a system of Lennard-Jones particles under the effect of a static confining field.

Predicting financial market crashes using ghost singularities

We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of that system coupled with standard multiplicative noise rationalises the log-periodic power law singularity pattern documented in many historical financial bubbles. The notion of ‘ghosts of finite-time singularities’ is introduced and used to estimate the end of an evolving bubble, using finite-time singularities of an approximate normal form near the bifurcation point. We test the forecasting skill of this method on different stochastic price realisations and compare with Monte Carlo simulations of the full system. Remarkably, the approximate normal form is significantly more precise and less biased. Moreover, the method of ghosts of singularities is less sensitive to the noise realisation, thus providing more robust forecasts.

Critical dynamics in host-pathogen systems

Host-pathogen interactions provide a fascinating example of two or more active genomes directly exerting mutual influence upon each other. These encounters can lead to multiple outcomes from symbiotic homeostasis to mutual annihilation, undergo multiple cycles of latency and lysogeny, and lead to coevolution of the interacting genomes. Such systems pose numerous challenges but also some advantages to modeling, especially in terms of functional, mathematical genome representations. The main challenges for the modeling process start with the conceptual definition of a genome for instance in the case of host-integrated viral genomes. Furthermore, hardly understood influences of the activity of either genome on the other(s) via direct and indirect mechanisms amplify the needs for a coherent description of genome activity. Finally, genetic and local environmental heterogeneities in both the host's cellular and the pathogen populations need to be considered in multiscale modeling efforts. We will review here two prominent examples of host-pathogen interactions at the genome level, discuss the current modeling efforts and their shortcomings, and explore novel ideas of representing active genomes which promise being particularly adapted to dealing with the modeling challenges posed by host-pathogen interactions.

Dichotomy in the definition of prescriptive information suggests both prescribed data and prescribed algorithms: biosemiotics applications in genomic systems

The fields of molecular biology and computer science have cooperated over recent years to create a synergy between the cybernetic and biosemiotic relationship found in cellular genomics to that of information and language found in computational systems. Biological information frequently manifests its "meaning" through instruction or actual production of formal bio-function. Such information is called Prescriptive Information (PI). PI programs organize and execute a prescribed set of choices. Closer examination of this term in cellular systems has led to a dichotomy in its definition suggesting both prescribed data and prescribed algorithms are constituents of PI. This paper looks at this dichotomy as expressed in both the genetic code and in the central dogma of protein synthesis. An example of a genetic algorithm is modeled after the ribosome, and an examination of the protein synthesis process is used to differentiate PI data from PI algorithms.

Network models in drug discovery and regenerative medicine

Network motifs and modelling paradigms are attracting increasing attention as modelling tools in drug design and development, and in regenerative medicine. There is a gradual but inexorable convergence between these hitherto disparate disciplines. This review summarizes some very recent work in these areas, leading to an understanding of the complementary roles networks play and factors driving this convergence: network paradigms can be excellent ways of modelling and understanding drug molecules and their action, an understanding of the robustness and vulnerabilities of biological targets may improve the efficacy of drug design and discovery, drug design has an increasingly large role to play in directing stem cell properties, stem cell regulatory networks can be modelled in useful ways using network models at a reasonable level of scale, and the network tools of drug design are also very useful for the design of biomaterials used in regenerative medicine.