Synchronous Subsequentiality and Approximations to Undecidable Problems

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an infinite automaton, then most decision problems (apart from membership) still remain undecidable (as they are for synchronous and subsequential rational relations), but on the positive side, they can be approximated in a meaningful way we make precise in this paper. This might make the class useful for some applications, and might serve to establish an intermediate position in the trade-off between issues of expressivity and (un)decidability.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Towards Understanding the Origin of Genetic Languages

Molecular biology is a nanotechnology that works--it has worked for billions of years and in an amazing variety of circumstances. At its core is a system for acquiring, processing and communicating information that is universal, from viruses and bacteria to human beings. Advances in genetics and experience in designing computers have taken us to a stage where we can understand the optimisation principles at the root of this system, from the availability of basic building blocks to the execution of tasks. The languages of DNA and proteins are argued to be the optimal solutions to the information processing tasks they carry out. The analysis also suggests simpler predecessors to these languages, and provides fascinating clues about their origin. Obviously, a comprehensive unraveling of the puzzle of life would have a lot to say about what we may design or convert ourselves into.Comment: (v1) 33 pages, contributed chapter to "Quantum Aspects of Life", edited by D. Abbott, P. Davies and A. Pati, (v2) published version with some editin

Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics

Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body physics by using tools that physicists have devised to analyze comparable hierarchies in other fields of science. We focus on a mesoscopic level that offers a multi-step pathway between the microscopic functions of neurons and the macroscopic functions of brain systems revealed by hemodynamic imaging. We use electroencephalographic (EEG) records collected from high-density electrode arrays fixed on the epidural surfaces of primary sensory and limbic areas in rabbits and cats trained to discriminate conditioned stimuli (CS) in the various modalities. High temporal resolution of EEG signals with the Hilbert transform gives evidence for diverse intermittent spatial patterns of amplitude (AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize in the beta and gamma ranges at near zero time lags over long distances. The dominant mechanism for neural interactions by axodendritic synaptic transmission should impose distance-dependent delays on the EEG oscillations owing to finite propagation velocities. It does not. EEGs instead show evidence for anomalous dispersion: the existence in neural populations of a low velocity range of information and energy transfers, and a high velocity range of the spread of phase transitions. This distinction labels the phenomenon but does not explain it. In this report we explore the analysis of these phenomena using concepts of energy dissipation, the maintenance by cortex of multiple ground states corresponding to AM patterns, and the exclusive selection by spontaneous breakdown of symmetry (SBS) of single states in sequences.Comment: 31 page

Educational neuroscience: Neural structure-mapping and the promise of oscillations

A critical goal for educational neuroscience is to specify causal developmental mechanisms of learning. In-depth understanding of neural information coding and transmission should enable understanding of how sensory systems build the cognitive systems critical for education–language, attention, memory-over developmental time. Cortical oscillatory encoding processes may offer mechanistic insights into how developmental trajectories unfold. All educators are familiar with children who show mastery of taught information one week, yet subsequently appear to lose it. Oscillatory research shows that sensory information that arrives out of phase with ongoing oscillations does not reach awareness, while complex combinations of bottom-up and top-down phase-phase and phase-power relations enable context and prior knowledge to influence current performance. Oscillatory studies of language are used to illustrate the promise of oscillations research for education.MRC (G0902375)This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.cobeha.2016.05.011

Making proofs without Modus Ponens: An introduction to the combinatorics and complexity of cut elimination

This paper is intended to provide an introduction to cut elimination which is accessible to a broad mathematical audience. Gentzen's cut elimination theorem is not as well known as it deserves to be, and it is tied to a lot of interesting mathematical structure. In particular we try to indicate some dynamical and combinatorial aspects of cut elimination, as well as its connections to complexity theory. We discuss two concrete examples where one can see the structure of short proofs with cuts, one concerning feasible numbers and the other concerning "bounded mean oscillation" from real analysis

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

Toda joia, toda beleza! Finding what is left in the margins or regime collisions: A pluralist take on managerialism

This paper has two authors, two titles and is written in the form of a dialogue,rather than conveying a unitary voice, as one would instead expect of a coauthored paper. The reason for this is that the articulation of the authors' disagreement, despite the identification of each of them with “the left”, is precisely the object of inquiry. After briefly introducing the problem on which the authors’ discussion takes place, namely regime collisions, and the clash of approaches that are available to (decide whether to) deal with them, a dialogue follows, in which the authors’ voices are clearly separated as they discuss the specific issue of the measurement of quality as a (managerialist) proposal to “solve” regime collisions, and contrast that to more openly politicised views of approaching regime collisions. In the end, the main features of such discussion are examined in such a way as to bring forth the peculiar self-consciousness that pluralist spaces give rise to, weakening and downsizing every point of view that appoints itself as the “higher” vantage point from which to describe the world and enumerate problems, and stimulating a constant oscillation between perspectives. This commitment to a pluralistic confrontation and the ensuing hybridization of perspectives is, we argue, at the heart of the idea of “the left” which we both identify with