Dualistic geometry of the manifold of higher-order neurons

Abstract Recursive Fractal Genome Function in the geometric mind frame of Tensor Network Theory (TNT) leads through FractoGene to a mathematical unification of physiological and pathological development of neural structure and function as governed by the genome. The cerebellum serves as the best platform for unification of neuroscience and genomics. The matrix of massively parallel neural nets of fractal Purkinje brain cells explains the sensorimotor, multidimensional non-Euclidean coordination by the cerebellum acting as a space-time metric tensor. In TNT, the recursion of covariant sensory vectors into contravariant motor executions converges into Eigenstates composing the cerebellar metric as a Moore-Penrose Pseudo-Inverse. The Principle of Recursion is generalized to genomic systems with the realization that the assembly of proteins from nucleic acids as governed by regulation of coding RNA (cRNA) is a contravariant multi-component functor, where in turn the quantum states of resulting protein structures both in intergenic and intronic sequences are measured in a covariant manner by non-coding RNA (ncRNA) arising as a result of proteins binding with ncDNA modulated by transcription factors. Thus, cRNA and ncRNA vectors by their interference constitute a genomic metric. Recursion through massively parallel neural network and genomic systems raises the question if it obeys the Weyl law of Fractal Quantum Eigenstates, or when derailed, pathologically results in aberrant methylation or chromatin modulation; the root cause of cancerous growth. The growth of fractal Purkinje neurons of the cerebellum is governed by the aperiodical discrete quantum system of sequences of DNA bases, codons and motifs. The full genome is fractal; the discrete quantum system of pyknonlike elements follows the Zipf-Mandelbrot Parabolic Fractal Distribution curve. The Fractal Approach to Recursive Iteration has been used to identify fractal defects causing a cerebellar disease, the Friedreich Spinocerebellar Ataxia -in this case as runs disrupting a fractal regulatory sequence. Massive deployment starts by an open domain collaborative definition of a standard for fractal genome dimension in the embedding spaces of the genome-epigenome-methylome to optimally diagnose cancerous hologenome in the nucleotide, codon or motif-hyperspaces. Recursion is parallelized both by open domain algorithms, and also by proprietary FractoGene algorithms on high performance computing platforms, for genome analytics on accelerated private hybrid clouds with PDA personal interfaces, becoming the mainstay of clinical genomic measures prior and post cancer intervention in hospitals and serve consumers at large as Personal Genome Assistants. References 1

Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations

The new digital economy has renewed interest in how digital agents can innovate. This follows the legacy of John von Neumann dynamical systems theory on complex biological systems as computation. The Gödel-Turing-Post (GTP) logic is shown to be necessary to generate innovation based structure changing Type 4 dynamics of the Wolfram-Chomsky schema. Two syntactic procedures of GTP logic permit digital agents to exit from listable sets of digital technologies to produce novelty and surprises. The first is meta-analyses or offline simulations. The second is a fixed point with a two place encoding of negation or opposition, referred to as the Gödel sentence. It is postulated that in phenomena ranging from the genome to human proteanism, the Gödel sentence is a ubiquitous syntactic construction without which escape from hostile agents qua the Liar is impossible and digital agents become entrained within fixed repertoires. The only recursive best response function of a 2-person adversarial game that can implement strategic innovation in lock-step formation of an arms race is the productive function of the Emil Post [58] set theoretic proof of the Gödel incompleteness result. This overturns the view of game theorists that surprise and innovation cannot be a Nash equilibrium of a game

Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems

This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto a state-space manifold having reduced dimensionality and possessing a Kahler potential of multi-linear form. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given, and methods for quantum state optimization by Dantzig selection are given.Comment: 104 pages, 13 figures, 2 table

Why Are Computational Neuroscience and Systems Biology So Separate?

Despite similar computational approaches, there is surprisingly little interaction between the computational neuroscience and the systems biology research communities. In this review I reconstruct the history of the two disciplines and show that this may explain why they grew up apart. The separation is a pity, as both fields can learn quite a bit from each other. Several examples are given, covering sociological, software technical, and methodological aspects. Systems biology is a better organized community which is very effective at sharing resources, while computational neuroscience has more experience in multiscale modeling and the analysis of information processing by biological systems. Finally, I speculate about how the relationship between the two fields may evolve in the near future