Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

The specific antigen-binding cell populations of individual fetal mouse spleens: repertoire composition, size, and genetic control

In order to analyze the genetic and physiological basis of controls affecting the generation of the repertoire of antigen-binding cells in fetal mice, we have measured the numbers of spleen cells specific for each of four antigens as a function of the total numbers of nucleated and Ig-bearing cells in inbred, hybrid, and random bred fetuses. For each of the two inbred strains BALB/c and CBA/J, the proportion of nucleated cells specific for a given antigen was the same for all individuals of the strain at the 18th day of gestation. The proportion did vary from antigen to antigen, however, and for each antigen the proportion of specific cells observed in CBA/J fetuses was approximately four times that observed in BALB/c fetuses. This difference appeared to be due to a difference between the two strains in the relative size of the repertoire of antigen-binding spleen cells at this stage of development, inasmuch as the frequency of Ig-bearing spleen cells in CBA/J fetuses was likewise approximately four times that observed in BALB/c fetuses. In random bred Swiss-L fetal mice at the 18th day of gestation, the proportion of cells specific for a given antigen varied significantly from one individual to the next. The ratio of proportions of the two antigens observed was constant from individual to individual, however, and this constant ratio differed significantly from the ratio observed for the same two antigens in fetal BALB/c and CBA/J inbred mice. These data suggest that the ontogeny of the repertoire of antigen-binding cells in fetal mice is subject to at least two independent sets of controls, one affecting the relative size of the repertoire in the spleen, and the other affecting the distribution of antigen-binding specificities within that repertoire. Analysis of repertoire size and composition in the spleens of hybrid fetuses confirmed the observation that the two parameters are controlled independently, and suggested further that the control of repertoire size in these fetuses is due to the action of one or a few closely-linked autosomal Mendelian genes. These data are consistent with models for the origin of antibody diversity in which the genes coding for the full repertoire of antibodies are generated somatically from a small number of germ-line genes early in development and in the absence of any strong positive or negative selection with respect to antigenic specificity

Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems

A generic mechanism - networked buffering - is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems. \ud \u

Degeneracy: a link between evolvability, robustness and complexity in biological systems

A full accounting of biological robustness remains elusive; both in terms of the mechanisms by which robustness is achieved and the forces that have caused robustness to grow over evolutionary time. Although its importance to topics such as ecosystem services and resilience is well recognized, the broader relationship between robustness and evolution is only starting to be fully appreciated. A renewed interest in this relationship has been prompted by evidence that mutational robustness can play a positive role in the discovery of adaptive innovations (evolvability) and evidence of an intimate relationship between robustness and complexity in biology. This paper offers a new perspective on the mechanics of evolution and the origins of complexity, robustness, and evolvability. Here we explore the hypothesis that degeneracy, a partial overlap in the functioning of multi-functional components, plays a central role in the evolution and robustness of complex forms. In support of this hypothesis, we present evidence that degeneracy is a fundamental source of robustness, it is intimately tied to multi-scaled complexity, and it establishes conditions that are necessary for system evolvability

"Meaning" as a sociological concept: A review of the modeling, mapping, and simulation of the communication of knowledge and meaning

The development of discursive knowledge presumes the communication of meaning as analytically different from the communication of information. Knowledge can then be considered as a meaning which makes a difference. Whereas the communication of information is studied in the information sciences and scientometrics, the communication of meaning has been central to Luhmann's attempts to make the theory of autopoiesis relevant for sociology. Analytical techniques such as semantic maps and the simulation of anticipatory systems enable us to operationalize the distinctions which Luhmann proposed as relevant to the elaboration of Husserl's "horizons of meaning" in empirical research: interactions among communications, the organization of meaning in instantiations, and the self-organization of interhuman communication in terms of symbolically generalized media such as truth, love, and power. Horizons of meaning, however, remain uncertain orders of expectations, and one should caution against reification from the meta-biological perspective of systems theory

The theory of brain-sign: a physical alternative to consciousness

Consciousness and the mind are prescientific concepts that begin with Greek theorizing. They suppose human rationality and reasoning placed in the human head by (in Christian terms) God, who structured the universe he created with the same kind of underlying characteristics. Descartes' development of the model included scientific objectivity by placing the mind outside the physical universe. In its failure under evidential scrutiny and without physical explanation, this model is destined for terminal decline. Instead, a genuine biological and physical function for the brain phenomenon can be developed. This is the theory of brain-sign. It accepts the causality of the brain as its physical characteristics, already under scientific scrutiny. What is needed is a new neurophysiological mapping language that specifies the relation of the structure and operation of the brain to organismic action in the world. Still what is lacking is an account of how neurophysiologies in different organisms communicate on dynamic, i.e. unpredictable, tasks. It is this evolved capacity that has emerged as brain-sign. Thus rather than mentality being an inner epistemological parallel world suddenly appearing in the head, brain-sign, as the neural sign of the causal status of the brain, facilitates the communicative medium of otherwise isolated organisms. The biogenesis of the phenomenon emerges directly from the account of the physical brain, and functions as a monistic feature of organisms in the physical world. This new paradigm offers disciplinary compatibility, and genuine development in behavioral and brain sciences

Rapid dissection and model-based optimization of inducible enhancers in human cells using a massively parallel reporter assay

Learning to read and write the transcriptional regulatory code is of central importance to progress in genetic analysis and engineering. Here we describe a massively parallel reporter assay (MPRA) that facilitates the systematic dissection of transcriptional regulatory elements. In MPRA, microarray-synthesized DNA regulatory elements and unique sequence tags are cloned into plasmids to generate a library of reporter constructs. These constructs are transfected into cells and tag expression is assayed by high-throughput sequencing. We apply MPRA to compare >27,000 variants of two inducible enhancers in human cells: a synthetic cAMP-regulated enhancer and the virus-inducible interferon-β enhancer. We first show that the resulting data define accurate maps of functional transcription factor binding sites in both enhancers at single-nucleotide resolution. We then use the data to train quantitative sequence-activity models (QSAMs) of the two enhancers. We show that QSAMs from two cellular states can be combined to design enhancer variants that optimize potentially conflicting objectives, such as maximizing induced activity while minimizing basal activity.National Human Genome Research Institute (U.S.) (grant R01HG004037)National Science Foundation (U.S.) ((NSF) grant PHY-0957573)National Science Foundation (U.S.) (NSF grant PHY-1022140)Broad Institut

Structure of a highly conserved domain of rock1 required for shroom-mediated regulation of cell morphology

Rho-associated coiled coil containing protein kinase (Rho-kinase or Rock) is a well-defined determinant of actin organization and dynamics in most animal cells characterized to date. One of the primary effectors of Rock is non-muscle myosin II. Activation of Rock results in increased contractility of myosin II and subsequent changes in actin architecture and cell morphology. The regulation of Rock is thought to occur via autoinhibition of the kinase domain via intramolecular interactions between the N-terminus and the C-terminus of the kinase. This autoinhibited state can be relieved via proteolytic cleavage, binding of lipids to a Pleckstrin Homology domain near the C-terminus, or binding of GTP-bound RhoA to the central coiled-coil region of Rock. Recent work has identified the Shroom family of proteins as an additional regulator of Rock either at the level of cellular distribution or catalytic activity or both. The Shroom-Rock complex is conserved in most animals and is essential for the formation of the neural tube, eye, and gut in vertebrates. To address the mechanism by which Shroom and Rock interact, we have solved the structure of the coiled-coil region of Rock that binds to Shroom proteins. Consistent with other observations, the Shroom binding domain is a parallel coiled-coil dimer. Using biochemical approaches, we have identified a large patch of residues that contribute to Shrm binding. Their orientation suggests that there may be two independent Shrm binding sites on opposing faces of the coiled-coil region of Rock. Finally, we show that the binding surface is essential for Rock colocalization with Shroom and for Shroom-mediated changes in cell morphology. © 2013 Mohan et al