Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

/pdf/collective-dynamics-of-small-world-networks-205zhem3gm.pdf

Collective dynamics of small-world networks

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

A 2.91-billion base pair (bp) consensus sequence of the euchromatic portion of the human genome was generated by the whole-genome shotgun sequencing method. The 14.8-billion bp DNA sequence was generated over 9 months from 27,271,853 high-quality sequence reads (5.11-fold coverage of the genome) from both ends of plasmid clones made from the DNA of five individuals. Two assembly strategies-a whole-genome assembly and a regional chromosome assembly-were used, each combining sequence data from Celera and the publicly funded genome effort. The public data were shredded into 550-bp segments to create a 2.9-fold coverage of those genome regions that had been sequenced, without including biases inherent in the cloning and assembly procedure used by the publicly funded group. This brought the effective coverage in the assemblies to eightfold, reducing the number and size of gaps in the final assembly over what would be obtained with 5.11-fold coverage. The two assembly strategies yielded very similar results that largely agree with independent mapping data. The assemblies effectively cover the euchromatic regions of the human chromosomes. More than 90% of the genome is in scaffold assemblies of 100,000 bp or more, and 25% of the genome is in scaffolds of 10 million bp or larger. Analysis of the genome sequence revealed 26,588 protein-encoding transcripts for which there was strong corroborating evidence and an additional approximately 12,000 computationally derived genes with mouse matches or other weak supporting evidence. Although gene-dense clusters are obvious, almost half the genes are dispersed in low G+C sequence separated by large tracts of apparently noncoding sequence. Only 1.1% of the genome is spanned by exons, whereas 24% is in introns, with 75% of the genome being intergenic DNA. Duplications of segmental blocks, ranging in size up to chromosomal lengths, are abundant throughout the genome and reveal a complex evolutionary history. Comparative genomic analysis indicates vertebrate expansions of genes associated with neuronal function, with tissue-specific developmental regulation, and with the hemostasis and immune systems. DNA sequence comparisons between the consensus sequence and publicly funded genome data provided locations of 2.1 million single-nucleotide polymorphisms (SNPs). A random pair of human haploid genomes differed at a rate of 1 bp per 1250 on average, but there was marked heterogeneity in the level of polymorphism across the genome. Less than 1% of all SNPs resulted in variation in proteins, but the task of determining which SNPs have functional consequences remains an open challenge.

http://science.sciencemag.org/content/sci/291/5507/1304.full.pdf

The sequence of the human genome.

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

A general and basic model of primordial evolution-a soup of reacting fini- tary and discrete processes-is employed to identify and analyze fundamental mechanisms that generate and maintain complex structures in prebiotic sys- tems. The processes?-machines as defined in computational mechanics-and their interaction networks both provide well defined notions of structure. This enables us to quantitatively demonstrate hierarchical self-organization in the soup in terms of complexity. We found that replicating processes evolve the strategy of successively building higher levels of organization by autocataly- sis. Moreover, this is facilitated by local components that have low structural complexity, but high generality. In e®ect, the finitary process soup sponta- neously evolves a selection pressure that favors such components. In light of the finitary process soup’s generality, these results suggest a fundamental law of hierarchical systems: global complexity requires local simplicity.

Primordial evolution in the finitary process soup

In the previous paper of this series [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Physical Review B, submitted] we detailed a procedure—ǫ-machine spectral reconstruction—to discover and analyze patterns and disorder in close-packed structures as revealed in x-ray diffraction spectra. We argued that this computational mechanics approach is more general than the current alternative theory, the fault model, and that it provides a unique characterization of the disorder present. We demonstrated the efficacy of computational mechanics on fourprototype spectra, finding that it was able to recover a statistical description of the underlying modular-layer stacking using ǫ-machine representations. Here we use this procedure to analyze structure and disorder in four previously published zinc sulphide diffraction spectra. We selected zinc sulphide not only for the theoretical interest this material has attracted in an effort to develop an understanding of polytypism, but also because it displays solid-state phase transitions and experimental data is available. With the first spectrum we find qualitative agreement with earlier fault-model analyses, although the reconstructed ǫ-machine detects structures not previously observed. In the second spectrum, the results cannot be expressed in terms of weak faulting and so no direct comparison between the fault model and the reconstructed ǫ-machine is possible. Nonetheless, we show that the ǫ-machine gives substantially better experimental agreement and a number of structural insights. In the third spectrum, the fault model fails completely due to the high degree of disorder present, while the reconstructed ǫ-machine reproduces the experimental spectrum well. In the fourth spectrum, we again find good quantitative agreement with experiment but find that the ǫ-machine has difficulty reproducing the shape of several Bragg-like peaks. We discuss the reasons for this. Using the ǫmachines reconstructed for each spectrum, we calculate a number of physical parameters—such as, stacking energies, configurational entropies, and hexagonality—and several quantities—including statistical complexity and excess entropy—that describe the intrinsic computational properties of the stacking structures.

/pdf/inferring-pattern-and-disorder-in-close-packed-structures-3qdrhde8pa.pdf

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part II: Structure and Intrinsic Computation in Zinc Sulphide

Author(s): James, Ryan G; Emenheiser, Jeffrey; Crutchfield, James P | Abstract: Recently, the partial information decomposition emerged as a promising framework for identifying the meaningful components of the information contained in a joint distribution. Its adoption and practical application, however, have been stymied by the lack of a generally-accepted method of quantifying its components. Here, we briefly discuss the bivariate (two-source) partial information decomposition and two implicitly directional interpretations used to intuitively motivate alternative component definitions. Drawing parallels with secret key agreement rates from information-theoretic cryptography, we demonstrate that these intuitions are mutually incompatible and suggest that this underlies the persistence of competing definitions and interpretations. Having highlighted this hitherto unacknowledged issue, we outline several possible solutions.

/pdf/a-perspective-on-unique-information-directionality-40945bxkpz.pdf

A Perspective on Unique Information: Directionality, Intuitions, and Secret Key Agreement.

Animals' sensory systems evolved to efficiently process information from their environmental niches. Niches often include irregular shapes and rough textures (e.g., jagged terrain, canopy outlines) that must be navigated to find food, escape predators, and master other fitness-related challenges. For most primates, vision is the dominant sensory modality and thus, primates have evolved systems for processing complicated visual stimuli. One way to quantify information present in visual stimuli in natural scenes is evaluating their fractal dimension. We hypothesized that sensitivity to complicated geometric forms, indexed by fractal dimension, is an evolutionarily conserved capacity, and tested this capacity in rhesus macaques (Macaca mulatta). Monkeys viewed paired black and white images of simulated self-similar contours that systematically varied in fractal dimension while their attention to the stimuli was measured using noninvasive infrared eye tracking. They fixated more frequently on, dwelled for longer durations on, and had attentional biases towards images that contain boundary contours with higher fractal dimensions. This indicates that, like humans, they discriminate between visual stimuli on the basis of fractal dimension and may prefer viewing informationally rich visual stimuli. Our findings suggest that sensitivity to fractal dimension may be a wider ability of the vertebrate vision system.

/pdf/macaques-preferentially-attend-to-visual-patterns-with-mbyel43eqt.pdf

Macaques preferentially attend to visual patterns with higher fractal dimension contours.

Author(s): Varn, DP; Canright, GS; Crutchfield, JP | Abstract: In a recent publication [D P Varn, G S Canright, and J P Crutchfield, Phys Rev B {\bf 66}:17, 156 (2002)] we introduced a new technique for discovering and describing planar disorder in close-packed structures (CPSs) directly from their diffraction spectra Here we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in materials By way of contrast, we give a detailed analysis of the current alternative approach, the fault model (FM), and offer several criticisms We then demonstrate that the computational mechanics description of the stacking sequence--in the form of an epsilon-machine--provides the minimal and unique description of the crystal, whether ordered, disordered, or some combination We find that we can detect and describe any amount of disorder, as well as materials that are mixtures of various kinds of crystalline structure Underlying this approach is a novel method for epsilon-machine reconstruction that uses correlation functions estimated from diffraction spectra, rather than sequences of microscopic configurations, as is typically used in other domains The result is that the methods developed here can be adapted to a wide range of experimental systems in which spectroscopic data is available

/pdf/inferring-pattern-and-disorder-in-close-packed-structures-10qwhuk4ab.pdf

James P. Crutchfield

Papers

Primordial evolution in the finitary process soup

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part II: Structure and Intrinsic Computation in Zinc Sulphide

A Perspective on Unique Information: Directionality, Intuitions, and Secret Key Agreement.

Macaques preferentially attend to visual patterns with higher fractal dimension contours.

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: epsilon-Machine Spectral Reconstruction Theory