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Fluctuation-driven dynamics of the internet topology.

We study the dynamics of the Internet topology based on empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the Internet dynamics. The network's overall growth can be described approximately by a single characteristic degree growth rate g(eff) approximately 0.016 and the fluctuation strength sigma(eff) approximately 0.14, together with the vertex growth rate alpha approximately 0.029. A stochastic model which incorporates these values and an adaptation rule newly introduced reproduces several features of the real Internet topology such as the correlations between the degrees of different vertices.

Internet↗

A linear stochastic model of the single motor unit.

The production of force and of the electrical signal by an active motor unit is theoretically described. Neural spikes are modelled using the Dirac delta function. Mechanisms for the generation of random impulse trains and the properties of the corresponding stochastic processes are discussed; the "renewal" model is proposed as the most appropriate. The possibility of using a linear model for the systems that produce force and electrical signal in the unit is examined. It is concluded that the linear assumption is justifiable during steady, constant-strength contractions of muscle. This linear stochastic model of the motor unit is used in two subsequent papers to study the muscle force and the electromyogram.

Animals↗

Language acquisition in the absence of explicit negative evidence: how important is starting small?

It is commonly assumed that innate linguistic constraints are necessary to learn a natural language, based on the apparent lack of explicit negative evidence provided to children and on Gold's proof that, under assumptions of virtually arbitrary positive presentation, most interesting classes of languages are not learnable. However, Gold's results do not apply under the rather common assumption that language presentation may be modeled as a stochastic process. Indeed, Elman (Elman, J.L., 1993. Learning and development in neural networks: the importance of starting small. Cognition 48, 71-99) demonstrated that a simple recurrent connectionist network could learn an artificial grammar with some of the complexities of English, including embedded clauses, based on performing a word prediction task within a stochastic environment. However, the network was successful only when either embedded sentences were initially withheld and only later introduced gradually, or when the network itself was given initially limited memory which only gradually improved. This finding has been taken as support for Newport's 'less is more' proposal, that child language acquisition may be aided rather than hindered by limited cognitive resources. The current article reports on connectionist simulations which indicate, to the contrary, that starting with simplified inputs or limited memory is not necessary in training recurrent networks to learn pseudonatural languages; in fact, such restrictions hinder acquisition as the languages are made more English-like by the introduction of semantic as well as syntactic constraints. We suggest that, under a statistical model of the language environment, Gold's theorem and the possible lack of explicit negative evidence do not implicate innate, linguistic-specific mechanisms. Furthermore, our simulations indicate that special teaching methods or maturational constraints may be unnecessary in learning the structure of natural language.

Artificial Intelligence↗

Dynamics of the neural discharge in snail neurons.

Spike trains recorded under weak sinusoidal driving from central neurons of Lymnaea stagnalis appear quite irregular and envisage the possibility of an underlying chaotic process. Therefore, the sequences of interspike intervals are analyzed in the framework of non-linear dynamics. Since, for several reasons, these sequences are rather short, the analysis is performed by using methods of non-linear forecasting. To reject the null hypothesis that the original time series is a realization of a linear stochastic process with the same autocorrelation function, the results obtained on the original data are compared with those from surrogate data sets. Some 'non-linear' predictability occurs only in narrow regions of the space of stimulus parameters and the frequency of perturbation is critical in determining it. Moreover, it is shown that such behavior can be qualitatively mimicked by the FitzHugh-Nagumo model driven by a weak sinusoidal signal plus noise. It is argued that the narrowness of the non-linear predictability regions renders quite unlikely the detection of deterministic dynamics in the activity of these neurons.

Action Potentials↗

Equilibrium free energies from nonequilibrium metadynamics.

In this Letter we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes, such as Wang-Landau sampling.

Journal Article↗

Structured Biological Modelling: a method for the analysis and simulation of biological systems applied to oscillatory intracellular calcium waves.

In biology signal and information processing networks are widely known. Due to their inherent complexity and non-linear dynamics the time evolution of these systems can not be predicted by simple plausibility arguments. Fortunately, the power of modern computers allows the simulation of complex biological models. Therefore the problem becomes reduced to the question of how to develop a consistent mathematical model which comprises the essentials of the real biological system. As an interface between the phenomenological description and a computer simulation of the system the proposed method of Structured Biological Modelling (SBM) uses top-down levelled dataflow diagrams. They serve as a powerful tool for the analysis and the mathematical description of the system in terms of a stochastic formulation. The stochastic treatment, regarding the time evolution of the system as a stochastic process governed by a master equation, circumvents most difficulties arising from high dimensional and non-linear systems. As an application of SBM we develop a stochastic computer model of intracellular oscillatory Ca2+ waves in non-excitable cells. As demonstrated on this example, SBM can be used for the design of computer experiments which under certain conditions can be used as cheap and harmless counterparts to the usual time-consuming biological experiments.

Calcium↗

Characteristic Functions and Process Identification by Neural Networks.

Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide only incomplete or misleading information on the statistical properties of the data. To handle such situations we propose neural network algorithms, with an hybrid (supervised and unsupervised) learning scheme, which constructs the characteristic function of the probability distribution and the transition functions of the stochastic process. Illustrative examples are presented, which include Cauchy and Lévy-type processes.

Journal Article↗

The kinetics of nerve-evoked quantal secretion.

Current views on quantal release of neurotransmitters hold that after the vesicle migrates towards release sites (active zones), multiple protein interactions mediate the docking of the vesicle to the presynaptic membrane and the formation of a multimolecular protein complex (the 'fusion machine') which ultimately makes the vesicle competent to release a quantum in response to the action potential. Classical biophysical studies of quantal release have modelled the process by a binomial system where n vesicles (sites) competent for exocytosis release a quantum, with probability p, in response to the action potential. This is likely to be an oversimplified model. Furthermore, statistical and kinetic studies have given results which are difficult to reconcile within this framework. Here, data are presented and discussed which suggest a revision of the biophysical model. Transient silencing of release is shown to occur following the pulse of synchronous transmitter release, which is evoked by the presynaptic action potential. This points to a schema where the vesicle fusion complex assembly is a reversible, stochastic process. Asynchronous exocytosis may occur at several intermediate stages in the process, along paths which may be differentially regulated by divalent cations or other factors. The fusion complex becomes competent for synchronous release (armed vesicles) only at appropriately organized sites. The action potential then triggers (deterministically rather than stochastically) the synchronous discharge of all armed vesicles. The existence of a specific conformation for the fusion complex to be competent for synchronous evoked fusion reconciles statistical and kinetic results during repetitive stimulation and helps explain the specific effects of toxins and genetic manipulation on the synchronization of release in response to an action potential.

Action Potentials↗

Evolutionary dynamics of predator-prey systems: an ecological perspective.

Evolution takes place in an ecological setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals--the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the context of predator-prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator-prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species.

Animals↗

Developmental stability and signalling among cells.

The production of stable phenotypes depends from the earliest stages of development upon high levels of somatic cellular selection amongst cells or cell lineages. The signals exchanged amongst cells can reveal important aspects of a cell's phenotype, and might thereby be used in darwinian processes of developmental selection. Based upon an optimality model, we suggest that stable phenotypes require a substantial investment in two mechanisms of inter-cellular selection: "quality-selection" mechanisms regulate the average phenotype of a group of cells; "stability-selection" mechanisms regulate the variance in cell phenotypes. Variance in cell phenotypes may arise from developmental-error or other stochastic processes, or be generated as is true of the immune system, as part of a developmental strategy. The model shows that stability-selection mechanisms may exert the stronger effect on overall organ or body performance. Selection based upon reliable inter-cellular signalling of phenotypic properties may be the key way that bodies anticipate and then constrain variance in cell phenotypes around the optimal cellular attributes, and suggests an advantage of developmentally-selected systems over instructional ones. High levels of investments in stability mechanisms also ensure homogeneous collections of cells that can translate "upwards" into developmentally stable organ systems and phenotypes. Environmental and genetic factors, as well as the prevalent mode of selection, may all affect developmental stability and thereby give rise to varying of somatic selection.

Animals↗

Interferometric data analysis based on Markov nonlinear filtering methodology.

For data processing in conventional phase shifting interferometry, Fourier transform, and least-squares-fitting techniques, a whole interferometric data series is required. We propose a new interferometric data processing methodology based on a recurrent nonlinear procedure. The signal value is predicted from the previous step to the next step, and the prediction error is used for nonlinear correction of an a priori estimate of the parameters phase, visibility, or frequency of interference fringes. Such a recurrent procedure is correct on the condition that the noise component be a Markov stochastic process realization. The accuracy and stability of the recurrent Markov nonlinear filtering algorithm were verified by computer simulations. It was discovered that the main advantages of the proposed methodology are dynamic data processing, phase error minimization, and high noise immunity against the influence of non-Gaussian noise correlated with the signal and the automatic solution of the phase unwrapping problem.

Algorithms↗

Links between annual, Milankovitch and continuum temperature variability.

Climate variability exists at all timescales-and climatic processes are intimately coupled, so that understanding variability at any one timescale requires some understanding of the whole. Records of the Earth's surface temperature illustrate this interdependence, having a continuum of variability following a power-law scaling. But although specific modes of interannual variability are relatively well understood, the general controls on continuum variability are uncertain and usually described as purely stochastic processes. Here we show that power-law relationships of surface temperature variability scale with annual and Milankovitch-period (23,000- and 41,000-year) cycles. The annual cycle corresponds to scaling at monthly to decadal periods, while millennial and longer periods are tied to the Milankovitch cycles. Thus the annual, Milankovitch and continuum temperature variability together represent the response to deterministic insolation forcing. The identification of a deterministic control on the continuum provides insight into the mechanisms governing interannual and longer-period climate variability.

Journal Article↗

Phlag: scalable detection of genomics regions with unexplained phylogenetic heterogeneity.

MOTIVATION: Phylogenetic analyses of entire genomes (phylogenomics) have revealed abundant heterogeneity of evolutionary histories. While much has been done to model this heterogeneity and to infer species trees despite it, the current toolkit has a limitation. Most methods assume that gene trees across the genome differ but are all sampled from the same distribution, defined by models such as the multi-species coalescent (MSC), and parametrized consistently across the genome. Empirical data strongly suggest this assumption is often violated because the species tree, its parameters, or the process generating the gene trees can all change across the genome. Errors in the data can further compound this heterogeneity. RESULTS: To address this challenge, we define the problem of detecting what segments of the genome are inconsistent with a putative species tree, even after allowing discordance according to MSC. We model gene trees not as a set, but rather as a series (a realization of a stochastic process) along genomic positions. We propose a Hidden Markov Model (HMM) approach applied to quartet statistics measured from gene trees and tie the model to MSC using simulations. The combined use of these three ideas leads to a scalable method called Phlag. On simulated and real data, we show that Phlag can detect many cases of change in underlying evolutionary processes, including reduced recombination rates, population size changes, and admixture, all using the same algorithm. AVAILABILITY AND IMPLEMENTATION: Phlag is available at github.com/bo1929/phlag. All results and scripts can be found at github.com/bo1929/shared.phlag.

Phylogeny↗

Phlag: Scalable detection of genomics regions with unexplained phylogenetic heterogeneity.

MOTIVATION: Phylogenetic analyses of entire genomes (phylogenomics) have revealed abundant heterogeneity of evolutionary histories. While much has been done to model this heterogeneity and to infer species trees despite it, the current toolkit has a limitation. Most methods assume that gene trees across the genome differ but are all sampled from the same distribution , defined by models such as the multi-species coalescent (MSC), and parametrized consistently across the genome. Empirical data strongly suggest this assumption is often violated because the species tree, its parameters, or the process generating the gene trees can all change across the genome. Errors in the data can further compound this heterogeneity. RESULTS: To address this challenge, we define the problem of detecting what segments of the genome are inconsistent with a putative species tree, even after allowing discordance according to MSC. We model gene trees not as a set, but rather as a series (a realization of a stochastic process) along genomic positions. We propose a Hidden Markov Model (HMM) approach applied to quartet statistics measured from gene trees and tie the model to MSC using simulations. The combined use of these three ideas leads to a scalable method called Phlag. On simulated and real data, we show that Phlag can detect many cases of change in underlying evolutionary processes, including reduced recombination rates, population size changes, and admixture, all using the same algorithm. AVAILABILITY AND IMPLEMENTATION: Phlag is available at github.com/bo1929/phlag . All results and scripts can be found at github.com/bo1929/shared.phlag .

Journal Article↗

Multivariate analysis of prefrontal cortical data from the Stanley Foundation Neuropathology Consortium.

Prefrontal cortical tissue from the Stanley Foundation Neuropathology Consortium, which contains samples from patients with schizophrenia, bipolar disorder, non-psychotic depression, and normal controls (n = 15 per group), was studied in a blinded fashion in 14 different laboratories between 1997 and 2000. The results of 69 separate data sets were analyzed with univariate and multivariate techniques. A total of 17 abnormal markers were identified that pertained to a variety of neural systems and processes, including neuronal plasticity, neurotransmission, signal transduction, inhibitory interneuron function, and glial cells. Schizophrenia was associated with the largest number of abnormalities, many of which were also present in bipolar disorder. Major depression was associated with relatively few abnormalities. The majority of abnormal findings represented a decline in function and could not be easily explained by exposure to psychotropic or illicit drugs. It is argued that the abnormal findings are not simply due to stochastic processes but represent viable markers for independent replication and further study as candidate genes or targets for new treatments.

Adult↗

The relationship between domain duplication and recombination.

Protein domains represent the basic evolutionary units that form proteins. Domain duplication and shuffling by recombination are probably the most important forces driving protein evolution and hence the complexity of the proteome. While the duplication of whole genes as well as domain-encoding exons increases the abundance of domains in the proteome, domain shuffling increases versatility, i.e. the number of distinct contexts in which a domain can occur. Here, we describe a comprehensive, genome-wide analysis of the relationship between these two processes. We observe a strong and robust correlation between domain versatility and abundance: domains that occur more often also have many different combination partners. This supports the view that domain recombination occurs in a random way. However, we do not observe all the different combinations that are expected from a simple random recombination scenario, and this is due to frequent duplication of specific domain combinations. When we simulate the evolution of the protein repertoire considering stochastic recombination of domains followed by extensive duplication of the combinations, we approximate the observed data well. Our analyses are consistent with a stochastic process that governs domain recombination and thus protein divergence with respect to domains within a polypeptide chain. At the same time, they support a scenario in which domain combinations are formed only once during the evolution of the protein repertoire, and are then duplicated to various extents. The extent of duplication of different combinations varies widely and, in nature, will depend on selection for the domain combination based on its function. Some of the pair-wise domain combinations that are highly duplicated also recur frequently with other partner domains, and thus represent evolutionary units larger than single protein domains, which we term "supra-domains".

Animals↗

Dynamic receptor team formation can explain the high signal transduction gain in Escherichia coli.

Evolution has provided many organisms with sophisticated sensory systems that enable them to respond to signals in their environment. The response frequently involves alteration in the pattern of movement, either by directed movement, a process called taxis, or by altering the speed or frequency of turning, which is called kinesis. Chemokinesis has been most thoroughly studied in the peritrichous bacterium Escherichia coli, which has four helical flagella distributed over the cell surface, and swims by rotating them. When rotated counterclockwise the flagella coalesce into a propulsive bundle, producing a relatively straight "run," and when rotated clockwise they fly apart, resulting in a "tumble" which reorients the cell with little translocation. A stochastic process generates the runs and tumbles, and in a chemoeffector gradient, runs that carry the cell in a favorable direction are extended. The cell senses spatial gradients as temporal changes in receptor occupancy and changes the probability of counterclockwise rotation (the bias) on a fast timescale, but adaptation returns the bias to baseline on a slow timescale, enabling the cell to detect and respond to further concentration changes. The overall structure of the signal transduction pathways is well characterized in E. coli, but important details are still not understood. Only recently has a source of gain in the signal transduction network been identified experimentally, and here we present a mathematical model based on dynamic assembly of receptor teams that can explain this observation.

Bacterial Physiological Phenomena↗

A complete classification of Darwinian extinction in ecological interactions.

The evolution of a population by individual-level natural selection can result in the population's extinction. Selection causes the spread of phenotypes with higher relative fitness, but at the same time, selection can also indirectly produce changes in the physical, biotic, or genotypical environment through population interactions (e.g., environment modification, interspecific interactions, and genomic conflict). Because fitness is environment dependent, this can cause mean fitness to decrease, resulting in extinction. I call this process "Darwinian extinction." Examples of Darwinian extinction include a variety of dynamics and modes of extinction, but the variation is constrained. I determine the complete classification of possible dynamics and modes of Darwinian extinction due to ecological interactions, using bifurcation theory and models with ecological and evolutionary changes occurring on different timescales. This classification is also extended to extinctions due to interactions within the population. The mode of extinction may be either sudden or gradual (requiring additional stochastic processes), and each mode has specific types of dynamics associated with it. Darwinian extinction is a robust and normal phenomenon, and this reasonably complete classification can help us understand more thoroughly its role in nature.

Animals↗