102,779 research outputs found

    Failed "nonaccelerating" models of prokaryote gene regulatory networks

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    Much current network analysis is predicated on the assumption that important biological networks will either possess scale free or exponential statistics which are independent of network size allowing unconstrained network growth over time. In this paper, we demonstrate that such network growth models are unable to explain recent comparative genomics results on the growth of prokaryote regulatory gene networks as a function of gene number. This failure largely results as prokaryote regulatory gene networks are "accelerating" and have total link numbers growing faster than linearly with network size and so can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. In the limit, these networks can undergo transitions so marked as to constrain network sizes to be below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are indeed characterized by an accelerating quadratic growth with gene count and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. We develop two "nonaccelerating" network models of prokaryote regulatory gene networks in an endeavor to match observation and demonstrate that these approaches fail to reproduce observed statistics.Comment: Corrected error in biological input parameter: 13 pages, 9 figure

    Scaling properties of scale-free evolving networks: Continuous approach

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    Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their validity. We show that main properties of scale-free evolving networks may be described in frames of a simple continuous approach. The simplest models of networks, which growth is determined by a mechanism of preferential linking, are used. We consider different forms of this preference and demonstrate that the range of types of preference linking producing scale-free networks is wide. We obtain also scaling relations for networks with nonlinear, accelerating growth and describe temporal evolution of arising distributions. Size-effects - cut-offs of these distributions - implement restrictions for observation of power-law dependences. The main characteristic of interest is so-called degree distribution, i.e., distribution of a number of connections of nodes. A scaling form of the distribution of links between pairs of individual nodes for the growing network of citations is also studied. We describe effects that produce difference of nodes. ``Aging'' of nodes changes exponents of distributions. Appearence of a single ``strong'' node changes dramatically the degree distribution of a network. If its strength exceeds some threshold value, the strong node captures a finite part of all links of a network. We show that permanent random damage of a growing scale-free network - permanent deleting of some links - change radically values of the scaling exponents. We describe the arising rich phase diagram. Results of other types of permanent damage are described.Comment: 21 pages revtex (twocolumn), 9 figure

    Inherent size constraints on prokaryote gene networks due to "accelerating" growth

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    Networks exhibiting "accelerating" growth have total link numbers growing faster than linearly with network size and can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value.Comment: Corrected error in biological input parameter: 15 pages, 10 figure

    Effect of the accelerating growth of communications networks on their structure

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    Motivated by data on the evolution of the Internet and World Wide Web we consider scenarios of self-organization of the nonlinearly growing networks into free-scale structures. We find that the accelerating growth of the networks establishes their structure. For the growing networks with preferential linking and increasing density of links, two scenarios are possible. In one of them, the value of the exponent Îł\gamma of the connectivity distribution is between 3/2 and 2. In the other, Îł>2\gamma>2 and the distribution is necessarily non-stationary.Comment: 4 pages revtex, 3 figure

    Scale free networks by preferential depletion

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    We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied before where the exponents are larger. Our approach applies in particular to biological networks where in fact we find interesting agreement with experimental measurements. We investigate the most important properties characterizing these networks, as the cluster size distribution, the average shortest path and the clustering coefficient.Comment: 8 pages, 4 figure

    Accelerating networks

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    Evolving out-of-equilibrium networks have been under intense scrutiny recently. In many real-world settings the number of links added per new node is not constant but depends on the time at which the node is introduced in the system. This simple idea gives rise to the concept of accelerating networks, for which we review an existing definition and -- after finding it somewhat constrictive -- offer a new definition. The new definition provided here views network acceleration as a time dependent property of a given system, as opposed to being a property of the specific algorithm applied to grow the network. The defnition also covers both unweighted and weighted networks. As time-stamped network data becomes increasingly available, the proposed measures may be easily carried out on empirical datasets. As a simple case study we apply the concepts to study the evolution of three different instances of Wikipedia, namely, those in English, German, and Japanese, and find that the networks undergo different acceleration regimes in their evolution.Comment: 12 pages, 8 figure

    A Fellowship Approach to Accelerating Social Entrepreneurs

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    When Echoing Green, a nonprofit focused on unleashing next-generation talent, was founded in 1987, the term "social entrepreneur" was not widely used. Emerging leaders who wanted to change the world had limited options to access capital and programmatic support aside from its Fellowship program. Forty million dollars in seed-stage funding and strategic assistance to nearly 700 entrepreneurs later, Echoing Green has witnessed social entrepreneurship become a global movement.In recent years, Echoing Green has recognized two field-level trends within its Fellow community. First, for-profit business models to effect social and environmental change and impact investing (investments made to generate social and environmental impact alongside a financial return) have increased in popularity. At the same time, the business accelerator landscape has grown, and many entrepreneurs are participating in multiple programs. Globally, a plethora of accelerator programs are now employing a variety of services and funding models to launch start-ups.Echoing Green also began accepting more entrepreneurs using for-profit business models into its Fellowship and deepening its engagement with its Fellow alumni community. In 2014, it piloted an impact investing "inflection cohort" of Fellow alumni running for-profit and hybrid social enterprises. Its goal was to fill gaps in support and funding through the Fellows' common critical inflection moment: transitioning from early-stage funding to raising more sophisticated institutional growth capital.In this white paper, Echoing Green describes this impact investing inflection cohort pilot and shares the social entrepreneurs' data to shed light on how and if the inflection cohort model succeeded in enabling the early-stage social entrepreneurs to grow, attract investment, and deliver impact
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