241 research outputs found
Local majority dynamics on preferential attachment graphs
Suppose in a graph vertices can be either red or blue. Let be odd. At
each time step, each vertex in polls random neighbours and takes
the majority colour. If it doesn't have neighbours, it simply polls all of
them, or all less one if the degree of is even. We study this protocol on
the preferential attachment model of Albert and Barab\'asi, which gives rise to
a degree distribution that has roughly power-law ,
as well as generalisations which give exponents larger than . The setting is
as follows: Initially each vertex of is red independently with probability
, and is otherwise blue. We show that if is
sufficiently biased away from , then with high probability,
consensus is reached on the initial global majority within
steps. Here is the number of vertices and is the minimum of
and (or if is even), being the number of edges each new
vertex adds in the preferential attachment generative process. Additionally,
our analysis reduces the required bias of for graphs of a given degree
sequence studied by the first author (which includes, e.g., random regular
graphs)
Survival and selection biases in early animal evolution and a source of systematic overestimation in molecular clocks
Important evolutionary events such as the Cambrian Explosion have inspired many attempts at explanation: why do they happen when they do? What shapes them, and why do they eventually come to an end? However, much less attention has been paid to the idea of a ‘null hypothesis’—that certain features of such diversifications arise simply through their statistical structure. Such statistical features also appear to influence our perception of the timing of these events. Here, we show in particular that study of unusually large clades leads to systematic overestimates of clade ages from some types of molecular clocks, and that the size of this effect may be enough to account for the puzzling mismatches seen between these molecular clocks and the fossil record. Our analysis of the fossil record of the late Ediacaran to Cambrian suggests that it is likely to be recording a true evolutionary radiation of the bilaterians at this time, and that explanations involving various sorts of cryptic origins for the bilaterians do not seem to be necessary
Lyapunov exponents and phase diagrams reveal multi-factorial control over TRAIL-induced apoptosis
Kinetic modeling, phase diagrams analysis, and quantitative single-cell experiments are combined to investigate how multiple factors, including the XIAP:caspase-3 ratio and ligand concentration, regulate receptor-mediated apoptosis
Theoretical size distribution of fossil taxa: analysis of a null model
BACKGROUND: This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. MODEL: New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. CONCLUSION: The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family
Semi-Markov Graph Dynamics
In this paper, we outline a model of graph (or network) dynamics based on two
ingredients. The first ingredient is a Markov chain on the space of possible
graphs. The second ingredient is a semi-Markov counting process of renewal
type. The model consists in subordinating the Markov chain to the semi-Markov
counting process. In simple words, this means that the chain transitions occur
at random time instants called epochs. The model is quite rich and its possible
connections with algebraic geometry are briefly discussed. Moreover, for the
sake of simplicity, we focus on the space of undirected graphs with a fixed
number of nodes. However, in an example, we present an interbank market model
where it is meaningful to use directed graphs or even weighted graphs.Comment: 25 pages, 4 figures, submitted to PLoS-ON
Modeling the scaling properties of human mobility
While the fat tailed jump size and the waiting time distributions
characterizing individual human trajectories strongly suggest the relevance of
the continuous time random walk (CTRW) models of human mobility, no one
seriously believes that human traces are truly random. Given the importance of
human mobility, from epidemic modeling to traffic prediction and urban
planning, we need quantitative models that can account for the statistical
characteristics of individual human trajectories. Here we use empirical data on
human mobility, captured by mobile phone traces, to show that the predictions
of the CTRW models are in systematic conflict with the empirical results. We
introduce two principles that govern human trajectories, allowing us to build a
statistically self-consistent microscopic model for individual human mobility.
The model not only accounts for the empirically observed scaling laws but also
allows us to analytically predict most of the pertinent scaling exponents
Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution
A birth-death process is a continuous-time Markov chain that counts the
number of particles in a system over time. In the general process with
current particles, a new particle is born with instantaneous rate
and a particle dies with instantaneous rate . Currently no robust and
efficient method exists to evaluate the finite-time transition probabilities in
a general birth-death process with arbitrary birth and death rates. In this
paper, we first revisit the theory of continued fractions to obtain expressions
for the Laplace transforms of these transition probabilities and make explicit
an important derivation connecting transition probabilities and continued
fractions. We then develop an efficient algorithm for computing these
probabilities that analyzes the error associated with approximations in the
method. We demonstrate that this error-controlled method agrees with known
solutions and outperforms previous approaches to computing these probabilities.
Finally, we apply our novel method to several important problems in ecology,
evolution, and genetics
Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon – the reversal paradox
This article discusses three statistical paradoxes that pervade epidemiological research: Simpson's paradox, Lord's paradox, and suppression. These paradoxes have important implications for the interpretation of evidence from observational studies. This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon – the reversal paradox – depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three. Although the three statistical paradoxes occur in different types of variables, they share the same characteristic: the association between two variables can be reversed, diminished, or enhanced when another variable is statistically controlled for. Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings. These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results
Authorship Analysis Approaches
This chapter presents an overview of authorship analysis from multiple standpoints. It includes historical perspective, description of stylometric features, and authorship analysis techniques and their limitations
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