scholarly journals When are bacteria really gazelles? Comparing patchy ecologies with dimensionless numbers

2021 ◽  
Author(s):  
Samuel S Urmy ◽  
Alli N Cramer ◽  
Tanya L Rogers ◽  
Jenna Sullivan-Stack ◽  
Marian Louise Schmidt ◽  
...  
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Natural Populations ◽  
Mean Field ◽  
Dimensionless Numbers ◽  
Mean Field Model ◽  
Spatially Explicit Models ◽  
Mean Fields ◽  
Resource Patches ◽  
Blue Whales

From micro to planetary scales, spatial heterogeneity - patchiness - is ubiquitous in ecological systems, defining the environments in which organisms move and interact. While this fact has been recognized for decades, most large-scale ecosystem models still use spatially averaged "mean fields" to represent natural populations, while fine-scale, spatially explicit models are mostly restricted to particular organisms or systems. In a conceptual paper, Grunbaum (2012, Interface Focus 2: 150-155) introduced a heuristic framework, based on three dimensionless ratios quantifying movement, reproduction, and resource consumption, to characterize patchy ecological interactions and identify when mean-field assumptions are justifiable. In this paper, we calculated Grunbaum's dimensionless numbers for 33 real interactions between consumers and their resource patches in terrestrial, aquatic, and aerial environments. Consumers ranged in size from bacteria to blue whales, and patches lasted from minutes to millennia, spanning spatial scales of mm to hundreds of km. We found that none of the interactions could be accurately represented by a purely mean-field model, though 26 of them (79%) could be partially simplified by averaging out movement, reproductive, or consumption dynamics. Clustering consumer-resource pairs by their non-dimensional ratios revealed several unexpected dynamic similarities between disparate interactions. For example, bacterial Pseudoalteromonas exploit nutrient plumes in a similar manner to Mongolian gazelles grazing on ephemeral patches of steppe vegetation. Our findings suggest that dimensional analysis is a valuable tool for characterizing ecological patchiness, and can link the dynamics of widely different systems into a single quantitative framework.

scholarly journals Small-scale spatial structure influences large-scale invasion rates

2019 ◽  
Author(s):  
Michael J. Plank ◽  
Matthew J. Simpson ◽  
Rachelle N. Binny
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Large Scale ◽  
Spatial Scales ◽  
Mean Field ◽  
Average Density ◽  
Small Scale ◽  
Local Interactions ◽  
Mean Field Model ◽  
Species Invasions

AbstractLocal interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.

scholarly journals On the Throughput Optimization in Large-Scale Batch-Processing Systems

2021 ◽  
Vol 48 (3) ◽  
pp. 128-129
Author(s):  
Sounak Kar ◽  
Robin Rehrmann ◽  
Arpan Mukhopadhyay ◽  
Bastian Alt ◽  
Florin Ciucu ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Queueing Network ◽  
Processing System ◽  
Batch Size ◽  
System Throughput ◽  
Throughput Optimization ◽  
Mean Field Model ◽  
Optimal Batch Size ◽  
Globally Attractive

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

scholarly journals Mean-Field Models for EEG/MEG: From Oscillations to Waves

2021 ◽  
Author(s):  
Áine Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

The nonlinear properties of a large-scale dynamo driven by helical forcing

2002 ◽  
Vol 456 ◽  
pp. 219-237 ◽  
Author(s):  
FAUSTO CATTANEO ◽  
DAVID W. HUGHES ◽  
JEAN-CLAUDE THELEN
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Mean Field ◽  
Forced Flow ◽  
Small Scale ◽  
Dynamo Action ◽  
Initial State ◽  
The Magnetic Field

By considering an idealized model of helically forced flow in an extended domain that allows scale separation, we have investigated the interaction between dynamo action on different spatial scales. The evolution of the magnetic field is studied numerically, from an initial state of weak magnetization, through the kinematic and into the dynamic regime. We show how the choice of initial conditions is a crucial factor in determining the structure of the magnetic field at subsequent times. For a simulation with initial conditions chosen to favour the growth of the small-scale field, the evolution of the large-scale magnetic field can be described in terms of the α-effect of mean field magnetohydrodynamics. We have investigated this feature further by a series of related numerical simulations in smaller domains. Of particular significance is that the results are consistent with the existence of a nonlinearly driven α-effect that becomes saturated at very small amplitudes of the mean magnetic field.

scholarly journals Cluster mean-field theory accurately predicts statistical properties of large-scale DNA methylation patterns

2021 ◽  
Author(s):  
Lyndsay Kerr ◽  
Duncan Sproul ◽  
Ramon Grima
Keyword(s):  
Dna Methylation ◽  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Statistical Properties ◽  
Stochastic Simulations ◽  
Model Parameters ◽  
Mean Field Model ◽  
Mean Field Models ◽  
Methylation Patterns

The accurate establishment and maintenance of DNA methylation patterns is vital for mammalian development and disruption to these processes causes human disease. Our understanding of DNA methylation mechanisms has been facilitated by mathematical modelling, particularly stochastic simulations. Mega-base scale variation in DNA methylation patterns is observed in development, cancer and ageing and the mechanisms generating these patterns are little understood. However, the computational cost of stochastic simulations prevents them from modelling such large genomic regions. Here we test the utility of three different mean-field models to predict large-scale DNA methylation patterns. By comparison to stochastic simulations, we show that a cluster mean-field model accurately predicts the statistical properties of steady-state DNA methylation patterns, including the mean and variance of methylation levels calculated across a system of CpG sites, as well as the covariance and correlation of methylation levels between neighbouring sites. We also demonstrate that a cluster mean-field model can be used within an approximate Bayesian computation framework to accurately infer model parameters from data. As mean-field models can be solved numerically in a few seconds, our work demonstrates their utility for understanding the processes underpinning large-scale DNA methylation patterns.

scholarly journals Turbulence in Large-Scale Two-Dimensional Balanced Hard Sphere Gas Flow

Atmosphere ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1520
Author(s):  
Rafail V. Abramov
Keyword(s):  
Turbulent Flows ◽  
Hard Sphere ◽  
Large Scale ◽  
Gas Flow ◽  
Spatial Scales ◽  
Mean Field ◽  
Current Work ◽  
Two Dimensional ◽  
Dynamical Mechanism ◽  
Wide Range

In recent works, we developed a model of balanced gas flow, where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large-scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the third dimension. The main motivation behind the current work is the following. According to observations, horizontal turbulent motions in the Earth atmosphere manifest in a wide range of spatial scales, from hundreds of meters to thousands of kilometers. However, the air density rapidly decays with altitude, roughly by an order of magnitude each 15–20 km. This naturally raises the question as to whether or not there exists a dynamical mechanism which can produce large-scale turbulence within a purely two-dimensional gas flow. To our surprise, we discover that our model indeed produces turbulent flows and the corresponding Kolmogorov energy spectra in such a two-dimensional setting.

scholarly journals Biologically realistic mean-field models of conductancebased networks of spiking neurons with adaptation

2018 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

AbstractAccurate population models are needed to build very large scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of Adaptive exponential Integrate and fire excitatory and inhibitory neurons. Using a Master Equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable to correctly predict the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high and low activity states alternate (UP-DOWN state dynamics), leading to slow oscillations. We conclude that such mean-field models are “biologically realistic” in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large scale models involving multiple brain areas.

Performance Analysis of Work Stealing in Large-scale Multithreaded Computing

2021 ◽  
Vol 6 (2) ◽  
pp. 1-28
Author(s):  
Nikki Sonenberg ◽  
Grzegorz Kielanski ◽  
Benny Van Houdt
Keyword(s):  
Fixed Point ◽  
Large Scale ◽  
Field Model ◽  
Unique Fixed Point ◽  
Mean Field ◽  
Response Time Distribution ◽  
Mean Field Model ◽  
Work Stealing ◽  
Poisson Arrivals ◽  
The Mean

Randomized work stealing is used in distributed systems to increase performance and improve resource utilization. In this article, we consider randomized work stealing in a large system of homogeneous processors where parent jobs spawn child jobs that can feasibly be executed in parallel with the parent job. We analyse the performance of two work stealing strategies: one where only child jobs can be transferred across servers and the other where parent jobs are transferred. We define a mean-field model to derive the response time distribution in a large-scale system with Poisson arrivals and exponential parent and child job durations. We prove that the model has a unique fixed point that corresponds to the steady state of a structured Markov chain, allowing us to use matrix analytic methods to compute the unique fixed point. The accuracy of the mean-field model is validated using simulation. Using numerical examples, we illustrate the effect of different probe rates, load, and different child job size distributions on performance with respect to the two stealing strategies, individually, and compared to each other.

scholarly journals Mean-field models for EEG/MEG: from oscillations to waves

2020 ◽  
Author(s):  
Á. Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been actively used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomeno-logical in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit to an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

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