scholarly journals Fluid Approximation–based Analysis for Mode-switching Population Dynamics

2021 ◽  
Vol 31 (2) ◽  
pp. 1-26
Author(s):  
Paul Piho ◽  
Jane Hillston
Keyword(s):  
Population Dynamics ◽  
Mode Switching ◽  
Fluid Limit ◽  
Fluid Approximation ◽  
Large Numbers ◽  
Piecewise Deterministic Markov Processes ◽  
Computer Based ◽  
The Mean ◽  
Scalable Analysis ◽  
Hybrid Fluid

Fluid approximation results provide powerful methods for scalable analysis of models of population dynamics with large numbers of discrete states and have seen wide-ranging applications in modelling biological and computer-based systems and model checking. However, the applicability of these methods relies on assumptions that are not easily met in a number of modelling scenarios. This article focuses on one particular class of scenarios in which rapid information propagation in the system is considered. In particular, we study the case where changes in population dynamics are induced by information about the environment being communicated between components of the population via broadcast communication. We see how existing hybrid fluid limit results, resulting in piecewise deterministic Markov processes, can be adapted to such models. Finally, we propose heuristic constructions for extracting the mean behaviour from the resulting approximations without the need to simulate individual trajectories.

scholarly journals Laws of Little in an open queueing network

2012 ◽  
Vol 17 (3) ◽  
pp. 327-342 ◽  
Author(s):  
Saulius Minkevičius ◽  
Stasys Steišūnas
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Queue Length ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Fluid Limit ◽  
Fluid Approximation ◽  
Large Numbers ◽  
Virtual Waiting Time ◽  
Open Queueing Network

The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of Little in OQN are presented.

scholarly journals Relaxation Times in Strictly Disk Systems

1971 ◽  
Vol 10 ◽  
pp. 15-19
Author(s):  
George B. Rybicki
Keyword(s):  
Numerical Experiments ◽  
Relaxation Times ◽  
Galactic Structure ◽  
Large Numbers ◽  
Order Of Magnitude ◽  
Vlasov Limit ◽  
The Mean ◽  
Gravitating Systems

AbstractIt is shown that the time of relaxation by particle encounters of self-gravitating systems in the plane interacting by 1/r2 forces is of the same order of magnitude as the mean orbit time. Therefore such a system does not have a Vlasov limit for large numbers of particles, unless appeal is made to some non-zero thickness of the disk. The relevance of this result to numerical experiments on galactic structure is discussed.

GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250013 ◽  
Author(s):  
IOANA DUMITRIU ◽  
ELLIOT PAQUETTE
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Law Of Large Numbers ◽  
Test Functions ◽  
Linear Statistics ◽  
Jacobi Ensemble ◽  
Large Numbers ◽  
The Mean ◽  
Shifted Chebyshev Polynomial ◽  
Global Fluctuations

We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.

PREDATION BY INSECTS AND SPIDERS INHABITING COLONIAL WEBS OF HYPHANTRIA CUNEA

1972 ◽  
Vol 104 (8) ◽  
pp. 1197-1207 ◽  
Author(s):  
R. F. Morris
Keyword(s):  
Population Dynamics ◽  
Nova Scotia ◽  
North America ◽  
Population Density ◽  
New Brunswick ◽  
Numerical Response ◽  
Initial Number ◽  
Hyphantria Cunea ◽  
The North ◽  
The Mean

AbstractThe number of predators inhabiting nests of Hyphantria cunea Drury was recorded annually for 13 years in four areas in New Brunswick and two areas on the coast of Nova Scotia. The most common groups were the pentatomids and spiders, which sometimes reproduced within the nests, but the mean number per nest was low in relation to the number of H. cunea larvae in the colonies. The rate of predation on fifth-instar larvae was low. Small or timid predators appeared to prey largely on moribund larvae or small saprophagans during the principal defoliating instars of H. cunea.No relationship could be detected between the number of larvae reaching the fifth instar and the number of predators in the colony; nor could any functional or numerical response of the predators to either the initial number of larvae per colony or the population density of colonies be found. It is concluded that the influence of the nest-inhabiting predators is small and relatively stable, and may be treated as a constant in the development of models to explain the population dynamics of H. cunea.H. cunea is a pest in parts of Europe and Asia, where it has been accidentally introduced from North America. The introduction to other continents of the North American predator, Podisus maculiventiis (Say), is discussed briefly.

scholarly journals Limit Theorems and Fluctuations for Point Vortices of Generalized Euler Equations

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Carina Geldhauser ◽  
Marco Romito
Keyword(s):  
Euler Equations ◽  
Mean Field ◽  
Point Vortices ◽  
Positive Temperature ◽  
Field Limit ◽  
Mean Field Limit ◽  
Large Numbers ◽  
The Mean ◽  
Formal Solutions ◽  
2D Torus

AbstractWe prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.

ASYNCHRONOUS UPDATING RESTORES THE LAW OF LARGE NUMBERS IN GLOBALLY COUPLED SYSTEMS

2002 ◽  
Vol 12 (03) ◽  
pp. 663-669 ◽  
Author(s):  
SUDESHNA SINHA
Keyword(s):  
Law Of Large Numbers ◽  
Mean Field ◽  
Coupled Systems ◽  
Large N ◽  
Large Numbers ◽  
Statistical Behavior ◽  
Remarkable Result ◽  
Asynchronous Updating ◽  
The Mean ◽  
The Law

It was observed in earlier studies, that the mean field of globally coupled maps evolving under synchronous updating rules violated the law of large numbers, and this remarkable result generated widespread research interest. In this work we demonstrate that incorporating increasing degrees of asynchronicity in the updating rules rapidly restores the statistical behavior of the mean field. This is clear from the decay of the mean square deviation of the mean field with respect to lattice size N, for varying degrees of asynchronicity, which shows 1/N behavior upto very large N even when the updating is far from fully asynchronous. This is also evidenced through increasing 1/f2 behavior regimes in the power spectrum of the mean field under increasing asynchronicity.

scholarly journals Population dynamics of the pea crab Austinixa aidae (Brachyura, Pinnotheridae): a symbiotic of the ghost shrimp Callichirus major (Thalassinidea, Callianassidae) from the southwestern Atlantic

2011 ◽  
Vol 101 (1-2) ◽  
pp. 5-14 ◽  
Author(s):  
Douglas F Peiró ◽  
Fernando L Mantelatto
Keyword(s):  
Population Dynamics ◽  
Sandy Beach ◽  
Southwestern Atlantic ◽  
Recruitment Pattern ◽  
Size Frequency Distribution ◽  
Ghost Shrimp ◽  
Density Values ◽  
Pea Crab ◽  
Biological Aspects ◽  
The Mean

The Pinnotheridae family is one of the most diverse and complex groups of brachyuran crabs, many of them symbionts of a wide variety of invertebrates. The present study describes the population dynamics of the pea crab Austinixa aidae (Righi, 1967), a symbiont associated with the burrows of the ghost shrimp Callichirus major (Say, 1818). Individuals (n = 588) were collected bimonthly from May, 2005 to September, 2006 along a sandy beach in the southwestern Atlantic, state of São Paulo, Brazil. Our data indicated that the population demography of A. aidae was characterized by a bimodal size-frequency distribution (between 2.0 and 4.0 mm and between 8.0 and 9.0 mm CW) that remained similar throughout the study period. Sex ratio does not differ significantly from 1:1 (p > 0.05), which confirms the pattern observed in other symbiontic pinnotherids. Density values (1.72 ± 1.34 ind. • ap.-1) are in agreement with those found for other species of the genus. The mean symbiosis incidence (75.6%) was one of the highest among species of the Pinnotheridae family, but it was the lowest among the three studied species of the genus. Recruitment pattern was annual, beginning in May and peaking in July, in both years, after the peak of ovigerous females in the population (from March to May). Our findings describe ecological and biological aspects of A. aidae similar to those of other species of this genus, even from different geographic localities.

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

scholarly journals Peningkatan Efisiensi Kerja Guru Melalui Pembuatan Aplikasi Rapor Berbasis Komputer

2019 ◽  
Vol 4 (2) ◽  
pp. 363-370
Author(s):  
Romy Budhi Widodo ◽  
Mochamad Subianto ◽  
Grace Imelda
Keyword(s):  
Junior High School ◽  
User Satisfaction ◽  
Information Quality ◽  
Application Development ◽  
Interface Quality ◽  
Software Application ◽  
Computer Based ◽  
The Mean ◽  
Spiral Model ◽  
Prototype Evaluation

The domain of the activity is technology for the society whereas the focus is practical computer science for the society. The background of our activity is based on the needs of YPK junior high school in Malang city, Indonesia. The school need to develop computer-based school report card and also daily grade card for teachers. The method for software/application development is spiral model which consist of the cycle of system identification, risk analysis, and enhancement of the prototype to be an operational prototype. Evaluation of the product was based on the Computer System Usability Questionnaire (CSUQ) from IBM. The CSUQ using 5 scale of Likert scale contains three categories: 1) system usefulness (SYSUSE), 2) information quality (INFOQUAL), and 3) interface quality (INTERQUAL). The mean rank’s result in order from the greatest to the lowest is SYSUSE, INTERQUAL, and INFOQUAL, respectively. It was reported that SYSUSE category was superior to INFOQUAL (U = 3369.5, p = 0.0005). Overall, the user satisfaction score is 78.4%, which is in the “worthy” category

scholarly journals Linking lineage and population observables in biological branching processes

2019 ◽  
Author(s):  
Reinaldo García-García ◽  
Arthur Genthon ◽  
David Lacoste
Keyword(s):  
Population Dynamics ◽  
Generation Time ◽  
Doubling Time ◽  
Branching Processes ◽  
Underlying Mechanism ◽  
Population Doubling ◽  
Population Doubling Time ◽  
Division Rate ◽  
Fluctuation Theorems ◽  
The Mean

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. We argue that testing these inequalities provides useful insights into the underlying mechanism controlling the division rate in such branching processes.

Sign in / Sign up

Export Citation Format

Share Document