scholarly journals A unified framework for analysis of individual-based models in ecology and beyond

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Stephen J. Cornell ◽  
Yevhen F. Suprunenko ◽  
Dmitri Finkelshtein ◽  
Panu Somervuo ◽  
Otso Ovaskainen
Keyword(s):  
Conservation Biology ◽  
Evolutionary Ecology ◽  
Movement Ecology ◽  
Algebraic Manipulation ◽  
Mathematical Framework ◽  
Unified Framework ◽  
Individual Based Models ◽  
Complex Models ◽  
Simulation Results ◽  
Scientific Fields

Abstract Individual-based models, ‘IBMs’, describe naturally the dynamics of interacting organisms or social or financial agents. They are considered too complex for mathematical analysis, but computer simulations of them cannot give the general insights required. Here, we resolve this problem with a general mathematical framework for IBMs containing interactions of an unlimited level of complexity, and derive equations that reliably approximate the effects of space and stochasticity. We provide software, specified in an accessible and intuitive graphical way, so any researcher can obtain analytical and simulation results for any particular IBM without algebraic manipulation. We illustrate the framework with examples from movement ecology, conservation biology, and evolutionary ecology. This framework will provide unprecedented insights into a hitherto intractable panoply of complex models across many scientific fields.

A unified framework for the design of low-complexity wavelet filters

2017 ◽  
Vol 15 (06) ◽  
pp. 1750054 ◽  
Author(s):  
Ameya K. Naik ◽  
Raghunath S. Holambe
Keyword(s):  
Feature Extraction ◽  
Compact Support ◽  
Low Complexity ◽  
Design Parameters ◽  
Unified Framework ◽  
Vanishing Moments ◽  
Wavelet Filters ◽  
Design Variables ◽  
Optimum Filter ◽  
Simulation Results

An outline is presented for construction of wavelet filters with compact support. Our approach does not require any extensive simulations for obtaining the values of design variables like other methods. A unified framework is proposed for designing halfband polynomials with varying vanishing moments. Optimum filter pairs can then be generated by factorization of the halfband polynomial. Although these optimum wavelets have characteristics close to that of CDF 9/7 (Cohen-Daubechies-Feauveau), a compact support may not be guaranteed. Subsequently, we show that by proper choice of design parameters finite wordlength wavelet construction can be achieved. These hardware friendly wavelets are analyzed for their possible applications in image compression and feature extraction. Simulation results show that the designed wavelets give better performances as compared to standard wavelets. Moreover, the designed wavelets can be implemented with significantly reduced hardware as compared to the existing wavelets.

scholarly journals The non-power model of the genetic code: a paradigm for interpreting genomic information

2016 ◽  
Vol 374 (2063) ◽  
pp. 20150062 ◽  
Author(s):  
Diego Luis Gonzalez ◽  
Simone Giannerini ◽  
Rodolfo Rosa
Keyword(s):  
Genetic Code ◽  
Power Model ◽  
Mathematical Framework ◽  
Genomic Information ◽  
Unified Framework ◽  
Hidden Symmetries ◽  
Protein Coding ◽  
The Core ◽  
Domains Of Life ◽  
Mitochondrial Code

In this article, we present a mathematical framework based on redundant (non-power) representations of integer numbers as a paradigm for the interpretation of genomic information. The core of the approach relies on modelling the degeneracy of the genetic code. The model allows one to explain many features and symmetries of the genetic code and to uncover hidden symmetries. Also, it provides us with new tools for the analysis of genomic sequences. We review briefly three main areas: (i) the Euplotid nuclear code, (ii) the vertebrate mitochondrial code, and (iii) the main coding/decoding strategies used in the three domains of life. In every case, we show how the non-power model is a natural unified framework for describing degeneracy and deriving sound biological hypotheses on protein coding. The approach is rooted on number theory and group theory; nevertheless, we have kept the technical level to a minimum by focusing on key concepts and on the biological implications.

Exploration of Spatial Scale Sensitivity in Geographic Cellular Automata

2005 ◽  
Vol 32 (5) ◽  
pp. 693-714 ◽  
Author(s):  
André Ménard ◽  
Danielle J Marceau
Keyword(s):  
Cellular Automata ◽  
Land Cover ◽  
Spatial Scale ◽  
Data Availability ◽  
Von Neumann ◽  
Geographic Context ◽  
Individual Based Models ◽  
Considerable Impact ◽  
Simulation Results ◽  
Transition Rules

Cellular automata (CA) are individual-based models in which states, time, and space are discrete. Spatiotemporal dynamics emerge from the simple and local interactions of the cells. When using CA in a geographic context, nontrivial questions have to be answered about the choice of spatial scale, namely cell size and neighbourhood configuration. However, the spatial scale decisions involved in the elaboration of geographic cellular automata (GCA) are often made arbitrarily or in relation to data availability. The objective of this study is to evaluate the sensitivity of GCA to spatial scale. A stochastic GCA was built to model land-cover change in the Maskoutains region (Quebec, Canada). The transition rules were empirically derived from two Landsat-TM (30 m resolution) images taken in 1999 and 2002 that have been resampled to four resolutions (100, 200, 500, 1000 m). Six different neighbourhood configurations were considered (Moore, Von Neumann, and circular approximations of 2, 3, 4, and 5 cell radii). Simulations were performed for each of the thirty spatial scale scenarios. Results show that spatial scale has a considerable impact on simulation dynamics in terms of both land-cover area and spatial structure. The spatial scale domains present in the results reveal the nonlinear relationships that link the spatial scale components to the simulation results.

scholarly journals A unified framework for dissecting the effects of common signals on functional and effective connectivity analyses: power, coherence, and Granger causality

2017 ◽  
Author(s):  
Dror Cohen ◽  
Naotsugu Tsuchiya
Keyword(s):  
Granger Causality ◽  
Effective Connectivity ◽  
Reference Electrode ◽  
Mathematical Framework ◽  
Connectivity Analysis ◽  
Unified Framework ◽  
Special Cases ◽  
Recorded Data ◽  
The Common ◽  
Common Signal

AbstractWhen analyzing neural data it is important to consider the limitations of the particular experimental setup. An enduring issue in the context of electrophysiology is the presence of common signals. For example a non-silent reference electrode adds a common signal across all recorded data and this adversely affects functional and effective connectivity analysis. To address the common signals problem, a number of methods have been proposed, but relatively few detailed investigations have been carried out. We address this gap by analyzing local field potentials recorded from the small brains of fruit flies. We conduct our analysis following a solid mathematical framework that allows us to make precise predictions regarding the nature of the common signals. We demonstrate how a framework that jointly analyzes power, coherence and quantities from the Granger causality framework allows us to detect and assess the nature of the common signals. Our analysis revealed substantial common signals in our data, in part due to a non-silent reference electrode. We further show that subtracting spatially adjacent signals (bipolar rereferencing) largely removes the effects of the common signals. However, in some special cases this operation itself introduces a common signal. The mathematical framework and analysis pipeline we present can readily be used by others to detect and assess the nature of the common signals in their data, thereby reducing the chance of misinterpreting the results of functional and effective connectivity analysis.

scholarly journals The importance of individual variation in the dynamics of animal collective movements

2018 ◽  
Vol 373 (1746) ◽  
pp. 20170008 ◽  
Author(s):  
Maria del Mar Delgado ◽  
Maria Miranda ◽  
Silvia J. Alvarez ◽  
Eliezer Gurarie ◽  
William F. Fagan ◽  
...  
Keyword(s):  
Individual Variation ◽  
Decision Rules ◽  
Movement Ecology ◽  
Individual Variability ◽  
Collective Movement ◽  
Individual Based Models ◽  
Theoretical Investigations ◽  
Group Heterogeneity ◽  
Collective Movements ◽  
The Individual

Animal collective movements are a key example of a system that links two clearly defined levels of organization: the individual and the group. Most models investigating collective movements have generated coherent collective behaviours without the inclusion of individual variability. However, new individual-based models, together with emerging empirical information, emphasize that within-group heterogeneity may strongly influence collective movement behaviour. Here we (i) review the empirical evidence for individual variation in animal collective movements, (ii) explore how theoretical investigations have represented individual heterogeneity when modelling collective movements and (iii) present a model to show how within-group heterogeneity influences the collective properties of a group. Our review underscores the need to consider variability at the level of the individual to improve our understanding of how individual decision rules lead to emergent movement patterns, and also to yield better quantitative predictions of collective behaviour. This article is part of the theme issue ‘Collective movement ecology’.

scholarly journals The Framework of Mechanics for Dynamic Behaviors of Fractional-Order Stochastic Dynamic Systems

2021 ◽  
Author(s):  
Ruibin Ren ◽  
George Yuan
Keyword(s):  
Fractional Order ◽  
Dynamic Systems ◽  
Stochastic Dynamics ◽  
Stochastic Dynamic ◽  
Frequency Noise ◽  
Mathematical Framework ◽  
Coupled Models ◽  
Dynamic Behaviors ◽  
Simulation Results ◽  
Stochastic Dynamic Systems

Abstract The main goal of this paper is to establish a general framework for dynamic behaviors of coupled fractional-order stochastic dynamic systems of particles by using star-coupled models. In particular, the general mechanics on the dynamic behaviors related to the stochastic resonance (SR) phenomenon of a starcoupled harmonic oscillator subject to multiplicative fluctuation and periodic force in viscous media are established by considering couplings, memory effects, the occurring of synchronization linked to the occurring of SR induced. Here the noise is modeled with the fractional power kernel function and analytical expressions for the first moment of the stability between system responses and parameters in the long-time (of asymptotic stability) are also given. The theoretic and simulation results show the non-monotonic dependence between the response output gain and the input signal frequency, noise parameters provided by fractional-order stochastic dynamics are significant different by comparing those exhibited under the traditional integer-order stochastic dynamics, which indicates that the bona fide resonance and the generalized SR phenomena would appear. Furthermore, the fluctuation noise, the number of the particles for the systems, and the fractional order work together, producing more complex dynamic phenomena compared with the traditional integral-order systems. The theoretical analyses are supported by the corresponding numerical simulations, and thus it seems that the results established in this paper would provide a possible fundamental mathematical framework for the study of Schumpeter’s theory on the economic development under the “innovation and capital paradigm” and related disciplines. In particular, the framework established by this paper allows us at the first time logically concluding that “in principle. the ratio of SMEs growing up successfully is less than one third”, this is consistent with what the market has been observed commonly, but similar conclusion not available from the existing literature today. Finally, we like to point out that the framework established in this paper actually shows that under the basic model established in Section 2, through numerical simulation results given in sections 3 and 4, the fractional derivative in the interval (0; 1) as a basic tool, which can provide a new world with a more refined description of the market financial scene, such as in identifying risk factors or describing mechanics for enterprises’ growths more precisely with extra features compared with the traditional integer derivative one.

scholarly journals Information Content-Based Gene Ontology Semantic Similarity Approaches: Toward a Unified Framework Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Gaston K. Mazandu ◽  
Nicola J. Mulder
Keyword(s):  
Gene Ontology ◽  
Information Content ◽  
Semantic Similarity ◽  
Experimental Evaluation ◽  
Similarity Measures ◽  
Mathematical Framework ◽  
Unified Framework ◽  
The Impact ◽  
Unified Description ◽  
Similarity Scores

Several approaches have been proposed for computing term information content (IC) and semantic similarity scores within the gene ontology (GO) directed acyclic graph (DAG). These approaches contributed to improving protein analyses at the functional level. Considering the recent proliferation of these approaches, a unified theory in a well-defined mathematical framework is necessary in order to provide a theoretical basis for validating these approaches. We review the existing IC-based ontological similarity approaches developed in the context of biomedical and bioinformatics fields to propose a general framework and unified description of all these measures. We have conducted an experimental evaluation to assess the impact of IC approaches, different normalization models, and correction factors on the performance of a functional similarity metric. Results reveal that considering only parents or only children of terms when assessing information content or semantic similarity scores negatively impacts the approach under consideration. This study produces a unified framework for current and future GO semantic similarity measures and provides theoretical basics for comparing different approaches. The experimental evaluation of different approaches based on different term information content models paves the way towards a solution to the issue of scoring a term’s specificity in the GO DAG.

The Virtual Kidney: an eScience interface and Grid portal

2009 ◽  
Vol 367 (1896) ◽  
pp. 2141-2159 ◽  
Author(s):  
Peter J. Harris ◽  
Rajkumar Buyya ◽  
Xingchen Chu ◽  
Tom Kobialka ◽  
Ed Kazmierczak ◽  
...  
Keyword(s):  
Communication Networks ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Grid Resource ◽  
Knowledge Resources ◽  
High Bandwidth ◽  
Complex Models ◽  
Simulation Results ◽  
Access To Knowledge ◽  
Parameter Values

The Virtual Kidney uses a web interface and distributed computing to provide experimental scientists and analysts with access to computational simulations and knowledge databases hosted in geographically separated laboratories. Users can explore a variety of complex models without requiring the specific programming environment in which applications have been developed. This initiative exploits high-bandwidth communication networks for collaborative research and for shared access to knowledge resources. The Virtual Kidney has been developed within a specialist community of renal scientists but is transferable to other areas of research requiring interaction between published literature and databases, theoretical models and simulations and the formulation of effective experimental designs. A web-based three-dimensional interface provides access to experimental data, a parameter database and mathematical models. A multi-scale kidney reconstruction includes blood vessels and serially sectioned nephrons. Selection of structures provides links to the database, returning parameter values and extracts from the literature. Models are run locally or remotely with a Grid resource broker managing scheduling, monitoring and visualization of simulation results and application, credential and resource allocation. Simulation results are viewed graphically or as scaled colour gradients on the Virtual Kidney structures, allowing visual and quantitative appreciation of the effects of simulated parameter changes.

Finite Element Method for Kinematic Analysis of Parallel Hip Joint Manipulator

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Gang Cheng ◽  
Song-tao Wang ◽  
De-hua Yang ◽  
Jian-hua Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hip Joint ◽  
Solution Process ◽  
Parallel Manipulators ◽  
Mathematical Framework ◽  
Simulation Results ◽  
Theory Base ◽  
Kinematic Solution ◽  
Element Method

This paper presents a finite element method (FEM) for the kinematic solution of parallel manipulators (PMs), and this approach is applied to analyze the kinematics of a parallel hip joint manipulator (PHJM). The analysis and simulation results indicate that FEM can get accurate results of the kinematics of the PHJM, and the solution process shows that using FEM can solve nonlinear and linear kinematic problems in the same mathematical framework, which provides a theory base for establishing integrated model among different parameter models of the PHJM.

Numerical Simulation of Rock Fracture under Dynamic Loading Using Manifold Method

2006 ◽  
Vol 324-325 ◽  
pp. 235-238 ◽  
Author(s):  
Peng Wan Chen ◽  
Tao Huang ◽  
Jun Yang ◽  
Guo Xin Zhang
Keyword(s):  
Crack Initiation ◽  
Rock Fracture ◽  
Stress Waves ◽  
The Other ◽  
Crack Initiation And Propagation ◽  
Unified Framework ◽  
Initiation And Propagation ◽  
Fragment Formation ◽  
Simulation Results ◽  
Good Agreement

Manifold Method provides a unified framework for solving problems with both continuous and discontinuous media. In this paper, by introducing a criterion of crack initiation and propagation, the second order manifold method is used to simulate two-hole blasting and Hopkinson spalling of rock. In the study of two-hole blasting, two different initiation conditions are considered. One is simultaneous initiation, the other is 0.1 ms delay initiation. The whole blasting process including crack initiation, crack growth and fragment formation is simulated. In the study of Hopkinson spalling, the propagation and interaction of stress waves and the spalling process caused by a reflected tensile stress wave are reproduced. The simulation results including the thickness of the formed scab and its velocity are in good agreement with theoretical values. Manifold method proves to be an efficient method in the study of dynamic fracture of rock.

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