Hybrid discrete-time neural networks

Cao, Hongjun; Ibarz, Borja

doi:10.1098/rsta.2010.0171

Cited by 15 publications

(8 citation statements)

References 44 publications

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“…Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time, also called map-based, the result is a hybrid discrete-time system (Cao & Ibarz, 2010).…”

Section: Mathematical Methodsmentioning

confidence: 99%

Quantitative Phenomics of Growth and Size in Animals

Stass¹

2019

IJB

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This study introduces a model of the growth phenotype dynamic in pigs by applying analytical methods. The model describes a transformation of the growth phenotype from 30kg live weight up to the species maximum weight. This paper focuses on a description of the determinants, which channel growth dynamic through animals' ontogeny. Theoretical notions about the growth are explicitly included in the concept. In the model, functional relations between relevant traits obtained in the experiments and field observations are analysed. Two focal variables, a feed conversion coefficient, and an invariant of growth are explicitly integrated in the model. The novelty of the research is a proposition that deterministic, analytical model is a conceivable approach to studying a phenotype of a quantitative trait. According to this proposition, processes that contribute to the growth and development continue in later life till a species maximum weight is attained. The concept is formulated as a deterministic, hybrid model. In the model, both standard continuum methods and discrete-time difference equations have been used. Applied to experimental data, the model has produced a new insight into the problem. In domestic pigs, the following three sets of ontogenetic growth phenotypes have been identified: one set with three species maximum weight phenotypes, one set with three rapid growth phenotypes, and one set with individual maximum weight phenotypes. In the study, not only the sets of growth phenotype are identified but also a possible interpretation of a conversion mode of the sets in ontogeny as well as a reading of growth trajectory dynamic are discussed.

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Section: Mathematical Methodsmentioning

confidence: 99%

Quantitative Phenomics of Growth and Size in Animals

Stass¹

2019

IJB

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“…In this field, neither a hybrid model for animal growth was published nor an appropriate modelling technique specified. Hybrid dynamical systems combine evolution equations with state transitions; when the evolution equations are discrete-time, also called map-based, the result is a hybrid discrete-time system (Cao & Ibarz, 2010). …”

Section: Hybrid Model For Animal Growthmentioning

confidence: 99%

An Analytical Model of Animal Growth

Stass¹

2017

ESJ

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The purpose of this study was to explain some aspects of ontogenetic growth in pigs by analysing the relationships between variables that are significant to the development of animals. The novelty of the study is a new modelling approach to the growth problem, with the attention that has been paid to both a new set of variables, and an analytical discrete-continuous hybrid model, innovative for the field. This is a first species-specific hybrid model for animal growth formulated in discrete-time difference equation technique. The efficiency of the model is not only due to the modelling technique but also due to a set of relevant variables, especially a feed conversion coefficient, which provides a link between macro and micro physiological scales. The model is based on functional relationships between relevant variables acquired from experimental data analyses, and field observations. The concept explains some aspects of growth in pigs from 30 kg to 600 kg, which is considered the maximum individual weight for a boar, and further growth up to a species maximum weight. The model predicts that boar can reach their maximum individual weight of 600 kg when 6,40 years old and are required to consume 62,51 kg of feed to put on the last kilogram. The phenotypes that can attain their maximum individual weight go through bifurcation of the growth trajectory, a transform in the growth mode. After bifurcation, the smallest number of the phenotypes go on the growth trajectory that leads to a set of species maximum weights of over 1205 kg, and the greatest number of phenotypes continue to live until aged 24,90 years, provided their maximum weights do not change. The study includes growth rate equations, identifies species maximum weight phenotypes, and produces insight into pig longevity. The results suggest that species maximum weight growth trajectories are phenotype-dependant. A modified discrete-time difference equation technique combined with standard continuum methods is an appropriate formalism to model ontogenetic growth in animals.

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“…The third set of topics of neurons, neural systems and neuromechanics is taken up by Izhikevich (2010), Cao & Ibarz (2010) and Proctor et al (2010).…”

Section: Hybrid Dynamical Systems In Biology and Medicinementioning

confidence: 99%

“…While the latter is represented as continuous and smooth interactions, the former provides a connection scheme with switching dynamics depending on spikes generated by neuronal firing. Cao & Ibarz (2010) examine discrete-time hybrid neural networks with not only chemical but also electrical synapses. As an example of a hybrid systems approach to higher brain functions, Sato et al (2007) formulated Bayesian inference with continuous and binary variables, the latter of which represents whether or not visual and auditory stimuli originate from the same source.…”

Section: Hybrid Dynamical Systems In Biology and Medicinementioning

confidence: 99%

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Theory of hybrid dynamical systems and its applications to biological and medical systems

Aihara

Suzuki

2010

Phil. Trans. R. Soc. A.

105

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In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on-off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.Keywords: hybrid dynamical systems; mathematical modelling; biological systems; medical systems; nonlinear dynamics; control Nonlinear dynamics and mathematical modellingThe history of natural science can be traced back to Isaac Newton in the seventeenth century. He formulated equations relating force and motion and co-invented calculus. This seminal work inaugurated the field of dynamical systems. His laws of force and motion are also the origin of mathematical modelling of dynamical phenomena in this world. Because calculus generally hates discontinuities and instabilities, most classical studies of dynamical systems and mathematical modelling concentrated on solutions that were smooth and stable. The universe was thus conceived of as a precision machine with smoothness and stability; based on the initial conditions, one could accurately predict future behaviour such as that of planets orbiting the Sun or that of a pendulum clock. However, in the 1960s and 1970s, 'catastrophe theory' (Thom 1975) and 'chaos theory' (Li & Yorke 1975;May 1976) were formulated as special branches of dynamical syst...

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Hybrid discrete-time neural networks

Cited by 15 publications

References 44 publications

Quantitative Phenomics of Growth and Size in Animals

Quantitative Phenomics of Growth and Size in Animals

An Analytical Model of Animal Growth

Theory of hybrid dynamical systems and its applications to biological and medical systems

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