Search Results

This chapter discusses foundational issues in modeling, such as the differences between deterministic and stochastic models as well as the strategic, tactical, and operational model guidance horizons. It also explains how agent-based modeling and simulation fits into this context.

This chapter talks about deterministic models as expressions of ecological hypotheses. These models are based on a deterministic equation or equations making predictions that can be compared with observations. The nature of the model ensures that there is no uncertainty in such predictions. Hence, the chapter first discusses the different ways that deterministic models have been used in ecology; identifying three main ones: theoretical, empirical, and simulation. It then outlines a few deterministic models widely used in ecology. Rather than attempting a comprehensive treatment of the subject, the chapter instead introduces a set of core functions that are widely used to represent ecological process across all subdisciplines.

This chapter describes basic biological mechanisms in a way that can be represented by simple dynamical models. It begins with a discussion of the basic modeling formalisms that will be utilized to model biomolecular feedback systems. The focus in this chapter (as well as the next) is on deterministic models using ordinary differential equations. Here, the chapter proceeds to study a number of core processes within the cell, providing different model-based descriptions of the dynamics that will be used in later chapters to analyze and design biomolecular systems. In this chapter, emphasis is placed on dynamics with time scales measured in seconds to hours and mean behavior averaged across a large number of molecules.

Many problems in economics require the solution to a functional equation as an intermediate step, and typically, decision functions are sought that satisfy a set of Euler conditions or a value function that satisfies Bellman's equation. However, in many cases, analytical solutions cannot be derived for these functions, and numerical methods are needed instead. Shows how to apply weighted residual and finite‐element methods to this type of problem by illustrating their application to various examples. The first type of problem involves a simple differential equation because the coefficients to be computed satisfy a linear system of equations, and no computer is needed for the solution. Weighted residual and finite‐element methods are then applied to a deterministic growth model and a stochastic growth model—two standard models used in economics; in these examples, the coefficients to be computed satisfy nonlinear systems of equations, which, fortunately, are exploitably sparse if they are derived from a finite‐element method.

This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the dynamics of a system using the input/output modeling formalism described in Chapter 1 and then studies the “robustness” of the system of a given function of the circuit. The chapter then discusses some of the underlying ideas for how to model biological oscillatory behavior, focusing on those types of oscillations that are most common in biomolecular systems. Hereafter, the chapter explores how the location of equilibrium points, their stability, their regions of attraction, and other dynamic phenomena vary based on the values of the parameters in a model. Finally, methods for reducing the complexity of the models that are introduced in this chapter are reviewed.

This chapter introduces mathematical and statistical modelling approaches in population ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to population ecology. The mathematical sections start by constructing an individual-based model in homogeneous space, and then simplifies the model to derive the classical model of logistic population growth. The models are then expanded to heterogeneous space in two contrasting ways, resulting in models called the plant population model and the butterfly metapopulation model. Both types of models are used to analyse the consequences of habitat loss and fragmentation at the population level. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on the analyses of time-series data, species distribution modelling, and metapopulation modelling.

Mathematical models are essential components of the toolbox of any disease ecologist. They should be used as an integral part of any investigation into the impact and management of infectious disease in wildlife populations. Simple models are important to conceptualize the processes occurring during host–pathogen interactions and to identify key components of these interactions. More detailed models, specific to the system in question, can be developed later in an investigation and are essential for evaluating the consequences of alternative management actions. Various models of infectious disease dynamics are available to assist in managing disease in wildlife, including single-host and multihost models, and are discussed here. The basic reproductive number R₀, the number of secondary cases per primary case when disease is rare, can be derived from these models. This is a key concept in practical epidemiology, because eliminating a pathogen from a population entails reducing R₀ to below one and disease emergence can only occur if R₀ becomes greater than one.

This chapter tackles four distinct objectives. The first is that it presents the general approach to developing the models of simple and complex systems which are to be used throughout the book in discussing energetic food webs. These models are deterministic models in nature, but are also applicable to the study of the uncertainty of random fluctuations in the environment. The second objective is to determine whether the special configurations of model systems, as well as other dynamic properties of the models, are all inherently stable. The third objective of the chapter is to develop and assess the dynamics and stability of two models: models based on primary producers, and models based on detritus. Finally, the fourth objective is to compare the structure and dynamics of these two models, and how each contributes to further knowledge of energetic food webs.

What need we know of the workings of Nature in order to appreciate how consciousness may be part of it? Does it really matter what are the laws that govern the constituent elements of bodies and brains? If our conscious perceptions are merely the enacting of algorithms, as many AI supporters would have us believe, then it would not be of much relevance what these laws actually are. Any device which is capable of acting out an algorithm would be as good as any other. Perhaps, on the other hand, there is more to our feelings of awareness than mere algorithms. Perhaps the detailed way in which we are constituted is indeed of relevance, as are the precise physical laws that actually govern the substance of which we are composed. Perhaps we shall need to understand whatever profound quality it is that underlies the very nature of matter, and decrees the way in which all matter must behave. Physics is not yet at such a point. There are many mysteries to be unravelled and many deep insights yet to be gained. Yet, most physicists and physiologists would judge that we already know enough about those physical laws that are relevant to the workings of such an ordinary-sized object as a human brain. While it is undoubtedly the case that the brain is exceptionally complicated as a physical system, and a vast amount about its detailed structure and relevant operation is not yet known, few would claim that it is in the physical principles underlying its behaviour that there is any significant lack of understanding. I shall later argue an unconventional case that, on the contrary, we do not yet understand physics sufficiently well that the functioning of our brains can be adequately described in terms of it, even in principle. To make this case, it will be necessary for me first to provide some overview of the status of present physical theory. This chapter is concerned with what is called ‘classical physics’, which includes both Newton’s mechanics and Einstein’s relativity.

The empirical literature on gun ownership and gun violence is influenced by philosophical considerations. In this way, “philosophy” is logically prior to empirical evidence. More important, the chapter argues, it affects the way in which one applies, or fails to apply, the results of empirical research to one’s own conduct. Instead, there are ethical reasons for not viewing normal human adults in this way.

The nuclear waste programs of the United States and other countries have forced geologists to think specifically about probabilities of natural events, because the legal requirements to license repositories mandate a probabilistic standard (US EPA, 1985). In addition, uncertainties associated with these probabilities and the predicted performance of a geologic repository must be stated clearly in quantitative terms, as far as possible. Geoscientists rarely have thought in terms of stochasticity or clearly stated uncertainties for their results. All scientists are taught to acknowledge uncertainty and to specify the quantitative uncertainty in each derived or measured value, but this has seldom been done in geology. Thus, the nuclear waste disposal program is forcing us to do now what we should have been doing all along: acknowledge in quantitative terms what uncertainty is associated with each quantity that is employed, whether deterministically or probabilistically. Uncertainty is a simple concept ostensibly understood to mean that which is indeterminate, not certain, containing doubt, indefinite, problematical, not reliable, or dubious. However, uncertainty in a scientific sense demonstrates a complexity which often is unappreciated. Some types of uncertainty are difficult to handle, if they must be quantified, and a completely satisfactory treatment may be impossible. Initially, only uncertainty associated with measurement, was quantified. The Gaussian, or normal, probability density function (pdf) was recognized by Carl Friedrich Gauss as he studied errors in his measurements two centuries ago and developed a theory of errors still being used today. This was the only type of uncertainty that scientists acknowledged until Heisenberg stated his famous uncertainty principle in 1928. As information theory evolved during and after World War II, major advances were made in semantic uncertainty. Today, two major types of uncertainty are generally recognized (Klir and Folger, 1988): ambiguity or nonspecificity and vagueness or fuzziness. These can be subdivided further into seven types having various measures of uncertainty based on probability theory, set theory, fuzzy-set theory, and possibility theory.

Henry Jenkins, former professor of humanities, MIT, is one of the leading science authorities in the analysis of New Media. Today, he is Professor of Communication, Journalism, and Cinematic Arts at USC. In this dialogue, Jenkins explains how technology is transforming the traditional view of humanities. He outlines his vision of convergence culture in his book, Convergence Culture: Where Old and New Media Collide. He explains why he thinks the idea of copyright is an aberration. He goes on to relate the causes for conglomerates losing control of media flows and how to deal with this situation. He describes the new logic framework under which our current participatory culture is run. He defines himself in this dialogue as a critical utopian trying to demonstrate how to harness the great power that changes taking place in new media have on people. Emphasizing the ‘new social skills’, which bring about new forms of ethics, interactions, politics, types of economic activities and legal culture, in the clash between the new digital media and the old mass media.