Search Results

Looking Back and Ahead

Daniel P. Steel

in Across the Boundaries: Extrapolation in Biology and Social Science

This chapter summarizes those that went before and ends by sketching some open questions.

Extrapolation and Its Limits

Stephen Yablo

in Aboutness

If A implies B, then is there always something that we can point to as what A adds to B? The logician, or logical engineer, says yes. The mysterian says no. To get a bead on the issue, this chapter ... More

If A implies B, then is there always something that we can point to as what A adds to B? The logician, or logical engineer, says yes. The mysterian says no. To get a bead on the issue, this chapter distinguished four types of extrapolation: inductive, as in Hume, projective, as in Goodman, alethic, as in Kripkenstein, and type 4, as in Wittgenstein's “conceptual problem of other minds” and his example of 5 o'clock on the sun. Logical subtraction is understood, to begin with, as type 4 extrapolation. A–B is the result of extrapolating A beyond the bounds imposed by B. The question is whether this can always be done.Less

Modeling Ecological Niches

A. Townsend Peterson, Jorge Soberón, Richard G. Pearson, Robert P. Anderson, Enrique Martínez-Meyer, Miguel Nakamura, and Miguel Bastos Araújo

in Ecological Niches and Geographic Distributions (MPB-49)

This chapter explains how environmental data can be used to create models that characterize species’ ecological niches in environmental space. It introduces a model, which is a function constructed ... More

This chapter explains how environmental data can be used to create models that characterize species’ ecological niches in environmental space. It introduces a model, which is a function constructed by means of data analysis for the purpose of approximating the true relationship (that is, the niche) in the form of the function f linking the environment and species occurrences. The chapter first considers the “meaning” of the function f that is being estimated by the algorithms before discussing the modeling algorithms, the approaches used to implement ecological niche modeling, model calibration, model complexity and overfitting, and model extrapolation and transferability. The chapter concludes with an overview of differences among methods and selection of “best” models, along with strategies for characterizing ecological niches in ways that allow visualization, comparisons, definition of quantitative measures, snf more.Less

Extrapolation and Heterogeneity

Daniel P. Steel

in Across the Boundaries: Extrapolation in Biology and Social Science

This chapter introduces the general methodological challenges that confront extrapolation in the biological and social sciences, and sketches the outlines of the mechanisms approach to those ... More

This chapter introduces the general methodological challenges that confront extrapolation in the biological and social sciences, and sketches the outlines of the mechanisms approach to those challenges that is developed in the rest of the book.Less

Extrapolation, Capacities, and Mechanisms

Daniel P. Steel

in Across the Boundaries: Extrapolation in Biology and Social Science

This chapter argues that previous accounts of extrapolation, either by reference to capacities or mechanisms, do not adequately address the challenges confronting extrapolation. It then begins the ... More

This chapter argues that previous accounts of extrapolation, either by reference to capacities or mechanisms, do not adequately address the challenges confronting extrapolation. It then begins the account of how the mechanisms approach can be developed so as to do better. The central concept in this account is what I term comparative process tracing.Less

Ceteris Paribus and Extrapolation

Daniel P. Steel

in Across the Boundaries: Extrapolation in Biology and Social Science

This chapter further develops the mechanisms approach to extrapolation begun in chapter 5 and explores its relevance to the hotly debated issue of ceteris paribus laws. It argues that the ... More

This chapter further develops the mechanisms approach to extrapolation begun in chapter 5 and explores its relevance to the hotly debated issue of ceteris paribus laws. It argues that the difficulties that beset the most problematic type of ceteris paribus law vanish if “ceteris paribus” is interpreted as indicating an inference schema concerning extrapolation rather than as qualifying a universally quantified generalization.Less

Mathematics

G. E. R. Lloyd

in Disciplines in the Making: Cross-Cultural Perspectives on Elites, Learning, and Innovation

This chapter explores the different ways in which what we can call mathematical investigations have been defined and practised in different societies. It argues that there is no one route that the ... More

This chapter explores the different ways in which what we can call mathematical investigations have been defined and practised in different societies. It argues that there is no one route that the development of mathematics had to, or did in practice, follow, once it became the subject of self-conscious inquiries. We have rich evidence on this issue from both ancient Greece and China in particular. Whereas some Greek mathematicians privilege demonstration in the axiomatic-deductive mode, Chinese mathematics was more concerned with heuristics and in growing the subject by extrapolation and analogy. There are also striking differences between Greek and Chinese, and understanding of the relation between mathematics and other areas of investigation, such as music theory and astronomy.Less

Epistemic Enhancers

Paul Humphreys

in Extending Ourselves: Computational Science, Empiricism, and Scientific Method

Extrapolation, conversion, and augmentation are three ways in which our natural observational and computational abilities can be extended. Examples of each are given and the possibility of and need ... More

Extrapolation, conversion, and augmentation are three ways in which our natural observational and computational abilities can be extended. Examples of each are given and the possibility of and need for a completely automated science is explored, with particular reference to the data explosion.Less

Wishful Extrapolation from Research to Patient Care

Charles F. Manski

in Patient Care under Uncertainty

This chapter critiques how evidence from randomized trials has been used to inform medical decision making. Trials have long enjoyed a favored status within medical research on treatment response and ... More

This chapter critiques how evidence from randomized trials has been used to inform medical decision making. Trials have long enjoyed a favored status within medical research on treatment response and are often called the “gold standard” for such research. The U.S. Food and Drug Administration (FDA) ordinarily considers only trial data when making decisions on drug approval. The well-known appeal of trials is that, given sufficient sample size and complete observation of outcomes, they deliver credible findings about treatment response within the study population. However, it is also well-known that extrapolation of findings from trials to clinical practice can be difficult. Researchers and guideline developers often use untenable assumptions to extrapolate. The chapter refers to this practice as wishful extrapolation. It discusses multiple reasons why extrapolation of research findings to clinical practice may be suspect.Less

‘It Is One Story’: Writing a Global Alternate History in Kim Stanley Robinson’s The Years of Rice and Salt

Chris Pak

in Sideways in Time: Critical Essays on Alternate History Fiction

Alternative histories create a ludic space where a game of allusion, extrapolation and speculation is played. Kim Stanley Robinson’s (2002) The Years of Rice and Salt depicts a world that might have ... More

Alternative histories create a ludic space where a game of allusion, extrapolation and speculation is played. Kim Stanley Robinson’s (2002) The Years of Rice and Salt depicts a world that might have developed had European civilisation been eradicated by the Black Death. This chapter examines how Robinson uses science fiction, utopia and the alternate history to examine and challenge assumptions about progress, memory, identity, culture and storytelling. It investigates how The Years of Rice and Salt portray the actors who make up the story of history, how this history is characterised and what repercussions these explorations have for reading the stories that make up contemporary “real-world” history.Less

Instrumental and Experimental Considerations

Eaton E. Lattman, Thomas D. Grant, and Edward H. Snell

in Biological Small Angle Scattering: Theory and Practice

Thic chapter describes some of the processes that are often carried out within specific data processing software associated with an instrument but are invisible to the user. It is useful to be aware ... More

Thic chapter describes some of the processes that are often carried out within specific data processing software associated with an instrument but are invisible to the user. It is useful to be aware of them. These include dealing with detector artifacts and limitations, and the integration of the signal from a two-dimensional image to produce a one-dimensional scattering profile, among other steps.Less

Many Paths, One Journey: Cixin Liu’s Three Body Problem Novels

Bradford Lyau

in Dis-Orienting Planets: Racial Representations of Asia in Science Fiction

Bradford Lyau, in “Many Paths, One Journey: Cixin Liu’s Three Body Problem Novels,” carefully places Cixin Liu’s Three Body trilogy within both Chinese and Western literary traditions before offering ... More

Bradford Lyau, in “Many Paths, One Journey: Cixin Liu’s Three Body Problem Novels,” carefully places Cixin Liu’s Three Body trilogy within both Chinese and Western literary traditions before offering a brief critical analysis of the first two books, where humanity struggles against an impending alien invasion and how humanity also faces its destiny. These two resonances with Western literature, both popular and elite, invite the reader to consider Liu’s novel’s different literary roots: 1) American genre science fiction, 2) the philosophical tale as it emerged in the West, 3) the role of philosophy in Chinese literature, and 4) Chinese science fiction.Less

Thinking ahead

Marian Stamp Dawkins

in Through Our Eyes Only?: The Search for Animal Consciousness

This chapter begins with the most basic ideas of what is meant by thinking. It has to do with ‘working things out in the head’ and so one needs to devise some way of showing that this is what an ... More

This chapter begins with the most basic ideas of what is meant by thinking. It has to do with ‘working things out in the head’ and so one needs to devise some way of showing that this is what an animal is doing. One of the simplest kinds of working things out in the head is extrapolation – an animal is shown something which then disappears and it has to work out where the object will reappear, given that it is behaving in some predictable manner. So, for example, if a piece of food is being dragged along in a particular direction and then goes behind a screen, will the animal look for the food at the place where it disappeared (no extrapolation) or at the far end of the screen where it is due to reappear (true extrapolation)? An animal that could anticipate where something is due to reappear would be showing a rudimentary ability to work things out in its head.Less

Genetic Algorithm (GA) and Internal Energy Transfer Calculations Using Neural Network (NN) Methods

Lionel Raff, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam

in Neural Networks in Chemical Reaction Dynamics

Genetic algorithms (GA), like NNs, can be used to fit highly nonlinear functional forms, such as empirical interatomic potentials from a large ensemble of data. ... More

Genetic algorithms (GA), like NNs, can be used to fit highly nonlinear functional forms, such as empirical interatomic potentials from a large ensemble of data. Briefly, a genetic algorithm uses a stochastic global search method that mimics the process of natural biological evolution. GAs operate on a population of potential solutions applying the principle of survival of the fittest to generate progressively better approximations to a solution. A new set of approximations is generated in each iteration (also known as generation) of a GA through the process of selecting individuals from the solution space according to their fitness levels, and breeding them together using operators borrowed from natural genetics. This process leads to the evolution of populations of individuals that have a higher probability of being “fitter,” i.e., better approximations of the specified potential values, than the individuals they were created from, just as in natural adaptation. The most time-consuming part in implementing a GA is often the evaluation of the objective or the fitness function. The objective function O[P] is expressed as sum squared error computed over a given large ensemble of data. Consequently, the time required for evaluating the objective function becomes an important factor. Since a GA is well suited for implementing on parallel computers, the time required for evaluating the objective function can be reduced significantly by parallel processing. A better approach would be to map out the objective function using several possible solutions concurrently or beforehand to improve computational efficiency of the GA prior to its execution, and using this information to implement the GA. This will obviate the need for cumbersome direct evaluation of the objective function. Neural networks may be best suited to map the functional relationship between the objective function and the various parameters of the specific functional form. This study presents an approach that combines the universal function approximation capability of multilayer neural networks to accelerate a GA for fitting atomic system potentials. The approach involves evaluating the objective function, which for the present application is the mean squared error (MSE) between the computed and model-estimated potential, and training a multilayer neural network with decision variables as input and the objective function as output. Less

Predictions by Correlations

James Wei

in Product Engineering: Molecular Structure and Properties

After searching the literature and making predictions based on theory without getting sufficient satisfactory results, the next move would be to make ... More

After searching the literature and making predictions based on theory without getting sufficient satisfactory results, the next move would be to make estimates. We need the property y of substances pi from a population P that has not been investigated and reported in the literature. Fortunately, there exists a subset S of P that has been investigated, and we have the values for the property y. For instance, we may want the boiling points of all the hydrocarbons, but we have only the boiling points of the normal paraffins from 1 to 20 carbon atoms. Can we use this piece of information on normal paraffins to estimate the boiling points for the rest of the hydrocarbon population? How much effort would be involved and how accurate would the results be? The number of isomers of paraffin is very large; see table 5.1. We see that the iso-paraffins are not as well investigated as the normal paraffins. We have the boiling points of all three isomers of pentane, but not the 75 isomers of decane. It is inevitable that we have to resort to estimations. When we have obtained a good correlation for normal paraffins, we would naturally want to know if we can extend this to the branched paraffins, and onward to the population of all the saturated hydrocarbons (by including the cyclic paraffins), and onward to the population of all hydrocarbons (by including olefins, acetylenes, and aromatic compounds), and then onward to the population of all organic compounds (by including compounds with heteroatoms, such as O, N, Cl). A correlation that applies accurately to a larger domain is more useful than one that works only for a smaller domain. Another example is polychlorinated biphenyls (PCBs), which have 10 hydrogen atoms that can be substituted by chlorine atoms. There are three types of site: the four α sites near the bridge between the two phenyl fragments, the four β sites farther away from the bridge, and the two γ sites that are the farthest away from the bridge. The number of isomers is shown in table 5.2. Less

Feed Forward Neural Networks

Lionel Raff, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam

in Neural Networks in Chemical Reaction Dynamics

In this section, we want to give a brief introduction to neural networks (NNs). It is written for readers who are not familiar with neural networks but are curious ... More

In this section, we want to give a brief introduction to neural networks (NNs). It is written for readers who are not familiar with neural networks but are curious about how they can be applied to practical problems in chemical reaction dynamics. The field of neural networks covers a very broad area. It is not possible to discuss all types of neural networks. Instead, we will concentrate on the most common neural network architecture, namely, the multilayer perceptron (MLP). We will describe the basics of this architecture, discuss its capabilities, and show how it has been used on several different chemical reaction dynamics problems (for introductions to other types of networks, the reader is referred to References 105-107). For the purposes of this document, we will look at neural networks as function approximators. As shown in Figure 3-1, we have some unknown function that we wish to approximate. We want to adjust the parameters of the network so that it will produce the same response as the unknown function, if the same input is applied to both systems. For our applications, the unknown function may correspond to the relationship between the atomic structure variables and the resulting potential energy and forces. The multilayer perceptron neural network is built up of simple components. We will begin with a single-input neuron, which we will then extend to multiple inputs. We will next stack these neurons together to produce layers. Finally, we will cascade the layers together to form the network. A single-input neuron is shown in Figure 3-2. The scalar input p is multiplied by the scalar weight w to form wp, one of the terms that is sent to the summer. The other input, 1, is multiplied by a bias b and then passed to the summer. The summer output n, often referred to as the net input, goes into a transfer function f, which produces the scalar neuron output a. Less

Mathematics

Patrick Magee and Mark Tooley

in The Physics, Clinical Measurement and Equipment of Anaesthetic Practice for the FRCA

Graphs are used to represent pictorially or clarify a relationship between two variables, say x and y, or t and function (t). If x and y are related by the linear ... More

Graphs are used to represent pictorially or clarify a relationship between two variables, say x and y, or t and function (t). If x and y are related by the linear equation y = mx + c, then the graphical relationship is a straight line as in Figure 1.1, where m is the slope, a constant value for a straight line and c is the value of y when x = 0. Figure 1.2 shows the relationship when m and c take negative values. Note that if c = 0, the line passes through the origin, 0, of the x–y axes. Examples of other linear relationships that can be represented in this way include the following (the bracketed symbols are the variables equivalent to x and y above): v = u + a t; (variables are t and v), where u is the starting velocity of an object that is subjected to acceleration a for time t, after which its velocity is v. Less