bluuebunny/crossref_metadata_2025 huggingface dataset:
Uncertainty In Geology
Authors: John Mann C.
Published: November 2020

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.
From Multivariate Sampling To Thematic Maps With An Application To Marine Geochemistry
Authors: Harff J.E. , Olea R.A.
Published: November 2020

Integration of mapped data is one of the main problems in geological information processing. Structural, compositional, and genetic features of the Earth's crust may be apparent only if variables that were mapped separately are studied simultaneously. Geologists traditionally solve this problem by the "light table method." Mathematical geologists, in particular, D.F. Merriam, have applied multivariate techniques to data integration (Merriam and Sneath, 1966; Harbaugh and Merriam, 1968; Merriam and Jewett, 1988; Merriam and Sondergard, 1988; Herzfeld and Merriam, 1990; Brower and Merriam, 1990). In this article a regionalization concept based on the interpolation of Bayes' probabilities of class memberships is described using a geostatistical model called "classification probability kriging." The problem of interpolation between data points has not been considered in most of the publications on multivariate techniques mentioned above. An attempt at data integration—including interpolation of multivariate data vectors—was made by Harff and Davis (1990) using the concept of regionalized classification. This concept combines the theory of classification of geological objects (Rodionov, 1981) with the theory of regionalized variables (Matheron, 1970; Journel and Huijbregts, 1978). The method is based on the transformation of the original multivariate space of observed variables into a univariate space of rock types or rock classes. Distances between multivariate class centers and measurement vectors within the feature space are needed for this transformation. Such distances can be interpolated between the data points using kriging. Because of the assumptions of multinormality and the fact that Mahalanobis' distances tend to follow a x2 distribution, the distances must be normalized before kriging (Harff, Davis and Olea, 1991). From the resulting normalized distance vectors at each node of a spatial grid, the Bayes' probability of class membership can be calculated for each class. The corresponding grid nodes will be assigned to the classes with the greatest membership probabilities. The result is a regionalization scheme covering the area under investigation. Let X(r) denote the multivariate field of features, modeled as a regionalized variable (RV).
The Prefix Problem And Its Applications
Authors: Lakshmivarahan S. , Dhall Sudarshan K.
Published: November 2020

With the emergence of parallel computing, the notion of prefix computation has gained considerable attention in the literature and it plays a central role in parallel algorithm design. This introductory chapter begins with the definition of the prefix problem. The ubiquitous nature of this problem is then illustrated using a host of examples drawn from a variety of application areas. Readers unfamiliar with a particular application area may choose to consult the appropriate references given in Section 1.4, Notes and References. After gaining sufficient familiarity with the remainder of this book, the reader will profit by revisiting Chapter 1 to apply the parallel prefix algorithms to several of the problems introduced here. In fact, many interesting class projects can be developed by cleverly mixing the problems and the algorithms. Let A be a set and o be a binary operation defined over the elements of A. It is assumed that Cl. A is closed under the binary operation o, that is, if a and b are in A, then so is a o b, and C2. the operation o is associative, that is, if a, b, and c are in A, Then . . . (a o b) o c = a o (b o c) = a o b o c. . . . The system (A, o) satisfying conditions Cl and C2 is called a semi-group (Birkhoff and Bartee [1970]). Examples include, (a) A is the set of integers (or real or complex numbers) and o denotes either the addition or the multiplication operation, and (b) A is a set of finite alphabet and o denotes the concatenation. To render our exposition self-contained, in Appendix A we discuss various properties of semigroups of interest to us in this book. Let d = ( d 1 , d2, • • • , 4N)', where di ∈ A, for 1≤ i ≤ N. Consider the problem of computing . . . xi =xi-1 o di. . . . for 2 ≤ i ≤ N, given that x1 = d1.
Parallel Prefix Circuits
Authors: Lakshmivarahan S. , Dhall Sudarshan K.
Published: November 2020

This chapter presents a survey of parallel algorithms for computing the prefixes using circuit models. The circuits considered in this Chapter are constrained by the fixed fan-in (equal to two) but are allowed to have arbitrary or unbounded fan-out. Prefix circuits with fixed fan-in and fan-out are described in Chapter 7, and those with unbounded fan-in in Chapter 8. The characteristics of algorithms described in this Chapter are judged according to a number of measures including the size, depth, and fan-out. (Refer to Chapter 2 for definitions.) The layout of the serial circuit, S(N), is given in Figure 1. Clearly, the size, s(N), of this circuit is (N - 1), and the depth, d(N), is (N - 1). The sum of the size and depth for this circuit is. . . s(N) + d(N) = 2N – 2. . . . (1) Each node has a constant fan-out. In Chapter 6, it is shown that the sum of the size and depth of any prefix circuit is lower-bounded by 2N - 2. From this, it follows that the serial circuit is optimal. Thus, any circuit that computes all prefixes in less than serial time must have sizes larger than (N - 1). Perhaps an easy approach to the design of a parallel prefix circuit is to invoke the well known divide-conquer strategy. Let N = 2". According to this strategy, if DC(N) is a circuit that computes the prefixes of N elements, then DC (N) can be designed according to the principle illustrated in Figure 1.
Risk Assessment and Risk Management: An Uneasy Divorce
Authors: Silbergeld Ellen K.
Published: November 2020

Over the past decade, the concept of risk has become central to environmental policy. Environmental decision making has been recast as reducing risk by assessing and managing it. Risk assessment is increasingly employed in environmental policymaking to set standards and initiate regulatory consideration and, even in epidemiology, to predict the health effects of environmental exposures. As such, it standardizes the methods of evaluation used in dealing with environmental hazards. Nonetheless, risk assessment remains controversial among scientists, and the policy results of risk assessment are generally not accepted by the public. It is not my purpose to examine the origin of these controversies, which I and others have considered elsewhere (see, e.g., EPA 1987), but rather to consider some of the consequences of the recent formulation of risk assessment as specific decisions and authorities distinguishable from other parts of environmental decision making. The focus of this chapter is the relatively new policy of separating certain aspects of risk assessment from risk management, a category that includes most decision-making actions. Proponents of this structural divorce contend that risk assessment is value neutral, a field of objective scientific analysis, while risk management is the arena where these objective data are processed into appropriate social policy. This raises relatively new problems to complicate the already contentious arena of environmental policy. This separation has created problems that interfere with the recognition and resolution of both scientific and transscientific issues in environmental policymaking. Indeed, both science and policy could be better served by recognizing the scientific limits of risk-assessment methods and allowing scientific and policy judgment to interact to resolve unavoidable uncertainties in the decisionmaking process. This chapter will discuss the forces that encouraged separating the performance of assessment and management at the EPA in the 1980s, which I characterize as an uneasy divorce. I shall examine some scientific and policy issues, especially regarding uncertainty, that have been aggravated by this policy of deliberate separation. Various interpretations of uncertainty have become central, and value-laden issues in decision making and appeals to uncertainty have often been an excuse for inaction.
Complex reactions
Authors: Schmickler Wolfgang
Published: November 2020

In the past two chapters we have already encountered examples of reactions involving several steps, and introduced the notion of rate determining step. Here we will elaborate on the subject of complex reactions, introduce another concept; the electrochemical reaction order, and consider a few other examples. The simplest type of complex electrochemical reactions consists of two steps, at least one of which must be a charge-transfer reaction. We now consider two consecutive electron-transfer reactions of the type: . . . Red ⇌ Int + e- ⇌ Ox + 2e- . . .(11.1) such as: Tl+ ⇌Tl2+ + e- ⇌ Tl3+ + 2e- . . . (11.2) For simplicity we assume that the intermediate stays at the electrode surface, and does not diffuse to the bulk of the solution.
Transient techniques
Authors: Schmickler Wolfgang
Published: November 2020

The classical electrochemical methods are based on the simultaneous measurement of current and electrode potential. In simple cases the measured current is proportional to the rate of an electrochemical reaction. However, generally the concentrations of the reacting species at the interface are different from those in the bulk, since they are depleted or accumulated during the course of the reaction. So one must determine the interfacial concentrations. There are two principal ways of doing this. In the first class of methods one of the two variables, either the potential or the current, is kept constant or varied in a simple manner, the other variable is measured, and the surface concentrations are calculated by solving the transport equations under the conditions applied. In the simplest variant the overpotential or the current is stepped from zero to a constant value; the transient of the other variable is recorded and extrapolated back to the time at which the step was applied, when the interfacial concentrations were not yet depleted. In the other class of method the transport of the reacting species is enhanced by convection. If the geometry of the system is sufficiently simple, the mass transport equations can be solved, and the surface concentrations calculated. The interpretation becomes complicated if several reactions take place simultaneously. Since the measured current gives only the sum of the rate of all charge-transfer reactions, the elucidation of the reaction mechanism and the measurement of several rate constants becomes an art. A number of tricks can be used, such as complicated potential or current programs, auxiliary electrodes, etc., which work for special cases. There are several good books on the classical electrochemical techniques. Here we give a brief outline of the most important methods. We mostly restrict ourselves to the study of simple reactions, but will consider one example in which the charge-transfer reaction is preceded by a chemical reaction. The measurement of current and potential provides no direct information about the microscopic structure of the interface, though a clever experimentalist may make some inferences.
Numerical Implementation
Authors: Phan-Thien Nhan , Kim Sangtae
Published: November 2020

Analytical solutions to a set of boundary integral equations are rare, even with simple geometries and boundary conditions. To make any reasonable progress, a numerical technique must be used. There are basically four issues that must be discussed in any numerical scheme dealing with integral equations. The first and most basic one is how numerical integration can be effected, together with an effective way of dealing with singular kernels of the type encountered in elastostatics. Numerical integration is usually termed numerical quadrature, meaning mathematical formulae for numerical integration. The second issue is the boundary discretization: when integration over the whole boundary is replaced by a sum of the integrations over the individual patches on the boundary. Each patch would be a finite element, or in our case, a boundary element on the surface. Obviously a high-order integration scheme can be devised for the whole domain, thus eliminating the need for boundary discretization. Such a scheme would be problem dependent and therefore would not be very useful to us. The third issue has to do with the fact that we are constrained by the very nature of the numerical approximation process to search for solutions within a certain subspace of L2, say the space of piecewise constant functions in which the unknowns are considered to be constant over a boundary element. It is the order of this subspace, together with the order and the nature of the interpolation of the geometry, that gives rise to the names of various boundary element schemes. Finally, one is faced with the task of solving a set of linear algebraic equations, which is usually dense (the system matrix is fully populated) and potentially ill-conditioned. A direct solver such as Gauss elimination may be very efficient for small- to medium-sized problems but will become stuck in a large-scale simulation, where the only feasible solution strategy is an iterative method. In fact, iterative solution strategies lead naturally to a parallel algorithm under a suitable parallel computing environment. This chapter will review various issues involved in the practical implementation of the CDL-BIEM on a serial computer and on a distributed computing environment.
Introduction
Authors: Bethke Craig M.
Published: November 2020

As geochemists, we frequently need to describe the chemical states of natural waters, including how dissolved mass is distributed among aqueous species, and to understand how such waters will react with minerals, gases, and fluids of the Earth's crust and hydrosphere. We can readily undertake such tasks when they involve simple chemical systems, in which the relatively few reactions likely to occur can be anticipated through experience and evaluated by hand calculation. As we encounter more complex problems, we must rely increasingly on quantitative models of solution chemistry and irreversible reaction to find solutions. The field of geochemical modeling has grown rapidly since the early 1960s, when the first attempt was made to predict by hand calculation the concentrations of dissolved species in seawater. Today's challenges might be addressed by using computer programs to trace many thousands of reactions in order, for example, to predict the solubility and mobility of forty or more elements in buried radioactive waste. Geochemists now use quantitative models to understand sediment diagenesis and hydrothermal alteration, explore for ore deposits, determine which contaminants will migrate from mine tailings and toxic waste sites, predict scaling in geothermal wells and the outcome of steam-flooding oil reservoirs, solve kinetic rate equations, manage injection wells, evaluate laboratory experiments, and study acid rain, among many examples. Teachers let their students use these models to learn about geochemistry by experiment and experience. Many hundreds of scholarly articles have been written on the modeling of geochemical systems, giving mathematical, geochemical, mineralogical, and practical perspectives on modeling techniques. Dozens of computer programs, each with its own special abilities and prejudices, have been developed (and laboriously debugged) to analyze various classes of geochemical problems. In this book, I attempt to treat geochemical modeling as an integrated subject, progressing from the theoretical foundations and computational concerns to the ways in which models can be applied in practice. In doing so, I hope to convey, by principle and by example, the nature of modeling and the results and uncertainties that can be expected. Hollywood may never make a movie about geochemical modeling, but the field has its roots in top-secret efforts to formulate rocket fuels in the 1940s and 1950s.
The Equilibrium State
Authors: Bethke Craig M.
Published: November 2020

Aqueous geochemists work daily with equations that describe the equilibrium points of chemical reactions among dissolved species, minerals, and gases. To study an individual reaction, a geochemist writes the familiar expression, known as the mass action equation, relating species’ activities to the reaction’s equilibrium constant. In this chapter we carry this type of analysis a step farther by developing expressions that describe the conditions under which not just one but all of the possible reactions in a geochemical system are at equilibrium. We consider a geochemical system comprising at least an aqueous solution in which the species of many elements are dissolved. We generally have some information about the fluid’s bulk composition, perhaps directly because we have analyzed it in the laboratory. The system may include one or more minerals, up to the limit imposed by the phase rule (see Section 3.4), that coexist with and are in equilibrium with the aqueous fluid. The fluid's composition might also be buffered by equilibrium with a gas reservoir (perhaps the atmosphere) that contains one or more gases. The gas buffer is large enough that its composition remains essentially unchanged if gas exsolves from or dissolves into the fluid. How can we express the equilibrium state of such a system? A direct approach would be to write each reaction that could occur among the system’s species, minerals, and gases. To solve for the equilibrium state, we would determine a set of concentrations that simultaneously satisfy the mass action equation corresponding to each possible reaction. The concentrations would also have to add up, together with the mole numbers of any minerals in the system, to give the system’s bulk composition. In other words, the concentrations would also need to satisfy a set of mass balance equations. Such an approach, however, is unnecessarily difficult to carry out. Dissolving even a few elements in water produces many tens of species that need be considered, and complex solutions contain many hundreds of species. Each species represents an independent variable, namely its concentration, in our scheme. For any but the simplest of chemical systems, the problem would contain too many unknown values to be solved conveniently.
Changing the Basis
Authors: Bethke Craig M.
Published: November 2020

To this point we have assumed the existence of a basis of chemical components that corresponds to the system to be modeled. The basis, as discussed in the previous chapter, includes water, each mineral in the equilibrium system, each gas at known fugacity, and certain aqueous species. The basis serves two purposes: each chemical reaction considered in the model is written in terms of the members of the basis set, and the system’s bulk composition is expressed in terms of the components in the basis. Since we could not possibly store each possible variation on the basis, it is important for us to be able at any point in the calculation to adapt the basis to match the current system. It may be necessary to change the basis (make a basis swap, in modeling vernacular) for several reasons. This chapter describes how basis swaps can be accomplished in a computer model, and Chapter 9 shows how this technique can be applied to automatically balance chemical reactions and calculate equilibrium constants. The modeler first encounters basis swapping in setting up a model, when it may be necessary to swap the basis to constrain the calculation. The thermodynamic dataset contains reactions written in terms of a preset basis that includes water and certain aqueous species (Na+, Ca++, K+, Cl-, HCO-3, SO4- -, H+, and so on) normally encountered in a chemical analysis. Some of the members of the original basis are likely to be appropriate for a calculation. When a mineral appears at equilibrium or a gas at known fugacity appears as a constraint, however, the modeler needs to swap the mineral or gas in question into the basis in place of one of these species. Over the course of a reaction model, a mineral may dissolve away completely or become supersaturated and precipitate. In either case, the modeling software must alter the basis to match the new mineral assemblage before continuing the calculation. Finally, the basis sometimes must be changed in response to numerical considerations (e.g., Coudrain-Ribstein and Jamet, 1989). Depending on the numerical technique employed, the model may have trouble converging to a solution for the governing equations when one of the basis species occurs at small concentration.
Plants and Vegetation
Authors: Haber William A.
Published: November 2020

The vegetation at Monteverde is characterized by two features that are immediately noted by visitors. The first is the overwhelming abundance of mosses, epiphytes, and tree trunk climbers in the cloud forest. The second is the striking variety of vegetation types, and consequent very high regional plant biodiversity, cramped into a small area by the narrow elevational zonation of habitats along the upper mountain slopes. This luxuriance and diversity have been important factors in the attraction of biologists to Monteverde. Lawton and Dryer (1980) described the characteristics and distribution of forest types in the upper Monteverde Cloud Forest Preserve (MCFP), emphasizing the effect of the northeast trade winds on forest structure. With exposure to the trade winds and the accompanying heavy mist and clouds, the forest is reduced in height, has a more broken canopy, and supports greater epiphyte loads. Areas in the lee of the winds develop a forest with less abundant epiphytes and mosses and much taller, straighter trees, forming a closed canopy and more open understory while the strong winds apparently limit the stature of the forest on the exposed ridges, the mist and rain carried in from the Atlantic side during the dry season maintain the diverse epiphyte community of the upper Pacific slope. In contrast, a short walk down the Pacific slope during the dry season leads to progressively drier vegetation zones where ferns, epiphytes, and climbers nearly disappear. Hartshorn (1983) described vegetation in the zones below the cloud forest, with a description of the Holdridge life zone system (Holdridge 1967) and the life zones in Monteverde. In this chapter, the focal area of the vegetation is the study area of the Monteverde Flora Project, which is more extensive than the area covered in the references cited above. The aim of the Monteverde Flora, a project of the Missouri Botanical Garden in collaboration with the Manual to the Plants of Costa Rica Project, is to collect and identify the flora of the Monteverde area and produce identification guides.
Reactions and Reactors Basic Concepts
Authors: Doraiswamy L. K.
Published: November 2020

Organic synthesis is replete with countless classes of reactions, including several that are named after their discoverers (the name reactions), but fortunately they can all be conducted in less than a half-dozen broad types of reactors. Choosing a reactor for a given reaction is based on several considerations and combines reaction analysis with reactor analysis. Thus in this chapter we consider the following aspects of reactions and reactors, much of which should serve as an introduction to chemists and a refresher to chemical engineers: reaction rates, stoichiometry, and rate equations; the basic reactor types, as a prelude to a more rigorous treatment of these in Parts III and IV; transport of mass (represented by reactant and product molecules) and heat across phase boundaries for heterogeneous reactions; and types of laboratory reactors used by chemists and chemical engineers for their specific objectives. The first step in any consideration of reaction rates is the definition of reaction time. This depends on the mode of reactor operation, batch or continuous. For the batch reactor, the reaction time is the elapsed time; whereas for the continuous reactor, it is given by the time the reactant spends in the reactor, called the residence time, that is measured by the ratio of reactor volume to flow rate (volume/volume per unit time with units of time). An equally important consideration is the concept of reaction space (which can have units of volume, surface, or weight), leading to different definitions of the reaction rate. We begin this section by considering different ways of defining the reaction rate based on different definitions of reaction time and space. The basis of all reactor design is an equation for the reaction rate.
The Electrostatic Moments of a Charge Distribution
Authors: Coppens Philip
Published: November 2020

The moments of a charge distribution provide a concise summary of the nature of that distribution. They are suitable for quantitative comparison of experimental charge densities with theoretical results. As many of the moments can be obtained by spectroscopic and dielectric methods, the comparison between techniques can serve as a calibration of experimental and theoretical charge densities. Conversely, since the full charge density is not accessible by the other experimental methods, the comparison provides an interpretation of the results of the complementary physical techniques. The electrostatic moments are of practical importance, as they occur in the expressions for intermolecular interactions and the lattice energies of crystals. The first electrostatic moment from X-rays was obtained by Stewart (1970), who calculated the dipole moment of uracil from the least-squares valence-shell populations of each of the constituent atoms of the molecule. Stewart’s value of 4.0 ± 1.3 D had a large experimental uncertainty, but is nevertheless close to the later result of 4.16 ± 0.4 D (Kulakowska et al. 1974), obtained from capacitance measurements of a solution in dioxane. The diffraction method has the advantage that it gives not only the magnitude but also the direction of the dipole moment. Gas-phase microwave measurements are also capable of providing all three components of the dipole moment, but only the magnitude is obtained from dielectric solution measurements. We will use an example as illustration. The dipole moment vector for formamide has been determined both by diffraction and microwave spectroscopy. As the diffraction experiment measures a continuous charge distribution, the moments derived are defined in terms of the method used for space partitioning, and are not necessarily equal. Nevertheless, the results from different techniques agree quite well. A comprehensive review on molecular electric moments from X-ray diffraction data has been published by Spackman (1992). Spackman points out that despite a large number of determinations of molecular dipole moments and a few determinations of molecular quadrupole moments, it is not yet widely accepted that diffraction methods lead to valid experimental values of the electrostatic moments.
X-ray Diffraction and the Electrostatic Potential
Authors: Coppens Philip
Published: November 2020

The distribution of positive and negative charge in a crystal fully defines physical properties like the electrostatic potential and its derivatives, the electric field, and the gradient of the electric field. The electrostatic potential at a point in space, defined as the energy required to bring a positive unit of charge from infinite distance to that point, is an important function in the study of chemical reactivity. As electrostatic forces are relatively long-range forces, they determine the path along which an approaching reactant will travel towards a molecule. A nucleophilic reagent will first be attracted to the regions where the potential is positive, while an electrophilic reagent will approach the negative regions of the molecule. As the electrostatic potential is of importance in the study of intermolecular interactions, it has received considerable attention during the past two decades (see, e.g., articles on the molecular potential of biomolecules in Politzer and Truhlar 1981). It plays a key role in the process of molecular recognition, including drug-receptor interactions, and is an important function in the evaluation of the lattice energy, not only of ionic crystals. This chapter deals with the evaluation of the electrostatic potential and its derivatives by X-ray diffraction. This may be achieved either directly from the structure factors, or indirectly from the experimental electron density as described by the multipole formalism. The former method evaluates the properties in the crystal as a whole, while the latter gives the values for a molecule or fragment “lifted” out of the crystal. Like other properties derived from the charge distribution, the experimental electrostatic potential will be affected by the finite resolution of the experimental data set. But as the contribution of a structure factor F(H) to the potential is proportional to H−2, as shown below, convergence is readily achieved. A summary of the dependence of electrostatic properties of the magnitude of the scattering vector H is given in Table 8.1, which shows that the electrostatic potential is among the most accessible of the properties listed.
The Charge Density in Extended Solids
Authors: Coppens Philip
Published: November 2020

Extended solids encompass all solids in which no well-defined molecular entities can be distinguished. This is the case for metals and alloys, covalently bonded solids like diamond and silicon, and ionic crystals of which the alkali halides are prototypes. Intermediate cases are common, such as crystals consisting of a charged covalent network with counterbalancing cations or anions. Silicates and their analogues are a prime example of often charged networks with partially covalent bonding. An increasing number of solids are known in which both an extended framework and molecular entities exist, with the molecules being embedded in the extended framework. Graphite intercalation compounds and a variety of host/guest complexes are examples of this class. The bonding features in the charge density are pronounced in crystals with extended covalent networks. The availability of perfect silicon crystals has allowed the measurement of uncommonly accurate structure factors, of millielectron accuracy. The data have served as a test of experimental formalisms for charge density analysis, and at the same time have provided a stringent criterion for quantum-mechanical methods. We will start the discussion in this chapter with silicon and its analogues, diamond and germanium, and proceed with the treatment of silicates, and metallic and ionic crystals. In the face-centered cubic structure of silicon, atoms are located at 1/8 1/8 1/8 and at the center-of-symmetry related position of −1/8 −1/8 −1/8.
Protein
Authors: Lüthy Roland , Eisenberg David
Published: November 2020

Given a protein sequence, the amino acid composition can be determined by counting the number of residues of each type. Then a molecular weight can be calculated by summing the molecular weights of the individual amino acid residues, taking into account the loss of one H2O molecule per peptide bond. Table 1 lists the molecular weights of the twenty amino acids and water. This approach assumes that the protein has not been covalently modified. Because of extensive glycosylation of some proteins, this approach can significantly underestimate the actual molecular weight. With the pKa values of Table 1, it is possible to calculate the theoretical charge of a protein at a given pH by summing the charges of the amino acid side chains and of the amino terminus and carboxyl terminus. By performing this calculation over a pH range, one obtains a theoretical titration curve and an isoelectric point (the pH at which the protein hasanetchargeof zero). This method assumes that all normally titratable groups are accessible to water, and that all side chains have the intrinsic pKa values listed in Table 1. This assumption is not completely correct, and consequently, the theoretical isoelectric point may differ from the experimentally determined value. Figure 1 shows the calculated titration curve for pancreatic ribonuclease: the calculated isoelectric point is 8.2, whereas the measured value is 9.6 (Lehninger, 1977). The calculation of extinction coefficients (Gill and von Hippel, 1989) is performed in much the same way as that of the isoelectric point Individual residues are treated as if they are free amino acids, and the overall extinction coefficient is calculated as the sum of the extinction coefficients of the residues. The same basic assumption is made: Residues are assumed to be in typical environments and not to show unusual absorption due to their local environments. In the case of the extinction coefficient, however, this assumption seems to be generally acceptable; calculated extinction coefficients are typically within a few percent of the experimentally determined value, and errors of more than 15% are rare (Gill and von Hippel, 1989).
Roads and Backstreets
Authors: Sperber Daniel
Published: November 2020

Let us now look at the roads and side streets in the Roman Palestinian town. The literary evidence about the width of such streets is somewhat problematic. In the baraita in B. Baba Batra 99ab we read as follows: . . .A private path is four cubits wide, a path from one town to another is eight cubits, a public path 16 cubits, and a path to the cities of refuge 32 cubits wide. . . . Likewise, M. Baba Kama .5, in the name of Rabbi Eliezer (late first century C.E.), tells us that a standard public path is 16 cubits wide. If we assume the cubit equals approximately 70 cm, we arrive at the following approximate road widths: . . .private path 2.80 m (=8.5 ft.). . . . . .from one town to another 5.60 m (=17 ft.). . . . . .public path 11.20 m (=34 ft.). . . . . .to cities of refuge 22.40 m (=68 ft.). . . This pattern does not correspond to the standard Roman road measurement. Most major Roman roads were about 16 ft. wide (10.5 cubits) and rarely more than 21.5 ft. wide (14 cubits). The narrower streets (angipontus or semitae) had to be at least 9.57 ft. (2.9 m) wide (a little more than 4 cubits) to allow for projecting balconies. The great trunk roads through Gaul or Italy or along the Euphrates frontier in Syria might be 24 ft. wide (16 cubits). Apparently, some roads were even broader than this, since the Pergamene law states that the minimum width of a main country road must be 30 ft. and that of a byroad 12 ft. Krauss noted these discrepancies, writing that “ordinary Roman stratae were about 5 m wide, making the Rabbinic stratae some 3 m broader, and we do not know wherefore there was this great difference between them.” He adds that in the “Palestinian town of Petra there are remains of the Roman road, which is only 2.8 m wide, and must therefore be considered as a via secundaria, but we cannot determine what is its equivalence in Rabbinic parlance.”
Organic Evolution and Problem Solving
Authors: Bäck Thomas
Published: November 2020

Evolutionary Algorithms (EAs), the topic of this work, is an interdisciplinary research field with a relationship to biology, Artificial Intelligence, numerical optimization, and decision support in almost any engineering discipline. Therefore, an attempt to cover at least some of these relations must necessarily result in several introductory pages, always having in mind that it hardly can be complete. This is the reason for a rather voluminous introduction to the fundamentals of Evolutionary Algorithms in section 1.1 without giving any practically useful description of the algorithms now. At the moment, it is sufficient to know that these algorithms are based on models of organic evolution, i.e., nature is the source of inspiration. They model the collective learning process within a population of individuals, each of which represents not only a search point in the space of potential solutions to a given problem, but also may be a temporal container of current knowledge about the “laws” of the environment. The starting population is initialized by an algorithm-dependent method, and evolves towards successively better regions of the search space by means of (more or less) randomized processes of recombination, mutation, and selection. The environment delivers a quality information (fitness value) for new search points, and the selection process favors those individuals of higher quality to reproduce more often than worse individuals. The recombination mechanism allows for mixing of parental information while passing it to their descendants, and mutation introduces innovation into the population. This process is currently used by three different mainstreams of Evolutionary Algorithms, i.e. Evolution Strategies (ESs), Genetic Algorithms (GAs), and Evolutionary Programming (EP), details of which are presented in chapter 2. This chapter presents their biological background in order to have the necessary understanding of the basic natural processes (section 1.1). Evolutionary Algorithms are then discussed with respect to their impact on Artificial Intelligence and, at the same time, their interpretation as a technique for machine learning (section 1.2). Furthermore, their interpretation as a global optimization technique and the basic mathematical terminology as well as some convergence results on random search algorithms as far as they are useful for Evolutionary Algorithms are presented in section 1.3.
Digital Filters
Authors: Polyak Ilya
Published: November 2020

In this chapter, several systems of digital filters are presented. The first system consists of regressive smoothing filters, which are a direct consequence of the least squares polynomial approximation to equally spaced observations. Descriptions of some particular univariate cases of these filters have been published and applied (see, for example, Anderson, 1971; Berezin and Zhidkov, 1965; Kendall and Stuart, 1963; Lanczos, 1956), but the study presented in this chapter is more general, more elaborate in detail, and more fully illustrated. It gives exhaustive information about classical smoothing, differentiating, one- and two-dimensional filtering schemes with their representation in the spaces of time, lags, and frequencies. The results are presented in the form of algorithms, which can be directly used for software development as well as for theoretical analysis of their accuracy in the design of an experiment. The second system consists of harmonic filters, which are a direct consequence of a Fourier approximation of the observations. These filters are widely used in the spectral and correlation analysis of time series. The foundation for developing regressive filters is the least squares polynomial approximation (of equally spaced observations), a principal notion that will be considered briefly.
Distillation-based Separation Systems Synthesis
Authors: Floudas Christodoulos A.
Published: November 2020

This chapter presents two applications of MINLP methods in the area of separations. Section 9.1 provides an overall introduction to the synthesis of separation systems. Section 9.2 focuses on sharp heat-integrated distillation sequencing. Section 9.3 presents an application of nonsharp separation synthesis. The synthesis of distillation-based separation sequences has been one of the most important subjects of investigation in the area of process synthesis. This is attributed to the significant contribution of separation processes to the total capital investment and operating expenses of a chemical plant. As a result, a lot of interest has been generated in the development of systematic approaches that select optimal sequences of distillation columns. Westerberg (1985) provided a comprehensive review of the distillation-based separation synthesis approaches, as well as presented a classification of different types of separation problems along with their associated challenges. Nishida et al. (1981) and Smith and Linnhoff (1988) reviewed the general separation synthesis problem (i.e., not only distillation-based) and presented the progress made. To illustrate the nature of the distillation-based separation system synthesis problem, let us consider its generic definition shown in Figure 9.1, which is as follows: . . . Given a number of input multicomponent streams which have specified amounts for each component, create a cost-optimal configuration of distillation columns, mixers, and splitters that produces a number of multicomponent products with specified composition of their components. . . The products feature components that exist in the input streams and can be obtained by redistributing the components existing in the input streams, while the cost-optimal configuration corresponds to the least total annual cost one. Most of distillation columns or sequences can be classified as (i) Sharp, (ii) Nonsharp, (iii) Simple, (iv) Complex, (v) Heat-integrated, and (vi) Thermally coupled. In (i), a column separates its feed into products without overlap in the components. An example is the separation of a stream consisting of four components A, B, (C, and D via a distillation column, into one product consisting of only A and another product featuring B, C, and D. If all columns are sharp, then the separation sequence is termed as sharp sequence.
Info Ecology
Authors: Heim Michael
Published: November 2020

InfoEcology is a hybrid name for a hybrid growth. The word refers to grafting information systems onto planetary health. As a sample of virtual realism, InfoEcology mixes high technology with the pragmatic maintenance of finite creatures. InfoEcology shows how permeable the fences have become between logical systems and survival anxieties. If the fences between fine arts and software engineering are falling, so too are the fences between information systems and planetary activism. The conventional barriers are proving as permeable as the graphic walls of a computerized architectural walkthrough: You push on the wall, and voilà! you are standing on the other side. Walls seem glaringly artificial today, and we acknowledge this with hybrid spellings like InfoEcology. The term was an offspring, as I recall, from the Amsterdam-based conference called “The Doors of Perception.” In January 1995, the planning session for the November 1995 third annual “Doors of Perception” conferences buzzed with the term “Info-Eco.” The plan was to bring together information theorists and ecologists from around the world. Ezio Manzini from the Domus Academy in Milan, John Thackara from England and the Netherlands Design Institute, and Willem Velthoven of Mediamatic Magazine convened the conference to bring together the “happy” information pioneers with the “worrying” ecologists. The meeting, they hoped, would inject information systems with global purpose. After the planning session, I began using the term in my own way to describe the pragmatics of information systems. Perhaps my usage was characteristically American rather than European. The predominantly European conference in Amsterdam focused its twelve workshops on social organization. They looked, for instance, at how people could cut down on the use of materials and energy by using the Internet to distribute local goods and services. My focus, on the other hand, turned to technological tools as they transform the engineers’ approach to ecological disasters on American soil. The Europeans saw InfoEcology as centering on people. The American InfoEcology I describe revolves around technology as a tool for transfiguring disaster.
Phase Space Analysis of Neuronal Excitability
Authors: Koch Christof
Published: November 2020

The previous chapter provided a detailed description of the currents underlying the generation and propagation of action potentials in the squid giant axon. The Hodgkin-Huxley (1952d) model captures these events in terms of the dynamical behavior of four variables: the membrane potential and three state variables determining the state of the fast sodium and the delayed potassium conductances. This quantitative, conductance-based formalism reproduces the physiological data remarkably well and has been extremely fertile in terms of providing a mathematical framework for modeling neuronal excitability throughout the animal kingdom (for the current state of the art, see McKenna, Davis, and Zornetzer, 1992; Bower and Beeman, 1998; Koch and Segev, 1998). Collectively, these models express the complex dynamical behaviors observed experimentally, including pulse generation and threshold behavior, adaptation, bursting, bistability, plateau potentials, hysteresis, and many more. However, these models are difficult to construct and require detailed knowledge of the kinetics of the individual ionic currents. The large number of associated activation and inactivation functions and other parameters usually obscures the contributions of particular features (e.g., the activation range of the sodium activation particle) toward the observed dynamic phenomena. Even after many years of experience in recording from neurons or modeling them, it is a dicey business predicting the effect that varying one parameter, say, the amplitude of the calcium-dependent slow potassium current (Chap. 9), has on the overall behavior of the model. This precludes the development of insight and intuition, since the numerical complexity of these models prevents one from understanding which important features in the model are responsible for a particular phenomenon and which are irrelevant. Qualitative models of neuronal excitability, capturing some of the topological aspects of neuronal dynamics but at a much reduced complexity, can be very helpful in this regard, since they highlight the crucial features responsible for a particular behavior. By topological aspects we mean those properties that remain unchanged in spite of quantitative changes in the underlying system. These typically include the existence of stable solutions and their basins of attraction, limit cycles, bistability, and the existence of strange attractors.