bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotically Locally Euclidean Metrics With Holonomy Su(M)
Authors: Joyce Dominic D
Published: November 2023

Let G be a finite subgroup of SO(n) acting freely on Rn\ (0). Then Rn/G has an isolated quotient singularity at 0. Suppose that X is a noncompact n-manifold with just one end which at infinity resembles Rn/G, and that g is a metric on X which approximates the Euclidean metric h0 on Rn/G by g = h0 +O(r −n), with appropriate decay in the derivatives of g. Then we call g Asymptotically Locally Euclidean, or ALE for short, and we call (X, g) an ALE manifold asymptotic to Rn/G.
Introduction To The Exceptional Holonomy Groups
Authors: Joyce Dominic D
Published: November 2023

For the rest of the book we shall discuss the exceptional holonomy groups G2 in 7 dimensions, and Spin(7) in 8 dimensions. This chapter introduces G2 and Spin(7), and explains some basic topological and geometrical properties of compact manifolds with these holonomy groups. Later, Chapters 11 and 12 will construct examples of compact 7-manifolds with holonomy G2, and Chapters 13, 14 and 15 examples of compact 8manifolds with holonomy Spin(7).
Examples Of Compact 7-Manifolds With Holonomy G
Authors: Joyce Dominic D
Published: November 2023

We shall now use the results of Chapter 11 to construct examples of compact 7manifolds with holonomy G2. Our general plan is to start with carefully explained, simple examples, and gradually introduce more complex behaviour. Later on we leave out a lot of the details, to keep the chapter to a manageable length.
Examples Of Compact 8-Manifolds With Holonomy Spin(7)
Authors: Joyce Dominic D
Published: November 2023

We now use the results of Chapter 13 to construct examples of compact 8-manifolds with holonomy Spin(7), in a similar way to the G2 case of Chapter 12. Our main aim is to show that many such manifolds exist, and to calculate their Betti numbers (b2, b3, b4).

We begin in §14.1 by discussing how to calculate the Betti numbers (b2, b3, b4) of a resolution M of T 8/ r, and to show that M has holonomy Spin(7). Then §14.2 gives a simple example of an orbifold T 8/r and its resolution M with holonomy Spin(7).
A Second Construction Of Compact 8-Manifolds With Holonomy Spin(7)
Authors: Joyce Dominic D
Published: November 2023

In this chapter we will describe a second method for constructing compact 8-manifolds with holonomy Spin(7), in which one starts not with a torus T 8 but with a Calabi–Yau 4orbifold Y with isolated singular points p1,>,⃛, pk. We use algebraic geometry to find a number of suitable complex orbifolds Y , which in the simplest cases are hypersurfaces in weighted projective spaces CP5 .
Electric charges and currents
Authors: Kovetz Attay
Published: November 2023

Electric charge is a property of bodies in nature. Logically speaking, it is a primitive: its status in electromagnetism is like that of point or plane in geometry, mass or force in mechanics, and energy or temperature in thermodynamics. For the time being we shall be concerned with those cases in which the charge Q is smoothly distributed over volume; more precisely.
Polarization and magnetization
Authors: Kovetz Attay
Published: November 2023

Experience shows that many materials respond, as it were, to an electromagnetic field by setting up charge and current distributions. This takes place in a myriad of forms, depending on the kind of material, on its state, and even on its history. Indeed, the resulting charge and current distributions are so diverse that, in constructing a theory of these phenomena, it is wise to keep an open mind. In particular, we should not impose on them any restrictions beyond those that we regard as absolutely necessary. Such a restriction is the principle of charge conservation, which we are certainly not about to renounce.
Electromagnetic wave propagation
Authors: Kovetz Attay
Published: November 2023

In Chapter 12 we treated the generation of electromagnetic waves, which was governed by inhomogeneous wave equations. The propagation of electromagnetic waves is characterized by homogeneous wave equations. This does not mean that we are going to set all charges and currents equal to zero, because that would limit us to materials without response. The homogeneity follows rather from the assumptions we shall make about the material, and from the structure of the equations.
Electric materials
Authors: Kovetz Attay
Published: November 2023

Thus the air pressure π0 must exceed the pressure π of the dielectric, and the right-hand side of (66.7) may be regarded as the electric tension pulling the dielectric fluid outward. For given air pressure, temperature and fields, (66.7) determines the density of the dielectric at the boundary.
Recovery of Visual Function Following Damage to the Striate Cortex in Monkeys
Authors: Moore Tirin , Rodman Hillary R , Gross Charles G
Published: November 2023

Damage to striate cortex (V1) in primates does not result in absolute blindness, but instead spares some rudimentary visual functions such as the ability to detect and localize visual stimuli in the affected visual field. In both humans and monkeys, early brain injury is typically associated with greater sparing or recovery of function, although this is not an invariable rule. We compared the visual function in monkeys with lesions of V1 sustained either in infancy or adulthood and found greater residual vision after the V1 lesions made in infancy. We describe the potential of these observations to explain the variability in the extent of residual visual function present in human subjects with damage to V1 and consider the possible mechanisms of the greater residual function after early V1 damage in primates. We also discuss the conspicuous similarities between the residual vision of monkeys with adult V1 lesions and human blindsight.
The Amygdala and Unconscious Fear Processing
Authors: Morris John
Published: November 2023

In both animals and humans, immediate threats in the environment trigger a fixed pattern of physiological and behavioural responses known as ‘fear’. Since rapid and appropriate responses to external danger are advantageous for survival, neural mechanisms mediating fear responses will be subject to strong evolutionary selection pressure and show conservation across species (Darwin, 1872). The amygdala, an almond-shaped nucleus in the medial temporal lobe, appears to be a crucial component of this phylogenetically ancient ‘fear system’ (LeDoux, 1996). Electrical stimulation of the amygdala, whether in human, monkey, rat, or lizard, consistently evokes fear responses (Halgren et al., 1978; Greenberg et al., 1984; LeDoux, 1987). Destruction of the amygdala, on the other hand, typically produces placid, tame animals that no longer respond appropriately to threatening stimuli (Kluver and Bucy, 1939; Weiskrantz, 1956). The amygdala has also been shown to have a central role in ‘fear’ conditioning, i.e. the process by which a previously neutral object (conditioned stimulus or CS+) acquires fear responses (LeDoux et al., 1990; Davis 1992; Kapp et al., 1992).
The nearly-free electron model
Authors: Singleton John
Published: November 2023

We are now going to consider the solutions of the Schrodinger equation for an electron in a periodic potential in the case that the potential is very weak, i.e. the electron is nearly free.
Line transects
Authors: Buckland S T , Anderson D R , Burnham K P , Laake J L , Borchers D L , Thomas L
Published: November 2023

The purpose of this chapter is to illustrate the application of the theory of Chapter 3 to line transect data, and to present the strategies for analysis outlined in Section 2.5. In general, the parameter f (0) in a line transect analysis does not have a closed form estimator. That is, for most models f(0) cannot be expressed as a formula that can be evaluated by simple substitution of the data. Instead, numerical methods are required. We therefore rely on specialized computer software to analyse distance sampling data. With such software, many more analysis options are possible and more reliable estimates can be obtained than if analysis is attempted without the aid of a computer.
Related methods
Authors: Buckland S T , Anderson D R , Burnham K P , Laake J L , Borchers D L , Thomas L
Published: November 2023

In this chapter, we describe distance sampling methods that are closely related to the standard line and point transect sampling of Chapters 4 and 5. We also consider models that do not fit into the key + adjustment formulation of earlier chapters. The material on these other models is not exhaustive, but is biased towards recent work, and models that may see future use and further methodological development. Most of the older models not described here are discussed in Burnham et al. (1980).
Study design and field methods
Authors: Buckland S T , Anderson D R , Burnham K P , Laake J L , Borchers D L , Thomas L
Published: November 2023

The analysis methods presented in Chapters 3–5 depend on proper field methods, a valid survey design and adequate sample size. This chapter presents broad guidelines for the design of a distance sample survey and outlines appropriate field methods. In general, a statistician or quantitative person experienced in distance methods should be consulted during the initial planning and design of the study. Just as important is the need for a pilot study, which can provide rough estimates of the encounter rate n/L (line transect sampling) or n/k (point transect sampling) and associated variances, from which refined estimates are obtained of n and of L or k for the main study. A pilot study also tests operational procedures and provides training for participants. It can also provide insights into how best to meet the key assumptions.
The future unveiled
Authors: Gray Jeremy J
Published: November 2023

On Wednesday 8 August 1900, David Hilbert stepped up to the rostrum at the International Congress of Mathematicians in Paris to give his lecture on Mathematical Problems. All lectures at conferences are pieces of theatre. The audience has some expectations, the lecturer some hopes. But on this occasion the hopes and expectations ran particularly high, because Hilbert was emerging as the leading mathematician of his generation, and his theme promised to be broader and more exciting than the usual technical accounts of mathematics, however successful.
The beacons are lit
Authors: Gray Jeremy J
Published: November 2023

When the audience left the auditorium in the Sorbonne they could begin to give their full attention to the printed paper with all the 23 Problems that Hilbert proposed. They would find that it divided into a small number of overlapping topics illuminated by the themes he had set out in his talk. The more they knew about his career to date, the more sense much of it would make.
The early response: 1900—1914/18
Authors: Gray Jeremy J
Published: November 2023

The Hilbert Problems were to be a great success, more than Hilbert could reasonably have predicted. Once brought to life by Hilbert they then lived a life of their own: growing up under his tutelage in Göttingen, moving abroad, and, in his old age, turning out unexpectedly. The children of his extraordinary optimism, some grew as he had predicted, while some were to turn obstinate, even recalcitrant. The insights on which they rested were not always sound, as Hilbert was painfully to discover. This outcome was by no means certain, and it requires some careful explanation.
After 1945
Authors: Gray Jeremy J
Published: November 2023

After the Second World War, Hilbert’s legacy could be viewed in many ways by his successors, and these different perceptions affected both the posthumous status of Hilbert himself and attitudes to the Hilbert Problems. The first concern was tied to his work as a profoundly creative pure mathematician, which is perhaps most intimately related to the Hilbert Problems themselves. Second came the implications he, and others, wished his work to have for applied mathematics. Third was his work on logic and the foundations of mathematics, with which he had been most actively involved in the final years of his career.
Epilogue
Authors: Gray Jeremy J
Published: November 2023

The story of the Hilbert Problems illustrates many things about mathematics. It is does indeed demonstrate that Hilbert lifted the veil on the future. As he intended, his Problems helped in a considerable way to shape that future. They may not always have done so in ways that he expected, but they did attract several generations of mathematicians to them, the best among them. That is surely because he chose them well and gave good reasons for caring about them, and that in turn reflects his penetrating insight into the relationship between problems and theory.
Nitrosothiol detection by HPLC coupled with flow reactors ofHg2+ and Griess reagent
Authors: Akaike Takaaki , Inoue Katsuhisa
Published: November 2023

NO-related intermediates, including NO1-like species, can participate in nitrosating additions to nucleophilic centres of biological molecules. Sulfhydrylcontaining molecules such as glutathione are particularly susceptible to nitrosation and form nitrosothiol adducts (nitrosothiols; RS-NOs). It seems that these adducts in biological systems play an important role in NO-mediated signalling cascades such as the downregulation of 7V-methyl-D-aspartate receptor, and the regulation of transcriptional factors (1); they might also be involved in non-adrenergic and non-cholinergic neuronal responses (2). It is, therefore, essential to identify nitrosothiols specifically and to quantify them in biological systems.
Vitamin E
Authors: Tamai Hiroshi
Published: November 2023

Extraction of vitamin E from tissue usually involves saponification with ethanolic potassium hydroxide. Direct extraction without saponification, however, is used for plasma.
Determination of flavonoids (catechins) by HPLC-ECD
Authors: Tomita Isao , Sano Mitsuaki
Published: November 2023

Flavonoids are ubiquitous in the plant kingdom and are very efficient antioxidants. High-performance liquid chromatography (HPLC) with electrochemical detection (ECD) is a sensitive, simple and selective method for determination of flavonoids.
Caeruloplasmin ferroxidase activity
Authors: Gutteridge J M C , Quinlan G J
Published: November 2023

The major copper-containing protein of human plasma, caeruloplasmin, can catalyse the oxidation of ferrous ions to the ferric state (ferroxidase activity). This activity is considered to be an important part of the antioxidant defence of the plasma (see Chapter 11). When ferric ions bind to apotransferrin they form a pink iron-transferrin complex absorbing at 460 nm.
Cholesterol and its oxides
Authors: Miyazawa Teruo
Published: November 2023

Several cholesterol oxidation products might play important roles in the development of atherosclerosis (1). This concept is fostered by mounting interest in the role of oxidatively modified lipoproteins and cholesterol in atherogenesis. Cholesterol oxides are widely encountered in foods and biological tissues. Here the analysis of plasma cholesterol oxidation products by high-performance liquid chromatography-mass spectrometry (HPLC-MS) (2, 3) is described.
Fluorescent products
Authors: Shimasaki Hiroyuki
Published: November 2023

Spectrofluorimetric analysis of fluorescent lipid peroxidation products is covered in detail elsewhere (2, 3). The method described here is a simple procedure for detection of lipid-soluble and water-soluble fluorescent products formed during lipid peroxidation of biological membranes.
Flow-cytometric analysis of lipid peroxides using DCFH-DA
Authors: Kayanoki Yoshiro
Published: November 2023

Flow cytometry is a method which measures the fluorescence of the cells after they have been labelled with a fluorescent antibody or a fluorescent dye. We here describe how to measure intracellular peroxides of cultured cells after labelling them with a peroxide-sensitive dye, 2’,7’-dichlorofluorescein diacetate (DCFH-DA), using a FACScan (Becton Dickinson, San Jose, CA, USA).
Tissue low molecular mass iron
Authors: Gutteridge J M C
Published: November 2023

Unlike extracellular fluids, cells usually contain a low molecular mass (LMr) pool of iron, which is required for the synthesis of iron-containing proteins and for the synthesis of DNA. This pool of iron is a target for iron chelators, and can be measured with the fluorescent probe calcein.
Total plasma copper
Authors: Gutteridge J M C , Quinlan G J
Published: November 2023

An average adult human contains approx. 80 mg copper. The plasma concentration is approx. 17 mM, most of which ( >98%) is associated with caeruloplasmin (see Chapter 31), which contains 6-7 copper ions per molecule of protein (Mr 132000). This chapter describes the determination of total plasma copper by A AS with a graphite furnace.
Low molecular mass chelatable copper: Reactive copper species (RCS)
Authors: Gutteridge J M C
Published: November 2023

Normal freshly taken human plasma does not contain chelatable forms of copper. Storage or mishandling of plasma does, however, lead to the formation of chelatable forms of copper by the proteolytic (rapid) degradation of caeruloplasmin. Redox active chelatable forms of copper can be detected and measured in biological fluids by use of the phenanthroline assay. Phenanthroline chelates copper and binds to DNA. Redox cycling of copper on DNA releases malondialdehyde from the deoxyribose sugar of DNA; this can be measured and related to the amount of copper present.
The expression of thioredoxin
Authors: Taniguchi Yoshih1sa
Published: November 2023

Adult T cell-derived factor (ADF) is a 13-kDa protein and is a human homologue of thioredoxin present in E. coll. ADF/Trx has a variety of biological activities, such as a co-cytokine effect on the promotion of the cellular proliferation and reducing activity by which the disulfide bond of proteins is reduced and cleaved. Because, moreover, the expression of ADF/Trx is induced by oxidative stresses, e.g., irradiation of UV, oxidative agents, and reperfusion injury, ADF/Trx is a factor involved in protective system against oxidative stress. We present here a Western blotting method for ADF/Trx protein.
GI tract ischaemia—reperfusion model
Authors: Yoshikawa Toshikazu , Naito Yuji
Published: November 2023

We introduced a new animal model of ischaemia-reperfusion-induced gastric mucosal injury in rats by applying a vascular clamp to the celiac artery, then removing it (1). As a result of the clamping of the celiac artery the gastric mucosal blood flow was reduced to 10% of that measured before clamping; the flow returned to the normal range on subsequent reperfusion.
Cell culture model for oxidative stress
Authors: Suzuki Keiiciiiro
Published: November 2023

Cells in culture are widely used as experimental models to study pro-oxidant and antioxidant responses. Although the conditions used are usually simple, and the results are obtained easily and rapidly, proteins, e.g. foetal calf serum, can act as radical scavengers, and iron and copper salts can also contaminate culture media during free-radical experiments. Appropriate controls must therefore be included and conditions carefully standardized, for example by using foetal calf serum (FCS)-free media.
The Triple Deck
Authors: Sobey I J
Published: November 2023

The singularity at the trailing edge is very severe. It is not the case that some local expansion near the trailing edge but deep within the boundary layer could remove the singularity.
Numerical Solution Of Triple Deck Equations
Authors: Sobey I J
Published: November 2023

Neither Stewartson (1969) nor Messiter (1970) computed a solution to the triple deck problem. Stewartson offered no assurance that a solution even existed, Messiter used a guessed displacement function A (X) to calculate an improved function and this way indicated how a numerical solution might be determined without directly solving the problem.
Introduction To Channel Flow
Authors: Sobey I J
Published: November 2023

Two-dimensional channel flow is important when flow occurs through a duct which is much wider than it is high. In such situations the effoct of the sides of the duct is relatively unimportant and the flow through much of the duct is essentially two-dimensional. Of course, it is much easier to organise manifolding for pipes than channels, so the greater number of flow devices used for heat and mass transfer are based on flow though or around cylinders but there are a significant number of situations where heat or mass transfer devices are made using plates and the flow between the plates is best described as channel flow.
Upstream Influence
Authors: Sobey I J
Published: November 2023

We saw in the last chapter that if a channel indentation was sufficiently small then the leading order term for the pressure was constant across the channel and further, the flow would be undisturbed until the channel indentation first occurred. It also emerged that the structure which was found for small channel indentations, an inviscid rotational core perturbation and two non-linear wall layers would still carry over to greater wall changes provided the pressure variation across the channel could be properly accounted for.
Properties of the electric dipole and the application of Gauss’s law when dielectrics are present
Authors: Edmonds D T
Published: November 2023

Most solids, liquids and gases are electrically polarizable in that, when placed in an electric field, electric charges are induced within the material and on its surface. To make physically realistic electrical predictions in the presence of such material, the origin of such induced charges must be understood and the electric fields they produce must be accounted for. In this chapter the origin and distribution of the induced charges are discussed and it is shown that the by formulating Gauss’s law in terms of a new electric field vector the presence of electrically polarizable material is simply dealt with. The properties of the new field vector are discussed and compared with those of the electric field. The continuity of the new vector and the electric field vector between adjacent blocks of different polarizable material are also discussed.
Magnetic polarization of material
Authors: Edmonds D T
Published: November 2023

In the same manner that electrically polarizable material complicated the application of Gauss’s law in electrostatics, the presence of magnetically polarizable material complicates the application of Ampe’re’s law in magnetostatics. However, as with electrostatics, the introduction of a new field vector enables this complication to be simply overcome in magnetism. The properties of the new field vector are discussed and contrasted with those of the magnetic field. The continuity of the new vector and the magnetic field vector across the boundary of two adjacent blocks of different magnetically polarizable material is described.
Ions in aqueous solution and the ionization of acids and bases
Authors: Edmonds D T
Published: November 2023

The behaviour of ions in aqueous solution is of paramount importance in biology and serves as an application of many of the equations that govern electrical behaviour that have been derived in previous chapters. The topics discussed in this chapter include the stability of the equilibrium state, electrical neutrality, pH and pKa and the influence of electric fields and dielectric environment on these parameters.
The behaviour of ions in narrow pores
Authors: Edmonds D T
Published: November 2023

Essentially because the ions within a solution passing rapidly through a narrow pore may not be in equilibrium with each other or with the charges on the walls of the pore, the behaviour of ions passing through a narrow pore is more difficult to predict than the behaviour of the same ions in bulk solution. In addition, the electrostatic self-energy of an ion in a narrow pore is very different from that of the same ion in bulk solution. A simple model of this enhanced self-energy is presented, and stronger electrostatic inter-ionic interactions within the pore are shown to be a consequence. The mechanisms that may lead to partial ordering of the electric dipole moments of water molecules in the pore are discussed, and the consequences of such order on the prediction of the ionic current through ion channels are described.
Ion traps
Authors: Foot C J
Published: November 2023

In a trap operating with a voltage of 10 = 500 V, singly-charged ions have a maximum ‘binding’ energy of order 500eV.3 This trap depth corresponds to the kinetic energy at a temperature of 6 x 106 K. This is more than enough to trap ions, even if the ions do receive a large recoil kick during the ionization process-to load an ion trap experimenters send a weak (neutral) atomic beam through the trapping region where an electron beam ionizes a few of the atoms by knocking an electron off. These ions created by electron bombardment have much greater kinetic energy than the thermal energy of atoms at room temperature (equivalent to only 1 / 40 eV). It would be unwise to try to be more precise about the typical energy of an ion since it depends on the voltage used. In contrast, a magnetic trap for neutrals has a maximum depth of only 0.07K.
Quantum computing
Authors: Foot C J
Published: November 2023

Quantum computing will be a revolutionary new form of computation in the twenty-first century, able to solve problems inaccessible to classical computers. However, building a quantum computer is very difficult, and so far only simple logic gates have been demonstrated in experiments on ions in a linear Paul trap. The ideas of quantum computing have also been tested in experiments using nuclear magnetic resonance (NMR). In the Paul trap, the ions sit in an ultra-high vacuum (pressure 007E 10-11 mbar) so that collisions rarely happen, and the ions are well isolated from the environment. We have seen that these conditions enable extremely high-resolution spectroscopy of single ions because of the very small perturbations to the energy levels.
Introduction
Authors: Andrews D F , Stafford J E
Published: November 2023

The theoretical basis of statistical methods is mathematics. The power of mathematics comes from the generality of its results. Because the relations are so general, only a few are required for a great variety of calculations. The power of computer algebra lies in rendering these genera) relations in a form for use by machine. As a result, a very limited amount of programming makes possible algebraic computation for a great variety of problems. Symbolic algorithms are to mathematics as numerical algorithms are to arithmetic. This is a book about the use of such algorithms in statistics. By symbolic computation, or computer algebra, we refer to the calculation of algebraic expressions such as £[X2]/n - (£[X]/n)2 for the variance of an average, rather than the numerical evaluation of this expression for a particular distribution.
Probability and random variables
Authors: Andrews D F , Stafford J E
Published: November 2023

The basic definitions and relations used in statistics may be specified in a language for symbolic computation and then used for calculation. Programming a machine to do symbolic computation in statistics is similar to teaching undergraduates. Although it is not as much fun, the machine has a superhuman attention span. The following sections present algorithms for many of the calculations faced by undergraduates. It is surprising how little needs to be specified for these calculations. As with undergraduates, we assume the language of implementation has (only) the basic prerequisite operational skills in algebra, arithmetic, and calculus, comparable to those required to complete a first-year course in calculus. We assume therefore that procedures for matrix multiplication, inversion, and simple integration are available. Aside from these. all of the definitions and procedures required are indicated in the text. In almost all cases. these are set out in displays.
The analytic bootstrap
Authors: Andrews D F , Stafford J E
Published: November 2023

Bootstrap methodology refers to a class of general resampling procedures for inference. The book by Efron and Tibshirani (1993) is an excellent introduction to the subject Many of the procedures they describe involve the use of averages of a large number of Monte Carlo samples to approximate an expectation. In this chapter, the procedures of Chapter 5 are used to compute series expansions of the same expectations. The evaluation of these series expansions is much faster than Monte Carlo sampling because it involves only the evaluation of a small number of averages. In addition, the analytic form of the expansions permits further analysis. For example. the moments and cumulants of the bootstrap estimates may be computed. These calculations are illustrated with a number of simple parameters. Boot strap estimates of variance, confidence intervals, and BCA confidence intervals for these parameters are computed. The same, fundamental procedures used for these examples may be applied to much more complex parameters. The computational procedures are beautiful in their simplicity. Appreciating the simplicity is difficult. Using the methods of Section 5.8, parameters of a distribution G are expanded about another, reference distribution F. When G is replaced with the empirical distribution Fn we immediately have the plug-in estimate in expanded form appropriate for further series computation. Alternatively, it may be evaluated to give the usual plug-in estimate. This is a good strategy because it simplifies computation although admittedly it is novel.
Graphs And Their Visibilities
Authors: Carbone Alessandra , Semmes Stephen
Published: November 2023

For the record, a graph is a (nonempty) set of vertices together with a collection of edges. Each edge has two endpoints, which are vertices in the graph. We allow edges whose endpoints are the same vertex, and we also allow multiple edges with the same endpoints.
Feasibility Graphs
Authors: Carbone Alessandra , Semmes Stephen
Published: November 2023

With formal proofs one has the possibility to represent objects only implicitly. The notion of feasibility provides a general mechanism for doing this, as in Sections 1.3 and 4.8. In this chapter, we present a simpler combinatorial framework in which similar effects can be achieved.

Roughly speaking, a feasibility graph is an optical graph in which the edges and branch points are labelled, in such a way that the graph represents some kind of construction or computation.
Bounds For Finite Visibilities
Authors: Carbone Alessandra , Semmes Stephen
Published: November 2023

Now we take up the matter of analyzing the size of the visibility when it is finite. This can be compared to similar questions about the size of regular languages when they are finite.
Duality And Np-Completeness
Authors: Carbone Alessandra , Semmes Stephen
Published: November 2023

Definition 13.1  Let G, H, and K be oriented graphs, and assume that G and H have no nontrivial oriented cycles. Let g: G→ K and h: H → K be orientation-preserving mappings. Fix vertices v in G and w in H, and assume that g(v)= h(w). Set z = g(v) = h(w), and letinduced mappings between visibilities, as in Section 10.1. Given these data, the visibility mapping problem asks whether the images of ĝ and ĥ inside V+ ( z, K) are not the same.
The Corona Decomposition Revisited
Authors: Carbone Alessandra , Semmes Stephen
Published: November 2023

We have discussed some notions of symmetry and compact descriptions for graphs in earlier chapters. In particular, one might say that the visibility of an oriented graph G enjoys a lot of symmetry when the visibility is much larger than G itself, even if this symmetry is not reflected in a perfect kind of periodicity (especially when the visibility is finite).
Bipolar transistors and integrated circuits
Authors: Holmes-Siedle Andrew , Adams Len
Published: November 2023

Bipolar transistors consist of a pair of closely spaced p-n junctions in a single semiconductor structure. The order can be ‘n-p-n’ or ‘p-n-p’. These devices, in both discrete and integrated form, are essential components in many electronic systems, especially in applications (such as in amplifiers), which require a high current gain or considerable ‘drive’ current. Radiation produces degradation of gain and an increase in leakage. The degradation of gain is well understood and derives from degradation of the transport of minority carriers across the base region. We will discuss the effects of electrons, neutrons, and gamma rays on this transport, dividing them into those occurring near the surface of the device and those that occur deeper in the material, i.e. bulk effects. In this chapter, we discuss the basic effects with emphasis on discrete silicon planar transistors. In this structure (see Fig. 5.I), the silicon substrate forms the collector region. Base and emitter regions are formed by the successive introduction of appropriate dopants by diffusion or ion implantation. The junctions are protected by a passivation layer which usually is thermally grown oxide. In general, this layer is thicker than that of MOS devices and accumulates charge when irradiated. Two books by pioneers in this field give detailed treatments of the semiconductor transport equations controlling transistor action in irradiated bipolar transistors (Larin 1968; Messenger and Ash 1992). This second edition has brought the description of radiation effects and electronic technology up to the millennium era. On the other hand, the acquisition of test data for current types of device is best pursued through the web references given in Appendix G, mainly those in Section GS, ‘Radiation effects databases’, in which will be found results for the devices and materials dealt with in this chapter, with the number increasing with time.
Equipment hardening and hardness assurance
Authors: Holmes-Siedle Andrew , Adams Len
Published: November 2023

The prime role of this handbook is to introduce tolerance to radiation (‘radiationhardness’) into large electronic systems. The essentials of the task are shown in Fig. 15.1. This diagram may appear simple but, if the radiation environment is severe, then–udging by experience in Europe and the USA–the task can require a large amount of effort. The skills required, mainly subspecialities of physics, chemistry and engineering, are those outlined in this handbook. In the case of a severe environment, if ‘radiation-hardening1 is to be successful, it has to be very thorough. In particular it has to permeate all stages of the development of a piece of equipment, including the earliest system engineering and technology development. This argument of the ‘early starf has been made over the past 30 years and largely responded to by large agencies (Holmes-Siedle 1974a, 1974b; Van Lint et al. 1977; Baur et al. 1981; Lauridsen 1995a,b,; Adams 2000). The serious effect of a late start is stressed by Messenger and Ash (1992): ‘… the cost [of radiation hardening] … is relatively modest when [it] is incorporated at the inception of the development … [but] … eleventh-hour add-ons to existing systems … are expensive, unduly extensive and … manifest reduced confidence … ‘. Nuclear power projects, previously paying most attention to metals and ceramics, are now devoting similar attention to electronics (see e.g. Baur et al. 1981).
Brains and brawn
Authors: Tweed Douglas
Published: November 2023

God said, ‘Let there be light’ and there was light, but God is a special case. If you want light, you can’t just will it; you have to proceed indirectly, for example by moving your feet and hands to search for a light switch. Outside your own nervous system, the only things you can reliably influence by a direct act of will are your skeletal muscles. These 656 muscles98 are the main output path between you and the rest of the world-they are the user interface of the universe. Every command issued by your brain must be shaped to act through this layer. Much of what goes on in the late stages of sensorimotor transformations, the stages just before the motor neuron, can be understood as the brain’s attempt to make optimal use of its interface.
History and philosophy
Authors: Silvester J R
Published: November 2023

Of all branches of mathematics, geometry has the most cheered and complicated history and offers the most bewildering choice of where to start and how to approach the subject. This chapter offers the briefest sketch of some of the more important stages in that history, together with some sort of justification for the particular approach to geometry in this book.
Drawings and constructions
Authors: Silvester J R
Published: November 2023

In this chapter, you are encouraged to draw for yourself lots of diagrams in order to get a feel for what geometry is about, to develop your visual skills, and to build up a catalogue of geometrical facts and experiences which will help illustrate and motivate later parts of the book. There are few theorems and no formal proofs in this chapter-they come later-but just exercises, interspersed with comments and hints.
Isometries of ℝ2
Authors: Silvester J R
Published: November 2023

We have met isometries in Section 3.5; recall that an isometry is a distance-preserving transformation of ℝ2. One can also define isometries in ℝ3: it is simply a matter of replacing ℝ2 by ℝ3 in Definitions 3.17 and 3.18. We shall continue to concentrate attention on ℝ2, but the reader who feels sufficiently confident is encouraged to generalize statements to ℝ3 where possible.
Isometries of ℝn
Authors: Silvester J R
Published: November 2023

In this chapter we shall make a brief excursion into n-dimensional geometry, in order to see how isometries can be written down, and to see a few examples of what can happen in dimensions higher than 2. The methods will be via matrices, so we first rewrite our isometries of ℝ2 in matrix form.
Circles and other conics
Authors: Silvester J R
Published: November 2023

So far, the objects we have been studying have been built up from points, lines, and circles (and, in higher-dimensions than 2, from the higher-dimensional analogues: planes, spheres, and so on).
More properties of likelihood
Authors: Pawitan Yudi
Published: November 2023

The idea of Fisher information (Section 2.5) captures the notion of ‘information ‘ only roughly. Owing to its association with a quadratic approximation of the likelihood, it is typically meaningful only in large samples. The qualitative concept of sufficiency (Fisher 1922) captures precisely the idea of information in the data. An estimate T (x) is sufficient for θ if it summarizes all relevant information contained in the data about θ. This is true if for any other estimate U (x), the distribution of U (x) given T (x) is free of θ. So, once T (x) is known U (x) does not carry any additional information.

It is a fundamental result that the likelihood function is minimal sufficient. This means the likelihood function captures all of the information in the data, and anything less involves some loss of information.
Complex data structures
Authors: Pawitan Yudi
Published: November 2023

The focus in this chapter is on problems with complex data structure, in particular those involving dependence and censoring. Modelling is crucial for simplifying and clarifying the structure. Compromises with the likelihood, for example using the marginal, conditional or estimated likelihood, also become a necessity. With some examples we discuss the simplest thing we can do with the data, with as little modelling as possible. This will provide a safety check for results based on more complex models; similar results would give some assurance that the complex model is not off the mark. It is important to recognize in each application the price and the reward of modelling.
EM Algorithm
Authors: Pawitan Yudi
Published: November 2023

Finding maximum likelihood estimates usually requires a numerical method. Classical techniques such as the Newton–Raphson and Gauss–Newton algorithms have been the main tools for this purpose. The motivation for such techniques generally comes from calculus. A statistically motivated EM (Expectation–Maximization) algorithm appears naturally in problems where
Random and mixed effects models
Authors: Pawitan Yudi
Published: November 2023

Regression models are the work horse of statistics, but while rich classes of models have been introduced to deal with various data types, in most cases the underlying mean structure is still the linear model h(μ) = Xβ, where β is a fixed parameter of dimension p, and p is typically quite small. Such a model is called a fixed effects model.
Introduction to advanced distance sampling
Authors: Buckland S T , Anderson D R
Published: November 2023

Distance sampling, primarily line transect and point transect sampling, has had a relatively short history. The earliest attempts to use distances to detected animals to estimate abundance date back to the 1930s, and the first line transect estimator with a rigorous mathematical basis was due to Hayne (1949). Nearly 20 years later, Gates et al. (1968) and Eberhardt (1968) made important contributions to the development of line transect sampling methodology. Neither the radial distance model of Hayne (1949) nor the negative exponential model of Gates et al. (1968) is based on plausible assumptions about the detection process. Eberhardt’s (1968) work was more conceptual, and attempted to provide a class of models that were robust to differing detection processes.
Microscopic mechanisms of biological motion
Authors: Derényi I , Vicsek Tamás
Published: November 2023

The origin of biological motion can be traced back to the function of tiny motor proteins operating at the molecular scale [1,2]. During the last few decades numerous different families of these molecular motors have been discovered, and the newest experimental techniques developed in recent years have allowed us to study in vitro the operation of individual motor proteins (for a review see [3]). Such studies have revealed that the motors move in discrete, unidirectional steps with step sizes in the range of a few nanometres and exert piconewton forces. The motors use the chemical energy stored in adenosine triphosphate (ATP) molecules or in a proton gradient as fuel and convert it into mechanical work.
The Dynamics Of Discrete Systems. Lagrangian Formalism
Authors: Fasano Antonio , Marmi Stefano
Published: November 2023

The mathematical modelling of the dynamics of a constrained system of point particles (P1, mi), ... , (Pn, mn) is based on the equations of motions for the single points: where Ri denotes the sum of all forces acting on the point (Pi, mi)- In addition to equations (4.1), one has to consider the constraint equations. The forces acting on a single particle can be classified in two different ways: either distinguishing between internal forces and external forces, or using instead the distinction between constraint reactions and the so-called active forces which we used in the study of the dynamics of a single point particle. These two different classifications yield two different mathematical schemes describing the dynamics of systems.
Analytical Mechanics: Hamiltonian Formalism
Authors: Fasano Antonio , Marmi Stefano
Published: November 2023

Within the Lagrangian formalism, the phase space for the equations of motion makes use of the coordinates (q, q). We start this chapter by studying the coordinate transformations in this space. We shall see that this study has wide and significant developments. The first objective is the transformation of the equations of motion into a form, the so-called canonical form, whose particular structure highlights many important properties of the motion. This objective is realised by an application of a transformation due to Legendre. In this section, we study the most important properties of this transformation. For simplicity, consider a real function f of a real variable w, defined in an interval (a, b) (not necessarily bounded), with continuous, positive second derivative,
Analytical Mechanics: Canonical Perturbation Theory
Authors: Fasano Antonio , Marmi Stefano
Published: November 2023

The so-called ‘perturbation methods’ for studying differential equations are traditionally of great importance for their applications to celestial mechanics (indeed, this field of study initially motivated their development). In spite of the efforts of generations of celebrated mathematicians (Lagrange, Laplace, Weierstrass and above all Poincare, who can be considered the father of the modern theory) until recently the majority of techniques used did not have a rigorous mathematical justification. Proving the convergence (or divergence) of the perturbation series is not just an abstract goal, of secondary interest for physicists. On the contrary, it stems from the need to understand in depth the domains of applicability to physical problems, and the limitations, of perturbation techniques.
Evolutionary considerations
Authors: Krause Jens , Ruxton Graeme D
Published: November 2023

This chapter investigates how grouping has evolved in animals. The preceding chapters, in particular Chapters 2 and 3, provided information on the effects of grouping on factors such as foraging efficiency and predation risk of individuals. Increasing group size has the potential for reducing predation risk and for increasing foraging efficiency (up to a certain threshold group size). What is the evidence then that these conditions select for grouping behaviour over evolutionary time? And in what way do they shape the social organization of animal groups? Before we can address these questions we have to deal with another issue.
Mechanisms
Authors: Krause Jens , Ruxton Graeme D
Published: November 2023

Grouping behaviour requires the recognition and localization of suitable group mates, which can be either conor heterospecifics (Section 9.2). Most of the research, however, has centred on the question of how conspecifics are recognized. As we discussed in Chapter 1, groups are brought about by social attraction between individuals that are usually found in close spatial proximity. In this chapter, we take a closer look at what the term ‘social attraction’ actually means (Section 9.3) and how it can be measured and modelled in terms of inter-individual distance regulation (Sections 9.3 and 9.5). First we will consider group formation under predation threat.
Remote Memory in Alzheimer’s Disease
Authors: Bright Peter , Kopelman Michael D
Published: November 2023

Ribot’s ‘law’ in 1882 stated that the ‘progressive destruction’ of memory would result in the most remote memories being spared relative to recent memories. While some studies of organic amnesia have failed to find evidence for such a pattern of memory loss (e.g. Sanders and Warrington 1971; Warrington and Sanders 1971), the majority have demonstrated a temporal gradient, although the size of gradient has differed considerably across patients and diagnostic groups (Kopelman et al.1999).
The Cognitive Psychopharmacology of Alzheimer’s Disease
Authors: Curran H Valerie , Kopelman Michael D , Rusted Jennifer M
Published: November 2023

Much recent research on Alzheimer’s disease (AD) has focused on molecular genetics, biological markers of dementia, and the neuropsychology of dementia. One goal of such studies is to identify ways forward for developing therapeutic agents. In this respect, it is still highly relevant to know which neurotransmitters are depleted in Alzheimer’s disease, and the functional roles that these neurotransmitters play in cognition (even though the sensitivity and specificity of these changes as diagnostic indexes tend to be low; Davies et al.1998). These two topics are the focus of this chapter. The related topic of the efficacy of pharmacological agents in replacement therapy is discussed elsewhere in this volume.
The zeta function and gamma distribution
Authors: Shai Haran M J
Published: November 2023

The mystery of the real prime is reflected in the difference between the local components of the (completed) zeta function
The q-gamma and q-beta chains
Authors: Shai Haran M J
Published: November 2023

We begin by describing the basic chain from which all our chains will be built. q ⸦(0,1), β⸦(0,∞). The state space is the integers ℕ, and the transition probabilities of the basic chain are given by