bluuebunny/crossref_metadata_2025 huggingface dataset:
Fields Incident On Bitransmission Lines
Authors: Olyslager Frank
Published: November 2023

In this chapter, the results of the previous chapter are generalized to general bianisotropic waveguides and junctions. The main difference is that for nonreciprocal waveguides and junctions the ad joint structures are also needed in order to apply the Lorentz reciprocity theorem. It will, however, suffice to know the eigenmodes that propagate in the ad joint waveguide and to know the fields generated in ad joint junctions by incident eigenmodes from adjoint waveguides connected to these junctions. The representation of incident fields by voltage and current sources in the reciprocity-based bitransmission lines of Chapter 5 is straightforward.
Mathematics
Authors: Olyslager Frank
Published: November 2023

In this final chapter, a number of mathematical topics are discussed which are used in the other chapters. The purpose of this chapter is to explain some concepts to a reader who is perhaps not too familiar with them. Rather than containing extensive mathematical analyses, each topic is discussed briefly in a pragmatic way, without aiming at mathematical rigour.
Homogenization of the heat equation
Authors: Donato Patrizia
Published: November 2023

In this chapter we are interested in the asymptotic behaviour as ε → 0 of the solution u  ε = u  ε  (x, t) of the problem where the operators div and ▽ are taken with respect to the space variable x ∈ Ω and ‘ denotes the derivative with respect to the time variable t ∈]0, T[, with T > 0.
B
Authors: Perrot Pierre
Published: November 2023

Bar—A Unit of pressure, multiple of the pascal (1 bar= 105 Pa). Since 1983, the standard pressure, unless otherwise stated, is fixed at 1 bar instead of 1 atm (1.01325 bar). This convention, doubtless motivated by concern not to spread alarm among students and engineers, is nevertheless unfortunate. The choice of the pascal would be more judicious, despite the necessity for complete recasting of thermodynamic tables.
C
Authors: Perrot Pierre
Published: November 2023

Caloric—The caloric theory, established in the eighteenth century, supplanted that of phlogiston for explaining many aspects of heat and combustion phenomena. Caloric is a weightless, conservative fluid, which builds up in hot materials. Its particles repel each other, but are attracted by matter. Around 1790, Benjamin Thompson, Count Rumford, raised doubts about the theory, by showing that caloric can be created. The theory was abandoned after 1824. By using caloric conservation, Sadi Carnot showed that every reversible engine working between two reservoirs at the same temperatures has the same efficiency. Actually, Carnot’s demonstration can be disproved, but his report becomes clearer on substituting the term entropy for ‘caloric’.
D
Authors: Perrot Pierre
Published: November 2023

Debye, Peter Joseph William (1884-1966)-Dutch-US physical chemist, author of important works on dipolar moments, X-ray scattering, and ionic interactions in solutions. Nobel prize in chemistry in 1936. Debye-Hiickel theory-The interaction energy between two neutral molecules, governed by London forces, follows a d-6 law, whereas the interaction energy between two ions, governed by Coulomb forces, follows a d-1 law. As a consequence, ionic solutions show important deviations from Henry’s law which are perceptible even at very weak concentrations, say 10-4mo!L-1 The Debye-Hiickel theory, pro posed in 1923, provides an assessment of the activity coefficient of an ion i in solution.
E
Authors: Perrot Pierre
Published: November 2023

Ebulliometry—Measurement of the initial boiling point of a mixture of solvent (index 1) plus solutes.
F
Authors: Perrot Pierre
Published: November 2023

Factor—The term ‘factor’ is reserved for the proportionality coefficient k linking two physical quantities A and B whose dimensions are the same: A=kB. A factor is therefore dimensionless.
I
Authors: Perrot Pierre
Published: November 2023

Ideal solution—A solution is called ideal when the activity of a constituent i is proportional to its composition, that is to say, when its activity coefficient y1, is constant. It is of course necessary to specify how the composition is expressed, because an ideal solution with mole fractions is no longer ideal with mo1 L-1, and vice versa. In order that a solution be ideal, it is sufficient that the ideality condition be verified with only one constituent.
J
Authors: Perrot Pierre
Published: November 2023

Kuhn, Thomas S. (1923-1996)-American philosopher, famous for his essay Structure of the scientific revolution (1962), in which he discusses the concept of paradigm and rejects the notion of falsifiability developed by Karl Popper. According to Thomas Kuhn, a statement is true or false only in the context of a particular paradigm. Thermodynamicists interested in the history of science will appreciate his Black body theory and the quantum discontinuity (1894-1912), published in 1978.
O
Authors: Perrot Pierre
Published: November 2023

Oersted, Christian (1777-1851) —Danish physicist, author of studies on the compressibility of condensed matter. He demonstrated the existence of the magnetic field created by a current.
P
Authors: Perrot Pierre
Published: November 2023

M: molar mass; r: surface tension at the liquid-vapour interface; p1 and Pv: volumetric masses of liquid and vapour. The parachor is a function of temperature, is directly related to the structure of the molecule, and may be calculated by adding increments relating to atoms and bonds.
Q
Authors: Perrot Pierre
Published: November 2023

On the other hand, to mix water and alcohol with the aim of preparing a product with attractive organoleptic properties and to put some bleach into a swimming pool to improve its bacteriological quality represent two processes of a very different nature. In the first case, the properties of the product (brandy, perhaps) will differ from those of its constituents: the quantities of mixing of interest will be integral quantities of mixing, symbolized by Δmix In the second case, the state of the swimming pool after bleaching will differ little from its initial state and the integral quantities of mixing will be of little consequence. On the other hand the bleach, concentrated before mixing and dilute after bleaching, will have seen its state modified.
R
Authors: Perrot Pierre
Published: November 2023

Radiation—-Radiation may be considered as a collection of photons, each being characterized by its energy hv and its momentum hv/c (v: frequency of the radiation; h: Planck constant; c: velocity of light in vacuum). Radiation in equilibrium with its surroundings is in thermal equilibrium. Its temperature is then, by definition, that of the matter which surrounds it.
S
Authors: Perrot Pierre
Published: November 2023

Sackur-Tetrode equation—Proposed in 1912, it allows one to evaluate, in Maxwell-Boltzmann statistics, the entropy of an ideal gas containing N indistinguishable particles with a mass m, occupying a volume Vat temperature T.
Y
Authors: Perrot Pierre
Published: November 2023

Young’s modulus—The ratio of the stress exerted on a wire to its strain, named from Thomas Young (1773-1829), English doctor and physicist, sometime Egyptologist. He is well known for having pro vided, through his experiments on interference, an experimental basis for the wave theory of light.
Special Functions Of Mathematics For Engineers
Authors: Andrews Larry C
Published: November 2023

Special functions are essential for solving problems in virtually all engineering disciplines. Assuming only knowledge of elementary calculus and differential equations, this concise, clearly written reference illustrates the properties and applications of the special functions most frequently needed by practising engineers. Copious illustrations of worked out sample problems from a wide range of real-world engineering applications distinguish this work from others.
Generalized Hypergeometric Functions
Authors: Andrews Larry C
Published: November 2023

The special properties associated with the hypergeometric and confluent hypergeometric functions have spurred a number of investigations into developing functions even more general than these. Some of this work was done in the nineteenth century by Clausen, Appell, and Lauricella (among others), but much of it has occurred during the last 70 years. Even the most recent names are too numerous to mention, but MacRobert and Meijer are among the most famous.
Applications Involving Hypergeometric-Type Functions
Authors: Andrews Larry C
Published: November 2023

In this final chapter we illustrate the use of the general family of hypergeometric functions in various applications. Although we have chosen specific examples from the fields of statistical communication theory, fluid mechanics, and random fields, the techniques we use are sufficiently general that they apply to a wider range of applications. As before, we assume only a working knowledge of the subjects in order to follow the exposition.
Perturbation methods
Authors: Jordan D W , Smith P
Published: November 2023

This Chapter describes techniques for obtaining approximations to periodic time solutions of nearly linear second-order differential equations subject to a harmonic forcing term, and to limit cycles of autonomous equations. The approximations take the form of an expansion in integer powers of a small parameter, having coefficients that are functions of time. There is some freedom in assigning the time-dependent coefficients; this is utilized to produce uniformly valid approximations under different circumstances, depending on the values of the main parameters of the equation. It is also shown how a homo clinic path can be approximated by using similar methods. The processes reveal physical features having no analogue in linear theory, despite the fact that the equations considered have small nonlinearities.
The existence of periodic solutions
Authors: Jordan D W , Smith P
Published: November 2023

Suppose that the phase diagram for a differential equation contains a single, unstable equilibrium point and a limit cycle surrounding it, as in the case of the van der Pol equation. Then in practice all initial states lead to the periodic oscillation represented by the limit cycle. In such cases the limit cycle, is the principal feature of the system from the practical point of view, and it is desirable to be able to decide with certainty whether it is there or not. Hitherto our attitude to this question has been intuitive; we assemble qualitative evidence that there is a limit cycle, from energy considerations or geometrical arguments, then attempt to estimate the radius by the methods of Chapters 4, 5, and 7, a definite result being taken as further confirmation that the limit cycle is really there. The present Chapter contains theorems and methods for proving positively the existence or non-existence of limit cycles and centers for certain types of equation. The cases chosen can be interpreted physically as involving a balance between energy gain and loss on various regions in the phase plane; they include the type discussed in Sections 1.5 and 4.1; also others with different symmetry. The latter serve as a guide to intuition for related types which do not quite fit the conditions of the theorems. Further theorems can be found, for example, in Andronov et al. (1973a) and Cesari (1971).
Abstract quantum cohomology
Authors: Guest Martin A
Published: November 2023

We shall describe a general method of producing D-modules which ‘resemble ‘ quantum cohomology D-modules, based on [62] and [72]. This could be considered as a method of construction of Frobenius manifolds (see Chapter 9). But it differs from other approaches in the literature both in its starting point (systems of scalar equations of a rather specfic type) and its goal (a wider class of integrable systems).
Hadamard Conjugation: An Analytic Tool for Phylogenetics
Authors: Hendy Michael D
Published: November 2023

A phylogeny (evolutionary tree) on a set of taxa X, is a tree T whose leaves are labelled by the elements of X. When we identify the root R of T; provide a distribution of nucleotides at R; and give a stich model of the nucleotide substitutions between the vertices of each edge e of T, we can calculate the probability of ea.ch possible distribution (which we will refer to as a ‘‘pattern’’) of nucleotides at the leaves. A set of aligned homologous nucleotide sequences of common length l, is then modeled as l samples drawn sequentially from this distribution, with the pattern of nucleotides at a common site representing one sample. The relative frequencies of each observed pattern provide estimates of these probabilities.
Conserved Segment Statistics and Rearrangement Inferences in Comparative Genomics
Authors: Sankoff David
Published: November 2023

‘l’he statistical treatment of chromosomal rearrangement has evolved along with the biological methods for producing pertinent data. We trace the development of conserved segment sta.tistics1 from the mouse linkage/human chromosome assignment data analysed by Nadeau and Taylor in 1984, through the comparative gene-order information on organelles (late 1980s) and prokaryotes (mid-1990s), to higher eukaryote genome sequences, whose rearrangements have been studied without prior gene identification. Each new type of data suggested new questions and led to new analyses.

We focus on the problems introduced when small sequence fragments are treated as noise in the inference of rearrangement history.
Genome Rearrangements with Gene Families
Authors: abrouk Nadia El-M
Published: November 2023

The genome rearrangement approach to comparative genomics infers divergence history in terms of global genomic mutations. The major focus in the last decades has been to infer the most economical scenario of elementary operations transforming one linear order of genes into another. Implicit in most of these studies is that each gene has exactly one copy in each genome. This hypothesis is clearly unsuitable for divergent species containing several copies of highly analogous gene, for example, multigame families. In this chapter, we review the different algorithmic methods that have been considered to account for multigame families in the genome rearrangement context, and in the phylogenetic context.
The natural laboratory paradigm
Authors: Whittaker Robert J , Fernández-Palacios José María
Published: November 2023

These words taken from Alfred Russel Wallace’s Island life encapsulate an over-arching idea that could be termed the central paradigm of island biogeography. It is that islands, being discrete, internally quantifiable, numerous, and varied entities, provide us with a suite of natural laboratories, from which the discerning natural scientist can make a selection that simplifies the complexity of the natural world, enabling theories of general importance to be developed and tested. Under this umbrella, a number of distinctive traditions have developed, each of which is a form of island biogeography, but only some of which are actually about the biogeography of islands. They span a broad continuum within ecology and biogeography, the end points of which have little apparently in common.
Emergent models of island evolution
Authors: Whittaker Robert J , Fernández-Palacios José María
Published: November 2023

Having considered the evidence for microevolutionary change on islands and the frameworks of speciation in the previous two chapters, we now examine how these building blocks fit together to produce neoendemics on islands. Although other categorizations are possible, we identify the following emergent patterns or models of evolutionary change on islands. The first is anagenesis, which refers to speciation without much radiation of lineages, and which may be most applicable to single isolated islands of moderate size and limited habitat heterogeneity. The second and third models, the taxon cycle and adaptive radiation, find their most dramatic illustrations within archipelagos and constitute multiagent evolutionary-ecological models: both stress adaptive changes. In contrast, the notion of non-adaptive radiation refers to the diversification of monophyletic lineages without apparent niche alterations, and emphasizes geographic isolation within or between islands.
Island remedies: the conservation of island ecosystems
Authors: Whittaker Robert J , Fernández-Palacios José María
Published: November 2023

Although generally distinct from continental environments, and therefore of interest in their own right, island environments have been generally misunderstood, misinterpreted, and mismanaged. The main reason is that they have been interpreted for management purposes largely by continent-trained observers . . . islands are not simply miniature continents and . . . continental solutions do not simply need to be scaled down in order to be successful. (Nunn 2004, pp. 311 and 319) In this final short chapter, we first illustrate some of the special problems facing contemporary island societies, the pressures on the environments and biotas of oceanic islands, and constraints within which those interested in promoting conservation must operate. Conservation in island archipelagos like the Canaries, the Maldives, the Lesser Antilles, and the Galápagos present distinctive challenges, which arise from the characteristics of the island environments and biota and from the socioeconomic and political situation of the island societies (e.g. Nunn 2004).
The pathology of decision making
Authors: Berthoz Alain
Published: November 2023

Making a decision requires above all that perception faithfully reflect reality. Yet that is not always the case—far from it! Crossing the street one day, a woman friend of mine passed a man she thought was her husband and moved to make a familiar gesture. Realizing her mistake just in time, she checked her impulse. How was she able to avoid finding herself in an embarrassing situation of extending her hand, or her cheek, to a man she didn’t know?How does the brain decide that a person is a friend, spouse, one’s own child, or stranger? Who has not experienced similar confusion in recognizing a face?

How do we go from ‘I see him’ to ‘I know him’? This ability to know another is not a question of language, because frequently we are able to recognize people without remembering their name.
Fight or flight
Authors: Berthoz Alain
Published: November 2023

One spring morning around 8:45, in front of the Lycée Montaigne, which was built simultaneously along the lines of a train station, a hospital, and a prison, the street was deserted aside from a few hurried latecomers. For a few minutes, a smooth flow of students invaded the building, but now it had managed to swallow them up, aided by the bells. A silent confrontation resumed between the school windows, which are always shut, and the Luxembourg Gardens, which invited wandering beside the apple trees, whose extended branches appeared to mimic the orderly rows of benches on which the sequestered students listened to their teachers. Motionless, alone on the street, a young girl was looking at the school, her bookbag slung across her shoulder.
To perceive visually is to decide: the physiology of doubt
Authors: Berthoz Alain
Published: November 2023

Perceiving is deciding, and deciding is gambling, to such an extent that we perceive the world not necessarily as an obvious and unique sense datum, but rather a probable one. To say, as Georg Riemann did, that several lines parallel to a given line can all pass through a single point is to make a decision about lived experience. It affirms that perception can give rise to a variety of possible solutions and that reason can arbitrate among them.

In the waiting rooms of the Banque de France, I had occasion to contemplate a painting by Fragonard, dated roughly 1715, that depicts a fair with feasts, couples, children playing, at left a stage set up in the garden, at right a Guignol theatre. Jean-Claude Trichet, the bank’s governor, had brought together his former classmates from the École des Mines at Nancy and given them a real-life demonstration of the fact that perceiving is also deciding.
The brain as emulator and generator of strategies: the vagabond thought
Authors: Berthoz Alain
Published: November 2023

Action and the sentient body, which construct the perceived world based on our desires, goals, and fears, are at the heart of the mechanisms of decision making, more than language and reason. Or rather, it is the language of the sentient body in its dialogue with the world that remains to be discovered: the gesture of thought. The role of space in the dynamic architecture of thought is also largely unknown. The Italian Renaissance placed at the centre of the world the new man and his freedom, his capacity to choose and to decide, to find several solutions to the same problem with no boundary conditions. This spirit is asserted in the interplay between softness and drama—each triumphing in turn—in the art of Fra Angelico and Donatello.
Brain, music and musicality: Inferences from neuroimaging
Authors: Turner Robert , Ioannides Andreas A
Published: November 2023

We approach the question of human musicality by considering the spatial and temporal patterns of brain activity that may be specific to the human experience of music. Commonalities in any activity or behaviour across people and cultures point towards biologically rather than culturally defined competencies of mind and brain. As brain scientists, we wish to discriminate such innate cerebral competencies for music from conventional, culturally learned skills, and to make sense of the functional localizations for both types of activity in particular parts of the brain that are amenable to study using neuroimaging techniques.
Supporting the development of mindfulness and meaning: Clinical pathways in music therapy with a sexually abused child
Authors: Robarts Jacqueline
Published: November 2023

In this chapter, I present music as a primary catalyst in the development of the therapeutic relationship and in the therapeutic processes of change. I describe how music therapy can assist a psychotic child with a history of early childhood sexual abuse. When the intersubjective sense of self is devastated at its core by such early relational trauma, music, used with clinical perception, may reach a child and work constructively in an evolving, musically mediated therapeutic relationship.
The Neuropathology Of Alzheimer‘s Disease
Authors: Esiri Margaret M
Published: November 2023

The neuropathology of Alzheimer‘s disease (AD) is arguably its most distinguishing feature. Although its clinical features of progressive dementia with prominent and early memory failure are characteristic, there are other dementing disorders from which distinction can be difficult and the definite diagnosis of AD still requires neuropathological examination of the brain. The diagnostic pathological features are microscopic and were first described in the late nineteenth and early twentieth centuries (Beljahow 1889; Alzheimer 1907). Despite long familiarity with this pathology, it is only recently that understanding about its development is beginning to be achieved.
Molecular Genetics Of Alzheimer‘s Disease
Authors: Kauwe John S K , Goate Alison M
Published: November 2023

Alzheimer‘s disease (AD) is a complex neurodegenerative disorder characterized by gradual onset and progression of memory loss combined with deficits in executive functioning, language, visuospatial abilities, personality, behaviour and self-care. In the USA, more than 4.5 million people are estimated to have AD. Citing the rapid growth of the oldest age groups in the US population, recent studies predict a rapid increase in the prevalence of AD unless more effective treatments can be developed (Hebert et al. 2003). Individuals with AD live from eight to 20 or more years after the onset of symptoms, making this dis ease both emotionally and financially devastating. The national direct and indirect costs of caring for individuals with AD are in excess of 100 billion dollars (Ernst and Hay 1994). It has been suggested that a 5 year delay in the onset of disease would result in half as many cases in just one generation (Brookmeyer et al. 1998). In order to diagnose AD earlier and to treat it more efficiently, we must identify both the genetic and environmental factors which modulate risk for disease.
Multiple Transgenic Mouse Models For Alzheimer‘s Disease
Authors: Terwel Dick , Dewachter Ilse , Dooren Tom Van , Vandebroek Tom , Helmont Thomas Van , Muyllaert David , Borghgraef Peter , Croes Sophie , Winderickx, Joris , Leuven Fred Van
Published: November 2023

The identification of the genetic causes of familial Alzheimer‘s disease (AD) and frontotemporal dementia (FTD) by clinical geneticists has yielded the necessary genes for experimental biologists to model these diseases in transgenic mice. The first models to be developed were transgenic mice that express wild-type and mutant forms of amyloid precursor protein (APP). Some of these models recapitulate surprisingly faith fully the formation of amyloid plaques in brain parenchyma as well as the accompanying cerebral amyloid angiopathy (CAA), typical of sporadic and familial AD. The mice have served as fundamental research tools and are also excellent preclinical test banks for proven or experimental drugs, diets and natural products, metals and metal chelators, and active and passive vaccination.
Cellular Targets Of Amyloid β Peptide: Potential Roles In Neuronal Cell Stress And Toxicity
Authors: Chen Xi , Stern, David , Yan Shi Du
Published: November 2023

Amyloid plaque formation, caused by deposition of amyloid beta peptide (AP), is a pathological hallmark of Alzheimer‘s disease (AD) (Glenner and Wong 1984; Hardy and Selkoe 2002). However, the role of AP in causing neuronal cell stress and toxicity, thereby leading to AD, is poorly understood. Debate continues regarding the pathological properties of Ap. Questions concerning whether the effects of AP are direct or indirect, and whether they reflect specific or non-specific mechanisms remain to be answered. These questions can only be addressed by identifying specific cellular targets for AP and assessing how interaction of AP with such targets impacts on cellular functions. As a molecule prone to aggregation and non-specific interactions, AP has been shown to interact with diverse macromolecular structures, including lipid bilayers (Terzi et al. 1997) and proteo glycans (Narindrasorasak et al. 1991; Buee et al. 1993; Snow et al.
Oku No Hosomichi Roads to Hamilton ’s ‘Wrightian ‘ Digital Parasites in Geneland
Authors: Sumida Brian
Published: November 2023

The title, too, is a tour de force. Basho_borrowed the name of a road he came across in his northbound odyssey. Laden with meaning, his inspired title is difﬁcult to translate. Some of the word oku ’s meanings are: ‘the far recesses, the inner reaches, the hinterland, the interior. ’ Oku is also an abbreviation of Michinoku, or Michi-no-Oku, ‘the road ’s far recesses. ‘ Japanese nouns are at once both singular and plural. In taking Oku-no-Hosomichi for his title, Bash-must have had in mind its wider meaning, embracing all the desolate, rugged footways penetrating the remote frontier. The original ‘Narrow Road ’ is now a busy thoroughfare in Iwakiri on the outskirts of the bustling city of Sendai.
Foreword to s. Turillazzi & m. J. West eberhard (eds) natural history and evolution of paper waspsऻ
Authors: Hamilton William D
Published: November 2023

Social wasps are among the least loved insects. Even dogs dislike them. Sharing an Englishman ’s jam sandwich half-way to his mouth, massing in hostility to the Amazonian ’s gliding and bumping canoe, raiding and even predating their angelic and useful social cousins the honeybees, and perhaps above all simply being born with that bold, swaying and ever-returning Fight, that remorseless buzz—all these things estrange us. Joylessly, most of us read texts stating them to be important predators, that without them flies and caterpillars would be even more abundant. Yet, where statistics will not alter a general impression, another approach might. Every school-child, perhaps as a part of religious education, ought to sit watching a Polistes wasp nest for just one hour. While probably not more than one in a thousand will be converted to become the kind of wasp addict that contributes to this book, I think that few will be unaffected by what they see.
Because Topics Often Fade Letters, essays, notes, digital manuscripts and other unpublished works
Authors: John1 Jeremy Leighton
Published: November 2023

I still have the note of a telephone message written by a flatmate in my absence. The words that stood out from the paper were: ‘.Prof. Hamilton is seriously ill ‘ With that brief pausing of the heart familiar to all who have lived long enough to know sorrow, concern turned to growing sadness and ultimately grief: a visit to Middlesex Hospital in London, telephoned, written and printed news of his death, a funeral in the Oxfordshire village of Wytham where as a student I had lived for four years with Bill Hamilton and family, a beautiful memorial service in New College Chapel with the music that had been played for Darwin (the musical score having been obtained from the British Library), the despair of a coroner ’s inquiry (a mundane proximal explanation for a desperate death), all these followed in tragically inexorable succession.
William Donald Hamilton
Authors: Grafen Alan
Published: November 2023

William Donald Hamilton was born in 1936 in Cairo to New Zealander parents, and was brought up for the most part in a rural and wooded part of Kent, England. He described his childhood as idyllic, full of freedom to roam, and of maternal inspiration and encouragement, and himself as a great burrower. He was fascinated by insects from an early age. A great-aunt gave him her insect collection, whose cases he used for his own (later ruing his discarding of the insects themselves), and also lent him a translation from Fabre, the great French naturalist and one of the first to study behaviour scientifically.
Integer-sided triangles
Authors: Bradley Christopher J
Published: November 2023

To say that a triangle has one side of integer length or that a circle has integer radius is not mathematically signiFB01cant, as the unit of length can always be adjusted so that this is the case. To say that a triangle has all its sides of integer length is mathematically signiFB01cant. It means that, whatever the unit of length, the ratio of any pair of side lengths is a rational number. However, even if signiFB01cant, it is scarcely interesting. This is because, if you are given three positive integers such that the greatest is smaller than the sum of the other two, then you can always construct a triangle having sides with these integer lengths. Integer-sided triangles become mathematically interesting only when some further condition is imposed.
lattices
Authors: Bradley Christopher J
Published: November 2023

In number theory work on lattices is of fundamental importance, and has been applied to problems as diverse as the rational approximation of real numbers and the representation of integers as the sum of four squares. In this chapter we do little more than scratch the surface. In Section 3.1 we give some basic deFB01nitions and theorems about two-dimensional lattices. Section 3.2 is devoted to an account of Pick’ s theorem, concerning the number of lattice points within or on the boundary of a polygon whose vertices are at lattice points. Finally, in Section 3.3 we show how to solve the problem of determining which lattice points lie on straight lines with equations of the form lx + my = n, where l, m, and n are integers, and then when l, m, and n are restricted to be positive integers.
Circles and conics
Authors: Bradley Christopher J
Published: November 2023

This chapter deals with some inFB01nite sets of circles and conics. The inFB01nite sequence of circles featured in Section 10.1 all have the same unit radius, and have intersection properties that may be seen in Fig. 10.1, where the start of such a sequence is shown. For further reading on inFB01nite sets of circles see the book Hahn (1994).The inFB01nite set of conics are those that circumscribe a triangle. In Section 10.2 we show how to generalize the Simson line property, normally associated with the circumcircle.
The origins of system dynamics: mechanics
Authors: Bertuglia Cristoforo Sergio , Vaio Franco
Published: November 2023

Classical mechanics started to emerge at the end of the seventeenth century, drawing its origins from the study of the movements of the planets, within the grandiose and revolutionary framework created in Newton’s Philosophiae naturalis principia mathematica (1687). The resulting vision of the natural processes is strictly deterministic: the knowledge of the present state of a system enables calculation of the system’s state in any future (or past) time without any ambiguity. Classical mechanics enjoyed considerable success right from the start, and for a long period of time it was considered to be of extreme importance, so much so that scientists (or better experts in natural philosophy) gave it their wholehearted support, reinforcing the conviction that Newton’s classical mechanics was able to provide complete descriptions of reality, and above all, its future evolution.
Introduction
Authors: Bertuglia Cristoforo Sergio , Vaio Franco
Published: November 2023

In Part 1 we looked at several examples of linear and nonlinear modelling in natural and social sciences. We also observed how nonlinear cases generally require much more sophisticated mathematical techniques, which still only enable us to obtain a partial description of the phenomena. In the linear case, on the other hand, we can obtain a complete description; if we have full knowledge of either the boundary conditions ( i.e. the coordinates at different times) or the initial values of the dynamics (i.e. the coordinates and their derivatives), the system’s future evolution is preordained and can be calculated.
Logistic growth as a population development model
Authors: Bertuglia Cristoforo Sergio , Vaio Franco
Published: November 2023

In this section we would like to return to the description of the dynamics of a single population interacting with the external environment, a subject that we have mentioned on several occasions in previous sections, however without ever going into any further detail. A population can consist of bacteria, insects, people, or any other type of entity able to reproduce itself. The growth model of a population describes how the number x of the members of the latter evolve, i.e. increase or decrease over time.
The logistic map: some results of numerical simulations and an application
Authors: Bertuglia Cristoforo Sergio , Vaio Franco
Published: November 2023

In this section we will be dealing with the evolution of the logistic map as a result of the numerical calculation of the states and we will be looking at some of its characteristics on the basis of the numbers supplied by the iterations. Figure 22.1 illustrates the contents of Chapter 21 regarding the splitting of the fixed points, of the subsequent doubling of the period that are at the origins of chaos and the presence of asymptotic equilibrium on a set of values travelled cyclically.
Chaos in systems: the main concepts
Authors: Bertuglia Cristoforo Sergio , Vaio Franco
Published: November 2023

To conclude this part, we would like to briefly review and summarize some of the most important points discussed. As we have seen, in specific circumstances, i.e. for certain values of parameters, the long-term prediction of the evolution of a nonlinear dynamic system can be achieved without error or ambiguity. In the case of the logistic map, this is true for values of the growth parameter λ that fall between 0 and 3, in which we have one fixed point attractor. This is the case we have called Case 1. Under these conditions, the most simple, the system inevitably evolves towards a previously known future, regardless of the initial conditions, even towards the extinction of a population, which occurs when λ < 1.
Inadequacy of reductionism
Authors: Bertuglia Cristoforo Sergio , Vaio Franco
Published: November 2023

To describe, interpret and predict phenomena of the environment (or of the world, the universe or whatever we wish to call it) in which we are immersed, we generally use models, where the meaning if the term model’, in a very general context, is a mental representation that, in a certain sense, replaces the environment (the world, the universe). In other words, since we have no means of going beyond the restricted window that our senses provide of reality, the latter is too complicated and substantially inaccessible to complete knowledge. All that we can do is to limit ourselves to constructing a representation of reality based on information gained from experience. In this vision, therefore, our knowledge is always relative to a perspective and is conditioned by a point of view, a product of the human mind, and not something inherent to the order of things. Science, therefore, does not study the physical world per se, but rather our way of depicting some regularities selected from our experience, that can be observed in certain conditions and from a particular perspective.
The need for a mathematics of (or for) complexity
Authors: Bertuglia Cristoforo Sergio , Vaio Franco
Published: November 2023

As we have said on a number of occasions, sciences exist as such because the world often appears algorithmicaHy compressible into laws, often expressed in mathematical forms, that are none other than reductions carried out starting from enormous sequences of data. Reductions are possible when the phenomena display recurrences; in a completely chaotic world, the latter would not appear and reductions would be impossible. The chaos in the measured data means precisely that the deterministic law that is assumed to be behind the phenomena and that should appear as a result of the reduction made on the observations, is not easily visible, so much so that it makes the same phenomena appear to be random, i.e. not due to a deterministic law. But even a complex world is difficult to describe in a deterministic way. The phenomenology of complex systems, in fact, is characterized by properties such as emergence, self-organization, etc. (see Chapters 27 and 28) and evades (at least for now) the possibility of a formulation that enables, a priori, the manifestation of such to be predicted. The situations of complex systems are not repeated in the same way, maybe similar, but never exactly the same, and it is precisely because of this that it is difficult to recognize the laws constructed following reductions. The phenomenology that we observe in nature and in society often appears to be characterized by chaos and/or complexity, and therefore, in reality, the operation of mathematically reducing the data, effective in other situations, in these cases, ceases to be so. Nonetheless, we want to find effective laws, expressed in a mathematical form, to describe chaotic and/or complex phenomenology.
Relative Consistency and Accessible Domains∗
Authors: Sieg Wilfried
Published: November 2023

Introduction

The goal of Hilbert’s program – to give consistency proofs for analysis and set theory within finitist mathematics – is unattainable; the program is dead. The mathematical instrument, however, that Hilbert invented for attaining his programmatic aim is remarkably well: proof theory has obtained important results and pursues fascinating logical questions; its concepts and techniques are fundamental for the mechanical search and transformation of proofs; and I believe that it will contribute to the solution of classical mathematical problems. Nevertheless, we may ask ourselves, whether the results of proof theory are significant for the foundational concerns that motivated Hilbert’s program and, more generally, fora reflective examination of the nature of mathematics.
Diffusions
Authors: Stirzaker David
Published: November 2023

All the Markov processes considered in the previous two chapters have been ‘jump processes’, which is to say that they make transitions between discrete states at times that may be fixed or random. But many stochastic processes in the real world do not have this property. In sharp contrast to jumps, there are random processes that are seen to move continuously between their possible states, which commonly lie in some interval subset of the real line. Examples include meteorological records, physiological data, and the noise that corrupts electronic signals. Of course it remains true that many of these processes still have the Markov property, and it is therefore natural to seek a general theory of such processes with continuous parameter and continuous state space. As usual, we begin with a simple but important example that illustrates many of the key ideas.
Inherited susceptibility to cancer
Authors: Bishop D Timothy
Published: November 2023

Chapter 2 describes the evidence regarding a number of different exposures such as diet and radiation on a person’s risk of cancer. Responses to such exposures may well be defined by the person’s genetic makeup while genetic factors them- selves could be the major determinant of risk. This chapter focuses on the evidence relating to inheritance and cancer risk. The most direct evidence for a role of genetic susceptibility to cancer comes from the clinical identification of relatively rare but clearly characterized inherited diseases in which the role of inheritance is unequivocal.
DNA repair and cancer
Authors: Köberle Beate , Wittschieben John P , Wood Richard D
Published: November 2023

This chapter concentrates on the main DNA repair mechanisms operating in human cells and the relationship of DNA repair to cancer. There are several pathways for repairing damaged DNA (Lindahl et al., 1997; Hoeijmakers, 2001).
Tumour suppressor genes
Authors: Laín Sonia , Lane David P
Published: November 2023

Tumour suppressor genes (TSGs) encode proteins whose absence, repression, expression inactivation, or mutation promotes oncogenesis. In some instances, reactivation of the function of a TSG suppresses the malignant phenotype. This type of TSG is referred to as a gatekeeper gene. Inactivation of other TSGs (caretaker genes), leads instead to genomic instability and therefore to an increase in the mutation of other genes that may be gate- keeper genes or influence tumour development. Caretaker genes include genes involved in DNA repair and genes that maintain the integrity of chromosomes and their numbers. Unlike gate- keeper genes, reconstitution of caretaker genes fails to override these secondary effects and does not suppress malignancy.
Apoptosis: molecular physiology and significance for cancer therapeutics
Authors: Fennell Dean A
Published: November 2023

Apoptosis, also referred to as programmed cell death, is a highly regulated, evolutionarily conserved, and biochemically stereotyped process with tremendous relevance to cancer therapeutics. Understanding the molecular basis of apoptosis regulation in cancer is a prerequisite for the development of new effective medicines. This chapter will broadly overview current knowledge of core apoptosis mechanisms, with a focus on the mammalian cell. Novel approaches for overcoming defects in apoptosis signalling have opened up an active and exciting area of drug discovery relevant to cancer, and will be highlighted.
The molecular pathology of cancer
Authors: Crnogorac-Jurcevic Tatjana , Poulsom, Richard , Lemoine Nicholas R
Published: November 2023

Molecular pathology is the study of basic mechan- isms involved in pathogenesis of diseases at the molecular level. In addition to ‘classical’ examina- tion of the morphology of diseased tissues and cells, it is now starting to embrace novel techniques of molecular biology that will enable us to reveal the origin and the development of the disease pro- cesses by examining the nucleic acids and proteins. Molecular pathology has a special role in both clinical oncology and translational research.
Screening
Authors: Sasieni Peter , Cuzick Jack
Published: November 2023

Screening is aimed at identifying selecting a small group of individuals who are likely to benefit from some form of intervention to reduce the morbidity and mortality from cancer. Screening can take several forms, can be aimed at different populations, and can have different goals. Very often it is a multistage process in which individuals positive at one stage are referred on to a more invasive or intensive procedure to see if cancer is present. There are several pitfalls in the evaluation of the efficacy of screening modalities and it is vitally important that screening should do more good than harm, since one is approaching a healthy population and asking them to undergo a medical procedure, as opposed to the usual clinical paradigm in which an unwell patient approaches the doctor and actively seeks advice and treatment.
Further topics
Authors: Cameron Peter J
Published: November 2023

The emphasis in this section is on finite groups. We prove Sylow’s theorems on the existence of subgroups of prime power order, and the Jordan–Hölder Theorem, which reduces the problem of describing all finite groups to describing the finite simple groups and fitting them together. There is also some discussion of these two sub-problems.
Analytic properties of quasiconformal maps
Authors: Fletcher A , Markovic V
Published: November 2023

In this chapter, we have a further definition of quasiconformality, which this time is analytic in flavour, and yet agrees with our previous definitions. This definition makes possible a way to show that quasiconformal maps are Hoolder continuous and thus satisfy important compactness properties.
Unique extremality
Authors: Fletcher A , Markovic V
Published: November 2023

We investigate conditions for unique extremality, including the frame mapping theorem, which gives a condition on when a Teichmuoller equivalence class has a uniquely extremal representative of Teichmuoller type. We will see that unique extremality corresponds to unique infinitesimal extremality. Uniquely extremal mappings need not be of Teichmuoller type, and indeed that they need not have constant modulus.
Bayesian hierarchical models in geographical genetics
Authors: Holsinger Kent E
Published: November 2023

The fundamental data of population genetics consists of allele counts at different loci within populations. The natural descriptive statistics associated with these data are locus specific allele frequencies and measures to describe the partitioning of genetic diversity within and among populations. F-statistics, which were first introduced by Sewall Wright and Gustave Malécot are the most widely used statistics for this purpose, but neither Wright nor Malécot paid close attention to problems associated with inference of parameters from data.
Cortical mechanisms of hypnotic pain control
Authors: Miltner Wolfgang HR , Weiss Thomas
Published: November 2023

Hypnosis has been known for centuries to modify significantly subjects ‘ perceptions and other psychological processes. Thus, several studies have shown that colourful visual stimuli can lose their brightness and colour, and physically strong auditory stimuli can become almost inaudible when subjects are exposed to corresponding hypnotic suggestions of colour blindness or deafness (Revenstorf 1993). Furthermore, the skin of fakirs can become deeply penetrated by knives, daggers or swords without pain and without negative emotions while being in a hypnotic-like trance, whereas the same physical event would be perceived as terribly painful by the same persons outside the trance state (Larbig 1988; Larbig and Miltner 1990).
Surface Bundles
Authors: Calegari Danny
Published: November 2023

The purpose of this chapter is to survey the Thurston theory of surface automorphisms and geometric structures on their mapping tori. We will emphasize those parts of the theory which will be generalized to arbitrary taut foliations in the remainder of the book. The exposition in this chapter is somewhat curt. We give few indications of the proof of the main lemmas and theorems, since rigorous and thorough treatments are easily available in many sources: [230], [234], [71], [47] and [193] are standard references.