bluuebunny/crossref_metadata_2025 huggingface dataset:
Elite Transforn1ation and Modes of Representation since the Mid-Nineteenth Century: Some Theoretical Considerations
Authors: Best Heinrich , Cotta Maurizio
Published: November 2023

It is now approximately thirty years since Stein Rokkan developed his theoretical framework and empirical grid for a comparative study of nation building and state formation in Western Europe. His systematizations became the intellectual guideline for several generations of sociologists and political scientists and the point of departure for numerous research projects in comparative political sociology. In Rokkan’s conceptual framework, political elites formed a central object of interest because their structure sets the stage for the formation of sociopolitical coalitions, which are in turn the decisive, explanatory factor for the variations among European party systems. In his initial proposal for a grid of indicators for the comparative study of political development, there was already a section on the recruitment of elite groups. Recruitment patterns were of particular interest for Rokkan because he maintained that the changing composition of elites reflects the processes of social and political mobilization, of societal integration, and the establishment of rules for access to positions and resources in a society (Rokkan 1967).
Aspects of Approximation with Emphasis on the Univariate Case
Authors: Watson G A
Published: November 2023

This paper focusses on some aspects of approximation which are seen to be important from the numerical analysis point of view, and which have seen activity in the last 10 years. Its emphasis is on univariate approximation, which is an extensive area, and many topics could be covered. Perhaps the development which has stimulated most interest over this period is that of wavelets. This subject has expanded extremely rapidly, there have been many theoretical advances, and it has been the focus of many potential and actual applications. It is clearly not possible to do justice to all of this here, particularly for a non-specialist audience: we content ourselves by providing an introduction to the topic which we hope will stimulate further interest. Of course, wavelets can also be multivariate, although we will not consider those here. For some approximation problems, the number of independent variables is actually not very important, and this is certainly true of some of the topics considered in the rest of the paper. However, what they all have in common is that they are not inherently multivariate, and so do not fit naturally into that category.
Methods for Nonlinear Constraints in Optimization Calculations
Authors: Conn Andrew R , Gould Nicholas I M , † Philippe L Toint
Published: November 2023

Ten years ago, the broad consensus among researchers in constrained optimization was that sequential quadratic programming (SQP) methods were the methods of choice. While, in the long term, this position may be justified, the past ten years have exposed a number of difficulties with the SQP approach. Moreover, alternative methods have shown themselves capable of solving large-scale problems. In this paper, we shall outline the defects with SQP methods, and discuss the alternatives. In particular, we shall indicate how our understanding of the subproblems which inevitably arise in constrained optimization calculations has improved. We shall also consider the impact of interior-point methods for inequality constrained problems, described elsewhere in this volume, and argue that these methods likely provide a more useful Newton model for such problems than do traditional SQP methods. Finally, we shall consider trust-region methods for constrained problems, and the impact of automatic differentiation on algorithm design.
Worst-case identification of functions
Authors: Partington Jonathan R
Published: November 2023

This chapter is the first one devoted largely to applications of the general theory of interpolation and recovery. After giving a brief summary of some of the ideas behind systems theory, we shall set up the standard worst-case identification problem, as formulated by Helmicki, Jacobson, and Nett, and relate it to the ideas developed in the previous chapters.
Combinatorial Designs and Tournaments
Authors: Anderson Ian
Published: November 2023

The mathematics of tournament design are surprisingly subtle, and this book, an extensively revised version of Ellis Horwood's popular Combinatorial Designs: Construction Methods, provides a thorough introduction. It includes a new chapter on league schedules, which discusses round robin tournaments, venue sequences, and carry-over effects. It also discusses balanced tournament designs, double schedules, and bridge and whist tournament design. Readable and authoritative, the book emphasizes throughout the historical development of the material and includes numerous examples and exercises giving detailed constructions.
Self-orthogonal Latin sqnares
Authors: Anderson Ian
Published: November 2023

In the previous chapter we presented a proof of the fact that, if n ≠ 2 or 6, two MOLS of order n exist. This result, the culmination of a great deal of effort spurred on by a conjecture almost 200 years old, is not, however, the end of the story. However, another remarkable development will be dealt with in this chapter: it will be shown that, for every n ≠ 2, 3, or 6, there exists a Latin square of order n which is orthogonal to its transpose! Such Latin squares are useful in the construction of other combinatorial structures such as whist tournaments.
League schedules
Authors: Anderson Ian
Published: November 2023

In a round robin tournament, every team plays every other team once. If there are 2n teams, and the n(2n -1) games are to be arranged into 2n -l rounds, with each team playing in one game in each round, we seek a resolvable (2n,2, 1) design. As we have already seen in sections 1.2 and 2.3, such league schedules can be obtained elegantly by the ‘circle method’ and, more generally, by the use of a difference system. For example, the Scottish Rugby Union used the design of Example 1.2.3 for its 1995 premier league, altering the home and away venues slightly (we shall discuss this further in section 8.2).
Completion
Authors: Lowen R
Published: November 2023

The fact that AP contains both TOP and pMET𝒯 as full and isomorphism-closed subconstructs implies that we have to consider both the notions of completion and of compactification, at least for uniform approach spaces. In the present chapter we construct a completion which coincides with the usual completion in the case of p-metric spaces and which is an epireflection from the subconstruct of Hausdorff uniform approach spaces to the subconstruct of complete Hausdorff uniform approach spaces. In the second section we look at the relationship between the pMET𝒯 -coreflection of this completion and the usual metric completion in the special case of function spaces.
A-DNA duplexes in the crystal
Authors: Whhl Markus C , Sundaralingam Muttaiya
Published: November 2023

More than four decades after the first crystallographic evidence for A-DNA (1), we are now confronted with a large number of single-crystal structures of short A-DNA duplexes, through which we are able to begin to understand some of the principles governing their helical structure and their interaction with ligands. The stunning diversity of fine structures promotes a picture of the DNA double helix in which A- and B-forms denote the hemispheres of the right-handed structural continuum (2,3).
Function fields and places
Authors: Pretzel Oliver
Published: November 2023

This chapter introduces the abstract algebraic concepts that correspond to the function fields of curves and the local rings of points on the curves. The field of rational functions, which corresponds to a straight line, is examined in detail. The chapter concludes with the existence theorem which shows that a function field contains enough structure to serve as an algebraic equivalent for a curve.
Valuations
Authors: Pretzel Oliver
Published: November 2023

Having found a satisfactory abstract equivalent for the points P of a curve the next step is to define an equivalent for the order function 𝒱p. Functions corresponding to good order functions of points are called ‘discrete valuations’.
Divisors
Authors: Pretzel Oliver
Published: November 2023

In this chapter we shall prove the degree theorem and Riemann’s theorem. For that we need to generalize the concept of the degree of a point to places and then extend the concept of a divisor to places in the natural way.
Twistors, Geometry, and Integrable Systems
Authors: Ward R S
Published: November 2023

I am delighted to be able to make this contribution to the celebration of Roger Penrose’s 65th birthday. The subject is that of integrable systems and their relation to geometry and twistor theory. When twistors were created, about thirty years ago, their creator did not have integrable systems as his primary motivation: Roger was aiming at a wider class of physical problems. In a sense, integrable systems are a cop-out: they deliberately avoid the messiest interactions and dynamics that occur in the real world. But they do provide a window onto nonlinear, coherent, nonperturbative phenomena—these become accessible, beautiful, and (if you look at them in the right way) geometrical. In the words of Mason and Woodhouse [8], “they combine tractability with nonlinearity, so they make it possible to explore nonlinear phenomena while working with explicit solutions”.
Hyperbolic 3-Manifolds
Authors: Matsuzaki Katsuhiko , Taniguchi Masahiko
Published: November 2023

In this chapter we give several models of the 3-dimensional hyperbolic space H3, the definition of hyperbolic 3-manifolds and the representation of them by Kleinian groups. In the last section, we briefly discuss some examples of hyperbolic 3-manifolds.
The basis of Kleinian group theory
Authors: Matsuzaki Katsuhiko , Taniguchi Masahiko
Published: November 2023

We have seen that Kleinian groups are discrete subgroups of PSL2(C) as well as properly discontinuous groups acting on the hyperbolic space H3. In Section 2.1, we state fundamental facts about the action of Kleinian groups on H3 and S. ∞
The sphere at infinity
Authors: Matsuzaki Katsuhiko , Taniguchi Masahiko
Published: November 2023

We have seen that a quasi-isometric automorphism of the hyperbolic space H3 extends to the quasiconformal automorphism of the sphere at infinity S ∞ (Theorem 3.22). By this fact, the interior and the boundary of a Kleinian manifold Mr are closely related; we analyze the action of r on S∞ for the investigation of deformations of the interior structure.
Algebraic and geometric convergence
Authors: Matsuzaki Katsuhiko , Taniguchi Masahiko
Published: November 2023

In this chapter, we discuss the geometric convergence of Kleinian groups. Algebraic convergence, which was defined in Section 4.3.1 from the natural topology of the representation space, is a basic concept of convergence; however it does not necessarily imply convergence of the corresponding Kleinian manifolds. In particular, they differ on boundaries of quasiconformal deformation spaces.
The probabilistic estimation of quintet invariants
Authors: Giacovazzo Carmelo
Published: November 2023

Which is the information exploited via the first phasing shell? In particular, which are the multipoles exploited via the first representation of Φ? In accordance with Section 6.4, Φ enters into ten tripoles (one for each cross-reflection).
Phasing via neutron and electron data
Authors: Giacovazzo Carmelo
Published: November 2023

Neutron and electron diffraction are much less used for structure analysis than X-ray diffraction. However, thanks to the recent advances in methods and instrumentation, they are receiving increasing attention as a means for obtaining structural information when this is not readily attainable with X-ray techniques.
Molecular replacement techniques and direct methods
Authors: Giacovazzo Carmelo
Published: November 2023

The same protein, under different crystallization conditions (e.g. change of pH, change of solvent) can crystallize in different space groups. On the other hand, homologous proteins (end points of divergent evolution from a single primitive protein, but very similar in tertiary structure) often crystallize in different space groups. We can expect that the diffraction patterns of such similar proteins will be related to each other. A third case may be considered: if more than one protein molecule is packed in the same asymmetric unit a local (or non- crystallographic) axis will relate the different units.
Geometries in collision: Einstein, Klein and Riemann
Authors: Norton John D
Published: November 2023

Of all the achievements of modern theoretical physics, one stands out as unique. Without discernible intermediaries, the general theory of relativity completely transformed our understanding of gravitation. Gravitation ceased to be a field in space and time like the electromagnetic field; it became the geometric curvature of space-time itself. And this transformation was effected essentially by just one scientist, Albert Einstein. Nonetheless, in the eight decades that have passed since Einstein ‘s achievement, a growing chorus of voices have cried that, in spite of his unique success, Einstein never understood the foundations of his own theory. The focus of these problems is Einstein ‘s claims concerning relativity principles, covariance principles and coordinate systems. Specifically, Einstein ‘s theory is generally covariant; its equations remain unchanged in form under arbitrary transformations of the coordinates. Through this property, Einstein claimed, his theory had effected the most complete generalization of the relativity of inertial motion of the special theory to a more general relativity that embraced acceleration.
Topological Classification of Continuous-Time Linear Hyperbolic Cocycles
Authors: Cong Nguyen Dinh
Published: November 2023

Theorem 7.4.2 can be rephrased as follows: two linear hyperbolic cocycles are conjugate if and only if they have stable subspaces of the same dimension and their restrictions to their stable subspaces are both orientation preserving or orientation reversing with respect to a measurable choice of orientations on those stable subspaces. We remark that in our continuous-time case the continuity int of linear cocycles plays an important role. As noted by Arnold [10), in the theory of random dynamical systems the interplay of measurability and dynamics is of crucial importance. Here, in our continuous-time case, the continuity in t of linear cocycles enters the game. It allows us to reduce the number of orientation conditions for a topological conjugacy from two in the discrete-time case (see Chapter 4) to one. So, roughly speaking, in general there are fewer topological classes of continuous-time linear hyperbolic cocycles than there are for discrete- time, but there are still more than for deterministic flows.
Introduction
Authors: Karpinski Marek , Rytter Wojciech
Published: November 2023

A graph is a useful abstraction of many real world situations. It occurs when a problem is essentially related to the structure of interconnections between some objects. For example, a road map can be viewed as a graph: the interconnected objects are cities and connections correspond to roads. The connections can be one-way or two-way, and the corresponding graph can be directed or undirected. Another real world example is a group of people, the connections between them corresponding to the relation “the person x knows the person y”. In abstract graph terminology the interconnected objects (cities, persons) are called vertices or nodes (these terms are equivalent terms in this book). The connections are called edges. In the case of relation “x knows y” we have an edge ( x, y). A graph G is formally given by a pair G = (V, E), where V is the set of vertices and E is the set of edges. The edges can be unordered pairs of different vertices: the graph is called undirected; or ordered pairs: the graph is directed. We consider only the case when all edges are undirected or all edges are directed. Also we do not allow multiple edges between the same vertices (in the directed case between the same ordered pair). We assume that V is finite and its cardinality is usually denoted by n. This is the main parameter related to the size of the graph. The second parameter is the number m of edges of a given graph.
Parallel algorithms for f-matchings
Authors: Karpinski Marek , Rytter Wojciech
Published: November 2023

In this chapter we present randomized and deterministic NC-algorithms for maximum and (inclusion) maximal f-matchings (which are natural generalizations of matchings). In particular each (usual) matching is a I-matching. Let G be an undirected graph with an integer capacity f(v) associated with each vertex v. A subset M of the set of edges of G is an f-matching if and only if each vertex v in G is incident to at most f(v) edges in M. An f-matching is maximal if and only if it is not properly contained in another f-matching. An example of a maximal f-matching containing 10 edges is illustrated in Figure 11.1; the maximum cardinality f-matching in this case has 11 edges. The parallel computation of a maximal f-matching is generally more difficult than that of a maximal matching. Obviously, a maximal f-matching can be computed in linear time by a greedy sequential algorithm. Unfortunately we do not know how to parallelize this algorithm. In Chapter 7 we presented an RNC¬ algorithm for maximal matchings. By generalizing this randomized algorithm we can present a simple randomized algorithm for maximal f-matching which runs in O(log3 n) time with O(n + m) processors. The deterministic NC-algorithm is much more complicated. It is based on the Israeli and Shiloach deterministic algorithm for maximal matchings, see [IS86]. It was generalized in [DGL93] to maximal f-matching.
The Heisenberg Group
Authors: David Guy , Semmes Stephen
Published: November 2023

The Heisenberg group is a nilpotent Lie group ‒ or rather a family of Lie groups, one for each odd dimension ≥ 3 ‒ which have many features in common with Euclidean spaces.
Reminiscences of the Early Days of the Spectrum of Ocean Waves
Authors: Ursell F
Published: November 2023

The wave spectrum was introduced into oceanography through the work of The Admiralty Wave Group (Group W) which was set up in June 1944 to develop rules for the forecasting of waves on ocean beaches. The work of Group W showed that the propagation of ocean waves outside the storm area follows the laws of classical linear dynamics: each wave component is propagated with the appropriate group velocity. It was thus found possible to use observations on shore to trace each component in dependently back into the storm area and to correlate its amplitude with weather data in the storm area. This work has since then become the basis of modern wave forecasting. The author was a member of Group W from its earliest days to 1947, and in the present paper he comments on the early work of Group W and on some of the scientists who were members of that Group.
Homogenization of Multiple Integrals
Authors: Braides Andrea , Defranceschi Anneliese
Published: November 2023

The object of homogenization theory is the description of the macroscopic properties of structures with fine microstructure, covering a wide range of applications that run from the study of properties of composites to optimal design. The structures under consideration may model cellular elastic materials, fibred materials, stratified or porous media, or materials with many holes or cracks. In mathematical terms, this study can be translated in the asymptotic analysis of fast-oscillating differential equations or integral functionals. The book presents an introduction to the mathematical theory of homogenization of nonlinear integral functionals, with particular regard to those general results that do not rely on smoothness or convexity assumptions. Homogenization results and appropriate descriptive formulas are given for periodic and almost- periodic functionals. The applications include the asymptotic behaviour of oscillating energies describing cellular hyperelastic materials, porous media, materials with stiff and soft inclusions, fibered media, homogenization of HamiltonJacobi equations and Riemannian metrics, materials with multiple scales of microstructure and with multi-dimensional structure. The book includes a specifically designed, self-contained and up-to-date introduction to the relevant results of the direct methods of Gamma-convergence and of the theory of weak lower semicontinuous integral functionals depending on vector-valued functions. The book is based on various courses taught at the advanced graduate level. Prerequisites are a basic knowledge of Sobolev spaces, standard functional analysis and measure theory. The presentation is completed by several examples and exercises.
Lysosmal Cysteine Proteases
Authors: Kirschke Heidrun
Published: November 2023

Lysosomal cysteine proteinases are proteolytic enzymes with a cysteine residue in the active site, which degrade proteins taken up by the cell or originating in other cell compartments. They catalyze the hydrolysis of peptide, amide, ester, and thiol bonds, dependent on pH and the presence of reducing compounds. This new volume in the protein profile series examines each known cathepsin in turn, examining gene structure and localization; precursors, purification, activation, and inhibition; and hydrolysis of synthetic substrates, polypeptides, and proteins. Other topics include structures and evolution, reaction with inhibitors, and physiological functions of lysosomal cysteine proteinases and their role in disease. The book also includes an extensive bibliography to assist the reader in further research.
Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras
Authors: Geck Meinolf , Pfeiffer Golz
Published: November 2023

Finite Coxeter groups and related structures arise naturally in several branches of mathematics, for example, the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are obtained by a certain deformation process. They have applications in the representation theory of groups of Lie type and the theory of knots and links. The aim of this book is to develop the theory of conjugacy classes and irreducible characters, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. The topics range from classical results to more recent developments and are treated in a coherent and self-contained way. This is the first book which develops these subjects both from a theoretical and an algorithmic point of view in a systematic way. All types of finite Coxeter groups are covered.
The best of alll possible worlds?
Authors: Acheson David
Published: November 2023

Suppose that a ray of light is reflected by a mirror from some given point A to another given point B. It is well known that the point of reflection, P, is such that the rays AP and PB make equal angles with the mirror (Fig. 8.1). But there is in fact a quite different and more intriguing way of expressing the same physical result, namely that the point of reflection P is such that the total distance AP + PB is as small as possible.
Cell assembly
Authors: Dudai Yadin
Published: November 2023

In 1949, Hebb published The organization of behavior, later to become the most influential book in the history of modern neuroscience (*classic). ‘In this book’, he wrote, ‘I have tried … to bridge the gap between neurophysiology and psychology’. In essence, Hebb’s monograph was about how the brain *perceives and represents the world. It has yielded important insights into brain function, as well as two major concepts.
Confabulation
Authors: Dudai Yadin
Published: November 2023

Confabulation in its broader meaning (definition 1) refers to a wide spectrum of phenomena. Some of these phenomena are within the normal range of the human behavioural repertoire. Minor, innocent confabulations may pop-up occasionally in some individuals in stressful social situations; they could be considered a sort of defence mechanism.
Flashbulb memory
Authors: Dudai Yadin
Published: November 2023

In recent years, brain research has unveiled clues to the biological mechanisms that encode the memory of intensely emotional and consequential events. These candidate mechanisms deal with two *levels of brain organization: the circuit level and the cellular level. The circuit mechanisms are assumed to involve subcortical modulation of the *cerebral cortex, which causes certain sensory events to be *perceived as highly salient because of the concomitant activation (*coincidence detection) of neuromodulator systems such as the *acetylcholine and the *noradrenaline systems (Naor and Dudai 1996; McGaugh and Cahill 1997; Tang et al. 1997).
Generalization
Authors: Dudai Yadin
Published: November 2023

The functional counterpart of ‘generalization’ is ‘discrimination’, which is the ability to distinguish one stimulus or response from another. This is why it is convenient to treat these faculties together. Discrimination increases the repertoire of fine-tuned *perception and response, but places a burden on *capacity; generalization diminishes the sensitivity to input noise, but limits the degrees of freedom of the behavioural repertoire and could increase the proportion of false-positive responses. A *subject could be well capable of discriminating among two events, but still generalize its response to them if this pays off behaviourally.
Glutamate
Authors: Dudai Yadin
Published: November 2023

L-glutamate is present in the mammalian brain at remarkably high concentrations. For a while this observation, coupled with the ability of glutamate to excite neurons all over the brain, cast doubt on its role in neurotransmission; for how can such a ‘non-specific’ agent mediate specific information? The case for glutamate as a neurotransmitter in the invertebrate neuromuscular junction was easier to establish (Usher wood 1994; *criterion). But with time it became clear that not only is glutamate a transmitter in mammalian brain—it is the major excitatory transmitter, and as such is critical for ongoing activity in the central nervous system. Furthermore, it is now known to play a key part in neuronal *plasticity and learning.
Lotus
Authors: Dudai Yadin
Published: November 2023

The Lotophagi (lotus eaters in Greek) were encountered by Odysseus and his sailors on an island in the troubled sea, shortly before facing the Cyclope (Homer, Odyssey IX 83–104). Whoever tasted the honey-sweet fruit of the flowering lotus, forgot the way home and desired to stay in lotus land. The fabulous lotus, never identified, is hence the ancient counterpart of modern *amnestic drugs. Actually, lotus was not the only potion renown in ancient times for its alleged amnestic powers.
Metamemory
Authors: Dudai Yadin
Published: November 2023

Although some authors consider the study of meta-memory a newcomer to the field of memory research, its roots are rather ancient. Already St Augustine (400) referred to ‘Memory of memories … I have remembered that I have remembered’. Interest in the self-appreciation of one’s own knowledge and performance was shared by introspectionists during the early days of experimental psychology, especially the so-called ‘Würzburg school’ of ‘systematic experimental introspection’ (Boring 1950a).
Method
Authors: Dudai Yadin
Published: November 2023

Selecting a method and following it is like choosing a road and embarking on a journey (this indeed is the origin of the word: meta-, which is Greek for beyond, after, along with, and hodos, which is way, journey). The road may guide to the goal but at the same time impose *a priori limits on the terrain travelled and on the expected outcome. ‘Methods’ are fundamental to human cognition and action (definition 1; e.g. Newell and Simon 1972). Here we shall confine ourselves to scientific methods (included in definition 2, which is an elaboration of definition 1), and particularly, to methods used in the experimental sciences. Discussion of the methodology of science at large far exceeds the scope of this treatment (Nagel 1979; Bechtel 1988).
Neurogenetics
Authors: Dudai Yadin
Published: November 2023

Dubnau and Tully 1998). Over the years, learning mutants of Drosophila have contributed significantly to our current knowledge about the molecular mechanisms of *acquisition and *consolidation of simple memory (*CREB, *intracellular signal transduction cascade). Yet Drosophila, in spite of offering unique advantages to the geneticist, is not the dream machine of the neurophysiologist. With time it became indeed possible to identify the effect of specific mutations in identified brain regions and even single neurons that subserve learning (Corfas and Dudai 1990; Waddell et al. 2000; Zars et al.
Nootropics
Authors: Dudai Yadin
Published: November 2023

The term ‘nootropics’ (from Greek, noos—mind, tropos—turn) was originally coined to denote chemical compounds that were reported to enhance cognitive function, including learning and memory, without possessing other significant effects (Giurgea 1973). The best known are piracetam and structurally related compounds (Giurgea 1973; Gouliaev and Senning 1994). Over the years, however, the term has acquired a peculiar flavour. Many authors reserve it for compounds that are reputed to boost cognition, but were not rigorously proven to do so. Others use it to refer to compounds that have proven beneficial effects on cognition but whose mechanism of action is yet unknown.
Matrix Metalloproteinases and TlMPs
Authors: Woessner J Frederick , Nagase Hideaki
Published: November 2023

The matrix metalloproteinases (MMPs) are a large family of enzymes that break down different components of the extracellular matrix. Their catalytic activity is dependent on the metal ion zinc. This issue of the Protein Profiles covers the sequence information, three-dimensional structures, activation, protein substrates, specificity requirements, inhibition, and biological roles of all the currently identified MMPs. The action of these enzymes must be carefully regulated. One way the cell does this is by releasing inhibitory molecules known as tissue inhibitors of metalloproteinases (TIMPs). This volume contains information on the sequences, three-dimensional structures, and biological roles of the four known TIMPs. Matrix metalloproteinases and TIMPs will therefore be an invaluable source of data for all researchers interested in MMPs and TIMPS.
Protein substrates of the MMPs
Authors: Woessner J Frederick , Nagase Hideaki
Published: November 2023

As emphasized in a recent review by Woessner [147] the natural substrates of MMPs acting in vivo remain largely unknown and unexplored. Although large compendia of substrates have been gathered, e.g. Chandler et al. [30], such lists comprise proteins that have been tested in vitro as potential substrates. This is no guarantee that the substrate in question is degraded in vi110 by the enzyme tested, it merely shows that the potential exists. Furthermore, the number of known constituents of the extracellular matrix is now well over 150 and only a small fraction of these have been tested as substrates. To establish the natural substrates it is necessary to isolate degradation pro ducts from the tissue and show by sequence analysis that the bond cleavage matches that produced by the MMP in question. This has been done in the case of three substrates: interstitial col lagens, aggrecan and link protein (see below). However, ambiguities still remain: often several different MMPs will digest the same protein at the same bond, and the fragments produced may undergo further digestion by other enzymes in the matrix. Another path to follow would be to show the absence of substrate degradation in a gene knockout experiment. In the section that follows, we will summarize known substrates, but with the three exceptions noted, there is no clear proof that any of these substrates is degraded in vivo by a particular MMP. A preliminary overview is provided by Table 7.
Inhibition of the MMPs
Authors: Woessner J Frederick , Nagase Hideaki
Published: November 2023

In addition to knowledge gained by studies of enzyme specificity, a good deal can also be learned about the active centre by the use of inhibitors. First, we will discuss inhibitors that act by chela tion or replacing zinc at the active centre. This will be followed by information on inhibitors that act by non-specific means, such as affecting the substrate, and inhibitors that are modelled on the pro peptides of MMPs. Inhibition by proteins in the macroglobulin class provides some information about specificity (much of it tabulated in the section on MMP specificity). Finally, the design of synthetic peptide derivatives or peptide mimetics will be considered. The inhibition by TIMPs will be treated in a separate section.
Introduction
Authors: Babuška Ivo , Strouboulis Theofanis
Published: November 2023

The finite element method is today one of the major tools of CAE (Computer Aided Engineering). The growth of computer power and the availability of software allows engineers to solve more and more complex linear and nonlinear problems rapidly and with diminishing computational and human cost. More precisely the availability of solid based CAD geometry, automatic meshing, associativity between geometry and finite elements, the development of eﬃcient solvers for system of linear equations, etc. has drastically reduced the time needed to solve complex problems. For a survey of various aspects of the use of the FEM in industry, refer to [Brown, 1997]. Many commercial and research codes are available and widely used, for example, MSC Nastran, ANSYS, ABAQUS, STRESS CHECK, MECCANICA, etc. These codes are used more and more as black boxes. Many times the detailed descriptions of the numerical algorithms employed in commercial FEM codes are not available to the user because they are proprietary. The graphical display of very high quality and sophistication often obscures the quality and reliability of the computed data and gives the user unsubstantiated confidence in the results. In addition, there is the trend of using the various commercial FEM codes as ‘black’ boxes by inexperienced analysts who may be unable to detect gross errors in the computed results. One has to ask the question: What is the purpose of computation? The answer is not simple; nevertheless, stated broadly the purpose is to obtain reliable data leading to the proper engineering decisions. Hence the emphasis on the problem of reliability, or a-posteriori error estimation, etc., is clearly coming to the forefront.
Preliminary results
Authors: Cazenave Thierry , Haraux Alain , Martel Yvan
Published: November 2023

We recall here some classical theorems of functional analysis that are necessary for the study of semilinear evolution equations. The proofs can be found in Brezis [2].
The Klein-Gordon equation
Authors: Cazenave Thierry , Haraux Alain , Martel Yvan
Published: November 2023

Preliminaries

In this section, we give some technical tools that are essential in this chapter. Proposition 6.2.3 justifies the study of the Klein-Gordon equation in the space X. Indeed, the energy Eis related to the X-norm and, as we will see in the next sections, the conservation of the energy (6.19) allows us, under certain hypotheses on g and (φ, ψ;), to obtain estimates for the solution in X (and so global existence), or results about blow-up in finite time.
Approximating Integrals via Monte Carlo and Deterministic Methods
Authors: Evans Michael , Swartz Tim
Published: November 2023

This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.
Multiple quadrature
Authors: Evans Michael , Swartz Tim
Published: November 2023

Methods of approximate integration based on quadrature are historically the oldest of the integration techniques. In fact, the term quadrature stems from the ancient Greek problem of “squaring the circle”. The squaring of a circle is the process of inscribing or circumscribing a circle with rectangles (or polygons) of known area for the purpose of estimating n (i.e. the area of a circle with unit radius). Engels (1980) provides a brief history of the development of quadrature.
Independent importance sampling
Authors: Evans Michael , Swartz Tim
Published: November 2023

We use the term independent importance sampling to refer to what might be considered the most straightforward Monte Carlo integration technique; namely generating independent values x  1, ... , Xn from a density w and then taking a weighted average of the integrand evaluated at the sampled points with the weights given by the reciprocal of w evaluated at the sample values.
Markov chain methods
Authors: Evans Michael , Swartz Tim
Published: November 2023

Here µ is a general support measure which may be Lebesgue measure defined on some Euclidean space or, for example, µ may be counting measure on a set of combinatorial objects. Since we are concerned with approximating integrals we focus on applications where µ is Lebesgue measure. On the other hand, there are many applications of this methodology where this is not the case and the reader should be aware of these; see, for example, Hammersley and Handscomb (1964), Sinclair (1993) and Madras and Slade (1993).
Birational geometry of surfaces
Authors: Liu Qing , Erné Reinie
Published: November 2023

In this chapter we introduce some basic tools for studying surfaces. In this book, a .surface will be a Noetherian integral (in general normal) scheme X of dimension 2, endowed with a projective flat morphism onto a base scheme S that is regular, connected, of dimension O or 1. The case when dim S = 0 (hence S is the spectrum of a field) has been abundantly treated in the literature.
Narrow Roads of Gene Land
Authors: Hamilton W D
Published: November 2023

The second volume of the collected papers of W D Hamilton, each one introduced by an autobiographical essay. Hamilton is the most important theoretical biologist of the 20th century and his papers, not especially numerous, have had, and continue to exert, an enormous influence. Many were originally published in obscure and inaccessible places. Volume 1 (OUP, still in print) was devoted mainly to selection for social behaviour, the first half of Hamilton's life's work; Volume 2 is on the other half, on sex and sexual selection, and it includes the 18 papers published between 1980 and 1991. Each paper is accompanied by a specially written introduction describing why the work was done, how the paper came to be written, and its eventual fate. The introductions, written in an accessible, non-technical style, include history, opinion, and excerpts from Hamilton's life.
The Hospitals are Coming
Authors: Hamilton W D
Published: November 2023

A comparison of this chapter’s paper with that of the last will show what I meant about Jon Seger and clarity but still I hope that it achieves some of what I intended—that even if its notions are hazy as they flash past, it can at least be a downhill and suggestive read. It is a good example of a ‘wild oat’, as I defined this very technical concept in Chapter 6 of Volume 1, and this and five other ‘conference’ papers already included in the present volume show how my prediction in those early pages about my increasing ‘promiscuity’ with age has come true.
Theory of Probability
Authors: Jeffreys Harold
Published: November 2023

Jeffreys' Theory of Probability, first published in 1939, was the first attempt to develop a fundamental theory of scientific inference based on Bayesian statistics. His ideas were well ahead of their time and it is only in the past ten years that the subject of Bayes' factors has been significantly developed and extended. Recent work has made Bayesian statistics an essential subject for graduate students and researchers. This seminal book is their starting point.
The Mathematical Theory of Black Holes
Authors: Chandrasekhar S
Published: November 2023

This volume has become one of the modern classics of relativity theory. When it was written in 1983 there was little physical evidence for the existence of black holes. Recent discoveries have only served to underscore the elegant theory developed here, and the book remains one of the clearest statements of the relevant mathematics.
Weber’s theory of induced magnetism.
Authors: Maxwell James Clerk
Published: November 2023

we have seen that poisson supposed the magnetization of iron to consist in a separation of the magnetic fluids within each magnetic molecule. If we wish to avoid the assumption of the existence of magnetic fluids, we may state the same theory in another form, by saying that each molecule of the iron, when the magnetizing force acts on it, becomes a magnet.
On temrrestrial magnetism
Authors: Maxwell James Clerk
Published: November 2023

Our knowledge of terrestrial magnetism is derived from the study of the distribution of magnetic force on the earth’s surface at any one time, and of the changes in that distribution at different times.
AmpÈre’s investigation of the mutual action of electric currents
Authors: Maxwell James Clerk
Published: November 2023

We have considered in the last chapter the nature of the magnetic field produced by an electric current, and the mechanical action on a conductor carrying an electric current placed in a magnetic field. From this we went on to consider the action of one electric circuit upon another, by determining the action on the first due to the magnetic field produced by the second. But the action of one circuit upon another was originally investigated in a direct manner by amp ère almost immediately after the publication of Örsted’s discovery. We shall therefore give an outline of ampère’s method, resuming the method of this treatise in the next chapter.
On the induction of a current on itself.
Authors: Maxwell James Clerk
Published: November 2023

Faraday has devoted the ninth series of his researches to the investigation of a class of phenomena exhibited by the current in a wire which forms the coil of an electromagnet.
On the equations of motion of a connected system.
Authors: Maxwell James Clerk
Published: November 2023

In the fourth section of the second part of his mécanique analytique, lagrange has given a method of reducing the ordinary dynamical equations of the motion of the parts of a connected system to a number equal to that of the degrees of freedom of the system.
Dynamical theory of electromagnetism.
Authors: Maxwell James Clerk
Published: November 2023

We have shewn, in art. 552, that, when an electric current exists in a conducting circuit, it has a capacity for doing a certain amount of mechanical work, and this independently of any external electromotive force maintaining the current. Now capacity for performing work is nothing else than energy, in whatever way it arises, and all energy is the same in kind, however it may differ in form. The energy of an electric current is either of that form which consists in the actual motion of matter, or of that which consists in the capacity for being set in motion, arising from forces acting between bodies placed in certain positions relative to each other.
Electromagnetic unit of resistance
Authors: Maxwell James Clerk
Published: November 2023

The resistance of a conductor is defined as the ratio of the numerical value of the electromotive force to that of the current which it produces in the conductor. The determination of the value of the current in electromagnetic measure can be made by means of a standard galvanometer, when we know the value of the earth’s magnetic force. The determination of the value of the electromotive force is more difficult, as the only case in which we can directly calculate its value is when it arises from the relative motion of the circuit with respect to a known magnetic system.
Combining modal logics
Authors: Gabbay Dov M
Published: November 2023

The most successful case of fibring is the case of modal logic. The reason for the ease in which it can be done is that the modality operators allow us to speak directly about the possible worlds, where the local fibring is done. We start with a motivating example for modal and intuitionistic fibring.
Proof of Theorem 8.3 on parameter-depending equations
Authors: Kuksin Sergei B
Published: November 2023

We shall prove the theorem after some elementary transformations of the problem which we perform in Section 10.1. The proof is rather technical and a reader who is not used to the KAM techniques is advised to read the Addendum first where the classical Kolmogorov theorem is proved using the same ideas which we exploit below in a more involved situation.
Boundary Conditions
Authors: Succi Sauro
Published: November 2023

The actual dynamics of fluid flows is highly dependent on the surrounding environment. This influence is described mathematically via the prescription of suitable boundary conditions. Boundary conditions play a crucial role since they select solutions which are compatible with external constraints. Accounting for these constraints may be trivial under idealized conditions (periodic flows) but generally speaking, it constitutes a very delicate (and sometimes nerve-probing!) task. In this chapter we illustrate the most common ways to impose boundary conditions to LBE flows.
Turbulent Flows
Authors: Succi Sauro
Published: November 2023

Knocking on Heaven’s doors . . .Bob DylanIn the previous chapter we discussed reasons why LBE represents an interesting alternative to traditional computational fluid dynamic methods for the numerical simulation of universal features of fluid flows. In this chapter we present an application of LBE methods to one of these problems ‘par-excellence’, incompressible turbulence.
Microsatellite evolution: inferences from population data
Authors: Estoup Arnaud , Cornuet Jean-Marie
Published: November 2023

A thorough understanding of the mutational events that shape microsatellite evolution is necessary to optimize the information provided by these markers. The application of statistical tests for theoretical mutation models (IAM, SMM, TPM, and KAM) to actual population data has arrived at rather contradictory or inconclusive results, reflecting the low power of these tests and the fact that basic assumptions such as mutation-drift equilibrium are not always met. However, they suggest that large differences in the mutation process exist among loci, and the involvement of more complex mutation processes than those assumed for the theoretical mutation models tested. Pedigree, sequencing, and phylogenetic studies have shown that mutations at microsatellite loci generally involve addition or loss of one repeat, and much less frequently of several repeat units. They have also indicated that the mutation of repeat arrays has a complicated dependence on allele size and purity, the mutation process is upwardly biased, and some constraints on allele length exist. The sequencing of imperfect, interrupted and/or compound microsatellite electromorphs revealed a substantial amount of size homoplasy, a result expected when considering the mutation processes of repeat arrays. Knowledge of the mutation processes at microsatellite loci is still insufficient to parametrize accurately the factors that have been found to be relevant to the evolution of these repeated sequences and hence to allow optimal representation in theoretical mutation models.