bluuebunny/crossref_metadata_2025 huggingface dataset:
Wiskott-Aldrich syndrome protein (WASP)
Authors: Abo Arie , Symons Marc
Published: November 2023

The WASP gene was isolated by positional cloning and was shown to be mutated in patients suffering from the immunodifficiency disorder, Wiskott-Aldrich syndrome (WAS). WASP expression is restricted to the haematopoietic lineage and encodes a 62 kDa protein. The recent identification of WASP as an effector of Cdc42 and the establishment of a function for WASP in the control of actin polymerization suggests that WASP may play a role in the reorganization of the actin cytoskeleton accompanying T cell polarization.
25 kDa inhibitor of actin polymerization (25 kDa IAP)
Authors: Geiger Benjamin
Published: November 2023

The 25 kDa IAP is a low molecular weight heat-shock protein which inhibits actin polymerization and is constitutively expressed in muscle tissues. The protein was originally detected in the vinculin-rich fraction from turkey and chicken smooth muscle and is, at least in part, responsible for the effect on actin viscosity originally attributed to vinculin.
Introduction
Authors: Cleveland Don W
Published: November 2023

Microtubule assembly in vivo from tubulin and associated proteins is a dynamic process. At one level this is obvious since the interphase array of microtubules radiating from a nuclear bound MTOC is disassembled as the cell enters mitosis and spindle microtubules are formed from the liberated subunits. What came unexpectedly was the discovery, both in vivo and in vitro, that even when assembly has reached an apparent steady state, individual microtubules remain very dynamic, a property termed dynamic instability.1 Microtubules coexist in growing and shrinking populations which interconvert rather infrequently. These states seem to reflect properties of the ends of the lattice and it is likely that cleavage of the GTP bound to the terminal subunit plays an important role in governing the transition between growing and shrinking.
CLIP-170
Authors: Rickard Janet E
Published: November 2023

protein with 100 per cent amino acid and DNA sequence homology to HeLa CLIP-170, except for a 35 amino acid insert in the coiled-coil region, has been termed restin.
E-MAP-115
Authors: Masson Danièle
Published: November 2023

E-MAP-115 was initially identified in human Hela cells in which it colocalizes with subsets or subdomains of microtubules.1 A detailed cellular distribution of murine E-MAP-115 mRNA and protein during embryogenesis and in adult organs indicated that E-MAP-115 is predominantly expressed in several epithelia from 9.5 days of embryogenesis onwards and that its expression levels increase during development.3 Later during embryogenesis and in the adult mouse, E-MAP-115 mRNA and protein are found in some neuronal cells as well.
MAPI A
Authors: Bloom George S
Published: November 2023

The sequence similarity between E-MAP-115 from both species is 81 per cent. E-MAP-115 has a predicted mass of 84 kDa for the human and 82 kDa for the murine protein and is mainly constituted of a very basic N-terminal domain connected to a neutral to acidic C-terminal region via a proline-and-alanine-rich sequence (PAPA box).
Tau protein
Authors: Friedhoff Peter , Mandelkow Eckhard
Published: November 2023

A synonymous name is MAPT, but it is not commonly used (only in GeneCards and OMIM databases, see below). There are several homologous proteins, recognized by common sequence motifs in the repeat domain (see below).
Teal
Authors: Mata Juan , Nurse Paul
Published: November 2023

Fission yeast cells are cylindrical and elongate along a single central axis. In the absence of tea1 growth no longer follows this single axis, causing bending and branching of the cells1,2 (see Fig. 1). The tea1 protein (130 kDa) contains six internal kelch repeats at the N-terminal half and several regions predicted to form coiled coils at the C terminus.
Centrosomin
Authors: Li Kaijun , Kaufman Thomas C
Published: November 2023

The major somatic isoform of centrosomin is a protein of 1148 amino acids, with a predicted molecular weight of 130 kDa and an isoelectric point of 5.3. This isoform runs aberrantly in SDS-PAGE at 150 kDa.
Katanin
Authors: McNally Frank
Published: November 2023

Katanin is a heterodimeric, ATP-dependent, microtubule-severing protein. Katanin utilizes ATP hydrolysis to generate internal breaks within microtubules and to disassemble microtubules to tubulin heterodimers without proteolysis or denaturation of tubulin.
Pericentrin
Authors: Doxsey Stephen J , Kirschner Marc
Published: November 2023

Pericentrin was originally identified by screening expression libraries with autoimmune sera from scleroderma patients.1 The gene is located on chromosome 21q22.3 in humans (ref. 2; N. Jenkins and S. Doxsey; unpublished observations) and the central region of mouse chromosome 10 (N. Jenkins and S. Doxsey; unpublished observations).
³-Tubulin
Authors: Oakley Berl R
Published: November 2023

³-Tubulin is located at microtubule organizing centres (MTOCs) and is often associated with mitotic spindle microtubules. It is essential for formation of functional mitotic spindles, and purified ³-tubulin ring complexes nucleate microtubule assembly and associate with the minus ends of microtubules in vitro. ³-Tubulin ring complexes have been found in centrosomes at the ends of microtubules. ³-Tubulin is, thus, likely to nucleate the assembly of microtubules from MTOCs and may cap the minus ends of other microtubules.
Introduction
Authors: Goldman Robert D , Chou Ying-Hao
Published: November 2023

All IF proteins share a tripartite secondary structure with a central α-helical rod domain of about 310 amino acids, flanked at both ends by non-a-helical domains. In the case of the type V IF proteins, the nuclear lamins, the rod domain is 42 residues (six heptad) longer. The variation in the molecular weights of different IF proteins derives mainly from the length of the end domains which can be as short as six amino acids and as long as over 1200 amino acids in the N and the C terminus of human nestin. Conservation of the primary sequence is extensive in the rod domain that forms the centre core of 10 nm filaments. Within the rod domain, two short stretches of sequence at the beginning and the end of the rod domain are the most conserved and have been shown to be the most essential for the building of 10 nm filaments. The sequence in the N- and (-terminal domains bears little homology among different types of IF proteins. These domains appear to be exposed on the surface of the IF and thereby might be responsible for the tissue-specific functions of different IF proteins.
Cytokeratins
Authors: Franke Werner W , Kartenbeck Jurgen
Published: November 2023

The human genome contains at least 21 different genes encoding epithelial (or ‘soft’) cytokeratin polypeptides, plus another dozen genes for cytokeratin polypeptides characteristic of hair- and nail-forming cells (‘trichocytic’ or ‘hard’ cytokeratins), and these are expressed in different patterns characteristic of the specific epithelial or trichocytic cell type (Fig. 1 and Table 1). The cytokeratin gene complexity in other vertebrate species, from mammals to amphibia and fish, is similar.
Gfap
Authors: Quinlan Roy A
Published: November 2023

GFAP, glial fibrilfary acidic protein, is a member of the intermediate filament protein superfamily. It is expressed almost exclusively in astrocytes of the CNS but is also found in some cells of the PNS such as non-myelinating Schwann cells. GFAP is extensively used in histology and pathology as a cell-type marker. It is an a-helical protein which can spontaneously self-associate, via coiled-coil interactions, to form 10 nm filaments. In cells, GFAP filaments are distributed as either individual or bundles of filaments throughout the cytoplasm, extending from around the nucleus out to the cell periphery. It functions in determining cell architecture and knockout of the GFAP gene subtly alters neuronal physiology.
α-lnternexin
Authors: Liem Ronald K H
Published: November 2023

α-lnternexin is the first neuronal intermediate filament expressed in differentiated neurones in the rat nervous system and in cultured neurones. Unlike the neurofilament triplet proteins, Ronald K. H. Liem-internexin can self-assemble and may play a role in neuronal differentiation and in the incorporation of the neurofilament triplet proteins into the mature intermediate filament network.
Covering the World
Authors: Higgins Peter M
Published: November 2023

In 1852, Francis Guthrie, a mathematics student of University College London, asked himself how many colours are required so that a map may be coloured to ensure that neighbouring regions are coloured differently. He became convinced that four colours were enough for any map but could not prove it and so the problem was brought to the attention of his teacher, the famous logician, De Morgan. The problem looks so natural and simple it is difficult at first sight to believe that it could be very hard. A professional mathematician would be wary of admitting of having tried unsuccessfully to solve such a problem in case it turned out to be as simple as it looks. It was, however, a completely fresh problem and all the centuries of mathematics that had gone before were hardly any use at all in the face of this little question and so all investigators of the four colour problem began on an equal footing, knowing practically nothing about how to tackle it.
Possible and Impossible Constructions
Authors: Higgins Peter M
Published: November 2023

Constructions with a straight edge and compasses formed a cornerstone of mathematical training for many hundreds of years until the latter part of the 20th century. They are now only taught in passing and are at best a peripheral part of school geometry. This is a pity as they are really quite fun—many people who are not at home with other parts of mathematics, notably algebra, find to their surprise and delight a natural ability at this aspect of geometry. On the one hand, the topic itself is visual and tactile in a way that mathematics often is not, while on the other it embodies the geometric ideal as it explores what can be built and transferred from one figure to another without the intervention of coordinates and scales. There is no corner of mathematics that represents such a happy marriage of practical skill and pure mathematical ideals.
Passing it on: redescribing scientific explanation
Authors: Turney Jon
Published: November 2023

Scientists often describe that eureka moment. The struggle to fathom some phenomenon, or to extract meaning from some experimental results, is suddenly rewarded with a flash of understanding. Common to many such accounts is the idea that part of the pleasure lies in seeing something no one else has seen before. But that benefit carries a price: then the newly enlightened one has to explain it all to everyone else.

That explanation is hard enough when it is directed at fellow professionals. If there is a radical reconceptualization involved there will, of course, be scope for numerous misunderstandings, for uncomprehending rejection as well as glad acknowledgement.
Revolution and Restoration: Literature 1620— 1690
Authors: Sanders Andrew
Published: November 2023

On the feast of the Epiphany (6 January) 1620, the year in which the Pilgrim Fathers set sail for America, Ben Jonson’s masque News from the New World Discovered in the Moon was presented at court before King James I. The masque formed the climax to the celebration of the twelve days of Christmas and it offered to the King a fantastically contrived vision of his own greatness. Moon creatures, formed in the image of man, and ‘animated, lightned, and heightened’ by a rapt contemplation of royal virtues, descended from a frosty stage heaven, shook off their icicles, sang of the King’s perfection, and danced to represent the harmony of his rule. Chief amongst the dancers was the King’s heir, Charles, Prince of Wales. The contrast between the extravagant courtly theatre of the masque and the determined refugees from James’s religious policies who were to establish Plymouth Plantation could not be more extreme. Those extremes characterize both the politics and the literature of the seventeenth century. The masque celebrated an ideal monarch whose merits could be studied, like the Bible, as ‘the booked of all perfection’; the narrow Bible-centred Puritanism of the Pilgrims demanded a rejection of a cornerstone of James’s idea of kingship, an integrated union of the English state with the English Church through the person of the King himself and the bishops appointed by him.
Eighteenth—Century Literature 1690—1780
Authors: Sanders Andrew
Published: November 2023

Alexander Pope’s epitaph for the monument erected to the memory of Sir Isaac Newton in Westminster Abbey in 1731 succinctly proclaims the extra ordinary intellectual virtue of the greatest scientific innovator of the age. A Latin inscription witnesses to Newton’s immortality, an immortality triply safeguarded by Time, Nature, and Heaven; a couplet in English, the sublime confidence of which has served to provoke later generations, unequivocally asserts that the systematized vision which he offered was divinely inspired. ‘Nature and Nature’s Laws lay hid in Night, I God said, Let Newton be! and All was Light.’ Pope’s epitaph is more than a personal tribute to a great man; it is a public statement displayed in a much frequented national church which sums up the gratitude of a proud civilization. Newton (1642-1727), ‘the Miracle of the present Age’ as Joseph Addison called him, had given his eighteenth century heirs a carefully reasoned theoretical framework on which a whole range of additional theories could be hung. His Principia of 1687 and his Opticks of 1704 suggested that there were indeed intelligible laws in nature which could be demonstrated by physics and mathematics, and, moreover, that the universe exhibited a magnificent symmetry and a mechanical certainty. This universe, Newton had declared, could not have arisen ‘out of a Chaos by the mere Laws of Nature’; such a ‘wonderful Uniformity in the Planetary System’ had to be the handiwork of an intelligent and benevolent Creator. To the many eighteenth century propagators of Newton’s thought, the great could be related to the less, the cosmic to the terrestrial, and the divine to the human by means of a properly tutored understanding of the natural scheme of things. By inter pretation, Newton’s heavens declared that there was order, law, and indeed design in creation. Largely thanks to the propagandist work of the Royal Society in London and European-wide advances in astronomy, mathematics, mechanics, physics, and optics, natural philosophy had shed the taint of forbidden knowledge. Religious mystery could be enhanced, and sometimes even replaced, by rational wonder. The revolution in scientific thought begun by Copernicus 150 years earlier was to be fulfilled as popular enlightenment.
Late Victorian and Edwardian Literature 1880—1920
Authors: Sanders Andrew
Published: November 2023

ON the title-page of his Past and Present of 1843 Thomas Carlyle had quoted Schiller’s strident sentiment ‘Ernstistdasleben’ (‘Life is earnest’). Some seven years later, in chapter 42 of David Coppetfield, Dickens’s hero expresses the opinion that ‘there is no substitute for thorough-going, ardent, and sincere earnestness’. By the closing years of the nineteenth century such mid-Victorian moral confidence had begun to sound oppressively, even comically, outmoded. Oscar Wilde, for one, mocked at the very idea in the title of his ‘Trivial Comedy for Serious People’, The Importance of Being Earnest (1895) and it was scarcely casually that Samuel Butler selected Ernest as the Christian name of the intellectually and morally flabby hero of his The Way of All Flesh (HJ03). By the 1880s, when Butler was working on his novel, the virtues of old-fashioned earnestness-which entailed moral probity, religious orthodoxy, sexual reserve, hard work, and a confident belief in personal and historical progress were open to question or had been supplanted by a new and more probing seriousness. In retrospect, the mid-Victorians looked both wrong, and, when their influence could be escaped, funny.
The Socio-Political Map of Europe, 400—1500
Authors: Dodgshon R A
Published: November 2023

The political map of Europe was repeatedly redrawn over the period AD 400—1500. The divide between Roman and Barbarian Europe began to dissolve into a more complex political geography from the fourth century onwards as large areas, including most of the western empire, were overwhelmed by the migration of Germanic tribes like the Goths, Sueves, Vandals, and Saxons. Out of these dislocations emerged the outlines of a new ordering of political space, one whose formative concepts and institutional forms are fundamental to any definition of the medieval world. In trying to understand this new ordering, and the processes which shaped its development over the medieval period, we need to look closely at four aspects of the problem. First, we need to grasp the nature and extent of the migrations which redrew the tribal and ethnic map of early medieval Europe; secondly, we need to consider how political space was redefined over the medieval period, notably through the institution of the state; thirdly, we need to review the actual pattern of European states as it unfolded over the medieval period; and, fourthly, we need to consider whether political space was structured in ways other than through the state system.
Towns and Trade, 400—1500
Authors: Verhulst A
Published: November 2023

As Chapter 2 has shown, the city, both as a geographical phenomenon and as a way of life, was introduced into Mediterranean Europe by the Greeks and spread through western Europe the Romans. Its diffusion through the latter paralleled the expansion of the Roman Empire. That is particularly true for north-west Europe, whose geographical position between the Rhine and Britain was particularly favourable for the implantation and development of towns like Paris, Trier, Rheims, Amiens, Cambrai, Arras, and several others. Towns and military camps were also established along the Rhine and the Danube, notably at Xanten, Neuss, Cologne, Bonn, and Mainz, and at Augsburg, Regensburg, and Passau. The same was true in England, where the coloniae of York, Lincoln, Gloucester, Colchester, and London were founded, as well as a large number of chief towns of civitates (for example Carlisle, ‘Wroxeter, Leicester, Winchester, Exeter, Canterbury) and other important towns (Bath, Ikhester, Chelmsford). Their foundation goes back to the first and second centuries AD.
The Urbanization of Europe since 1500
Authors: Sutcliffe A
Published: November 2023

Thanks to the central role of the town in European development in the Middle Ages, almost all of the western part of the continent was integrated into a mature urban system by the sixteenth century (see e.g. De Vries, 1984: 9—10). Town foundations were very rare in western Europe after 1500. In eastern Europe, and especially in Russia, on the other hand, the very low level of economic development sustained a sparse distribution in which towns could grow, contract, or even disappear in just a few years of fickle fortune or tragedy (Bairoch, 1988: 170—2). In Russia, no functioning urban network existed. Most Russian towns were virtually isolated, with Bairoch estimating a national urbanization level of 3—6 per cent in 1500 (Bairoch, 1988: 179). Even the capital, Moscow, had a population of only 36,000 in 1500, and the largest cities in Russia were the Black Sea port of Feodosia and the Dnieper river port of Smolensk, both with about 50,000 inhabitants (Bairoch, et al., 1988: 60—5).
Sensorial Exploration of Environmental Information
Authors: Camara Anrfonio S
Published: November 2023

Multimedia environmental information systems and models produce multi dimensional information: symbolic and numerical data, static and dynamic images, and sounds. Scientific visualisation (and auralisation) enables the trans formation of the symbolic and numerical data into geometric computer gen erated images (and sounds). Static and dynamic images and sounds, obtained either from the above transformation or reflecting realistic phenomena, can be explored using methods such as exploratory data analysis, data mining, anima tion, and real-time generation of three-dimensional graphics and sounds.
Interaction Design for Environmental Applications
Authors: Camara Anrfonio S
Published: November 2023

‘Interaction’ means that when one performs an action, there will be changes in what happens next (Robinett, 1994). In today’s major computer user interfaces, one acts through an input device and can then see the results of that action on the computer screen. This type of interface, called direct manipulation (Shneiderman, 1988), requires the user to initiate all tasks explicitly and to over view all the events. Most environmental software is based on this user interface. Developments on direct manipulation interface designs for environmental applications include the use of filters, sketching, sound, virtual environments, ubiquitous computing, and collaborative tools.
Ludwig van Beethoven (1770–1827)
Authors: Phillips Lois
Published: November 2023

Lonely your friend wanders in the spring garden, wrapped in a soft, enchanted light, that trembles through swaying blossoms, Adelaide!

In the mirroring waves, in the snow of the Alps, in the golden clouds of declining day, in the firmament of stars your image shines, Adelaide!

Evening breezes whisper in the delicate foliage; little silver bells of May stir in the grass; waves murmur and nightingales call: Adelaide!
Richard Wagner (1813–1883)
Authors: Phillips Lois
Published: November 2023

When I was very young, I often heard tell of angels, who left the sublime joys of heaven for the sunny earth,

where hidden from the world a heart was pining in anxious grief, silently bleeding and wasting away mid floods of tears;

its prayer fervently begging only for deliverance. Then an angel would descend and bear it tenderly to Heaven.
Johannes Brahms (1833–1897)
Authors: Phillips Lois
Published: November 2023

‘Sink,O sink your grief, my child, in the ocean, the deep ocean!’ A stone will stay at the bottom of the sea, but my grief will always rise again.

‘And the love that you bear in your heart–tear it out, tear it out, my child!’ A flower that is plucked may die, but not so soon true love.

‘True love, true love, are only words–throw them to the winds!’
Hugo Wolf (1860–1903)
Authors: Phillips Lois
Published: November 2023

At night, at night, grief steals silently in, and if you wake, 0 my sorrow, you will greet the dawn with weeping and with care.

At night, at night joy steals silently in, and if you wake,0 blessed destiny, the dark dream is banished and joy is triumphant.

At night, at night joy and sorrow both steal in, and quick as thought, they leave you, and go to the Lord to tell Him how you have borne them.
Gustav Mahler (1860–1911)
Authors: Phillips Lois
Published: November 2023

The day my sweetheart weds will be my saddest day. I will go in my room, my little dark room, and weep for my treasure, my dear treasure!

Little blue flower, do not wither! Little singing bird, on the green heath–how beautiful is the world! Tchk!

Sing no more, bloom no more–for spring is now past–all singing is at an end. Each night when I go to bed, I think of my grief.
Richard Strauss (1864–1949)
Authors: Phillips Lois
Published: November 2023

Yes, you know, dear heart, that far from you I am tormented. Love makes the heart sick–for this I give thanks!

Once, reveller of freedom, I raised high a goblet of amethyst, and you blessed the draught–for this I give thanks!

And you drove the evil away, till I was purified as never before, and sank on your breast–for this I give thanks!
Pitch
Authors: Pratt George
Published: November 2023

The aim in this chapter is first to consider pitching notes accurately, in tune, and incidentally some approximation to perfect pitch. Then we shall consider pitches sounded together in chords, creating an infinite variety of timbre and density. Finally we shall focus on some of the conventions of tonal harmony, progressing from one chord to another by singing and by playing.
Criticism
Authors: Pratt George
Published: November 2023

Most of the exercises in the three previous chapters have been concerned with identifying the presence of particular musical features but not necessarily deciding whether their presence is desirable. The process has been one of observation rather than exercising critical judgement. In the timbral analysis of six bars of Britten’s ‘Narcissus’ (Ex. 6.2a) there proved to be a remarkable number of differences between the four performances. Yet we have studiously avoided declaring that one performance was ‘better’ than the others, or even that the use of a single accent, any one moment of vibrato, a specific gradient of dynamic change, was preferable to the other performers’ interpretations.
Improvisation
Authors: Pratt George
Published: November 2023

Chapter 10 was concerned with imitating instrumental performances. Most of the do-it-yourself exercises, though, involved imitating music which existed only in your mind. As soon as this process is virtually instantaneous, it becomes improvisation.
The American and the European Models of Society: Not so Different After All
Authors: Martinelli Alberto
Published: November 2023

The aim of this concluding chapter is to discuss the basic questions of this work in light of the findings of the various chapters. More specifically: (a) What kind of society do the United States and the European Union constitute?How similar and how diﬀerent are they?Are they two variants of Western modernity or two wholly distinct models of society (American exceptionalism and European uniqueness)?Are the two societal models converging or diverging?(b) Which are the distinctive features of the American model of society?Is it departing from its core culture and institutions?(c ) Is there a European society in the making?How diverse are the member countries of the EU?What shape is taking the European project of building unity through diver sity?and (d) Which model of society seems more reactive to the challenges of globalization?In the first part of this concluding chapter, I discuss salient similarities and diﬀerences and interpret trends of convergence and divergence in selected aspects of European and American societies, building on the analyses of previous chapters.
Finite difference method
Authors: Allaire Gregoire
Published: November 2023

In this chapter we analyse numerical schemes of finite differences. We define the stability and consistency of a scheme and show that, for linear constant coefficient, partial differential equations, stability plus consistency of a scheme implies its convergence.
Variational formulation of elliptic problems
Authors: Allaire Gregoire
Published: November 2023

In this chapter we are interested in the mathematical analysis of elliptic partial differential equations (PDEs) (see definition 1.5.5). In general, these elliptic equations correspond to stationary physical models, that is, models which are independent of time. We shall see that boundary value problems are well-posed for these elliptic PDEs, that is, they have a solution which is unique and depends continuously on the data. The approach that we shall follow is called the variational approach First we should say that the interest of this approach goes far beyond the framework of elliptic PDEs and even the framework of the ‘pure’ mathematical analysis to which we restrict ourselves.
Finite element method
Authors: Allaire Gregoire
Published: November 2023

In this chapter, we present the method of finite elements which is the numerical method of choice for the calculation of solutions of elliptic boundary value problems, but is also used for parabolic or hyperbolic problems as we shall see. The principle of this method comes directly from the variational approach that we have studied in detail in the preceding chapters.
Eigenvalue problems
Authors: Allaire Gregoire
Published: November 2023

This chapter is dedicated to the spectral theory of partial differential equations, that is, to the study of eigenvalues and eigenfunctions of these equations. The motivation of this study is twofold. On the one hand, this will allow us to study particular solutions, which are oscillations in time (or vibrations), of the evolution problems associated with these equations. On the other hand, we shall deduce a general method for solving these evolution problems which we shall implement in Chapter 8.
Introduction to optimization
Authors: Allaire Gregoire
Published: November 2023

Optimization is a very old subject, which has shown a resurgence since the appearance of computers and whose methods are applied in numerous domains: economics, management, planning, logistics, robotics, optimal design, engineering, signal processing, etc. Optimization is also a vast subject which touches on calculus of variations, operations research (optimization of management or decision processes), and optimal control. We will only mention these subjects since we would need complete notes for each of them if we want to treat them thoroughly.
Optimality conditions and algorithms
Authors: Allaire Gregoire
Published: November 2023

In Chapter 9 we were interested in questions of existence of a minimum in optimization problems. In this chapter, we shall obtain necessary and sometimes sufficient conditions for minimality. The objective is in a certain way much more practical, since these optimality conditions will be more often used to try to calculate a minimum (sometimes even without having shown its existence!). The general idea of optimality conditions is the same as writing that the derivative must be zero, when we calculate the extremum of a function over ℝ.
Methods of operational research
Authors: Allaire Gregoire
Published: November 2023

In this chapter, we present several tools from OR (operational research). In OR, the word ‘operational’ was initially used in its proper sense: OR was born, mainly, from planning problems which arose during the Second World War and shortly after. Thus G. Dantzig, the inventor of the simplex algorithm, was an adviser for the American airforce, and the planning of the Berlin airlift in 1943 is a famous application of linear programming (see [31] for more detail). Since then the domain has been considerably developed and civilized.
Examples in algebra and analysis
Authors: Scarani Valerio , Thew Rachael
Published: November 2023

Algebra is what most people associate with mathematics. In a sense, this is justiﬁed. Mathematics is the study of abstract objects, numerical, logical, or geometrical, that follow a set of several carefully chosen axioms. And basic algebra is about the simplest meaningful thing that can satisfy the above deﬁnition of mathematics. There are only a dozen or so postulates, but that is enough to make the system beautifully symmetric.
Euclidean geometry
Authors: Scarani Valerio , Thew Rachael
Published: November 2023

Euclidean geometry was the ﬁrst branch of mathematics to be treated in anything like the modern fashion (with postulates, deﬁnitions, theorems, and so forth); and even now geometry is conducted in a very logical, tightly knit fashion. There are several basic results which can be used to systematically attack and resolve questions about geometrical objects and ideas. This idea can be taken to extremes with coordinate geometry, which transforms points, lines, triangles, and circles into a quadratic mess of coordinates, crudely converting geometry into algebra.
Lie groups and homogeneous spaces
Authors: Félix Yves , Oprea John , Tanré Daniel
Published: November 2023

Lie groups and homogeneous spaces form an important family of examples of manifolds. We will use them systematically in many different parts of this book, to give an illustration for a specific method or, as well, to show that new viewpoints can be obtained by using algebraic models. Therefore, it is important for us to understand basic ideas and results about Lie groups in order to appreciate the development and application of algebraic models to geometry in general. What we also want to articulate in the next several chapters is that some of the basic ideas of Sullivan’s rational homotopy theory were already present in this particular case.
Manifolds
Authors: Félix Yves , Oprea John , Tanré Daniel
Published: November 2023

A smooth compact manifold has many properties that make it distinct from an ordinary topological space. From the topological viewpoint, the existence of Poincaré duality in (co)homology is crucial to almost any result about the manifold. From the geometric viewpoint, the existence of a Riemannian metric allows the manifold to be studied using analytic techniques. In subsequent chapters, we shall see how these two points of view mix together to yield interesting results in both directions: topology applied to geometry and geometry applied to topology.
Blow-ups and Intersection Products
Authors: Félix Yves , Oprea John , Tanré Daniel
Published: November 2023

As we mentioned in the Preface, models play an important role in understanding various properties of complex and symplectic blow-ups. They also can be used to study features of the Chas–Sullivan loop product, a rather mysterious new topological tool. In this chapter we will consider two types of questions.
Students Of Gene H. Golub
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

Roger Hockney 1966

Richard Bartels 1968

Michael Jenkins 1969

Lyle Smith 1969

George Ramos 1970

Richard Brent 1971

Michael Saunders 1972

John Palmer 1974

Richard Underwood 1975

Dianne Prost O’Leary 1976

John Lewis 1976

Margaret Wright 1976

Michael Heath 1978

Franklin Luk 1978

Michael Overton 1979

Petter Bjørstad 1980

Daniel Boley 1981

Eric Grosse 1981

Stephen Nash 1982

Mark Kent 1989

Ray Tuminaro 1990

Hongyuan Zha 1993

Oliver Ernst 1994

Xiaowei Zhan 1997

Tong Zhang 1998

Nhat Nguyen 2000

Urmi Holz 2002

Yong Sun 2003

James Lambers 2003
Commentary, By Anne Greenbaum
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

From the very early days, Gene Golub has been a driving force in the development and analysis of iterative methods for solving large sparse linear systems – problems for which Gaussian elimination is often prohibitive in terms of both storage and computation time. We review five of his seminal papers in this field. Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II, by Golub and Varga [10] This paper is probably less well-known today than it should be. In it the authors show the remarkable similarity between the Chebyshev semi-iterative method, the successive overrelaxation (SOR) method applied to an expanded matrix equation, and the second-order Richardson iterative method. They conclude that the Chebyshev semi-iterative method is to be preferred over the other two, since its iteration matrix has the smallest spectral norm, while the work per iteration is the same as that for the other methods. They present numerical results with the different methods used to solve elliptic difference equations.
Hermitian And Skew-Hermitian Splitting Methods For Non-Hermitian Positive Definite Linear Systems (With Zhong-Zhi Bai And Michael K. Ng)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

It was in 1997 when I first met Gene at Hong Kong on the Workshop on Scientific Computing dedicated to his 65th birthday. Then Gene introduced me to my first two foreign teachers, Iain S. Duff and Andrew J. Wathen, whom I visited for one year from August 1997 to August 1998. The communication and discussion with Gene, Iain, and Andy on solving nonsymmetric linear systems arising from discretization of the convection–diffusion equations by making use of efficient preconditioning techniques changed my research interest and also my academic life, as I then began to study more application-oriented problems and computation-based methods.
Commentary, By ake Bjo Rck
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

The method of least squares has been the standard procedure for the analysis of data from the beginning of the 1800s. A famous example of its use is when Gauss successfully predicted the orbit of the asteroid Ceres in 1801. In the simplest case The five papers collected here are all related to various least squares problems.
Numerical Methods For Solving Linear Least Squares Problems
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

A common problem in a Computer Laboratory is that of finding linear least squares solutions. These problems arise in a variety of areas and in a variety of contexts. Linear least squares problems are particularly difficult to solve because they frequently involve large quantities of data, and they are ill-conditioned by their very nature. In this paper, we shall consider stable numerical methods for handling these problems. Our basic tool is a matrix decomposition based on orthogonal House-holder transformations.
Calculating The Singular Values And Pseudo-Inverse Of A Matrix (With W. Kahan)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

But in floating-point calculations it may not be so easy to decide whether some number is effectively zero or not. Rather, one will try to determine the rank r by observing whether all rows after the rth are negligible in comparison to the first r, with the expectation that the same will be true of the singular values. Even this criterion is hard to apply, as the following ex-ample.
J. H. Welsch)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also presented for computing the three term recurrence relation from the moments of the weight function.
Commentary, By G. W. Stewart
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

The four papers treated here reflect Gene Golub’s interest in eigenvalue problems. However, they do not exhibit a general theme. Rather the papers are organized around specific problems or topics and have little connection with one another. For this reason we will treat the papers separately and make no attempt to describe interconnections. This paper is a potpouri of problems that can be resolved by considering the eigensystems of certain matrices.
Some Modified Matrix Eigenvalue Problems
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

We consider the numerical calculation of several matrix eigenvalue problems which require some manipulation before the standard algorithms may be used. This includes finding the stationary values of a quadratic form subject to linear constraints and determining the eigenvalues of a matrix which is modified by a matrix of rank one. We also consider several inverse eigenvalue problems. This includes the problem of determining the coefficients for the Gauss-Radau and Gauss-Lobatto quadrature rules. In addition, we study several eigenvalue problems which arise in least squares.
The Block Lanczos Method For Computing Eigenvalues (With R. Underwood)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

In this paper, we describe a Block Lanczo method for computing a few of the least or greatest eigenvalues of a sparse symmetric matrix. A basic result of tactile and Paige describing the reset of convergence of Lanczos’ method will be effctended to the Block Lanczos method. The results of experiments conducted with this methods will be presented and discussed.
Geometrical Aspects Of Plane Autonomous Systems
Authors: Jordan D W , Smith P
Published: November 2023

In this chapter, we discuss several topics which are useful for establishing the structure of the phase diagram of autonomous systems. The ‘index ‘ of an equilibrium point provides supporting information on its nature and complexity, particularly in strongly nonlinear cases, where the linear approximation is zero. Secondly, the phase diagram does not give a complete picture of the solutions; it is not sufficiently specific about the behaviour of paths at infinity beyond the boundaries of any diagram, and we show various projections which include ‘points at infinity ‘ and give the required overall view.
Singular Perturbation Methods
Authors: Jordan D W , Smith P
Published: November 2023

This chapter is concerned with approximating to the solutions of differential equations containing a small parameter ε in what might be called difficult cases where, for one reason or another, a straightforward expansion of the solution in powers of ε is unobtainable or unusable. Often in such cases it is possible to modify the method so that the essential features of such expansions are redeemed. Ideally, we wish to be able to take a few terms of an expansion, and to be able to say that for some small fixed numerical value of ε supplied in a practical problem the truncated series is close to the required solution for the whole range of the independent variable in the differential
Plane autonomous systems and linearization
Authors: Jordan D W , Smith P
Published: November 2023

2.1. A classification table for equilibrium points of the general linear system is given in Section 2.5 (see also Figure 2.10 in NODE). The key parameters are p a d, q ad bc, p 4q. All the systems below have an isolated equilibrium point at the origin. The scales on the axes are the same for each phase diagram but actual scales are unnecessary since the equations are homogeneous in x and y. Directions are determined by continuity from directions of x and y at convenient points in the plane. Alternatively, classification can be decided by finding the eigenvalues of the matrix of The eigenvalues take the imaginary values ±2i, which is to be expected for a centre.
Probability
Authors: Krzanowski Wojtek J
Published: November 2023

Much, if not most, statistical reasoning is built upon a foundation of probability; so if a good understanding of statistical principles is to be gained, then the basic ideas of probability must ﬁrst be understood. This is the reason why many introductory books on statistics begin with a survey of probability theory. However, an equally compelling reason might be the increasing importance that probability in its own right is playing in the world about us, and the fact that some facility with probability calculations or assessments can be invaluable in our day-to-day lives. Most people are perfectly comfortable with simple probability statements, such as that there is an even chance of obtaining a head as opposed to a tail on the spin of a coin, but once familiar physical frameworks are abandoned then the ground quickly becomes shakier.
Population Models
Authors: Krzanowski Wojtek J
Published: November 2023

We have seen that the population is generally the focus of any statistical investigation. It is the collection of all possible individuals that we think are relevant to our study, and the purpose of most statistical investigations is to obtain information about some specific measurement of interest in this population. Usually, the population is too large for us to be able to observe every individual in it, so we will hardly ever be in a position to know all we can about this measurement of interest.
Statistical Inference—the Frequentist Approach
Authors: Krzanowski Wojtek J
Published: November 2023

So far we have looked mainly at the ideas of probability, with their extension to the concept of a population of individuals having a probability distribution of some measurements of interest. However, we have also gone on to consider probability models for populations, the collection and summarisation of sample data from these populations, and the use of the sample data to guide us when formulating probability models. All these topics form the necessary base for one of the central topics in statistics, namely the use of sample data in making statements about populations.
The historiography and history of mathematics in the Third Reich
Authors: Siegmund-Schultze Reinhard
Published: November 2023

After Hitler became chancellor of the German Reich on 30 January 1933 and the Nazi regime consolidated its power in March 1933, serious effects for science and mathematics became visible. Mathematics was, by and large, less important to the regime than biology, chemistry, the technical sciences, or history. It could not be used for propaganda like biology and historiography and it did not have immediate importance for armament and war production (with the possible exceptions of aerodynamics and ballistics).
Assessing the Effect of Genetic Mutation: A Bayesian Framework for Determining Population History from DNA Sequence Data
Authors: Brooks S P , Manolopoulou I , Emerson B C
Published: November 2023

In cases where genetic sequence data are collected together with associated physical traits it is natural to want to link patterns observed in the trait values to the underlying genealogy of the individuals. If the traits correspond to specific phenotypes, we may wish to associate specific mutations with changes observed in phenotype distributions, whereas if the traits concern spatial information, we may use the genealogy to look at population movement over time.In this paper we discuss the standard approach to analyses of this sort and propose a new framework which overcomes a number of shortcomings in the standard approach. In particular, we allow for uncertainty associated with the underlying genealogy to fully propagate through the model to directly interact with the inferences of primary interest, namely the effects of genetic mutations on phenotype and/or the dispersal patterns of populations over time.
A Gamma Model for DNA Mixture Analyses*
Authors: Cowell Robert G , Lauritzen Steffen L , Mortera Julia
Published: November 2023

We present a new methodology for analysing forensic identification problems involving DNA mixture traces where several individuals may have contributed to the trace. The model used for identification and separation of DNA mixtures is based on a gamma distribution for peak area values. In this paper we illustrate the gamma model and apply it on a real example from forensic casework.
Identification of Thyroid Gland Activity in Radiotherapy*
Authors: Jirsa Ladislav , Quinn Anthony , Varga Ferdinand
Published: November 2023

The Bayesian identification of a linear regression model for time dependence of thyroid gland activity in 131I radiotherapy is presented. Prior knowledge is elicited via hard parameter constraints and via the merging of information from an archive of patient records. This prior regularization is shown to be crucial in the reported context, where data typically comprise only 2-3 highnoise measurements. The posterior distribution is simulated via a Langevin diffusion algorithm, whose optimization for the thyroid activity application is explained. Improved patient-specific predictions of thyroid activity are reported. The posterior inference of the total patient radiation dose is presented, allowing the uncertainty of the dose to be quantified in a consistent manner.