bluuebunny/crossref_metadata_2025_split huggingface dataset:
DNA mismatches in solution
Authors: Chou Shan-Ho , Reid Brian R 
Published: November 2023

Abstract
The DNA double helix, with its complementary G:C and A:T Watson—Crick base pairing, is a remarkably efficient device for the storage and expression of information and the stable transmission of this information through successive generations. Although normal, or Watson-Crick, base pairing is mediated through hydrogen bonding between A and T residues and between G and C residues, the double helix is also stabilized by a variety of other ‘stacking’ interactions which obviously differ from one sequence to the next. In the process of copying each of the two strands of DNA to produce two identical double helices, i.e. daughter cells with the same genetic composition, incorrect or mismatch pairings (G or C with T or A, or with themselves) inevitably occur.
Basic error processing
Authors: Pretzel Oliver 
Published: November 2023

Abstract
The theoretical properties of a class of codes only bear fruit if there exists a practical error processing scheme that exploits them. So there have been continuing efforts to produce practical error processors for Goppa codes. The first processing algorithm was published by Justesen et al. (1989). It applied only to a somewhat restricted class of codes based on smooth plane curves and could not correct errors up to the full designed capability of the code.
Roger Penrose—a Personal Appreciation
Authors: Atiyah Michael 
Published: November 2023

Abstract
Roger Penrose and I were research students together in Cambridge from 1952 to 1955. Moreover, we were both algebraic geometers at the time. I did my research under Hodge, and Roger, after starting with Hodge, moved over to work with Todd. In view of later events it is perhaps interesting to review briefly what areas our research was concerned with. Under Hodge I was steered towards differential geometry and topology. From Hodge’s book I learnt about harmonic forms and their origin in Maxwell’s equations, while from the work of the French school (Leray, Cartan, Serre) I learnt about sheaf cohomology. Although I had attended Dirac’s course on quantum mechanics it was not until some years later that I became acquainted with spin and the Dirac operator.
Quantum Geometric Origin of All Forces in String Theory
Authors: Veneziano Gabriele 
Published: November 2023

Abstract
I am a great admirer of Roger, but I cannot pretend to know him as well as most of you here. Let me, however, start my talk with a small episode of my life indirectly related to him. A couple of years ago I bought The Emperor’s New Mind just before leaving for summer vacations in southern France. I took the book with me, hoping, of course, to enjoy my holiday so much as to “forget” the book in my suitcase. Things went differently: at my first tennis lesson I was struck by lumbago and finished my vacation reading the book over and over again by the hotel’s swimming pool ... This morning I went to a local bookstore and bought Shadows of the Mind. I am planning to take holidays in Italy in a couple of weeks and start to feel a strange ache at my left shoulder: I am not superstitious, but⃛
Interaction-Free Measurements
Authors: Vaidman Lev 
Published: November 2023

Abstract
I am greatly indebted to Roger Penrose. I have learned very much from his papers, from his exciting books, and from our (too short) conversations. I am most grateful to Roger for developing the idea of Avshalom Elitzur and myself on interaction-free measurements (IFM). The version of IFM Penrose described in his book (1994) is conceptually different from our original proposal, and although it is much more difficult for practical applications it has the advantage of demonstrating even more striking quantum phenomena. So I will start with presenting Penrose’s version of IFM.
Geometrically Finite Kleinian Groups
Authors: Matsuzaki Katsuhiko , Taniguchi Masahiko 
Published: November 2023

Abstract
Kleinian groups which are cofinite (namely, which correspond to complete hyperbolic 3-manifolds with finite volume) have several desirable properties. The cofiniteness can be generalized to the concept of geometric finiteness, which we discuss in this chapter. In Section 3.1, we give various definitions of geometrically finite Kleinian groups and prove that they are equivalent. Next in Section 3.2 we explain some of the fundamental properties of such groups. In Section 3.3, we consider the variety and rigidity of geometrically finite hyperbolic structures admitted in a given topological manifold or represented by isomorphic Kleinian groups.
Structure invariants, seminvariants and the origin problem
Authors: Giacovazzo Carmelo 
Published: November 2023

Abstract
Any ordered arrangement of atoms, that is any crystal structure, can be mathematically described provided the origin of the reference system is fixed. Vice versa, the phases of the structure factors define (through a Fourier transform) the atomic positions with respect to a given origin. Thus a mechanism must exist according to which phasing reflections simultaneously involves the fixing of the origin in direct space. This intriguing correspondence will be elucidated throughout this chapter by making use of the concepts of structure invariants and semivariants, which will prove to be central to direct methods theory.
Triplet invariant estimation and classical direct phasing procedures
Authors: Giacovazzo Carmelo 
Published: November 2023

Abstract
In the first part of this chapter we describe the use of the central limit theorem for the probabilistic estimation of the most important s.i., the triplet invariant. We limit our treatment to the case in which X-ray diffraction data are used without anamalous dispersion effects (see Chapter 16 for such an extension).
The method of joint probability distributions
Authors: Giacovazzo Carmelo 
Published: November 2023

Abstract
The joint probability distribution of a set of n normalized structure factors was first introduced by Hauptman and Karie (1953b) and was developed further by several authors (e.g. Bertaut 1955a, b, 1960a, b; Klug 1958; Naya et al. 1964, 1965; Vaughan 1959). The importance of their work lies in the introduction of the idea that a certain phase or combination of phases may be estimated when other related s.f.s have their observed values.
Maximum entropy techniques for crystal structure solution
Authors: Giacovazzo Carmelo 
Published: November 2023

Abstract
Maximum entropy techniques have found application in many scientific fields, like statistical mechanics, spectroscopy, nuclear physics, radio astronomy, image enhancement, economics, and last, but not least, in crystallography. The method has its root in probability theory and can be considered a modern extension of this: it aims to derive the most convincing conclusions from given sets of data and prior information eventually available.
Names
Authors: Freer Stephen 
Published: November 2023

Abstract
Nomenclature , the second (151) foundation of botany, after the arrangement has been done (152), should first of all apply the names. If you do not know the names of things, the knowledge of them is lost too. Where there is a single genus, there will be a single name. Section 215. The names given by the ancients are mostly excellent; those given by more recent [writers] have been inferior. [My] Critica Botanica proposed nomenclature for genera, species, and varieties, with reasons and examples; hence there is not much about that subject in the present work.
Transformations of ℝk
Authors: Priestley H A 
Published: November 2023

Abstract
The preceding chapter emphasized the connections between integrals on JR and on JR2. There are aspects of the integral on ℝ2 (and likewise on ℝkfor k &gt; 2) which are interesting and important in their own right, notably the relationship between Lebesgue measure and the rich geometry of ℝ We have defined the measure of a bounded measurable subset S of ℝkto be ∫ 𝒳S. This agrees, by definition, with the expected area when S is a bounded interval. Is the same true for other familiar figures, such as parallelograms? What happens to measure under transformations of the plane? Substitution is a valuable technique for evaluating integrals on JR. In the same way, it is useful to be able to make changes of variables in higher dimensional integrals. In full generality these topics involve multi-dimensional calculus beyond the scope of this book. Our aim here is to validate in the Lebesgue framework the use of the transformations which are most useful in practice. Beginners may wish to omit the proof of the main theorem, 27.4.
L2-spaces as Hilbert spaces
Authors: Priestley H A 
Published: November 2023

Abstract
In analysing an L2-space we can profitably exploit the interplay of its inner product structure with the convergence notions associated with its norm. An inner product space X is called a Hilbert space if the associated norm makes X a Banach space (that is, Cauchy sequences in X converge). Theorem 28.16 tells us that L2 is a Hilbert space, as is L2 (I) for any interval I.
Introduction
Authors: Cong Nguyen Dinh 
Published: November 2023

Abstract
Originating in the work of the French mathematician Henri Poincare in the last century, the theory of dynamical systems has become a major branch of the mathematical sciences. Its importance is explained by the fact that everything in the world evolves with time, so that a dynamical approach is required. Even those processes which seem to be unchanged with time can be viewed as stationary solutions (fixed points) of more general models. The theory of dynamical systems deals with long-term behavior of systems. It has three sub-areas: measurable dynamics (or ergodic theory), topological dynamics and differentiable dynamics. The set-up of the system under investigation determines whether we should deal with measurable, topological or differentiable properties. Of course, to make a mathematical investigation of possible long-term behavior, the evolution law is assumed to preserve the structure of the system.
Random Dynamical Systems: Foundations
Authors: Cong Nguyen Dinh 
Published: November 2023

Abstract
The theory of random dynamical systems is a relatively new field of research. It continues, extends and unites various developments in probability theory and the theory of dynamical systems. Suppose we wish to investigate a process of the real world. It often happens, one may say always happens, that this process is influenced by many factors, which are called noise. The first thing we can do is model the so-called ideal process, i.e. ignoring the noise, and assuming that the process evolves by its internal laws we model it by a dynamical system using a physical theory, certain biological or chemical laws, etc. Now, to take the influence of the external environment into account we should also model the noise.
The Linearization Of Nonlinear Random Dynamical Systems
Authors: Cong Nguyen Dinh 
Published: November 2023

Abstract
Linearization of a nonlinear system is the first step in the theory of topological dynamics which leads to a simplification of the system under investigation. Since Hartman-Grohman theory has successfully solved the linearization problem in the classical theory of dynamical systems one would naturally like to generalize it to the random case. It turns out that many results of the Hartman-Grohman theory permit more or less direct generalization to the random situation. In this chapter we shall present the linearization theory for smooth random dynamical systems. The last section of the chapter is devoted to the bifurcation theory of random dynamical systems.
Topological Classification of Discrete-Time Linear Hyperbolic Cocycles
Authors: Cong Nguyen Dinh 
Published: November 2023

Abstract
In this chapter we shall deal with the problem of the topological classification of linear hyperbolic cocyclcs. Looking back at the deterministic case, the work of Robbin [134] gives us an overview of random dynamical systems both from the ‘local’ and ‘global’ points of view. It also gives us very important tools and some initial ideas for dealing with random dynamical systems. We recall some deterministic results from Chapter 1.
Maximum cardinality matchings
Authors: Karpinski Marek , Rytter Wojciech 
Published: November 2023

Abstract
In this chapter we use algebraic tools (in particular parallel interpolation algorithms for large polynomials) to find maximum cardinality matchings in undirected graphs. We explore the correspondence between graphs and some black-box polynomials (Tutte’s symbolic polynomials). The crucial point is the use of determinants instead of permanents. There are NC-algorithms to compute determinants but there is a good chance (and our general belief) that there does not exist even a polynomial time sequential algorithm to compute permanents. Recall that A(n) denotes the number of processors needed to compute the determinant of an n x n matrix and the determinants of its minors in O(log2 n) time. We stated in Chapter 5 that A(n) = O(n3·5 • m), if our numbers have O(m log(m)) bits. We emphasize the importance of A since any improvement in the growth of A leads directly to an improvement in the parallel matching for general graphs. In this chapter two basic algorithms are presented: one based on partial interpolation and the second one using the smallest-degree algorithm. The first one is simpler, but deals with integers of exponential size 0(2m), so it needs O(n3·5 • m) processors, and it is O(m) times less efficient (in the sense of processor bound) than the second one. The second algorithm uses modular arithmetics in a clever way, thus reducing the size of the integers which are processed in the algorithm. Its efficiency (in the sense of the number of processors) is O(n3·5). Hence it is essentially the same as the complexity of matrix inversion: the matching problem is reduced to the computation of the determinant of the whole matrix and its minors.
Maximal independent sets
Authors: Karpinski Marek , Rytter Wojciech 
Published: November 2023

Abstract
The line graph of G is a graph L whose vertices are edges of G. Two vertices are neighbors in L if they have a common endpoint (as edges) in G. Then a set M of edges of G is a matching in G iff it is independent (as a set of vertices) in L. The NC-construction of a maximal independent set is also related to matchings in the following way: the basic part of the algorithm is a parallel construction of a matching with sufficiently small weight. In this chapter we show how to construct in parallel a maximal independent set. Of course construction of a maximum cardinality independent set is a much harder problem, since it is NP-complete. We present two very simple randomized algorithms due to Luby [186], one of which can be derandomized using the technique from Chapter 4. However, the number of processors of a derandomized version is too large. We then show a completely different and more efficient NC-algorithm, due to Goldberg and Spencer. We also mention some extensions to hypergraphs. The maximal independent sets problem is much harder for hypergraphs than for standard graphs and no NC-algorithm is known to solve it. Another generalisation of maximal independent sets is the notion of a k-dependent set, we cover this subject at the end of the chapter.
Pfaffians, counting the number of matchings, and planar graphs
Authors: Karpinski Marek , Rytter Wojciech 
Published: November 2023

Abstract
In this chapter we study ‘the notion of the Pfaffian of a graph and its connection to the problem of counting the number of matchings, and the problem of computing a Pfaffian orientation of a planar graph. In Section 6.1 we introduced the notions of Edmonds’ and Tutte’s matrices, and investigated the relation of their determinants to the problem of deciding the existence of a perfect matching. Towards the end of this section we will introduce the notion of a Pfaffian of Tutte’s matrix A corresponding to the two-cycle permutations over {1, ... , 2n}.
Some aspects of topological sequence spaces
Authors: Boos Johann , Cass Peter 
Published: November 2023

Abstract
In this chapter we consider several aspects of sequence spaces which have their origin in summability or which are links between topological sequence spaces and summability. Some (see Sections 11.1, 11.2 and 11.4) are based on ‘inclusion theorems’ where we show the equivalence of certain functional analytic properties of a sequence space Y with a statement about summability.
Rest Stop
Authors: David Guy , Semmes Stephen 
Published: November 2023

Abstract
So far we have the concepts of BPI spaces and BPI equivalence and some basic properties of them. In Chapters 6 and 7 we saw how the BPI condition and BPI equivalence are related to various other conditions. The techniques were based on coverings and cutting spaces up into little pieces. In Chapters 8 and 9 we established the basic machinery of compactness.
Iterative Domain Decomposition Methods at the Discrete Level
Authors: Quarteroni Alfio , Valli Alberto 
Published: November 2023

Abstract
In this chapter the iterative methods introduced in Sections 1.3 and 1.5 will be reformulated at the discrete level for the solution of the finite element problem (2.1.1). Their relation with domain decomposition preconditioners will be pointed out, and several acceleration techniques will be considered for the case where many subdomains are used. The convergence analysis will be carried out in Chapter 4.
Some applications of the kinematical theory of X-ray diffraction
Authors: Bradaczek Hans 
Published: November 2023

Abstract
Max von Laue’s detection (1912) of the X-ray diffraction (von Laue, 1960) by crystals simultaneously proved two facts: crystals have an internal lattice structure and X-rays have a wave nature. In subsequent years, an almost closed theory of X-ray diffraction has been developed by several scientists: von Laue, the Braggs, Ewald, Guinier, Borrmann, Hosemann and, of course, many others. Using function algebra, mainly developed by Hosemann and Bagchi (1962), most of the mathematical problems of diffraction theory can be solved and described in a very elegant way. The following derivations are almost exclusively using functional algebra. Only a few samples can be presented here.
Profile fitting and analytical functions
Authors: Enzo Stefano , Schiffini Liliana 
Published: November 2023

Abstract
Abstract
It is common to ascribe the line-broadening effects observed in X-ray powder diffraction patterns to various microstructural features like crystallite finiteness, microstrain and stacking faults. A presentation is given on an empirical basis of the parametric functions which are most popular in the Rietveld method of structure refinement in order to account for the observed broadening. The shape parameters obtained after the best fit of one or more profiles can be successfully used to determine physical values of interest, provided that the assumptions of the theory are reasonably well respected in the sample under investigation.
Effects of instrument function, crystallite size, and strain on reflection profiles
Authors: Honkimaki V , Suortti P 
Published: November 2023

Abstract
Abstract
A new approach to the analysis of reflection profiles is introduced. The basic idea is to calculate the instrument function by ray-tracing and include in the whole-pattern fitting a background function of the correct dependence on the scattering vector. In this way, only the effects of crystallite size and strain remain to be modeled. The instrument function is presented in general form, which can be adapted to energy-dispersive or angle-dispersive powder diffraction. The effects of the source size and wavelength distribution, equatorial and axial divergences, beam penetration in the sample, and different slits are included. Most of these aberrations are independent and can be cast in analytical forms, and the total instrument function is found by successive convolutions. The background arising from inelastic and resonant scattering is calculated from theory, while disorder scattering is modeled by a pair-correlation function and thermal diffuse scattering (TDS) by the Debye model for acoustic phonons and by the Einstein model for optical phonons. The total TDS is calculated as the part of the Bragg reflections lost due to thermal motion. The effects of crystallite size are treated in a general formalism where the reflection profile is the Fourier transform of the common volume of the crystallite and its ‘ghost’ shifted a distance tin the direction of the scattering vector k.The effects of strain are included in a distribution function of unit-cell displacements. Long-distance strain is described by a characteristic function, and the local strain by a correction term to the structure factor. Formulae that cover transition from local strain to long-distance strain are given. Anisotropic crystallite size and strain are described in terms of spherical harmonics which obey the crystal symmetry. The diffraction pattern of PbBr2 measured using CuKa1radiation is resolved using the procedure described above. The model parameters include only the thermal motion amplitudes and coefficients of the spherical harmonics that give the anisotropic crystallite size and strain.
Classical treatment of line profiles influenced by strain, small size, and stacking faults
Authors: Houska C R , Kuiel R 
Published: November 2023

Abstract
Progress in quantitative XRD profile analysis has been closely linked with instrumental improvements, which include higher intensity fine focus diffractometers equipped with electronic detectors. Early profiles measured without automation were described by a Fourier series. Numerical transforms were obtained using Lipson-Beevers strips and non-programmable, slowly responding mechanical calculators. These forgotten tedious efforts placed limitations on further advances in analytical profile analyses. Despite the absence of time-saving instrumentation, as it is known today, some of the best data and most complete analyses of XRD profiles go back to this early period (McKeehan and Warren, 1953). With high speed desktop computers now commonly available in most laboratories, one can make full use of recent analytical advances beyond the classical approaches to attain new levels of understanding. Modern instrumentation equipped with highly monochromatic radiation, greatly improved detectors, and labor saving automation allows us to examine smaller and more subtle profile changes.
Analytic functions describing line profiles influenced by size distribution, strain and stacking faults
Authors: Houska C R , Kuiel R 
Published: November 2023

Abstract
This chapter, describing XRD profiles computed from basic analytic functions, is best introduced by reading Chapter 6. Here we provide a brief review of the classical Fourier series treatment of microstrain variations and particle size as described by Warren (1959, 1969). Stacking fault broadening, related asymmetries, and shifts are treated as an expansion of the original development. These are limited primarily to fee, bee, and hep metals. Statistical results of highly deformed powders are obtained from a series of Fourier transforms of the experimental data corrected for instrumental broadening. In using this procedure, results remain closely linked to experimental profiles.
The dislocation-based model of strain broadening in X-ray line profile analysis
Authors: Ungar T 
Published: November 2023

Abstract
Shortly after the discovery of X-ray diffraction, materials scientists were surprised to find that severely deformed metallic materials retain their crystalline structure as indicated by the almost unaffected Debye–Scherrer diffraction lines (cf. Becker, 1927; Wilkens, 1988). This ‘almost unaffectedness’ has since become the field we know now as ‘X-ray line profile analysis’. Diffraction-line broadening has many physical sources: (i) size, (ii) strain, (iii) diffuse scattering of coherent precipitates, (iv) small misfits between phases with slightly different chemical compositions, including coherent precipitates, etc. The different effects interplay with each other and very often are not easy to separate.