bluuebunny/crossref_metadata_2025_split huggingface dataset:
From Quantum Code-making to Quantum Code-breaking
Authors: Ekert Artur 
Published: November 2023

Abstract
Human desire to communicate secretly is at least as old as writing itself and goes back to the beginnings of our civilisation. Methods of secret communication were developed by many ancient societies, including those of Mesopotamia, Egypt, India, and China, but details regarding the origins of cryptology remain unknown (Kahn 1967). We know that it was the Spartans, the most warlike of the Greeks, who pioneered military cryptography in Europe. Around 400 BC they employed a device known as a scytale. The device, used for communication between military commanders, consisted of a tapered baton around which was wrapped a spiral strip of parchment or leather containing the message. Words were then written lengthwise along the baton, one letter on each revolution of the strip. When unwrapped, the letters of the message appeared scrambled and the parchment was sent on its way. The receiver wrapped the parchment around another baton of the same shape and the original message reappeared.
Decaying Neutrinos and the Geometry of the Universe
Authors: Sciama D W 
Published: November 2023

Abstract
It is a great privilege and also a great pleasure to be invited to speak at this celebration of Roger Penrose’s 65th birthday. We first met about 45 years ago when, as a research student at Cambridge, I shared an office with several colleagues, one of whom was Oliver Penrose, Roger’s older brother, and now a distinguished authority in statistical mechanics. My own first research interest was also in statistical mechanics, but when I changed to relativity and cosmology in the middle of my PhD studies, Oliver told me that I should meet his brother “who thinks geometrically”. When we did meet, we soon became close friends, and I found Roger’s global way of thinking of tremendous value to me. At that-time, and also over the years since, I have learnt so much from him. I am grateful for this opportunity to be able to thank him publicly for the warmth of his friendship and for the influence on me of his very special insights into the subtle relations between physics and geometry.
Geometric Models for Quantum Statistical Inference
Authors: Brody Dorje C , Hughston Lane P 
Published: November 2023

Abstract
Our purpose here is to draw attention to an interesting relationship that can be shown to hold between (a) information geometry, and (b) quantum geometry. By ‘information geometry’, we mean the natural geometry associated with families of probability distributions. This is a subject that goes back more than half a century to the pioneering work of Rao (1945), who showed that the Fisher information matrix associated with a parametrised family of probability dis tributions gives rise to a natural Riemannian metric on the parameter space. This then allows one to speak in a precise way of the ‘distance’ between two probability distributions, an idea that turns out to be useful in problems of statistical inference. An extensive literature has thus developed, following this line of enquiry, on applications of differential geometry to statistics (see, e.g., Amari (1985), Barndorff-Nielsen et al. (1986), Murray and Rice (1993)). By ‘quantum geometry’, on the other hand, we mean the geometry of the manifold of states associated with a given quantum mechanical system. In particular, we consider the manifold of ‘pure’ states associated with a given complex Hilbert space. This is the space of ‘rays’ through the origin in the Hilbert space, which has the structure of a complex projective space. It is known that the usual rules of quantum mechanics allow one to construct a natural metric on this space, namely the Fubini-Study metric, the specification of which is equivalent to all the familiar structure associated with ordinary quantum mechanics.
The Sen Conjecture for Distinct Fundamental Monopoles
Authors: Gibbons Gary 
Published: November 2023

Abstract
I review some recent progress in understanding the interactions of BPS monopoles for higher rank groups. S-duality predicts the existence of a middle-dimensional square integrable harmonic form on the moduli space of distinct fundamental BPS monopoles of an arbitrary Lie group. These harmonic forms are exhibited and their uniqueness is discussed. The properties of distinct fundamental monopoles are contrasted with those of identical SU(2) monopoles.
The probabilistic estimation of qnartet invariants
Authors: Giacovazzo Carmelo 
Published: November 2023

Abstract
Hauptman’s and Giacovazzo’s approaches differ principally on two points: Hauptman regards the reciprocal lattice vectors as the primitive random variables, while Giacovazzo considers the atomic positional vectors as the primitive random variables; different mathematical techniques are used. Giacovazzo (1977J) showed that Hauptman’s results may be obtained from (5.15) and (5.18) no matter whether the atomic positional vectors or the reciprocal lattice vectors are the primitive random variables.
Probabilistic determinantal approaches
Authors: Giacovazzo Carmelo 
Published: November 2023

Abstract
In Chapter 4, where direct methods were explicitly related to real space properties, we dedicated Sections 4.7-4.9 to Karie-Hauptman matrices. In particular we showed that the positiveness of the Karie-Hauptman determinants is caused by the positivity of the electron density, we studied their algebraic properties, and we argued about their possible connection with the probabilistic approach.
Introduction
Authors: Gray Jeremy 
Published: November 2023

Abstract
The rich series of developments described in this book raises historical, mathematical, scientific and philosophical issues. Some of these naturally concern classical electromagnetic theory which itself, as it was created, raised questions about the relationship between mathematics and physics and about the role of geometry. Current historial scholarship also points up interesting differences in the ways in which the history of mathematics and the history of science are conducted. I shall consider the historiographic question first. It has been aptly said that it is the historian ‘s task to give back to the past its sense of the future. The ways in which historians of science and historians of mathematics attempt to do this differ among themselves, and it would seem that there are significant differences in approach between the two groups. To some extent, this may reflect a difference between doing mathematics and doing science that may also be worth thinking about. This difference is apparent even when only those historians of science are considered who write history of science with the science left in (I shall say nothing of the fashion for history of science with the science left out, nor of the previous vogue for the history of mathematics or science with the history left out).
Einstein, Poincaré, and the testability of geometry
Authors: Miller Arthur 
Published: November 2023

Abstract
The topic of the testability of geometry as it was approached by Henri Poincare and Albert Einstein requires that we go back to their views on the origins of this subject. By origins scientists like Poincare and Einstein meant the psychological as well as scientific. For Poincare the problem of the origins of geometry was of particular importance because from it came the philosophical view with which he has become associated, conventionalism. I will focus more on Poincare for two reasons: Can there be non-Euclidean geometries? This problem had been bandied about ever since Euclid ‘s codification of geometry in about 300 B.C. (if not before see Toth, 1967). All inquiries focused on Euclid ‘s fifth postulate, or axiom, which we can state in two equivalent forms. (I) Consider a straight line and a point outside of this line; then only one line can be drawn through that point which is parallel to the already drawn line.
The library
Authors: Freer Stephen 
Published: November 2023

Abstract
It gives information about discoveries, events, proceedings, locations, and method. The botanist must know which authors he should consult about the plant that is the subject of his enquiry. European [vegetables]. C. Bauhin (with systematic [arrangement]) Ray 3, Vaillant. Alpine. Ray, Linnaeus, Haller, Gmelin. Authors who are famous for any work (5) on vegetables, whether they are botanists or amateurs of botany are called PHYTOLOGISTS .
Synonyms
Authors: Freer Stephen 
Published: November 2023

Abstract
Synonyms are variant names given to the same plant by phytologists ([6]), and they refer to genera (VII), species (VIII), and varieties (IX). The fathers, Section 9, mostly agreed on the names of plants, content with those of the genera only. The commentators, Section 10, owing to he lack of descriptions and figures in the writings of the fathers, have applied their names to plants in various ways. The describers, Sections 11 and 12, discovered a greater number of plants, and gave them names arbitrarily. Caspar Bauhin, in a labour of forty years, put together the names given by his predecessors and reduced them to 6,000 species in his Pinax of 1622. The meticulous, Section 14, have doubled the number of plants, by finding new ones on all sides.
Sketches
Authors: Freer Stephen 
Published: November 2023

Abstract
The method of demonstration proposed in [my] Systema naturae [ed.] 6. p.222. establishes the order according to which the history of a plant ought to be put together. A sketch must contain everything that is relevant to the history of the plant, such as its names, marks, appearance, nature, and use. A complete description should not be satisfied, in the usual manner, with the root, stem, leaves and fruit-body, but must take proper notice of the petioles, peduncles, stipules, bracts, glands, hairs, buds, the foliation, and the whole habit. RICINUS with shield-shaped, saw-toothed leaves, and petioles bearing glands. [My] Hortus Cliffortianus 450. Root branchy and fibrous.
Deterministic Dynamical Systems
Authors: Cong Nguyen Dinh 
Published: November 2023

Abstract
In the late nineteenth century Henri Poincaré created a new field of research in mathematics—the theory of dynamical systems—by publishing his famous memoir [129] on the qualitative theory of differential equations. Now, as a result of rapid development over the last four decades, the theory of dynamical systems has become a major branch of mathematics which interacts with almost all other branches of mathematics and finds application in many other sciences, such as physics, chemistry, biology, engineering, and so on.
Combinatorial tools
Authors: Karpinski Marek , Rytter Wojciech 
Published: November 2023

Abstract
Recall that MatchNum(G) is the size (number of edges) of a maximum cardinality matching of a graph G = (V, E) and a perfect matching is a matching of size IVl/2. There are two basic combinatorial tools needed to compute this number: augmenting paths (to construct a matching of a maximal size k); witness sets (to provide an NC-proof that there is no matching of size larger thank). Almost all efficient sequential algorithms use augmenting paths, contrary to NC¬ algorithms. On the other hand witness sets are not used frequently in sequential computations but they are needed in parallel randomized computations. If an algorithm returns a matching of cardinality k then we are not certain if this cardinality is the maximum possible, even if there is a very small probability of failure. Our algorithm is a Monte Carlo algorithm. A better situation occurs when the algorithm provides a maximum cardinality matching and an easy (checkable in NC) proof that it is maximum. In this case the algorithm becomes the so-called Las Vegas algorithm. If a matching is perfect then it gives the optimality proof by itself.
Four easy subclasses of graphs
Authors: Karpinski Marek , Rytter Wojciech 
Published: November 2023

Abstract
In this chapter we consider three easy cases of matchings in special graphs: trees, dense graphs and regular bipartite graphs. They are easy in the sense of possessing simple NC-algorithms for the matching problem. Usually efficient sequential algorithms for trees also have quite efficient parallel implementations. Regular bipartite and dense graphs are among the few known families of graphs which possess perfect matchings. A tree is an undirected connected graph without cycles. Assume we choose a vertex called a root and direct all edges top down. The root is the topmost vertex. The leaves are degree 1 vertices (except the root). A tree can have no perfect matching, even if the number of vertices is even. For example, K1,n has only one edge in the maximum cardinality matching. Our approach to construct an NC-algorithm for trees is to ca greedy sequential algorithm in parallel.
Parallelization of sequential algorithms
Authors: Karpinski Marek , Rytter Wojciech 
Published: November 2023

Abstract
In this chapter we show several implementations of sequential algorithms. Unfortunately in the case of parallel matchings such an approach does not usually give NC-algorithms for general graphs, though a reasonable parallel speed-up can be achieved. In some special cases (e.g. expander graphs, approximations) the implementation of sequential algorithms leads to NC-algorithms. We have already shown an application of maximal matchings to maximum matchings in the construction of an NC-algorithm for maximum matchings in dense graphs. In this chapter we show yet another application of NC-algorithms for maximal matchings: the sublinear time computation of maximum matchings in bipartite graphs. Denote by NC_Maxima_Match(G) an NC-function returning any maximal matching of a given graph G. Any of the algorithms presented in Chapter 7 can be used as a function NC_Maxima_Match(G) returning a maximal matching and working in polylogarithmic time with a linear number of processors. A parallel version of Hopcroft-Karp algorithm will be presented using NC_Maxima_Match as the main subroutine in the crucial operation Disjoint_Paths.
Comparison With Rectifiability
Authors: David Guy , Semmes Stephen 
Published: November 2023

Abstract
Let d and n be integers, 0 &lt; d &lt; n, fixed. Definition 3.1 (Rectifiable sets) A subset E of Rn is said to be rectifiable if there exists a sequence of subsets {Ej} of E, each bilipschitz equivalent to a subset of Rd, such that Hd (E\L⋃j Ej) = 0. Strictly speaking we should say something like “rectifiable of dimension d” , but it is simpler to let the dimension be understood implicitly.
Stronger Self-Similarity For Bpi Spaces
Authors: David Guy , Semmes Stephen 
Published: November 2023

Abstract
Roughly speaking, the BPI condition requires that the space have pieces all around that look like each other. There is an annoying ambiguity here; not only might these pieces be small, but a priori they might behave quite differently from place to place. We would be much happier to say that all the pieces look like each other. It turns out that we can always do this, at least to some extent. Let us begin with a couple of definitions.
Sets Made From Nested Cubes
Authors: David Guy , Semmes Stephen 
Published: November 2023

Abstract
In this chapter we shall look at sets constructed in the manner of Section 2.5. These sets provide a nice “universe” in which to work. They behave well and simply in terms of compactness and weak tangents. We would like to understand the geometric and combinatorial conditions under which there are regular mappings between sets of this type, or bilipschitz mappings or Lipschitz mappings with nontrivial image, but we are far from having definitive answers to these questions. We shall provide some observations about these matters, using the notion of “blocking” sets, and related forms of quantitative topology.
Big Pieces of Bilipschitz Mappings
Authors: David Guy , Semmes Stephen 
Published: November 2023

Abstract
Definition 14.1Let (M,d(·,·))and (N,p(·,·))be metric spaces, and suppose that f :M →N is Lipschitz. We say that f has a big bilipschitz pieceif there is a closed subset E of M such that the restriction off to E is bilipschitz and if H κ (E) &gt; 0,where κis the Hausdorff dimension of M. Of course the restriction to closed sets comes for free, since a Lipschitz mapping which is bilipschitz on a subset is also bilipschitz on the closure.
Uniformly Disconnected Spaces
Authors: David Guy , Semmes Stephen 
Published: November 2023

Abstract
Roughly speaking, we are asking that there be an isolated “island” inM at any point and with practically arbitrary diameter whose distance to the rest ofM is at least a fixed multiple of its diameter. Basic examples include our usual self similar Cantor sets, as in Section 2.3. Later, when we discuss doubling measures, we shall discuss some amusing ways to deform the geometry of a Cantor set. For the moment let us merely point out that the set described in Section 11.6 is also uniformly disconnected.
Convergence Analysis for Iterative Domain Decomposition Algorithms
Authors: Quarteroni Alfio , Valli Alberto 
Published: November 2023

Abstract
In this chapter we present some abstract theorems that are useful for proving the convergence of iteration-by-subdomain methods. The main part of our analysis will cover the case of substructuring procedures (for disjoint subdomains). The convergence analysis of the Schwarz method for overlapping partitions will be addressed in the last section of this chapter. For a complete analysis of Schwarz methods we refer to Dryja and Widlund (1990, 1995), J. Xu (1992) and Smith et al. (1996).
Advection-Diffusion Equations
Authors: Quarteroni Alfio , Valli Alberto 
Published: November 2023

Abstract
This chapter deals with a class of elliptic equations that are not symmetric, due to the presence of first-order terms in the differential operator. These operators describe advection –diffusion processes, and typically arise in fluid dynamics. Our emphasis is on the case in which the transport phenomena, driven by the advective terms, are dominant with respect to the diffusive ones, which are related to the principal second-order part of the operator. The case of a non-symmetric advection –diffusion equation with dominant diffusion was considered in Section 5.1.
Diffraction-line broadening analysis of dislocation configurations
Authors: Vermeulen A C , Delhez R , Keijser Th.H de , Mittemeijer E J 
Published: November 2023

Abstract
In order to understand the properties of polycrystalline solids, one must be aware of the concerted action of all dislocations in all crystals. Hence, it is desired to characterize the dislocation configuration. The analysis of diffraction-line broadening provides a powerful means for such a characterization in a statistically justified way. Until now, an interpretation of diffraction-line broadening by solids containing dislocations has not been performed in a detailed way. Normally, only some ‘overall’ dislocation density value is presented, which is obtained by applying a questionable formalism (see Section 11.2). This chapter provides a new interpretation of line broadening in terms of densities of the types of dislocations present on all possible slip systems in all groups of crystals; in the solid a group contains all crystals that have the same dislocation configuration. The subdivision of the specimen in groups of crystals may be dictated by, for example, the presence of preferred orientation, the imposition of a state of macroscopic stress, etc. (see Sections 11.4 and 11.5).
Effect of planar defects in crystals on the position and profile of powder diffraction lines
Authors: Ustinov A I 
Published: November 2023

Abstract
A lot of theoretical and experimental work (Landau, 1937; Wilson, 1941; Hendricks and Teller, 1942; Jagodzinski, 1949a–c; Kakinoki and Komura, 1952, 1954; Gevers, 1952, 1954a,b; Warren, 1959; Alegra, 1964) has demonstrated that planar defects, stacking faults, twin boundaries, antiphase boundaries, etc., influence both the location and profiles of diffraction peaks. It is important to take the potential planar defects in a crystal into account in cases when the intensity distribution in a peak is utilized for determination of other real crystal characteristics [size of coherent scattering units (crystallites), stress value in a crystal, lattice period, atom locations, etc.].
Effect of stacking disorder on the profile of the powder diffraction line
Authors: Weiss Z , Čapková P 
Published: November 2023

Abstract
Among the different types of defects in layer structures, translation stacking faults are particularly frequent in natural and synthetic materials alike. This disorder is due to an irregular translation of the layers, parallel to their own planes. The occurrence of translation stacking faults is not limited to metal elements (such as cobalt), or simple structures like ZnS, CdS, SiC, which are based on close-packed layer structures. More complicated layer structures, such as phyllosilicates or high Tcsuperconductors, also exhibit translation stacking faults. Stacking faults play an important role in the solid-state transformations and in the formation of polytype structures.
Restoration and preprocessing of physical profiles from measured data
Authors: Cernansky Marian 
Published: November 2023

Abstract
Profiles of diffraction lines contain important information about the real structure of polycrystalline materials, e.g. about crystallite size and lattice strains (Langford and Louer, 1996). However, the physical interpretation is related to pure or physical diffraction profiles, f,which in most cases cannot be measured directly and are obtained from really measured profiles, h,by removing the instrumental distortion described by the instrumental function, g.This function includes both geometrical factors (finite width of source and slits, divergence of beams, flat-specimen surface, its transparency and displacement, imperfect focusing, etc.) and spectral factors, e.g. the finite wavelength interval of the primary radiation (see, for example, Stokes, 1955; Wilson, 1963; Azaroff et al.,1974; Klug and Alexander, 1974; Jenkins, 1989a). The instrumental function, g,is obtained in practice by the measurement of a suitable standard without diffraction broadening-an ideal standard. The case of a non-ideal standard was discussed by de Keijser and Mittemeijer (1978, 1980) and Delhez et al.(1980, 1982).