bluuebunny/crossref_metadata_2025 huggingface dataset:
Ricci and Levi-Civita: from differential invariants to general relativity
Authors: Bottazzini Umberto
Published: November 2023

When one thinks of Ricci-Curbastro (henceforth usually referred to in this chapter as Ricci) and Levi-Civita and of their contributions to the early history of general relativity, one recalls Ricci ‘s pioneering role in the development of the tensor calculus and also Levi-Civita ‘s contributions to the mathematical refinement of Einstein ‘s theory. In recent times, important historical studies have been devoted to both the origins and early development of tensor calculus and Ricci ‘s part in it.1 Therefore, in this paper I will not discuss this matter again. Instead, it is of interest to try to look at the emergence of the absolute differential calculus (ADC in the rest of this chapter) from the viewpoint of the mathematical community of the time. Then, as Einstein ‘s essential use of it in his own work on general relativity apparently marked a turning point in the appreciation of ADC, I will discuss this change in mathematicians ‘ point of view, and eventually consider Levi-Civita ‘s main contribution to Einstein ‘s theory, as presented in his 1917 paper on the concept of parallel displacement. Ricci developed his calculus over a period of some 15 years, from 1884 to the end of the nineteenth Century.
Plants
Authors: Freer Stephen
Published: November 2023

The VEGETABLES comprise seven families: funguses, algae, mosses, ferns, grasses, palms, and plants. Either the buds differentiate the shrubs from the trees, or there is no distinction; for size is of no importance: therefore Pontedera called [all] the producers of buds trees.
The fruit-body
Authors: Freer Stephen
Published: November 2023

The FRUIT-BODY (79), a temporary part of vegetables, dedicated to reproduction, ending the old and beginning the new; seven parts of it are included in the reckoning. The CALYX , the bark of the plant that is present in the fruit-body. The perianth, the calyx of the plant (78), adjoining the fruit-body. Of the fruit-body, enclosing the stamens and the ovary. Of the flower, containing the stamens, but not the ovary. Of the fruit, containing the ovary, but not the stamens. The involucre, fig. 135; the calyx of the umbel (29), distant from the flower. Universal, placed under the universal umbel. Partial, placed under the partial umbel. The catkin, fig. 137; a calyx consisting of a chaffy bud-like common receptacle.
Introduction to Integration
Authors: Priestley H A
Published: November 2023

Introduction to integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditional Riemann integral), intended for a first course in integration. This suffices for elementary applications, and serves as an introduction to the core of the book. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measure. The book is designed primarily as an undergraduate or introductory graduate textbook. It is similar in style and level to Priestley's Introduction to complex analysis, for which it provides a companion volume, and is aimed at both pure and applied mathematicians. Prerequisites are the rudiments of integral calculus and a first course in real analysis.
Building foundations
Authors: Priestley H A
Published: November 2023

We have developed an integral on Lstep and from it an integral defined for any continuous function on a compact interval. Now we examine an alternative way to define the integral of f ∈ C[a, b]. This revised approach, via increasing sequences of step functions, extends to a much wider class of functions. We want to bring in some powerful machinery and it is necessary first to construct the foundations to support it. Thus this chapter is in two parts. The first sections discuss the integration of continuous functions on compact intervals and the remainder present some highly technical results on sequences of step functions which underpin the later theory. We recommend that the proofs of these results be omitted on a first reading.
Null sets
Authors: Priestley H A
Published: November 2023

In Chapter 9 we introduced null sets as the sets which are negligible in an integration-theoretic sense. On a null set the values of an integrable function f may be altered without changing ∫ f, and on a null set delinquent behaviour is condoned. Certainly any finite set must be null. In general, null sets can be very complicated, reflecting the rich structure of the real line. We do not explore far in this direction, since our emphasis is on functions (modulo their behaviour on negligible sets), rather than on sets per se. The harder sections of this chapter and many of the exercises may without detriment be omitted or delayed.
The Continuous DCT
Authors: Priestley H A
Published: November 2023

This is a parallel problem to that which the convergence theorems are designed to solve, the difference being that here we have a limit involving a continuous variable, namely h, while before we had a discrete variable, n. Thus we need convergence theorems with a continuous variable.
Fubini’s Theorem and Tonelli’s Theorem
Authors: Priestley H A
Published: November 2023

This chapter presents two theorems which allow us to relate the integral on JR with the integral on ℝk for k > l and to evaluate and manipulate higher dimensional integrals. These theorems are attributed to Fubini and Tonelli, whose names sound rather appropriately like those of a conjuring act. Tonelli’s magic spell proves integrability assertions, while Fubini’s interchanges the order of integration with respect to different variables. Like all conjuring tricks, Fubini’s and Tonelli’s theorems are not as mysterious as they might seem. They are a direct consequence of the way in which the integrals are set up. In Chapter 25 we introduced L(ℝk). Here we shall work throughout with k = 2, noting that extensions to higher dimensions are easy to formulate if needed.
The spaces L1, L2, and LP
Authors: Priestley H A
Published: November 2023

We have hitherto exploited the vector space structure of L, and dealt with various approximating sequences to integrable functions: Linc -sequences, truncations, etc. This chapter brings these ideas together in a systematic way and sets spaces of integrable functions in their rightful place in the mathematical orchestra. We can play here only a snatch of the overture to the symphony in which integration theory and functional analysis come together in concert. More advanced texts take up the refrain from where we are forced to leave it.
Fourier series: convergence reassessed
Authors: Priestley H A
Published: November 2023

In Chapter 29 we studied pointwise convergence of Fourier series. When solving a differential equation by Fourier methods we want the solution to be a super-position of trigonometric functions at all points of a given range. Thus, tacitly, pointwise convergence is the natural choice in this situation.
Integration in probability theory
Authors: Priestley H A
Published: November 2023

No account of integration theory would be complete without some discussion of its role in probability theory. This is a very large subject and we seek to do no more in this chapter than to build a bridge to specialized texts, such as [10], which we recommend for further reading. We address only readers with some prior familiarity with probabilistic ideas, at the level, for example, of [7]—space precludes us introducing with proper motivation the concepts of random variable, independence, and so on. Like Chapter 24 this is a spectators’ chapter, for which we set no exercises.
Structural Stability Of Discrete-Time Linear Hyperbolic Cocycles
Authors: Cong Nguyen Dinh
Published: November 2023

This chapter is devoted to the problem of structural stability of linear hyperbolic cocycles in the discrete-time case. In the deterministic case, there are many different kinds of structural stability and they are well investigated; for a bibliography we refer to Robbin [134] and Irwin [66] and the references therein. In some sense random dynamical systems can be viewed as dynamical systems which have a measure-preserving dynamical system as a factor, or, in other words, are extensions of such a factor. Hence, a crucial role will be played by the interrelation of measurability and dynamics. Therefore, random dynamical systems require not only more complicated tools for investigation, but also new approaches to them.
Structural Stability of Continuous-Time Linear Hyperbolic Cocycles
Authors: Cong Nguyen Dinh
Published: November 2023

We remark that in our continuous-time case the continuity in t of linear cocycles plays an important role. In the structural stability problem it allows us to prove constructively the structural stability of any uniformly contracting (or expanding) cocycle. This result is a random version of the deterministic Lemma 1.3.13 and is presented in Section 6.2. For the main result on the structural stability of linear hyperbolic cocycles we shall need some deep properties of Lyapunov scalar products and Lyapunov norms in the continuous-time case. These results are given in Section 6.3, where we also prove a theorem on canonical forms of (non-uniformly) contracting (or expanding) cocycles. In the last section we give an application of the results obtained.
Topological Invariants of Linear Cocycles
Authors: Cong Nguyen Dinh
Published: November 2023

It is well known that the stable and unstable subspaces of deterministic linear dynamical systems are invariant under topological conjugacies of linear systems. This follows from the topological characterization of those subspaces as the sets of points which go to the origin under the action of the system as the time tends to ±∞ while the trajectories of points on the center subspace remain bounded away from the origin. Note that the latter fact follows from the theory of Jordan normal forms of matrices. A natural question to ask is: Are the stable and unstable subspaces of linear cocycles invariant under topological conjugacies analogously to the deterministic case? The answer is ‘yes’, and in this chapter we prove that under topological conjugacies the stable and unstable subspaces of linear cocyclcs are invariant.
Inclusion maximal matchings
Authors: Karpinski Marek , Rytter Wojciech
Published: November 2023

In this chapter we consider matchings M which are maximal with respect to inclusion. This means that in a given graph G there is no matching M’ ≠. M such that M ⊂ M’. If X is a set of vertices then denote by Incident(X) the set of edges incident to any vertex in X. Denote also the set of edges incident with any endpoint of an edge in M by Incident(M); hence M ⊆ Incident(M). Observation Let M be a set of independent edges, and X be the set of endpoints of edges in M. Then the following conditions are equivalent: (a)M is an inclusion maximal matching. (b) E = Incident(M). (c) E = Incident(X).
Families of intervals
Authors: Karpinski Marek , Rytter Wojciech
Published: November 2023

A matching in a bipartite graph corresponds to a system of distinct representatives for a certain set family I. In this chapter we consider the case when the family I is particularly natural, it is a family of intervals on the same line, and the intervals are indexed by elements of a set X. Formally there are integers firstv, lastv such that I−{γυ:γυ=[firstυ⋯lastυ],υ∈X} The matching problem for convex graphs is equivalent to the problem of finding a maximum cardinality system of distinct representatives for a family I of intervals.
Matrix methods: basic classical theory
Authors: Boos Johann , Cass Peter
Published: November 2023

As we have already mentioned, in this and the following chapters we will deal mainly with matrix methods, in particular with their domains and the notion of convergence generated by them. Corresponding to the questions formulated in Section 1.3 we aim in Chapter 2 to give the most basic inclusion, comparison and consistency theorems. We will make use exclusively of classical (analytical) methods; some of these results we will re-prove in Parts II and III by functional analytic methods.
Matrix methods: structure of the domains
Authors: Boos Johann , Cass Peter
Published: November 2023

In the first part of this chapter (8.1-8.5) we continue the investigation of the structure of domains which we started in Chapter 2. Whereas in Chapter 2 we made use exclusively of classical methods we now apply functional analytic methods, which we discussed in Chapters 6 and 7. However, we should remark that within the scope of this book it is not possible to present all the details of the structure of domains. For more details we refer the interested reader to Wilansky’s book [254].
Fractured Fractals and Broken Dreams
Authors: David Guy , Semmes Stephen
Published: November 2023

Fractal patterns have emerged in many contexts, but what exactly is a pattern? How can one make precise the structures lying within objects and the relationships between them? This book proposes new notions of coherent geometric structure to provide a fresh approach to this familiar field. It develops a new concept of self-similarity called "BPI" or "big pieces of itself," which makes the field much easier for people to enter. This new framework is quite broad, however, and has the potential to lead to significant discoveries. The text covers a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. Although fractal geometries arise in many different ways mathematically, comparing them has been difficult. This new approach combines accessibility with powerful tools for comparing fractal geometries, making it an ideal source for researchers in different areas to find both common ground and basic information.
Background Information
Authors: David Guy , Semmes Stephen
Published: November 2023

Let (M, d(x, y)) be a metric space, and let Ebe a nonempty subset of M. Suppose that we have a Lipschitz mapping f : E → R. Then we can extend f to a Lipschitz function on all of M, and with the same Lipschitz constant. This is well known, but let us quickly recall the proof. Suppose that f is L-Lipschitz.
Convergence of Metric Spaces
Authors: David Guy , Semmes Stephen
Published: November 2023

One of the basic tools for studying BPI spaces is to take limits of them, and to pass to weak tangents. This will enable us to make compactness arguments, which will sometimes permit us to derive quantitative statements from qualitative statements. In this chapter we discuss convergence of metric spaces in general, leaving BPI spaces to the next chapter. We discuss also convergence of mappings between spaces that are converging, convergence of subsets, and convergence of measures on converging spaces.
Weak Tangents
Authors: David Guy , Semmes Stephen
Published: November 2023

Now we want to apply the notions of convergence from Chapter 8 to BPI spaces. This will permit us to make some compactness arguments. Let(M,d(x,y)) be a metric space. For eachp ∈M and O <t  ≤ diamM we useMp,t to mean the pointed metric space(M,t‒  d(x, y),p). Notice thatMp,t always has diameter ≥ 1.
Spaces Looking Down On Other Spaces
Authors: David Guy , Semmes Stephen
Published: November 2023

Definition 11.1 (Looking down)  Let M and N be two BPI spaces of the same dimension. We say that M looks downon N if there is a closed subset A of M and a Lipschitz mapping f :A  → N such that f(A) has positive measure. This should be compared with BPI equivalence, or more precisely Proposition 7.1, in which we would ask thatf be bilipschitz. Now we are trying to split BPI equivalence into two pieces, so to speak.
Doubling Measures And Geometry
Authors: David Guy , Semmes Stephen
Published: November 2023

We shall discuss examples soon, but notice that Hausdorff measure of the correct dimension on any Ahlfors regular metric space is doubling. We shall often be interested in other doubling measures on Ahlfors regular spaces, for which we think of the doubling measure as some kind of controlled deformation of Hausdorff measure.We shall discuss examples soon, but notice that Hausdorff measure of the correct dimension on any Ahlfors regular metric space is doubling. We shall often be interested in other doubling measures on Ahlfors regular spaces, for which we think of the doubling measure as some kind of controlled deformation of Hausdorff measure.
Deformations Of Bpi Spaces
Authors: David Guy , Semmes Stephen
Published: November 2023

It is natural to try to make a notion of “continuous families” of BPI spaces. The idea of continuous families of geometries is very old. One can think of continuous families of Riemann surfaces, for instance. These might be realized concretely as algebraic varieties, as solution sets of some collection of polynomial equations, and one can get continuous families by varying the coefficients.
Some Sets That Are Far From Bpi
Authors: David Guy , Semmes Stephen
Published: November 2023

Proposition 19.1 There is a I-dimensional regular set F ⊆ R with the property that if A ⊆ F is closed, if f: A → F is Lipschitz, and A  0  = {x ∈ A: f(x)  ≠ x}, then |f(A  0)| = 0.

Of course | · | refers to H measure here.

We already know from Section 9.5 that there are regular sets whose intersection with a BPI set always has zero measure, but this is a stronger example of non-BPI behavior. Notice that the set mentioned in Proposition 19.1 has the property that it cannot have a nontrivial intersection with a CPI set (Definition 6.10) of dimension l.
Other Boundary Value Problems
Authors: Quarteroni Alfio , Valli Alberto
Published: November 2023

The theory that was developed in the previous chapters for the Poisson equation and for symmetric elliptic equations can be extended to the case of a more general differential problem of the form where Ω is a bounded domain in Rd, d = 2, 3, with a Lipschitz boundary, ℒ is a partial differential operator, f is a given data, and u is the unknown solution. More precisely, we will consider: non-symmetric elliptic problems; the linear elasticity problem; the Stokes and Oseen problems for incompressible flows; a Stokes-like problem that arises from the analysis of compressible flows; the advection equation; and the time-harmonic Maxwell system.
Time-Dependent Problems
Authors: Quarteroni Alfio , Valli Alberto
Published: November 2023

In this chapter we illustrate how the domain decomposition techniques that have been presented so far can be applied in the process of solving time-dependent problems. As usual we assume that ℒ is a bounded domain in Rd, d = 2, 3, with a Lipschitz boundary.
Introduction to defect and microstructure analysis or the analysis of real structure
Authors: Fiala Jaroslav , Snyder Robert L
Published: November 2023

The first applications of X-ray diffraction served to reveal the periodic, regular structure of crystalline matter. However, it was soon discovered that the real structure of crystalline matter is not perfectly periodic. Gradually, it has been found that crystalline matter, as it really exists in nature and manufactured products, has many deviations from an ideal order (von Laue, 1960). In 1950, Hosemann introduced the concept of paracrystals (Hosemann, 1950a,b) to describe the structures of material which lie somewhere between ideal crystals and completely disordered, amorphous matter. So, in fact, all materials are paracrystalline. That is why it is so important to study the real aspects of the structure of solids. The various deviations from ideal crystalline order.
Use of pattern decomposition or simulation to study microstructure: theoretical considerations
Authors: Langford J Ian
Published: November 2023

Abstract

An overview of the diffraction effects arising from structural imperfections is given and line profiles due to the finite size of crystallites or domains are considered in detail. Structural ‘mistakes’ and lattice distortion (microstrain) are only discussed briefly, since these topics are covered more rigorously elsewhere. Although this chapter is mainly concerned with studies of microstructure based on the integral breadth, the theoretical treatment of size effects is equally applicable to an analysis based on Fourier series or on the simulation of diffraction line profiles. The last part of the chapter is concerned with a procedure based on the Voigt function for characterizing structural imperfections.
X-ray analysis of the inhomogeneous stress state
Authors: Kraus I , Ganev N
Published: November 2023

Stress measurement, especially that of residual stresses, represents one of the most widespread and technically important applications of X-ray diffraction. Traditionally much attention has been paid to X-ray stress analysis, namely for its possibility of reliable and effective checking of metal and alloy surface treatment technologies. That is why all the Czech X-ray laboratories are trying to keep pace in X-ray tensometry with leaders such as Germany, USA, UK, France, Japan and Russia, both in computer-assisted control of experiments and in finding new ways of interpretation of measured strains in interatomic distances.
A new whole-powder pattern-fitting approach
Authors: Scardi P
Published: November 2023

Abstract

A new algorithm for the modelling of crystallite size and microstrain (size/strain) effects on profile broadening has been introduced in a traditional Rietveld refinement routine for powder diffraction data. In spite of the simplifying assumptions at the basis of the method, a considerable improvement in quality and reliability of structural refinements has been achieved. This was particularly evident when the studied samples exhibited anisotropic size/strain effects, or when several phases with different microstructural features were present. The proposed method is specially suited to applications in materials science, where the structure of the present phases is frequently known, and the microstructure is the main object of study. In this case, the method can be used as a whole-powder pattern-fitting (WPPF), that takes advantage of the structural constraints of the refinement routine. Several applications are described in this chapter, mainly regarding phase mixtures and samples containing finely dispersed crystals. A further development regarding multi-layered systems is also presented: the refinement algorithm was adapted to properly consider the layered structure typical of thin films and coatings in order to obtain a direct evaluation of the phase content in terms of layer thicknesses.
Turbulent Flow Over Growing Waves
Authors: Belcher S E , Hunt J C R , Cohen J E
Published: November 2023

Growth and decay of ocean waves is strongly influenced by both the sheltering effect induced by turbulent stresses in the air flow, and by dynamical effects of the critical height. Here we show how the effect of the critical level can be analysed in the asymptotic framework used previously to investigate sheltering. The new analysis of the critical layer leads to results that are consistent with classical analyses of the critical level that use more specialised energy arguments, but only when the waves grow slowly. This study shows how the sheltering and critical layer effects can operate together, which indicates a new mechanism for growth of waves as they pass through a wave group.
Structure in the Atmospheric Surface Layer over Open Ocean Waves: Representation in Terms of Phase Averages
Authors: Hristov T , Friehe C , Miller S , Edson J , Wetzel S
Published: November 2023

We present a method of identifying the wave-coherent fields (wind velocity, stress, pressure fluctuations, etc.) in the surface layer flow over gravity waves. Wave-coherent fields are responsible for the exchange of momentum and kinetic energy between the turbulent air flow and under lying wave field, so their extraction from field experiment data is of primary interest. The method we developed uses the concept of an analytic signal based on the Hilbert transform. This method performs well even if the waves are substantially non-monochromatic. The representation reveals the role of the phase shifts of the wave-induced fields for momentum and energy exchange.
Benjamin Memorial Lecture: Side-Band, Benjamin-Feir and Eckhaus Instabilities
Authors: Stuart J T
Published: November 2023

Brooke Benjamin was responsible for a wealth of important and significant advances in our understanding of the dynamics of fluids in motion. Thus he worked on surface instabilities of fluid in a vibrating container, on the hydraulic jump, on the mechanics of bubbles, on shear flows over wavy surfaces, on the instabilities of the flow over a compliant surface (the “Dolphin” problem), on the instability of flow down an inclined plane, on “Vortex Breakdown”, on “Modern” mathematical methods in fluid mechanics, on “Transitions” in Taylor-vortex flows, and on Water Waves in all their glory. He was a brilliant experimentalist and theorist, with beautiful experiments and penetrating theories to his credit.
Flow of Air Over Sharp Crested Water Waves
Authors: Croft A J , Sajjadi S G
Published: November 2023

Croft and Sajjadi [1] constructed a model for the high speed flow of wind over a rigid periodic boundary with sharp crests, where the undisturbed flow was perpendicular to the crests. In that model, the flow separated at each crest creating a region of vortical flow on the leeward side of each wave. This vortical flow was modelled by a line vortex parallel to the crest and situated below it. The theory predicted the strength and position of each vortex and the resulting flow field.
An Attempt to Simulate the Effect of Wave Breaking on Momentum - and Mass-Transfer by Imposing Intermittent Near-Interface Transport Properties
Authors: Eifler Walter
Published: November 2023

A coupled 1-D air-water model is proposed for simulating momentum and high Schmidt number gas-transfer under the condition of periodic wave breaking. The model is driven by prescribed wind speed and by a concentration difference between water and air. Periodic time dependence is forced by imposing intermittent near surface transport properties simulating temporary interface disruption due to wave breaking. The model is calibrated for a range of wind speeds with respect to experimental wind drag coefficients. Then it is applied for high Schmidt !1umber gas transfer. Comparison of predicted and measured mass transfer rates shows excellent agreement for both laboratory and open sea measurements.
Parabolic subgroups
Authors: Geck Meinolf , Pfeiffer Golz
Published: November 2023

Subgroups that deserve special attention are those which share defining properties of their parent groups. In the case of a Coxeter group W with its distinguished generating set S, a subgroup generated by a subset of S is a Coxeter group in its own right. These 2n subgroups of W (where n = |S |) are the parabolic subgroups of Wand this chapter is devoted to their structure and properties-both individually as well as seen as a collection.
The braid monoid and good elements
Authors: Geck Meinolf , Pfeiffer Golz
Published: November 2023

In this chapter, we consider the braid group and the braid monoid associated with a Coxeter system (W, S). We introduce the braid group from a purely algebraic point of view, as a group given by a presentation which is similar to that of W, but where the quadratic relations are omitted. Our aim is to prove the basic results due to Deligne and Brieskorn-Saito about a normal form for the elements in the braid group. This will be achieved in Sections 4.1 and 4.2. The subsequent section deals with the application of these results to the problem of finding elements with certain “good” properties in the conjugacy classes of W (assuming W to be finite). The desired property is formulated in Definition 4.3.1; note that it refers in an essential way to the corresponding braid group. We determine, case by case, “good” elements of minimal length in the conjugacy classes of all finite Coxeter groups. These results will play a crucial role in our discussion of rationality properties and the computation of the values of the irreducible characters of Iwahori-Hecke algebras.
Characters of Iwahori-Hecke algebras
Authors: Geck Meinolf , Pfeiffer Golz
Published: November 2023

In the previous chapter we have seen that a generic Iwahori-Hecke algebra H associated with a finite Coxeter group W is isomorphic to the group algebra of W and that, moreover, we have a bijection between the irreducible characters of H and of W via a specialization process. We will now carry this relation further by studying in more detail the irreducible characters of H. Similar to the induction of representations from a subgroup of a finite group, one can also define a process of induction of representations from parabolic subalgebras of Iwahori-Hecke algebras. This will be discussed in detail in Section 9.1. The basic result is that this process of induction is compatible with specializations. This will allow us to transfer the results about induced characters for finite Coxeter groups (e.g., the results on characters of parabolic type in Chapter 6) to the case of Iwahori-Hecke algebras.
Computer solution methods
Authors: Acheson David
Published: November 2023

It is often quite impossible to solve a differential equation exactly, especially if the equation in question is nonlinear. Even if a ‘solution’ can be obtained, it may involve such awkward integrals or infinite series as to be virtually useless.
Elementary oscillations
Authors: Acheson David
Published: November 2023

One of the oldest and best-known oscillating systems is the so-called simple pendulum. This consists of a light rigid rod of length / with a point mass at one end, the other end being pivoted at a fixed point 0, so that the pendulum can swing freely in one particular vertical plane (Fig. 5.1).
The conceptual framework
Authors: Dudai Yadin
Published: November 2023

I am a functionalist1 with a biologist’s *bias and with *conscious awareness of other disciplines. My approach to memory research is guided by the following tenets:(a) the function of the brain is to create and retain *internal representations of the world that could guide behaviour; (b) the function of *learning is to permit the adaptation of internal representations to a changing world (*memory is the retention of these adaptations over time); (c) learning and memory require neural *plasticity for their actualization; and (d) learning and memory are *system properties, made possible by the concerted operation of multiple *levels of the system.
Acetylcholine
Authors: Dudai Yadin
Published: November 2023

learning and memory. As is the case with other neurotransmitters and neuromodulators, the physiological roles of Ache in brain should be judged not only by its independent activation of specific cellular receptors and their downstream intracellular signal transduction cascades, but also by its contribution to the activation and cross-talk of webs of signalling cascades induced by coactive sets of neurotransmitters and neuromodulators (* coincidence detector, *context). Similarly, at the circuit *level, the function of the cholinergic system must be assessed in the context of the concerted activity of multiple neurotransmission and neuromodulator pathways on the target circuit (Decker and McGaugh 1991).
Acquisition
Authors: Dudai Yadin
Published: November 2023

Multiple approaches are used to investigate the neurobiology of acquisition. Cellular physiology, neuropharmacology, neurochemistry, and molecular biology are all applied to dissect the molecular and cellular mechanisms involved. Candidate ‘cellular acquisition devices’ are *ion channels and membrane *recepduring the training (Wagner et al. 1998b). It is not yet known, however, which of the activated areas is indispensable for acquisition (*criterion), which area is causally related to the strength of the engram, and what are the specific roles of each of the areas in the encoding and registration of information in the first milliseconds and seconds after engraphy has been triggered.
Algorithm
Authors: Dudai Yadin
Published: November 2023

‘Begin at the beginning’, said the King of Hearts, ‘and go on till you come to the end: then stop’. He thus provided White Rabbit with an algorithm (Carroll 1865). The term ‘algorithm’ is derived from Latinization of the name of one of the most creative mathematician in medieval Islam, Al-Kwarizmi (780–c. 850; Boyer 1989; Colish 1997). In modern times algorithmic is a field fundamental to the science of computing (Harel 1987). In the neurosciences algorithms are encountered in multiple contexts (Marr 1982; Hinton 1989; Church land and Sejnowski 1992). One of these is in *models of biological learning.
Amnesia
Authors: Dudai Yadin
Published: November 2023

Amnesia is ‘forgetfulness’ in Greek (*mnemonics). The adverse effect of certain types of brain injury and mental trauma on memory was recognized long ago. But the systematic analysis of amnesia started only in the nineteenth century, with Ribot (1882) and Korsak off (1887). Till the introduction of *functional neuroimaging, the study of amnesia has been the only practical approach to the investigation of brain substrates of memory in humans. Some information could be also obtained from electrical stimulation of patients undergoing brain surgery, but this was very limited in scope and controversial in interpretation (*engram).
Amygdala
Authors: Dudai Yadin
Published: November 2023

The amygdala (alias the amygdaloidal or amygdalar complex), first described and named by the German anatomist Burdach in the early nineteenth century (Meyer 1971), is so called because in the primate brain its shape resembles an almond (amugdale-in Greek). About a dozen different nuclei and specialized cortical areas are currently discerned in the amygdala, and many intra- and extramygdalar connections have been identified (Amaral et al. 1992; Pitkanen et al. 1997; Swanson and Petrovich 1998; Aggleton 2000). Indeed, the heterogeneity of the nuclei, areas, and pathways raised some doubts whether ‘amygdala’ as a whole is a discrete anatomical entity in situ, or only an artificial construct of the human mind (e.g. Kirkpatrick 1996; Swanson and Petrovich 1998; de Olmos and Heimer 1999).
Anthropomorphism
Authors: Dudai Yadin
Published: November 2023

The term is derived from Greek: ánthropo-s—human being, morphé—form. Anthropomorphism owes much to anthropocentricity, i.e. our *a priori inclination to regard ourselves as the centre of the universe and see the world through our *biased eyes. By doing so we probably hope to gain some illusory control over reality. Anthropomorphism is intensively and recurrently exemplified in ancient myths, literature, and art (e.g. Burkert 1985). Occasionally, it had also infiltrated other social activities: throughout Europe in the Middle Ages, horses and pigs were dragged to public trial because it was believed that they are *consciously aware of their own acts and hence are liable for them (Evans 1906).
Assay
Authors: Dudai Yadin
Published: November 2023

Assays (from exagiere, Latin for ‘to weigh out’) are not merely research tools. They play a decisive part in the development and workings of scientific disciplines. They are also important in shaping the feasibility, progression, and outcome of particular research programmes. Sometimes they even play a decisive part in moulding the fate of individual academic careers.
Bias
Authors: Dudai Yadin
Published: November 2023

Frances Bacon, trusting that ‘the subtlety of nature is greater many times over than the subtlety of the senses and understanding’ (Bacon 1620), distinguished four 1994; *observational learning). In addition, multiple sources of bias stem from implicit interactions of the subject with the *context and the experimenter. In many behavioural experiments, the subject is actively involved more than the experimenter is inclined to admit. The subject pays attention to the experimental demands, could try to extract *cues about the objective of the test, reacts to involuntary signs emitted by the experimenter (*Clever Hans), and sometimes attempts to comply with a perceived goal (Pierce 1908).
Calcium
Authors: Dudai Yadin
Published: November 2023

Calcium (calx, Latin for lime) fulfils many regulatory, computational, and representational functions in the brain. Furthermore, it is instrumental in translating information across *levels and time domains in the brain (see below). In recent years much has been learned about the ways in which calcium ions encode and modulate neuronal information, but the picture is far from being comprehensive.
Collective memory
Authors: Dudai Yadin
Published: November 2023

Discussion of collective memory is at the interface of psychology, sociology, and history (Halbwachs 1925; Pennebaker and Banasik 1997). Collective memory is unique among the types of memory covered in this book because it is not confined to an individual nervous system. Rather, at any given moment in time it is encoded in a distributed *system of individual brains in the relevant social group, as well as in elements of the contemporary *culture of that group (Bartlett 1932; Wertsch 1985; d’Andrade 1995; *context, *real-life memory).
CREB
Authors: Dudai Yadin
Published: November 2023

In technical terms, which will be explained below, CREB, CAMP-response element-binding protein, is a protein that modulates the transcription of genes with CAMP-response elements in their promoters. CREB is one of the most commonly used acronyms in neurobiology these days, and also one of the few words in the jargon of molecular biology that even experimental psychologists and computational neuroscientists might have encountered. And if they did n’t, they should. Because the more we advance our knowledge in molecular neurobiology, the more we realize that CREB plays a pivotal role in the response of neurons to external stimuli. CREB is a transcription factor.
Delay task
Authors: Dudai Yadin
Published: November 2023

Delay tasks were introduced into experimental psychology by Hunter (1913), who found that a variety of species can learn to respond to a light stimulus after a delay, which in his hands ranged from a few seconds in rats to about half an hour in children. The procedures were later refined by Yerkes and Yerkes (1928) in their investigation on mnemonic capabilities in the chimpanzee. Since then, a variety of delay tasks have been developed and proven highly useful in the measurement of short-term and *working memory, *recognition, and *recall.
Enigma
Authors: Dudai Yadin
Published: November 2023

Science is driven by the unknown as much as by the known, and therefore, noting enigmas is often as useful as listing facts (aînos, Greek for ‘fable’, aínigma, ‘to speak in riddles’). Below is a list of 10 enigmas of memory. Some refer to baffling concepts, others to technological shortcoming, and most to both. Although many investigators may agree with much of the choice, some may not. Scientific enigmas tend to reflect the *bias of their compiler. The reader is fully encouraged to expand or shrink the list unabashedly. But at least, it is a starting point.
Functional neuroimaging
Authors: Dudai Yadin
Published: November 2023

The search for the *engram is a mapping expedition. It requires *maps that chart both anatomy and function. Anatomy per se only rarely tells us what specific brain structures do. This is evident, by the way, from some neuroanatomical terms that mean only a fruit or a sea monster (e.g. *amygdala, *hippocampus). Surely if early anatomists would have known something about what these structures do, they would have called them by other names. Indeed, some idea on function could occasionally be obtained from tracing the connections between various sites, e.g. a pathway from the olfactory bulb to the piriform cortex does suggest that the latter deals with olfaction, not vision.
Hippocampus
Authors: Dudai Yadin
Published: November 2023

In 1587 the Italian anatomist Arantius introduced the term ‘hippocampus’ (seahorse) to describe ‘an elevation of white substance’ that rises at the base of the lateral ventricles (Lewis 1923). He wondered, however, whether ‘a white silk-worm’ (Bombyx) might provide a better description. Two centuries later, a spark of dubious imagination led to a new suggestion, ‘hippopotamus’. At about the same time, a structure in that same brain region also came to be called ‘ram’s horn’, or, ‘calculated to impress whoever hears it for the first time’ (ibid.), the ‘horns of Ammon’ (after the Egyptian deity Ammon, which was represented as a ram or a human form with a ram’s head).
Immediate early genes
Authors: Dudai Yadin
Published: November 2023

The term immediate early gene (IEG) was borrowed from virology. During the infectious cycle, the viral proteins are expressed in an orderly programme, which involves immediate early, delayed early, and late proteins (Honess and Roizman 1974; Weinheimer and McKnight 1987). For example, in the virus Herpes simplex, products of IEGs are detectable at 1 h of infection, of delayed early genes at 3 h, and of *late response genes at 6–7 h (Weinheimer and McKnight 1987).
Insight
Authors: Dudai Yadin
Published: November 2023

Some types of learning, such as the acquisition of *skill, progress gradually, through numerous repetitions. This is termed ‘incremental learning’, or ‘rote learning’ (Hebb 1949). In contrast, other types of learning, both in *real-life and in laboratory setting, occur abruptly, following a step function. Two examples are *flashbulb memory and *conditioned taste aversion. There is, however, a type of abrupt learning that differs from explain ‘insight’ by rather complex chaining of stimulus– response contingencies (Keller and Schoenfeld 1950; Bower and Hilgard 1981).
Internal representation
Authors: Dudai Yadin
Published: November 2023

‘Representation’ and ‘internal representation’ are used in multiple senses in philosophy, linguistics, and the cognitive sciences. The meaning of ‘internal representation’ as used here deserves, therefore, careful clarification, especially as it is ardently *reductionistic. Generally speaking, ‘representation’ is the expression of things in one language transformed into another. ‘Language’ is any set of symbols with rules for putting them together (Marr 1982). We are not engaged here, however, in the formal treatment of representations at large, but rather in the application of the concept to memory research.
Learning set
Authors: Dudai Yadin
Published: November 2023

The roots of ‘learning set’ can be traced back to the beginning of the twentieth century, to a group of psychologists at Würzburg University, Germany, known collectively as ‘The Würzburg School’. They pioneered experimental approaches to thought processes (Boring 1950). In the course of their investigation they noted that with proper preparation of a *subject for a mental task, upon the presentation of the stimulus the thoughts of the subject would run off automatically to perform the task.
Observational learning
Authors: Dudai Yadin
Published: November 2023

‘Whatever you see me do, do like-wise’, said Gid’on to his selected three hundred men, blew the shofar, waved the torch, and surprised the Midyanites in their camp (Judges 7: 17–22). He was a master demonstrator in an observational learning class. A lot of what we learn in our lifetime, from others we learn, frequently by observing a model and adapting its actions. In *real-life, the model is a conspecific; in the lab it could be an individual of another species or a behaving inanimate.1 This capability, to gain from the experience of others, clearly expands the behavioural repertoire of individuals much beyond the limits of their own innate (*a priori) responses and solo experience combined.
Persistence
Authors: Dudai Yadin
Published: November 2023

If we only abandon highly simplistic *metaphors of memory storage, such as ‘cabinet files’ or ‘computer disks’, ‘persistence’ (per-sistere, Latin for ‘to stand’) becomes a prominent *enigma of memory research. As memory is the retention of acquired information over time, persistence is clearly its central attribute. Generally speaking, there is a family of ‘persistence problems’. The *classic philosophical problem (definition 2 above) is also known in metaphysics as ‘The Ship of Theseus’: the ship of the mythical Greek hero was placed on display in Athens, and with time, parts of it were replaced, one by one, till none of the original remained.
Synapse
Authors: Dudai Yadin
Published: November 2023

The term ‘synapse’ (Greek for syn-haptein, ‘to make contact’) is commonly attributed to Sherrington (Foster and Sherrington 1897). It was actually proposed by Verrall, an expert on *classical drama, to replace syndesm (Greek for ‘chained together’), which was Sherrington’s first choice (Shepherd and Erulkar 1997). ‘Synapse’ was preferred because it was judged to yield a better adjectival form. It is left for the reader to judge whether ‘synaptic *plasticity’ indeed rhymes better than ‘syndesic plasticity’, but, in any case, it is too late for a change.
Taxonomy
Authors: Dudai Yadin
Published: November 2023

The tendency to categorize the world into ‘similar’ and ‘different’ is fundamental to human cognition. It underlies folk knowledge systems in orally-reliant societies as well as sophisticated taxonomies in science (Durkheim 1912; Levi-Strauss 1962; Smith and Medin 1981; Sokal 1985; Berlin 1992). It is shared to some degree even by species far remote from us on the phylogenetic scale (Giurfa et al. 1996). The term ‘taxonomy’ itself is, however, a newcomer to language: taxinomie, or taxonomie, was introduced in 1813 into French to denote classification of entities, and the discipline that deals with such classifications (from taxis nomie, meaning arrangement method in Greek; Le Maxidico 1996). It then found its way into English.
Zeitgeist
Authors: Dudai Yadin
Published: November 2023

‘Zeitgeist’ (German for ‘spirit of the time’) was introduced into intellectual dialectics by the Romanticism, the anti*classical cultural movement originating in late eighteenth century Europe that displayed heightened interest in nature, emotional expression, and imagination. In the beginning, the meaning of ‘zeitgeist’ ranged from a semi-mystical force that shapes human history (Hegel 1820) to an opinionated cultural world view (Goethe 1827). Its current meaning is conveyed by definition 2 above. Occasionally the use of the term in the exact and natural sciences is considered purple prose. But what should concern us here is not whether the term itself is trendy or not, but rather what the concept tells us about the way science is practised.
Biological roles of the MMPs
Authors: Woessner J Frederick , Nagase Hideaki
Published: November 2023

The contributions of MMPs to biological processes are difficult to assess. For the most part, our knowledge stems from correlations-that is, enzyme levels are high in a given situation and therefore are postulated to play an important role. The role cannot be proven by use of inhibitors, such as the natural TIMPs or the synthetic hydroxamates, because these do not, in general, inhibit only a single MMP. Moreover, we do not yet know any pathologies directly attributable to a mutation in one of the MMPs. It is not possible to survey the thousands of papers dealing with the biological roles of MMPs, so attention will be given to review articles in various areas of interest and these will be limited to the past three years only.