bluuebunny/crossref_metadata_2025_split huggingface dataset:
Long-term potentiation in the dentate gyrus of the anaesthetized rat is accompanied by an increase in extracellular glutamate: real-time measurements using a novel dialysis electrode
Authors: Errington M L , Galley P T , Bliss T V P 
Published: November 2023

Abstract
We have used a glutamate-specific dialysis electrode to obtain real-time measurements of changes in the concentration of glutamate in the extracellular space of the hippocampus during low-frequency stimulation and following the induction of long-term potentiation (LTP). In the dentate gyms, stimulation of the perforant path at 2 Hz for 2 min produced a transient increase in glutamate current relative to the basal value at control rates of stimulation (0.033 Hz). This activity-dependent glutamate current was significantly enhanced 35 and 90 min after the induction of LTP.
Long-term potentiation and the ageing brain
Authors: Barnes C A 
Published: November 2023

Abstract
Ageing is associated with learning and memory impairments. Data are reviewed that suggest that age-related impairments of hippocampal-dependent forms of memory, may be caused, in part, by altered synaptic plasticity mechanisms in the hippocampus, including long-term potentiation (LTP). To the extent that the mechanisms responsible for LTP can be understood, it may be possible to develop therapeutic approaches to alleviate memory decline in normal ageing.
Genetic neuroscience of mammalian learning and memory
Authors: Tonegawa Susumu , Nakazawa Kazu , Wilson Matthew A 
Published: November 2023

Abstract
Our primary research interest is to understand the molecular and cellular mechanisms on neuronal circuitry underlying the acquisition, consolidation and retrieval of hippocampus-dependent memory in rodents. We study these problems by producing genetically engineered (i.e. spatially targeted and/or temporally restricted) mice and analysing these mice by multifaceted methods including molecular and cellular biology, in vitro and in vivo physiology and behavioural studies. We attempt to identify deficits at each of the multiple levels of complexity in specific brain areas or cell types and deduce those deficits that underlie specific learning or memory. We will review our recent studies on the acquisition, consolidation and recall of memories that have been conducted with mouse strains in which genetic manipulations were targeted to specific types of cells in the hippocampus or fore-brain of young adult mice.
MAPK, CREB and zif268 are all required for the consolidation of recognition memory
Authors: Bozon Bruno , Kelly Aine , Josselyn Sheena A , Silva Alcino J , Davis Sabrina , Laroche Serge 
Published: November 2023

Abstract
There has been nearly a century of interest in the idea that encoding and storage of information in the brain requires changes in the efficacy of synaptic connections between neurons that are activated during learning. Recent research into the molecular mechanisms of long-term potentiation (LTP) has brought about new knowledge that has provided valuable insights into the neural mechanisms of memory storage. The evidence indicates that rapid activation of the genetic machinery can be a key mechanism underlying the enduring modification of neural networks required for the stability of memories.
Representations of astrolabes in Western art
Authors: Cleempoel Koenraad Van 
Published: November 2023

Abstract
The relatively infrequent depiction of astrolabes in works of art seems disproportionately small in relation to the large amount of instruments that have survived and to the high number of contemporary treatises that discuss the astrolabe. In comparison, its three-dimensional counterparts – the armillary sphere, and the celestial and the terrestrial globe – have experienced wider acclaim from artists throughout the ages. The immediate ornamental and didactic appeal of these other instruments may be responsible for this trend. But also, in a broader sense, the image of the globe and the armillary sphere became a popular visual metaphor for disciplines such as geometry and astronomy, where they are still used until the present day.
Fibre bundles
Authors: Kawakubo Katsuo 
Published: November 2023

Abstract
Given two topological spaces X and Y, the construction of the Cartesian product X × Y is a method of constructing new topological spaces out of old. A generalization of this Cartesian product is the notion of fibre bundles, which have the Cartesian product structures locally. Its definition is given in terms of transformation groups; hence one may say that the theory of fibre bundles is an application of the theory of transformation groups.
Manifolds and Lie groups
Authors: Kawakubo Katsuo 
Published: November 2023

Abstract
The aim of this chapter is to provide an introduction to the theory of differentiable manifolds and Lie groups.
The Euclidean space ℝ is the most important space in mathematics in general; for example, differential calculus is performed extensively on Euclidean space. It is natural enough that we are then led to study those spaces which are locally like ℝ, and more precisely those spaces in which each point has a neighbourhood homeomorphic to ℝ. We call such spaces manifolds.
Solution of a Classical Problem on Finite Inversive Planes
Authors: Thas J A 
Published: November 2023

Abstract
Let Ibe a finite inversive plane of odd order q, qr/.{11, 23,59). If for at least one point pof Ithe internal affine plane Ipis Desarguesian, then Iis Miquelian. Other formulation: for q (/.{11,23,59) the finite Desarguesian affine plane of odd order qhas a unique extension; this extension is the Miquelian inversive plane of order q.As a direct corollary we obtain a computer-free proof of the uniqueness of the inversive plane of order 7.Let Cbe a circle of the inversive plane I,let pE Cand let pbe a point not on C.Since Ipis an affine plane it follows that there is a unique circle C’ through pand pwhich has only pin common with C.We say that the circles C1 and C2 are tangentif C1 = C2 or IC1 n C2I = l. Now it is clear that tangency is an equivalence relation on the set of all circles. If Ois an ovoid[7] of PG(3, q), then the points of Otogether with the intersections 1rnO, with ,r a non-tangent plane of O,form an inversive planeof order q.Such an inversive plane is called egglike.For an egglike inversive plane Ieach internal plane Ipis Desarguesian. By a celebrated theorem of P. Dembowski [7] each finite inversive plane of even order is egglike. If the ovoid Ois an elliptic quadric, then the corresponding inversive plane is called classicalor Miquelian.By a celebrated theorem of A. Barlotti [14] each egglike inversive plane of odd order is Miquelian.
First-Order Partial Differential Equations
Authors: Collins Peter J 
Published: November 2023

Abstract
This chapter considers the equation where p, q denote the partial derivatives of the real-valued function z = z(x, y) and P, Q, R are continuous real-valued functions of r = (x, y, z) in an appropriate domain in ℝ3. The equation is linear in p, q and quasi-linear because, in addition, P, Q, R are functions of z as well as of x and y. We search for real-valued solutions z = z(x, y) of (1). It is often useful to visualise our methods geometrically, and we shall refer to such solutions, because of the objects they represent, as solution surfaces. There is one important picture to hold in one’s mind, and this is illustrated in section 5.5, where it forms an integral part of our discussion. Otherwise, our aim is to encourage the reader’s analytic intuition. The main problem, the Cauchy problem, is to discover whether there is a unique solution surface which contains (‘passes through’) a given ‘boundary’ curve. This is in general not possible and when it is, there is usually a restriction to be placed on the domain of the independent variables x, y in order that such a unique solution exists. The restricted domain is called the domain of definition of the solution.
Iterative Methods and Neumann Series
Authors: Collins Peter J 
Published: November 2023

Abstract
In this chapter we take a new look at the iterative method introduced in Chapter 1. Our goal will be to introduce the Neumann series, the terms of which involve iterations of the kernel of an integral equation, and use this series to derive the solution of the equation. Throughout the chapter we shall be concerned solely with the non-homogeneous Fredholm equation where K and f are real-valued continuous functions and λ is a constant. The kernel K = K(x, t) need not be symmetric. We first suggest that the reader review Picard's method as used in section 1.2 to solve the non-homogeneous Fredholm equation. We now introduce a simple example to which we shall return at various points in this chapter. It is used here to continue the review of Picard's method and will also be used to exemplify the new procedures which will appear later.
The Sturm–Liouville Equation
Authors: Collins Peter J 
Published: November 2023

Abstract
This chapter concerns the homogeneous equation where p : [a, b] → ℝ is continuously differentiable, q : [a, b] → ℝ and ⍴: [a, b] → ℝ are continuous, p(x) &gt; 0 and ⍴(x) &gt; 0, for all x in [a, b], and λ is a real constant. The equation generalises (H) of section 4.2 and L denotes the operator that was defined in that section. Further, we shall impose the same homogeneous boundary conditions, namely: where A 1, A 2, B 1, B 2 are constants (A 1, B 1 not both zero and A 2, B 2 not both zero). A value of the constant λ, for which (SL), together with (α) and (β), has a solution y = y(x) which is not identically zero on [a, b], is called an eigenvalue of (SL), (α), (β), and such a non-zero solution y = y(x) is called an eigenfunction of (SL), (α), (β) (‘corresponding to the eigenvalue λ’). Our discussion will bring together much of the work in earlier chapters, from Green's functions, the correspondence between integral and differential equations and the existence-uniqueness theorems for the latter, to the use of the Calculus of Variations, of the Fredholm Alternative Theorem and of the Expansion Theorem for symmetric kernels. We should like to stress the importance of the material in this chapter for applications, especially in physics. The Note following Exercise 5 below gives an important example. Others can be found via the list of references in the Bibliography.
Series Solutions
Authors: Collins Peter J 
Published: November 2023

Abstract
In this chapter, we investigate a special technique which provides solutions to a wide class of differential equations. Again, we concentrate on the homogeneous linear second-order equation where p 0, p 1, p 2 are continuous functions which we shall suppose throughout this chapter to have no common zeros. We do not, for the moment, specify the domain of these functions, though it will in general be taken to be an interval, finite or infinite. Hitherto, we have often specified that the function p 2 is never zero. A point x 0 in the domain of p 2 for which p 2(x 0) ≠ 0 is called an ordinary point of the differential equation (1). We shall discuss how solutions y to (1) in a neighbourhood of an ordinary point x 0 can, in rather general circumstances, be represented as a power series For example, the geometric series convergent for |x| &lt; 1, is the solution of the equation satisfying y(0) = y′(0) = 1, in the open interval (–1; 1) about the ordinary point 0. The reader can easily check this by first noting that the series solution (2) can be represented in (–1; 1) in the closed (or finite) form.
Project 12
Authors: Grandine Thomas A 
Published: November 2023

Abstract
ACME’s new Humble Automatic Lackey 9000, an industrial robot (also mentioned in Project 1), has not been as reliable as the competition’s robot, i.e. AJAX’s Newfangled Electronic Robotic Device. The main difficulty is that the arm movement is not smooth and this has placed undue strain on the various joints and mechanisms. Because of your reputation as a trouble-shooter you have been asked to investigate this problem.
Project 22
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The Modern Electronic Lifting Team, a division of ACME, is designing a grabber arm for the Humble Automatic Lackey 9000, ACME’s industrial robot (mentioned in Project 1 and Project 12). The grabber arm is intended to enable HAL to grab objects which are much too hot for him to grab directly. Because the competition from the AJAX Newfangled Electronic Robotic Device (mentioned in Project 12) is so stiff, MELT needs to minimize its costs as much as possible when designing and building the grabber arm. MELT has asked SOLVE for assistance with this design problem, and Biro Kratt has decided that the problem is important enough to warrant putting his best person on the project, so you have been asked to help out. The main component of the grabber arm is a metal dowel made up of a mixture of two alloys, namely insulatinum and conductivitum. One end of the dowel will be exposed to temperatures as high as 850 K, while the other end will be attached directly to HAL, who cannot tolerate temperatures in excess of 375 K without suffering thermal circuitry failure. You have been asked to design the MELT dowel so that HAL does not fail.
Ordinals
Authors: Potter Michael D 
Published: November 2023

Abstract
The simple and general principles of induction are powerful tools for proving things about the natural numbers: we intend now to investigate ways in which they can be generalized to apply to a very much wider class of ordered collections than the subsets of ro. The basis of our study will be the observation that the general principle of induction follows trivially from the least element principle and can therefore be applied to any ordered collection which shares this property: we call such collections ‘well ordered’. Our strategy will be to apply the same techniques to the study of isomorphism between well ordered sets as we used in Chapter 4 to investigate equinumerosity between sets: just as the work of Chapter 4 produced an arithmetic of cardinals, in this chapter we shall get an arithmetic of ordinals.
Elementary Categories, Elementary Toposes
Authors: McLarty Colin 
Published: November 2023

Abstract
The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis.
Introduction
Authors: McLarty Colin 
Published: November 2023

Abstract
Eilenberg and Mac Lane created categories in the 1940s as a way of relating systems of algebraic structures and systems of topological spaces in algebraic topology. The spread of applications led to a general theory, and what had been a tool for handling structures became more and more a means of defining them. Grothendieck and his students solved classical problems in geometry and number theory using new structures —including toposes — constructed from sets by categorical methods. In the 1960s, Lawvere began to give purely categorical definitions of new and old structures, and developed several styles of categorical foundations for mathematics. This led to new applications, notably in logic and computer science.
External semantics
Authors: McLarty Colin 
Published: November 2023

Abstract
We have interpreted formulas in a topos E by assigning each an extension. This is called the internal semantics. The external semantics, also called Kripke-Joyal semantics, describes which generalized elements satisfy each formula. The idea is that the extension collects the instances of a formula internally to E, while the class of generalized elements satisfying it is an external collection. A generalized element satisfies a formula iff it is a member of the formula’s extension, and this external viewpoint is often handy for more complicated formulas.
Categories in a topos
Authors: McLarty Colin 
Published: November 2023

Abstract
In this chapter small categories and functors in a topos E are defined. Functors are then defined from a small category A to E, and the category EA of such functors, and it is proved that £A is a topos. Examples of functor categories on the topos Set are given in Chapter 22. Section 20.l really only applies naive constructions given in Part II to small categories in E. It generalizes the results in Chapter 12 on small categories in a universe of sets.
Mesh Data Surface Fitting
Authors: Dierckx Paul 
Published: November 2023

Abstract
In this chapter we will present efficient methods for calculating least-squares or smoothing splines if the data values are specified at the nodes of a rectangular mesh. We will also explore a number of possibilities of using these methods in case the latter condition is not (completely) satisfied or in case we are faced with extremely large data sets which necessitate a piecemeal treatment.
Interpretability
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
We need very little from model theory: just two concepts, and no real results, not even the compactness theorem. The concepts, definability and interpretability, are dealt with in this chapter and the next. The algebraist who has gi en no thought to formal languages will need to look carefully at the material of this section as well as its first few applications subsequently. The motivation comes from algebraic geometry over algebraically closed fields, where definable sets in the technical sense turn out to be the Zariski constructible sets (Zariski open subsets of algebraic varieties) in affine space. The notion of the dimension of an irreducible variety extends to a notion of dimension for constructible sets with little change in its properties, though it becomes somewhat harder to define irreducibility and impossible to define connectivity in this context.
Basic Properties
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
Perhaps the single most important property of groups of finite Morley rank is the descending chain condition on definable subgroups, a rather direct consequence of Axiom A (bearing in mind the discussion of degree in Section 4.2). This leads in the first place to the notion of the connected component of a definable subgroup, and the definable closure of an arbitrary subgroup. The chain condition is discussed in Section 5.1, the connected component is discussed in Section 5.2, and definable closures are discussed in Section 5.5. The main result is Theorem5.12: a connected group has degree 1 (the converse is almost obvious). The other results of Section 5.2 are straightforward but important, and we give 22 exercises (some of them more or less obvious remarks) which the reader should linger over. Exercise 22, page 80, deals with a Schur-Zassenhaus type of theorem and is one of the most interesting exercises, and is not known to hold if Pis assumed to be infinite (or even infinite and central) unless G is solvable (see Theorem 9.32). Section 5.3 prepares for the proof ofZil’ber’s Incomposability Theorem in Section 5.4. This major result proves (simultaneously) the definability and connectedness of certain subgroups of groups of finite Morley rank. In particular if G is connected of finite Morley rank, then its commutator subgroup G’ is definable and connected, and hence by induction the same applies to the higher commutator subgroups aCn) (Corollary 5.30). A similar argument applies to the lower central series on (also in Corollary 5.30). In Section 5.5 we consider the definable closure of an arbitrary subgroup Hof a group G of finite Morley rank, which is by definition the smallest definable subgroup of G containing H. The properties of the definable closure are elementary but useful, particularly Corollary 5.38: the definable closure of a solvable or nilpotent subgroup of given class is again solvable or nilpotent, respectively, of the same class. Again the 13 exercises listed deserve close attention.
Elementary Geometry
Authors: Roe John 
Published: November 2023

Abstract
The geometry of two- and three-dimensional space has long been studied for its own sake, but its results also underlie modern developments in fields as diverse as linear algebra, quantum physics, and number theory.
This text is a careful introduction to Euclidean geometry that emphasizes its connections with other subjects. Glimpses of more advanced topics in pure mathematics are balanced by a straightforward treatment of the geometry needed for mechanics and classical applied mathematics. The exposition is based on vector methods; an introductory chapter relates these methods to the more classical axiomatic approach.
Conics and other curves
Authors: Roe John 
Published: November 2023

Abstract
In this chapter we will study in more detail some curves in the plane described by ‘locus equations’ of the form f(x, y) = 0, where f is a function of the two variables x and y. Our main attention will be devoted to conics, which are the curves that arise when f(x, y) is a quadratic function of the variables x and y; at the end of the chapter we will also take a look at some examples where f(x, y) is a cubic function of x and y.
Differential geometry of surfaces
Authors: Roe John 
Published: November 2023

Abstract
In this chapter we will study the differential geometry of curved surfaces in three-dimensional space. This subject owes its origin to Euler, but it came to maturity at the hands of Carl Friedrich Gauss (1777-1855), one of the greatest mathematicians of all time. In a memoir entitled General Investigations of Curved Surfaces, published in 1827, Gauss showed that a curved surface could be considered, not just as sitting in some extrinsic three-dimensional space, but as having its own intrinsic geometry; a geometry which, moreover, might be non-Euclidean.
The ruled surface method
Authors: Huxley M N 
Published: November 2023

Abstract
The methods of this chapter are mostly elementary number theory. We want to count the number of integer solutions in bounded regions for certain sets of equations and inequalities. The difficulties are partly algebraic, partly analytic. A system of polynomial equations defines an algebraic variety in affine space. The geometry is dominated by two integers, the dimension and the genus of the variety. The size of the set of integer solutions is usually much smaller than the dimension of the variety would suggest. In the case of projective curves, there are only finitely many integer solutions unless the genus is zero or one (Fallings 1983) (an integer point on a projective curve corresponds to a rational point on an affine curve).
Consecutive minor arcs
Authors: Huxley M N 
Published: November 2023

Abstract
The elementary methods for the First Spacing Problem used the divide-and- conquer method, dividing the solutions of the inequalities into families parametrized by a real number t. The expressions in the different inequalities were related by differentiation with respect to t, and if one inequality held for a long interval of t, then the inequality corresponding to its derivative became sharper.
The Third and Fourth Conditions
Authors: Huxley M N 
Published: November 2023

Abstract
We put together the ideas of the two previous chapters. We want to count coincident pairs among the vectors y constructed from polynomial approximations on the minor arcs. The parameters of the method, M and T, and also H in Chapters 8 and 9 are immutable. The choice of N, the length of the short sums, was made at the outset, and determines R, and so which arcs are major, which are minor. Some fine tuning can be done before applying the large sieve.