bluuebunny/crossref_metadata_2025 huggingface dataset:
Lymphoscintigraphy of Upper Limbs: A Bayesian Framework
Authors: Petr Gebouský , Miroslav Kárný , Anthony Quinn
Published: November 2023

Lymphoscintigraphy is a sensitive diagnostic technique in nuclear medicine. One of its principal applications is the investigation of upper limb lymphedema, a complication of breast cancer. Typically, only two or three snapshots of the distribution of the radioactive tracer in the limb can be obtained, implying a sparse data problem. Hence, traditional inferences of important physiological indicators are completely unreliable. In this paper, the Bayesian paradigm, exploiting available prior information in conjunction with a simplified model of the diffusion dynamics, is used to obtain reliable quantitative evaluations for the first time.
Bayesian Analysis of Matched Pairs in the Presence of Covariates
Authors: Martínez F Javier Girón M Lina , Moreno Elías , Torres Francisco
Published: November 2023

In this paper, we address three main questions connected with the statistical analysis of matched pairs in the presence of covariates, from a Bayesian viewpoint. These sort of data appear when measurements are made on the same individuals before and after a treatment, at possibly different dose levels, is applied. The first question refers to the issue of how to construct statistical models for matched pairs data that reflect the dependency of the post-treatment on the pre-treatment observation, the dose level and the values of the covariates. The second one addresses the problem of seeking suitable statistical models for which inferences on the effect of the treatment only depends on some simple summaries of the data, for instance, the differences or ratios of the corresponding paired data. The third issue is concerned with testing the effectiveness or not of the treatment, the relevance of the different dose levels, and the influence of the covariates. Explicit solutions and formulae are derived for the case of an additive linear normal model. These problems are addressed here from a Bayesian default model choice perspective. Comparison of this novel approach to testing with classical and standard (non informative) Bayesian approaches are given, based on a simulation study.
On the Application of Logistic Regression Modelling in Microarray Studies
Authors: Mertens Bart j. A
Published: November 2023

Microarrays (sometimes also referred to as “DNA chips”) simultaneously record sample responses on a large collection of genes, thus yielding data of extremely high dimensionality. The methodology is to a considerable extent driven by advances in technology. It is envisaged that the chips will eventually be produced in large numbers from standard “matrices” or templates (which are in themselves costly to produce), thus allowing economies of scale. Evaluation of the chip responses is largely automated. At present, microarrays (and sample preparation) are still expensive. Hence, sample sizes from microarray experiments are small, which exacerbates the singularity problems which are encountered with such high-dimensional data.
Bayesian Inference for Derivative Prices
Authors: Polson Nicholas G , Stroud Jonathan R
Published: November 2023

This paper develops a methodology for parameter and state variable inference using both asset and derivative price information. We combine theoretical pricing models and asset dynamics to generate a joint posterior for parameters and state variables and provide an MCMC simulation strategy for inference. There are several advantages of our inferential approach. First, more precise parameter estimates are obtained when both asset and derivative price information are used. Second, we provide a diagnostic tool for model misspecification based on agreement of the state and parameter estimates with and without derivative price information. Furthermore, the time series properties of the state variables can also be used to evaluate model fit. We illustrate our methodology using daily equity index options on the Standard and Poor’s (S&P 500) index from 1998-2002.
Objective Bayesian Comparison of Laplace Samples from Geophysical Data
Authors: Álvarez Abel Rodr íguez Giselle , Sans Bruno
Published: November 2023

We consider a Bayesian reference analysis for comparing two samples which follow Laplace distributions as well as the analysis of the performance of a Bayesian classification procedure for such a model. The methodology is motivated by an oil exploration problem where the geological structure of a reservoir has to be described. The aim is to characterize the lithology of the reservoir using well registers and seismic traces. We use a continuous wavelet transformation (CWT) of the original data and estimate the power of the transformation that links the energy of the CWT to its scale. For both well logs and seismic traces, we found that such an estimate follows a Laplace distribution with location depending on whether the lithology corresponds to gravel or sand. In this work we explore the comparison problem from an objective Bayesian viewpoint through the use of the Intrinsic Bayes Factor.
Bayesian Object Matching with Hierarchical Priors and Markov Chain Monte Carlo
Authors: Tamminen Toni , Lampinen Jouko
Published: November 2023

We present an object matching system where Bayesian inference is used for estimating the probability distribution of object feature locations in a digital image. The representation of the object contains two parts: the likelihood part which defines the probability of perceiving a pixel image corresponding to the object detail, and a hierarchical prior part which defines the distributions of the feature locations relative to the other features. In this study the objects are human faces. The likelihood part is based on Gabor filters, which are a type of optimal bandpass digital filters. A distortion-tolerant measure of feature similarity is produced by performing statistical analysis on the filter response vectors, and the actual likelihood of observing an image detail given the feature location is computed by analyzing the distribution of the similarities. The prior part defines a priori distributions for the relative locations of the features, which correspond to their average locations on the object. The prior is hierarchical in nature, that is, a hyperprior is set for the width of the prior distribution, which allows the system to automatically determine the feature location variance appropriate for the image at hand. The object matching is carried out as Bayesian inference: the goal is to find the posterior probability distribution of the possible matches given the image and the hierarchical prior. Markov Chain Monte Carlo methods, especially Gibbs sampling, are used to draw samples from the posterior distributions of the feature locations, allowing simple estimation of the essential distribution statistics.
Lucky for some-miscellanea
Authors: Haigh John
Published: November 2023

There are 52C13 = 635013 559 600 ways of selecting 13 objects from 52, so that is the total number of different bridge or whist hands that you could hold. From the work in Chapter 7, you would need to hold about a million hands for a 50% chance of being dealt a repeat, and it is most unlikely that you would notice! Effectively, every hand is a new challenge, even without the help of your ‘partner’, the polite name applied to the person opposite. The number of different deals is much larger.
Oxford Textbook of Philosophy and Psychiatry
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

The 'Oxford Textbook of Philosophy of Psychiatry' provides a detailed introduction to the field of philosophy of psychiatry, a framework for study and skill development, and an overview of current research. Each case study is supported by selected readings, thinking skills exercises, and self-test questions.
Progress in five parts
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

Things have changed a lot since Anthony Quinton, a British philosopher, formerly at Oxford and then a member of the House of Lords, made this observation in a lecture to the Royal Institute of Philosophy (Quinton, 1985). Philosophers are nowadays actively interested in a wide range of topics from mental health practice and research. Conversely, mental health practitioners (including both professionals and users of services) are actively interested in a wide range of philosophical topics. Indeed, the explosive growth in cross-disciplinary contact in the last few years (see Reading Guide) has been as remarkable as the earlier long period of mutual neglect.
Introduction
Authors: Ockendon John , Howison Sam , Lacey Andrew , Movchan Alexander
Published: November 2023

Partial differential equations are central to mathematics, whether pure or applied. They arise in mathematical models whose dependent variables vary continuously as functions of several independent variables, usually space and time. Their most striking attribute is their universality, a property which has enabled us to motivate every mathematical idea in this book by real-world examples from fluid or solid mechanics, electromagnetism, probability, finance and a host of other areas of application. Moreover, this applicability is growing day by day because of the flexibility and power of modern software tailored to suitable discretised approximations of the equations. Equally dramatic is the way in which the equations that arise in all these areas of application can so easily motivate the study of fundamental mathematical questions of great depth and significance and, conversely, benefit from the results of such investigations.
First-order scalar quasilinear equations
Authors: Ockendon John , Howison Sam , Lacey Andrew , Movchan Alexander
Published: November 2023

Even though this chapter deals only with the simplest category of partial differential equations, the theory that emerges is relevant to many important and fascinating practical situations. An example is the flow of a thin coat of paint down a wall, as illustrated in Fig. 1.l(a). Because the layer is thin, the velocity, say u(x, y, t), is approximately unidirectional down the wall.
Hyperbolic equations
Authors: Ockendon John , Howison Sam , Lacey Andrew , Movchan Alexander
Published: November 2023

Hyperbolic equations are the easiest scalar second-order equations to classify from the point of view of the Cauchy problem. They occur commonly in practical applications, as is evident from studying the models of Chapter 2.
Parabolic equations
Authors: Ockendon John , Howison Sam , Lacey Andrew , Movchan Alexander
Published: November 2023

As we have already mentioned, and as this chapter emphasises, parabolic equations probably occur more commonly than any other type of partial differential equation in applied science. However, that is not the only reason why this chapter is one of the longest of the book. It also reflects the vast amount of knowledge that has been gained about many parabolic problems over recent decades. This has come about as the result of the stimulus of the many practical applications combined with the applicability of a wide variety of mathematical techniques.
An introduction to functional magnetic resonance imaging of the brain
Authors: Matthews Paul M
Published: November 2023

This chapter is intended to provide an overview of fMRI methods and applications. Like the rest of the book, it is intended to highlight key concepts or strategies rather than to provide a review of the literature. It also should provide a guide to the chapters that follow. We hope that it will help to place them in context. In doing so, this chapter makes later repetition inevitable, but we have embraced this in the belief that learning can be made easier by having ideas presented more than one time and in more than one way.
Reciprocity
Authors: Villegas Fernando Rodriguez
Published: November 2023

We saw in §2.1 how the quadratic reciprocity law can be interpreted as describing the variation of the number of solutions N(p) of a quadratic equation modulo primes p. We will now consider the situation for polynomials still in one variable but of higher degree. Let us fix a prime p. In order to formulate the general reciprocity law (of Artin) it turns out to be necessary to consider not just the number of solutions to an equation modulo p but the result of other related countings as well.
Remarks On Selected Exercises
Authors: Villegas Fernando Rodriguez
Published: November 2023

Ex. 1.13 The connection is in the general spirit of reciprocity as in §3.2.2 but goes beyond the scope of this book. See for example [26], (4.24) and chapter III, 14 C. Ex. 1.26 Here is a simple GP script that will plot the ratio of Rk(n) and the volume of the corresponding sphere for fixed k and n 1 through a given bound
An Introduction to Algebraic Geometry and Algebraic Groups
Authors: Geck Meinolf
Published: November 2023

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.
Neuropsychological perspectives on sensorimotor integration: Eye-hand coordination and visually-guided reaching
Authors: Carey David P
Published: November 2023

Neuroimaging work has done much to confirm hypotheses of a role for the posterior parietal cortex (PPC) in sensorimotor integration. Nevertheless, in the future such studies will need to test more specific models of the processes in which the PPC participates. A recurrent theme cutting across neuropsychology, physiology, and computational modeling is the idea of transformations in reference frames from retinal- to arm- (or hand-) centered coordinates. Understanding sensorimotor control processes at this level with neuroimaging will always be difficult. Evidence from neurophysiology suggests that any populations of cells related to encoding target location, preparing, and executing saccadic eye movements, and preparing, executing, and monitoring arm movements overlap considerably.
The achievement of brain imaging: Past and future1
Authors: Posner Michael I
Published: November 2023

Brain imaging has forged an impressive link between psychology and neuroscience. Many studies show consistent activation of a small number of widely separated brain areas that differ among tasks. Do these results imply a modular organization of the human brain? One view of modularity requires that there be no top down or cognitive input from other systems. This view has almost no support even for primary sensory cortex, which can be influenced by attention. A less restrictive version of modularity requires the ability to manipulate one area of activation independently from another. The studies in the sections of this volume on visual pathways and on orienting of attention, provide support for this form of modularity, but require specification of the time course and the connections involved.
The Poisson Equation
Authors: Elman Howard C , Silvester David J , Wathen Andrew J
Published: November 2023

The source (or load) function f is given on some two- or three-dimensional domain denoted by Ω ⊂ ℝ.
Population ecology
Authors: Gibson David J
Published: November 2023

Population ecology seeks to understand the relationship between groups of individuals of a single species in an area (a population) and their environment. The ‘father’ of plant population ecology was John L. Harper, following the publication of his Population Biology of Plants in 1977, and, indeed, much of his work was undertaken in a Lolium per- enne–Trifolium repens sheep pasture in North Wales (e.g. Sackville Hamilton and Harper 1989; Sarukhán and Harper 1973; Turkington and Harper 1979). Many topics in the population ecology of grasses and grasslands are covered in the book edited by G.P. Cheplick (1998a) (see review in Gibson 1998). In this chapter, some of these important topics are explored. First, reproduction and population growth of grasses is discussed (§5.1), followed by a discussion of how fungi infecting grasses either above or below ground affect their population ecology (§ 5.2), and finally, ecotypes, polyploidy, hybridization, and genetic structure are covered under the heading of genecology (§5.3).
Ecosystem ecology
Authors: Gibson David J
Published: November 2023

Ecosystem ecology is the study of the biotic and abiotic components of the environment; in other words, the study of living organisms and their interaction with their environment. It was introduced as a concept to ecology by Tansley (1935). At this level of study, less emphasis is placed on individual species or communities; rather, the focus is on the integrated components of the environment and their involvement in fundamental processes of energy flow and material cycling. Ecosystems can be viewed a comprising three subsystems connected by the transfer of energy and matter: the plant subsystem, the herbivore subsystem, and the decomposer subsystem. The initial fixation of carbon through photosynthesis via green plants characterizes the plant subsystem (see §7.1.2). The recycling of dead organic matter (detritus) represents the decomposer subsystem (see §7.3). The role of herbivores is discussed in Chapter 9.
Management and restoration
Authors: Gibson David J
Published: November 2023

This chapter deals with applied grassland ecology and discusses means of managing grasslands for human needs and conservation. The discussion in §10.1 focuses on pastoralism as an ancient method of rangeland utilization, and the use of management tools such as grazing, fire, fertilizers, herbicides, and pesticides. Rangeland assessment (§10.2) is important for determining the suitability of grasslands for various uses and to allow the development of management plans. Where grass- land has been destroyed or degraded, restoration is necessary and is described in §10.3 where the focus is on management and restoration of natural or semi-natural grassland. Management of amenity and turf grassland, e.g. golf courses and other sports facilities, parks, and roadsides, largely through mowing, weeding, irrigation and herbicide application, is outside the scope of this book and is covered elsewhere (Aldous 1999; Brown 2005; Rorison and Hunt 1980) Depending on the desired use, grasslands are managed for one of several goals, including pro- duction of forage for raising domestic and wild animals, production of biofuels, or conservation of natural areas. Grassland management and conservation objectives can be focused either on the system as a whole, on specific plant functional types (e.g. tussock grasses, Díaz et al. 2002), or for particular species (e.g. to promote rare species or species of high forage value, or reduce undesirable or invasive species). Many natural areas require management intervention because natural disturbance regimes are disrupted or no longer in place (Chapters 1 and 9).
Understanding autism: insights from mind and brain
Authors: Hill Elisabeth L , Frith Uta
Published: November 2023

Autism is a developmental disorder characterized by impaired social interaction and communication as well as repetitive behaviours and restricted interests. The consequences of this disorder for everyday life adaptation are extremely variable. The general public is now more aware of the high prevalence of this lifelong disorder, with around 0.6% of the population being affected. However, the signs and symptoms of autism are still puzzling. Since a biological basis of autism was accepted, approaches from developmental cognitive neuroscience have been applied to further our understanding of the autism spectrum. The study of the behavioural and underlying cognitive deficits in autism has advanced ahead of the study of the underlying brain abnormalities and of the putative genetic mechanisms.
Disentangling weak coherence and executive dysfunction: planning drawing in autism and attention-deficit/hyperactivity disorder
Authors: Booth Rhonda , Charlton Rebecca , Hughes Claire , Happe Francesca
Published: November 2023

A tendency to focus on details at the expense of configural information, ‘weak coherence’, has been proposed as a cognitive style in autism. In the present study we tested whether weak coherence might be the result of executive dysfunction, by testing clinical groups known to show deficits on tests of executive control. Boys with autism spectrum disorders (ASD) were compared with age- and intelligence quotient (IQ)-matched boys with attention-deficit/hyperactivity disorder (ADHD), and typically developing (TD) boys, on a drawing task requiring planning for the inclusion of a new element. Weak coherence was measured through analysis of drawing style. In line with the predictions made, the ASD group was more detail-focused in their drawings than were either ADHD or TD boys. The ASD and ADHD groups both showed planning impairments, which were more severe in the former group. Poor planning did not, however, predict detail-focus, and scores on the two aspects of the task were unrelated in the clinical groups. These findings indicate that weak coherence may indeed be a cognitive style specific to autism and unrelated to cognitive deficits in frontal functions.
Investigating individual differences in brain abnormalities in autism
Authors: Salmond H , de Haan M , Friston K J , Gadian G , Vargha-Khadem F
Published: November 2023

Autism is a psychiatric syndrome characterized by impairments in three domains: social interaction, communication, and restricted and repetitive behaviours and interests. Recent findings implicate the amygdala in the neurobiology of autism. In this paper, we report the results of a series of novel experimental investigations focusing on the structure and function of the amygdala in a group of children with autism. The first section attempts to determine if abnormality of the amygdala can be identified in an individual using magnetic resonance imaging in vivo. Using single-case voxel-based morphometric analyses, abnormality in the amygdala was detected in half the children with autism. Abnormalities in other regions were also found. In the second section, emotional modulation of the startle response was investigated in the group of autistic children. Surprisingly, there were no significant differences between the patterns of emotional modulation of the startle response in the autistic group compared with the controls.
Quantum rules
Authors: Baggott Jim
Published: November 2023

The development of quantum theory was driven by a consistently repeated failure of classical physics to accommodate the results of ever more sophisticated experiments on the microphysical world of radiation, elementary particles, atoms, and molecules. Each break-through in the development of the theory’s conceptual structure was followed (sometimes very rapidly) by new experimental data that just did not fit, pointing to the need for yet further refinements. As is typical in such a radical change in the approach to acquiring scientific understanding, old and often unsuitable concepts were forced into service to meet the needs of the new description. Confusion reigned. The major figures in the theory’s early development took up radically different positions on the theory’s interpretation, and, as we will see, the debate became polarized in ways that remain relevant today.
Complementarity and entanglement
Authors: Baggott Jim
Published: November 2023

The results of the experiments described in the last chapter all point fairly unambiguously to a reality that is decidedly non-local in nature, at least in the quantum domain. Of course, these are results that come as no surprise to those willing to accept one of the most fundamental principles of the Copenhagen interpretation — that quantum phenomena are describable only in terms of the dual classical physical concepts of waves and particles. The wave properties of quantum entities lend them inherently non-local characteristics, and it is only when we forcibly ‘collapse’ the wave function by making a measurement that we are taken aback by what appears to be contradictory or counter-intuitive behaviour.
I think, therefore
Authors: Baggott Jim
Published: November 2023

The orthodox Copenhagen interpretation of quantum theory is silent on the question of the collapse of the wave function. The field is therefore wide open. If we choose to reject the strict Copenhagen interpretation, we are, given our present level of understanding, free to choose exactly how we wish to fill the void. Any suggestion, no matter how strange, is in principle legitimate, provided that it does not produce a theory inconsistent with the predictions of quantum theory known to have been upheld so far by experiment. We are not constrained to a specific solution. Our choice is therefore a matter of personal taste.
A History of Mathematics
Authors: Hodgkin Luke
Published: November 2023

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.
A chaotic end?
Authors: Hodgkin Luke
Published: November 2023

I am not thinking of the ‘practical’ consequences of mathematics ... at present I will say only that if a chess problem is, in the crude sense, ‘useless’, then that is equally true of the best mathematics; that very little of mathematics is useful practically, and that that little is profoundly dull.
The geodesic problem and Gromov—Hausdorff convergence
Authors: Ambrosio Luigi , Tilli Paolo
Published: November 2023

This chapter is devoted to the geodesic problem in a general metric space E.
Trees and topologies
Authors: Hein Jotun , Schierup Mikkel H , Wiuf Carsten
Published: November 2023

The simplicity of the coalescent process allows various quantities to be calculated from combinatorial arguments. This is the focus of the present chapter. However, first we will specify some concepts regarding coalescent trees and their relationships to the well-known concept of phylogenetic trees.

In Kingman ‘s original formulation of the coalescent he separated the process into two independent processes, the jump process and the waiting time process. Figure 3.1 illustrates these processes for a sample of five genes. The waiting time process describes the waiting times to the next coalescent event when there are k genes left and is described by exponentially distributed variables as derived in Chapter 1. The jump process describes which pair of genes coalesce at each coalescence event and was originally phrased in terms of equivalence classes. An equivalence class for a set of genes is a specific separation of the set of genes into disjoint sets covering the whole set of genes. In Figure 3.1 the first equivalence class is the separation of the genes into five different sets. After the first coalescence event, two genes (4 and 5) are merged into the same set. The jump process thus determines a path through equivalence classes from the initial state to the final state which consists of a single set containing all the genes.
Gaussian processes
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

We return in this chapter to the general Bayesian formalism for a single model. So far we have worked out everything in terms of the posterior distribution p(w D) of the model parameters w, given the data D; to get predictions, we need to integrate over this distribution. Often the model parameters w are not easy to interpret, so knowing their distribution is in itself not particularly desirable. Also, it is not easy to see exactly what prior assumptions on the input–output relation are implicit in choosing, for example, a Gaussian prior on w.
Notes and suggestions for further reading
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

Information theory in its modern formulation has come upon us mainly through the seminal work of Claude Shannon [57–59] which, in turn, builds on earlier work of Nyquist [60] and Hartley [61] on problems related to transmission of information. The proposal to quantify information in terms of the logarithm of the size of a message set in case of equally likely messages appears in fact to have been made first by Hartley, but its generalization to ensembles of messages that are not equally likely—using entropy as the appropriate measure—was achieved only in 1948, independently by Shannon [57, 58] and Wiener [62, 63].
Gardner theory of task realizability
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

Our convergence proofs and dynamical analyses of learning processes have so far always relied on the existence of a solution, that is, on the existence of a specific allocation of values to the network’s parameters (synapses and thresholds) such that the resulting network faithfully generates the correct outputs for the input data presented in the learning stage. This guaranteed that we could regard the input–output relationships to be learned as having been generated by a suitable ‘teacher network’, a property on which our methods have relied quite heavily. Here we turn to the following complementary question: how can we predict beforehand whether certain families of tasks are indeed solvable by the architecture at hand, without actually constructing the teacher network?
AMPA receptor trafficking and long-term potentiation
Authors: Malinow Roberto
Published: November 2023

Activity-dependent changes in synaptic function are believed to underlie the formation of memories. A prominent example is long-term potentiation (LTP), whose mechanisms have been the subject of considerable scrutiny over the past few decades. I review studies from our laboratory that support a critical role for AMPA receptor trafficking in LTP and experience-dependent plasticity. There is general belief that a long-lasting change in synaptic function is the cellular basis of learning and memory (Eccles 1964; Hebb 1949; Alkon and Nelson 1990; Kandel 1997). The most thoroughly characterized example of such synaptic plasticity is LTP.
How long will long-term potentiation last?
Authors: Abraham Wickliffe C
Published: November 2023

The paramount feature of long-term potentiation (LTP) as a memory mechanism is its characteristic persistence over time. Although the basic phenomenology of LTP persistence was established 30 years ago, new insights have emerged recently about the extent of LTP persistence and its regulation by activity and experience. It is now evident that LTP, at least in the dentate gyms, can either be decremental, lasting from hours to weeks, or stable, lasting months or longer. Although mechanisms engaged during the induction of LTP regulate its subsequent persistence, the maintenance of LTP is also governed by activity patterns post-induction, whether induced experimentally or generated by experience.
In search of general mechanisms for long-lasting plasticity: Aplysia and the hippocampus
Authors: Pittenger Christopher , Kandel Eric R
Published: November 2023

Long-term synaptic plasticity is thought to underlie many forms of long-lasting memory. Long-lasting plasticity has been most extensively studied in the marine snail Aplysia and in the mammalian hippocampus, where Bliss and Lomo first described long-term potentiation 30 years ago. The molecular mechanisms of plasticity in these two systems have proven to have many similarities. Here, we briefly describe some of these areas of overlap. We then summarize recent advances in our understanding of the mechanisms of long-lasting synaptic facilitation in Aplysia and suggest that these may prove fruitful areas for future investigation in the mammalian hippocampus and at other synapses in the mammalian brain.
Elements of a neurobiological theory of the hippocampus: the role of activity-dependent synaptic plasticity in memory
Authors: Morris R G M , Moser E I , Riedel G , Martin S J , Sandin J , Day M , Carroll C O’
Published: November 2023

The hypothesis that synaptic plasticity is a critical component of the neural mechanisms underlying learning and memory is now widely accepted. In this article, we begin by outlining four criteria for evaluating the ’synaptic plasticity and memory (SPM)’ hypothesis. We then attempt to lay the foundations for a specific neurobiological theory of hippocampal (HPC) function in which activity-dependent synaptic plasticity, such as long-term potentiation (LTP), plays a key part in the forms of memory mediated by this brain structure. HPC memory can, like other forms of memory, be divided into four processes: encoding, storage, consolidation and retrieval.
The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems
Authors: Etingof Pavel , Latour Frédéric
Published: November 2023

The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.
Background Material
Authors: Etingof Pavel , Latour Frédéric
Published: November 2023

This chapter contains well-known facts about semisimple finite-dimensional Lie algebras. For proofs the reader is referred to the standard text (Humphreys (1972)).
Intertwiners, Fusion and Exchange Operators for Lie Algebras
Authors: Etingof Pavel , Latour Frédéric
Published: November 2023

Definition 3.1 Given two representations V1 and V2 of a Lie algebra 𝔤, we can define the tensor product V1 ⊗ V2 to be the representation of 𝔤 given by the formula πV1 ⊗V2 (a) = πV1 (a) ⊗ 1 + 1 ⊗ πV2 (a) for all a ∈ 𝔤; in other words, a(v1 ⊗ v2) = av1 ⊗ v2 + v1 ⊗ av2.
Dynamical R-Matrices and Integrable Systems
Authors: Etingof Pavel , Latour Frédéric
Published: November 2023

In this chapter, we will make a connection between dynamical R-matrices and integrable systems. We start with a brief discussion of classical and quantum mechanics and of classical and quantum integrable systems.
Traces of Intertwiners and Macdonald Polynomials
Authors: Etingof Pavel , Latour Frédéric
Published: November 2023

Consider 𝔤 = 𝔰 𝔩n with weight lattice P. It is checked directly that for every symmetric polynomial f, the residue of ℳ1  f at the hyperplane x  i = x  j is zero. Hence the result.
Exploring the rates of astrolabes
Authors: Dekker Elly
Published: November 2023

In the last decade, several studies of the stars on the rates of astrolabes have been carried out. My own approach to this problem has developed considerably over the years, as I have learned from every new instrument that was studied. To date, I have investigated the rates of about fifteen instruments, and have yet to find a simple recipe for treating all of the problems that are encountered. Many more instruments have to be studied before the work that has been done so far can be systematised. For this reason, four case studies are presented in this chapter (cases I to IV) in which several problems regarding the study of the rates of astrolabes are discussed in detail.
The problem of authenticity
Authors: Cleempoel Koenraad Van
Published: November 2023

A ntique scientific instruments are part of our material and intellectual patrimony. They bear witness to an increasing understanding of natural phenomena through observation and measurement. It is, therefore, valuable to explore when, where, and by whom certain instruments were made in order to assess their standing within a known tradition and, consequently, improve our knowledge of the history and the geography of inventions and changes in man’s perception and conception of the material world. Before embarking on any such study, a historian of scientific instruments would wish to confirm that the date inscribed on a particular instrument actually coincides with the period in which it was allegedly made. Unfortunately, this is not always the case.
Convex polytopes
Authors: Webster Roger
Published: November 2023

This chapter gives a much fuller account of convex polytopes than is customary in an elementary text on convexity. Indeed, the first three chapters of the book could serve as a general introduction to convex sets with an emphasis on polytopes.
Selected topics
Authors: Webster Roger
Published: November 2023

The topics in this final chapter reflect the author ‘s own personal preferences.

The six sections are independent of one another and draw largely upon the first two chapters. Section 7.4, however, uses ideas relating to volume, such as are discussed in Chapter 6. By assuming that the familiar volume in IR3 extends naturally to IRn, the reader should have little difficulty in following this introduction to the geometry of numbers. Not all the applications of Helly ‘s theorem in Section 7.1 should be needed to show that it is one of the most versatile in the whole of convexity.
Notes on further reading
Authors: Webster Roger
Published: November 2023

General accounts of convexity are given in Eggleston (1958), Valentine (1964), Benson (1966), Roberts and Varberg (1973), Kelly and Weiss (1979), Lay (1982), and van Tiel (1984). Of these, Eggleston and Valentine can be considered graduate texts, the remaining ones (primarily) undergraduate. A comprehensive survey of the subject, written for the expert, is the two volume Handbook of convex geometry by Gruber and Wills (1993).
Universal Algebra
Authors: Dunn J Michael , Hardegree Gary M
Published: November 2023

In this chapter, we present some very general ideas from the field initiated in its modem form by Garrett Birkhoff and called by him “universal algebra. “ The fundamental notion of universal algebra is that of an algebra. Basically, an algebra is a set together with various operations that take elements of that set and yield elements of that same set. A simple, and familiar, example is the set of natural numbers together with the operations of addition and multiplication. In particular, any two natural numbers can be added (or multiplied), and the result is moreover a natural number. By contrast, the natural numbers together with the operation of subtraction do not form an algebra; for although the difference of any two natural numbers exists, it need not be a natural number. A more dramatic non-example is the set of natural numbers together with the operation of division; in particular, there is no such thing as 1 divided by 0. In the first non-example, the operation can yield a result not in the set; in the second non-example, the operation can yield no result at all.
Logic
Authors: Dunn J Michael , Hardegree Gary M
Published: November 2023

We take the view that “consequence “ (what follows from what) is the central business of logic. Strangely, this theme, clear from the time of Aristotle ‘s syllogistics, has been obscured in modem times, where the emphasis has often been on the laws of logic, where these laws are taken not as patterns of inference (relations between statements) but rather as logical truths (statements themselves). Actually it seems that Aristotle himself was at least partly responsible for starting this perverse view of logic, with his so-called three laws of thought (non-contradiction, excluded middle, and identity), but we lay the major blame on Frege, and the logistic tradition from Peano, Whitehead and Russell, Hilbert, Quine, and others. This tradition views logic along a model adapted from Euclid ‘s geometry, wherein certain logical truths are taken as axioms, and others are then deduced from these by way of a rule or two (paradigmatically, modus ponens). Along the way there were some divergent streams, in particular the tradition of nature.
Abstract logics
Authors: John P. Cleave
Published: November 2023

There are many formal logics- classical logic (already encountered in Chapter 2), intuitionistic logic, various modal and temporal logics, and numerous logics arising in various ways from applications such as the logic of automata and the logic of quantum mechanics. Moreover, there are many structures-such as context-free languages, combinatorial systems, etc.-which are sufficiently logic-like to deserve the name logic. Many logics are primarily the embodiment of some notion of truth. They are thereby mainly concerned with the generating theories-a corpus of theorems or ‘universal truths’--thus tending to obscure the view of formal logic as the science of valid inference. In Chapter 1, §1.3.2, there arose the problem of treating neutrality as if it were a truth-value. What has to be done to it to make a logic out of truth, falsehood and neutrality’? Truth-values alone do not constitute a logic. Our strategy must clearly be guided by the various extant logics. In the brief treatment of classical logic in Chapter 2 the notion of logical consequence played some part, though it was subordinate to the idea of theoremhood. But in the discussion of scientific theories in Chapter 1 special significance was given to the deductive postulate. On grounds of generality, it can be claimed that logical consequence is more fundamental than theoremhood, as all that needs to be said about theoremhood can also be stated in terms of logical consequence.
Constructing logics
Authors: John P. Cleave
Published: November 2023

An important class of logics, typified by classical logic (Chapter 2), is based primarily on a concept of truth. The logical consequence functions of such logics are derived from the interpretation of a language by structures of truth-values. These logics could therefore be called semantic logics.
Modal logics
Authors: Cleave John P
Published: November 2023

Questions about modal logic were posed by Aristotle and were thoroughly investigated by the Scholastics, but the subject seems to have been completely neglected until it acquired a new lease of life in mathematical logic, particularly through the work of McColl and Lewis. A recent nodal point in the development of the modal industry was the introduction of ‘possible world’ semantics (Kripke) which has lead to an unprecedented boom.
Finite Geometries via Algebraic Affine Buildings
Authors: Kantor’ William M
Published: November 2023

Thepurpose of this note is (1) to give a vague description of algebraic affine buildings, (2) to give a brief description of arithmetic groups, and then (3) to combine these subjects in order to discuss finite quotients of algebraic affine buildings modulo suitable arithmetic groups. is intended to be thought of in terms of matrix groups, in which entries are taken from the indicated rings.) Using G(Q) and B,an affine building .6. is obtained as follows (cf. [10]):The maximal simplexes (chambers) are j11St the conjugates of B.There are ntypes of vertices, which are the conjugates of the subgroups of matrices blocked as follows:* Supported in part by NSF grant DMS 87-01794 and NSA Grant MDA 904-88-H-2040. special amounts to the fact that the associated diagram is the extended Dynkin diagram corresponding to the Dynkin diagram of the finite group G(k); the group G(K)always contains such subgroups [10]. In the example given above, all the vertex stabilizers are special.
Local recognition of graphs, buildings, and related geometries
Authors: Cohen Arjeh M
Published: November 2023

Brief overview of results and problems concerning the local recognition f graphs is given, and special attention is drawn toward graphs related to uildings. here Xstands for the class of all grids.Although it was probably apparent to quite a few finite group theorists 1at some of the local characterization problems in the classification of finite local recognition problems for graphs. These are the two main reasons by I want to survey what is known on the local recognition problem.Much of the material in this paper can be found scattered in [BCN 989]. For notions of shadow space, point-line geometry and the like, the ader is referred to [Cob 1986].
Special Graphs
Authors: Read Ronald C , Wilson Robin J
Published: November 2023

In this chapter we depict a number of sped.al graphs:

Platonic graphs: these are the graphs formed by the vertices and edges of the Platonic solids—the polyhedra in which all the faces are identical regular polygons and where the arrangement of polygons at each vertex is the same. There are five Platonic graphs, corresponding to the tetrahedron, octahedron, cube, icosahedron and dodecahedron.

Archimedean graphs: these are the graphs formed by the vertices and edges of the Archimedean solids—the polyhedra in which each face is a regular polygon (but not all faces are of the same type) and where the arrangement of polygons at each vertex is the same; these arrangements of polygons are indicated under the diagrams. There are thirteen such graphs, and two infinite families—the prisms and the antiprisms.
Polynomials
Authors: Read Ronald C , Wilson Robin J
Published: November 2023

Spectral polynomials: we list the spectral (characteristic) polynomials of graphs, trees, cubic graphs and quartic graphs. For graphs and trees, each polynomial is presented in power form, together with its frequency and its spectrum (usually with zeroand integer eigenvalues listed first, and the remainder listed in decreasing order); for cubic and quartic graphs, only the polynomial is given.

The spectral polynomials of graphs with up to 7 vertices are listed on pages 402–419. The spectral polynomials of trees with up to 12 vertices are listed on pages 420–432. When the number of vertices is even, each spectrum number denotes two roots, one positive and one negative; when the number of vertices is odd, then there is one extra zero root. The spectral polynomials of cubic graphs with up to 14 vertices are listed on pages 433–441, and those for quartic graphs with up to 11 vertices are listed on pages 442–446.