bluuebunny/crossref_metadata_2025 huggingface dataset:
Goodness of fit
Authors: Lindsey J K
Published: November 2023

Throughout the previous chapters, we have seen various aspects of the model building process. In Chapter 3, we generally assumed that the chosen family of models, 𝒫, was suitable, and studied how to rank the relative merits of different members of that family, whether different functional forms or simply different parameter values, in the light of the observed data. We were investigating the validity of prior theoretical knowledge in the light of observed empirical data. Thus, for example, we could claim that sufficient statistics contain all the information about parameters, given the model. Now we shall be concerned more with scientific discovery, with the development of new theory. This is a further step in the model selection process which can never be a very formalized procedure. Here, we might say that the only sufficient statistic is the complete set of observations, including all details about how they were collected, because no model is correct. Thus, our approach up until now has provided little general indication of the overall goodness of fit of the (family of) models. We have already seen that any acceptable model should be applicable for previous observations (Section 3.6.4, and also Section 6.4.1). Hopefully, it should also be useful for any future ones, which will provide the ultimate check. However, we generally wish to make as many verifications as possible about the suitability of the model before these become available.
Poisson regression
Authors: Lindsey J K
Published: November 2023

To summarize the different approaches to statistical inference and decisionmaking, an analogy with practice in the medical profession may be useful. This profession has an accumulated knowledge of many diseases - the statistical models. A task of the doctor is to discover which one applies to a particular patient. When a radically new drug is developed, doctors will conduct a randomized study to compare its effect to a control group to determine what possible effects the medication has - direct likelihood inference. However, before the drug is released on the market,the hypothesis that it has no effect, or that it is inferior to existing medication, must be rejected in favour of a positive effect, optimizing a long term criteria in the population - frequentist decision-making. Once a doctor begins to use the drug on patients, information obtained from these studies can be incorporated into the diagnoses to decide what is the optimal treatment - Bayesian decision-making.
The psychotic patient
Authors: Mynors-Wallis Dr Laurence , Moore Dr Michael , Maguire Mr Jon , Hollingbery Mr Timothy
Published: November 2023

Psychotic symptoms are found in several psychiatric diagnoses: schizophrenia, delusional disorder, drug-induced psychosis, affective disorders (mania and depression) and dementia. Usually, specialist services are involved in attempting to make broad diagnostic sense of psychotic symptoms. The GP, however, has a key role to play in detecting psychotic symptoms, arranging appropriate referral, and in the continuing management of patients with chronic psychotic disorders. Details about the specific management of depressive and manic disorders, dementia and substance misuse will be found in the relevant chapters.
Parallel parietofrontal circuits for sensorimotor transformations
Authors: Caminiti Roberto , Ferraina Stefano , Battaglia-Mayer Alexandra , Mascaro, Massimo , Burnod Yves
Published: November 2023

The functional interplay between the parietal and frontal lobes is based on the operations of a continuum of cortical areas linked by reciprocal association connections. Some of these are very selective, since they connect a specific parietal area to only one specific frontal area. However, these private routes are rather uncommon. In most instances, any given parietal area is linked to a discrete number of frontal areas, and vice versa, in a gradient-like fashion.
Cerebellar motor and cognitive functions
Authors: Schmahmann Jeremy D
Published: November 2023

Cerebellar disorders typically manifest with deficits in motor control. It has become apparent that many cerebellar patients also experience changes in intellect and mood, and mounting evidence suggests that cerebellar pathology may be associated with alterations principally in mental function, rather than motor performance. There is a new realization that defining the role of the cerebellum in higher-order behavior is not only of academic interest to the fields of behavioral neurology and psychiatry, but has the potential to help explain the fundamental function of the cerebellum and to benefit patients with cerebellar diseases by devising optimal therapeutic and rehabilitation strategies.
Motor learning
Authors: Hallett Mark
Published: November 2023

Very little of human motor performance is innate, and humans certainly need to modify performance constantly to meet environmental conditions. Therefore it is obvious that motor learning is a critical mechanism of integrative physiology. Motor learning is a complex phenomenon with a number of different components and has been defined in different ways. In this chapter, it will be defined as ‘a change in motor performance with practice’. This will include a number of aspects such as increasing the repertoire of motor behavior and maintenance of a new behavior over a period of time. Motor learning is classified as a type of procedural learning, different from the more extensively studied declarative learning of facts and events (Squire 1986).
Action recognition disorders following parietal damage
Authors: Daprati Elena , Sirigu Angela
Published: November 2023

From the moment of our birth, we act in the world. Despite such a large motor experience, we have a poor subjective knowledge of the entire set of processes that underlie our motor skills. Interestingly, even if we remain largely unaware of the contents of our actions, we are usually good at judging whether an action has originated from ourselves or not. In the present chapter, we will review the putative mechanisms responsible for recognition of self-generated actions. We will suggest that the ability of an individual to perceive and visually recognize a given movement as his or her own (i.e. his or her motor awareness) relies on the opportunity to process anticipatory information on motor production as well as on the capacity to monitor motor execution online. Moreover, we will emphasize the necessity of mapping the acting limb correctly on a reliable body representation. Evidence for this hypothesis will be drawn from the study of brain-damaged subjects.
Psychogenic motor disorders
Authors: Pringsheim Tamara , Chen, Robert , Lang Anthony
Published: November 2023

Psychogenic motor disorders make up a small percentage of referrals seen by neurologists and movement disorder specialists, but present a real diagnostic and treatment challenge. Psychogenic motor disorders are disorders for which no known organic syndrome can explain the symptoms experienced by the patient, and which appear clinically to have significant psychiatric or psychological contributing or causative factors. Psychogenic motor disorders encompass a variety of disorders of motor function, such as paralysis, gait disturbance, dystonia, tremor, myoclonus, and parkinsonism.
Frontostriatal circuits and disorders of goal-directed actions
Authors: Manes Facundo , Leiguarda Ramon
Published: November 2023

The basal ganglia receive inputs from a wide variety of neocortical domains that subserve not only motor but also sensory, limbic, and associative functions (Parent and Hazrati 1995a,b). Therefore the basal ganglia process information associated with higher functions accompanying motor behaviour including learning, memory, attention, motivation, emotion, and volitional behaviour (Evarts and Wise 1984; Rolls 1994; Saper 1996; Schultz et al. 2000). The main driving force of the basal ganglia is the frontal cortex.
Introduction
Authors: Graham Philip
Published: November 2023

Now that women have been liberated, the grey power of the elderly has been asserted, racism is publicly ostracized, and facilities for the disabled are legally required in all public places, the teens have become the last group whose disempowerment is invisible because it is so much taken for granted. In many ways, of course, the teens are only too visible—they are always making the headlines. But too often these merely confirm their stigmatized position in society. The word ‘adolescent ‘ has again become, as it has in the past, a term of condescending mockery. In this book I have tried to take a critical look at the way western society thinks about and treats those in their teen years. I have then gone on to suggest ways in which the adult world might rethink its attitudes to the young so that they are more in line with the way they think and behave rather than with the way those in the media and even sometimes those who write textbooks make them out to be.
Orders
Authors: Reiner I
Published: November 2023

Throughout this chapter let R denote a noetherian integral domain with quotient field K, and let A be a finite dimensional K-algebra. Our aim here is to define orders, and to develop some of their basic properties. In later chapters we shall concentrate on maximal orders. Usually R will be a Dedekind domain, or at the very least, an integrally closed domain (see (1.12)), but occasionally theorems will be stated for the general situation in which R is only assumed to be noetherian.
Maximal orders in skewfields (local case)
Authors: Reiner I
Published: November 2023

Throughout this chapter, let R be a complete discrete valuation ring, that is, R is a principal ideal domain with a unique maximal ideal P = ᚂR ≠ is complete relative to the P-adic valuation.
Language elements
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

Written prose in a natural language, such as an English text, is composed firstly of basic elements — the letters of the alphabet. These are combined into larger entities, words, which convey the basic concepts of objects, actions, and qualifications. The words of the language can be further combined into larger units, phrases and sentences, according to certain rules. One set of rules defines the grammar. This tells us whether a certain combination of words is correct in that it conforms to the syntax of the language, that is those acknowledged forms which are regarded as correct renderings of the meanings we wish to express. Sentences can in turn be joined together into paragraphs, which conventionally contain the composite meaning of their constituent sentences, each paragraph expressing a larger unit of information. In a novel, sequences of paragraphs become chapters and the chapters together form a book, which usually is a self-contained work, largely independent of all other books.
Specification statements
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

In the preceding chapters we have learnt the elements of the Fortran language, how they may be combined into expressions and assignments, how we may control the logic flow of a program, how to divide a program into manageable parts, and have considered how arrays may be processed. We have seen that this knowledge is sufficient to write programs, when combined with a rudimentary print statement and with the end statement.
Floating-point exception handling
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

Exception handling is required for the development of robust and efficient numerical software, a principal application of Fortran. Indeed, the existence of such a facility makes it possible to develop more efficient software than would otherwise be possible. The clear need for exception handling, something that had been left out of Fortran 95, led to a facility being developed on a ‘fast track’ as a Technical Report,1 suitable for immediate implementation as an extension to Fortran 95. In this chapter, we describe the extensions to Fortran 95 that were detailed in this Report and which are all now part of Fortran 2003. We also describe the few related Fortran 2003 features that were not in the Report, with a clear indication of this in each case.
Enhanced module facilities
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

The module facilities of Fortran 95, while adequate for programs of modest size, have some shortcomings for very large programs. The extent of these shortcomings was not properly appreciated when the main features of Fortran 2003 were chosen and a straightforward solution was not devised until the development of Fortran 2003 was nearly complete. Therefore, instead of risking a delay to the whole of Fortran 2003, it was decided to define the submodule feature as an extension in a Technical Report,1 with the promise that the next revision of Fortran would include it, apart from correcting any defects found in the field. Since the formal approval procedures for a Technical Report are simpler than those for a Standard, we expect its final approval and publication to take place at about the same time as the Standard.
Input/output enhancements
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

In this chapter, we explain the enhancements to input/output processing that have been made in Fortran 2003. Non-default derived-type input/output (Section 19.2) allows the programmer to provide formatting specially tailored to a type and to transfer structures with pointer components. Asynchronous input/output (Sections 19.3 and 19.4) has been available as compiler extensions for many years and is now standardized. Since the advent of IEEE arithmetic many compilers have provided facilities for input/output of the exceptional values; this is now standardized (Section 19.5). Stream access (Section 19.6) allows great flexibility for both formatted and unformatted input/output. The remaining sections detail miscellaneous simple enhancements.
Missed diagnosis in myotonic dystrophy: frequency, characteristics, consequences, and how to prevent it
Authors: Eymard Bruno , Dobon I
Published: November 2023

Myotonic dystrophy is one of the most frequent muscular dystrophies in adults, with a prevalence of around of 5 per I 00 000 (Harper and Rudel 1994). The clinical features include myotonia, distal weakness and systemic symptoms (cataract, atrio-ventricular block, dysrhythmias, endocrine dysfunction, mainly diabetes, and central nervous dysfunction). The diagnosis is theoretically easy for physicians if considered in the context of autosomal dominant inheritance, with a characteristic combination of muscular and extramuscular signs (Harper 2001 ). However, the diagnosis of myotonic dystrophy can be problematic for the following reasons: (I) difficulty in identifying specific symptoms as myotonia; (2) prominent systemic manifestations requiring initial advice from specialists other than neurologists; and (3) the occurrence of neonatal and infantile forms of myotonic dystrophy that may have a very atypical clinical presentation, with mental retardation and facial dysmorphy, whereas classical signs such as myotonia and distal weakness are absent before adolescence or early adulthood. In this chapter, our objective is to describe the features of misdiagnosis in myotonic dystrophy: the frequency of misdiagnosis, the nature of unrecognized symptoms, the categories of physicians involved, and the consequences of ignored diagnosis. First we present the French experience concerning a series of myotonic dystrophy patients assessed for missed diagnosis. Principles of a strategy for a proper and early diagnosis are proposed in the second section. Unless stated otherwise, all information given here refers to patients with the CTG expansion mutation.
Genetic counselling and genetic testing in myotonic dystrophy
Authors: Harper Peter S , Brunner Han G
Published: November 2023

Genetic counselling is undoubtedly one of the most important aspects of management for patients with myotonic dystrophy and their relatives. Initial diagnosis of the disorder in one person almost invariably leads to the recognition that other family members are at risk, or even affected, with a series of concerns and queries regarding their own status and the risks for their existing or future children, even if these concerns are not immediately raised or expressed.
Rural service delivery
Authors: Neese Jane B
Published: November 2023

To provide a thorough examination of psychogeriatric service delivery, this chapter presents a review of rural mental health, barriers and service delivery issues related to the older adult population. This chapter focuses on the United States and many of the issues identified are relevant to rural areas in other countries, but there are also likely to be differences. The term ‘rural ‘ carries many definitions depending upon the academic institution, politicians and country. According to Coward and colleagues ( 1994), an acceptable definition of rural has been elusive. Most traditional methods of identifying rural areas are based on population size, sparseness of towns, remoteness or distance to urban resources, degree of economic activity and commuting pattern (Magilvy et al., 1994).
The future of psychogeriatric services
Authors: Draper Brian , Brodaty Henry , Melding Pamela
Published: November 2023

What are going to be the key issues that shape psychogeriatric service delivery over the next few decades? In this chapter we will address this question from different perspectives ranging from developing countries to developed countries, from health policy considerations to specific new treatments and technology, and from ethics to economics. As described by John Snowdon and Tom Arie in Chapter I, psychogeriatrics is a young discipline with a formal history of only about 50 years. Much, however, can be learnt from this brief history when considering the future.
Evidence Supporting The Use Of Problem-Solving Treatment
Authors: Mynors-Wallis Dr Laurence
Published: November 2023

Problem-solving can be defined as the process by which an individual attempts to identify effective coping skills for specific problematic situations in everyday living. Problems are those situations for which an immediate and easily recognisable solution is not apparent. The impact of these problems upon an individual’s psychological functioning depends on their particular circumstances. An individual’s personal coping skills form a link between problems and whether psychological symptoms develop. These coping skills are the result not only of personality and previous experience, but also may fluctuate depending on whether the individual is suffering from a psychological illness. The appraisal of problems as challenging or threatening, and the individual’s self-perception as possessing robust or fragile coping skills, will also play a part in whether problems lead to the development of psychological symptoms.
The Seven Stages Of Problem-Solving Treatment
Authors: Mynors-Wallis Dr Laurence
Published: November 2023

Problem-solving treatment is a structured and focused treatment. There is an emphasis on getting the patient to quickly engage in activities which will bring about some early successes with the difficulties that they face. The challenge for the therapist is to facilitate the necessary patient activity and sense of achievement, without the patient feeling rushed and pushed into tasks for which they do not feel committed or adequately prepared. When patients, who have been treated with problem-solving, are asked what was helpful about the treatment, they identify not only the fact that they were helped to solve problems in a clear and structured way, but also that the therapist listened to their difficulties and helped to order their thoughts appropriately. The structure and focus of problem-solving treatment, therefore, must take place within a therapeutic context in which the patient feels supported and able to explain their thoughts and feelings.
Methodology and implementation of systematic reviews
Authors: McQuay H J
Published: November 2023

Systematic reviews and large randomized trials constitute the most reliable sources of evidence we can muster (Table 2.1). Put simply, they are the best chance we have to determine what is true. We discuss how to find trials, and how to appraise their quality. Further on there is advice on how to appraise the quality of systematic reviews themselves. The randomized controlled trial (RCT) is the most reliable way to estimate the effect of an intervention. The simple principle of randomization is that each randomized patient has the same probability of receiving any of the interventions being compared. Randomization abolishes selection bias because it prevents investigators influencing who has which intervention. Randomization also helps to ensure that other factors, such as age or sex distribution, are equivalent for the different treatment groups. Inadequate randomization, or inadequate concealment of randomization, lead to exaggeration of therapeutic effect.
Prophylactic drugs II: discussion summary
Authors: Schoenen J
Published: November 2023

The presentations, posters, and discussion during this session devoted to beta-blockers, amine antagonists, and antiepileptic drugs confirmed well-known concepts and provided some novel insights in migraine prophylaxis. Regarding trial methodology, it was pointed out that the outcome measure ‘migraine periods’ which covers the total duration of a migraine attack does not add much to ‘migraine attacks’ and ‘migraine days’ proposed in the IHS guidelines for clinical trials. Referring to valproate studies, attention was drawn to the fact that some cross-over studies, such as the Danish one, were superior in statistical power than certain large trials on parallel patient groups.
Antidepressants: mechanisms of action
Authors: Richelson E
Published: November 2023

Antidepressants, particularly tricyclic antidepressants, are widely used for the pro phylaxis of migraine headaches. In fact, the tricyclic antidepressant amitriptyline is reported to be the second most prescribed antimigraine drug, with propranolol being the first. In addition, amitriptyline is the only antidepressant for which there is consistent reports of efficacy for the prevention of migraine headaches, although 11 other antidepressants have been recommended for use. Interestingly, although their effects in the prophylaxis of migraine headaches appear to be unrelated to effects in treating depression, the general theoretical mechanisms of action involved in treating these two diseases are thought to be similar. That is, the down-regulation of certain receptors for serotonin (5-hydroxytryptamine or 5-HT) may play a role.. However, the serotonergic receptors that are down-regulated may be different for preventing migraine headaches than for treating depression.
Antagonizing peripheral sensitization in migraine
Authors: Bolton S , O’Shaughnessy C
Published: November 2023

Migraine is an episodic brain disorder characterized by attacks of throbbing head pain and sensitization of the cutaneous facial skin. Current research indicates that the dural blood vessels and their neural connectivity with the trigeminocervical complex play a fundamental role in the generation of these symptoms. As such, characterization of this pathway may provide an insight into the pathological processes occurring during a migraine attack and offer new targets for the development of novel anti-migraine treatment strategies. Utilizing various experimental techniques such as in vivo electrophysiology, intravital microscopy and fos immunohistochemistry, several studies have explored the consequences of trigeminal primary afferent neuronal activation both under ‘normal’ conditions and during sensitized conditions.
Migraine Prophylaxis With Drugs Influencing The Angiotensin System
Authors: Stovner L J , Tronvik E , Schrader H , Helde G , Sand, T , Bovim G
Published: November 2023

Various antihypertensive drugs have proven effective in migraine prophylaxis, most notably some of the -blockers and a calcium antagonist (flunarizin). Contraindications and side effects do, however, limit their use. Angiotensin converting enzyme (ACE) inhibitors and angiotensin II (All) receptor inhibitors are extensively used for both hypertension and cardiac failure, and with a very favourable side effect profile. A small open study with ACE inhibitors from 1995 indicated efficacy against migraine, and a meta-analysis involving 12 000 patients who were treated with an All receptor blocker for other conditions, but in whom headache was registered, indicated that the risk of headache was about one-third lower compared with those taking placebo. In addition, we tried on selected migraine patients first the ACE inhibitor lisinopril and later the All blocker candesartan, and these trials also indicated a prophylactic effect. For these reasons, our group con ducted two studies with almost identical designs, first with lisinopril (in 1999-2000), and later with candesartan cilexitil (in 2001-2002) for migraine prophylaxis.
What is the mechanism of action of ACE inhibitors in migraine prophylaxis?
Authors: Peatfield R
Published: November 2023

Cough is a common side effect of angiotensin converting enzyme(ACE) inhibitors. It is believed to be due to the inhibiting effect of these drugs on bradykinin metabolism, and in the management of hypertension it can be circumvented by substituting angiotensin II receptor blocking drugs, which control the blood pressure without inducing cough. I report a patient with frequent intractable migraine, who proved unresponsive to most prophylactic drugs and had side effects when on the only ones that influenced his migraine. He responded well to lisinopril, though the drug induced an unacceptable cough, and when losartan was substituted, his cough soon settled but the migraine recurred.
New targets I: discussion summary
Authors: Olesen J
Published: November 2023

Two posters from France demonstrated the potential of modern techniques for studying agonist receptor interaction and the subsequent intracellular cascade of events using dihydroergotamine (DHE). This substance is a 5-HT1A receptor agonist, a mechanism known to give antianxiolytic effects. The effect was shared with the main metabolite of DHE. DHE is also a potent agonist at 5-HT1B and 5-HTD receptors. At the 5-HT2B receptor both DHE and its metabolite induce desensitization, which perhaps could be responsible for its prophylactic effect. DHE is also a 5-HT7 receptor antagonist. Thus, DHE seems to have all the desired properties of a universal antimigraine agent in relation to the 5-HT receptors. Nevertheless, it is a fairly poor prophylactic agent as was illustrated by a large double-blind study, presented as a poster, that showed no significant difference between active and placebo.
Calcitonin gene-related peptide and migraine
Authors: Doods H , Just S , Schindler M , Eberlein W , Engel W , Rudolf, K , Arndt K
Published: November 2023

Although the so-called triptans are efficacious and are generally well-tolerated drugs for the treatment of migraine headache, there is still a need for improvement of migraine therapy. The relatively low number of patients becoming pain free in addition to the relatively high number of patients experiencing a recurrence of headache and lacking consistency of relief, together with the potential for cardio vascular adverse effects, reflect the limitations of the triptans as the present therapeutic standards. Since the introduction of triptans to the market, several other treatment approaches targeting different aspects of migraine pathogenesis have reached clinical status, but most of them failed or showed no real therapeutic advantage.
The prostaglandin-E1-analog misoprostol in the prophylactic treatment of refractory cluster headache and trigeminal neuralgia
Authors: Evers S , Frese A , Schwaag S , Lttmann, R , Husstedt 1.-W
Published: November 2023

Chronic cluster headache is a severe disease extremely affecting the quality of life. In many cases, the common prophylactic treatment options are unsatisfactory and do not lead to a continuous freedom from pain. Trigeminal neuralgia is a rare, although typical, brainstem symptom of multiple sclerosis (MS) occurring in about 2 % of all MS patients. In most cases, the semiology of this type of trigeminal neuralgia cannot be differentiated from the idiopathic form of trigeminal neuralgia and the principles of treatment are similar for both types. The pathophysiology of trigeminal neuralgia associated with MS is not fully understood. It has been suggested that demyelinating plaques in the entry zones of the trigeminal roots are responsible for the lancinating pain by ephaptic conduction. Inhibition of T-cell functions by prostaglandins could be a mechanism to decrease their inflammatory activity in the plaques and, thus, could be a specific therapy of this type of trigeminal neuralgia.
Long-Term Illness as a Journey
Authors: Campling Frankie , Sharpe Michael
Published: November 2023

Long-term illness can be thought of as a journey, which started when you first noticed symptoms or when you were given a diagnosis. Diagnosis can be such an important part of your journey that it is worth looking more closely at what it might mean to you.
Managing disease
Authors: Campling Frankie , Sharpe Michael
Published: November 2023

If your illness is associated with a disease, part of managing your illness is to manage your disease. This requires that you get the right disease diagnosis, obtain and accept treatment for it, and monitor your progress. For a long-term illness, treatment for the disease almost always involves the people who are suffering from it taking an active part. For example, in diabetes, people have to check their blood sugar themselves and use diet, insulin or medicine appropriately. How well this is done influences not only how well you feel, but also the progress of the disease itself. Managing disease on an on-going basis is an essential part, though only a part, of managing your illness.
The epidemiology and aetiology of malignant mesothelioma
Authors: King J E , Hasleton P S
Published: November 2023

Introduction

Malignant mesothelioma is a primary tumour of the serosal membranes (mesothelium) which line the thoracic and abdominal cavities. It is most commonly described in the pleura, which accounts for approximately 75 per cent of cases in most series, but can also arise in the peritoneum, pericardium, and tunica vaginalis.
Viral factors in the pathogenesis of malignant mesothelioma
Authors: Powers A , Bocchetta M , Carbone M
Published: November 2023

Simian virus 40 (SV40) is a DNA tumour virus endogenous to Asian macaques that was first isolated in1960. Early studies demonstrated that the virus was highly oncogenic when injected into rodents and was capable of transforming cells from many species in tissue culture. Since then it has been used extensively in medical research because of its potent transforming ability.
Novel therapies for mesothelioma
Authors: Blackhall F , Fennell D , Baka S , Danson S , O’Byrne K , Ranson M
Published: November 2023

Malignant mesothelioma presents a major therapeutic challenge and new approaches are urgently required. Considerable progress has been made in understanding the molecular pathogenesis of cancer over recent decades. Despite the unique aetiology and clinical behaviour of mesothelioma compared with other common cancers, many of the molecular characteristics are shared. Malignant cell growth has been eloquently summarized as six essential alterations in cell physiology [1]: self-sufficiency in growth signals, insensitivity to antigrowth signals, evasion of programmed cell death (apoptosis), limitless replicative potential, sustained angiogenesis, and ability to metastasize.
Risk estimation in breast cancer
Authors: Evans D Gareth R , Kerr Bronwyn , Lalloo Fiona
Published: November 2023

Breast cancer is the most common form of cancer affecting women. One in nine to twelve women will develop the disease in their lifetime in the developed world. Every year 39 000 women develop the disease in England and Wales (population 55 million) and as a result, 13 000 will die (Cancer Research Campaign Statistics). While the gen- eral population risk of breast cancer that is widely quoted of 1 in 10, is a lifetime risk, the risk in any given decade is never greater than 1 in 34. This needs to be considered in the context of death rates from other causes (1) (Table 5.1).
A rough history of logic
Authors: Bornat Richard
Published: November 2023

You don’t need to know history in order to understand modern formal logic, but a glimpse of history can help you to understand why formal logic is the way it is, and how it fits with the study of computer science. So I begin with a historical tale.
Rule shapes and formula shapes
Authors: Bornat Richard
Published: November 2023

The inference rules of Natural Deduction are patterns, shapes, schemes which you can use to make particular proof steps. You use a rule scheme to make an instance that suits your needs.
The logical quantifiers
Authors: Bornat Richard
Published: November 2023

So far we have been able to deal with logical claims about particular things: claims about somebody called Richard, claims about the name Richard, claims about Richard being a cabbage and/or a Martian. We haven’t yet been able to relate claims about generalities to claims about particulars.
Constructive semantics
Authors: Bornat Richard
Published: November 2023

The model itself is due to Saul Kripke, and it relates formal proof to real-world reasoning in very much the way that programming relates to reality: there are things we can do (claims we can prove), things we can’t do (claims we can disprove) and things we’re still trying to do (claims we can only speculate about).
Disproof calculation
Authors: Bornat Richard
Published: November 2023

The proof strategy of Part II is almost a mechanical procedure, in which the discovery of a proof is driven by the shape of the formulae and some simple slogans. Disproof, especially constructive disproof, doesn’t seem to be so straightforward.
Gödel incompleteness
Authors: Kaye Richard
Published: November 2023

This chapter is devoted to the proof of Godel’s first incompleteness theorem for recursively axiomatized theories extending PA−. Godel’s theorem is often considered because of its role in foundational issues in mathematics (in this context the first incompleteness theorem tells us that ‘arithmetic truth is not axiomatizable’). We shall be also interested in it for a different reason: the incompleteness theorem, in conjunction with the completeness theorem, equips us with a rich supply of interesting models. The techniques we employ, such as the representability of recursive functions in PA- and the diagonalization lemma, will also yield other well-known and interesting results in logic, such as Tarski’s theorem on the undefinability of truth and Godel's second incompleteness theorem.
Some number theory in PA
Authors: Kaye Richard
Published: November 2023

We will now start developing number theory in PA. One of our main goals is to prove a version of the Chinese remainder theorem. This will enable us to prove Godel’s lemma (Lemma 3.2) for arbitrary models of PA. As an application we will show how to derive Euclid’s theorem on the infinitude of the primes in PA. (This theorem, coincidentally, is the first ‘real’ mathematical theorem that Hardy proves in his Apology!) In fact, equipped with Godel’s lemma, the reader will see that it is routine to transcribe the proofs of many theorems in number theory into PA.
Prime models
Authors: Kaye Richard
Published: November 2023

If T is a complete consistent extension of PA there is a ‘smallest’ model of T having some very pleasant features. This chapter is about these models and the various ways in which they can be regarded as ‘small’. Section 8.2 contains an application (the famous MacDowell-Specker theorem) showing that any countable model of PA has an elementary end-extension.
Saturation
Authors: Kaye Richard
Published: November 2023

Recall from Chapter 8 that, given a theory T, a type over T is a set p(x) of formulas in finitely many free-variables x such that T⋃ p(x) is consistent. If M⊂T then the type p(x) is either realized or omitted by M, and there is always some model of T that realizes p(x). Chapter 8 showed that the models KT(for complete extensions T of PA) omit as many types as possible. In this chapter we shall look at those types that are realized in nonstandard models of PA.
The standard system
Authors: Kaye Richard
Published: November 2023

If M is a nonstandard model of PA, its ‘memo-pad’ is its standard system of of sets A⊆ℕ that are coded in M. In particular we can consider computations that consult this memo-pad to determine whether or not a given integer n is in some A ∈ SSy(M). In this chapter we shall investigate the structure of these standard systems further: in particular we will find certain closure conditions that characterize them exactly. This will allow us to construct models with a given standard system, and in Chapter 14 we will use these ideas together with the embedding theorems of the last chapter to construct new interesting initial segments.
Introduction
Authors: Pinch Enid R
Published: November 2023

The shortest distance between two points in a plane is obtained by drawing the straight line that joins them. The circle is the shape that encloses maximum area for a given length of perimeter. These well-known facts were known to the Ancient Greeks and are the oldest known solutions in the class of problems discussed in what we now call optimization theory. But, although the Greeks’ geometrical insight gave them the answers to a few problems in this field, it was not until the eighteenth century that a systematic theory began to emerge. That the theory of optimization continues to be an area of active research for mathematicians is an indication both of the inherent beauty of the subject and of its relevance to modern developments in science, industry and commerce.

Our aim is to understand the theory of optimal control, an area developed since the 1950s in response to American and Russian efforts to explore the solar system. The mathematical problems of space navigation include optimization problems. One wishes to construct trajectories along which a space vehicle, controlled by a small rocket motor, will reach its destination in minimum time or using the minimum amount of fuel. These new problems were not soluble by the methods that were currently available and the theory, whose roots lay back in the eighteenth century, had to be extended to meet the new challenge.
Submanifold theory
Authors: Willmore T J
Published: November 2023

In this chapter we shall consider the immersion of a manifold M into a Riemannian manifold (N, g), and examine the structures on M induced from the given structure on N. This is a natural generalization of the study of surfaces in Euclidean 3-space with properties induced from the Euclidean metric-which was the origin of the classical theory of surfaces.
Special Riemannian submanif olds
Authors: Willmore T J
Published: November 2023

We shall begin by studying the very special case of Willmore surfaces immersed in Euclidean 3-space. Even here there remain many unsolved problems. My interest in the subject dates from the early 1960s when I gave several talks on the topic at the Mathematical Institute, Ober- wolfach, Germany. This was followed by my first paper on the topic, Willmore (1965).
Eigenvalue problems with indefinite weights and reaction-diffusion models in population dynamics
Authors: Cosner Chris
Published: November 2023

The object of this article is to illustrate how the theory of linear elliptic eigenvalue problems with indefinite weight functions can be used to analyze reaction-diffusion models in mathematical ecology and population genetics. It is not intended to be a comprehensive survey, but rather an introduction to some of the principal ideas and methods. Reaction-diffusion equations arise in ecological modelling when nonlinear dynamics describing the growth or decline of a population are combined with a diffusion process describing the spatial dispersal of that population. Solutions to the reaction-diffusion models typically represent population densities, or in related problems of population genetics, the distribution of certain alleles within a population.
Network Reliability and Algebraic Structures
Authors: Shier Douglas R
Published: November 2023

Networks of computer systems, distribution systems, and telecommunication systems play an increasingly important role in our lives. This book is concerned with analysing and assessing the reliability of such networks whose components are prone to possible failure. The field of network reliability has expanded rapidly to provide various mathematical models and computational procedures. In this book the emphasis is on identifying a number of algebraic structures that serve to unify the study of networks, and to suggest new techniques and procedures for analysing the probabilistic behaviour of networks. Consequently, amongst the topics covered are pseudopolynomial algorithms, lattice structures, spaces of polynomials, reliability covering problems, and stochastic path problems. The result is a book which will be an invaluable account of the subject for all mathematicians, computer scientists, reliability engineers, and operations researchers whose work touches on network reliability.
Overview of network reliability
Authors: Shier Douglas R
Published: November 2023

The broad theme of reliability theory is the study of the overall performance of a system comprising failure-prone elements. That is, the components of the system are not perfect in operation, but their failure is assumed to be governed by certain probabilistic laws. It is thus of interest to describe the stochastic behavior of the system in terms of the given stochastic characteristics of its components. Not only are the reliabilities of individual components of importance, but the manner in which they are assembled can have a significant influence on the overall performance of the system. For example, as noted over thirty years ago by Moore and Shannon (1956), it is possible to obtain a reliable system by properly configuring unreliable components through the use of redundancy.
An algebraic formulation of network reliability problems
Authors: Shier Douglas R
Published: November 2023

This chapter presents an algebraic approach for studying network reliability problems, concentrating, in particular, on the calculation of R(G). Instead of working with numerical quantities (probabilities), the emphasis is on algebraic objects (polynomials) and their appropriate transformation. This algebraic perspective not only provides a unifying theoretical framework for studying network reliability problems, but also suggests a number of new algorithmic approaches. We will see, in particular, that several standard linear algebraic techniques can be readily adapted to solve network reliability problems. In this case, however, symbolic manipulations rather than numerical calculations will be carried out. The symbolic form of the resulting answer is especially useful in conducting sensitivity analyses, since the change in overall reliability with changes in component reliabilities can be directly ascertained from this form.
Planar nearrings
Authors: Clay James R
Published: November 2023

In the summer of 1967, the author hoped to discover some geometric interpretations for nearrings. Since planar nearfields had already proven useful to geometry, he hoped that planarity could be extended to nearrings which were not nearfields. After the author developed a suitable concept for planarity for nearrings, Michael Anshel constructed numerous examples in which the algebraic structure of planar nearrings had nice geometric interpretations. Some of these original examples provide the motivation for much of what is being done, and has been done, in planar nearrings. Almost concurrently, Giovanni Ferrero was concerned with constructing finite integral nearrings. It turned out that his nearrings were planar. Ferrero then gave a new and very important direction to the study of planar nearrings. Parallel to the geometric interpretation of the algebraic structure of Anshel’s examples, Ferrero showed that some finite planar nearrings could be used to construct new balanced and partially balanced incomplete block designs. He suggested that these might be useful for coding theory, and his insight has proven to be prophetic.
Parallel and Sequential Methods for Ordinary Differential Equations
Authors: Burrage Kevin
Published: November 2023

This book presents an up-to-date exposition of the current `state of the art' of numerical methods for solving ordinary differential equations in a parallel computing environment. Although the main focus is on problems of initial value type, consideration will also be given to boundary value problems and partial differential equations. Furthermore, because linear algebra is an important component of the solution of differential equations, a complete chapter is devoted to the parallel solution of linear systems of equations. In addition to presenting an overview of parallel computing in general, two chapters are devoted to a summary of existing sequential differential equation methods. The parallel techniques discussed include parallelism across the method, parallelism across the step, parallelism across the system, and dynamic iteration. The book concludes with a chapter on the behaviour of a parallel code based on waveform relaxation. This comprehensive book is unique in its content and provides a balance between theoretical and practical issues by providing general frameworks in which to study parallel methods.
Patterns, related to rational numbers; periodic decimal fractions, repunits, and visible lattice points
Authors: Cofman Judita
Published: November 2023

Numbers expressible as fractions a/b, where a and bare integers and b > 0, are called rational numbers. Each rational number can be expanded as a decimal fraction (e.g. 2/5 = 0.4, 5/3 = 1.666 ... ) with either a finite or infinite number of decimal places. In Sections 3.1 and 3.2 we shall study sequences of digits in decimal expansions of rational numbers; we shall also deduce a divisibility criterion for repunits - important numbers in computer science and coding theory.
Two famous inequalities and some related problems
Authors: Cofman Judita
Published: November 2023

We shall focus attention on two classical inequalities, with vanous applications in modern mathematics: The isoperimetric theorem has a long history. It was formulated more than 2000 years ago; however its first rigorous proof was carried out as late as the nineteenth century. All known proofs of the isoperimetric theorem are far from elementary and cannot be presented in this book. We shall limit ourselves to giving a brief outline of the ideas behind the proof suggested by Jacob Steiner (1796-1863) and corrected by Karl Weierstrass (1815—1897). This will be done in Section 6.3. This section contains a number of problems dealing with special cases of the isoperimetric theorem.

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‘Mysteries’ of the third dimension: on cubes, pyramids, and spheres
Authors: Cofman Judita
Published: November 2023

Is it possible to double the cube - that is, to construct with compasses and straightedge the edge of a cube the volume of which. is twice that of a given cube? Are any two pyramids with congruent bases and congruent corresponding heights equidecomposable? (In other words, is it possible to dissect one of them into finitely many polyhedra, which can be assembled to form the other pyramid?) Can thirteen congruent solid spheres touch simultaneously a given sphere of the same size? The above questions became famous because they occupied mathematicians for centuries; finally they could be answered each of them with a ‘no’.