Reaction-diffusion systems which have reaction term satisfying f(-q) = -f(q) tend strongly to form striped patterns. Haken’s slaving principle is used to derive differential equations for unstable mode amplitudes close to the Turing instability. This connects a dynamical symmetry to pattern selection, with possible relevance to biological and chemical pattern-forming phenomena.

We present a technique for the analysis of pattern formation by a class of models for the formation of ocular dominance stripes in the striate cortex of some mammals. The method, which employs the adiabatic approximation to derive a set of ordinary differential equations for patterning modes, has been successfully applied to reaction-diffusion models for striped patterns [1]. Models of ocular dominance stripes have been studied [2,3] by computation, or by linearization of the model equations. These techniques do not provide (...) a rationale for the origin of the stripes. We show here that stripe formation is a non-linear property of the models. Our analysis indicates that stripe selection is closely linked to a property in the dynamics of the models which arises from a symmetry between ipsilateral and contralateral synapses to the visual cortex of a given hemisphere. (shrink)

Development of the shapes of living organisms and their parts is a field of science in which there are no generally accepted theoretical principles. What form these principles are likely to take, when they emerge, is a subject in which there is a wide gulf of disagreement between physical scientists and experimental biologists. This book contains both an extensive philosophical commentary on this dichotomy in views and an exposition of the type of theory most favoured by physical scientists. In this (...) theory living form is a manifestation of the dynamics of chemical change and physical transport or other physics of spatial communication. The reaction-diffusion theory, as initiated by Turing in 1952 and since elaborated by Prigogine and by Gierer and Meinhardt among others, is discussed in detail at a level that requires a good knowledge of a first course in calculus, but no more than that. The great growth of molecular biology has tended to overshadow the increase in our understanding of the nature of these kinetic processes. This book seeks to reawaken interest in dynamics in the hope that a better balance between the importance of things and the importance of actions may emerge in the biology of the 21st century. (shrink)

This paper argues that professionals who make boundary-related decisions should be guided by relationship-based practice. In our roles as service users and professionals, drawing from our lived experiences of professional relationships, we argue we need to move away from distance-based practice. This includes understanding the boundary stories and narratives that exist for all of us – including the people we support, other professionals, as well as the organisations and systems within which we work. When we are dealing with professional boundary (...) issues, we should centre relationship-building skills that are central to many other aspects of our work. Skills that foster relationships at all levels – between professionals, service users, and services – need to be revalued. Our final recommendation is to create, develop, and foster safer spaces within and outside of organisations, as well as inter-professionally, for the discussion and exploration of boundary-related issues and practice. We are interested in hearing from those with experiences of being marginalised by boundaries so that they can inform a reshaping of our collective ideas around boundary related practices. To foster relationship-based practices in organisations, we have outlined several recommendations here; however, we recognize that these do not go far enough, and that collective action is needed to inform systemic change. (shrink)

These essays offer a fascinating and lively synopsis of the work of some of the most important thinkers in Britain today. The authors represent a wide cross-section of BritainÕs current philosophical spectrum, resulting in a stimulating intellectual profile of the leaders of a community which dominated Western philosophy for much of the twentieth century. What makes a man or woman a philosopher? What are the new directions being pursued by British philosophy today? How do philosophers see their own development, and (...) what are the roots of their distinctive contributions? What are the major problems which preoccupy British philosophers today? The distinguished philosophers who have contributed to this book address these questions as well as other topics of interest. All have provided brief 'intellectual autobiographies,' including sketches of their individual concerns and how those concerns have developed throughout their careers. (shrink)

Two general features of metameric patterning in Drosophilaare considered: (1) maintenance of a constant number of metameres (segments or parasegments) in the face of variation in length of the embryo; (2) expression of pattern by on‐off switchings of particular genes, with only three or four rows of cells to each element of pattern. For each of these features, the general strategic question is raised: could reaction‐diffusion theory account for this? In both cases, it is answered affirmatively. For the second feature, (...) this review contains some hitherto unpublished computer simulations by one of us (K. Y. T.), illustrating that a reaction‐diffusion mechanism can be transformed into a patterned switching mechanism by nothing more than compartmenting of the diffusion region. For the scale of three compartments to one pattern repeat unit (representing three rows of cells to a segment) the switching pattern predicted by computation is two‐off to one‐on. This resembles the pattern of expression of the engrailed gene, posteriorly localized in each segment. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Theologian's Doubts:Natural Philosophy and the Skeptical Games of GhazālīLeor HaleviIn the history of skeptical thought, which normally leaps from the Pyrrhonists to the rediscovery of Sextus Empiricus in the sixteenth century, Abū Ḥāmid Muḥammad al-Ghazālī (1058-1111) figures as a medieval curiosity. Skeptical enough to merit passing acknowledgment, he has proven too baffling to be treated fully alongside pagan, atheist, or materialist philosophers. As a theologian defending certain Muslim (...) dogmas, Ghazālī has not met what historians consider the mark of the true skeptic, a mind doubting the possibility of all systems of knowledge. But what is fascinating about him is that he brought into practical operation the tools of what I call "functional skepticism."1He denied the claims to truth of Aristotelian physics—whose basis he showed to rest on groundless belief—then turned and argued for the possibility of the Resurrection tooth and nail. The scholarly debate on The Incoherence of the Philosophers (Tahāfut al-falāsifa) has concentrated on the extent to which Ghazālī qua Ashcarite theologian was seduced into Aristotelian philosophy despite himself.2 In my view this debate has been misguided in the attempt to distill the [End Page 19] essence of Ghazālī from the book's eclectic theology; I will argue for a different view of Ghazālī on the basis of a close reading of key passages. In the unusual sections where Ghazālī applies Aristotelian language to a world not following the ordinary laws of physics, some have found Ghazālī slipping, unconsciously perhaps, into an Aristotelian frame of mind. I will show that, as a skeptical theologian with a dialogic imagination, he was rather deconstructing Aristotelian discourse while playing a Wittgensteinian sort of language game.Natural Philosopher or Speculative Theologian?The disagreement about the extent to which philosophy infected Ghazālī is ancient. Ghazālī might have studied philosophy only in order to refute it. He himself defended his philosophizing with the claim that one cannot deconstruct a system of thought until one has understood it so deeply as to elaborate upon its fundamental principles.3 His Maqāṣid al-falāsifa was in fact received, especially in trans-Pyrenean Europe, as a philosopher's genuine summary of the object of philosophy.4 The book strikes me as suspiciously creative in its representation of philosophical discourse, but it appears in any case as an expert and surprisingly unbiased treatment.5 Arabic readers knew that Ghazālī had also written a polemical treatise against philosophy, Tahāfut al-falāsifa, but they still wondered about his engagement with the ideas he challenged. Abū Bakr Ibn al-cArabī, for example, commented that Ghazālī had been unable to extricate himself from philosophy.6 Other philosophers pondered whether or not he had been a closeted member of their charmed circle and sought in his writings traces of esoteric philosophy.7Averroës's own sober sense of distance between philosophy and theology was partially a reaction to what he perceived as Ghazālī's dangerous and carefree mixture of the two sciences.8 He attacked Ghazālī's book in The Incoherence [End Page 20] of the Incoherence to restore philosophy's sense of purity, an aim he sought to accomplish by separating religious concerns from the philosopher's field of inquiry.9 Ironically, such a separation is precisely what Ghazālī might have wished to provoke by crisscrossing and blurring the line between religion and philosophy.The modern debate on chapter 17 of Tahāfut al-falāsifa has concentrated on defining Ghazālī as either a natural philosopher or an occasionalist theologian. In his defense of the possibility of miracles Ghazālī presented two theories of causation, one denying the logical basis of Aristotelian notions of natural causality, and the other more or less adopting these notions. Jointly, the two theories have seemed incompatible, and for this reason scholars have attempted to sort Ghazālī out of the apparent confusion. In 1978 L. E. Goodman argued persuasively that Ghazālī exploited rather than denied the philosophers' ideas of causality. In two articles Michael Marmura challenged Goodman, contending... (shrink)

This article focuses on the ways that sexual risk behaviors are related to race, class, and gender among low-income, culturally diverse women in South Florida. Data concerning sexual risk and gender are presented in terms of race and class variations. Results indicate that, in general, these women have a high degree of knowledge about acquired immune deficiency syndrome, a quite contemporary awareness of women's gendered subordination, and a lack of trust in heterosexual relationships. Attitudes, beliefs, and knowledge, however, are not (...) translated into sexual behaviors with men partners that would reduce their vulnerability to infection with the human immunodeficiency virus. The data indicate that race is a major factor that places women into an underclass position. Consequently, without socioeconomic resources, gendered behaviors have a direct influence on sexual risk. Multivariate analyses indicate that those women who are sex workers are significantly more likely to negotiate safe sex with clients than with main partners. The research not only challenges mainstream thinking about race, class, and gender but also provides overdue information on the vulnerability of women to HIV infection. (shrink)