The increasing complexity of biological problems and the increase of mathematical means to handle them on the one hand, and the possibility of automatized computation at the other, necessitate a revaluation of the present interactions between biology and mathematics; in this connection interrelations occur which can be divided into three kinds: mathematical biology, biological mathematics, and general biomathematics or methodology of the biomathematical sciences, by which are meant those scientific branches which arise from the said interactions.

The ArgumentThe development of modern mathematical biology took place in the 1920s in three main directions: population dynamics, population genetics, and mathematical theory of epidemics. This paper focuses on the first trend which is considered the most significant. Modern mathematical theory of population dynamics is characterized by three aspects (the first two being in a somewhat critical relationship): the emergence of the mathematical modeling approach, the attempt at establishing it in a reductionist-mechanist conceptual framework, and the revival of Darwinism. The (...) first section is devoted to the analysis of the concept of mathematical model and the second one presents an example of a mathematical model (Van der Pol's model of heartbeat) which is a good prototype of that concept. In section 3 the main trends of mathematization of biology and the cultural and scientific contexts in which they found their development are discussed. Sections 4 and 5 are devoted to the contributions of V. Volterra and A. J. Lotka, to the analysis of the differences of their scientific conceptions, and to a discussion of a case study: the priority dispute concerning the discovery of the Volterra-Lotka equations. The historical analysis developed in this paper is also intended to detect the roots of some recent trends of mathematization of biology. (shrink)

Fetal alcohol syndrome , the most common avoidable human birth defect, is the extensive irreversible brain damage caused by heavy prenatal alcohol exposure. Following the discovery of FAS in 1973, a multidisciplinary research community began applying discipline-specific methods to investigate the mechanisms underlying FAS and its consequences for the victims’ cognition and social behavior. An academic biomathematician and statistician, since 1984 I have collaborated with one American research group studying this condition.

Defending Robert Rosen’s claim that in every confrontation between physics and biology it is physics that has always had to give ground, it is shown that many of the most important advances in mathematics and physics over the last two centuries have followed from Schelling’s demand for a new physics that could make the emergence of life intelligible. Consequently, while reductionism prevails in biology, many biophysicists are resolutely anti-reductionist. This history is used to identify and defend a fragmented but progressive (...) tradition of anti-reductionist biomathematics. It is shown that the mathematicoephysico echemical morphology research program, the biosemiotics movement, and the relational biology of Rosen, although they have developed independently of each other, are built on and advance this antireductionist tradition of thought. It is suggested that understanding this history and its relationship to the broader history of post-Newtonian science could provide guidance for and justify both the integration of these strands and radically new work in post-reductionist biomathematics. (shrink)

A long history of research has revealed many neurophysiological changes and concomitant behavioral impacts of sleep deprivation, sleep restriction, and circadian rhythms. Little research, however, has been conducted in the area of computational cognitive modeling to understand the information processing mechanisms through which neurobehavioral factors operate to produce degradations in human performance. Our approach to understanding this relationship is to link predictions of overall cognitive functioning, or alertness, from existing biomathematical models to information processing parameters in a cognitive architecture, leveraging (...) the strengths from each to develop a more comprehensive explanation. The integration of these methodologies is used to account for changes in human performance on a sustained attention task across 88 h of total sleep deprivation. The integrated model captures changes due to time awake and circadian rhythms, and it also provides an account for underlying changes in the cognitive processes that give rise to those effects. The results show the potential for developing mechanistic accounts of how fatigue impacts cognition, and they illustrate the increased explanatory power that is possible by combining theoretical insights from multiple methodologies. (shrink)

This rare publication continues an exploratory journey in relational biology, a study of biology in terms of the organization of networked connections in living systems. It builds on the author's two earlier monographs which looked at the epistemology of life and the ontogeny of life. Here the emphasis is on the intangibility of life, that the real nature of living systems is conveyed not by their tangible material basis but by their intangible inherent processes. Relational biology is the approach that (...) hails 'function dictates structure'; it is mathematics decoded into biological realizations. Therefore, the work begins with a concise introduction to category theory, equiping the reader with the mathematical metalanguage of relation biology. The book is organized around three parts: Part I is a comprehensive study of the most important functor in relational biology, the power set functor. The author lays the set-theoretic foundations of the functorial connections in relational biology, exploring relations, mappings, and set-valued mappings. In Part II, Natural Law receives a new mathematical formulation founded on two axioms: 'Everything is a set.' and 'Every process is a set-valued mapping.' The reader sees how Metabolism-Repair networks, equipped with set-valued processors, expand their role from models of biological entities to generic models of all natural systems. Part III expounds the various shades of invertibility in general, and the inversion of encoding to decoding in particular. A plethora of mathematical and biological examples illustrate the category-theoretic concepts of equivalence and adjunction. This book's algebraic approach to biological models will appeal to researchers and graduate students in mathematics, biology, and the philosophy of science. (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics.

Richard Levins (1930-2016) was an outstanding ecologist, population geneticist, biomathematician, philosopher of science, complexity theorist, and Marxist. Key to all aspects of his work was a dialectical logic of process and change. His work provides a framework for the understanding of crises in environment and society and their analytic relationship with capitalism and imperialism, as well as the tools for the critique of biological determinist justifications for the existing structures of power. This anthology pays tribute to Levins by carrying forward (...) his work in the development of the understanding of the dialectics of nature and society. -/- The contributions are organized into four sections--Dialectics in Wholistic Research; Political Ecology and Health; Complex Systems; and Reminiscences and Tributes. The authors are as almost as hard to label as Levins; the fields they draw from range from biomathematics to NGO activism; environmental policy to island and aquatic ecology; eco-justice podcasting to biogeochemistry; reflective practice to science-in-society, agroecology to public health. (shrink)

Dans la mythologie grecque, Prométhée - le 'prévoyant' - déroba le feu aux dieux et le transmit aux hommes. Zeus, courroucé par ce transfert technologique, condamna Prométhée à un châtiment itéré à l'identique, à l'infini, algorithmique. Le problème que pose l'ancien mythe est celui des limites de la connaissance. En termes modernes, jusqu'à quel point pouvons-nous transformer la nature sans une connaissance des conséquences de nos actions sur elle? Cette question nous pousse à analyser les limites des sciences : à (...) une techno-science devenue toujours plus invasive, la science répond en se donnant à elle-même des limites"--Page 4 of cover. (shrink)

This book offers a unique perspective on Zionism. The author, a geneticist by training, focuses on science, rather than history. He looks at the claims that Jews constitute a people with common biological roots. An argument that helps provide justification for the aspirations of this political movement dedicated to the return of the Jewish people to their homeland. His study explores two issues. The first considers the assertion that there is a biology of the Jews. The second deals with attempts (...) to integrate this idea into a consistent history. Both issues unfolded against the background of a romantic national culture of Western Europe in the 19th century: Jews, primarily from Eastern Europe, began to believe these notions and soon they took the lead in the re-formulation of Jewish and Zionist existence. The author does not intend to present a comprehensive picture of the biological literature of the origins of a people and the blood relations between them. He also recognizes that the subject is emotionally-loaded. The book does, however, present a profound mediation on three overlapping questions: What is special or unique to the Jews? Who were the genuine Jews? And how can one identify Jews? This volume is a revised and edited English version of Tzionut Vehabiologia shel Hayehudim, published in 2006. (shrink)

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called "Chargaff's grammar of biology" by providing the conceptual theoretical framework necessary to generalize Chargaff's rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a (...) natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties. (shrink)