Inventing life: Intellectual property and the new biology

In 2009, the National Research Council of the National Academies released a report on A New Biology for the 21st Century. The council preferred the term ‘New Biology’ to capture the convergence and integration of the various disciplines of biology. The National Research Council stressed: ‘The essence of the New Biology, as defined by the committee, is integration—re-integration of the many sub-disciplines of biology, and the integration into biology of physicists, chemists, computer scientists, engineers, and mathematicians to create a research community with the capacity to tackle a broad range of scientific and societal problems.’ They define the ‘New Biology’ as ‘integrating life science research with physical science, engineering, computational science, and mathematics’. The National Research Council reflected: 'Biology is at a point of inflection. Years of research have generated detailed information about the components of the complex systems that characterize life––genes, cells, organisms, ecosystems––and this knowledge has begun to fuse into greater understanding of how all those components work together as systems. Powerful tools are allowing biologists to probe complex systems in ever greater detail, from molecular events in individual cells to global biogeochemical cycles. Integration within biology and increasingly fruitful collaboration with physical, earth, and computational scientists, mathematicians, and engineers are making it possible to predict and control the activities of biological systems in ever greater detail.' The National Research Council contended that the New Biology could address a number of pressing challenges. First, it stressed that the New Biology could ‘generate food plants to adapt and grow sustainably in changing environments’. Second, the New Biology could ‘understand and sustain ecosystem function and biodiversity in the face of rapid change’. Third, the New Biology could ‘expand sustainable alternatives to fossil fuels’. Moreover, it was hoped that the New Biology could lead to a better understanding of individual health: ‘The New Biology can accelerate fundamental understanding of the systems that underlie health and the development of the tools and technologies that will in turn lead to more efficient approaches to developing therapeutics and enabling individualized, predictive medicine.’ Biological research has certainly been changing direction in response to changing societal problems. Over the last decade, increasing awareness of the impacts of climate change and dwindling supplies of fossil fuels can be seen to have generated investment in fields such as biofuels, climate-ready crops and storage of agricultural genetic resources. In considering biotechnology’s role in the twenty-first century, biological future-predictor Carlson’s firm Biodesic states: ‘The problems the world faces today – ecosystem responses to global warming, geriatric care in the developed world or infectious diseases in the developing world, the efficient production of more goods using less energy and fewer raw materials – all depend on understanding and then applying biology as a technology.’ This collection considers the roles of intellectual property law in regulating emerging technologies in the biological sciences. Stephen Hilgartner comments that patent law plays a significant part in social negotiations about the shape of emerging technological systems or artefacts: 'Emerging technology – especially in such hotbeds of change as the life sciences, information technology, biomedicine, and nanotechnology – became a site of contention where competing groups pursued incompatible normative visions. Indeed, as people recognized that questions about the shape of technological systems were nothing less than questions about the future shape of societies, science and technology achieved central significance in contemporary democracies. In this context, states face ongoing difficulties trying to mediate these tensions and establish mechanisms for addressing problems of representation and participation in the sociopolitical process that shapes emerging technology.' The introduction to the collection will provide a thumbnail, comparative overview of recent developments in intellectual property and biotechnology – as a foundation to the collection. Section I of this introduction considers recent developments in United States patent law, policy and practice with respect to biotechnology – in particular, highlighting the Myriad Genetics dispute and the decision of the Supreme Court of the United States in Bilski v. Kappos. Section II considers the cross-currents in Canadian jurisprudence in intellectual property and biotechnology. Section III surveys developments in the European Union – and the interpretation of the European Biotechnology Directive. Section IV focuses upon Australia and New Zealand, and considers the policy responses to the controversy of Genetic Technologies Limited’s patents in respect of non-coding DNA and genomic mapping. Section V outlines the parts of the collection and the contents of the chapters.

Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Introducing the multi-faceted teaching experiment

A mathematics classroom is comprised of many mathematicians with varying understanding of mathematics knowledge, including the teacher, students and sometimes researchers. To align with this conceptualisation of knowledge and understanding, the multi-faceted teaching experiment will be introduced as an approach to study all classroom participants’ interactions with the shared knowledge of mathematics. Drawing on the experiences of a large curriculum project, it is claimed that, unlike a multi-tiered teaching experiment, the multi-faceted teaching experiment provides a research framework that allows for the study of mathematicians’ building of knowledge in a classroom without privileging the experience of any one participant.

Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

How should biologists engage with controversial mathematical theory?

Mathematics is beautiful and precise and often necessary to understand complex biological phenomena. And yet biologists cannot always hope to fully understand the mathematical foundations of the theory they are using or testing. How then should biologists behave when mathematicians themselves are in dispute? Using the on-going controversy over Hamilton's rule as an example, I argue that biologists should be free to treat mathematical theory with a healthy dose of agnosticism. In doing so biologists should equip themselves with a disclaimer that publicly admits that they cannot entirely attest to the veracity of the mathematics underlying the theory they are using or testing. The disclaimer will only help if it is accompanied by three responsibilities - stay bipartisan in a dispute among mathematicians, stay vigilant and help expose dissent among mathematicians, and make the biology larger than the mathematics. I must emphasize that my goal here is not to take sides in the on-going dispute over the mathematical validity of Hamilton's rule, indeed my goal is to argue that we should refrain from taking sides.

Multiscale Coupling: Challenges and Opportunities

Multiscale coupling is ubiquitous in nature and attracts broad interests of scientists from mathematicians, physicists, machinists, chemists to biologists. However, much less attention has been paid to its intrinsic implication. In this paper, multiscale coupling is introduced by studying two typical examples in classic mechanics: fluid turbulence and solid failure. The nature of multiscale coupling in the two examples lies in their physical diversities and strong coupling over wide-range scales. The theories of dynamical system and statistical mechanics provide fundamental methods for the multiscale coupling problems. The diverse multiscale couplings call for unified approaches and might expedite new concepts, theories and disciplines.

El principio energía

Resumen: El autor declara que la concepción de la energía, tal como ha arribado a nuestro tiempo, tiene sus orígenes en la Antigua Grecia , pero la noción contemporánea de energía incluye muchas dificultades como para ser aceptada sin crítica . De hecho, los físicos y filósofos discrepan con sus alcances en el mundo natural, y, además, con su naturaleza entitativa. En este artículo se discuten las opiniones de varios fisicomatemáticos y filósofos. No obstante, e n la conclusión final se expresa la necesidad de retornar a la teoría aristotélico-tomista que identifica la energía con el acto de ser, ya de cada cosa mundana, ya de las substancias separadas, porque el acto propio de Dios, que es su misma esencia, no es nada diferente de la energía concebida como el acto puro de la metafísica de Aristóteles y de Santo Tomás de Aquino.

O surgimento dos números irracionais

Este é um trabalho de pesquisa sobre um conjunto de números (irracionais) que é pouco trabalhado no ensino básico de matemática. Foi uma procura muito interessante e enriquecedora, pois encontrei matemáticos e historiadores com visões bem diferentes. Muitos deles não aceitavam este novo conjunto. Para Leopold Kronecker, só existia o conjunto dos números inteiros. Já para Cantor e Dedekind, o aparecimento dos irracionais foi extremamente importante para o desenvolvimento da matemática, abrindo novos horizontes. Menciono aqui um pouco da vida e da obra de alguns matemáticos que se envolveram com os números irracionais. Tratamos ainda da descoberta dos incomensuráveis, ou seja, como iniciou-se o problema da incomensurabilidade, e do retângulo áureo e sua importância em outras áreas. O trabalho mostra também dois grupos de números que não são mencionados quando ensinamos equações algébricas, que são os números algébricos e os números transcendentes, assim como teoremas essenciais para a prova da transcendência dos irracionais especiais e . Por fim, proponho uma aula para uma turma do 3 ano do Ensino Médio com o objetivo de mostrar a irracionalidade de alguns números, usando os teoremas pertinentes

Symbolic Mathematical Laboratory

A large computer program has been developed to aid applied mathematicians in the solution of problems in non-numerical analysis which involve tedious manipulations of mathematical expressions. The mathematician uses typed commands and a light pen to direct the computer in the application of mathematical transformations; the intermediate results are displayed in standard text-book format so that the system user can decide the next step in the problem solution. Three problems selected from the literature have been solved to illustrate the use of the system. A detailed analysis of the problems of input, transformation, and display of mathematical expressions is also presented.

The Experience of Security in Mathematics

In this paper, we report some findings from an investigation of a topic related to affect and mathematics which is not well-represented in the literature. For some mathematicians, mathematics itself is a source of security in an uncertain world, and we investigated this feeling and experience in the case of 19 adult mathematicians working in universities and schools in Greece. The focus reported here is on ways that a relationship with mathematics offers a sense of permanence and stability on the one hand, and an assurance of novelty and progress on the other.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

[Book review] Piero della Francesca: A Mathematician's art by J.V. Field, Yale University Press.

Review of the book 'Piero della Francesca: A Mathematician’s Art' by J.V. Field, Yale University Press, 420 pp, £35 ISBN 0300103425.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

[Reviews] Finding moonshine: a mathematician's journey through symmetry

Review of 'Finding Moonshine: A Mathematician’s Journey Through Symmetry' by Marcus du Sautoy, published by Fourth Estate, 2008 (ISBN 0-007-214618).

New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1