Abstract: One of the fundamental questions in developmental biology is how the vast range of pattern and structure we observe in nature emerges from an almost uniformly homogeneous fertilized egg. In particular, the mechanisms by which biological systems maintain robustness, despite being subject to numerous sources of noise, are shrouded in mystery. Postulating plausible theoretical models of biological heterogeneity is not only difficult, but it is also further complicated by the problem of generating robustness, i.e. once we can generate a pattern, how do we ensure that this pattern is consistently reproducible in the face of perturbations to the domain, reaction time scale, boundary conditions and so forth. In this paper, not only do we review the basic properties of Turing's theory, we highlight the successes and pitfalls of using it as a model for biological systems, and discuss emerging developments in the area.

Abstract: Results of the first systematic study on feedback control of nonequilibrium pattern formation in networks are reported. Effects of global feedback control on Turing patterns in network-organized activator-inhibitor system have been investigated. The feedback signal was introduced into one of the parameters of the system and was proportional to the amplitude of the developing Turing pattern. Without the control, the Turing instability corresponded to a subcritical bifurcation and hysteresis effects were observed. Sufficiently strong feedback control rendered, however, the bifurcation supercritical and eliminated the hysteresis effects.

Abstract: George Dyson's fascinating account of the early years of computers: "Turing's Cathedral" is the story behind how the PC, ipod, smartphone and almost every aspect of modern life came into being. In 1945 a small group of brilliant engineers and mathematicians gathered at the Institute for Advanced Study in Princeton, determined to build a computer that would make Alan Turing's theory of a 'universal machine' reality. Led by the polymath emigre John von Neumann, they created the numerical framework that underpins almost all modern computing - and ensured that the world would never be the same again. George Dyson is a historian of technology whose interests include the development (and redevelopment) of the Aleut kayak. He is the author of "Baidarka"; "Project Orion"; and "Darwin Among the Machines". "Unusual, wonderful, visionary". (Francis Spufford, "Guardian"). "Fascinating...the story Dyson tells is intensely human...a gripping account of ideas and invention. Fascinating...the story Dyson tells is intensely human...a gripping account of ideas and invention." ("Jenny Uglow"). "Glorious...as much a story of the personalities involved as of the discoveries they made, and you do not need any knowledge of computers or mathematics to enjoy the ride. ..a ripping yarn". (John Gribbin, "Literary Review").

Abstract: In his pioneering work, Alan Turing showed that de novo pattern formation is possible if two substances interact that differ in their diffusion range. Since then, we have shown that pattern formation is possible if, and only if, a self-enhancing reaction is coupled with an antagonistic process of longer range. Knowing this crucial condition has enabled us to include nonlinear interactions, which are required to design molecularly realistic interactions. Different reaction schemes and their relation to Turing's proposal are discussed and compared with more recent observations on the molecular–genetic level. The antagonistic reaction may be accomplished by an inhibitor that is produced in the activated region or by a depletion of a component that is used up during the self-enhancing reaction. The autocatalysis may be realized by an inhibition of an inhibition. Activating molecules can be processed into molecules that have an inhibiting function; patterning of the Wnt pathway is proposed to depend on such a mechanism. Three-component systems, as discussed in Turing's paper, are shown to play a major role in the generation of highly dynamic patterns that never reach a stable state.

Abstract: For most of its history, mathematics was algorithmic in nature. The geometric claims in Euclid’s Elements fall into two distinct categories: “problems,” which assert that a construction can be carried out to meet a given specification, and “theorems,” which assert that some property holds of a particular geometric configuration. For example, Proposition 10 of Book I reads “To bisect a given straight line.” Euclid’s “proof” gives the construction, and ends with the (Greek equivalent of) quod erat faciendum, or Q.E.F., “that which was to be done.” Proofs of theorems, in contrast, end with quod erat demonstrandum, or “that which was to be shown”; but even these typically involve the construction of auxiliary geometric objects in order to verify the claim. Similarly, algebra was devoted to discovering algorithms for solving equations. This outlook characterized the subject from its origins in ancient Egypt and Babylon, through the ninth century work of al-Khwarizmi, to the solutions to the cubic and quadratic equations in Cardano’s Ars magna of 1545, and to Lagrange’s study of the quintic in his Reflexions sur la resolution algebrique des equations of 1770. The theory of probability, which was born in an exchange of letters between Blaise Pascal and Pierre de Fermat in 1654 and developed further by Christian Huygens and Jakob Bernoulli, provided methods for calculating odds related to games of chance. Abraham de Moivre’s 1718 monograph on the subject was

Abstract: Turing models have been proposed to explain the emergence of digits during limb development. However, so far the molecular components that would give rise to Turing patterns are elusive. We have recently shown that a particular type of receptor-ligand interaction can give rise to Schnakenberg-type Turing patterns, which reproduce patterning during lung and kidney branching morphogenesis. Recent knockout experiments have identified Smad4 as a key protein in digit patterning. We show here that the BMP-receptor interaction meets the conditions for a Schnakenberg-type Turing pattern, and that the resulting model reproduces available wildtype and mutant data on the expression patterns of BMP, its receptor, and Fgfs in the apical ectodermal ridge (AER) when solved on a realistic 2D domain that we extracted from limb bud images of E11.5 mouse embryos. We propose that receptor-ligand-based mechanisms serve as a molecular basis for the emergence of Turing patterns in many developing tissues.

Abstract: In this paper we offer a formal definition of Artificial Intelligence and this directly gives us an algorithm for construction of this object. Really, this algorithm is useless due to the combinatory explosion. The main innovation in our definition is that it does not include the knowledge as a part of the intelligence. So according to our definition a newly born baby also is an Intellect. Here we differs with Turing's definition which suggests that an Intellect is a person with knowledge gained through the years.

Abstract: 1. Click to Open 2. Turing's Universal Machine 3. Sinking Hilbert 4. The Intuitive Mathematician 5. Breaking Enigma 6. Tunny - Hitler's BlackBerry 7. The Colossus of Computers 8. ACE- A Month's Work in a Minute 9. The Manchester "Electronic Brain" 10. Artificial Intelligence 11. The Imitation Game 12. Educating Machinery 13. Computer Chess 14. Artificial Life 15. Epilogue

Abstract: In his seminal 1952 paper, ‘The Chemical Basis of Morphogenesis’, Alan Turing lays down a milestone in the application of theoretical approaches to understand complex biological processes. His deceptively simple demonstration that a system of reacting and diffusing chemicals could, under certain conditions, generate spatial patterning out of homogeneity provided an elegant solution to the problem of how one of nature's most intricate events occurs: the emergence of structure and form in the developing embryo. The molecular revolution that has taken place during the six decades following this landmark publication has now placed this generation of theoreticians and biologists in an excellent position to rigorously test the theory and, encouragingly, a number of systems have emerged that appear to conform to some of Turing's fundamental ideas. In this paper, we describe the history and more recent integration between experiment and theory in one of the key models for understanding pattern formation: the emergence of feathers and hair in the skins of birds and mammals.

Abstract: We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.

Abstract: Efforts to engineer synthetic gene networks that spontaneously produce patterning in multicellular ensembles have focused on Turing's original model and the “activator-inhibitor” models of Meinhardt and Gierer. Systems based on this model are notoriously difficult to engineer. We present the first demonstration that Turing pattern formation can arise in a new family of oscillator-driven gene network topologies, specifically when a second feedback loop is introduced which quenches oscillations and incorporates a diffusible molecule. We provide an analysis of the system that predicts the range of kinetic parameters over which patterning should emerge and demonstrate the system's viability using stochastic simulations of a field of cells using realistic parameters. The primary goal of this paper is to provide a circuit architecture which can be implemented with relative ease by practitioners and which could serve as a model system for pattern generation in synthetic multicellular systems. Given the wide range of oscillatory circuits in natural systems, our system supports the tantalizing possibility that Turing pattern formation in natural multicellular systems can arise from oscillator-driven mechanisms.

Abstract: For most of its history, mathematics was algorithmic in nature. The geometric claims in Euclid’s Elements fall into two distinct categories: “problems,” which assert that a construction can be carried out to meet a given specification, and “theorems,” which assert that some property holds of a particular geometric configuration. For example, Proposition 10 of Book I reads “To bisect a given straight line.” Euclid’s “proof” gives the construction, and ends with the (Greek equivalent of) quod erat faciendum, or Q.E.F., “that which was to be done.” Proofs of theorems, in contrast, end with quod erat demonstrandum, or “that which was to be shown”; but even these typically involve the construction of auxiliary geometric objects in order to verify the claim. Similarly, algebra was devoted to discovering algorithms for solving equations. This outlook characterized the subject from its origins in ancient Egypt and Babylon, through the ninth century work of al-Khwarizmi, to the solutions to the cubic and quadratic equations in Cardano’s Ars magna of 1545, and to Lagrange’s study of the quintic in his Reflexions sur la resolution algebrique des equations of 1770. The theory of probability, which was born in an exchange of letters between Blaise Pascal and Pierre de Fermat in 1654 and developed further by Christian Huygens and Jakob Bernoulli, provided methods for calculating odds related to games of chance. Abraham de Moivre’s 1718 monograph on the subject was

Abstract: This paper is based on the talk given on 5 June 2004 at the conference at Manchester University marking the 50th anniversary of Alan Turing's death. It is published by the British Computer Society on http://www.bcs.org/ewics. It was submitted in April 2006; some corrections have been made and references added for publication in November 2007.

Abstract: We attempt to put the title problem and the Church-Turing thesis into a proper perspective and to clarify some common misconceptions related to Turing's analysis of computation. We examine two approaches to the title problem, one well-known among philosophers and another among logicians.

Abstract: In 1950, when Turing proposed to replace the question "Can machines think?" with the question "Are there imaginable digital computers which would do well in the imitation game?" computer science was not yet a field of study, Shannon’s theory of information had just begun to change the way people thought about communication, and psychology was only starting to look beyond behaviorism. It is stunning that so many predictions in Turing’s 1950 Mind paper were right. In the decades since that paper appeared, with its inspiring challenges, research in computer science, neuroscience, and the behavioral sciences has radically changed thinking about mental processes and communication, and the ways in which people use computers has evolved even more dramatically. Turing, were he writing now, might still replace "Can machines think?" with an operational challenge, but it is likely he would propose a very different test. This paper considers what that might be in light of Turing’s paper and advances in the decades since it was written.

Abstract: Thirty-two of the 39 living A.M. Turing Award laureates gathered in San Francisco to pay tribute to "the father of CS" and discuss the past, present, and future of computing.

Abstract: In this article, I outline the three main philosophical lessons that we may learn from Turing's work, and how they lead to a new philosophy of information. After a brief introduction, I discuss his work on the method of levels of abstraction (LoA), and his insistence that questions could be meaningfully asked only by specifying the correct LoA. I then look at his second lesson, about the sort of philosophical questions that seem to be most pressing today. Finally, I focus on the third lesson, concerning the new philosophical anthropology that owes so much to Turing's work. I then show how the lessons are learned by the philosophy of information. In the conclusion, I draw a general synthesis of the points made, in view of the development of the philosophy of information itself as a continuation of Turing's work.

Abstract: On 30 July 1947 Wittgenstein penned a series of remarks that have become well-known to those interested in his writings on mathematics. It begins with the remark “Turings ‘machines’: these machines are humans who calculate. And one might express what he says also in the form of games”. Though most of the extant literature interprets the remark as a criticism of Turing’s philosophy of mind (that is, a criticism of forms of computationalist or functionalist behaviorism, reductionism and/or mechanism often associated with Turing), its content applies directly to the foundations of mathematics. For immediately after mentioning Turing, Wittgenstein frames what he calls a “variant” of Cantor’s diagonal proof. We present and assess Wittgenstein’s variant, contending that it forms a distinctive form of proof, and an elaboration rather than a rejection of Turing or Cantor.

Abstract: Turing’s o-machine discussed in his PhD thesis can perform all of the usual operations of a Turing machine and in addition, when it is in a certain internal state, can also query an oracle for an answer to a specific question that dictates its further evolution. In his thesis, Turing said 'We shall not go any further into the nature of this oracle apart from saying that it cannot be a machine.’ There is a host of literature discussing the role of the oracle in AI, modeling brain, computing, and hypercomputing machines. In this paper, we take a broader view of the oracle machine inspired by the genetic computing model of cellular organisms and the self-organizing fractal theory. We describe a specific software architecture implementation that circumvents the halting and un-decidability problems in a process workflow computation to introduce the architectural resiliency found in cellular organisms into distributed computing machines. A DIME (Distributed Intelligent Computing Element), recently introduced as the building block of the DIME computing model, exploits the concepts from Turing’s oracle machine and extends them to implement a recursive managed distributed computing network, which can be viewed as an interconnected group of such specialized oracle machines, referred to as a DIME network. The DIME network architecture provides the architectural resiliency through auto-failover; autoscaling; live-migration; and end-to-end transaction security assurance in a distributed system. We demonstrate these characteristics using prototypes without the complexity introduced by hypervisors, virtual machines and other layers of ad-hoc management software in today’s distributed computing environments.

Abstract: Historians have the luxury of looking back at human endeavor over long periods of time, but most scientists are too busy working in the present and thinking anxiously about the future and have no time to view their work in the context of what has gone before. I once remarked that all graduate students in biology divide history into two epochs: the past 2 years and everything else before that, where Archimedes, Newton, Darwin, Mendel—even Watson and Crick—inhabit a time-compressed universe as uneasy contemporaries. It seems remarkable that historians once thought that science progressed by the steady addition of knowledge, building the edifice of scientific truth, brick by brick. In his 1962 book The Structure of Scientific Revolutions , Thomas Kuhn argued that progress occurs in revolutionary steps by the introduction of new paradigms, which may be new theories—new ways of looking at the world—or new technical methods that enhance observation and analysis. Between Kuhn's revolutions, scientific knowledge does advance by accretion, as there is much to do to consolidate the new science. But then, inevitably, unsolved problems accumulate and, in many cases, the inconsistencies have been put to one side and everybody hopes that they will quietly go away. The edifice becomes rickety; some of its foundations are insecure and many of the bricks have not been well-baked. This is when a new revolutionary wave in the form of new ideas or new techniques appears, which allows us to condemn and demolish the unsafe or corrupt parts of the edifice and rebuild truth. Often there is great resistance to the new wave, but as Max Planck pointed out, it succeeds because the opponents grow old and die. The process is then repeated: The radicals become liberals, the liberals become conservatives, the conservatives become reactionaries, and the reactionaries disappear. Students of evolution will recognize this process in the theory of punctuated equilibrium: Organisms stay much the same for very long periods of time; this is interrupted by bursts of change when novelty appears, followed again by stasis. ![Figure][1] CREDIT: ANDREY PROKHOROV/ISTOCKPHOTO.COM The life sciences have undergone a radical revolution in my lifetime, and it is interesting to view this from the vantage point of the present to understand its full meaning and impact. In the first half of the 20th century, physics underwent two revolutions: Einstein's theory of relativity, connected with large scales of time and space, and quantum mechanics, concerned with the very small and dealing with fundamental questions of matter and energy. Although Newton still reigned supreme in the human-scale world, the revolutions opened up totally new fields of the physical sciences whose impact continues today. In the meantime, genetics had shown that chromosomes were the carriers of genes that specified the phenotypic characteristics of organisms and were the modern version of the factors postulated by Mendel—but beyond that, very little was known about the material basis of genes and how they accomplished their proposed functions in living organisms. This property attracted the attention of theoretical physicists; one, Schrodinger, wrote a book ( What Is Life? ) that speculated on the physical nature of the genetic material. Many of my contemporaries read this book and claimed it had a great influence on them. I read it but did not understand it, largely because I did not know what Schrodinger meant by an aperiodic crystal. Later, I came to realize that he had made a profound error when he claimed that the chromosomes not only contained the plan for the development of the organism but also had the means to execute it. Chromosomes were known to contain both DNA and proteins, but many biologists did not believe that DNA could be the carrier of genetic information because its chemical structure was too simple; they thought proteins had to be involved. Avery's demonstration that DNA was the transforming principle of Pneumococcus was ignored by most biochemists, but in 1953, the discovery of the double-helical structure of DNA by Watson and Crick changed everything. Very little happened in the first few years, but by 1956, the new molecular biology began to gather momentum, and the rest of the story is well known. We can now see exactly what constituted the new paradigm in the life sciences: It was the introduction of the idea of information and its physical embodiment in DNA sequences of four different bases. Thus, although the components of DNA are simple chemicals, the complexity that can be generated by different sequences is enormous. In 1953, biochemists were preoccupied only with questions of matter and energy, but now they had to add information. In the study of protein synthesis, most biochemists were concerned with the source of energy for the synthesis of the peptide bond; a few wrote about the “patternization” problem. For molecular biologists, the problem was how one sequence of four nucleotides encoded another sequence of 20 amino acids. It should now be evident what is needed to add to physics to account for living systems. The fundamental theory was formulated by Turing in his notion of a universal Turing machine and deployed by von Neumann in his theory of self-reproducing machines. Given a description of any computation, a universal Turing machine can read the description and perform the computation; in the same way, a von Neumann universal constructor can build any machine when provided with its description, but to preserve the self-reproducing property, it is necessary for the parent machine to copy its description and insert a copy into the progeny machine. We can now recognize Schrodinger's mistake: The chromosomes do not contain the means for executing the plan of the organism, but only a description of the means. There are no causal relationships between Turing's and von Neumann's ideas and those of Watson and Crick. They got their ideas of the genetic code from common parlance; Francis Crick once told me that he saw it like the Morse code—as a table transforming the alphabet of letters into the binary code of dots and dashes. The connections exist only in the plane of the history of ideas. We also can provide the answer for those physicists who looked for new laws of physics in biology: Biology is essentially (very low energy) physics with computation. Fundamental theory in biology is concerned principally with viewing living organisms as the only part of the natural world whose members contain internal descriptions of themselves. That is why I could once tell a Buddhist priest that mountains were not alive: You can't clone a mountain. It is also why the whole of biology must be rooted in DNA, and our task is still to discover how these DNA sequences arose in evolution and how they are interpreted to build the diversity of the living world. Physics was once called natural philosophy; perhaps we should call biology “natural engineering.” [1]: pending:yes

Abstract: I review history, starting with Turing’s seminal paper, reaching back ultimately to when our species started to outperform other primates, searching for the questions that will help us develop a computational account of human intelligence I answer that the right questions are: What’s different between us and the other primates and what’s the same I answer the what’s different question by saying that we became symbolic in a way that enabled story understanding, directed perception, and easy communication, and other species did not I argue against Turing’s reasoning-centered suggestions, offering that reasoning is just a special case of story understanding I answer the what’s the same question by noting that our brains are largely engineered in the same exotic way, with information flowing in all directions at once By way of example, I illustrate how these answers can influence a research program, describing the Genesis system, a system that works with short summaries of stories, provided in English, together with low-level common-sense rules and higher-level concept patterns, likewise expressed in English Genesis answers questions, notes abstract concepts such as revenge, tells stories in a listener-aware way, and fills in story gaps using precedents I conclude by suggesting, optimistically, that a genuine computational theory of human intelligence will emerge in the next 50 years if we stick to the right, biologically inspired questions, and work toward biologically informed models

Abstract: Promoting a clock-free paradigm that fits everything learned about programming since Turing.