Search

The 'See the World – Winchester' programme was funded by the UK Turing scheme in 2021–2022 and aimed to broaden the horizons of historically marginalised students who may not otherwise have had access to extracurricular opportunities such as international travel. The purpose of this article is twofold. Firstly, the authors reflect on the successes, failures and challenges involved with running internationalisation activities during a time of travel disruption. Secondly, this article presents findings from a small-scale evaluation that sought to measure the impact of short-term mobility with historically marginalised or under-represented students. The paper is useful for institutions looking to run international mobilities with students during a period of travel disruption using the COVID-19 pandemic as a case study. In addition, the findings highlight the experiences and benefits to students participating in short mobilities, which include, a cultural experience, opportunity for personal growth and development, enhanced employability, and ultimately, broader horizons. [ABSTRACT FROM AUTHOR]

In this article we propose an analysis of the controversy between Geoffrey Jefferson and Alan Turing in terms of a Kuhnian account of thought experiments. In this account, the main task is not to evaluate intuitions or (only) to rearrange concepts. Instead, we propose that the main task is to construct scenarios by proposing relevant experiences in which shared assumptions and conflicting lines of inquiry can be made explicit. From this perspective, we can understand the arguments and assumptions in the Jefferson-Turing thinking machine controversy [ABSTRACT FROM AUTHOR]

The "somewhat vague, intuitive" notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that the effectively calculable functions on natural numbers are exactly the general recursive functions), cannot be proved. However, it is logically provable from the notion of an effective procedure, without reliance on any (partially) mathematical thesis or conjecture concerning effective procedures, such as the Church–Turing thesis, that the class of effective procedures is undecidable, i.e., that there is no effective procedure for ascertaining whether a given procedure is effective. The proof does not even appeal to a precise definition of 'effective procedure'. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of such a procedure. Though the result itself is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure is, in fact, a decision procedure, i.e., effective—for example, that it invariably terminates with the correct verdict. [ABSTRACT FROM AUTHOR]

This article provides a detailed analysis of the transfer of a key cluster of ideas from mathematical logic to computing. We demonstrate the impact of certain of Turing's logico-philosophical concepts from the mid-1930s on the emergence of the modern electronic computer—and so, in consequence, Turing's impact on the direction of modern philosophy, via the computational turn. We explain why both Turing and von Neumann saw the problem of developing the electronic computer as a problem in logic, and we describe their joint journey from logic to electronic computation. While much has been written about Turing's and von Neumann's individual contributions to the development of the computer, this article investigates less well-known terrain: their interactions and mutual influences. Along the way we argue against 'logic skeptics' and 'Turing skeptics', who claim that neither logic nor Turing played any significant role in the creation of the modern computer. [ABSTRACT FROM AUTHOR]

An investigation of the concept of "surveyability" as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the "surveyability" of symbols, sequences, and structures of proof in all these thinkers. Hilbert initiated the idea within his metamathematics, Wittgenstein took up a kind of game formalism in the 1920s and early 1930s in response. Turing carried Hilbert's conception of the "surveyability" of proof in metamathematics through into his analysis of what a formal system (what a step in a computation) is in "On computable numbers, with an application to the Entscheidungsproblem" (1936). Wittgenstein's 1939 investigations of the significance of surveyability to the concept of "proof "in Principia Mathematica were influenced, both by Turing's remarkable everyday analysis of the Hilbertian idea, and by conversations with Turing. Although Turing does not use the word "surveyability" explicitly, it is clear that the Hilbertian idea plays a recurrent role in his work, refracted through his engagement with Wittgenstein's idea of a "language-game". This is evinced in some of his later writings, where the "reform" of mathematical notation for the sake of human surveyability (1944/45) may be seen to draw out the Hilbertian idea. For Turing, as for Wittgenstein, the need for "surveyability" earmarks the evolving culture of humans located in an evolving social and scientific world, just as it had for Hilbert. [ABSTRACT FROM AUTHOR]

Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs. Legacy wmma APIs are more easy-to-use but can only exploit limited features and power of Tensor Cores. Specifically, wmma APIs support fewer operand shapes and can not leverage the new sparse matrix multiplication feature of the newest Ampere Tensor Cores. However, the performance of current programming interface has not been well explored. Furthermore, the computation numeric behaviors of low-precision floating points (TF32, BF16, and FP16) supported by the newest Ampere Tensor Cores are also mysterious. In this paper, we explore the throughput and latency of current programming APIs. We also intuitively study the numeric behaviors of Tensor Cores MMA and profile the intermediate operations including multiplication, addition of inner product, and accumulation. All codes used in this work can be found in https://github.com/sunlex0717/DissectingTensorCores. [ABSTRACT FROM AUTHOR]

1936 was a watershed year for computability. Debates among Gödel, Church and others over the correct analysis of the intuitive concept "human effectively computable", an analysis at the heart of the Incompleteness Theorems, the Entscheidungsproblem, the question of what a finite computation is, and most urgently—for Gödel—the generality of the Incompleteness Theorems, were definitively set to rest with the appearance, in that year, of the Turing Machine. The question I explore here is, do the mathematical facts exhaust what is to be said about the thinking behind the "confluence of ideas in 1936"? I will argue for a cultural role in Gödel's, and, by extension, the larger logical community's absorption of Turing's 1936 model. As scaffolding I employ a conceptual framework due to the critic Leo Marx of the technological sublime; I also make use of the distinction within the technological sublime due to Caroline Jones, between its iconic and performative modes—a distinction operating within the conceptual art of the 1960s, but serving the history of computability equally well. [ABSTRACT FROM AUTHOR]

In this paper I argue that Turing proposed a new approach to the concept of thinking, based on his claim that intelligence is an 'emotional concept'; and that the response-dependence interpretation of Turing's 'criterion for "thinking"' is a better fit with his writings than orthodox interpretations. The aim of this paper is to clarify the response-dependence interpretation, by addressing such questions as: What did Turing mean by the expression 'emotional'? Is Turing's criterion subjective? Are 'emotional' judgements decided by social consensus? Turing's take on these issues impacts current philosophical debates on response-dependent concepts and on the nature of artificial intelligence. [ABSTRACT FROM AUTHOR]

An effective method is a computational method that might, in principle, be executed by a human. In this paper, I argue that there are methods for computing that are not effective methods. The examples I consider are taken primarily from quantum computing, but these are only meant to be illustrative of a much wider class. Quantum inference and quantum parallelism involve steps that might be implemented in multiple physical systems, but cannot be implemented, or at least not at will, by an idealised human. Recognising that not all computational methods are effective methods is important for at least two reasons. First, it is needed to correctly state the results of Turing and other founders of computation theory. Turing is sometimes said to have offered a replacement for the informal notion of an effective method with the formal notion of a Turing machine. I argue that such a view only holds under limited circumstances. Second, not distinguishing between computational methods and effective methods can lead to mistakes when quantifying over the class of all possible computational methods. Such quantification is common in philosophy of mind in the context of thought experiments that explore the limits of computational functionalism. I argue that these 'homuncular' thought experiments should not be treated as valid. [ABSTRACT FROM AUTHOR]

Eco-cognitive computationalism explores computing in context, adhering to some of the key ideas presented by modern cognitive science perspectives on embodied, situated, and distributed cognition. First of all, when physical computation is seen from the perspective of the ecology of cognition it is possible to clearly understand the role Turing assigned to the process of "education" of the machine, paralleling it to the education of human brains, in the invention of the Logical Universal Machine. It is this Turing's emphasis on education that furnishes the justification of the conceptualization of machines as "domesticated ignorant entities", that is proposed in this article. I will show that conceptualizing machines as dynamically active in distributed physical entities of various kinds suitably transformed so that data can be encoded and decoded to obtain appropriate results sheds further light on my eco-cognitive perspective. Furthermore, it is within this intellectual framework that I will usefully analyze the recent attention in computer science devoted to the importance of the simplification of cognitive and motor tasks caused in organic entities thanks to morphological features: ignorant bodies can be computationally domesticated to make an intertwined computation simpler, relying on the "simplexity" of animal embodied cognition, which represents one of the main qualities of organic agents. Finally, eco-cognitive computationalism allows us to clearly acknowledge that the concept of computation evolves over time as a result of historical and contextual factors, and we can construct an epistemological view that depicts the "emergence" of new types of computations that exploit new substrates. This new viewpoint demonstrates how the computational domestication of ignorant entities might result in the emergence of novel unconventional cognitive embodiments. [ABSTRACT FROM AUTHOR]

In the famous paper in which he introduced what is now known as the Turing machine, Alan Turing gave a definition of computable real numbers under which it turns out that multiplication by 3 is uncomputable. This shortcoming vanished in a Correction to his paper that Turing himself published shortly afterwards, but it clearly illustrates the subtlety of defining computability issues correctly. In this paper, we give the name "printable" to real numbers that Turing originally called "computable", we recall what is now the generally accepted definition of computable real numbers (which is not quite Turing's amended definition, but is equivalent to it), and we contrast the two notions. Despite the fact that the multiplication by 3 of printable numbers is uncomputable, as opposed to the same operation on computable numbers, a real number is computable if and only if it is printable. The resolution of this apparent paradox is that no machine can transform the "computable" description of a real number to its "printable" description, as Turing proved in his Correction. Finally, we address the subtle issue of allowing or not the printable description of a real number to end with an infinite sequence of 9s (or of 1s in binary), which was left open by Turing in his Correction. Several of these results were already known, as they appear in scattered places, some in non-refereed publications, but we give a unified treatment with some different proofs and a historical perspective. • Alan Turing's original definition of computable real numbers was inadequate. • Turing's use of the word Entscheidungsproblem led us to invent the Druckproblem. • The correct definition of computable real numbers is very subtle. • All computable real numbers are printable, but this is inherently non-constructive. • Discontinuous functions of the real numbers on closed intervals are uncomputable. [ABSTRACT FROM AUTHOR]

In diverse living organisms, bionanocoatings provide multiple functionalities, to the surfaces they cover. We have, previously, identified the molecular mechanisms of Turing-based self-assembly of insect corneal nanocoatings and developed forward-engineering approaches to construct multifunctional soft bionic nanocoatings, encompassing the Drosophila protein Retinin. Here, we expand the versatility of the bionic nanocoatings, by identifying and using diverse Retinin-like proteins and different methods of their metallization, using nickel, silver, and copper ions. Comparative assessment, of the resulting bactericidal, antiviral, and cytotoxic properties, identifies the best protocols, to construct safe and anti-infective metalized bionic nanocoatings. Upscaled application of these protocols, to various public surfaces, may represent a safe and economic approach to limit hazardous infections. [ABSTRACT FROM AUTHOR]

In July 1939, at the dawn of the Second World War, Polish cryptologists revealed their mastery of the Enigma encryption machine to their French and British counterparts. The Enigma machine was the main encryption method used by the German armed forces at the time. An alliance was born: XYZ (the letters are codes identifying each of the allies: X represents the French, Y represents the English, and Z represents the Polish). The Poles transmitted their methods to their allies, starting with the sheets invented by Zygalski. These sheets were made by the English, who then sent copies to the French and the Polish. These joined the French after the Polish defeat. With these sheets, from January 1940 onward, the allies were able to read the messages of the enemy. Unfortunately, in May 1940, the Germans changed their system, and the Zygalski sheets became obsolete. Only the English managed to continue breaking the Enigma keys via manual methods. In all, thousands of messages were read. In June, France capitulated, and consequently, the triple alliance ended. This story has been told before, but recently declassified French archives have allowed us to clarify several points, particularly the central place of the Cyclometer. [ABSTRACT FROM AUTHOR]

Despite his unreserved appreciation of Turing's analysis for being a "precise and unquestionably adequate definition" of formal system or mechanical computability, Gödel nevertheless published a short note in 1972 claiming to have found a "philosophical error" in Turing's argument with regard to the finite nature of mental states and memory. A natural question arises: how could Gödel enjoy the generality conferred on his results by Turing's work, despite the error of its ways? Previous interpretative strategies by Feferman, Shagrir and others have mainly tried to resolve the disparity by distinguishing different types of arguments in Turing and taking Gödel to approve only some of them. By a more integral examination of their ideas, especially Turing's response to the "mathematical objection" based on Gödel's incompleteness theorem and Gödel's own conception of finite yet non-mechanical procedures, and taking some of the main ideas of current developments in machine learning into consideration, I will try to present a new explanation for the apparent disparity, arguing that there is no "error" on Turing's side and the seemingly conflicting views held by Turing and Gödel should best be seen as complementary, keeping intuition and ingenuity together. [ABSTRACT FROM AUTHOR]

Max Newman became Professor of Pure Mathematics at Manchester University in 1945, having led the outstandingly successful Colossus cryptanalytical project at Bletchley Park during the war. He obtained Royal Society funding to set up a Computing Machine Laboratory at Manchester to apply similar digital electronic technologies to the solution of as-yet unsolved problems in pure mathematics. But what kind of (special-purpose) digital computer was likely to be most suitable? Using new evidence, this article charts the progress of Newman's project in some detail, attempting for the first time to set Newman's Colossus-centric vision in the context of John von Neumann's IAS architecture. We contrast mathematical and engineering perspectives. Though Max Newman's original plans were not realized, innovative computer design at Manchester flourished in directions unforeseen by Newman. It was his 1946 initiative that led, somewhat indirectly, to significant computing milestones. [ABSTRACT FROM AUTHOR]

Lady Lovelace's notes on Babbage's Analytical Engine (1843) never refer to the concept of surprise. Having some pretension to 'originate' something—unlike the Analytical Engine—is neither necessary nor sufficient to being able to surprise someone. Turing nevertheless translates Lovelace's 'this machine is incapable of originating something' in terms of a hypothetical 'computers cannot take us by surprise' objection to the idea that machines may be deemed capable of thinking. To understand the contemporary significance of what is missed in Turing's 'surprise' translation of Lovelace's insight, one needs to distinguish between trivial surprises (which stem from our limited ability to store data and process it) and those events, propositions or encounters that lead us to question our understanding of ourselves or what surrounds us. Only some of these non-trivial surprises are the product of originality endeavours. Not only is it uncommon for surprises to track such endeavours, the type of autonomy that would be required on the part of 'digital computers' for originality and surprise to intersect in that way goes far beyond the operational autonomy that can be achieved by 'learning machines'. This paper argues that a salient translation of Lovelace's originality insight—for contemporary and future 'learning machines'—is an upside-down version of Turing's surprise question: can computers be surprised by us in a non-trivial, 'co-produced' way? [ABSTRACT FROM AUTHOR]

The nature of shell growth in gastropods is useful because it preserves the ontogeny of shape, colour, and banding patterns, making them an ideal system for understanding how inherited variation develops, is established and maintained within a population. However, qualitative scoring of inherited shell characters means there is a lack of knowledge regarding the mechanisms that control fine variation. Here, we combine empirical measures of quantitative variation and 3D modeling of shells to understand how bands are placed and interact. By comparing five‐banded Cepaea individuals to shells lacking individual bands, we show that individual band absence has minor but significant impacts upon the position of remaining bands, implying that the locus controlling band presence/absence mainly acts after position is established. Then, we show that the shell grows at a similar rate, except for the region below the lowermost band. This demonstrates that wider bands of Cepaea are not an artifact of greater shell growth on the lower shell; they begin wider and grow at the same rate as other bands. Finally, we show that 3D models of shell shape and banding pattern, inferred from 2D photos using ShellShaper software, are congruent with empirical measures. This work therefore establishes a method that may be used for comparative studies of quantitative banding variation in snail shells, extraction of growth parameters, and morphometrics. In the future, studies that link the banding phenotype to the network of shell matrix proteins involved in biomineralization and patterning may ultimately aid in understanding the diversity of shell forms found in molluscs. [ABSTRACT FROM AUTHOR]

The Turing Test (TT) is best regarded as a model to test for intelligence, where an entity's intelligence is inferred from its ability to be attributed with 'human-likeness' during a text-based conversation. The problem with this model, however, is that it does not care if or how well an entity produces a meaningful conversation, as long as its interactions are humanlike enough. As a consequence, the TT attracts projects that concentrate on how best to fool the judges. In light of this, I propose a new version of the TT: the Questioning Turing Test (QTT). Here, the entity has to produce an enquiry rather than a conversation; and it is parametrised along two further dimensions in addition to 'human-likeness': 'correctness', evaluating if the entity accomplishes the enquiry; and 'strategicness', evaluating how well the entity accomplishes the enquiry, in terms of the number of questions asked (the fewer, the better). [ABSTRACT FROM AUTHOR]

In the 70 years since Alan Turing's 'Computing Machinery and Intelligence' appeared in Mind, there have been two widely-accepted interpretations of the Turing test: the canonical behaviourist interpretation and the rival inductive or epistemic interpretation. These readings are based on Turing's Mind paper; few seem aware that Turing described two other versions of the imitation game. I have argued that both readings are inconsistent with Turing's 1948 and 1952 statements about intelligence, and fail to explain the design of his game. I argue instead for a response-dependence interpretation (Proudfoot 2013). This interpretation has implications for Turing's view of free will: I argue that Turing's writings suggest a new form of free will compatibilism, which I call response-dependence compatibilism (Proudfoot 2017a). The philosophical implications of rethinking Turing's test go yet further. It is assumed by numerous theorists that Turing anticipated the computational theory of mind. On the contrary, I argue, his remarks on intelligence and free will lead to a new objection to computationalism. [ABSTRACT FROM AUTHOR]

It has been 50 years since Lewis Wolpert introduced the French flag model proposing the patterning of different cell types based on threshold concentrations of a morphogen diffusing in the tissue. Sixty-seven years ago, Alan Turing introduced the idea of patterns initiating de novo from a reaction–diffusion network. Together these models have been used to explain many patterning events in animal development, so here we take a look at their applicability to flower development. First, although many plant transcription factors move through plasmodesmata from cell to cell, in the flower there is little evidence that they specify fate in a concentration-dependent manner, so they cannot yet be described as morphogens. Secondly, the reaction–diffusion model appears to be a reasonably good description of the formation of spots of pigment on petals, although additional nuances are present. Thirdly, aspects of both of these combine in a new fluctuation-based patterning system creating the scattered pattern of giant cells in Arabidopsis sepals. In the future, more precise imaging and manipulations of the dynamics of patterning networks combined with mathematical modeling will allow us to better understand how the multilayered complex and beautiful patterns of flowers emerge de novo. [ABSTRACT FROM AUTHOR]

NVIDIA's latest processor family, the Turing GPU, was designed to realize a vision for next-generation graphics combining rasterization, ray tracing, and deep learning. It includes fundamental advancements in several key areas: streaming multiprocessor efficiency, a Tensor Core for accelerated AI inferencing, and an RTCore for accelerated ray tracing. With these innovations, Turing unlocks both real-time ray-tracing performance and deep-learning inference in consumer, professional, and datacenter solutions. [ABSTRACT FROM AUTHOR]

In his Tractatus Logico-Philosophicus, Wittgenstein conveyed the idea that ethics cannot be located in an object or self-standing subject matter of propositional discourse, true or false. At the same time, he took his work to have an eminently ethical purpose, and his attitude was not that of the emotivist. The trajectory of this conception of the normativity of philosophy as it developed in his subsequent thought is traced. It is explained that and how the notion of a 'form of life' (Lebensform) emerged only in his later thought, in 1937, earmarking a significant step forward in his philosophical method. We argue that the concept of Lebensform represents a way of domesticating logic itself, the very idea of a claim or reason, supplementing the idea of a 'language game', which it deepens. Lebensform is contrasted with the phenomenologists' Lebenswelt through a reading of the notions of 'I', 'world' and 'self' as they were treated in the Tractatus, The Blue and Brown Books and Philosophical Investigations. Finally, the notion of Lebensform is shown to have replaced the notion of culture (Kultur) in Philosophical Investigations. Wittgenstein's spring 1937 'domestication' of the nature of logic is shown to have been fully consonant with the idea that he was influenced by his reading Alan Turing's 1936/1937 paper, 'On computable numbers, with an application to the Entscheidungsproblem '. [ABSTRACT FROM AUTHOR]

This article will rework the classical question 'Can a machine think?' into a more specific problem: 'Can a machine think anything new?' It will consider traditional computational tasks such as prediction and decision-making, so as to investigate whether the instrumentality of these operations can be understood in terms of the creation of novel thought. By addressing philosophical and technoscientific attempts to mechanise thought on the one hand (e.g. Leibniz's mathesis universalis and Turing's algorithmic method of computation), and the philosophical and cultural critique of these attempts on the other, I will argue that computation's epistemic productions should be assessed vis-à-vis the logico-mathematical specificity of formal axiomatic systems. Such an assessment requires us to conceive automated modes of thought in such a way as to supersede the hope that machines might replicate human cognitive faculties, and to thereby acknowledge a form of onto-epistemological autonomy in automated 'thinking' processes. This involves moving beyond the view that machines might merely simulate humans. Machine thought should be seen as dramatically alien to human thought, and to the dimension of lived experience upon which the latter is predicated. Having stepped outside the simulative paradigm, the question 'Can a machine think anything new?' can then be reformulated. One should ask whether novel behaviour in computing might come not from the breaking of mechanical rules, but from following them: from doing what computers do already, and not what we might think they should be doing if we wanted them to imitate us. [ABSTRACT FROM AUTHOR]

This personal, yet scientific, letter to Alan Turing, reflects on Turing's personality in order to better understand his scientific quest. It then focuses on the impact of his work today. By joining human attitude and particular scientific method, Turing is able to "immerse himself" into the phenomena on which he works. This peculiar blend justifies the epistolary style. Turing makes himself a "human computer", he lives the dramatic quest for an undetectable imitation of a man, a woman, a machine. He makes us see the continuous deformations of a material action/reaction/diffusion dynamics of hardware with no software. Each of these investigations opens the way to new scientific paths with major consequences for contemporary live and for knowledge. The uses and the effects of these investigations will be discussed: the passage from classical AI to today's neural nets, the relevance of non-linearity in biological dynamics, but also their abuses, such as the myth of a computational world, from a Turing-machine like universe to an encoded homunculus in the DNA. It is shown that these latter ideas, which are sometimes even made in Turing's name, contradict his views. [ABSTRACT FROM AUTHOR]

Modern theories of intelligence have been constructed in an intellectual environment characterized by the results of on-going work by computational theorists on artificial intelligence and by philosophers and cognitive psychologists on the nature of human intelligence. One result of this work is that the line of demarcation between what is human and what is a machine (an artefact) is often blurred or even erased. Were one to seek an alternative general research program aimed at understanding human intelligence especially, then key elements of Aristotle's theory laid out in the first two books of De Anima would be a good place to start. [ABSTRACT FROM AUTHOR]

Abstract Breaking symmetry in populations of uniform cells, to induce adoption of an alternative cell fate, is an essential developmental mechanism. Similarly, domain and boundary establishment are crucial steps to forming organs during development. Notch signaling is a pathway ideally suited to mediating precise patterning cues, as both receptors and ligands are membrane-bound and can thus act as a precise switch to toggle cell fates on or off. Fine-tuning of signaling by positive or negative feedback mechanisms dictate whether signaling results in lateral induction or lateral inhibition, respectively, allowing Notch to either induce entire regions of cell specification, or dictate binary fate choices. Furthermore, pathway activity is modulated by Fringe modification of receptors or ligands, co-expression of receptors with ligands, mode of ligand presentation, and cell surface area in contact. In this review, we describe how Notch signaling is fine-tuned to mediate lateral induction or lateral inhibition cues, and discuss examples from C.elegans , D. melanogaster and M. musculus. Identifying the cellular machinery dictating the choice between lateral induction and lateral inhibition highlights the versatility of the Notch signaling pathway in development. Highlights • Lateral patterning mediate precise spatial cues during development. • Notch signaling drives both lateral inhibition and lateral induction patterning. • Inhibitive cues prevent cells adopting default states. • Inductive cues prompt adoption of specific cell fates. • Here, we discuss examples of Notch lateral signaling in flies, worms and mammals. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider reaction–diffusion model with modified Leslie–Gower and Holling-type II functional response and by varying simultaneously three model parameters, our model exhibits different types of complex dynamics. This allowed us to delimit several bifurcation surfaces with higher codimension corresponding to: Turing, Turing-Transcritical, Turing–Bogdanov–Taken, Turing–Hopf–Andronov, Turing-Saddle–node. Moreover by varying at least three bifurcation parameters, we show that small variations in the ratio of the diffusion coefficients can significantly alter bifurcation structure. Finally, the paper ends with the emergence of spatio-temporal patterns via numerical simulations. These simultaneous parameter variations leaded to spatio-temporal local and global bifurcations which are always catastrophic. Our results give new insights about how simultaneous changes in environmental and life history parameters drive different distribution dynamics of predator–prey populations. This only underscores the importance of including global bifurcations in the analysis of food chain models. Such results can be used to improve ecological decision-making on species conservation. Highlights • We found five types of bifurcations in our model. • We have characterized the parameters that can lead to these bifurcations. • We characterized the complex domains of parameter space delimiting the different types of dynamics. • We have determined by simulation the types of dynamics corresponding to these instabilities. [ABSTRACT FROM AUTHOR]

This introduction begins by posing the question that this Special Issue addresses and briefly considers historical precedents and why the issue is important. The discussion then moves on to the consideration of important milestones in the history of computing, up until the present time. A brief specification of the essential components of computational systems is then offered. The final section introduces the papers that are included in this volume. [ABSTRACT FROM AUTHOR]

In 1932, Marian Rejewski, who was a young mathematician working at the Polish Cipher Bureau, brilliantly recovered the internal wiring of the military Enigma. His initial efforts were unsuccessful because he assumed that the entry permutation was the same as in the commercial machine. Luckily he tried the identity permutation as an alternative and that proved to be correct. This note describes how Rejewski’s equations may be used to deduce the entry permutation without any guesswork, a technique that was later rediscovered by Alan Turing and by Lieutenant Andrew Gleason. [ABSTRACT FROM AUTHOR]

The article focuses on the chess rules and the game being created by the mathematician Alan Turning before the development of computers.

We give an introduction to the Turing degrees, aimed principally at those who have some experience with computability theory, but not necessarily with techniques specific to the study of the local degrees. The focus is on establishing which definable properties are satisfied by the degrees in the various jump classes, as introduced by Cooper and Soare in the 1970s. Along the way, we also point to a good number of open problems. [ABSTRACT FROM AUTHOR]

This is a tale about how the Colossus was first revealed to the computing community. It centers on the first conference to be devoted to computing history, held in Los Alamos, New Mexico, in June 1976. The most important player was Brian Randell, a professor of computer science who was one of the first who might be considered a computer historian. It begins in 1976 and finishes in 2016 when Randell and I discovered a recording of that event. [ABSTRACT FROM AUTHOR]

Victorywas the name of the first prototype Bombe that was developed for breaking the German Enigma messages of World War II. It lacked the diagonal board and simultaneous scanning that was provided for all the later models, but these disadvantages were overcome by the ingenious use of a column menu (a special Bombe menu where the Enigma fast rotors are all in the same position) to break six days of naval traffic, 22–27 April 1940, following the pinch of material from an armed trawlerSchiff 26(Polares). These were the first naval decrypts of the War, and their solution took several months to complete. No further naval breaks occurred until November. This article examines the decryption process in some detail in order to explain the difficulties, highlight the role ofVictoryin this process, and provide detailed workings of the processes. It also sheds some light on the early development of the British Bombe. [ABSTRACT FROM AUTHOR]

Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fingerprint ridges are epithelial structures that undergo a truncated hair follicle developmental program and fail to recruit a mesenchymal condensate. Their spatial pattern is established by a Turing reaction-diffusion system, based on signaling between EDAR, WNT, and antagonistic BMP pathways. These signals resolve epithelial growth into bands of focalized proliferation under a precociously differentiated suprabasal layer. Ridge formation occurs as a set of waves spreading from variable initiation sites defined by the local signaling environments and anatomical intricacies of the digit, with the propagation and meeting of these waves determining the type of pattern that forms. Relying on a dynamic patterning system triggered at spatially distinct sites generates the characteristic types and unending variation of human fingerprint patterns. [Display omitted] • Early fingerprint ridges are epithelial buds molecularly analogous to hair placodes • Fingerprint ridges do not recruit mesenchymal cells or express late hair follicle markers • Interacting WNT and BMP signaling defines the spacing interval between ridges • Ridge initiations from anatomically variable sites determine fingerprint pattern type Signaling pathways that determine formation of human fingerprint ridges. [ABSTRACT FROM AUTHOR]

The National Strategic Computing Initiative will inevitably produce new computer hardware, but what about software? [ABSTRACT FROM AUTHOR]

In this paper, we consider the new version of the Turing model proposed by Kondo (2017), which is called the kernel-based Turing model. The main aim is to study the sharp changes of interaction between local and nonlocal on the solutions of Turing model. Our results reveal that the kernel (or nonlocal) makes a key effect on the long time behavior of evolution equation, where the stable patterns appear in the diffusive nonlocal Kondo model. [ABSTRACT FROM AUTHOR]

Abstract The Turing morphogens cAMP and ATP are considered as electrolytes. Each is made of a slow anion and fast cation. The unequal diffusion of the of the cation and the anion creates an electric field which accelerates the anion and decelerates the cation. This effect is more pronounced for ATP than cAMP since ATP has higher charge and greater concentration than cAMP. [ABSTRACT FROM AUTHOR]

The molecular analysis of limb bud development in vertebrates continues to fuel our understanding of the gene regulatory networks that orchestrate the patterning, proliferation and differentiation of embryonic progenitor cells. In recent years, systems biology approaches have moved our understanding of the molecular control of limb organogenesis to the next level by incorporating next generation 'omics' approaches, analyses of chromatin architecture, enhancer-promoter interactions and gene network simulations based on quantitative datasets into experimental analyses. This Review focuses on the insights these studies have given into the gene regulatory networks that govern limb development and into the fin-to-limb transition and digit reductions that occurred during the evolutionary diversification of tetrapod limbs. [ABSTRACT FROM AUTHOR]

Reports on the life and work of Alan Turing that was presented in this book. Discusses the time in which Alan Turing conducted his work in attempting to crack the enigma code. Perceptions and options of Turing work changed after the publication of this book. Since 1983 a tsunami of information has become available about almost every aspect of the operations of Bletchley Park and its parent organization GCCS (the predecessor of GCHQ, the present-day U.K. signals intelligence and information security organization). This includes the release of the 500+ page ?General Report on Tunny? in 2000 (?Tunny? was the code name for an important online German teleprinter encryption device), as well as wartime manuals and technical papers of Turing, Alexander, and others, other archival materials, and memoirs of many people who worked in the different units at Bletchley. The book under review is a reissue of Hodges?s original 1983 biography. [ABSTRACT FROM PUBLISHER]

Nipple-like nanostructures covering the corneal surfaces of moths, butterflies, and Drosophila have been studied by electron and atomic force microscopy, and their antireflective properties have been described. In contrast, corneal nanostructures of the majority of other insect orders have either been unexamined or examined by methods that did not allow precise morphological characterization. Here we provide a comprehensive analysis of corneal surfaces in 23 insect orders, revealing a rich diversity of insect corneal nanocoatings. These nanocoatings are categorized into four major morphological patterns and various transitions between them, many, to our knowledge, never described before. Remarkably, this unexpectedly diverse range of the corneal nanostructures replicates the complete set of Turing patterns, thus likely being a result of processes similar to those modeled by Alan Turing in his famous reaction−diffusion system. These findings reveal a beautiful diversity of insect corneal nanostructures and shed light on their molecular origin and evolutionary diversification. They may also be the first-ever biological example of Turing nanopatterns. [ABSTRACT FROM AUTHOR]

The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions--sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-- accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these earlywarning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizurelike events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction. [ABSTRACT FROM AUTHOR]

This set of Reviews covers Open Standards in the Digital Age: History, Ideology, and Networks by Andrew L. Russell (Cambridge University Press, 2014); Pioneer Programmer: Jean Jennings Bartik and the Computer that Changed the World (Truman State University Press, 2013), a memoir by Jean Jennings Bartik; the Warner Bros. feature film Interstellar (directed by Christopher Nolan); and TWC feature film The Imitation Game (directed by Morten Tyldum). [ABSTRACT FROM PUBLISHER]

How periodic patterns are generated is an open question. A number of mechanisms have been proposed-most famously, Turing's reactiondiffusion model. However, many theoretical and experimental studies focus on the Turing mechanism while ignoring other possible mechanisms. Here, we use a general model of periodic patterning to show that different types of mechanism (molecular, cellular, mechanical) can generate qualitatively similar final patterns. Observation of final patterns is therefore not sufficient to favour one mechanism over others. However, we propose that a mathematical approach can help to guide the design of experiments that can distinguish between different mechanisms, and illustrate the potential value of this approach with specific biological examples. [ABSTRACT FROM AUTHOR]

This article explores conventions used by the Government Code and Cypher School (GC&CS) in Britain and the U.S. Navy's OP-20-G in the United States to describe and correct Enigma wiring data recovered cryptanalytically during World War II. Examples are presented and analyzed using wiring information for several machines attacked by the ISK (Intelligence Services–Knox) section of GC&CS and by Unit 387 (the cryptanalytic unit of the United States Coast Guard, absorbed into the U.S. Navy's OP-20-G during the war). [ABSTRACT FROM PUBLISHER]

When it comes to the question of what kind of moral claim an intelligent or autonomous machine might have, one way to answer this is by way of comparison with humans: Is there a fundamental difference between humans and other entities? If so, on what basis, and what are the implications for science and ethics? This question is inherently imprecise, however, because it presupposes that we can readily determine what it means for two types of entities to be sufficiently different-what I will refer to as being 'discontinuous'. In this paper, I will sketch a formal characterization of what it means for types of entities to be unique with regard to each other. This expands upon Bruce Mazlish's initial formulation of what he terms a continuity between humans and machines, Alan Turing's epistemological approach to the question of machine intelligence, and Sigmund Freud's notion of scientific revolutions dealing blows to the self-esteem of mankind. I will discuss on what basis we should regard entities as (dis-)continuous, the corresponding moral and scientific implications, as well as an important difference between what I term downgrading and upgrading continuities-a dramatic difference in how two previously discontinuous types of entities might become continuous. All of this will be phrased in terms of which scientific levels of explanation we need to presuppose, in principle or in practice, when we seek to explain a given type of entity. The ultimate purpose is to provide a framework that defines which questions we need to ask if we argue that two types of entities ought (not) to be explained (hence treated) in the same manner, as well as what it takes to reconsider scientific and ethical hierarchies imposed on the natural and artificial world. [ABSTRACT FROM AUTHOR]