We focus on a particular class of computably enumerable degrees, the array noncomputable degrees defined by Downey, Jockusch, and Stob, to answer questions related to lattice embeddings and definability in the partial ordering of c. e. degrees under Turing reducibility. We demonstrate that the latticeM5 cannot be embedded into the c. e. degrees below every array noncomputable degree, or even below every nonlow array noncomputable degree. As Downey and Shore have proved that M5 can (...) be embedded below every nonlow2 degree, our result is the best possible in terms of array noncomputable degrees and jump classes. Further, this result shows that the array noncomputable degrees are definably different from the nonlow2 degrees. We note also that there are embeddings of M5 in which all five degrees are array noncomputable, and in which the bottom degree is the computable degree 0 but the other four are array noncomputable. (shrink)

We examine notions of genericity intermediate between 1-genericity and 2-genericity, especially in relation to the Δ20 degrees. We define a new kind of genericity, dynamic genericity, and prove that it is stronger than pb-genericity. Specifically, we show there is a Δ20 pb-generic degree below which the pb-generic degrees fail to be downward dense and that pb-generic degrees are downward dense below every dynamically generic degree. To do so, we examine the relation between genericity and array noncomputability, deriving some structural (...) information about the Δ20 degrees in the process. (shrink)

We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of${\rm{\Delta }}_2^0$functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jockusch, and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable antichain.

We introduce a natural strengthening of prompt simplicity which we call strong promptness, and study its relationship with existing lowness classes. This notion provides a ≤ wtt version of superlow cuppability. We show that every strongly prompt c.e. set is superlow cuppable. Unfortunately, strong promptness is not a Turing degree notion, and so cannot characterize the sets which are superlow cuppable. However, it is a wtt-degree notion, and we show that it characterizes the degrees which satisfy a wtt-degree notion very (...) close to the definition of superlow cuppability. Further, we study the strongly prompt c.e. sets in the context of other notions related promptness, superlowness, and cupping. In particular, we show that every benign cost function has a strongly prompt set which obeys it, providing an analogue to the known result that every cost function with the limit condition has a prompt set which obeys it. We also study the effect that lowness properties have on the behaviour of a set under the join operator. In particular we construct an array noncomputable c.e. set whose join with every low c.e. set is low. (shrink)

Current conceptions of the integration of computers into society often depend on the view that the human mind, as well as the computer, is a computational system. This view is widely taken to have broad implications for educational policy. We present a critique of the premise and some of the conclusions of the above argument. It is here shown that the thesis that the human mind is a computational system is, in principle, not scientifically supportable. It is also shown that, (...) even if the computational theory of mind were held for non-scientific reasons, the educational implications often derived from it do not follow. (shrink)

We use a method suggested by Kolmogorov complexity to examine some relations between Kolmogorov complexity and noncomputability. In particular we show that the method consistently gives us more information than conventional ways of demonstrating noncomputability . Also, many sets which are awkward to embed into the halting problem are easily shown noncomputable. We also prove a gap-theorem for outputting consecutive integers and find, for a given length n, a statement of length n with maximal proof length.

I explain why, within the nonclassical framework for cognitive science we describe in the book, cognitive-state transitions can fail to be tractably computable even if they are subserved by a discrete dynamical system whose mathematical-state transitions are tractably computable. I distinguish two ways that cognitive processing might conform to programmable rules in which all operations that apply to representation-level structure are primitive, and two corresponding constraints on models of cognition. Although Litch is correct in maintaining that classical cognitive science is (...) not committed to the first constraint, it is committed to the second. This fact constitutes an illuminating gloss on our claim that one foundational assumption of classicism is that human cognition conforms to programmable, representation-level, rules. (shrink)

Stoffregen & Bardy propose an absolutist transmodal array structure model, intended to displace models of specification in all existing perceptual theories. Absolute specification of world structure in array structures, either unimodal or transmodal, may not be provable, but might be falsifiable. Absolute specification, moreover, may not be a necessary postulate in an ecological approach to understanding perception-action.

In this paper we prove that a degree a is array nonrecursive (ANR) if and only if every degree b ≥ a is r.e. in and strictly above another degree (RRE). This result will answer some questions in [ASDWY]. We also deduce an interesting corollary that every n-REA degree has a strong minimal cover if and only if it is array recursive.

We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure M. We prove that if T is a complete L-theory, then T is mutually algebraic if and only if there is some model M of T for which every atomic formula has uniformly bounded arrays. Moreover, an incomplete theory T is mutually algebraic if and only if every atomic formula has uniformly bounded arrays in every model M of T.

Subjects exposed to strings of letters generated by a finite state grammar can later classify grammatical and nongrammatical test strings, even though they cannot adequately say what the rules of the grammar are (e.g., Reber, 1989). The MINERVA 2 (Hintzman, 1986) and Medin and Schaffer (1978) memory‐array models and a number of connectionist outoassociator models are tested against experimental data by deriving mainly parameter‐free predictions from the models of the rank order of classification difficulty of test strings. The importance (...) of different assumptions regarding the coding of features (How should the absence of a feature be coded? Should single letters or digrams be coded?), the learning rule used (Hebb rule vs. delta rule), and the connectivity (Should features be predicted only by previous features in the string, or by all features simultaneously?) is investigated by determining the performance of the models with and without each assumption. Only one class of connectionist model (the simultaneous delta rule) passes all the tests. It is shown that this class of model can be regarded by abstracting a set of representative but incomplete rules of the grammar. (shrink)

John Searle and Roger Penrose are two staunch critics of computationalism who nonetheIess believe that with the right framework the mind can be naturalized. while they may be successful in showing the shortcomings of computationalism, I argue that their alternative noncomputational frameworks equally fail to carry out the project to naturalize the mind. The main reason is their failure to resolve some fundamental incompatibilities between mind and science. Searle tries to resolve the incompatibility between the subjectivity of consciousness and the (...) objectivity of silence by means of conceptual clarification. He, howeve4 fails to deal with the concepts crucial to this incompatibility, namely, the publicness of scientific knowledge and the privacy of psychological knowledge. Penrose tries to resolve the incompatibility between the non-computationality of psychological process and the computationality of scientific process by expanding the scope of science through some radical changes in quantum physics. His strategy, howeve4 has the danger of trivializing the distinction between science and non-science thereby putting into question the very value of the project to naturalize the mind. In addition, the feasibility of this strategy remains dubious in light of the mysteries that still surround quantum physics. (shrink)

This paper explores the hypothesis that first-order linguistic activities are better understood in terms of ecological, values-realizing dynamics rather than in terms of rule-governed processes. Conversing, like other perception-action skills is constrained by multiple values, heterarchically organized. This hypothesis is explored in terms of three broad approaches that contrast with models of language which view it as a cognitive system: conversing as a perceptual system for exploring dialogical arrays ; conversing as an action system for integrating diverse space-time scales ; (...) and conversing as a caring system for embodying the context-sensitivity and interdependency necessary to realize values. Approaching language as a caring action-perception system leads to a reconsideration of cognitive dimensions of linguistic activities, including consciousness, pragmatics, suffering, and hope. (shrink)

DNA arrays have become the preferred method for large-scale expression measurement. Such data are needed in view of the large amounts of sequence data available: expression levels in a number of different tissues or situations provide a first step toward functional characterisation of new entities revealed by DNA sequencing. Although the basic principle of measurement is in all cases based on hybridisation of a mixed probe derived from tissue RNA to large sets of DNA fragments representing many genes, a number (...) of different forms of implementation of this principle are at hand. They are briefly described and compared, emphasizing the important issue of sensitivity and sample requirements and the accessibility of the methods to academic scientists. When these factors are taken into account, it appears that, contrary to a largely prevalent impression, the “best” approach is not necessarily always provided by the widely advertised glass microarrays or oligonucleotide chips. BioEssays 21:781–790, 1999. © 1999 John Wiley & Sons, Inc. (shrink)

The array seen when saccading across a point light source blinking in the dark is displaced in the direction of the saccade. This displacement reflects an abrupt shift of spatiotopic coordinates that precedes the actual eye movement. The extraretinal signal mediating this discrete shift appears to be an oculomotor reference signal, specifying intended eye orientation, that changes discretely before saccades.

A.D. Smith opens his excellent paper, “Space and Sight,” by remarking, One of the most notable features of both philosophy and psychology throughout the eighteenth and nineteenth centuries is the almost universal denial that we are immediately aware through sight of objects arrayed in three-dimensional space. This was not merely a denial of Direct Realism, but a denial that truly visual objects are even phenomenally presented in depth (481). Times have changed. As Smith writes, “It is hard to think of (...) a more radical reversal in thinking than the one that separates such an outlook from that which prevails today; for this erstwhile orthodoxy is hardly given even serious consideration in our own times, at least among philosophers” (482). Even so, how could this doctrine come and go? How can there be fashion in phenomenology?1 Let me answer the question indirectly, by considering Locke’s reasons for advancing the doctrine. He writes, “When we set before our Eyes a round Globe, of any uniform colour, v.g. Gold, Alabaster, or Jet, ‘tis certain, that the Idea thereby imprinted in our Mind, is of a flat Circle variously shadow’d, with several degrees of Light and Brightness coming to our Eyes” (2.9.8).2 Adults have acquired ideas of three-dimensional objects (presumably by.. (shrink)

Field-Programmable Gate Arrays (FPGAs) have emerged as an attractive means of implementing logic circuits, providing instant manufacturing turnaround and negligible prototype costs. They hold the promise of replacing much of the VLSI market now held by mask-programmed gate arrays. FPGAs offer an affordable solution for customized VLSI, over a wide variety of applications, and have also opened up new possibilities in designing reconfigurable digital systems. Field-Programmable Gate Arrays discusses the most important aspects of FPGAs in a textbook manner. It provides (...) the reader with a focused view of the key issues, using a consistent notation and style of presentation. It provides detailed descriptions of commercially available FPGAs and an in-depth treatment of the FPGA architecture and CAD issues that are the subjects of current research. The material presented is of interest to a variety of readers, including those who are not familiar with FPGA technology, but wish to be introduced to it, as well as those who already have an understanding of FPGAs, but who are interested in learning about the research directions that are of current interest. (shrink)

We find Stoffregen & Bardy's argument that the senses are united and that specificity exists within the global array compelling. However, this view is not entirely new and research on the development and the origins of perception in infancy, inspired by Gibson's ecological perspective, also supports their claims. The inclusion of this developmental research will strengthen and challenge some of Stoffregen & Bardy's views.

We present some abstract theorems showing how domination properties equivalent to being $\overline{GL}_{2}$ or array nonrecursive can be used to construct sets generic for different notions of forcing. These theorems are then applied to give simple proofs of some known results. We also give a direct uniform proof of a recent result of Ambos-Spies, Ding, Wang, and Yu [2009] that every degree above any in $\overline{GL}_{2}$ is recursively enumerable in a 1-generic degree strictly below it. Our major new result (...) is that every array nonrecursive degree is r.e. in some degree strictly below it. Our analysis of array nonrecursiveness and construction of generic sequences below ANR degrees also reveal a new level of uniformity in these types of results. (shrink)

The suggestion of seeking specificity in a higher-order array is attractive, but Stoffregen & Bardy fail to provide a compelling empirical basis to their claim that specificity exists solely in the global array. Using the example of relative motion, the alternate hypotheses that must be considered are presented.

Level measurements, thickness measurement or remote surface detection using ultrasonic pulse transit method require that the target surface be at 90 O to the incident beam so that reflected beam comes back at 180-degree angle to effectively use this method. This is perfectly true in case of flat, solid surface at right angle to the incident beam. But surface irregularities of a porous, non-smooth, uneven material such as snow cause penetration of incident wave into the surface, absorption of the incident (...) energy, scatter of energy in many directions and further attenuation of reflected signal making it difficult to detect the reflected echo. Such a received reflected echo is very low in amplitude and is heavily noise-ridden. The successful surface detection with excellent repeatability and accuracy without any false measurement in this case requires combination of physical acoustic, mechanical, hardware and software techniques together. In this paper we discuss the suitable physical, mechanical, electronics design to physically implement the theory of Arrayed Ultrasonic transducers to shape up the directional response, beam width and avoid interference to improve the chances of proper and sufficient reflection from the non-smooth, highly porous, uneven, non-planar irregular surface. (shrink)

We discuss issues raised by the commentators, such as specification in single-energy arrays, task-specific pickup of information, general principles of the ecological approach to perception and action, and how specification may be constrained by the facts of physical relativity. While the commentaries raise many important issues we conclude that they do not undermine our argument that specification exists solely in the global array.

In electrical resistance tomography technology for human lung, under the same experimental conditions, the width of the sensitive field boundary electrode has a significant impact on the calculation accuracy of the inverse problem besides the finite element model topology. Aiming to improve the quality of reconstructed images, the FEM for human lung was set up based on prior knowledge. On this basis, the electrode width of the FEM was optimised by comparing the morbidity degrees of the sensitivity matrix and Hessian (...) matrix, the uniformity of sensitivity distribution, and the quality of reconstructed images, which can improve the accuracy of solving the inverse problem significantly. (shrink)

The basic premise of the host‐defense theory is that genomic imprinting, the parent‐of‐origin expression of a subset of mammalian genes, derives from mechanisms originally dedicated to silencing repeated and retroviral‐like sequences that deeply colonized mammalian genomes. We propose that large clusters of tandemly‐repeated C/D‐box small nucleolar RNAs (snoRNAs) or microRNAs represent a novel category of sequences recognized as “genomic parasites”, contributing to the emergence of genomic imprinting in a subset of chromosomal regions that contain them. Such a view is supported (...) by evidence derived from studies of the imprinted snoRNA‐ and/or miRNA‐encoding Dlk1‐Dio3, Snurf‐Snrpn, Sfbmt2, and C19MC domains. While adding a new piece to the challenging puzzle of mammalian genome history, this hypothesis also reinforces the notion that dissecting the features and molecular mechanisms that discriminate between “foreign” and “endogenous” sequences is of crucial importance in the field of mammalian epigenetics. (shrink)