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 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)

We develop a new method for constructing hyperimmune minimal degrees and construct an ANR degree which is a minimal cover of a minimal degree.

Productive sets are sets which are “effectively non recursively enumerable”. In the same spirit, we introduce a notion of “effectively nonrecursive sets” and prove an effective version of Post's theorem. We also show that a set is recursively enumerable and effectively nonrecursive in our sense if and only if it is effectively nonrecursive in the sense of Odifreddi [1].

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)

We prove that the statement “there is aksuch that for everyfthere is ak-bounded diagonally nonrecursive function relative tof” does not imply weak König’s lemma over${\rm{RC}}{{\rm{A}}_0} + {\rm{B\Sigma }}_2^0$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that everyk-bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of${\rm{I\Sigma }}_2^0$.

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.

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)

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.

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.

The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of variables, one obtains, (...) for each number of variables, a fragment of the theory that is indeed Turing-decidable. In a 1982 conversation, Alfred Tarski announced that he believed the theory to be decidable, despite this contradicting CTT. The article gives the background for this proclamation, considers alternate interpretations, and sets the stage for further research. (shrink)

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, recursion theory, and from the negative solution to Hilbert’s 10th Problem ([3], [1], and [2]).

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.

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)

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)

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)

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.

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)

Prenatal genetic diagnosis with new high-performance technologies such as genomic array adds great complexity to the ethical dilemmas that already exist in current medicine. The main objective of this study was to carry out an analysis and bioethical reflections centred on the outcome associated with the use of the genetic array technique in 185 pregnancies at the Hospital Universitario y Politécnico La Fe (Valencia, Spain). It is an observational, descriptive and cross-sectional study during the years 2014 to 2017, (...) inclusive. We analyse the results and the follow-up of the 185 cases in which this prenatal genetic study was carried out by array technique. Of the 185 prenatal genetic studies carried out, 165 showed no copy number variants (normal result) and in the 20 remaining pregnancies (10.81%), a dose change was detected. Abortion was carried out in 11 cases with pathological and/or probably pathological abnormalities. Of the 165 cases in which no dose variant was detected, an abortion was carried out in 49 cases, which represents 29.7%. The introduction of new genomic analysis techniques to invasive prenatal diagnosis highlights the ethical problems that arise above all in the interpretation of genetic variants detected and genetic counselling, while emphasising the need for correct informed consent and it adds, if possible, more controversy to a subject with great bioethical substance such as abortion. (shrink)

The poor denoising effect for noisy grayscale images with traditional processing methods would be obtained under strong noise condition, and some image details would be lost. In this paper, a parallel array model of Fitzhugh–Nagumo neurons was proposed, which can restore noisy grayscale images well with low peak signal-to-noise ratio conditions and the image details are better preserved. Firstly, the row-column scanning method was used to convert the 2D grayscale image into a 1D signal, and then the 1D signal (...) was converted into a binary pulse amplitude modulation signal by signal modulation. The modulated signal was input to an FHN parallel array for stochastic resonance. Finally, the array output signal was restored to a 2D gray image, and the image restoration effect was analyzed based on the PSNR and Structural SIMilarity index. It is shown that the SR effect can be exhibited in an array of FHN neuron nonlinearities by increasing the array size, and the image restoration effect is significantly better than the traditional image restoration method, and larger PSNR and SSIM can be obtained. It provides a new idea for grayscale image restoration in a low PSNR environment. (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)

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)

This paper attends to find out the relationship among religious belief, society and Song-Jiang Battle Array in southern Taiwan, by using the qualitative methods which include literature analyses and the fieldwork investigations. In the process of research, the origin and development of Song-Jiang Battle Array are emerging step by step, which demonstrates that development and evolvement of Song-Jiang Battle Array are most related to contemporaneous social formations. They influenced the relationship between government and people and also affected (...) the relationship between religious belief and Song-Jiang Battle Array. In the end, people’s devotions toward religion are the main force of uniting people in rural society of southern Taiwan and have played an essential role in helping maintain their heritage. All of that is not established in one night. It has been evolving for hundreds of years. Keywords: Song-Jiang Battle Array , S outhern Taiwan , R eligious belief , Government , F olk art array. (shrink)

This article argues for a new interpretation of the Sanskrit compound gaṇḍa-vyūha as it is used in the common title of the Mahāyāna text the Gaṇḍavyūha-Sūtra.The author begins by providing a brief history of the sūtra’s appellations in Chinese and Tibetan sources. Next, the meanings of gaṇḍa (the problematic member of the compound) are explored. The author proposes that contemporary scholars have overlooked a meaning of gaṇḍa occurring in some compounds, wherein gaṇḍa can mean simply “great,” “big” or “massive.” This (...) general sense is particularly common in the compound gaṇda-śaila (a “massive rock” or “boulder”) and is found in such texts as the Bhāgavata Purāṇa, the Harivaṃśa and the Harṣacarita. Following the discussion of Gaṇḍa, the author examines the term vyūha (“array”) as it is used in the Gaṇḍavyūha-sūtra. The article concludes with the suggestion that a more appropriate translation of the Gaṇḍavyūha-sūtra would be “The Supreme array Scripture.”. (shrink)