Uniform Diagonalization Theorem for Complexity Classes of Promise Problems including Randomized and Quantum Classes

Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform Diagonalization Theorem allows the construction of problems outside complexity classes while still being reducible to a specific decision problem. This paper provides a generalization of the Uniform Diagonalization Theorem by extending it to promise problems and the complexity classes they form, e.g. randomized and quantum complexity classes. The theorem requires from the underlying computing model not only the decidability of its acceptance and rejection behaviour but also of its promise-contradicting indifferent behaviour - a property that we will introduce as "total decidability" of promise problems. Implications of the Uniform Diagonalization Theorem are mainly of two kinds: 1. Existence of intermediate problems (e.g. between BQP and QMA) - also known as Ladner's Theorem - and 2. Undecidability if a problem of a complexity class is contained in a subclass (e.g. membership of a QMA-problem in BQP). Like the original Uniform Diagonalization Theorem the extension applies besides BQP and QMA to a large variety of complexity class pairs, including combinations from deterministic, randomized and quantum classes.Comment: 15 page

Своє – чуже. Дике – культурне. Базові структури міфологічних когнітивних моделей (до проблеми інваріанта і трансформації в інформаційному просторі)

Відтворення логічних законів міфологічних когнітивних структур, необхідне для виокремлення інваріантів у трансформованому емпіричному етнографічному масиві, зумовлює пошук базових когнітивних структур міфологічної доби. Базові когнітивні структури елементарних суспільств – бінарні символічні класифікації, які починають розгортатися із просторово-часової дихотомії: освоєний – неосвоєний простір, час архетипів – час їхньої реалізації. У статті аналізуються системи спорідненості дуально-родового суспільства, які, на думку авторки, використовувалися як засіб формалізації ієрархічної класифікації понять міфологічної доби.The reconstruction of the logical laws of mythological cognitive structures which is necessary to single out the invariants in the trasforming ethnographic material leads us to the search of basic cognitive structures of the mythological epoch. The basic cognitive structures of elementary societies are the binaric symbolical classifications which begin to develop from the spatialtemporal opposition: assimilated space – space which is not assimilated, the time of the archetypes – the time of their realization. In the article there is an analysis of a system of consanguinity of dual-clan society which on author's mind was used as means of formalization of the hierarchial classification of the mythological epoch concepts

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In this study, age of onset (AoO) was investigated in five- and six-year-old bilingual Frisian-Dutch children. AoO to Dutch ranged between zero and four and had a positive effect on Dutch receptive vocabulary size, but hardly influenced the children's accurate use of Dutch inflection. The influence of AoO on vocabulary was more prominent than the influence of exposure. Regarding inflection, the reverse was found. Accuracy at using Frisian inflection emerged as a significant predictor; this transfer effect was modulated by lexical overlap between the two languages. This study shows that 'the sooner the better' does not necessarily hold for language development. In fact, for the correct use of inflection, it does not matter whether children start at age zero or four. For rapidly learning words in a new language it may be helpful to first build a substantial vocabulary in the first language before learning a new language

On the Nature of MeV-blazars

Broad-band spectra of the FSRQ (flat-spectrum-radio quasars) detected in the high energy gamma-ray band imply that there may be two types of such objects: those with steep gamma-ray spectra, hereafter called MeV-blazars, and those with flat gamma-ray spectra, GeV-blazars. We demonstrate that this difference can be explained in the context of the ERC (external-radiation-Compton) model using the same electron injection function. A satisfactory unification is reachable, provided that: (a) spectra of GeV-blazars are produced by internal shocks formed at the distances where cooling of relativistic electrons in a jet is dominated by Comptonization of broad emission lines, whereas spectra of MeV-blazars are produced at the distances where cooling of relativistic electrons is dominated by Comptonization of near-IR radiation from hot dust; (b) electrons are accelerated via a two step process and their injection function takes the form of a double power-law, with the break corresponding to the threshold energy for the diffusive shock acceleration. Direct predictions of our model are that, on average, variability time scales of the MeV-blazars should be longer than variability time scales of the GeV-blazars, and that both types of the blazar phenomenon can appear in the same object.Comment: Accepted for publication in the Astrophysical Journa

The Diffuse Gamma-Ray Background from Supernovae

The Cosmic Gamma-ray Background (CGB) in the MeV region is believed to be due to photons from radioactivity produced in SNe throughout the history of galaxies in the universe. In particular, gamma-ray line emission from the decay chain 56Ni-> 56Co->56Fe provides the dominant photon source. Although iron synthesis occurs in all types of SNe, the contribution to the CGB is dominated by SNIa events due to their higher photon escape probabilities. Estimates of the star formation history in the universe suggest a rapid increase by a factor \~ 10 from the present to a redshift z_p ~ 1.5, beyond which it either remains constant or decreases slowly. We integrate the observed star formation history to determine the CGB from the corresponding SN rate history. In addition to gamma-rays from short-lived radioactivity in SNIa and SNII/Ibc we also calculate the minor contributions from long-lived radioactivities (26Al, 44Ti, 60Co, and electron-positron pair annihilation). Although progenitor evolution for SNIa is not yet fully understood, various arguments suggest delays of order 1-2 Gy between star formation and the production of SNIa's. The effect of this delay on the CGB is discussed. We emphasize the value of gamma-ray observations of the CGB in the MeV range as an independent tool for studies of the cosmic star formation history. If the delay between star formation and SNIa activity exceeds 1 Gy substantially, and/or the peak of the cosmic star formation rate occurs at a redshift much larger than unity, the gamma-ray production of SNIa would be insufficient to explain the observed CGB. Alternatively, the cosmic star formation rate would have to be higher (by a factor 2-3) than commonly assumed, which is in accord with several upward revisions reported in the recent literature.Comment: Minor changes, 26 pages, 9 figures, Accepted by Ap

Spaceborne radar observations: A guide for Magellan radar-image analysis

Geologic analyses of spaceborne radar images of Earth are reviewed and summarized with respect to detecting, mapping, and interpreting impact craters, volcanic landforms, eolian and subsurface features, and tectonic landforms. Interpretations are illustrated mostly with Seasat synthetic aperture radar and shuttle-imaging-radar images. Analogies are drawn for the potential interpretation of radar images of Venus, with emphasis on the effects of variation in Magellan look angle with Venusian latitude. In each landform category, differences in feature perception and interpretive capability are related to variations in imaging geometry, spatial resolution, and wavelength of the imaging radar systems. Impact craters and other radially symmetrical features may show apparent bilateral symmetry parallel to the illumination vector at low look angles. The styles of eruption and the emplacement of major and minor volcanic constructs can be interpreted from morphological features observed in images. Radar responses that are governed by small-scale surface roughness may serve to distinguish flow types, but do not provide unambiguous information. Imaging of sand dunes is rigorously constrained by specific angular relations between the illumination vector and the orientation and angle of repose of the dune faces, but is independent of radar wavelength. With a single look angle, conditions that enable shallow subsurface imaging to occur do not provide the information necessary to determine whether the radar has recorded surface or subsurface features. The topographic linearity of many tectonic landforms is enhanced on images at regional and local scales, but the detection of structural detail is a strong function of illumination direction. Nontopographic tectonic lineaments may appear in response to contrasts in small-surface roughness or dielectric constant. The breakpoint for rough surfaces will vary by about 25 percent through the Magellan viewing geometries from low to high Venusian latitudes. Examples of anomalies and system artifacts that can affect image interpretation are described

Theory of anomalous magnetic interference pattern in mesoscopic SNS Josephson junctions

The magnetic interference pattern in mesoscopic SNS Josephson junctions is sensitive to the scattering in the normal part of the system. In this paper we investigate it, generalizing Ishii's formula for current-phase dependence to the case of normal scattering at NS boundaries in an SNS junction of finite width. The resulting flattening of the first diffraction peak is consistent with experimental data for S-2DEG-S mesoscopic junctions.Comment: 6 pages, 5 figures. Phys. Rev. B 68, 144514 (2003

A Quasi-Universal Nonword Repetition Task as a Diagnostic Tool for Bilingual Children Learning Dutch as a Second Language.

PURPOSE: This study evaluated a newly developed quasi-universal nonword repetition task (Q-U NWRT) as a diagnostic tool for bilingual children with language impairment (LI) who have Dutch as a 2nd language. The Q-U NWRT was designed to be minimally influenced by knowledge of 1 specific language in contrast to a language-specific NWRT with which it was compared. METHOD: One hundred twenty monolingual and bilingual children with and without LI participated (30 per group). A mixed-design analysis of variance was used to investigate the effects of LI and bilingualism on the NWRTs. Receiver operating characteristic analyses were conducted to evaluate the instruments' diagnostic value. RESULTS: Large negative effects of LI were found on both NWRTs, whereas negative effects of bilingualism only occurred on the language-specific NWRT. Both instruments had high clinical accuracy in the monolingual group, but only the Q-U NWRT had high clinical accuracy in the bilingual group. CONCLUSIONS: This study indicates that the Q-U NWRT is a promising diagnostic tool to help identify LI in bilingual children learning Dutch as a 2nd language. The instrument was clinically accurate in both a monolingual and bilingual group of children and seems better able to disentangle LI from language disadvantage than more language-specific measures

Super-resolution provided by the arbitrarily strong superlinearity of the blackbody radiation

Blackbody radiation is a fundamental phenomenon in nature, and its explanation by Planck marks a cornerstone in the history of Physics. In this theoretical work, we show that the spectral radiance given by Planck's law is strongly superlinear with temperature, with an arbitrarily large local exponent for decreasing wavelengths. From that scaling analysis, we propose a new concept of super-resolved detection and imaging: if a focused beam of energy is scanned over an object that absorbs and linearly converts that energy into heat, a highly nonlinear thermal radiation response is generated, and its point spread function can be made arbitrarily smaller than the excitation beam focus. Based on a few practical scenarios, we propose to extend the notion of super-resolution beyond its current niche in microscopy to various kinds of excitation beams, a wide range of spatial scales, and a broader diversity of target objects

First Person Perspective of Seated Participants Over a Walking Virtual Body Leads to Illusory Agency Over the Walking

Agency, the attribution of authorship to an action of our body, requires the intention to carry out the action, and subsequently a match between its predicted and actual sensory consequences. However, illusory agency can be generated through priming of the action together with perception of bodily action, even when there has been no actual corresponding action. Here we show that participants can have the illusion of agency over the walking of a virtual body even though in reality they are seated and only allowed head movements. The experiment (n = 28) had two factors: Perspective (1PP or 3PP) and Head Sway (Sway or NoSway). Participants in 1PP saw a life-sized virtual body spatially coincident with their own from a first person perspective, or the virtual body from third person perspective (3PP). In the Sway condition the viewpoint included a walking animation, but not in NoSway. The results show strong illusions of body ownership, agency and walking, in the 1PP compared to the 3PP condition, and an enhanced level of arousal while the walking was up a virtual hill. Sway reduced the level of agency. We conclude with a discussion of the results in the light of current theories of agency