Interval type-2 fuzzy automata and Interval type-2 fuzzy grammar

The purpose of the present work is to introduce and study the concept of interval type-2 (IT2) fuzzy grammar which recognizes the given IT2 fuzzy languages. The relationship between IT2 fuzzy automata and IT2 fuzzy (weak) regular grammars is discussed. Specifically, the results we obtained here are (i ) IT2 fuzzy weak regular grammar and IT2 fuzzy regular grammar generate the same classes of IT2 fuzzy languages (ii ) for a given IT2 fuzzy regular grammars, there exists an IT2 fuzzy automata such that they accept the same IT2 fuzzy languages, and vice versa. In addition, we define some operations on IT2 fuzzy languages and it is shown that IT2 fuzzy languages recognized by IT2 fuzzy automata are closed under the operations of union, intersection, concatenation and Kleene closure, but are not closed under complement

Spinocerebellar Ataxia Type 2

1. Introduction: The autosomal dominant cerebellar ataxias (ADCA) are a clinically, pathologically and genetically heterogeneous group of neurodegenerative disorders caused by degeneration of cerebellum and its afferent and efferent connections. The degenerative process may additionally involves the ponto- medullar systems, pyramidal tracts, basal ganglia, cerebral cortex, peripheral nerves (ADCA I) and the retina (ADCA II), or can be limited to the cerebellum (ADCA III) (Harding et al., 1993). The most common of these dominantly inherited autosomal ataxias, ADCA I, includes many Spinocerebellar Ataxias (SCA) subtypes, some of which are caused by pathological CAG trinucleotide repeat expansion in the coding region on the mutated gene. Such is the case for SCA1, SCA2, SCA3/MJD, SCA6, SCA7, SCA17 and Dentatorubral-pallidoluysian atrophy (DRPLA) (Matilla et al., 2006). Among the almost 30 SCAs, the variant SCA2 is the second most prevalent subtype worldwide, only surpassed by SCA3 (Schöls et al., 2004; Matilla et al., 2006; Auburger, 2011)..

Sugar and Type 2 diabetes

Background: Consumption of sugar, specifically sugar-sweetened beverages, has been widely held responsible by the media for the global rise in Type 2 diabetes (T2DM). Sources of data: Systematic reviews and dietary guidelines relating dietary sugars to T2DM. Areas of agreement: Weight gain and T2DM incidence are associated with diet and lifestyle patterns characterized by high consumptions of any sweetened beverages. High sugar intakes impair risk factors for macrovascular complications of T2DM. Areas of controversy: Much of the association between sugars and T2DM is eliminated by adjusting data for body mass index (BMI). However, BMI adjustment does not fully account for adiposity (r2=0.65–0.75). Excess sugar can promote weight gain, thus T2DM, through extra calories, but has no unique diabetogenic effect at physiological levels. Growing points: Ethical concerns about caffeine added to sweetened beverages, undetectable by consumers, to increase consumption. Areas timely for developing research: Evidence needed for limiting dietary sugar below 10% energy intake

An Infrared Comparison of Type-1 and Type-2 Quasars

We model the optical to far-infrared SEDs of a sample of six type-1 and six type-2 quasars selected in the mid-infrared. The objects in our sample are matched in mid-IR luminosity and selected based on their Spitzer IRAC colors. We obtained new targeted Spitzer IRS and MIPS observations and used archival photometry to examine the optical to far-IR SEDs. We investigate whether the observed differences between samples are consistent with orientation-based unification schemes. The type-1 objects show significant emission at 3 micron. They do not show strong PAH emission and have less far-IR emission on average when compared to the type-2 objects. The SEDs of the type-2 objects show a wide assortment of silicate features, ranging from weak emission to deep silicate absorption. Some also show strong PAH features. In comparison, silicate is only seen in emission in the type-1 objects. This is consistent with some of the type-2s being reddened by a foreground screen of cooler dust, perhaps in the host galaxy itself. We investigate the AGN contribution to the far-IR emission and find it to be significant. We also estimate the star formation rate for each of the objects by integrating the modeled far-IR flux and compare this with the SFR found from PAH emission. We find the type-2 quasars have a higher average SFR than the type-1 quasars based on both methods, though this could be due to differences in bolometric luminosities of the objects. While we find pronounced differences between the two types of objects, none of them are inconsistent with orientation-based unification schemes.Comment: Accepted for publication in Ap

A Classic Type 2 QSO

In the Chandra Deep Field South 1Msec exposure we have found, at redshift 3.700 +- 0.005, the most distant Type 2 AGN ever detected. It is the source with the hardest X-ray spectrum with redshift z>3. The optical spectrum has no detected continuum emission to a 3sigma detection limit of ~3 10^{-19} ergs/s/cm^2/AA and shows narrow lines of Ly_alpha, CIV, NV, HeII, OVI, [OIII], and CIII]. Their FWHM line widths have a range of ~700-2300 km/s with an average of approximately ~1500 km/s. The emitting gas is metal rich (Z ~2.5-3 Z_solar). In the X-ray spectrum of 130 counts in the 0.5-7 keV band there is evidence for intrinsic absorption with N_H > 10^{24} cm^{-2}. An iron K_alpha line with rest frame energy and equivalent width of ~6.4 keV and ~1 keV, respectively, in agreement with the obscuration scenario, is detected at a 2sigma level. If confirmed by our forthcoming XMM observations this would be the highest redshift detection of FeK_alpha. Depending on the assumed cosmology and the X-ray transfer model, the 2-10 keV rest frame luminosity corrected for absorption is ~10^{45 +- 0.5} ergs/s, which makes our source a classic example of the long sought Type 2 QSOs. From standard population synthesis models, these sources are expected to account for a relevant fraction of the black-hole-powered QSO distribution at high redshift.Comment: 24 LaTeX pages including 6 postscript figures. Revised version, accepted by Ap

Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets

Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

Detecting z > 2 Type IIn Supernovae

Type IIn supernovae (SNe IIn) dominate the brightest supernova events in observed FUV flux (~1200-2000A). We show that multi-band, multi-epoch optical surveys complete to m_r = 27 can detect the FUV emission of ~25 z > 2 SNe IIn deg^-2 yr^-1 rest-frame (~10 SNe IIn deg^-2 yr^-1 observed-frame) to 4 sigma using a technique monitoring color-selected galaxies. Moreover, the strength and evolution of the bright emission lines observed in low redshift SNe IIn imply that the Ly-a emission features in ~70% of z > 2 SNe IIn are above 8m-class telescope spectroscopic thresholds for ~2 yr rest-frame. As a result, existing facilities have the capability to both photometrically detect and spectroscopically confirm z > 2 SNe IIn and pave the way for efficient searches by future 8m-class survey and 30m-class telescopes. The method presented here uses the sensitivities and wide-field capabilities of current optical instruments and exploits (1) the efficiency of z > 2 galaxy color-selection techniques, (2) the intrinsic brightness distribution ( = -19.0 +/-0.9) and blue profile of SNe IIn continua, (3) the presence of extremely bright, long-lived emission features, and (4) the potential to detect blueshifted SNe Ly-a emission shortward of host galaxy Ly-a features.Comment: 26 pages (pre-print), 6 figures, accepted Ap

Type II compactifications on manifolds with SU(2) x SU(2) structure

We study compactifications of type II theories on SU(2) x SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive the structure of their moduli spaces. We show that in contrast to SU(3) x SU(3) structure compactifications, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we formulate type II compactifications on SU(2) x SU(2) structures in the context of exceptional generalized geometry which makes the U-duality group manifest and naturally incorporates the scalar degrees of freedom arising in the Ramond-Ramond sector. Via this formalism we derive the structure of the moduli spaces as it is expected from N=4 supergravity.Comment: 69 pages, v2 published versio