Light Diacritic Restoration to Disambiguate Homographs in Modern Arabic Texts

Diacritic restoration (also known as diacritization or vowelization) is the process of inserting the correct diacritical markings into a text. Modern Arabic is typically written without diacritics, e.g., newspapers. This lack of diacritical markings often causes ambiguity, and though natives are adept at resolving, there are times they may fail. Diacritic restoration is a classical problem in computer science. Still, as most of the works tackle the full (heavy) diacritization of text, we, however, are interested in diacritizing the text using a fewer number of diacritics. Studies have shown that a fully diacritized text is visually displeasing and slows down the reading. This article proposes a system to diacritize homographs using the least number of diacritics, thus the name “light.” There is a large class of words that fall under the homograph category, and we will be dealing with the class of words that share the spelling but not the meaning. With fewer diacritics, we do not expect any effect on reading speed, while eye strain is reduced. The system contains morphological analyzer and context similarities. The morphological analyzer is used to generate all word candidates for diacritics. Then, through a statistical approach and context similarities, we resolve the homographs. Experimentally, the system shows very promising results, and our best accuracy is 85.6%.

Remark on Algorithm 992: An OpenGL- and C++-based Function Library for Curve and Surface Modeling in a Large Class of Extended Chebyshev Spaces

We provide a number of corrections to the software component that accompanied this Algorithm submission [3]. An updated version of the code is available from the ACM Collected Algorithms site [1].

Galois covers of ℙ1 and number fields with large class groups

For each finite subgroup [Formula: see text] of [Formula: see text], and for each integer [Formula: see text] coprime to [Formula: see text], we construct explicitly infinitely many Galois extensions of [Formula: see text] with group [Formula: see text] and whose ideal class group has [Formula: see text]-rank at least [Formula: see text]. This gives new [Formula: see text]-rank records for class groups of number fields.

Gauged 2-form symmetries in 6D SCFTs coupled to gravity

We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both (2, 0) and (1, 0) theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.

LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR-preinvex interval-valued functions (LR-preinvex I-V-Fs) and to establish Hermite–Hadamard type inequalities for LR-preinvex I-V-Fs using partial order relation (≤p). Furthermore, we demonstrate that our results include a large class of new and known inequalities for LR-preinvex interval-valued functions and their variant forms as special instances. Further, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.

The impact of Fishers Reproductive Compensation on raising equilibrium frequencies of semi-dominant, non-lethal mutations under mutation/selection balance.

Fishers reproductive compensation (fRC) occurs when a species demography means the death of an individual allows increased survival of his/her relatives, usually assumed to be full sibs. This likely occurs in many species, including humans. Several important recessive human genetic diseases cause early foetal/infant death allowing fRC to act on these mutations. The impact of fRC on these genetic conditions has been calculated and shown to be substantial as quantified by w, the fold increase in equilibrium frequencies of the mutation under fRC compared to its absence i.e. w=1.22 and w =1.33 for autosomal and sex-linked loci, respectively. However, the impact of fRC on the frequency of the much large class of semi-dominant, non-lethal mutations is unknown. This is calculated here by a mixture of simulation and algebra and shown that w is approximately 2-h*s and 2-0.19s-0.85h*s for autosomal and sex-linked loci respectively where h is dominance (varied between 0.05 and 0.95) and s is selection coefficient (varied between 0.05 and 0.9). These results show that the actions of fRC can almost double equilibrium frequency of mutations with low values of h and/or s. The dynamics of fRC acting on this type of mutation are also identified and discussed.

On rectifiable measures in Carnot groups: representation

This paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in terms of the existence of flat tangent measures, is equivalent to the global definition given in terms of coverings with intrinsically differentiable graphs, i.e., graphs with flat Hausdorff tangents. In general we do not have the latter equivalence if we ask the covering to be made of intrinsically Lipschitz graphs. Second, we show a geometric area formula for the centered Hausdorff measure restricted to intrinsically differentiable graphs in arbitrary Carnot groups. The latter formula extends and strengthens other area formulae obtained in the literature in the context of Carnot groups. As an application, our analysis allows us to prove the intrinsic $$C^1$$ C 1 -rectifiability of almost all the preimages of a large class of Lipschitz functions between Carnot groups. In particular, from the latter result, we obtain that any geodesic sphere in a Carnot group equipped with an arbitrary left-invariant homogeneous distance is intrinsic $$C^1$$ C 1 -rectifiable.