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%.

A new 1.375-approximation algorithm for sorting by transpositions

Background sorting by transpositions (SBT) is a classical problem in genome rearrangements. In 2012, SBT was proven to be $$\mathcal {NP}$$ NP -hard and the best approximation algorithm with a 1.375 ratio was proposed in 2006 by Elias and Hartman (EH algorithm). Their algorithm employs simplification, a technique used to transform an input permutation $$\pi$$ π into a simple permutation$${\hat{\pi }}$$ π ^ , presumably easier to handle with. The permutation $${\hat{\pi }}$$ π ^ is obtained by inserting new symbols into $$\pi$$ π in a way that the lower bound of the transposition distance of $$\pi$$ π is kept on $${\hat{\pi }}$$ π ^ . The simplification is guaranteed to keep the lower bound, not the transposition distance. A sequence of operations sorting $${\hat{\pi }}$$ π ^ can be mimicked to sort $$\pi$$ π . Results and conclusions First, using an algebraic approach, we propose a new upper bound for the transposition distance, which holds for all $$S_n$$ S n . Next, motivated by a problem identified in the EH algorithm, which causes it, in scenarios involving how the input permutation is simplified, to require one extra transposition above the 1.375-approximation ratio, we propose a new approximation algorithm to solve SBT ensuring the 1.375-approximation ratio for all $$S_n$$ S n . We implemented our algorithm and EH’s. Regarding the implementation of the EH algorithm, two other issues were identified and needed to be fixed. We tested both algorithms against all permutations of size n, $$2\le n \le 12$$ 2 ≤ n ≤ 12 . The results show that the EH algorithm exceeds the approximation ratio of 1.375 for permutations with a size greater than 7. The percentage of computed distances that are equal to transposition distance, computed by the implemented algorithms are also compared with others available in the literature. Finally, we investigate the performance of both implementations on longer permutations of maximum length 500. From the experiments, we conclude that maximum and the average distances computed by our algorithm are a little better than the ones computed by the EH algorithm and the running times of both algorithms are similar, despite the time complexity of our algorithm being higher.

Mean exit time in irregularly-shaped annular and composite disc domains

Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass transfer. While many exact results for MET are known for diffusion in simple geometries involving homogeneous materials, calculating MET for diffusion in realistic geometries involving heterogeneous materials is typically limited to repeated stochastic simulations or numerical solutions of the associated boundary value problem (BVP). In this work we derive exact solutions for the MET in irregular annular domains, including some applications where diffusion occurs in heterogenous media. These solutions are obtained by taking the exact results for MET in an annulus, and then constructing various perturbation solutions to account for the irregular geometries involved. These solutions, with a range of boundary conditions, are implemented symbolically and compare very well with averaged data from repeated stochastic simulations and with numerical solutions of the associated BVP. Software to implement the exact solutions is available on \href{https://github.com/ProfMJSimpson/Exit_time}{GitHub}.

Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings

A classical problem in real geometry concerns the representation of positive semidefinite elements of a ring A as sums of squares of elements of A. If A is an excellent ring of dimension $$\ge 3$$ ≥ 3 , it is already known that it contains positive semidefinite elements that cannot be represented as sums of squares in A. The one dimensional local case has been afforded by Scheiderer (mainly when its residue field is real closed). In this work we focus on the 2-dimensional case and determine (under some mild conditions) which local excellent henselian rings A of embedding dimension 3 have the property that every positive semidefinite element of A is a sum of squares of elements of A.

Linear stability of a rotating liquid column revisited

We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this article. Although the literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous stability criteria has not yet been clarified. While the viscous criterion for stability, given by $We < n^2 + k^2 -1$ , is both necessary and sufficient, this relation has only been shown to be sufficient in the inviscid case. Here, $We = \rho \varOmega ^2 a^3 / \gamma$ is the Weber number and measures the relative magnitudes of the centrifugal and surface tension forces, with $\varOmega$ being the angular velocity of the rigidly rotating column, $a$ the column radius, $\rho$ the density of the fluid and $\gamma$ the surface tension coefficient; $k$ and $n$ denote the axial and azimuthal wavenumbers of the imposed perturbation. We show that the subtle difference between the inviscid and viscous criteria arises from the surprisingly complicated picture of inviscid stability in the $We$ – $k$ plane. For all $n > 1$ , the viscously unstable region, corresponding to $We > n^2 + k^2-1$ , contains an infinite hierarchy of inviscidly stable islands ending in cusps, with a dominant leading island. Only the dominant island, now infinite in extent along the $We$ axis, persists for $n=1$ . This picture may be understood, based on the underlying eigenspectrum, as arising from the cascade of coalescences between a retrograde mode, that is the continuation of the cograde surface-tension-driven mode across the zero Doppler frequency point, and successive retrograde Coriolis modes constituting an infinite hierarchy.

Generalized Methodology Application for System Design

The design process for analogue circuit design is formulated on the basis of the optimum control theory. The artificially introduced special control vector is defined for the redistribution of computational costs between network analysis and parametric optimization. This redistribution minimizes computer time. The problem of the minimal-time network design can be formulated in this case as a classical problem of the optimal control for some functional minimization. There is a principal difference between the new approach and before elaborated methodology. This difference is based on a higher level of the problem generalization. In this case the structural basis of design strategies is more complete and this circumstance gives possibility to obtain a great value of computer time gain. Numerical results demonstrate the effectiveness and prospects of a more generalized approach to circuit optimization. This approach generalizes the design process and generates an infinite number of the different design strategies that will serve as the structural basis for the minimal time algorithm construction. This paper is advocated to electronic systems built with transistors. The main equations for the system design process were elaborated.

Ideal planar fluid flow over a submerged obstacle: Review and extension

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour. doi:10.1017/S1446181121000341

Quantum absentminded driver problem revisited

The aim of the paper is to study the problem of absentminded driver in the quantum domain. In the classical case, it is a well-known example of a decision problem with imperfect recall that exhibits lack of equivalence between mixed and behavioral strategies. The optimal payoff outcome is significantly lower than the maximum payoff appearing in the game. This raises the question whether a quantum approach to the problem can increase the strategic position of the decision maker. The results that we present in the paper clearly reveal the benefits from playing the absentminded problem with the aid of quantum objects. Through appropriately chosen initial quantum state, the unitary strategies enable the decision maker to obtain the maximum possible payoff. At the same time, our scheme comes down to the classical problem with a suitable restriction of unitary strategies.

Analysis of Terms as an Instrument of Comparative Philosophy

The article continues the polemics on the problems of interaction of philosophical cultures in the era of globalization, which was started at the meetings of the Round Table "Geography of Rationality". The author gives answers to critical questions, explains the methodology and principles of her work with Indian philosophical texts. A short research of the meta-term "cognitive subject" is an example of her methods. The analysis of cognitive subject aimed to justify the absence of the concepts of reason and rationality in Indian epistemic culture, the cornerstones of Western epistemic culture, since Modern times. The justification was carried out by comparing the generalized model of the cognitive subject, abstracted from the writings of empiricists and rationalists of the XVII–XVIII centuries, with the generalized models of the cognitive subject, reconstructed on the basis of authoritative writings of three variants of Indian epistemological teachings: Advaita Vedānta, Jainism and Buddhism. From the author's point of view, the absence of the concepts of reason and rationality in India leads to the non-classical problem of pluralism of epistemic cultures, and the exploration of the meta-term "cognitive subject" allows us to find, on the one hand, intersections in the contents of epistemologies in Indian philosophy and Western metaphysics of Modern times, and on the other, their incompatible contents, which are specific manifestations of pluralism of epistemic cultures. For her reconstruction of the cognitive subject models the author takes the principle of "double perspective" in combination with the methods of hermeneutical and logical analysis of philosophical terms. The principle determinates the consideration of the theoretical object from two sides: European and Indian. Having appeared in the Western epistemic culture, these methods effectively work to objectify the results of socio-humanitarian research, thanks to which they are becoming increasingly widespread among non-Western cross-cultural philosophers. When the author applies the method of logical analysis to justify the absence of the concepts of reason and rationality in India, she is guided by the rules of logical semantics and the principles of semiotics. The compared terms, Western and Indian, are considered as signs with their own meanings and senses. The senses are understood as sets of predicates important for solving the author’s task. The author of the article, taking into account the experience of famous philosophers, negatively assesses the possibility of solving the problem of unambiguously correct translation.

Hormonal Influences on Pod–Seed Intercommunication during Pea Fruit Development

Angiosperms (from the Greek “angeion”—vessel, and “sperma”—seed) are defined by the presence of specialised tissue surrounding their developing seeds. This tissue is known as the ovary and once a flower has been fertilised, it gives rise to the fruit. Fruits serve various functions in relation to the seeds they contain: they often form tough physical barriers to prevent mechanical damage, they may form specialised structures that aid in dispersal, and they act as a site of nutrient and signal exchange between the parent plant and its offspring. The close coordination of fruit growth and seed development is essential to successful reproduction. Firstly, fertilisation of the ovules is required in most angiosperm species to initiate fruit growth. Secondly, it is crucial that seed dispersal facilitated by, e.g., fruit opening or ripening occurs only once the seeds have matured. These highly coordinated events suggest that seeds and fruits are in close communication throughout development and represent a classical problem of interorgan signalling and organismic resource allocation. Here, we review the contribution of studies on the edible, unicarpellate legume Pisum sativum to our understanding of seed and fruit growth coregulation, and propose areas of new research in this species which may yield important advances for both pulse agronomy and natural science.